Simulations of hydraulic fracturing and leakage in sedimentary basins

by

Ane Elisabet Lothe

The thesis has been submitted to Department of Geology University of Bergen

in partial fulfilment of the requirement for the Norwegian academic degree

Doctor Scient

January 2004

Summary

Hydraulic fracturing and leakage of water through the caprock is described from sedimentary basin over geological time scale. Abnormal pressure accumulations reduce the effective stresses in the underground and trigger the initiation of hydraulic fractures. The major faults in the basin define these pressure compartments.

In this Thesis, basin simulations of hydraulic fracturing and leakage have been carried out. A simulator (Pressim) is used to calculate pressure generation and dissipitation between the compartments. The flux between the compartments and not the flow within the compartments is modelled. The Griffith-Coulomb failure criterion determines initial failure at the top structures of overpressured compartments, whereas the frictional sliding criterion is used for reactivation along the same fractures. The minimum horizontal stress is determined from different formulas, and an empirical one seems to give good results compared to measured pressures and minimum horizontal stresses.

Simulations have been carried out on two datasets; one covering the Halten Terrace area and one the Tune Field area in the northern North Sea. The timing of hydraulic fracturing and amount of leakage has been quantified in the studies from the Halten Terrace area. This is mainly controlled by the lateral fluid flow and the permeability of the major faults in the basin. Low fault permeability gives early failure, while high fault permeabilities results in no or late hydraulic fracturing and leakage from overpressured parts of the basin. In addition to varying the transmissibility of all faults in a basin, the transmissibility across individual faults can be varied. Increasing the transmissibility across faults is of major importance in overpressured to intermediately pressured areas. However, to obtain change in the flow, a certain pressure difference has to be the situation between the different compartments.

The coefficient of internal friction and the coefficient of frictional sliding, used as input in the failure criteria, have minor impact on timing and amount of leakage. However, high values result in some time-delay, and thereby less leakage from overpressured compartments. Sensitivity tests of the Poisson’s ratio and Young’s modulus of the caprock, which controls Biot’s constant, show an effect on the overpressure. Defining Biot’s constant to 1, gives too early pressure accumulation. Lower values of Biot’s constant (>0.85) give a present day pressure distribution closer to the one observed in wells.

How to obtain a pressure difference across faults is tested on the Tune Field data set. Two different fault maps are used, one with only large faults interpreted, and one with both large and small faults included. High-pressure differences are difficult to obtain when the transmissibility across one individual fault is reduced. The transmissibilities of a network of small faults have to be reduced to match the pressure measured in wells. Then, either our transmissibility fault models are wrong, or a relay zone between larger faults is more sealing than expected. In addition, the fluid flow path can be more complex than expected, and can only be understood with a multi-layer model. The secondary oil migration modelling carried out using different pressure history cases; show that overpressures have a major impact on the migration pathways. The resolution in the fault interpretation is important for the simulation results, both for pressure distribution and for hydrocarbon migration.

Minor deformation bands are described from experiments and from onshore fieldwork in Brumunddal. These are small faults situated in a sandstone reservoir that will have influence on lateral fluid flow.

Samandrag

Hydraulisk oppsprekking og strømming av vatn gjennom takbergarten, er skildra frå ulike sedimentære basseng på geologisk tidsskala. Dette grunna abnorme overtrykk som fører til ein reduksjon i effektivspenningane i undergrunnen. Dei store forkastningane i bassenget definere dei ulike trykkcellene.

I denne oppgåva blir simuleringar av hydraulisk oppsprekking og lekkasje på bassengskala presentert. Ein trykksimulator (Pressim) er brukt for å kunne kalkulere trykkgenerering og dissipering mellom cellene. Trykkendringar mellom cellene og ikkje strømming internt i cellene er simulert. Griffith-Coulomb brotkriterium vert brukt for a finne når forkastninga startar å utvikle seg frå toppen av cella med overtrykk, mens friksjonsglide brotkriteriet er brukt for å determinere reaktivering langs forkastninga. Minste horisontal spenning kan bli kalkulert frå ulike formlar, men ein empirisk formel gjev realistiske resultat for simulert trykk og spenning samanlikna med målte verdiar.

I simuleringane er to datasett brukt; eit frå Haltenterrassen og eit frå Tunefeltet, i nordlige Nordsjøen. I studiet frå Haltenterrassen, er starttidspunktet for hydraulisk oppsprekking og lekkasje kvantifisert. Dette er hovudsakleg styrt av lateral strømming og permeabiliteten til dei store forkastningane i bassenget. Lave permeabilitetar til forkastningane gjev tidleg brot, mens høge permeabilitetar gjev sein eller ingen hydrauliske forkastningar eller lekkasje frå område med anormalt høgt trykk. I tillegg til å variere transmissibiliteten til alle forkastningane i eit basseng, kan transmissibiliteten på tvers av enkelt forkastningar endrast. Å auke transmissibiliteten til forkastningar er vesentleg i område med høgt eller relativt høgt trykk, men for idet heile tatt få endra flømmingsmønsteret, må det være ein viss trykkdifferanse mellom cellene.

Koeffisienten for intern friksjon og koeffisienten for friksjonsgliding, som er brukt som inngangsdata i brotkriteria, har vesentleg mindre påverknad på starttidspunkt for forkastninga og mengde lekkasje. Sjølv om høge verdiar gjev noko forsinkelsar, og dermed mindre lekkasje frå celler med høgt overtrykk. Sensitivitetstestar for Poisson ratio og Young modul til takbergarten, som kontrollerar Biot konstant, viser over tid ei effekt på overtrykket. Biot konstant sett til 1, gjev tidleg trykkakkumulering. Mindre verdiar av Biot konstant (>0.85) gjev ei trykkfordeling i dag, som er nærmare det som er observert i brønnar.

På datasettet frå Tunefeltet har vi testa korleis trykkdifferansar over forkastningar kan simulerast. To ulike kart over forkastningane er brukt, ein med berre store forkastningar, og det andre med på store og små forkastningar inkludert. Det er vanskelig å oppnå store trykkskilnader, berre ved å redusere transmissibilitet over ei forkastning. Transmissibiliteten til eit nettverk av mindre forkastningar må reduserast for å same trykket som er målt i brønnane. Det tyder, at enten er modellen som er brukt for transmissibiliteten til forkastningane feil, eller so er ei ”relay” sone mellom store forkastningar meir forseglande enn venta. For å kunne fullt ut forstå væskestraumen, bør ein gjere simuleringar med ein modell med fleire lag. Ved å modellere sekundær oljemigrasjon med ulike trykkhistorier, ser ein vesentlege endringar på migrasjonen med ulike trykkscenario. Detaljerte tolkingar av forkastningar er viktig både for trykkfordeling og hydrokarbonmigrasjon.

Deformerte band er skildra både frå eksperiment og frå feltarbeid i Brumunddal, Noreg. Dette er små forkastningar utvikla i sandsteinreservoar, som vil vere viktig for lateral strømming.

Acknowledgement

First of all, I would like to thank my supervisor Prof. Roy H. Gabrielsen, UiB for his advices and encouragement in the research work. I would also want to thanks Hans Borge, at SINTEF Petroleum Research for a lot of help doing the coding in PRESSIM and for always looking at the bright side of life. Without him, this thesis would have not been a reality. Also Idar Larsen contributes with coding in the final work. Øyvind Sylta has been very nice to discuss with. My other colleagues at SINTEF Petroleum Research have contribute with ideas and discussion, mainly versus rock mechanics; Prof. Rune Holt, Erling Fjær, Angela Maria Pillitteri Gotusso and Olav Flornes.

Norsk Hydro ASA is thanked for their funding of the thesis, providing data and giving permission to publish. I would specially like to thanks Christian Zwarch for having the idea to the thesis together with Øyvind Sylta. Then I would like to thanks Michel Erdmanns, Arnt Williams, Olav Lauvrak, Susanne Sperrevik, Geir Mørk and the Halten Terrace group in Oslo for interest discussions and useful help.

The SMIFF2 steering committee and work group (IFE, NGI, SINTEF) is thanked for nice input, especially in the first years, when everything was difficult.

I would also like to thank the structural geology group in Bergen, for never forgetting me, though I have been emigrating to Trondheim. Special thanks to Silje Berg, Tore Skar and Rune Kyrkjebø for fun and nice discussions.

Finally, I would like to thank my parents and my sisters for support and encourage in many years.

Table of contents

Summary

Samandrag

Acknowledgement

Chapter 1 Introduction p. 11-24

Chapter 2 Modelling of hydraulic leakage by pressure and stress p. 25-56 simulations and implications for Biot’s constant: An example from the Halten Terrace area, offshore Norway: Lothe, A.E., Borge, H. & Gabrielsen, R.H.

Chapter 3 Effect of different formulas of the minimum horizontal p. 57-80 stress in a basin simulator, and the impact on pressure and hydraulic leakage. Lothe, A.E., Borge, H., Larsen, I. & Gabrielsen, R.H.

Chapter 4 Evaluation of late caprock failure on hydrocarbon p. 81-104 trapping using a linked pressure and stress simulator. Lothe, A.E., Borge, H. & Sylta, Ø.

Chapter 5 Sub-seismic faults and their possible influence on p. 105-126 overpressure and hydraulic leakage - examples from offshore Mid-Norway. Lothe, A.E., Borge, H. & Gabrielsen, R.H.

Chapter 6 Influence of pore pressure on secondary hydrocarbon p. 127-1152 migration - A case study from the Tune area, Viking Graben. Lothe, A.E., Sylta, Ø., Lauvrak, O. & Sperrevik, S.

Chapter 7 An experimental study of the texture of deformation p. 153-180 bands: effects on the porosity and permeability of sandstones. Lothe, A.E., Gabrielsen, R.H., Bjørnvoll Hagen, N. & Larsen, B.T.

Chapter 8 Discussion and Conclusions p.181-183

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Chapter 1

Introduction

The theme of this thesis is the relationship between overpressure and stresses, and their control on hydraulic fracturing and hydraulic leakage. In overpressured hydrocarbon bearing sedimentary basin it is of great importance to understand the different processes and be able to simulate the occurrence and timing of hydraulic fracturing. In previous studies, hydraulic fracturing and leakage have been described from outcrop and from offshore field studies, but little effort has been put on simulating such processes on the scale of geological time. In association with the present study, the Pressim simulator that calculates water flow on basin scale (Borge 2000) has been further developed to include both pressure and stress to handle this problem. The hypothesis is that pressures and stress are interrelated and therefore need to be simulated simultaneously. The pressure builds up and the differential stress will control the failure in the cap rock. Both shear failure and tensile failure can be hydraulic driven and are dependent on the burial depth and the overpressure. Using such a tool, the timing and amount of hydraulic fracturing and leakage, due to overpressure, can be evaluated in different parts of a basin.

To simulate such complex processes it is necessary to understand of the entire system, including from both the reservoir and the caprock, focusing on sandstone reservoirs and shaly

-12- caprocks. The basin is assumed to be tectonic stable, thus changes in the large-scale horizontal stresses are tested in Chapter 3. To carry out the study different processes have been evaluated:

1) Overpressure and pressure generating mechanisms.

2) Stress generating mechanisms at different scales. Particularly the minimum horizontal and the vertical stresses are of importance when the possibility of hydraulic leakage is evaluated in an extensional regime.

3) Geo-mechanical properties of the caprocks

4) Existing fault zones, on both basin and reservoir scales and their relation to lateral fluid flow and the interplay between the lithostratigraphic architecture and the structural setting.

5) Initiation and mechanism for hydraulic fracturing and leakage, either along single fractures, in fracture swarms or as percolation leakage.

1) Overpressure and pressure generating mechanisms Overpressure in basins may be results from different processes such as burial depth, tectonics, hydrocarbon generation, mineral transformation and temperature increase (e.g. Swarbrick & Osborne 1998). Swarbrick et al. (2002) reviewed the magnitude of overpressures and found that rapid sedimentary burial is the most important factor for generating overpressure in young sediments. In addition to the burial rate, the controlling mechanisms are the permeability evolution of the sediments and the compressibility of the rocks and fluids. Yassir & Addis (2002) point to two types of overpressure related to stress; namely vertical loading and tectonic loading, where the effect of the last process is poorly understood. One example of an overpressured, laterally compressed sedimentary basin is the East Coast Basin, New Zealand, where an overpressure of 128 bar at 600 m depth is measured (Darby & Funnell 2001). White & Swarbrick (2001) compared the leak-off pressure, which define the lower limit of the minimum stress gradient, in different compartments from different areas. They report that the minimum horizontal stress- overpressure (Sh-Pp) coupling (increase in the magnitude of the minimum horizontal stress is observed in overpressured zones) are seen in the Central North Sea, Brunei, onshore Nigeria and offshore West Africa. It is also observed in the central North Sea (Gaarenstroom et al. 1993). Engelder & Fisher (1994) explains this by poroelasticity. Data from the Gulf of Mexico and the Mid-Norway area show no connection between in-situ stresses and pore pressures (White & Swarbrick 2001). White & Swarbrick (2003) concludes from the Mid-Norway area that the late stage development of overpressure post-dates normal compaction. In this case, the well-compacted sediments have developed a plastic rheology that prevents a pressure-stress coupling seen in more elastic rocks.

2) Stress generating mechanisms at different scales An important controlling mechanism for pressure distribution in a sedimentary basin is the orientation of the principal stresses and their magnitude and lateral variations through time. The stress generating mechanisms contribute to the total stress pattern on different lateral scales; continental, regional and local (e.g. Engelder 1993, Fejerskov & Lindholm 2000; Table 1). On the plate tectonic scale, stress fields are generated when forces from convections and buoyancy within the lithosphere and asthenosphere are opposed by tractions, either within

-13- the lithosphere or at the edges and the base of lithospheric plates (Engelder 1993). On the regional lateral scale the stresses are caused by the redistribution of masses within the lithospheric plates or loading at the edges of the lithospheric plates. Finally, on the local scale the stresses are gravitationally, mechanically or thermally induced.

3) Geo-mechanical properties of the caprock Shales are often effective top seals for overpressured zones, where the seal capacity is controlled by the degree of mechanical and chemical compaction. Mechanical compaction is a function of effective stress, grain size distribution and mineralogy. Chemical compaction involves dissolution and precipitation of minerals mainly as a function of temperature (Bjørlykke 1999). The mineralogy and the depth of burial control both the permeability and the porosity of shales. For similar porosities, there are five orders of magnitude in difference between the permeability of pure kaolinite and smectite. In mixed lithology, permeability decreases sharply with shale content as the pores of sands are filled. On the other hand, pure shale has higher permeability than a sand-shale mixture (Revil & Cathles 1999). Permeability in shales is reduced by the progressive collapse of large pores due to increasing effective stresses (Dewhurst et al. 1999). The elasticity and stiffness of the rocks depends on the burial depth and the mineralogy. The mechanical properties of the rocks are used as input in the simulations and will be discussed further in Chapter 2.

4) Flow properties to pre-existing faults Faults on different scales are important barriers, but also conduits of lateral fluid flow. A fault can change properties from open to sealing depending on burial history, reactivation, mineralogy and diagenesis. In a sedimentary basin will the pressure pattern mainly be controlled by the faults (Heppard et al. 1998). Often, the interpretation of a fault, the length and size would vary depending on the seismic interpreter (e.g. Townsend 2002). The sub- seismic continuation of a fault along strike is important, when the pressure compartments should be defined in the simulator (Borge & Sylta 1998). Outcrop studies (e.g. Antonellini et al. 1994, Caine et al. 1996) and experiments (e.g. Fossen & Gabrielsen 1996) indicate that a network of smaller faults is commonly present around the main fault. This zone would not always be visible in reflection seismic data. Also the continuation of a fault, often defined as “process zone” (zone formed in response to deformation associated with tip propagation), would not be visible on the seismic (Fossen & Hesthammer 2000). The relation between small-scale features as deformation bands and larger faults, as observed in the field is discussed further in Chapter 6 and 7.

5) Initiation and mechanism for hydraulic fracturing and leakage Hydraulic fracturing and leakage are processes, which are fairly well understood from man- made hydraulic fracturing to increase production possibilities in a reservoir, but are less understood as a natural phenomena generated due to overpressure. Natural hydraulic leakage can be related to either continuum or discrete failure. Discrete failure can further be subdivided into single fracture, swarms of fractures and reactivation of existing faults/fractures. When assessing hydraulic fracturing, it is common to start the analysis by focusing upon single fractures as end-models. Lancette & Engelder (1992) pointed to four major processes, which contribute to stresses around a fracture: a) Increase in joint volume during joint propagation b) fluid flow from the pore space in the host rock to the joint, c) compressibility of the fluid within the joint and d) fluid flow within the joint. The latter includes flow from the main body of the joint into the newly created portion at the joint tip. Fluid flow along a single fracture can be modelled as flow between parallel, smooth plates. This approach is widely used in hydrogeology and is referred to as the cubic law (Bear 1993).

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There is little field evidence of how hydraulic leakage occurs. Verbeek & Grout (1993) showed that hydrocarbons are found in gilsonite dykes several meters wide and several kilometres long, in Uinta Basin in the western United States. The fracture surfaces in the dykes show plumose structure, typically for dilatant fractures. From well data, there is evidence that the dykes were formed in high fluid pressure environment. Large, parallel oriented fractures have taken up the deformation in the area.

Hydraulic leakage can occur through a network or swarms of small fractures. Such can develop both in the tensile and in the shear regime. Cosgrove (1998) discussed how different fracture pattern develop depending on the differential stresses in the tensile regime (Figure 1). Vertical tensile fractures develop under high differential stresses and by low differential stresses (shallow burial) a randomly oriented fracture pattern will occur (Cosgrove 1998). The permeability of the percolation fractures depends on the failure mode and the later sealing. Sealing can occur due to crack healing by physical diffusion or crack sealing by mineral precipitation. Crack healing is a time-dependent process driven by surface tension and elastic energy. The kinetics is controlled by temperature, stress and initial shape of the crack (Renard et al. 2000). Crack healing corresponds to the closure of a small fracture without any precipitation of matter inside. An crack sealing mechanisms is mineral precipitation from formation water. The chemical composition of water will depend on burial depth and the mineral composition. Experiments (Gutierrez et al. 2000) show that fractures will remain conductive, even when the effective normal stress approaches the uniaxial compressive strength of the undeformed rock.

Table 1 Lithospheric stress generation mechanisms (Fejerskov & Lindholm 2000). Stress field 1st order Continental 2nd order Regional 3rd order Local

Lateral stress >1000 km 100-1000 km <100 km field extent Large-scale density Plate tectonic forces inhomogeneities; Topography Stress Ridge push Continental margin Geological features; generation Basal drag Flexural stresses; Faults mechanism Slab pull Sedimentary loading Hard and soft inclusions Deglaciations Wide topographic loads

Figure 1 Different tensile fracture pattern depending on the differential stresses. From Cosgrove (1998).

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Scope of the present work The aim of the present work is to show how hydraulic fracturing and leakage can be simulated in an overpressured sedimentary basin. In such cases, large faults are likely to control the lateral fluid flow in the overpressured areas. A good understanding of the fracture zones both in the reservoir unit and in the caprock unit are requested to be able to study the whole system.

The Chapters 2-7 are arranged according to their scope and focus in two parts, namely:

Part I Simulation of hydraulic fracturing and leakage from overpressured reservoirs and Part II Small-scale faults and deformation bands in the sandstone reservoir unit.

Part I consists of four papers from the Halten Terrace and one paper from the northern North Sea. In the work from the Halten Terrace, the focus is on the development of pressures and stresses from Cretaceous to present. It is mainly influenced by a late pressure build-up the last 5 Ma, with development of hydraulic fractures and leakage in some areas. The effects of hydraulic fracturing and leakage have been simulated, where the resulting pressure distribution have been compared to measured pressure data from wells. In Chapter 3 also the magnitude of the minimum horizontal stress has been varied using different empirical and theoretical formulas. The results from the simulations are compared with measured leak-off tests from wells in the study area. The other dataset from the Tune Field area, is used to test the impact pressure history has on hydrocarbon migration. The pressure distribution is largely controlled by the fault pattern and sealing potential to the faults. Part II consists of one paper where small scale deformation bands in sandstone reservoir are studied. Data from the Brumunddal area, onshore Norway, and experiments on the Rotligendes sandstone are used. Methods and main architecture of the thesis The Pressim simulator calculates the pressure distribution in a sedimentary basin through geological time, as presented in detail in Borge (2000). In the following an overview of which pressure generating mechanisms are included in the simulator is given. The simulator calculates generation and dissipation of pressure in a single-layer reservoir unit by quantifying the geological processes listed in Table 2. The pressure compartments are defined by the faults as interpreted on the top of the reservoir unit, usually from reflection seismic data. The overlying and underlying rocks are vertical seals of the compartments. The numerical solution method used is the “Forward Euler” which is stabilized by using minimum volume during dissipation. The lateral flow between the compartments, were modelled using fault transmissibilities defined by the dip-slip displacement and burial depths to the faults (Borge & Sylta 1998). The permeability versus depth is defined as input for all faults in the study area. Shale drainage in the caprocks is defined depending on burial depth, with a drainage zone, a transition zone and a accumulation zone. The drainage properties are uniform in the study area. The code also includes processes as mechanical compaction of shales (Baldwin & Butler 1985), and mechanical and chemical compaction of sand to sandstone (Walderhaug 1996). The established model use fluid mechanical properties of the pore water to estimate the pressure distribution as a function of time. The calculation of accumulated pressure in each compartment was based upon mean depth and depth to top of each pressure compartment.

The main objective of Chapter 2 is to incorporate failure criteria in the pressure simulator to estimate the timing of hydraulic failure and the amount of leakage from the top point of each pressure compartment with a greater certainty (Figure 2). The Griffith-Coulomb failure

-16- criterion was used for the first failure, while the frictional sliding criterion is used for the reactivation of the failure (Figure 3). Simulations varying the coefficient of internal friction and frictional sliding were carried out. Secondly, we discuss the geo-mechanical parameters for the caprock can be simulated, with special emphasis on Young’s modulus and Poisson’s ratio. We assume that these to parameters have a direct influence on Biot’s constant. These geo-mechanical parameters are important when the link between increasing overpressure and leakage in overpressured part of the study area, are to be simulated.

In Chapter 2, the minimum horizontal stress (σ 3 ) was handled in a simplistic way, by using an empirical equation to express the depth-dependence to (σ 3 ). The aim with the work presented in Chapter 3 is to incorporate different theoretical (Elastic Theory, Zoback & Healy 1984), and empirical formulas (Breckels & van Eekelen 1982, Grauls 1996, 1998) for the minimum horizontal stress to better constrain the limits of the formulas. Another aim was to test the effect of the large-scale generated lateral stresses on hydraulic fracturing and leakage from overpressured compartments in the study area. To quantify the quality of the simulations, both the simulated overpressure and minimum horizontal stress were calibrated to data from wells.

In Chapter 4 we focus on how simulation of the timing and the amount of hydraulic leakage will play an impact on hydrocarbon migration. Quantifying of the uncertainty in the simulations is important when we want to improve risk prediction of hydrocarbon shows in undrilled traps. First we vary the coefficient of internal friction and frictional sliding, finding no large influence on the timing and amount of leakage. Then, we varied the lateral permeability across the major fault zones, defining the extent of the pressure compartments in the simulator. The measured pressure from wells where used to quantify the possibilities of the simulations.

The main work presented in Chapter 4, is followed up in Chapter 5. Thus, instead for varying the transmissibility across all major faults in the study area, the transmissibility across individual faults is examined. Often, large uncertainties are associated with the interpretation of hardly detectable faults either as continuations of larger faults on seismic or as smaller faults with small dip-displacement. Such sub-seismic faults can be important pressure barriers in a basin. It would be of interest to study how these small faults influence the pressure distribution and also on the probability of hydraulic fracturing and leakage in overpressured areas. Is the transmissibility across certain individual faults of critical importance when evaluating new hydrocarbon prospects?

In Chapter 6 the main focus is on overpressure and its influence on hydrocarbon migration over geological time scale. As presented earlier in Chapter 4 and 5, the overpressure distribution is mainly controlled by the faults and their transmissibilities. In this paper two fault maps with different resolution are used in the simulations. It is a low-resolution fault map, with only the large faults interpreted and a high-resolution fault map, with both small and large faults interpreted. The data set used in Chapter 6, is not from the Halten Terrace presented in the previous chapters, but from the Tune Field area, situated in the northern North Sea. The aim by selecting this study area is a) to study what influence the pressure will have on hydrocarbon migration and b) to simulate the large pressure differences across small faults that is characteristic in the area, and simulate the measured pressures in wells (Childs et al. 2002).

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In part II the focus is on the reservoir unit and it’s internal fractures that will influence on the lateral fluid flow. Although, in the Pressim simulator is the pressure compartments considered as internal homogenous, with no flow barriers, which is a simplification. This was illustrated in Chapter 6, that even using the high-resolution fault map, small faults where shown to be capable of sustaining large pressure differences. Such can be achieved by deformation bands in the reservoir unit, as will be discussed in Chapter 7. In this part, the Brumunddal Sandstone and associated sedimentary rocks, in northern part of Oslo Graben are used as a case study area. This is a rotated fault block, of syn-rift age with an approx. 0.8 km thick package with continental eolian deposits.

Part II consists of one paper, Chapter 7 in this thesis. The paper gives a more detail analysis based field observations and laboratory experiments, of the texture of deformation bands, and its effect on porosity and permeability. This gives an understanding of possible flow barriers that exits in a reservoir unit. At this stage, such sealing mechanisms are not taken directly into account in the simulator, but as discussed in Chapter 6, the effect can be seen indirectly on the pressure distribution in a basin.

Table 2 Geological processes modelled in the simulator Models lateral flow of formation water across low-permeable Lateral flow faults. Using the explicit forward Euler solution technique (Borge 2002). Divides the cap-rocks into a draining, accumulating and sealing Shale drainage zone (Borge 2002) Model mechanical compaction of shale (Baldwin & Butler 1995), Compaction mechanical compaction of sand and chemical compaction of sand (Walderhaug 1996). Modelling hydraulic fracturing using Griffith-Coulomb failure criterion for the first failure, and the sliding failure criterion for Hydraulic leakage reactivation of the fault zone (Lothe et al. in prep). The minimum horizontal stress is determined using an empirical formula (Grauls 1996). The vertical stress depends on the overburden.

Pressure

Tensile fractures Caprock Hydraulic fracturing

Shear fractures Reservoir

Overpressured zonezone Depth

Figure 2 The principal sketch shows how hydraulic failure, along a network of shear faults is assumed to occur at the top of overpressured reservoir compartments at deep burials. Failure along one single fault should not be ruled out.

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τ Frictional µ ' µ sliding failure envelope Griffith-Coulomb failure envelope

σ n σ σ 3 1 Figure 3 Failure criteria used in the simulator to calculate timing of hydraulic failure.

Results

Chapter 2

Modelling of hydraulic leakage by pressure and stress simulations and implications for Biot’s constant: An example from the Halten Terrace area, offshore Norway A coupled pressure and stress simulator was applied to the reservoir sandstone unit, the Middle Jurassic Garn Formation in the Halten Terrace area, offshore Mid-Norway, in order to simulate hydraulic fracturing and leakage due to overpressure. The shales below and above the reservoir unit were vertical seals to the compartments, while the faults delineated the pressure units. The overpressure generation within the pressure compartments was modelled quantifying the mechanical and chemical compaction. An empirical model for the minimum horizontal stress was applied to the Mohr circle and the Griffith-Coulomb failure criterion to estimate the pressure levels at which hydraulic fracturing occurs.

Sensitivity tests of the rock mechanical parameters indicate that the values of Poisson’s ratio and Young’s modulus have impact on the accumulation of overpressure during time. Both the coefficient of internal friction (µ) and the coefficient of sliding friction (µ’), which are used in the failure criteria, were varied showing a large impact on the pressure build up, hydraulic fracturing and leakage. The modelled timing and location of hydraulic fracturing and subsequent leakage depend upon the rock mechanical models used in the simulations. The simulations show hydraulic leakage to occur in one pulse with continuous flow through the leaking compartment.

Lothe, A.E., Borge, H. & Gabrielsen, R.H. submitted: Modelling of hydraulic leakage by pressure and stress simulations and implications for Biot’s constant: An example from the Halten Terrace area, offshore Norway. Petroleum Geoscience.

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Chapter 3

Effect of different formulas of the minimum horizontal stress in a basin simulator, and the impact on pressure and hydraulic leakage

Different empirical (Breckels & van Eekelen 1982, Grauls 1996, 1998) and theoretical formulas (Zoback & Healy 1984, Elastic Theory) for the minimum horizontal stress are implemented in a basin simulator, to be able to simulate the relationship between stresses and pressure changes on geological time scale. Also, the largest horizontal stresses are varied in magnitude and direction in the simulator, to simulate the pressure build up in the basin, and the possible influence on hydraulic fracturing and leakage. To calculate the stresses, the stress mechanisms are subdivided into regional and continental scale. The simulated minimum horizontal stress is compared with minimum horizontal stresses measured from leak-off tests in wells. The predicted pressure is compared with today’s pressure distribution in wells.

The simulations show that both Breckels & van Eekelen and the Elastic theory, give too high values for the minimum horizontal stress, and thereby too late caprock failure. Using Zoback & Healy’s formula on the other hand, too early leakage occurred with following no pressure build up. The best results are obtained using Grauls (1996, 1998) empirical equations. Using Grauls (1996) to simulate the regional stress contribution, the magnitude of the continental stress contribution from the ridge push is varied. Increasing the maximum horizontal stresses, give a later hydraulic failure and leakage in the overpressured part of the study area.

Lothe, A.E., Borge, H. & Gabrielsen, R.H. in prep: Effect of different empirical and theoretical formulas of the minimum horizontal stress in a basin simulator, and the possible impact on pressure build up and hydraulic leakage - example from the Halten Terrace, offshore Mid-Norway.

Chapter 4

Evaluation of late caprock failure and hydrocarbon trapping using a linked pressure and stress simulator

Hydraulic fracturing and leakage can be controlling factors for hydrocarbon leakage in overpressured sedimentary basins over geological time. Knowledge of the lateral flow properties in major faults are needed to simulate how pressure generation and dissipation will influence on the sealing potential of caprocks. The properties of hydraulic fracture processes should be evaluated to quantify timing and amount of hydraulic leakage.

Varying the coefficient of internal friction and frictional sliding, there are none or minor changes in the timing and amount of hydraulic fracturing and leakage in the pressure compartments. Low fault permeabilities give early failure, while high permeabilities results in late or no hydraulic fracturing and leakage. Leakage in one pressure compartment will influence the neighbouring compartments. Large compartments will control the leakage pattern in surrounding areas. The amount of cumulative leakage depends on timing and the size of the compartment. Using the pressure measured in the wells today as calibration, uncertainties of timing and leakage for different cells can be estimated. The uncertainty estimates can be used as guidelines for possible hydrocarbon leakage risks.

Lothe, A.E., Borge, H. & Sylta, Ø. in press: Evaluation of late caprock failure on hydrocarbon trapping using a linked pressure and stress simulator. Accepted for publication in AAPG Hedberg Special Publication.

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Chapter 5

Sub-seismic faults and their possible influence on overpressure and hydraulic leakage - examples from offshore Mid-Norway

The sealing properties of the major fault in a sedimentary basin are potentially important, time-variable parameters in the evaluation of lateral fluid flow. The sealing capacity of a fault depends on lithology, burial depth, diagenesis and dip-slip displacement. Still, large uncertainties are associated with the interpretation of hardly detectable faults where such occur in the continuation of larger fault zones on reflection seismic data. Such sub-seismic faults can contribute to the establishment of pressure compartments in sedimentary basin.

Simulations show that the transmissibilities across individual fault situated in highly to intermediate overpressured areas in the sedimentary basin, have a major influence on the pressure distribution in the neighbouring compartments. The higher the transmissibility the major fault has the larger are the neighbouring area, which are influenced. In the whole basin, the changes in pressure are minor. Changing the transmissibilites in low-pressured areas gives minor changes in the simulated pressure distribution. Several simulator runs in which sub- seismic faults are removed as pressure barriers have been carried out. Predictions have been carried out to quantify the uncertainty regarding timing and amount of hydraulic leakage from these areas. The results can be used in basin modelling to estimate hydrocarbon fills in undrilled prospects.

Lothe, A.E., Borge, H. & Gabrielsen, R.H. in prep: Sub-seismic faults and their possible influence on overpressure and hydraulic leakage - examples from offshore Mid-Norway.

Chapter 6 Influence of pore pressure on secondary hydrocarbon migration - A case study from the Tune area, Viking Graben

Modelling has been carried out in the intermediately pressured Tune field area, in the northern Viking Graben. Two different fault maps at top Brent Group level are used; one with only the large faults interpreted and one with both small and large faults mapped. The simulations show high overpressure generated in the western area, into the deeper part of Viking Graben, and hydrostatic pressure in the eastern Oseberg area. Tune is situated in an intermediately pressured area (well 30/5-2), with a large pressure difference measured towards east (well 30/8-3; nearly hydrostatic). To be able to simulate this, using the low-resolution fault model, one fault has lowered transmissibility. Using the high-resolution fault map, many small faults have to have lowered transmissibilities. Most likely, the intermediate pressure in the western area is in connection with the lower part of the sedimentary column in the compartment where well 30/8-3 is situated. The second oil migration models show that the overpressure distribution has a major impact on migration paths. Detailed interpretations of the faults are substantial to do reliable simulations of both pressure distribution and hydrocarbon migration.

Lothe, A.E., Sylta, Ø., Lauvrak, O. & Sperrevik, S. in prep: Influence of pore pressure on secondary hydrocarbon migration - A case study from the Tune area, Viking Graben.

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Summary of Chapter 7

An experimental study of the texture of deformation bands: effects on the porosity and permeability of sandstones

We investigated the texture and formation of deformation bands, in accordance to the permeability and porosity. Video image analysis of the Brumunddal sandstone showed a decrease in the number of large pores in the deformed zones. The frequency of small pores is increasing in the intermediate zone, compared to the undeformed rock and the central zone of a deformation band.

Tri-axial compression tests were performed on Red Wildmoor sandstone with constant confining pressure (8 MPa). Axial P- and S-wave velocities measured during loading showed structural changes in development of a deformation band: Stage I and II closure of micro- cracks and pores and tighter grain packing parallel to the maximum stress direction and simultaneously dilation perpendicular to the maximum stress direction. Stage III both the P- and the S- wave are decreasing, reflecting tighter grain packing and development of micro- fractures. These observations are supported by permeability measured before, under and after tri-axial compression, with recovering of permeability due to elastic effect and static reduction due to tighter packing and ultimately grain size reduction. NMR images of oil saturated samples after loading to failure shows stage III, grain size reduction, stage IV secondary fracturing, and stage IV, development of a slip plane.

Lothe, A.E., Gabrielsen, R.H., Bjørnvoll Hagen, N. & Larsen, B.T. 2002: An experimental study of the texture of deformation bands: effects on the porosity and permeability of sandstones. Petroleum Geoscience, 8, 195-207.

References Antonellini, M., Aydin, A. & Pollard, D. D. 1994. Microstructure of deformation bands in porous sandstones at Arches National Park, Utah. Journal of Structural Geology, 16, 941-959. Baldwin, B. & Butler, C. O. 1985. Compaction curves. AAPG, 69(4), 622-662. Bear, J. 1993. Modeling flow and contaminate transport in fractured rocks. In: Bear, J., Tsang, C. F. & Marsily, G.D. (eds) Flow and Contaminant Transport in Fractured Rock. Academic Press, New York, 1-37. Bjørlykke, K. 1999. Principal aspects of compaction and fluid flow in mudstones. In: Aplin, A. C., Fleet, A. J. & Macquaker, J. H. S. (eds) Mud and Mudstones: Physical and Fluid Flow Properties. Geological Society of London, London, 158, 73-78. Borge, H. 2000. Fault controlled pressure modelling in sedimentary basins. An thesis for the degree of Doktor Ingenør of the Norwegian University of Norway, Trondheim, Norway, 148 pp. Borge, H. & Sylta, Ø. 1998. 3D modelling of fault bounded pressure compartments in the North Viking Graben. Energy, Exploration and Exploitation, 16, 301-323. Breckels, I. M. & Eekelen, H. A. M. v. 1982. Relationship between horizontal stress and depth in sedimentary basins. Journal of Petroleum Technology, 34, 2191-2199. Caine, J. S., Evans, J. P. & Forster, C. B. 1996. Fault zone architecture and permeability structure. Geology, 24(11), 1025-1028. Childs, C., Manzocchi, T., Nell, P. A. R., Walsh, J. J., Strand, J. A., Heath, A. E. & Lygren, T. H. 2002. Geological implications of a large pressure difference across a small fault in the Viking Graben. In: Koestler, A. G. & Hunsdale, R (eds) Hydrocarbon Seal Quantification. NPF Special Publication, Elsevier Science, Amsterdam, 11, 187-201.

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Cosgrove, J. W. 1998. The role of structural geology in reservoir characterization. In: Coward, M. P., Daltaban, T. S. & Johnson, H. (eds) Structural Geology in Reservoir Characterization. Geological Society Special Publications, London, 127, 1-13. Darby, D. & Funnell, R. H. 2001. Overpressure associated with a convergent plate margin: East Coast Basin, New Zealand. Petroleum Geoscience, 7, 291-299. Dewhurst, D. N., Aplin, A. C. & Yang, Y. 1998. Compaction driven evolution of porosity and permeability in natural mudstones: an experimental study. Journal of Geophysical Research, 103(B1), 651-661. Dewhurst, D. N., Yang, Y. & Aplin, A. C. 1999. Permeability and fluid flow in natural mudstones. In: Aplin, A. C., Fleet, A. J. & Macquaker, J. H. S. (eds) Mud and Mudstones: Physical and Fluid Flow Properties. Geological Society of London, London, 158, 23-43. Engelder, T. 1993. Stress regimes in the lithosphere. Princeton University Press, New Jersey, pp. 399. Engelder, T. & Fisher, M. P. 1994. Influence of poroelastic behaviour on the magnitude of minimum horizontal stress, Sh, in overpressured parts of sedimentary basins, Geology 22, 949-952. Fejerskov, M. & Lindholm, C. 2000. Crustal stress in and around Norway: an evaluation of stress- generating mechanisms. In: Nøttvedt, A. (ed.) Dynamics of the Norwegian Margin. Geological Society of London, London, 167, 451-467. Fossen, H. & Gabrielsen, R. H. 1996. Experimental modeling of extensional fault systems by use of plaster. Journal of Structural Geology, 18, 673-687. Fossen, H. & Hesthammer, J. 2000. Possible absence of small faults in the Gullfaks Field, northern North Sea: implications for downscaling of faults in some porous sandstones. Journal of Structural Geology, 22, 851-863. Grauls, D. 1996. Minimum Principal Stress as a Control of Overpressures in Sedimentary Basins. In: Proceeding of the8th Conference on Exploration and Production. IFP Report No43313, IFP Ruil- Malmaison. Grauls, D. 1998. Overpressure assessment using a minimum principal stress approach. In: Overpressures in petroleum exploration; Proc. Workshop 22. Bull. Centre Rech. Elf Explor. Prod., Pau, France, 137-147. Gutierrez, M., Øino, L. E. & Nygård, R. 2000. Stress-dependent permeability of a de-mineralised fracture in shale. Marine and Petroleum Geology, 17, 895-907. Gaarenstroom, L., Tromp, R. A. J., Jong, M. C. d. & Brandenburg, A. M. 1993. Overpressures in the Central North Sea: implications for trap integrity and drilling safety. In: J. R. (ed). Petroleum Geology of Northwest Europe: Proceedings of the 4th Conference Parker, The Geological Society, London, 1305-1313. Heppard, P. D., Cander, H. S. & Eggertson, E. B. 1998. Abnormal Pressure and the Occurrence of Hydrocarbons in Offshore Eastern Trinidad, West Indies. In: Law, B. E., Ulmishek, G. F. & Slavin, V. I (eds) Abnormal Pressures in Hydrocarbon Environments. AAPG Memoir, 70, 215-246. Lacazette, A. & Engelder, T. 1992. Fluid-driven Cyclic Propagation of a Joint in the Ithaca Siltstone, Appalachian Basin, New York. In: Fault Mechanics and transport properties of rocks. Academic Press Ltd., 297-323. Renard, F., Dysthe, D., Jamtveit, B. & Feder, J. 2000. Experimental Evidence of Complex Behaviour During Crack Healing. In: 3rd Euroconference on Rock Physics and Rock Mechanics, Bad Honnef, Germany. Revil, A. & Cathles, L. M. 1999. Permeability of shaly sands. Water Resources Research, 35, 651-662. Swarbrick, R. E. & Osborne, M. J. 1998. Mechanisms that generate abnormal pressures: an overview. In: Law, B. E., Ulmishek, G. F. & Slavin, V. I. (eds) Abnormal Pressures in Hydrocarbon Environments. AAPG Memoir, 70, 13-34. Swarbrick, R. E., Osborne, M. J. & Yardly, G. S. 2002. Comparison of overpressure magnitude resulting from the main generating mechanisms. In: Huffman, A. R. & Bowers, G. L. (eds) Pressure regimes in sedimentary basins and their prediction. AAPG Memoir, 76, 1-12.

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Townsend, C. 2002. Realistic fault description for reservoir modelling. In: AAPG Hedberg Research Conference: Evaluating the hydrocarbon sealing potential of faults and caprocks, Barossa Valley, South Australia. Verbeek, E. R. & Grout, M. A. 1993. Geometry and structural evolution of gilsonite dikes in the eastern Uinta basin, Utah. U.S. Geological Survey Bulletin, 1787, 42. Walderhaug, O. 1996. Kinetic modelling of quartz cementation and porosity loss in deeply buried sandstone reservoirs. AAPG Bulletin, 80(5), 731-745. White, A. & Swarbrick, R. 2003. Minimum in-situ stress and pore pressures in Mid-Norway. In: "Fault and Top Seals" What do we know and where do we go? EAGE, Montpellier, France. White, A. J. & Swarbrick, R. E. 2001. LOPs: "Minimum stress gradients" and in-situ stress-pore pressure coupling. In: EAGE 63rd Conference & Technical Exhibition, Amsterdam, The Netherlands, 4. Yassir, N. & Addis, M. A. 2002. Relationships between pore pressure and stress in different tectonic settings. In: Huffman, A. R. & Bowers, G. L. (eds) Pressure regimes in sedimentary basins and their prediction. AAPG Memoir, 76, 79-88. Zoback, M. D. & Healy, J. H. 1984. Friction, faulting, and "in situ" stress. Annales Geophysicae, 2(6), 689-698.

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Chapter 2

Modelling of hydraulic leakage by pressure and stress simulations and implications for Biot’s constant: An example from the Halten Terrace, offshore Mid-Norway

Lothe, A.E. 1,2, Borge, H. 1 & Gabrielsen, R.H. 2

1SINTEF Petroleum Research, N-7465 Trondheim, Norway, 2Geological Institute, University of Bergen, Allégaten 41, N-5007 Bergen, Norway

Abstract______

A coupled pressure and stress simulator has been applied to the reservoir sandstone unit, the Middle Jurassic Garn Formation in the Halten Terrace, offshore Mid-Norway, in order to simulate hydraulic fracturing and leakage due to overpressure. The over- and underlying rocks are used as vertical seals to the compartments. The overpressure generation within the pressure compartments was modelled quantifying the mechanical and chemical compaction. An empirical model for the minimum horizontal stress was applied to the Griffith-Coulomb failure criterion to estimate the pressure levels at which hydraulic fracturing occurs.

Sensitivity tests of the Poisson’s ratio and Young’s modulus, which controls Biot’s constant, show an effect on the accumulations of overpressure during time. Defining Biot’s constant equal to 1, results in too early pressure build up and hydraulic leakage in the western parts of the basin. Lower values of the Biot’s constant (>0.85) give a present day pressure distribution closer to the measured pressures in wells. The Kristin compartment is simulated to experience hydraulic failure around 1.5 Ma. High values of the coefficient of internal friction (µ) and the coefficient of sliding friction (µ’), which are used in the failure criteria, results in a time-delay in failure, and thereby less leakage from overpressured compartments.

Keywords: hydraulic leakage, overpressure, basin modelling, Halten Terrace______

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Introduction In sedimentary basins, hydraulic fracturing and leakage (Cosgrove 1998) can occur from reservoir units where high overpressures (Swarbrick & Osborne 1998) have built up over geological time (Fig. 1). Empirical models have traditionally been used to predict hydraulic leakage in basin modelling studies, assuming leak-off pressure to be between 85-95% of the overburden (e.g. Roberts & Nunn 1995, Wang & Xie 1998). The intention behind the work presented in this paper has been to simulate the relation between hydraulic fracturing, stress, pressure history and the geo-mechanical properties to the overlying cap rocks. Then, rock-mechanical models have been added to the Pressim pressure compartment simulator (Borge 2000, 2002) where generation and dissipation of overpressure can be modelled on a geological time scale.

Hydraulic fracturing is defined as the formation and opening of fractures by the action of fluid under pressure (Lapidus 1990). Following Lawn & Wilshaw (1975), the term fracture encompasses all types of mode I (tensile) fractures such as joints and veins, mode II (shear) fractures and mode III (hybrid) fractures. The types of fracture that initiate due to hydraulic fracturing depend on the fluid pressure, stress condition, burial depth and the mechanical properties of the rock unit. On a geological time scale, high fluid pressure can cause hydraulic fracturing of the cap rock above an overpressured unit.

Field studies describing hydraulic fracturing are rare, in spite of the fact that this phenomenon is much discussed in the literature from a theoretical point of view (Cosgrove 1998). This is probably because the most common lithology in overpressured zones is mudstone, which may be difficult to sample and which preserves fractures to a limited degree. Also, fractures in such lithology are difficult to interpret (Gabrielsen & Kløvjan 1997, Cosgrove 1998), and hydraulic fracturing is likely to be generated at great depth and samples are not easily accessible. Finally, such structural features are likely to become disturbed during uplift and to become masked by later fractures. An onshore field example of large-scale hydraulic fractures is presented by Verbeek & Grout (1993) from the Uinta Basin in the Western United States. Hydrocarbons are found in dikes about several meters wide and several kilometres long. The dikes are conduits for hydrocarbon migration and flow, and they show plumose structure pointing towards a dilatant original. Borehole data indicate a high-pressure environment during initiation.

The effects of changing the geo-mechanical parameters as a function of burial depth is studied in this paper through several simulations, acknowledging that the fracture criterion, which is a depth- and time-function, will influence the timing and location of hydraulic fracturing. Several assumptions have to be made in order to simulate the complex processes of hydraulic leakage. These include definition of fracture criteria and the definition of the geo-mechanical properties of the caprock. Also, a depth-dependant model for the minimum horizontal stress and the vertical stress is used. In the following, a presentation of the geological setting will be given, an overview and evaluation of the most important criteria as applied in the simulations is presented. Thereafter, the basis and results of the sensitivity study for the most central input parameters are given.

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Lateral flow Shale drainage

Shale compaction Quartz cementation

Hydraulic leakage Figure 1 Schematic representation of processes simulated in the Pressim/Stressim code. Geological Setting The study area is located between 64˚15’ N - 65˚25’ N and 6˚20’E - 8˚10’ E at the Halten Terrace, offshore mid-Norway (Fig. 2a) and covers an area of approximately 10000 km2. The Halten Terrace is bordered eastward by the N-S striking Bremstein Fault Complex, which separates the terrace from the Trøndelag Platform (Fig. 2b). The N-S striking Klakk Fault Complex delineates the terrace from the deeper Vøring Basin in the west. Internally on the Halten Terrace area, there are minor fault zones trending N-S to NE-SW. The Halten Terrace has suffered multiple stages of extensional faulting, mainly during the Middle Jurassic and Early Cretaceous rifting period. Tilted fault blocks were formed during this early stage (e.g. Blystad et al. 1995, Koch & Heum 1995). Significant structuring took place during Late Cretaceous deformation, which particularly included faulting associated with the Bremstein Fault Complex and Vingleia Fault Complexes (Blystad et al. 1995). The latest rift episode affecting this area was the opening of the northern part of the North Atlantic Ocean during the earliest Eocene time (Skogseid et al. 1992).

A generalized stratigraphic column (Dalland et al. 1988) of the area is shown in Figure 3. The base of the Jurassic syn-rift sequence on the Halten Terrace is traditionally interpreted as the contact between the Middle Jurassic shallow marine sandstones of the Fangst Group (Ile, Not and Garn Formations) and the overlying shelf mudstones of the Upper Jurassic Viking Group (Melke and Spekk Formations; Dalland et al. 1988, Koch & Heum 1995). The Garn Formation is suggested as homogenous sandstone, with a lateral extent of 10’s of km. However, Gjelberg et al. (1987) demonstrated a facies diachroneity of the Garn and Melke Formations on regional scale, and Corfield et al. (2001) support this view on a local scale (Smørbukk area).

In the Halten Terrace area, well logs show an overpressure in the Middle Jurassic Fangst Group and the Late Cretaceous Lysing Formation. Skar et al. (1998) divided the Halten Terrace into three pressure compartments based upon pressure observations. The western area, which is limited by the Klakk Fault Complex, is highly overpressured (>300 bar). The northeastern area, between the Heidrun and Tyrihans South fields is a moderately overpressured zone, and in the southeastern part there is low or no overpressure. Since the porosity in the overpressured shales is only slightly influenced by the present overpressure (Teige et al. 1999), Skar et al. (1998) suggested that the

-28- overpressure developed in recent time. They proposed a pressure transfer from the deeper Rås Basin to the western part of the Halten Terrace, through the Klakk Fault Complex. Recent fluid pressure simulation by Borge (2000, 2002) suggests that the pressure build-up is due to rapid Pliocene subsidence, shale compaction and quartz cementation. 4° 6° 8° 10°

Tertiary dome Vøring e x p l Cretaceous high m Basin C o Cretaceous basin t l Platform area 66° u n a i Terrace HeidrHeidruunn F s Permo-Triassic basin x a Fault B x e l

s

p s

m e å o

C l

R KKrristinistin

t Trøndelag

l

F

K

u

a l

F Platform a

k n i

e

k

HaltenHalten t

s

m

Terrrraceace e r

B ault Comple

F a

u

l x t 64°

C Vingleiault Comple

o Fa m

p l

e

x Trondheim Fault Complex Bremstein F NORWAY Møre Trøndelag 50 km 20 km Figure 2 a) Overview map of the Mid-Norwegian sea region, where study area are marked. The main structural elements are shown. Modified from Blystad et al. (1995). b) The Halten Terrace area used in the simulation. Calibration wells are marked, and major fault zones at top Garn Formation horizon.

Ma PERIOD AGE FORMATION

65 GROUP Maastrichtian 70 SPRINGAR Campanian 80

L SHETLAND NISE Santonian Coniacian KVITNOS 90 Turonian LYSING Cenomanian 100 LANGE ACEOUS Albian 110 CRET Aptian 120 E LYR

Barremian CROMER KNOLL

130 Hauterivian Valanginian

140 Ryazanian

Volgian SPEKK 150 L Kimmeridgian ROGN Oxfordian 160 VIKING Callovian Bathonian MELKE 170 M Bajocian GARN 180 Aalenian NOT ANGST JURASSIC Toarcian F ILE Figure 3 Simplified stratigraphic column for the Halten Terrace area. From Dalland et al. (1988).

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Fracture criteria A failure envelope for brittle failure can be used to evaluate hydraulic fracturing. This is determined by the Mohr-Coulomb criterion for shear failure and by the Griffith criterion for extensional failure (Fig. 4). The parabolic part (Griffith) is given by the first part of equation 1, while the linear part (Coulomb) is given by the second part of equation 1. This part states that the shear stress is resisted by the cohesion of the material (C) and by the normal stress (σ n ) across the fault plane. The two parts of the Griffith-Coulomb criteria are coupled under the assumption of a continuous first derivative (Secor 1965).

T (1 − µ 2 ) τσ2 −−44TT2 =0σ<0 00n µ 2 (1) T (1 − µ 2 ) τµ=+C σ σ>0 µ 2

τ denotes the shear stress, T0 the tensile strength, µ the coefficient of internal friction, and σn the normal stress (Jaeger & Cook 1963). The theory leading to the Griffith criterion neglects the fact that cracks may be expected to close under sufficiently high compressive stresses. McClintock & Walsh (1962) proposed a modification that takes this effect into consideration, known as the Modified Griffith Theory. This modification leaves the early stage unaltered, introduces a transition zone where first some of the cracks become closed, before all cracks close so that the criterion is identical to the Mohr-Coulomb theory which results in a linear stress-strain curve.

When the fault is established, no cohesion will exist along the fault plane, and the frictional sliding criterion should be used (Twiss & Moores 1992). The frictional sliding failure envelope (Equation 2) is an appropriate criterion because this line defines the tensile strength to be zero at origo. The fact that the coefficient of sliding friction is larger than the coefficient of internal friction ( µ > µ ) implies that the differential stress required to produce sliding is less than the stress necessary to initiate another fracture at low confining stresses.

τ = µσ n (2)

To quantify the minimum horizontal stress, empirical models (e.g. Breckels & van Eekelen 1982), and elastic and viscoelastic models (Engelder & Fisher 1994) have been established. The vertical stress caused by the overburden is assumed to constitute the maximum stress and the two remaining main stresses are horizontal and equal. Grauls (1996) suggested equation 3 to estimate the minimum horizontal stress for passive margins.

z ⎛⎞− 2650 σ hv=−⎜⎟0.85 0.18e σ (3) ⎝⎠

where σ h is the minimum horizontal stress, σ v is the vertical stress and z is the burial depth in meters. In the present work equation 3 is used to quantify the minimum horizontal stress.

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µ ' µ τ Frictional sliding failure Griffith-Coulomb envelope failure envelope

σ n σ σ 3 1 Figure 4 A combination of the Griffith-Coulomb failure criterion and the frictional sliding criterion is used in the present simulations. The Griffith-Coulomb failure criterion is parabolic in the tensile regime, and a straight line in the compressive regime. The dotted line shows the frictional sliding criterion when the rock material possesses no cohesion. Geo-mechanical input parameters We have applied different rock mechanical properties for the cap rocks in the simulations to calculate the failure criterion and the effective stresses. The most important factor for control of the Mohr-Coulomb failure criterion is the coefficient of frictional strength (µ). Zoback & Healy (1984) assumed that in-situ stresses at depth in areas of active faulting and the frictional strength of the faults are in a state of equilibrium. Data from Barton et al. (1995) and Townend & Zoback (2000) shows that critically stressed faults have different conductivities depending upon the frictional strength of the fault. Thus, critically stressed faults with µ between 0.6 and 1.0, are hydraulic conductive, whereas those that are not critically stressed are not hydraulic conductive. This means that fractures have to be critically stressed according to the Coulomb failure criterion to focus pore water flow along fractures (Townend & Zoback 2000).

When considering reactivation of a fault zone, the frictional sliding criterion should be used. The coefficient of sliding friction (µ’) is the most important rock mechanical parameter in this equation, which has to correspond to the coefficient of internal friction for the same fault as outlined in Twiss & Moores (1992) (Fig. 4).

In addition, the cohesion plays an important role in the Mohr-Coulomb failure criterion. However, the cohesion was treated as a separate parameter in the simulations because the Griffith and Coulomb failure envelopes were combined as described above. Still, it was necessary to provide the tensile strength accordingly to the Griffith failure criterion (Equation 1). The value of the tensile strength is defined to the uniaxial strength. The relationship between the tensile strength and compressive strength are known from Griffith. However the ratio is difficult to quantify exactly, since there can be small flaws in the rock samples (Fjær et al. 1992). The plane Griffith criterion gives C0= 8T0, while the Murell’s extension of the Griffith criterion in 3D gives C0=12T0 (Murell 1963). Since there is no clear consistence in literature, we have set the tensile strength to equal

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1/10 of the uniaxial strength, but this may be open for discussion. Equation 4 (Horsrud 2001) is used to estimate the uniaxial compressive strength (bar), where φ is the porosity.

−0.96 C0 = 243.6φ (4)

Thus, the tensile strength increases with depth (m), depending on the porosity to the cap rock.

Biot’s constant

Biot’s constant αB controls pressure influence on the effective stress field. The different elastic and inelastic processes may be controlled by different effective stress laws (see ref. in Corapcioglu 1994). Equation 5 (Biot & Willis 1957) relates the Biot’s constant to the frame bulk modulus (Kfr) and to the bulk modulus of the solid (Ks). The frame bulk modulus can be related to Young’s modulus (E) and Poisson’s ratio (ν) as shown in equation 6.

K fr α B =−1 (5) Ks E K = (6) fr 3(1- 2ν )

The formulae are derived for isotropic, linearly elastic, materials with interconnected pores. Hence, Biot’s constant depends on Young’s modulus and Poisson’s ratio and the bulk modulus of the solid. Ks is a constant depending on the chemical composition (Table 1). For clay minerals it varies from 9.3 GPa (smectite) to 165 GPa (chlorite), measured on artificial composite samples of clay (Wang et al. 1998). Poisson’s ratio is a measure of lateral expansion relative to longitudinal contraction and is one of the most difficult parameters to measure in the laboratory due to large variations within similar rocks (Table 1). Poisson’s ratio for shales typically varies between 0.10 and 0.30. The effect of spherical or penny-shaped microcracks on the Poisson’s ratio is discussed in Zimmerman (1991, 1994). Young’s modulus is a measure of the stiffness of the sample, i.e. the resistance of the sample against being compressed during uniaxial stress. For shales, Young’s modulus varies from 0.4 to 70 GPa (Fjær et al. 1992)(Table 1).

Table 1 Geo-mechanical properties for clay and shales Rock unit Poisson’s Young’s mod Bulk mod Shear mod Reference ratio (GPa) (GPa) (GPa) Clay ~0.40 0.06-0.15 Fjær et al. (1992) Shale 0-0.30 0.4-70 Fjær et al. (1992) North Sea Shale 0.13-0.38 0.8-3.8 Horsrud et al. (1998) “Gulf clays” a 0.34 25 9 Han et al. (1986), Mavko et al. (1998) “Gulf clays” a 0.35 21 7 Tosaya (1982), Mavko e al. (1998) a Clay velocities were interpreted by extrapolating empirical relations for mixed lithologies to 100-percent clay (Castagna et al. 1993)

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Methods The fault pattern on the top of the reservoir formation defines the lateral extent of the pressure (Borge 2000 & 2002) and stress compartments used in the simulator. The overlying cap rocks are used as vertical seals of the compartments. The simulator calculates generation and dissipation of pressure in a single-layer reservoir unit by quantifying the geological processes listed in Table 2. The numerical solution method used is the “Forward Euler”, which is stabilized by using minimum volume during dissipation. The code includes such processes as mechanical and chemical compaction of the sediments and caprock sealing efficiency. The established model use fluid mechanical properties of the pore water to estimate the pressure distribution as a function of time. The lateral fluid flow was modelled using a transmissibility algorithm defined by the dip-slip displacement and burial depths of the faults. Hence, the geo- mechanical properties for the caprock vary through time as a function of subsidence. Depth-converted maps of the overlying sediments were used to construct a time- dependent decompacted burial history. Pressure and stress results are reported for a series of time steps, which are correlated to the depositional ages of the stratigraphic horizons.

The rupture of the cap rock and subsequent is defined as the point when the Mohr circle crosses the Griffith-Coulomb failure envelope. From this point on, the simulator shifts to the frictional sliding criterion, this implies loss of cohesion in the cap rock casing a vertical fluid leakage from the pressure compartment. The empirical model for minimum horizontal stress presented by Grauls (1996; Equation 3), modelled overpressure and the geomechanical properties are used to model Mohr-Coulomb circle.

Table 2 Geological processes modelled in the simulations Processes Comments Models lateral flow of formation water across low-permeable faults. Lateral flow Using the explicit forward Euler solution technique (Borge 2002). Shale drainage Divides the cap-rocks into a draining, accumulating and sealing zone (Borge 2002) Model mechanical compaction of shale (Baldwin & Butler 1995), Compaction mechanical compaction of sand and chemical compaction of sand (Walderhaug 1996). Modelling hydraulic fracturing using Griffith and Mohr-Coulomb failure criterion for the first failure, and the sliding failure criterion for reactivation of the fault Hydraulic leakage zone. The minimum horizontal stress is determined using an empirical equation (Grauls 1996). Vertical stress is estimated depending on the overburden.

Data Depth grids of the stratigraphic units were used to depth convert a subsidence history for the Jurassic Garn Formation for the time steps: 90, 80, 65, 20, 5, 2 Ma and present (see Discussion). The fault trace map of the top Garn Formation was used to divide the reservoir into pressure compartments. Pressure and stress simulation was performed for the time period ranging from 90 Ma till Present, assuming no pressure accumulation had taken place prior to the mid Cretaceous. Pressure data (drill stem and formation pressure tests) from 43 exploration wells in the area were used to calibrate the simulations (Appendix B). The pressure at the top Garn Formation was selected to calibrate the simulations.

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Sensitivity analysis A sensitivity study was carried out to evaluate the fracture potential and the sealing capacity of the cap rock. Special attention was paid to the rock mechanical parameters (Young’s modulus and Poisson’s ratio), because varying these parameters will affect the

Biot’s constant (αB ; Biot & Willis 1957). Accordingly, the effective stress (σ i ) depends on the difference between pore pressure (PP) and applied stress (σ i ) (Terzaghi 1925):

σσi = i− PP (7)

Terzaghi’s equation was later extended by Biot (1955) to account for soil/rock grains:

σσi =−iαBPP (8)

In the simulations, equation 8 is used. Then, Biot’s constant will influence the effective stresses, which in turn control possible hydraulic fracturing and leakage (see Discussion).

Varying Poisson’s ratio and Young’s modulus

As a first approach, all the input parameters were kept constant (Appendix A) while Poisson’s ratio was varied, starting with a base-, followed by a low- and a high case. In all cases the Poisson’s ratio for the cap rock unit was varied with depth (Fig. 5a), using laboratory measurement of North Sea shales in the calibration (Horsrud et al. 1998). Utilizing equations (3) and (4), the Biot’s constant as a function of depth was calculated for each scenario (Fig. 5b). Figures 6a, b, c show the present modelled overpressure for the entire basin as simulated by varying the Poisson’s ratio for the three different cases (low, base and high). The modelling shows that for the higher Poisson’s ratio, the higher overpressure is predicted to occur in the western part of the study area. The low case results in the establishment of a low overpressure, the simulation suggesting that this will lead to enhanced hydraulic leakage (Figs 6a, d). Figures 6d, e and f, shows the cumulative leakage through time (from 90 Ma to present), for all the compartments. Comparing the three different cases, the low case shows a higher cumulative leakage than the other cases, due to a higher value of Biot’s constant, resulting in a higher overpressure build-up and thus a higher cumulative leakage. In addition, the compartment marked P shows hydraulic leakage in the low and base cases, but not in the high case. In petroleum exploration, this would be an important aspect because it indicates a late leakage from this pressure compartment (see Discussion). In the high case, which uses high values for Poisson’s ratio and then a low Biot’s ratios, less hydraulic leakage is observed. This is because more overpressure is allowed to build up before hydraulic leakage occurs, as illustrated in the maps showing the present pattern of overpressure. Consequently, the overpressure (Figs 6a, b & c) and hydraulic leakage (Figs 6d, e & f) are dependent on the Poisson’s ratio of the cap rock.

The average deviation between simulated present day overpressure and measured overpressure in wells, are calculated for the base case to be 11 bar (Table 3; Appendix B). Both in the low and high case, is the average deviation acceptable, 13 and 12 bar, respectively. The large deviation is observed in single compartments, like in the Kristin

-34- compartment, where the low case is -95 bar lower than the measured pressure. The high-case results are more appropriate, since deviation is reduced to -20 bar. In the high case however, an excessively high pressure is observed in compartments B and C, of 49 bar and 33 bar, respectively (Figure 6c, Table 3).

The differences in pressure build-up using the low- and the high case values for Poisson’s ratio are illustrated in Figure 7. The largest changes are observed in the western area, where the largest pressures are accumulated. Thus, the changes in overpressure will be of the order of 100 bar in compartment P, with progressively smaller changes towards the east. An exception is seen in the Kristin field area and in the north, where the Smørbukk Fault delineates the changes in overpressure (Fig. 7).

Similar trends are observed performing a corresponding sensitivity test on Young’s modulus (Figs 8, 9). Laboratory measurement of North Sea shales was used as reference. However, this dataset is quite restricted, since all except one of the samples are taken from shallower than 2.8 km of burial depth. For rocks with low stiffness (low Young’s modulus) and high Biot’s constant (Fig. 8), the same effect is observed. This is characterized by a marked reduction in the effective stress, which in turn leads to a higher cumulative leakage in the compartments where hydraulic fracturing exists (Figs 9d, e). Comparing the cumulative leakage for the different cases, leakage from some few compartments is observed in the high case, whereas more compartments are predicted to fail in the low case (Figs 9d, e). In concert with what is seen for the low case - Poisson’s ratio (Fig. 6d), the low case - Young’s modulus shows leakage from the Presidenten area. This is in accordance with the observation that the compartment which hosts well 6406/3-1 and its northwesterly neighbouring cell, shows sign of hydraulic fracturing and leakage.

Based upon the modelled deviations, the main trends of the Young’s modulus sensitivity analysis are the same as for the Poisson’s ratio. If low values for Poisson’s ratio and/or Young’s modulus are used, the Biot’s constant is high. This in turn, will lead to an increase in pressure accumulation, which favour hydraulic fracturing and leakage in certain compartments (Figs 6d, e, f and 9d, e). By comparing the low case- and the high case-maps of the distribution of overpressure, it is clear that the effects of varying Young’s modulus and Poisson’s ratio are similar. In both cases the largest changes can be seen in the western study area, with large overpressure generated (Figs 6 & 9).

-35-

Table 3 Deviation between modelled and measured overpressure for different values of rock mechanical properties Wells Measured Difference between measured and simulated overpressure (bar) overpressur e (bar) Poisson’s ratio Young’s modulus Biot’s Base case Low case High case Low case High case constant ≈ 1.0 6407/4-1 81-92 -58.7 -58.8 -58.6 -58.8 -58.6 -59.4 6407/1-1, 2 & 0-7 22.6 22.4 23.1 22.3 23.1 20.8 3 6407/2-1 0 22.8 22.7 23.0 22.7 23.0 22.0 6406/8-1 336 7.6 -5.0 48.6 -7.7 50.2 -106.0 6406/3-1 288-290 23.6 8.1 33.4 -30.8 33.6 -85.8 6406/6-1 298-299 6.5 2.4 16.3 -26.5 16.4 -80.5 6406/2-6 408 -19.3 -42.3 12.4 -47.3 24.4 -161.4 Lavrans 6406/2-3 433 -64.2 -94.8 -20.5 -101.8 -3.5 -179.7 Kristin Mean square deviation 21.9 27.7 21.0 30.6 21.2 66.3 Average deviation 11.3 12.8 11.8 15.9 11.6 35.8

a) b)

Poisson's ratio Biot's constant 0 0.1 0.2 0.3 0.4 0.5 0.7 0.8 0.9 1 0 0 1000 1000 Base case 2000 ) 2000 High case m

3000 Low case h ( 3000 pth (m) pt e e D 4000 Horsrud et al. (1998) 4000 D 5000 5000 6000 6000

Figure 5 a) Graphic representation of relation between Poisson’s ratio and depth, used for the base, low and high cases. The curves were calibrated by using laboratory measurements of Poisson’s ratio from North Sea Shales (Horsrud et al. 1998). b) Calculated Biot’s constant-curves for low, base and high cases based on the Poisson’ ratio relations shown in a).

-36-

Low case Base case High case a) b) c)

A A A

C C C B B B Overpressure (bar) 20 km 20 km 20 km d) e) f)

K K K

P P P Cumulative hydraulic leakage (log 3 20 km 20 km 20 km m )

Figure 6 Results of simulations carried out using similar input parameters as presented in Figure 6, with a low, base and a high case, where Poisson’s ratio is varied. a, b & c) Present overpressure simulated (bar). Pressure changes in compartment denoted A, B & C are discussed in the text. d, e & f) Cumulative hydraulic leakage (log m3). K is the Kristin field and P is “Presidenten”.

-37-

Smørbukk Fault

20 km

Figure 7 The difference in accumulated pressure generated using the low and high case values for Poisson’s ratio. The largest differences are observed in the western, deeper pressure compartments. The colour-coded scale is shown in bars.

a) b)

Young's modulus (bar) Biot's constant 0 50000 100000 150000 0.7 0.8 0.9 1 0 0 1000 1000 Base case 2000 ) High case 2000 h (m) 3000 Low case 3000 pt pth (m e

4000 Horsrud et al. (1998) e D 4000 D 5000 5000 6000 6000

Figure 8 a) Young’s modulus as a function of depth, in the low case, base and high case. The Poisson’s ratio is kept according to the base case in Figure 6. b) The graphs show how Biot’s constant versus depth is varying for each case.

-38-

Low case High case Biot = 1.0 a) b) c)

Overpressure (bar) 20 km 20 km 20 km d) e) f)

Cumulative hydraulic leakage (log 20 km 20 km 20 km m3)

Figure 9 Corresponding simulations carried out, with the same input as presented in Figure 9, for Young’s modulus varies according to low, base and high case. a, b & c) Present overpressure simulated (bar). d, e & f) Cumulative hydraulic leakage (log m3).

Simulation of pressure build-up in the Kristin field

The pressure generation within and dissipation between the compartments was estimated every for 10000 years. It is seen that hydraulic fracturing will occur in the compartments that accumulate overpressure faster than the lateral and vertical dissipation can remove it. To illustrate this, a plot of one pressure compartment; the Kristin field, was performed. The Kristin structure is a large rotated Jurassic horst, found within blocks 6506/11 and 6406/2, in the western part of the Halten Terrace (Fig. 2b).

The geological input data and the Pressim model suggest a distinct pressure build-up during the last 5 Ma (Fig. 10). By using equation 3, modelling suggests that the minimum horizontal stress will build up linearly by increasing depth. Two major Pliocene events of increased overpressure are simulated for the Kristin compartment (Fig. 10). The increase in overpressure will reduce the effective stresses, both horizontally and vertically (Fig. 10). Looking even closer at the last two million years,

-39- we see that the overpressure will build up to a peak, before it declines and eventually flattens out around 1.5 Ma. The instantaneous reduction in the overpressure in this model is in the order of 40 bars. From the time-dependent leakage rate and the cumulative leakage from the overpressured compartment, the hydraulic fracturing and leakage would occur at approx. 1.5 Ma (Fig. 11). A peak in the leakage curve is modelled when leakage occurs, due to breakage of the seal. This event is followed by a stable leakage rate (Fig. 11).

According to this model, the first leakage in the compartment of the Kristin field occurred at a burial depth of approximately 4.0 km (Fig. 12). When calculating the point of first leakage versus depth and time, it seems that most of the compartments would fail at depth of burial between 3.8 km to 4.6 km, corresponding to a time window between 2 Ma to 0.8 Ma. The most recent breakage was modelled in the Presidenten structure at approx. 0.8 Ma (Fig. 12). Five of the compartments were modelled to leak at an earlier time. From Figure 12 one cell seems to start leaking even earlier (around 13 Ma), but this is maybe due to boundary effects, since the cell is situated in the northwestern corner of the study area. No pressure support was gained from outside the study area. The other cells that failed early (around 5 Ma) are very small and insignificant. All the simulated failures are fractured in accordance to the Mohr- Coulomb failure criterion, suggesting shear failure.

The coefficients of internal friction and of frictional sliding

The coefficients of internal friction and of frictional sliding are important input parameters in the Mohr-Coulomb failure criterion and the frictional sliding criterion, because both the parameters will control the pressure build-up, the fracturing and the associated rate of leakage.

In the first simulation series, the coefficient of internal friction was kept constant at µ = 0.6, whereas the coefficient of frictional sliding was varied from µ’ = 0.7 to 1.0. For the different cases the logarithmic cumulative leakage for each compartment was displayed in a colour coded map. Figure 13a shows the simulated logarithmic cumulative leakage, for µ = µ’ = 0.6 and with a relatively high cumulative leakage from the large compartments which have failed. The Kristin field is one of the compartments in which hydraulic fracturing was predicted. Plotting leakage versus time for this compartment it is indicated that fracturing occurred at approximately 1.5 Ma in one major pulse. Following this event, the leakage rate dropped to a stable level, resulting in an approximately linear cumulative leakage (Fig. 13b), assuming that µ < µ’ (e.g. Twiss & Moores 1992).

By application of gradually increasing values for the coefficient of frictional sliding, the leakage from the large compartments was calculated. The results indicate that leakage decreased slightly with increasing values of the coefficient of frictional sliding (Figs 13a, c, e). The same trend can be observed in the modelled leakage from the Kristin structure, where the rate of the leakage decreased when a higher coefficient of frictional sliding was used (Figs 13b, d, f). The simulations that utilized µ = 0,6 and µ’ = 0.6-0.9, produced results indicating leakage from two large compartments, namely the Kristin structure and the Presidenten. The amount of escaped formation fluid decreased with increasing values of the coefficient of frictional sliding. However, the timing for hydraulic fracturing did not change, because the coefficient of internal friction was kept

-40-

constant. The largest changes in lateral flow and hydraulic leakage, was observed using µ = 0.6 and µ’ = 1.0 (Figs 13e & f). To study the effect of the coefficient of internal friction, the coefficient of the sliding friction was held constantly higher than the coefficient of internal friction (Fig 14). From this study, it is clear that the variation of internal friction between 0.5 and 0.9 causes only a minor difference with regards to timing of the failure of the different compartments. This is illustrated for the Kristin field, where changes from 1.6 Ma to 1.5 Ma (Figs 14b, d, f). The volume of leakage, however, varies significantly in the Kristin structure. The modelled cumulative Quaternary leakage decreased from 4.2⋅ 107 m3 to 2.6⋅ 107 m3 moving from µ = 0.5 and µ’ = 0.6, to µ = 0.9 and µ’ = 1.0, respectively (Figs 14b& f).

Figure 15 illustrate the modelled leakage from the Kristin and Presidenten structures for the last 2 Ma years as a function of the coefficient of sliding friction, keeping µ = 0.6 and setting µ’ = 0.7 and 1.0. Although failure is predicted for these two compartments, the leakage rate were significantly decreased using µ’ = 1.0, as compared to using µ’ = 0.7 (Figs 15). In addition, a quite large compartment east of Kristin (compartment Z) is predicted to fail at 0.05 Ma (Fig. 15c, d). It seems clear that this recent hydraulic fracturing has a direct influence on the pressure and the leakage in neighbouring compartments in spite of its late occurrence. Thus, significant decrease in leakage-rate for the Kristin structure should be expected at this time (Fig 15d).

800 700

600 )

500 ar Horizontal stress b (

e Overpressure 400 r

su sig_3'

300 es r sig_1' P 200

100

0 8 6 4 2 0 Time (Ma)

Figure 10 Simulated overpressure, horizontal stress and effective stresses for the reservoir unit in the Kristin field, from 8 Ma years to Present. Note the rapid increase in the overpressure at 5 Ma and 2 Ma years, and a corresponding decrease in the effective stresses. The decrease in overpressure around 1.8 Ma corresponds to the timing of hydraulic leakage from this compartment.

-41-

160 4.0E+07

140 3.5E+07 3) m (

120 3.0E+07 e 3) g

m 100 2.5E+07 e ( 80 2.0E+07 eaka Cum.leakage kag ve l

60 1.5E+07 i

a Leak-rate t e a l L 40 1.0E+07 u

20 5.0E+06 m u 0 0.0E+00 C 2 1.5 1 0.5 0 Time (Ma)

Figure 11 Simulated leakage and cumulative leakage from the Kristin field compartment. An marked pulse is observed when hydraulic fracturing occurs.

Time (Ma) 14 12 10 8 6 4 2 0 2000

2500

3000 ) m

h ( 3500 pt e

D 4000

4500

5000

Figure 12 Depth versus time at the first failure with hydraulic fracturing. Timing for the Kristin field and the Presidenten project are indicated.

-42-

a) b) 30 4.0E+07

µ = 0.6 ) 3.5E+07 3

25 m

µ’ = 0.6 3.0E+07 e ( 3)

20 ag K m 2.5E+07 e ( 15 2.0E+07 eak Cum.Leakage ve l akag 10 1.5E+07 Leak-rate e ati l L 1.0E+07 u

5 5.0E+06 m 0 0.0E+00 Cu 2 1.5 1 0.5 0 10 km Time (Ma) c) d) µ = 0.6 30 4.0E+07 3.5E+07 3)

25 m ( e µ’ = 0.9 ) 3.0E+07 3 20 K m 2.5E+07 e ( 15 2.0E+07 eakag Cum.Leakage ve l

1.5E+07 i Leak-rate 10 t eakag a l L 1.0E+07 u

5 5.0E+06 m u 0 0.0E+00 C 2 1.5 1 0.5 0 10 km Time (Ma) e) f) 30 4.0E+07

µ = 0.6 ) 3.5E+07 3

25 m

µ’ = 1.0 3.0E+07 e ( 3)

20 ag

K m 2.5E+07 e ( 15 2.0E+07 eak Cum.Leakage ve l akag 10 1.5E+07 Leak-rate e ati l L 1.0E+07 u

5 5.0E+06 m 0 0.0E+00 Cu 10 km 2 1.5 1 0.5 0 Time (Ma)

Figure 13 Maps a, c and e) illustrate the modelled cumulative hydraulic leakage from the compartments in the study area following failure (denotation log m3). In the three cases studied, the coefficient of sliding friction has been varied between 0.6 and 1.0. The Kristin field is denoted with K. Graphs b, d and f) show cumulative leakage and leak-rates from the Kristin field for a similar set of conditions.

-43-

a) b) µ = 0.5 30 4.0E+07 3.5E+07 3)

25 m

µ’ = 0.6 K 3.0E+07 e ( 3) 20

m 2.5E+07 e ( 15 2.0E+07 eakag Cum.Leakage ve l

1.5E+07 i Leak-rate 10 t eakag a l L 1.0E+07 u

5 m 5.0E+06 u 0 0.0E+00 C 2 1.5 1 0.5 0 10 km Time (M a) c) d) µ = 0.8 30 4.0E+07 3.5E+07 3)

25 m

µ’ = 0.9 3.0E+07 e ( K 3) 20

m 2.5E+07 akag e ( 15 2.0E+07 e Cum.Leakage ve l

1.5E+07 i Leak-rate 10 t eakag a l L 1.0E+07 u

5 5.0E+06 m 0 0.0E+00 Cu 2 1.5 1 0.5 0 10 km Time (M a) e) f) µ = 0.9 30 4.0E+07 3.5E+07 3)

25 m

µ’ = 1.0 3.0E+07 e ( K 3) 20

m 2.5E+07 e ( 15 2.0E+07 eakag Cum.Leakage ve l

1.5E+07 i Leak-rate 10 t eakag a l L 1.0E+07 u

5 m 5.0E+06 u 0 0.0E+00 C 10 km 2 1.5 1 0.5 0 Time (M a)

Figure 14 Maps a, c and e) illustrate the cumulative hydraulic leakage from the compartments in the study area following failure (denotation log m3). In the three case studies, the coefficient of internal friction and the coefficient of sliding friction have been varied. Kristin field is denoted with K. Graphs b, d and f) show cumulative hydraulic leakage and leak- rate from the Kristin field for a similar set of conditions.

-44-

Figure 15 Hydraulic cumulative leakage from compartments Kristin, Presidenten and Z (denotation log m3). Using a low coefficient of sliding friction (µ’ = 0.7), leakage is observed from e.g. Kristin and Presidenten. Using a high coefficient of sliding friction (µ’ = 1.0), it is too hard to continue flow from the Kristin and the Presidenten fields, and leakage from new compartment, Z is observed. Discussion Hydraulic fracturing and leakage take place at a certain burial depth and under high overpressure. Therefore, it may be difficult to obtain good data of the physical properties of the caprock in general and, particularly, of the rocks within the fractured zones. In addition, the caprock commonly consists of tight shale and is associated with a fracture system that cannot easily be distinguished from those generated by hydraulic fracturing. The spatial distribution, length and width of the fractures are not evaluated in this paper, because data is not available. Therefore, instead of evaluating flow and evaluation of the fractures, we use the Mohr-Coulomb failure criterion at large burial depth, and Griffith failure criterion at shallower depth, which both depend upon the stress and the pressure. Hence, it is not within the scope of this work to discuss the specific fault zone permeability as related to the failure mode. It is still realized that both shear and tensile fractures in tight rocks contribute to increasing the permeability compared to that of the intact rocks.

Whether flow from hydraulic fractures takes place in a pulsating and/or a steady-state process is not known. Lacazette & Engelder (1992) suggested a fluid-driven cyclic progradation of joints in the Ithaca Siltstone, Appalachian Basin, New York. Also, Sibson (1981) points to cyclic behaviour of observed seismicity, which can be explained as pressure build-up followed by transient flow as the fluid is expelled from the

-45- sediments. This view is supported by experimental work by Bolton & Maltman (1998) showing how permeability of sediments varies with progressive strain. They found that volume changes are linked to permeability fluctuations and the drainage capacity of the material. Studies of the cap rock of the Snorre field in the North Sea, suggested a dynamic trap, where constant pressure regime is controlled by regulations like hydraulic leakage at the top of the reservoir (Caillet 1993). In our modelling, hydraulic leakage occurred in one major pulse, where leakage occurred. This event was followed by steady-leakage rate, depending on the pressure support in the compartment. If hydraulic leakage occurred in a neighbouring pressure cell, this may influence on the other cells (Fig. 18). A total closure of the hydraulic fracturing, with a re-open due to new pressure build-up can be an option. However, in the Halten Terrace area, the simulating results suggest that the pressure build-up and hydraulic leakage occurred at a late. Hence, the possible leakage rate and following closure cannot be calculated.

The relationship between stresses and pressure; the use of Biot’s constant Equation 8 is applied in the simulator, where the effective stresses are dependent on Biot’s constant. However, defining Biot’s constant to 1.0 in the simulator results in extensive hydraulic leakage at unexpected low pressures in the basin (Figs 9c, f & Table 3). Relating Biot’s constant to Poisson’s ratio and Young’s modulus as shown in equation 8 seems to be reasonable and realistic according to the results. This procedure can be debated, however because during the last decade a consensus has been achieved in rock mechanics that Terzaghi’s rather than Biot’s effective stress should be used in the failure criteria (see also Boutéca & Guéguen 1999). The use of Biot’s effective stress in the failure criteria - as we have done in the simulator - corresponds approximately to the use of Terzaghi’s effective stress, with the modification that µ →=µ* αµ and CCC→=*+µ ((1−αα)) . Thus, our procedure effectively implies that we have used a smaller coefficient on internal friction and a larger cohesion than the nominal values, if Terzaghi’s effective stress concept is adopted for the failure criteria. We know from the literature that the coefficient of internal friction may well be smaller than the value we have used. Dewhurst (2003) studied shales and found µ =−0.3 0.6 . In addition, the observed increase in magnitude of the horizontal stresses in overpressured zones, are not sufficiently taken into account in the simulator, using an empirical approach (equation 3). By using Biot’s equation as we have done, some effects of the geo-mechanical properties of the caprock are however taken into account.

Geo-mechanical parameters Since Poisson’s ratio is difficult to measure in the laboratory, we have chosen to vary the size of this input parameter versus depth. Another way to simulate Poisson’s ratio, would be to use equation 9, where the bulk modulus is given by equation 10 and by equation 11

32KG− ν = fr fr (9) 2(3KGfr + fr )

ϕ η KKfr =−s (1 ) (10) ϕc

ϕ η GGfr =−s (1 ) (11) ϕc

-46-

and where ϕ is the porosity and ϕc is the critical porosity. Critical porosity relates to distinctive changes in pore material microstructures and is closely linked to pore size, geometry and connectivity (Chen & Nur 1994; p. 193). Experimental work shows that the critical porosity is approx. 40-50% for sandstones. For mud in suspension or unconsolidated materials the critical porosity can be up to 70-80% (e.g. Chen & Nur 1994 and references therein). η is a lithology-dependent property, where η = 2 is used for sandstones (Holt, pers. comm.), the η - values for shale is more uncertain but η = 1 seems to be appropriate value. Hence, the Poisson’s ratio may be given by:

32KG− ν = ss (12) 2(3KGss+ )

For quartz Gs = 41 GPa and for clay minerals Gs is in the order of 5-10 GPa (Fjær et al. 1992). Accordingly, Poisson’s ratio is only dependent on the mineralogical composition of the rock sample. Substituting the constants in the equation 12, one finds that Poisson’s ratio for quartz is approximately 0.09 and for shale 0.31. This corresponds with the measured values found in the literature (Table 1). Still, it is obvious that Poisson’s ratio does not only depend upon the mineralogy, but also on chemical diagenesis and composition. Therefore Poisson’s ratio is varied with burial depth in the simulations.

A porosity dependent model for the Young’s modulus can be derived combining equation 9 and equation 12:

ϕ η EK=−3(s 12ν )(1−) (13) ϕc

The compaction and thereby the porosity, were simulated using an empirical depth- dependent relationship for hydrostatic pressured and overpressured shales (Baldwin & Butler 1985, see also Borge 2000). Then, in one way, it would be more consistent to have the Young’s modulus in agreement with the porosity used elsewhere in the simulator. However, since the values of η for shales are uncertain, an empirical calibration for the Young’s modulus has been used.

Varying Poisson’s ratio and Young’s modulus as a function of depth, gives large changes in the simulated overpressure accumulation in the western part of the study area (Figs 6, 7a, b, c & 9a, b). The changes caused by different values for Poisson’s ratio and Young’s modulus are less pronounced in the moderately overpressured areas (<100 bar overpressure). The wells 6407/4-1, 6407/2-1, 6407/1-1, 2 and 3, which are situated in three different compartments where a low overpressure is observed, show no changes in the simulated pressures (Table 3). In contrast, large changes are observed in simulated overpressure for the compartments where high overpressure is measured in the wells. A fairly good match between observed and modelled overpressure in the compartments that contains wells 6406/8-1, 6406/3-1 and 6406/6-1 is achieved for the low case Poisson’s ratio simulations. In this case, however, unrealistically low pressure was obtained for the Kristin and Lavrans fields (wells 6406/2-6 & 6406/2-3). The best fit is achieved using moderate values for both Poisson’s ratio and Young’s modulus, allowing for some mismatch in Kristin field. This deviation in the Kristin field is most

-47- probably due to boundary conditions. Since this compartment delineates the study area, pressure support from the deeply buried areas in the west was not included.

Griffith-Coulomb fracture criterion A change in fracture mode was introduced in the simulations from fracturing controlled by the Griffith-Coulomb failure criterion to the frictional sliding criterion when the fractures were reactivated. The frictional sliding criterion implies that fault reactivation occurs more easily. The frictional sliding failure curve crosses the Mohr-Coulomb failure envelope at larger depths, indicating that it is more difficult to reopen a fault than to initiate a new fracture at these depths. This implies that chemical or mechanical processes are important factors when it comes to changes in the properties to the faults.

Coefficients of internal friction and frictional sliding The sensitivity study demonstrates that the coefficient of frictional sliding has an impact on the occurrences of hydraulic leakage, and that it affects the leakage rates. An increase in µ’ from 0.7 to 1.0 (Figs 15b, d), resulted in a significantly lowered leakage from those compartments that had already failed. In addition, when the coefficient of frictional sliding was increased, the compartment situated east of the Kristin field becomes fractured rather than the compartments being reactivated. It is of importance to determine weather these observations are real or modelling artefacts. It is difficult to get laboratory measurement of the coefficient of the sliding friction at high confining pressure. In order to obtain a realistic measurement, the time scale should be sufficiently long from an experimental point of view to account for the chemical processes, which is difficult. However, by varying both the coefficient of internal friction and sliding friction (Figs 14a, c, e) mostly the same compartments expire hydraulic leakage, while the leakage rate have changed. Using moderate values, e.g. µ = 0.6 and µ’ = 0.7, would be a good first approach simulating the hydraulic fracturing and leakage in an area.

For some wells, a mismatch between measured and simulated overpressure does not change when the coefficient of internal friction and frictional sliding are varied. This is due to the fact that no hydraulic leakage has yet occurred in these compartments or in the neighbour compartments. This observations are made for well 6407/4-1, where a too low pressure is simulated (-59 bar), whereas an overpressure in the order of 81-92 bars was measured in the well in a depth of 2489 m. Studying this compartment in more detail, we see that the pressure compartment is rather large, covering an area of approximately 7.1⋅ 108 km2. The pressure measurement in this single well is probably not valid as a pressure calibration for the entire compartment, because the well is situated in its northwestern corner (Fig. 2). Hence, a higher overpressure should be expected in this western area than in the more eastern part of the compartment. In the eastern part of the Halten Terrace, it would be more natural to assume a lower overpressure, maybe in the range of 20-30 bar. Keeping these assumptions in mind, our simulations fit quite well with the overall pressure distribution in the area.

When the average deviation is evaluated, the most consistent results are archived by the use of high values for coefficient for internal friction and sliding friction (e.g. µ=0.9 and µ’=1.0). From these results it is seen that a higher overpressure can build up before hydraulic fracturing will occur when such input parameters are used.

-48-

The largest deviations in modelled pressure are observed in the western part of the study area, which is characterized by high overpressure. Here, hydraulic fracturing and leakage take place either within or in a nearby compartment. The largest variations in size of the simulated present pressure are observed in well 6406/2-3, in the Kristin field. Still, all the simulations give too low pressure build-up, but by using very low coefficients (µ = 0.5 and µ’ = 0.6) a very low pressure is obtained (-85.6; Table 4). Using the base case conditions (µ = 0.6 and µ’=0.7) a slightly higher pressure is obtained (-64.2 bar; Table 4). This result corresponds to the pressure measured in this well was achieved by using very high values for the coefficient of internal frictional and sliding friction: In this case a mismatch of -28.9 bar was modelled (Table 4). One can argue that the Kristin field, which is situated at the rim of the simulated area, would have pressure support from west. Skar et al. (1998) suggested this, proposing that the overpressure generation due to mechanical compaction, induced by the weight of the Plio-Pleistocene sediments is not sufficient to explain the overpressure magnitude in this western area. Migration of overpressured fluids may have occurred through the Klakk Fault Complex, separating the deep Rås Basin from the Halten Terrace.

The quality of the stress and pressure simulations that were carried out, only in one reservoir unit may be discussed. Strontium analysis from the Smørbukk field (Ehrenberg et al. 1992, Stølum et al. 1993) states that the Garn Formation has good vertical communication, but is isolated from the underlying Not and Ila Formation and from the overlying Melke Formation. Although Corfield et al. (2001) shows that the Garn Formation can be subdivided into at least three Garn sandstones in the Smørbukk area, the overall pressure pattern demonstrates that it can be simulated as one homogenous package (Olstad et al. 1997). From this, we find it sufficient for our purpose of simulating pressure generating and accumulation in a basin, to use a one- layer model.

One of the strengths of the simulator used in the present study is that stresses and pressure are coupled in a way that facilitates quantitative evaluation of hydraulic fracturing and leakage in a sedimentary basin on a geological time scale. In addition, chemical compaction is included as a pressure generating mechanism. An empirical model estimates the minimum horizontal stress in the version of Pressim used in the simulations. A 3D version of the stress routine is now being developed and will be available for future studies.

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Table 4 Deviation between modelled and measured overpressure for different values of coefficient of internal friction (µ) and of frictional sliding (µ’). Wells Measured Difference between measured and simulated overpressure (bar) overpressure (bar) Cases varying µ & µ’ µ 0.6 0.6 0.6 0.6 0.6 0.5 0.8 0.9 µ’ 0.6 0.7 0.8 0.9 1.0 0.6 0.9 1.0 6407/4-1 81-92 -58.7 -58.7 -58.7 -58.7 -58.7 -58.8 -58.7 -58.6 6407/1-1 0-7 22.8 22.6 22.7 22.7 22.8 22.5 22.7 22.8 2 & 3 6407/2-1 0 22.9 22.8 22.9 22.9 22.9 22.8 22.9 22.9 6406/8-1 336 21.4 7.6 14.3 19.2 21.4 -0.8 19.5 23.4 6406/3-1 288-290 24.1 23.6 23.8 24.0 24.1 17.1 28.6 29.5 6406/6-1 298-299 10.3 6.5 8.2 9.4 10.3 4.0 9.8 10.9 6406/2-6 408 -16.3 -19.3 -17.8 -16.6 -16.3 -28.9 -3.8 1.8 6406/2-3 433 -29.0 -64.2 -48.9 -37.5 -29.0 -85.6 -37.5 -28.9 Mean square deviation 25.6 21.9 20.0 19.0 18.4 25.5 19.0 18.5 Average deviation 12.3 11.3 10.9 10.6 10.3 12.0 10.2 9.9

Conclusions A method for simulating hydraulic leakage from overpressured reservoir over geological time scale has been presented. The simulations show hydraulic leakage to occur from a compartment, in one pulse followed by a continuous flow. The compartments will fail at different times and have different leak-rates, depending on burial depth and pressure accumulation. The hydraulic fracturing can adequately be explained as Mohr-Coulomb failure at the top point of the overpressured compartments, defined by faults. Geo-mechanical parameters for the caprocks (Poisson’s ratio and Young’s modulus) will influence Biot’s constant and thereby effect the pressure accumulation in the compartments. Biot’s constant set to 1, gives too early pressure build up and hydraulic leakage in the western part of the basin, while lower values (>0.85) give better simulations of the pressure distribution today, compared to measured pressure in wells. The coefficient of the internal friction and the coefficient of the sliding friction are important parameters when using Coulomb and the sliding failure criterions, because these control the timing and location of hydraulic fracturing and leakage. High values of coefficients of the internal friction will reduce the leakage. Using low coefficients of internal friction and high coefficients of sliding friction, reactivation of existing failure will become more difficult and a new compartment may fail.

The simulations described in this paper suggest that some of the compartments in the highly overpressured western part of the Halten Terrace area are candidates for hydraulic fracturing and leakage. According to the simulating results, hydraulic fracturing and leakage from the Kristin field occurred around 1.5 Ma, with a later failure for the Presidenten prospect around 0.8 Ma. However, there exists some uncertainty related to the leakage from the Presidenten compartment, since it is simulated to fail at a

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Acknowledgements The authors would like to thank Norsk Hydro ASA for providing the data, financial support in the form of a PhD-grant and for the permission to publish this article. Thanks to SINTEF Petroleum Research for computing support, and interesting discussions with Prof. Rune Holt and Erling Fjær. The article has benefited from informal discussion and co-work in the Smiff2 group.

References Baldwin, B. & Butler, C.O. 1985. Compaction curves. American Association of Petroleum Geologist Bulletin, 69, 622-662. Barton, C.A., Zoback, M.D. & Moos, D. 1995. Fluid flow along potentially active faults in crystalline rock. Geology, 23, 686-686. Dewhurst, D. 2003. Geomechanical properties related to top seal leakage in the Carnarvon Basin, Northwest Shelf, Australia. Petroleum Geoscience, 9, 255-263. Biot, M.A. 1955. Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics, 26, 182-185. Biot, M.A. & Willis, D.G. 1957. The elastic coefficients of theory of consolidation. Journal of Applied Mechanics, 24, 596-601. Blystad, P., Færseth, R.B., Larsen, B.T., Skogseid, J. & Tørudbakken, B. 1995. Structural elements of the Norwegian continental shelf, Part II. The Norwegian Sea Region. Norwegian Petroleum Directorate Bulletin, 8. Bolton, A. & Maltman, A. 1998. Fluid-flow pathways in actively deforming sediments: the role of pore fluid pressures and volume changes. Marine and Petroleum Geology, 15, 281-297. Borge, H. 2000. Fault controlled pressure modelling in sedimentary basins, An thesis for the degree of Doktor Ingenør of the Norwegian University of Science and Technology, Trondheim, Norway, 148 pp. Borge, H. 2002. Modelling generation and dissipation of overpressure in sedimentary basins: an example from the Halten Terrace, offshore Norway. Marine and Petroleum Geology, 19, 377-388. Boutéca, M. & Guéguen, Y. 1999. Mechanical properties of rocks: pore pressure and scale effects. Oil & Gas Science and Technology- Rev. IFP, 54, 703-714. Breckels, I.M. & van Eekelen, H.A.M. 1982. Relationship between horizontal stress and depth in sedimentary basins. Journal of Petroleum Technology, 34, 2191-2199. Caillet, G. 1993. The caprock of the Snorre Field, Norway: a possible leakage by hydraulic fracturing. Marine and Petroleum Geology, 10, 42-50. Castagna, J.P., Batzle, M.L. & Kan, T.K. 1993. The link between rock properties and AVO responses. In: Castagna, J.P. & Backus, M. (eds), Offset-Dependent Reflectivity - Theory and Practice of AVO Analysis. Society of Exploration Geophysicists, Society of Exploration Geophysicists, 135-171. Chen, Q. & Nur, A. 1994. Critical concentration models of porous materials. In: Corapcioglu, M.Y. (eds), Advances in Porous Media. Elsevier, Amsterdam, 169- 308. Corapcioglu, M.Y. 1994. Advances in porous media. Elsevier, Amsterdam, 451.

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Corfield, S., Sharp, I., Hager, K.-O., Dreyer, T. & Underhill, J. 2001. An integrated study of the Garn and Melke formations (Middle to Upper Jurassic) of the Smørbukk area, Halten Terrace, mid-Norway. In: Martinesen, O.J. & Dreyer, T. (eds), Sedimentary Environments Offshore Norway - Paleozoic to Recent. NPF Special Publication. Elsevier Science, Amsterdam, 199-210. Cosgrove, J.W. 1998. The role of structural geology in reservoir characterization. In: Coward, M.P., Daltaban, T.S. & Johnson, H. (eds), Structural Geology in Reservoir Characterization. Geological Society Special Publications, 1-13. Dalland, A.G., Worsley, D. & Ofstad, K. 1988. A lithostratigraphic scheme for the Mesozoic and Cenozoic succession offshore mid- and northern Norway. Norwegian Petroleum Directory, 65. Ehrenberg, S.N., Gjerstad, H.M. & Hadler-Jacobsen, F. 1992. Smørbukk field - a gas condensate fault trap in the Haltenbanken province, offshore Mid-Norway. American Association of Petroleum Geologists Memoir, 54, 323-348. Engelder, T. & Fisher, M.P. 1994. Influence of poroelastic behaviour on the magnitude of minimum horizontal stress, Sh, in overpressured parts of sedimentary basins. Geology, 22, 949-952. Fjær, E., Holt, R.M., Horsrud, P., Raaen, A.M. & Risnes, R. 1992. Petroleum Related Rock Mechanics, Developments in Petroleum Science, 33. Elsevier, Amsterdam, 320. Gabrielsen, R.H. & Kløvjan, O.S. 1997. Late Jurassic-early Cretaceous caprocks of the southwestern Bartens Sea: fracture systems and rock mechanical properties. In: Møller-Pedersen, P. & Koestler, A.G. (eds), Hydrocarbon Seals: Importance for Exploration and Production. NPF Special Publication, Elsevier, Amsterdam, 73-89. Gjelberg, J., Dreyer, T., Høie, A., Tjelland, T. & Lilleng, T. 1987. Late Triassic to Mid- Jurassic development on the Barents and Mid-Norwegian shelf. In: Brooks, J. and Glennie, K. (eds), Petroleum Geology of North West Europe. Graham and Trotman, London, 1105-1129. Grauls, D. 1996. Minimum Principal Stress as a Control of Overpressures in Sedimentary Basins. Proceeding of the 8th Conference on Exploration and Production. IFP, Rueil-Malmaison, 9-10 December, IFP Report No. 43313. Han, D.-H., Nur, A. & Morgan, D. 1986. Effects of porosity and clay content on wave velocities in sandstones. Geophysics, 51, 2093-2107. Horsrud, P. 2001. Estimating Mechanical Properties of Shale From Empirical Correlations. SPE Drilling & Completion, 67-74. Horsrud, P., Sønstebø, E.F. & Bøe, R. 1998. Mechanical and Petrophysical Properties of North Sea Shales. International Journal of Rock Mechanical Mining Science, 35, 1009-1020. Jaeger, J.C. & Cook, N.G.W. 1963. Extension Failures in Rocks Subject to Fluid Pressure. Journal of Geophysical Research, 68, 6066-6067. Koch, J.-O. & Heum, O.R., 1995. Exploration trends of the Halten Terrace. In: Hanslien, S. (eds), Petroleum Exploration and Exploitation in Norway. NPF Special Publication. Elsevier, Amsterdam, 235-251. Lacazette, A. & Engelder, T. 1992. Fluid-driven Cyclic Propagation of a Joint in the Ithaca Siltstone, Appalachian Basin, New York. Fault Mechanics and Transport Properties of Rocks. Academic Press Ltd., 297-323. Lapidus, D.F. 1990. Dictionary of Geology. Collins, Glasgow, 565. Lashkaripour, G.R. & Dusseault, M.B. 1993. A statistical study on shale properties: Relationships among principal shale properties. Probabilistic Methods in Geotechnical Engineering, 195-200. Rotterdam.

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Lawn, B.R. & Wilshaw, T.R. 1975. Fracture of Brittle Solids. Cambridge University Press, 204. Mavko, G., Mukerji, T. & Dvorkin, J. 1998. The Rock Physics Handbook. Cambridge University Press, Cambridge, 324. McClintock, F.A. & Walsh, J.B. 1962. Friction on Griffith cracks under pressure. Fourth U.S. National Congress of Applied Mechanical Proc., 1015-1021. Murell, S.A.F. 1963. A criterion for brittle fracture of rocks and concrete under triaxial stress and the effect of pore pressure on the criterion. Proc. Fifth Rock Mechanical Symposium, University of Minnesota. In: Fairhurst, C. (eds), Rock Mechanics. Oxford, Pergamon, 563-577. Olstad, R., Bjørlykke, K. & Karlsen, D.A. 1997. Pore water flow and petroleum migration in the Smørbukk field area, offshore mid-Norway. In: Møller-Pedersen, P. & Koestler, A.G. (eds), Hydrocarbon Seals: Importance for Exploration and Production. NPF Special Publication. Elsevier, Amsterdam, 201-217. Roberts, S.J. & Nunn, J.A. 1995. Episodic fluid expulsion from geopressured sediments. Marine and Petroleum Geology, 12, 195-204. Secor, D.T. 1965. Role of fluid pressure in jointing. American Journal of Science, 263, 633-646. Sibson, R.H. 1981. Fluid flow accompanying faulting: field evidence and numerical models. In: Simpson, D.W. & Richards, P.G. (eds), Earthquake prediction; an International review. Maurice Ewing Series. American Geophysical Union, 593-603. Skar, T., Balen, R.v. & Hansen, S. 1998. Overpressuring in Cretaceous shales on the Halten Terrace, offshore Mid-Norway: nature and causes. Overpressures in petroleum exploration, 69-75. Pau, France. Skogseid, J., Pedersen, T., Eldholm, O. & Larsen, B.T. 1992. Tectonics and magmatism during NE Atlantic continental break-up: the Vøring Margin. In: Storey, B.C., Alabaster, T. & Plankhurst, R.J. (eds), Magmatism and the Causes of Continental Break-Up. Special Publication. Geological Society of London, 305-320. Stølum, H.H., Smalley, P.C. & Hanken, N.M. 1993. Prediction of large-scale communication in the Smørbukk field from strontium fingerprinting. Petroleum Geology of the North West Europe, 1421-1432. London. Swarbrick, R.E. & Osborne, M.J. 1998. Mechanisms that generate abnormal pressures: an overview. In: Law, B.E., Ulmishek, G.F. & Slavin, V.I. (eds), AAPG Memoir, 13-34. Teige, G.M.G., Hermanrud, C., Wensaas, L. & Bolås, H.M.N. 1999. The lack of relationship between overpressure and porosity in North Sea and Haltenbanken shales. Marine and Petroleum Geology, 16, 321-335. Terzaghi, K. 1925. Erbdbaumeckanik auf bodenphsikalischer Grundlage. Deuticke. Tosaya, C.A. 1982. Acoustical Properties of Clay-bearing Rocks. PhD Thesis, Stanford University. Townend, J. & Zoback, M.D. 2000. How faulting keeps the crust strong. Geology, 28, 399-402. Twiss, R.J. & Moores, E.M., 1992. Structural Geology. W.H. Freeman and Company, 499. Verbeek, E.R. & Grout, M.A. 1993. Geometry and structural evolution of gilsonite dikes in the eastern Uinta basin, Utah. U.S. Geological Survey Bulletin, 1787, 42. Walderhaug, O. 1996. Kinetic Modeling of Quartz Cementation and Porosity Loss in Deeply Buried Sandstone Reservoirs. AAPG Bulletin, 80, 731-745.

-53-

Wang, C. & Xie, X. 1998. Hydrofracturing and Episodic Fluid Flow in Shale-Rich Basins - A Numerical Study. AAPG Bulletin, 82, 1857-1869. Wang, Z.Z., Wang, H. & Cates, M.E. 1998: Elastic properites of Solid Clays. SEG Extended Abstracts, 1045-1048. Zimmerman, R.W. 1991: Elastic moduli of a solid containting spherical inclusions. Mechanics of Materials, 12, 17-24. Zimmerman, R.W. 1994: Behavior of the Poisson ratio of a two-phase composite material in the high-concentration limit. Zoback, M.D. & Healy, J.H. 1984. Friction, faulting, and "in situ" stress. Annales Geophysicae, 2, 689-698.

Appendix A Values of parameters used in the Stressim 3D model (see Borge (2000) for explanation of parameters and nomenclature) Description Symbol Value Unit Pressure generation and accumulation

Accumulating depth zA 2500 m

Generating depth zS 4100.0 m Salinity s 50000 ppm Accumulating exponent A 3.45 Shale drainage thickness γ 100.0 m

Minimum reservoir thickness zmin 0.10 m Minimum net/gross ratio N/Gmin 0.050 Maximum shale compaction depth zshale 10000.0 m Hydrostatic gradient 0.1030 bar/m ρw g Lithostatic gradient ρg 0.220 bar/m Time step ∆t 10000 years Diameter of quartz grain size D 0.0003 m Fraction of detrital quartz f 0.65 Molar mass of quartz M 0.06009 kg/mole Density of quartz 2650.0 -3 ρquartz kg ⋅ m D Temperature at which quartz cementation starts TC0 80.0 C D Temperature at which quartz cementation is TC1 175.0 C completed 2 Quartz precipitation rate factor r1 1.98e-18 mole/m s D -1 Quartz precipitation rate exponent r2 0.022 C Sand porosity at seabed 0.45 φS 0 Sand porosity constant 1 2400 m η1 Sand porosity constant 2 0.50 η2 D Temperature at seabed T0 4.0 C Temperature gradient ∂Tz/ ∂ 0.035 D Cm-1 Irredusible water saturation (Garn Formation) 0.040 φC1 Clay coating factor (Garn Formation) C 0.50 3 Minimum dissipation volume Vmin 1.0e+06 m Hydraulic leakage

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Poisson’s ratio (shales) at surface ν 0.40 z0 Poisson’s ratio (shales) at accumulating depth ν 0.27 zA Poisson’s ratio (shales) at sealing depth ν 0.20 zS Poisson’s ratio (shales) at max. shale comp. depth ν 0.02 zshale Young’s modulus (shales) at surface E 600 bar z0 Young’s modulus (shales) at accumulating depth E 20000 bar zA Young’s modulus (shales) at sealing depth E 40000 bar zS Young’s modulus (shales) at max. shale comp E 90000 bar depth zshale Coefficient of thermal expansion 1.00e-05 αT

Bulk modulus (shale) Ks 170000.0 bar Coefficient of internal friction µ 0.6 Coefficient of sliding friction µ 0.7 Lateral transmissibility Lateral transmissibility 0.00069 Percent transmissibility remaining at no overlap p 0.05 Width of fault blocks b 20.0 m Porosity at seabed 0.45 φ0 Rate of change in porosity versus depth c 0.00039 m-1 Porosity where the K - curve changes between 0.1 φ φb deep and shallow relationships Permeability where the K - φ curve changes Kb 0.00001 mD between deep and shallow relationships -1 Rate of change in fault zone permeability (log) δ 7.0 mDm versus depth (log) for shallow faults sh -1 Rate of change in fault zone permeability (log) δ 5.0 mDm versus depth (log) for deep faults de

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Appendix B Measured and simulated pressure for the exploration wells available in the “base case” study Well Simulated Difference between Measured Depth overpressure measured and overpressure (m) (bar) simulated (bar) overpressure (bar) 6407/8-2 0 0 0 1515.7 6407/7-3, 5 24.1 0 0 - 110 2881.8 6407/9-1, 2, 3, 0 0 0 1359.5 4, 5 & 6 6407/4-1 22.3 -58.7 81-92 2489.3 6407/9-7 0 0 0 1578.4 6406/8-1 344.1 7.6 336 4008.2 6407/2-1 22.9 22.8 0 2674.3 6407/6-4 0 0 0 2302.1 6406/3-1 313.6 23.6 288-290 3624.1 6407/2-3 0 0 0-6 1748.6 6406/6-1 305.5 6.5 298-299 3931.1 6406/2-6 388.7 -19.3 408 4278.0 6506/12-1, 3, 5 42.6 0 3-61 2361.7 & 8 6407/1-1, 2 & 3 29.6 22.6 0-7 3089.2 6406/3-2 & 4 8.9 0 5-13 3678.3 6406/2-3 368.8 -64.2 433 4371.8 6507/11-4 0 0 0 1926.0 6507/12-1,2 & 3 0 0 0 1507.7 6407/2-2 0 0 0 1894.4 6507/11-2 0 0 0 1580.7

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Chapter 3

Effect of different formulas of the minimum horizontal stress in a basin simulator, and the impact on pressure and hydraulic leakage

Lothe, A.E.1,2, Borge, H. 1, Larsen, I.1 & Gabrielsen, R.H.2

1Sintef Petroleum Research, N-7465 Trondheim, Norway, 2Geological Institute, University of Bergen, Allégaten 41, N-5007 Bergen, Norway

Abstract______

Different empirical and theoretical formulas for the minimum horizontal stress are implemented in a basin simulator, in order to simulate and compare the relationship between stress and pressure changes on geological time scale. The magnitude of the horizontal stress axes (σ H = σ h ), are varied to simulate the pressure build up in the basin and the influence on hydraulic fracturing and leakage. The pressure and stress simulations are carried out based on a dataset from the Halten Terrace area, offshore Mid-Norway. The stresses are varied both with respect to time and burial depth. The simulated minimum horizontal stress is compared to measured stresses from leak-off tests in wells, while modelled pressure is compared to present day pressure measurements.

The simulations show that both Breckels & van Eekelen formula and the Elastic theory, overestimate the minimum horizontal stress, resulting in a very late caprock failure. A too high overpressure build up is the result in western part of the basin. Using Zoback & Healy’s formula on the other hand, resulted in no pressure build up due to early leakage. The best results are obtained using Grauls empirical equations. The magnitude of the continental stress contribution from the ridge push is varied using Grauls to simulate the regional stress contribution. Increasing the maximum horizontal stresses, give a later hydraulic failure and leakage in the overpressured parts of the study area.

Keywords: basin modelling, minimum horizontal stress, hydraulic leakage, overpressure ___

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Introduction The interaction between fluid pressures and stresses in sedimentary basins is a key to understand natural hydraulic fractures and leakage of fluids through the cap rock. An increase in the magnitude of the minimum horizontal stress is observed in overpressured zones compared to normal pressured zones at equivalent depth in many deep sedimentary basins (Engelder & Fisher 1994). This is observed in e.g. Scotian Shelf, Canada (Yassir & Bell 1994) and in the central North Sea (Gaarenstroom et al. 1993). Yassir & Bell (1994) describe that the minimum horizontal stress increase in magnitude at the top of the overpressured zone. The data indicate that the minimum horizontal stresses increase in a rate proportional to, but less than, the rate of the overpressures. The reason for this is debated, but Engelder & Fisher (1994) suggest that poroelastic behaviour is an important factor. Zoback & Healy (1984) propose that the rock friction acts to limit differential stresses. The tectonic setting is an important controlling mechanism for pressure distribution in a sedimentary basin. This is especially important in compressive regimes like East Coast Region, New Zealand (Darby & Ellis 2001) or South East Asia (Bour et al. 1995). But also in passive margins the lateral stresses will be off major importance, like in the Halten Terrace area, offshore Norway (Skar & Beckman in press) and the North Sea (Gaarenstroom et al. 1993). It is realized that rapid changes in the state of stress due to tectonic forces will influence on the pressure build-up and hence, the potential for hydraulic fracturing in overpressured zones. Overpressure can be generated by several mechanisms like tectonics, mineral transformation and temperature increase (Osborne & Swarbrick 1997). The stresses, in similarity with the overpressure, are generated by several mechanisms on different scales from continental to regional and local (e.g. Engelder 1993, Fejerskov & Lindholm 2000)(Table 1).

The aim with this study has been to simulate the influence of variation of vertical and horizontal stresses on the pressures in a reservoir unit. Simulations were carried out using different approaches: First the different algorithms for estimating the minimum horizontal stresses were done, using both empirical (Grauls 1996, 1998, Breckels & van Eekelen 1982) and theoretical approaches (Elastic Theory and Zoback & Healy 1984). Secondly, an algorithm where regional stress is included was investigated. Measured pressures and stresses in wells from the Halten Terrace area were used to calibrate the simulations. Finally, the simulations will be used to evaluate possible hydraulic fracturing and leakage in the basin.

Table 1 Stress generation mechanisms (Fejerskov & Lindholm 2000). Stress field 1st order Continental 2nd order Regional 3rd order Local Lateral >1000 km 100-1000 km <100 km extent Plate tectonic forces Large-scale density Topography Stress Ridge push inhomogeneities; Fjords and mountain ranges generation Basal drag Continental margin Geological features; mechanism Slab pull Flexural stresses; Faults Sedimentary loading Hard and soft inclusions Deglaciations Wide topographic loads

Stress in the Halten Terrace area The study area covers a part of the Halten Terrace, at the Mid-Norwegian continental shelf, of approximately 10000 km2, bordered in the east by the Bremstein Fault Complex (Figure 3). The N-S striking Klakk Fault Complex limits the terrace to the west from the deeper Vøring

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Basin (e.g. Blystad et al. 1995). The Halten Terrace developed through multiple rift events during the Middle Jurassic and Early Cretaceous time. The latest rift episode affecting the area was the opening of the North Atlantic Ocean during the Earliest Eocene time (Skogseid et al. 1992). The stress field changed from E-W to WNW-ESE extension in Devonian time, to WNW-ESE extension during the late Permo-Triassic (Gabrielsen et al. 1999) to NW-SE compression in Cenozoic time (Fejerskov & Lindholm 2000). The present crustal stress state in the Halten Terrace area, as determined from earthquake focal mechanisms and bore hole break out, show a NW-SE directed maximum horizontal stress (e.g. Bungum et al. 1991, Lindholm et al. 2000). This first-order stress field is assumed to be set up by ridge push from the Mid-Atlantic ridge (Bungum et al. 1991), though regional contribution from density variations, sediment load and deglaciation is likely (Byrkjeland et al. 2000) (Table 2). Overcoring in the onshore Mid-Norway indicates high tectonic stress (up to 30 MPa; Hansen & Myrvang 1986). This is in line with the modelled stress field in the order of 20-30 MPa in the oldest crust performed by Fejerskov & Lindholm (2000). Two stress-generating mechanisms on regional scale (100-1000 km) are likely to contribute in the Halten Terrace area, namely large-scale density inhomogeneities on the continental margin and secondly flexural stress connected to sedimentary loading. The areas offshore Mid- Norway have a fairly stable stress field, with an NW-SE oriented maximum horizontal stress. This stress is compatible with the expected ridge-push force direction, but also perpendicular to the orientation of the glacial wedge and to the continental margin itself, with crustal inhomogeneities (Byrkjeland et al. 2000). The effect of the continental margin is quantitatively assumed to be between 10-50 MPa (Fejerskov & Lindholm 2000).

4° 6° 8° 10°

Tertiary dome Vøring e x p l Cretaceous high m Basin C o Cretaceous basin t l Platform area 66° u n a i Terrace HHeidreidruunn F s Permo-Triassic basin x a Fault B x e l

s

p s

m e å o

C l

R KKrristinistin

t Trøndelag

l

F

K

u

a l

F Platform a

k n i

e

k

HaltenHalten t

s

m

Terrrraceace e r

B ault Comple

F a

u

l x t 64°

C Vingleia

o Fault Comple m

p l

e

x Trondheim Bremstein F NORWAY Møre Trøndelag Fault Complex 50 km 20 km

Figure 1 a) Overview map of the Mid-Norway sea region, where the study area is marked. The main structural fault complexes are marked. Reworked from Blystad et al. (1995). b) The Halten Terrace area as used in the simulations. Calibration wells for the pressure simulations are marked.

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Table 2 Stress generating mechanism active on the Halten Terrace Stress Lateral Stress generation Comments field extent mechanism st 1 order >1000 Plate tectonic forces; Cretaceous-Paleocene volcanic rifted margin, σ Continent km Ridge push H direction NW-SE; compatible with expected ridge- al push direction (Hicks et al. 2000) 2nd order 100- Large-scale density Normal to margin, with compression in the oceanic Regional 1000 km inhomogeneities: crust. Magnitude: 10-50 MPa (Fejerskov & Continental Lindholm 2000) margin

Flexural stresses; Depositional model: Sedimentary Late Miocene (10.5-5.5 Ma) increased continental loading erosion and depositional of prograding wedges Early-Middle Pliocene (5.5-2.6 Ma) extensive local ice-sheets reaching the coastline, deposition of prominent wedges Northern Hemisphere glaciation (2.6-0.01 Ma) wedges farther west, covered by Quaternary deposits (Stuevold & Eldholm 1996 ) 3rd order <100 km Geological feature Local Faults

Methods and data The methods and models used are described in Borge & Sylta (1998), Borge (2000), Lothe et al. (in prep.), and only the main parts are therefore summarized here. Pressure generation and dissipitation was simulated in compartments as defined by the fault pattern at the top reservoir level. The pressure generation included quartz cementation in the sandy reservoir (Walderhaug 1996), mechanical shale compaction (Baldwin & Butler 1985) and a simplified model for shale drainage (Borge 2002; Figure 2). The numerical simulation method (Forward Euler) was stabilized using sufficient small time steps and introduction a minimum volume dissipation. The lateral fluid flow was modelled using a transmissibility algorithm defined by the dip-slip displacement and burial depth to the faults. The geo-mechanical properties of the caprocks (Poisson’s ratio and Young’s modulus), were depth-dependent, and define the Biot’s constant indirectly (e.g. Lothe et al in prep.). The hydraulic fracturing was defined by two failure criteria. The Griffith-Coulomb failure criterion was used for the initial failure, whereas the frictional sliding criterion was used for the reactivation along the same fracture (Figure 3). Thus, the rupture of the caprock was defined whenever the Mohr circle crosses the Griffith- Coulomb failure envelope. Once hydraulic fracturing occurred the failure criterion was changed to frictional sliding due to loss of cohesion in the cap rocks.

The vertical stress is calculated in the simulator by σ v = ρgz , where ρ is the density, g is the gravitational constant and z is the depth of burial. The calculation of the horizontal stresses (σh and σH) is more complex, depending on the scale of the stress processes. The stress is generated from processes at different scale; continental and regional. At continental scale, large-scale processes include plate-tectonic effects such as ridge push (Table 1). These far- field forces affect the entire sedimentary basin and may vary in magnitude and orientation through time. Hence, and in accordance with the literature, the stress history should be used as input in the simulations for each time step. The contribution from the far-field stress is calculated in the top point of the reservoir unit in all the pressure compartments. On the regional scale, the stress is generated from large-scale density inhomogeneities, as flexural stress and wide topographic loads (e.g. Fejerskov & Lindholm 2000).

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Depth grids of the Jurassic Garn Formation were provided from seven timesteps: 90 Ma, 80 Ma, 65 Ma, 20 Ma, 5 Ma and Present. Fault trace map at top Garn Formation was used to define pressure and stress compartments. The paleo-water depth was set constant to 200 m. Pressure data from 43 wells were used to calibrate the pressure simulations. Data from drill stem tests and formation pressure tests were carried out in the Garn Formation. The Leak-off tests to calibrate the minimum horizontal stress were measured in the Cretaceous Cromer Knoll Group, and the Jurassic Melke Formation (Figure 4).

Lateral flow Shale drainage

Shale compaction Quartz cementation

Hydraulic leakage Figure 2 The sketch presents all the processes taken into account in the simulator.

µ ' µ τ Frictional sliding failure Griffith-Coulomb envelope failure envelope

σ n σ σ 3 1 Figure 3 A combination of the Griffith-Coulomb failure criterion and the frictional sliding criterion is used in simulations.

Pressure (bar) 0 200 400 600 800 1000 1500

2000 Overpr

) 2500 High overpr m LOT h ( 3000 pt LOT in high overpr De 3500 Min horiz stress 4000

4500

Figure 4 Overpressure (Garn Formation), and minimum horizontal stress measured as leak off pressure (Melke Formation) for the same wells in the study area. The minimum horizontal stress graph is calculated for the wells with hydrostatic pressure in the reservoir unit.

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The minimum horizontal stress relations- empirical and theoretical The intention behind this work is to perform a sensitivity test coupling pressure and stress in a basin simulator. Different methods to estimate the minimum horizontal stress have been chosen like (1) empirical approaches (e.g. Grauls 1996, 1998, Beckels & Van Eekelen 1982) (2) theoretical approaches (Zoback & Healy 1984, Warpinski 1986).

Empirical approaches Assuming that the vertical stress caused by the overburden is the maximum stress and the horizontal stress axes are equal, equation (1; Grauls 1996) can be used to estimate the minimum horizontal stress for passive margins:

− z 2650 (14) σ hv=−(0.85 0.18e )σ

Grauls (1998) suggested an equation (2) based on empirical data where the exponent of the power law function is depending on the stress regime:

n (15) σσh =+hsf 0.0055(z −zsf )

Here, σ hsf is the minimum horizontal stress at the seafloor, zsf is the depth of the seafloor and n is the power law function. For a Type I (normal fault), n varies so that 1.141

Breckels & van Eekelen (1982) used regional fracture data to derive the relationship between total horizontal stress and depth. They also took abnormal pore pressure into account, suggesting the following relation for the US Gulf Coast:

σ =+0.0053zp1.145 0.46( −p) z<3500m (16) hffn σ hf=−0.0264zp31.7 +0.46( −pfn) z>3500m

where z is depth below sealevel given in meters, p f is the pore pressure given in MPa, p fn is the normal pore pressure corresponding to an gradient of 0.0105 MPa/m and σ h is the total horizontal stress given in MPa. The relation is considered to by fairly reliable down to 3500 m (Breckels & van Eekelen 1982).

Theoretical approaches Two theoretical approaches are tested; one proposed by Zoback & Healy (1984) and one based on the Elastic theory. The model described in Zoback & Healy (1984) is based on the assumption that in situ stress at depth in areas of active faulting, and that the frictional strength of the faults are in a state of equilibrium. Their theory is general, and claims to be valid for all tectonic stress regimes and fault types, as long as fault motion is possible for the faults in the area. The equation is given as:

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σ − p 2 (17) 1 f =+⎡ µ 2 1 +µ ⎤ ⎣ ⎦ σ 3 − p f

σ1 denotes the maximum stress, σ 3 the minimum stress, µ the coefficient of internal friction and pf the fluid pressure.

In the Elastic theory (Voight & St.Pierre 1974, Engelder & Fisher 1994), follows the assumption of Warpinski (1986) that an equation including the effect of the stress-strain relations in a linear elastic, homogenous and isotropic material may be written in a differential form as in Equation (5):

ναEdT Edε ν Edε ddσσ=+T +x +y xz11−−ν νν1−221−ν (18) ναEdT Edε ν Edε ddσσ=+T +y +x yz11−ν −−νν1221−ν

dσ i denotes incremental effective stress, E the Young’s modulus, ν the Poisson’s ratio, αT the linear coefficient of thermal expansion and dT the temperature changes. This equation is valid for dry rocks. Introduction of pore fluids have an effect on the properties of porous solids (Terzaghi 1925) and the effective stresses depend on the difference between pore pressure ( Pp ) and applied stress (σ i );

(19) ddσσi =−iBαdPp

Substituting relation (6) into equation (5), we get

ναE 12− ν Edε ν Edε dσσ=+d T dT +αdP +x +y xz11−−ν νν1−Bp1−ν221−ν (20) ναE 12− ν Edε ν Edε dσσ=+d T dT +αdP +y +x yz11−ν −−νν1Bp1−ν221−ν

It should be noted that, in our simulations, strain is set to zero.

Results from simulations In the present study the different empirical (Grauls 1996, 1998, Breckels & van Eekelen 1982) and theoretical (Zoback & Healy 1984, elastic theory) formulas, which describe the minimum horizontal stress, were implemented in the pressim pressure simulator and tested on the data from the Halten Terrace. The resulting pressure and stress simulations will be presented for the whole basin (Figures 5, 6 & 7) and then for only one compartment through time (Figures 8, 9 & 10). In addition, the lateral stresses were varied as a function of time. The results were used to evaluate possible hydraulic fracturing and leakage in the basin.

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The Grauls approach As presented earlier in Equation (1), Grauls (1996) use empirical data to give a relationship between burial depth and the magnitude of the minimum horizontal stress. Applying this formula in the simulations result in a relatively good fit between measured and simulated overpressure in the basin. The mean deviation between measured and simulated pressure in the corresponding compartments are presented in Table 3. The mean deviation is approximately 11 bar using Grauls (1996). High overpressures are simulated in the western area, while intermediate pressures are simulated in a transition zone into the more hydrostatic pressured eastern area (Figure 5). Furthermore, a good match between measured and simulated minimum horizontal stresses should be gained. Figure 6 shows the simulated minimum horizontal stress in the present top points of the compartments compared with data from Leak Off Tests (LOT). The simulated stresses fit the observations well down to approximately 3.8 km. The measured stresses below 3.8 km show some spreading while the simulated stresses show a linear trend versus depth.

Grauls (1998) presented in Equation (2), is only a variation of Grauls (1996) using an empirical approach, giving a slightly lower estimate of the minimum horizontal stress. Plotting the simulated present overpressure in the study area, the same overall pressure distribution is obtained (Figure 7a). However, the simulated overpressure is lower in the south-western area, using Grauls (1998), compared to Grauls (1996). The mean deviation in the simulated overpressure is 16 bar. The lower simulated pressure is caused by the lower estimated minimum horizontal stress. This results in an earlier hydraulic failure in the overpressured compartments, and more vertical leakage of formation water out of the basin. This in turn, gives an overall lower simulated overpressure in the western part of the basin.

The time-dependent changes in the effective vertical stress and the minimum horizontal stress are plotted for a pressure compartment located in the overpressured western part of the study area. The simulated minimum horizontal stress in the compartment increase rapidly between 90 Ma and 80 Ma, followed by a moderate increase until approximately 5 Ma (Figure 8). A rapid decrease in the stress magnitude is noted around 5 Ma due to an increase in overpressure (Figure 9). A rapid burial rate and subsequent increased quartz cementation in the reservoir unit caused this pressure build-up (Lothe et al. in prep.). The two formulas by Grauls give similar major trends for the stress/pressure relationship. However, at 10 Ma, the algorithm proposed by Grauls (1998) gives a simulated minimum horizontal stress in a magnitude of 230 bar, whereas Grauls (1996) gives 260 bar (Figure 8). The compartment fails around 1.8 Ma, using both models (Figure 9).

Table 3 Mean deviation in overpressure in the different runs Runs using minimum horizontal stress Mean deviation between measured and simulated from overpressure in all wells in the basin (bar) Grauls (1996) 11 Grauls (1998) 16 Breckels & van Eekelen (1982) 49 Zoback & Healy (1984) 66 Elastic Theory 47 Lateral stress 50 bar* 11 Lateral stress 100 bar* 18 Lateral stress 150 bar* 32 * In these simulations, Grauls (1996) is used to calculate the minimum horizontal stress. The lateral stress is set at 10000 m depth in the sedimentary basin, with a linear depends with depth.

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Figure 5 Map presenting simulated present overpressure in the study area using Grauls (1996) equation for the minimum horizontal stress. Colour scale in bars.

Stre ss (ba r) 200 400 600 800 1000 1000

2000 )

m 3000 Min hor stress h (

pt LOT

e 4000 D 5000

6000

Figure 6 Stresses (bar) versus depth (m). Pink squares show measured stresses using LOT in the Cromer Knoll Group. Blue diamonds show simulated stresses at the top point of all the compartments in the study area today.

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a ) Grauls (1998) b)

Stre ss (ba r) 200 400 600 800 1000 1000

2000 )

m 3000 Min hor stress

h ( LOT pt

e 4000 D 5000

6000

c) Breckels & van Eekelen d)

Stress (bar) 200 400 600 800 1000 1000

2000 )

m 3000 Min hor stress

h ( LOT pt

e 4000 D 5000

6000 e) Zoback & Healy (1984) f)

Stress (bar) 200 400 600 800 1000 1000

2000 )

m 3000 Min hor stress

h ( LOT pt

e 4000 D 5000

6000

Figure 7 Simulated a), c) and e) overpressure (bars) today and b), d) and f) Simulated minimum horizontal stress compared with measured Leak Off Test data from Cromer Knoll Group. a) and b) using Grauls (1998) equation, c) and d) using Brekels & van Eekelen (1982) equation and e) and f) Zoback & Healy (1984).

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450

σv Grauls (96) 400 σh Grauls (96) σv Grauls (98) 350 σh Grauls (98) 300

ar]

b 250 ss [

re 200 St 150

100

50

0 90 80 70 60 50 40 30 20 10 0 Time [Ma] Figure 8 Minimum horizontal stress and vertical stress plotted in one compartment for the last 90 Ma using a) Grauls (1996) equation and b) elastic theory (ν).

450

σv Grauls (96) 400 σh Grauls (96) σ Grauls (98) 350 v σh Grauls (98) 300

] 250

ress [bar 200 t S 150

100

50

0 6 5 4 3 2 1 0 Time [Ma] Figure 9 Changes in one overpressured compartment the last 10 Ma till Today, using different models. Grauls (1996) empirical equation and Elastic theory (ν). The elastic theory gives lower minimum horizontal stresses, and thereby earlier failure.

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Breckels & van Eekelen (1982) Breckels & van Eekelen (1982) do also use an empirical based approach (Equation 2) to estimate the minimum horizontal stress. Using this approach in the simulator, it results in extreme and unrealistic high overpressure in the western area and hydrostatic pressure in the eastern area (Figure 7c). Hardly any intermediately pressured areas were obtained in this simulation. The mean deviation in the estimated overpressure using Breckels & van Eekelen (1982) equation is 49 bar (Table 3).

The simulated stress fit quite well with the simulated stress also for this algorithm at shallow depths (<3 km). The simulated minimum horizontal stress is generally too high at deeper burial depth, and much higher than the measured stresses in some compartments (Figure 7d). The magnitude of the minimum horizontal stress controls the timing of the hydraulic failures in the overpressured basin. In this case, using Breckels & van Eekelen (1982), too high minimum horizontal stress was obtained (Figure 7d). These results in relatively low differential stress and more overpressures are allowed to build up before caprock failure occurs.

Studying the changes in stress in only one compartment, Breckels & van Eekelen (1982) empirical equation gives greater values for the effective minimum horizontal stress, than Grauls (1996; Figure 10a). The largest differences between the models are noticed when the pressure increased from approximately 5 Ma (Figure 10b). Since the method proposed by Breckels & van Eekelen (1982) use a balanced equation were the overpressure is taken into account, the increase in overpressure does not decrease the magnitude of the minimum horizontal stress much. The magnitude of the minimum horizontal stress using Grauls (1996) is reduced to approximately 50 bar after pressure build up, while Breckels & van Eekelen (1982) gives values around 250 bar. The vertical stress, on the other hand, drops dramatically in value when the overpressured increased, and becomes σz< σh from 3.8 Ma (Figure 10b). This implies that the pressure increases, while the diameter of the Mohr circle shrink s. Finally the compartment failed at 1.3 Ma, resulting in a small increase in the vertical stress.

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450 450 σ v Grauls (96) σ v Grauls (96) 400 σ h Grauls (96) 400 σ h Grauls (96) σ v Breckels & van Eekelen σ v Breckels & van Eekelen 350 350 σ h Breckels & van Eekelen σ h Breckels & van Eekelen 300 300

] r a ar]

b 250 250 [ [b s ss s

re 200 200 St Stre 150 150

100 100

50 50

0 0 90 80 70 60 50 40 30 20 10 0 6 5 4 3 2 1 0 Time [Ma] Time [Ma] c) d)

450 450

σv Grauls (96) σ v Grauls (96) 400 400 σ σh Grauls (96) h Grauls (96) σ σv Zoback & Healy v Zoback & Healy 350 350 σ Zoback & Healy σh Zoback & Healy h 300 300

] ] r a

250 b 250 [ ss [bar ss e

200 re 200 Str St 150 150

100 100

50 50

0 0 90 80 70 60 50 40 30 20 10 0 6 5 4 3 2 1 0 Time [Ma] Time [Ma] e) f)

450 450

σv Grauls (96) σv Grauls (96) 400 Grauls (96) 400 σh σh Grauls (96)

σv ν σv ν 350 350 σh ν σh ν 300 300

] ] r r a a

b 250 b 250 [ [ ss ss e e

r 200 r 200 St St 150 150

100 100

50 50

0 0 90 80 70 60 50 40 30 20 10 0 6 5 4 3 2 1 0 Time [Ma] Time [Ma]

Figure 10 Changes in simulated minimum horizontal stress and vertical stress for one compartment using a) and b) Grauls (1996) and Breckels & van Eekelen (1982) equations c) and d) Grauls (1996) and Zoback & Healy (1984) equations, e) and f) Grauls (1996) equation and the Elastic theory.

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Zoback & Healy (1984) The opposite trend in pressure and stress distributions is seen making simulations using Zoback & Healy’s equation (Equation 4). The simulations give very low values for the horizontal stress (Figure 7f), compared to the measured minimum horizontal stress. The very low estimated minimum horizontal stress gives large differential stress, and less overpressure can build up in the basin, before caprock will fail. The low minimum horizontal stress results in unrealistic low pressure build up at basin scale, (mean deviation 66 bar, Figure 7e).

Following the time-stress dependence in one compartment, using the model presented by Zoback & Healy (1984) in the simulator, gives very low estimate for the minimum horizontal stress, around 150 bar at 6 Ma (Figure 10c & d). The low magnitude of the minimum horizontal stress results in early leakage from the compartment and low pressure build-up.

Elastic Theory Applying the Elastic Theory (Voight & St. Pierre 1974, Warpinski 1986) in the simulations give much lower estimates of the minimum horizontal stresses, compared to the empirical Grauls (1996) approach (Figure 10e). The timing of hydraulic failure varies in the reference compartment, depending of which model used. When using the elastic model, this compartment was brought to failure at 4.1 Ma, whereas Grauls (1996) model suggest hydraulic leakage from 1.8 Ma (Figure 10f). Using the Elastic Theory, however a stress increase is observed around 3 Ma, but since the neighbour compartment failed, the failure was delayed in this compartment.

The deviation between measured and simulated pressure in the corresponding pressure compartment are used to evaluate the different runs. We find the mean deviation for the overpressure in the study area of 11 bar using Graul’s, and 47 bar using Elastic Theory. The large deviation in the simulated overpressure that results using the Elastic Theory is caused because the calculated minimum horizontal stress becomes too low. Too low minimum horizontal stress gives early hydraulic failure in many overpressured compartments. The caprocks are not capable to hold large overpressures, and the fluid leak out vertically through the early generated hydraulic fracture systems, and the resulting overpressure in the basin become to low. The reduction of the effective stress, when using the Elastic Theory is illustrated in Figure 11. An increase in the overpressure gives to high reduction in the minimum horizontal stress. In fact, the minimum horizontal stress approach zero, with increasing overpressure. From the present simulations it seems like the Elastic Theory underestimate the magnitude of the minimum horizontal stress, and therefore is not valid on basin scale and through geological time (e.g. Figure 11). Though the formula is correct in laboratory experiments.

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150

(bar)

100 ress

ear st 50 h S

0 100 200 300 400 500 Normal stress (bar)

Figure 11 Mohr-circles shows the calculated stresses using elastic theory when overpressure increases. Overpressure = 0, 50, 200, 300 and 350 bar. Depth = 4500 m. Black graphs show Griffith-Coulomb failure criterion.

Comparison of all of the different approaches A good match between simulated and measured pressures in the basin is obtained using Grauls (1996) expression to estimate the minimum horizontal stress. Furthermore, we want to compare the Grauls (1996) model with the other formulas and presented. Figure 12 presents all the different estimates of the minimum horizontal stress versus depth. Note the much lower values of the minimum horizontal stresses calculated using Elastic Theory and Zoback & Healy’s models, compared to the other models. This point can be illustrated plotting the deviation between the other models from the Grauls (1996) model (Figure 13), where the Elastic Theory and Zoback & Healy gives too low estimate of the minimum horizontal stress. Both Grauls (1998) and Breckels & van Eekelen (1982) estimate lower stresses at shallow depths, and higher stresses at depths larger than 3 km and 3.8 km, respectively (Figure 13).

As a result of testing the different empirical and theoretical formulas for the minimum horizontal stress, Grauls (1996) equation was used in the simulations. Also, Grauls (1998) could have been chosen, but neither of the other should be used with any confidence.

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0 200 400 600 800 1000 1200 0 Grauls (1996) 500 Grauls (1998) Breckels & van Eekelen (1982) 1000 Zoback & Healy (1984) Elastic theory 1500

2000

2500 3000

3500

4000

4500 5000

Figure 12 Horizontal stress (bar) versus depth (m) using different formulas.

-250 -200 -150 -100 -50 0 50 100 0 Grauls (1998) 500 Breckels & van Eekelen (1982) Zoback & Healy (1984) 1000 Elas tic theory 1500

2000

2500 3000

3500

4000

4500 5000

Figure 13 Deviation in horizontal stress in bars from Grauls (1996). Note the very low minimum horizontal stresses calculated using the Elastic Theory and Zoback & Healy (1984).

Simulations with varying magnitude of continental scale stress The stress field in the Halten Terrace area have been rather stable after the mid Jurassic- Early Cretaceous rifting event. Some faults were active into Campanian time with movement along the Revfallet, Bremstein and Vingleia Fault Complex (Blystad et al. 1995). Focusing on the last 90 Ma, which is the time span the simulations cover, some events can be particularly significant (Table 4). From Late Cretaceous to the break-up of the North Atlantic margin in the Early Eocene times (55 Ma; anomaly A24b, Talwani & Eldholm 1977, Eldholm et al. 1987), a pre-break up extension NW-SE should be expected. It is speculative to quantify the stress contribution form such events. However, magnitudes up to 15 MPa at 10 km depth are used in the simulations presented. The mid-oceanic ridge set up a ridge push, which would increase in magnitude depending on age and cooling of the oceanic lithosphere. The ridge push

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force will be zero at the ridge crest and increase linearly with age (Fejerskov & Lindholm 2000). We have chosen to set the maximum horizontal stress to zero at the break up (Early Eocene), and linearly increase the magnitude of the stress till end of the Pliocene.

Table 4 Stress and magnitude changes through time in the Halten Terrace area Time steps Regional stress Regional stress field Reference (Ma years) field direction magnitude 90 Late Cretaceous Pre-Break up ??? Blystad et al. (1995) 90-80 Late Cretaceous extension, NW-SE (Turonian-Early Campanian) 80-65 Late Cretaceous (Late Campanian)- Early Paleocene 65-54 Early Paleocene- Early Eocene

54-20 Early Eocene- Ridge push, Linear increase in Reference in Early Miocene maximum deviatoric stress Fejerskov & horizontal stress is depending on age and Lindholm NW-SE depth (2000) 20-5 Early Miocene- Pliocene

5-2 Pliocene 2 - in Quaternary Ridge push, 20-30 MPa in old Fejerskov & situ maximum oceanic crust Lindholm horizontal stress (2000) is NW-SE Hansen & Myrvang Overcoring on land in (1986). mid-Norway; < 30 MPa

Results of simulations varying the magnitude of the largest horizontal stress Assuming that Grauls (1996) equation is valid in a passive margin, and since Halten Terrace area have been under compressional stress the last million years, the simulations have been carried out by including large-scale continental generated stresses (Table 3). The magnitudes of the stresses are varied. The simulated lateral stress is depth-dependent and increases linearly with burial depth. The maximum magnitude is set at 10 000 m depth, and is varied in the different runs, between 50 bar, 100 bar and 150 bar. As an example; if the lateral stress contribution is set to 50 bar, the lateral stress contribution will be in the order of 20 bar at 4 km burial depth.

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No lateral stresses were included in the reference simulation. Then hydraulic fracturing and leakage occurs from several pressure compartments in the western part of the study area (Figure 14). Increasing the minimum horizontal stress slightly time-delay in the initiation of hydraulic failure in some compartments and a reduction in the cumulative leakage in the compartments that fail, are seen (Figure 15a & b). If the magnitude of the lateral stresses is increased even further, some of the compartments that have been leaking with smaller minimum horizontal stress will not fail. This is the case for some small compartments in the central part and western part of the study area (Figure 15a, b & c).

The simulated minimum horizontal stresses increases gradually with depth, when including different lateral stresses (Figure 15b, d & f). Thus, compared to the measured leak-off pressure, the simulated minimum horizontal stresses are generally greater; expect for the overpressured areas at around 3.7 km depths (Figure 15b, d, & f). The mean deviation between modelled and observed pressure, which is a measure of the quality of the calibration of the model, increases adding the continental large-scale stress effects (Table 3).

Figure 14 Simulated cumulative leakage using Grauls (1996). No lateral stresses are incorporated in the model.

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a) 50 bar b)

Stress (bar) 250 350 450 550 650 750 850 950 1500 Min hor stress LOT 2500 ) m h ( pt e

D 3500 Log cumulative leakage 4500 (m3) b) 100 bar d)

Stress (bar) 250 350 450 550 650 750 850 950 1500 Min hor stress LOT

) 2500 m ( h t p

Log De 3500 cumulative leakage 3 (m ) 4500

c) 150 bar f)

Stress (bar) 250 350 450 550 650 750 850 950 1500 Min hor stress LOT 2500 ) m h ( pt e

D Log 3500 cumulative leakage 3 (m ) 4500

Figure 15 Different large-scale lateral stresses are included in the simulations. Grauls (1996) is used in all runs. a, b, & c) Maps show logarithmic cumulative leakage, using increasing lateral stresses; 50, 100 and 150 respectively. The compartments with colour failed. d, e & f) show simulated minimum horizontal stress versus measured stress from leak- off tests.

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Discussion The interaction between pressure and stress on basin scale is complicated. The relations between pore pressure and stress have been discussed in different papers (Yassir & Addis 2002, Miller et al. 2002). The main item in this paper is to test how various concepts for calculating the minimum horizontal stresses can be included in a pressure simulator and how different scenarios of pressure and stress interaction can be studied over a geological time scale.

Grauls (1996, 1998) empirical equations depend on the tectonic regime in the study area. We used the Type I input parameters for offshore passive margins, deltas and normal faulted context in the Halten Terrace area. As shown, the equations give good fit, both for the pressure and the stresses. Though, the minimum horizontal stress is a little bit underestimated in the highly overpressured part of the study area (Figure 7b).

Breckels & van Eekelen (1982) used empirical data from U.S. Gulf Coast, Venezuela and Brunei to establish a relationship between horizontal total stress and depth. Too high present day minimum horizontal stresses were modelled in the Halten Terrace area using these models as input to the simulations methodology presented (Figure 7d). Though, the simulated minimum horizontal stresses are higher than what is measured by leak-off tests in the Halten Terrace. The Breckels & van Eekelen’s formula are the only of the tested formulas that show an increase of the minimum horizontal stresses in the overpressured depth intervals which is in accordance with the measured data (Figure 7d).

Zoback & Healy (1984) presented an alternative theoretical model for the minimum horizontal stress. This model was implemented in the present simulator. Zoback & Healy’s model is valid provided that active faulting should take place in the modelled basin. This assumption is not fulfilled, because the simulator does not take strain into account, and some deviation in the simulations may be expected. Simulating using Zoback & Healy’s model gives very low minimum horizontal stresses for the present day compared to the measured minimum horizontal stresses in the basin (Figure 7f): The simulated minimum horizontal stress at 4 km depth is up to 100 bar lower than the measured stresses from wells. The low horizontal stress values result in no simulated overpressure in the studied area. This is caused by the low leak-off pressures that do not allow significant overpressure to accumulate before the compartments fail due to hydraulic fracturing (Figure 7e). Engelder & Fischer (1994) tested the formula of Zoback & Healy on data from the North Sea, the United Kingdom and the Sable subbasin. They found that the formula underestimate the magnitude of the minimum horizontal stress. The same observations are made applying Zoback & Healy’s frictional slip method to our methodology.

The Elastic Theory is often used to model changes in the minimum horizontal stress connected to depletion in reservoirs (Hettema et al. 1998, Teufel et al. 1991, Fisher & Engelder 1994) and is in addition well know from laboratory work (Kümpel 1991). Fisher & Engelder (1994) used the Elastic Theory on data from the North Sea and the Scotian Shelf on a geological time scale. They concluded that this concept could successfully be applied over millions of years, if overpressure generated by maturation of kerogen to hydrocarbon is taken into account. The simulations presented in this paper show that the differential stress goes to zero when the overpressures increase over geological time scale. In addition, the minimum horizontal stresses approaches zero when the overpressure increases (Figure 11). It is indicated that the Elastic Theory gives unrealistically low minimum horizontal stresses

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compared to the empirical formulas (Grauls 1996, 1998, Breckels & van Eekelen 1982). In the present simulations it causes too early hydraulic fracturing and leakage. Furthermore, the simulator fails to accumulate overpressure within the available timeframe. We therefore conclude that the formula cannot be used with any confidence in basin simulations over geological time scale. Probably, on reservoir time scale the equation can give realistic estimates of the relation between overpressure and the stresses (Kümpel 1991).

Lateral stresses It is important to take the level of uncertainty of the simulated parameters into account evaluating the quality of the simulations. In this context we have a quite good understanding of the present stress distribution and direction on large scale in the study area when maximum horizontal stress is concerned (e.g. Bungum et al. 1991, Lindholm et al. 2000). Still, the magnitude of the maximum horizontal stress is not well known.

The Grauls (1996) equation seems to be the best stress model simulating the regional horizontal stress contribution and the far-field compressive continental stresses. Large stresses gave high deviation between measured and simulated overpressure. An increase of 50 bar at 10.000 m depth gave the same deviation, as simulations no lateral compressive stresses included. Overcoring in the Mid-Norway indicated high compressive stresses up to 300 bar (Hansen & Myrvang 1986). But, lateral stresses in such order, seems from this simulations a bit too high.

One of the questions is how large differences should be expected between different compartments coming to horizontal stresses. Pascal & Gabrielsen (2001) work from the mid- Norwegian Sea illustrated the large scale gradually changes in the stress field and how this are largely controlled by master faults like the Møre-Trøndelag Fault Complex. On smaller scale models by Maerten et al. (2002) showed the importance of minor fault systems in the North Sea. Strain is taken into account in both of these model studies. This is off course, one of the weaknesses in our simulations that the strain is not taken into account. In addition, the minimum horizontal stress is only treated at the top point of each pressure compartment. Then, the changes in the stress distribution laterally around the faults are not taken into account. This is of great importance, as shown by Su & Stephansson (1999). They studied how a fault will influence on the in situ stresses by using the distinct element method. Skar & Beekman (in press) modelled the influence of compression on the in-situ stress field in the Haltenbanken area found considerable spatial variations in the horizontal stresses. These were due to structural variations, contrast in rock properties and magnitude of horizontal loading. However, the simulations were only 2D in their work, without including pressure.

The simulator may benefit by handling the stresses in a different way in the future. As it is today, the stresses are defined in compartments in the same way as the pressure by the faults in the area. In the future finite element models may provide the stress-strain relationship around faults and at the fault tips. Then, pressure and stress simulations can further be integrated through time providing a better insight, and new possibilities and applications in basin modelling.

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Conclusions The main conclusions drawn from these basin simulations at the Halten Terrace area are; • Grauls (1996, 1998) empirical equations are the one formula that gives the most realistic simulations of both the fluid pressure and minimum horizontal stress in the study area. • Using Breckels & van Eekelen equation gives too highly simulated horizontal stresses, especially in the overpressured part of the basin. This in turn results in an extreme overpressure build up in the western part, hydrostatic in the eastern part and no intermediate pressure transit zone in between, as should be expected from wells in the area. • Zoback & Healy’s theoretical equation gives too low minimum horizontal stress, and thereby a too early hydraulic fracturing and leakage. Also in this case a too low overpressure is the result in the simulations. • The Elastic theory is not well suited to simulate stress and pressure changes over geological time scale. With increasing overpressure, the minimum effective horizontal stress approach zero, giving a very early hydraulic fracturing and leakage, resulting in too low overpressure build up. • An increase of the maximum horizontal stress in the simulator gives later failure and less hydraulic leakage in the caprock. The method presented here is too rough, and further work should be carried out to give a more complete modelling of the stresses. Not only in the top points of the compartments, but in the whole compartments. Acknowledgement We would like to thank our colleagues at SINTEF for great support with the work. Norsk Hydro ASA has provided funding and data for the work presented.

References

Baldwin, B. & Butler, C. O. 1985. Compaction curves. AAPG Bulletin, 69(4), 622-662. Blystad, P., Færseth, R. B., Larsen, B. T., Skogseid, J. & Tørudbakken, B. 1995. Structural elements of the Norwegian continental shelf, Part II. The Norwegian Sea Region. Norwegian Petroleum Directorate Bulletin, 8. Borge, H. & Sylta, Ø. 1998. 3D modelling of fault bounded pressure compartments in the North Viking Graben. Energy, exploration and exploitation, 16, 4, 301-323. Borge, H. 2000. Fault controlled pressure modelling in sedimentary basins. An thesis for the degree of Doktor Ingenør of the Norwegian University of Science and Technology, Trondheim, Norway, 148 pp. Borge, H. 2002. Modelling generation and dissipation of overpressure in sedimentary basins: an example from the Halten Terrace, offshore Norway. Marine and Petroleum Geology, 19, 377-388. Bour, O., Lerche, I. & Grauls, D. 1995. Quantitative models of very high fluid pressure: the possible role of lateral stresses. Terra Nova 7, 68-79. Breckels, I. M. & Eekelen, H. A. M. v. 1982. Relationship between horizontal stress and depth in sedimentary basins. Journal of Petroleum Technology, 34, 2191-2199.

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Bungum, H., Alsaker, A., Kvamme, L. B. & Hansen, R. A. 1991. Seimicity and Seismotectonics of Norway and Nearby Continental Shelf Areas. Journal of Geophysical Research, 96(B2), 2249-2265. Byrkjeland, U., Bungum, H. & Eldholm, O. 2000. Seismotectonics of the Norwegian continental margin. Journal of Geophysical Research, 105(B3), 6221-6236. Darby, D. & Funnell, R. H. 2001. Overpressure associated with a convergent plate margin: East Coast Basin, New Zealand. Petroleum Geoscience, 7, 291-299. Engelder, T. 1993. Stress regimes in the lithosphere. Princeton University Press, New Jersey. 399 pp. Engelder, T. & Fisher, M. P. 1994. Influence of poroelastic behaviour on the magnitude of minimum horizontal stress, Sh, in overpressured parts of sedimentary basins. Geology, 22, 949-952. Fejerskov, M. & Lindholm, C. 2000. Crustal stress in and around Norway: an evaluation of stress-generating mechanisms. In: Nøttvedt, A. (eds) Dynamics of the Norwegian Margin. Geological Society of London, London, 167, 451-467. Gabrielsen, R. H., Odinsen, T. & Grunnaleite, I. 1999. Structuring of northern Viking Graben and the Møre Basin; the influence of basement structural grain, and the particular role of the Møre-Trøndelag Fault Complex. Marine and Petroleum Geology, 16, 443-465. Grauls, D. 1996. Minimum Principal Stress as a Control of Overpressures in Sedimentary Basins. Proceeding of the8th Conference on Exploration and Production. IFP Report No43313, IFP Ruil-Malmaison. Grauls, D. 1998. Overpressure assessment using a minimum principal stress approach. Overpressures in petroleum exploration, Proc. Workshop Bull. Centre Rech. Elf Explor. Prod., Pau, France, 22, 137-147. Gaarenstroom, L., Tromp, R. A. J., Jong, M. C. d. & Brandenburg, A. M. 1993. Overpressures in the Central North Sea: implications for trap integrity and drilling safety. In: Parker, J. R. (ed.) Petroleum Geology of Northwest Europe. Proceedings of the 4th Conference, The Geological Society, London, 1305-1313. Hansen, T. H. & Myrvang, A. 1986. Rock stress and rock stress effects in the Kobbelv area, northern Norway. Proceedings of the International Symposium on Rock Stress Measurements, Stockholm, 625-627. Hettema, M. H. H., Schutjens, P. M. T. M., Verboom, B. J. M. & Gussinklo, H. J. 1998. Production-Induced Compaction of Sandstone Reservoirs: The Strong Influence of Field Stress. SPE European Petroleum Conference, The Haghe, The Netherlands, 1-8. Hicks, E. Bungum, H., Lindholm, C. 2000. Stress inversions of earthquake focal mechanism solutions from onshore and offshore Norway, Nor. Geol. Tidsskr., 80, 235-250. Kümpel, H. J. 1991. Poroelasity Parameters reviewed. Geophysical Journal International, 105, 783-799. Lindholm, C. D., Bungum, H., Hicks, E. & Villagran, M. 2000. Crustal stress and tectonics in Norwegian regions determined from earthquake focal mechanisms. In: Nøttvedt, A. (ed.) Dynamics of the Norwegian Margin, Geological Society, London, 167, 429-439. Lothe, A.E., Borge. H., Gabrielsen, R.H. in press. Modelling of hydraulic leakage by pressure and stress simulations and implications for Biot’s constant: An example from the Halten Terrace, offshore Mid-Norway, Accepted for publication in Petroleum Geoscience. Maerten, L., Gillespie, P. & Pollard, D. D. 2002. Effects of local stress perturbation on secondary fault development. Journal of Structural Geology, 24, 145-153. Miller, T. W., Luk, C. H. & Olgaard, D. L. 2002. The interrelationships between overpressure mechanisms. In: Huffman, A. R. & Bowers, G. L. Pressure regimes in sedimentary basins and their prediction, AAPG Memoir, 76, 13-20. Osborne, M. J. & Swarbrick, R. E. 1997. Mechanisms for generating overpressure in sedimentary basins: a reevaluation. AAPG Bulletin, 81(6), 1023-1041.

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Pascal, C. & Gabrielsen, R. H. 2001. Numerical modeling of Cenozoic stress pattern in the mid- Norwegian margin and the northern North Sea. Tectonics, 20(4), 585-599. Skar, T. & Beekman, F. in press. Modelling the Influence of Tectonic Compression on the In- Situ Stress Field with Implications for Seal Integrity: The Haltenbanken Area, Offshore Mid-Norway. Submitted to Geological Society Special Publication. Skogseid, J., Pedersen, T., Eldholm, O. & Larsen, B. T. 1992. Tectonism and magmatism during NE Atlantic continental break-up: the Vøring Margin. In: Storey, B. C., Alabaster, T. & Plankhurst, R. J (eds) Magmatism and the Causes of Continental Break-Up. Special Publication, Geological Society of London, London, 68, 305-320. Stuevold, L. M. & Eldholm, O. 1996. Cenozoic uplift of Fennoscandia inferred from a study of the mid-Norwegian margin. Global and Planetary Change, 12, 359-386. Su, S. & Stephansson, O. 1999. Effect of a fault on in situ stresses studied by the distinct element method. International Journal of Rock Mechanics and Mining Sciences, 36, 1051-1056. Terzaghi, K. 1925. Erbdbaumeckanik auf bodenphsikalischer Grundlage. Deuticke, Leipzig. Teufel, L. W., Rhett, D. W. & Farrell, H. E. 1991. Effect of reservoir depletion and pore pressure drawdown on insitu stress and deformation in the Ekofisk field, North Sea. In: Rogiers, J.- C. (ed.) Rock mechanics as multidisciplinary science. Balkema, Rotterdam, Netherlands, 63-72. Voight, B. & St. Pierre, H. P. S. 1974. Stress history and rock stress. In: Proceedings of the Third Congress of the International Society for Rock Mechanics, Denver, 2, 580-582. Walderhaug, O. 1996. Kinetic modelling of quartz cementation and porosity loss in deeply buried sandstone reservoirs. AAPG Bulletin, 80(5), 731-745. Warpinski, N. R. 1986. Elastic and Viscoelastic Calculations of Stresses in Sedimentary Basins. Society of Petroleum Engineers, Louisville, 1-14. Yassir, N. & Addis, M. A. 2002. Relationship between pore pressure and stress in different tectonic settings. In: Huffman, A. R. & Bowers, G. L (eds.) Pressure regimes in sedimentary basins and their prediction. AAPG Memoir, 76, 79-88. Yassir, N. A. & Bell, J. S. 1994. Relationship between Pore Pressure, Stresses, and Present-Day Geodynamics in the Scotian Shelf, Offshore Eastern Canada. AAPG Bulletin, 78(12), 1863- 1880. Zoback, M. D. & Healy, J. H. 1984. Friction, faulting, and "in situ" stress. Annales Geophysicae, 2(6), 689-698.

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Chapter 4

Evaluation of late caprock failure and hydrocarbon trapping using a linked pressure and stress simulator

Lothe, A.E.1, 2, Borge, H.1 & Sylta, Ø.1

1Sintef Petroleum Research, N-7465 Trondheim, Norway, 2Geological Institute, University of Bergen, Allégaten 41, N-5007 Bergen, Norway

Abstract______

Hydraulic fracturing and leakage can be controlling factors for hydrocarbon leakage in overpressured sedimentary basins over geological time. Knowledge of the lateral flow properties of major faults is needed to simulate how pressure generation and dissipation can influence the sealing potential of caprocks. The hydraulic fracture processes within the caprock need to be evaluated to quantify timing and the amount of hydraulic leakage.

In order to address these issues we use a simulator, which calculates pressure generation resulting from mechanisms such as shale compaction and drainage, and mechanical and chemical compaction in sandstones. Pressure dissipation and lateral flow are simulated between different pressure and stress compartments defined by major fault patterns at the top reservoir level. An empirical model for the minimum horizontal stress is applied to the Griffith-Coulomb failure criterion and the sliding criterion to estimate hydraulic fracturing.

When varying the coefficient of internal friction and frictional sliding there are no or minor changes in the amount and timing of hydraulic fracturing and leakage in the modelled pressure compartments. When varying fault permeability, low fault permeabilities give early leakage, while high permeabilities result in late or no hydraulic fracturing and leakage. Our simulations also suggest that leakage in one pressure compartment influences the neighbouring compartments and large compartments control the leakage pattern in surrounding areas. The amount of cumulative leakage depends on the timing and size of the compartment. Uncertainties of timing and leakage for different compartments can be estimated by using the pressure measured in the wells today as calibration. The uncertainty in the estimates can be used as guidelines for possible hydrocarbon leakage risks. ______Keywords: hydraulic fracturing, hydraulic leakage, overpressure, basin modelling

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Introduction Knowledge of the timing and distribution of hydraulic fractures is essential for evaluating hydrocarbon potential in many overpressured sedimentary basins (Grauls 1998, Hermanrud & Bolås 2002). Overpressure can be generated by several mechanisms including rapid sedimentation and compaction disequilibrium of sediments, hydrocarbon diagenesis, sediment diagenesis (Swarbrick & Osborne 1998), aquathermal pressuring (Chapman 1980, Miller & Luk 1993) and lateral compression (Bour et al. 1995). Field data indicate that overpressuring of sedimentary units can cause episodic fluid expulsion into overlying layers during basin subsidence (Hunt 1990). The understanding of hydraulic fracturing and leakage has been limited by lack of good field exposures and also lack of cores from fractured caprocks (Cosgrove 1998). One way to achieve new knowledge of which parameters that influence hydraulic failure of caprocks leading to leakage, is to use basin simulators that couple pressure (Borge & Sylta 1998, Borge 2000) and time-related stress (Lothe et al. in press).

The relation between hydraulic fracturing and leakage in sedimentary basins is not well known. It is recognized that large volumes of fluid can become trapped during significant overpressure build up in pressure compartments (Darby et al. 1996). A rapid fluid pressure release should be expected when the caprock fails (Cosgrove 1998). Capillary leakage of hydrocarbons is not taken into account in this work, because only the water phase flow is modelled. The failure mode will depend on the burial depth, stress regime and pressure. The simplest scenario assumes leakage along one fault (Verbeek & Grout 1993). Overpressures in this case will be highest at the top of the pressure compartment resulting in fault nucleation and growth from the reservoir into and through the caprock. Alternatively, fracture swarms may develop as shear failures in the deeper parts of the caprock and tensile failures in the shallower parts (Cosgrove 1998). This is illustrated in Figure 1, where high overpressures have build up in the deepest part of the reservoir. Low transmissibilities across non-juxtapost reservoir faults decrease the lateral fluid flow and hydraulic failure and leakage will occur. Reactivation of pre-existing faults is a third possibility (Wiprut & Zoback 2002). However, mechanisms involving slip along pre-existing fault zones facilitated by overpressure build-up or tectonism are not considered. We will analyse possible overpressure initiated failure at the highest point of the compartments along faults with shear failures at deep burial depths and mixed or tensile failures at shallower depths (Figure 1).

Lateral fluid flow between pressure compartments is an important and sometimes controlling factor on pressure build-up in an overpressured basin. Lateral fluid flow in faulted reservoir systems is predominately controlled by the permeability of the major bounding faults. Different attempts have been made to measure fault permeabilities in the laboratory (Morrow et al. 1984, Zhang et al. 2001, Sperrevik et al. 2002). Sperrevik et al. (2002) observed a relationship between the fault permeability and the mineralogy of the faulted rock, the effective stress conditions, and the history to the reservoir prior to, during and after deformation. They measured very low permeabilites (<10-7 mD) in faults with clay smears at depth (>3.5 km). The fault rock permeability with a phyllosilicate-framework lies in the order of <10-4 mD at >3.5 km depth. Revil & Cathles (1999) present examples of measurements in shaly sands, and demonstrated a rapid decrease in permeability with increasing clay content. Zhang et al. (2001) claimed that large permeability anisotropy due to anisotropic alignment of clay shape fabrics is important in focusing flow along faults in clay-rich rocks. In the present work we do not discuss the mechanisms of how lateral flow across a major fault could occur, but rather

-83- consider how changes in the fault permeability may influence hydraulic fracturing and leakage.

Hydrocarbon leakage is expected to be sensitive to hydraulic fracturing and water fluid leakage in an overpressured area. Hydrocarbon fill history is also time-dependent and relies on the charge, trapping, hydraulic fracturing and leakage histories. In this study we are concerned with the aim of predicting and quantifying the uncertainties regarding the timing and amount of leakage from overpressured areas. The results may be used in basin modelling estimates for undrilled prospects.

The simulations in this study are carried out on a data set from the Halten Terrace, offshore Mid-Norway (Figure 2). The pressure distributions in this area is described in e.g. Teige et al. (1999), Skar et al. (1999) and Berg et al. (2000), and pressure simulations have been carried out by Borge (2000, 2002) and Lothe et al. (in press). The geology in the area has been extensively described; see Koch & Heum (1995) and Blystad et al. (1995) for further information. The study area is selected because of two main reasons: 1) None of eight wells penetrating Jurassic reservoir rocks at Haltenbanken prior to 1996 found hydrocarbon, and cap rock leakage seemed to be the main explanation for these results. Later drilling have however results in hydrocarbon discoveries (Hermanrud & Bolås 2002). 2) A pressure compartmentalisation is described in the area (e.g. Berg et al. 2000). The main focus of this paper, however, will be on the method and not on the specific study area.

Pressure

Tensile fractures Caprock Hydraulic fracturing

Shear fractures Reservoir

Overpressured zonezone Depth

Figure 1 Sketch showing hydraulic fracturing and leakage of fluids from overpressured reservoir units.

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4° 6° 8° 10°

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Trøndelag NORWAY Møre 50 km 20 km

Figure 2 Left map shows the Mid-Norwegian region, where study area is marked. Modified from Blystad et al. (1995). Right map shows present-day depth map of the top reservoir (top Garn Formation). Calibration wells and major faults at top reservoir are marked. Frame shows area presented in Figures 8 and 12.

Methods and data In the present study the fault traces mapped at the top reservoir level delineate the lateral extent of the pressure and stress compartments that are utilized in a pressure and stress simulator (“Pressim”, Borge 2000, Lothe et al. in press). The lateral Darcy flow of formation water across low-permeable faults is calculated using an explicit forward Euler solution technique (Borge 2002). Effective top seals stop flows out of compartments. Depth-converted maps of the overlying sediments are used to construct the burial history that is adjusted for decompaction. The development of pressure and stresses are reported for a series of time steps. Time steps are correlated to the depositional ages of the stratigraphic horizons that are used to build the model. Porosity-depth relation in the shales is used to model mechanical compaction and a kinetic model for quartz cementation (Walderhaug 1996) is used to model chemical compaction of the sands. Hydrocarbon migration is not taken into account in this work that present one-phase simulation.

The geo-mechanical properties for the caprock are allowed to vary through time with changing burial depths (Lothe et al. in press). Isotropic horizontal stresses are assumed and the minimum horizontal stress is estimated using an empirical formula (Grauls 1996). The vertical stress varies versus time depending on sedimentary loading. No strain is included and a passive sedimentary margin is assumed. Fault permeability is

-85- modelled as depth dependent. The fault transmissibility depends on the burial depth, the length, width and the dip-slip displacement of the faults, thickness of the reservoir layers and the permeability inside the fault block (Borge & Sylta 1998). Juxtaposition faults (faults where the reservoir is self-juxtaposed) have high transmissibilites, while faults with no overlap have lower transmissibilites. The Griffith-Coulomb failure criterion and the frictional sliding criterion are used to simulate hydraulic fracturing from the overpressured compartments (Figure 3).

The data used are a present-day depth-converted map of the top reservoir unit (top Garn Formation), the present-day thickness of the reservoir, and a fault map at top reservoir level (Figure 2 & Table 1). Drill stem tests and formation tests are used for the pressure measurement in the different wells. The pressure data from 43 wells in the area are available at the top reservoir level, and are used to calibrate the model (Table 1). The 1 n mean deviation ( mean deviation= ∑ Pi, measured − Pi,modelled ) is calculated between n i=1 modelled and measured overpressure in the pressure compartments containing pressure observations from wells. An arbitrary paleo-water depth of 200 m is used in the study area. Poisson’s ratio and Young’s modulus are varied with depth, based on calibration with laboratory measurement of North Sea Shale (Horsrud et al. (1998), see Lothe et al. in press). The input parameter used in the base case is listed in Appendix. The fault permeability used in the base case is empirical (see discussion), but will be varied in the sensitivity runs. The simulations covers the flow and stress development for the last 90 Ma.

Table 1 Input data used in the simulations Input data Pressim - water flow simulations Depth-converted Seven time-steps; 90 Ma, 80 Ma, 65 Ma, 20 Ma, 5 Ma, 2 Ma and Present seismic horizons Isopach map reservoir Garn Formation (185 Ma - 160 Ma) Fault maps Fault map at top Garn Formation level Pressure data Pressure measurements in Garn Formation from 43 wells used to calibrate the simulations. The wells are 6407/8-2, 6407/7-3, -5, 6407/9-1, -2, -3, -4, -5, -6, 6407/4-1, 6407/9-7, 6406/8-1, 6407/2-1, 6407/6-4, 6406/3-1, 6407/2-3, 6406/6-1, 6406/2-6, 6506/12-1, -3, -5, -8, 6407/1-1, -2, -3, 6406/3-2, -4, 6406/2-3, 6507/11-4, 6507/12-1,2, -3, 6407/2-2, 6507/11-2 (see also Lothe et al. in press).

Shear stress (τ) Frictional µ' µ sliding failure envelope Griffith-Coulomb failure envelope

Normal stress (σn) σ σ3 1

Figure 3 Failure criteria used in the simulations.

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Results The aim of the simulations was to determine which input parameters will have a major impact on the timing and extent of hydraulic leakage in an overpressured sedimentary basin. A base case was run to use as a reference for simulation methods. The base case illustrates the variations in the modelled pressure and hydraulic leakage. Different simulations were carried out by varying the coefficient of internal friction (µ) and the coefficient of frictional sliding (µ’; see also Lothe et al., in press). The time-dependent sensitivity of late hydraulic fracturing and amounts of leakage were studied by varying the permeability and thereby the transmissibility of major faults that control the lateral extent of the pressure compartments.

The pressure build-up over the last 90 Ma was simulated for the base case. Figure 4 illustrates the overpressure distribution in the area from 5 Ma to present day. Hydrostatic pressures prevail in nearly the whole basin at 5 Ma. Between 5 Ma and 2 Ma a rapid pressure increase occurs in the western part of the area. This trend continues until today, with an increase in overpressure in the most deeply buried units and a spreading of the overpressured part of the simulated area (Figures 4 & 5). The high overpressures lead to hydraulic fracturing and leakage through the caprock above the reservoir between 2 and 1.5 Ma (Figure 5). The modelling shows that the failure strength is exceeded only in the compartments with the high overpressures (Figures 4 & 5). One of the compartments where hydraulic fracturing occurs is compartment K (Figures 6 & 7, located in Fig. 8a). In the simulation this compartment reaches its limits for hydraulic fracturing at 1.9 Ma, which is marked with a peak in the leakage rate (Figure 7). When we study the changes in effective stress through time in this compartment, we observe a rapid decrease when the pressure increases (Figure 7). The first rapid increase in overpressure starts around 5 Ma. At around 3.2 Ma the overpressure decreases, before a new peak builds up around 1.9 Ma.

From the evaluation of the overpressure curves one would perhaps expect hydraulic leakage to occur around 3 Ma in compartment K. However, the model suggests that this does not happen until 1.9 Ma (Figure 7). The reason is that the neighbouring compartments to K, WK and EK start to leak around 3.2 Ma (Figure 8). This leads to a loss in accumulated overpressure in K around 3 Ma and illustrates that leakage from one compartment may have a critical effect on leakage from neighbouring compartments. The same effect is observed in the south, where early leakage in compartment P controls the timing of later leakage in compartment WP.

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20 km 20 km 20 km 20 km 5 Ma 2 Ma 1.5 Ma Today pressure (bar) Figure 4 The development of simulated overpressure using the base case during the last 5 Ma in the western part of the study area. Grey scale shows overpressures in bars.

20 km 20 km 20 km 20 km Cum. leakage 5 Ma 2 Ma (m3/comp) 1.5 Ma Today Figure 5 Development of hydraulic fracturing and leakage during the last 5 Ma in western part of study area for the base case. Grey scale indicates cumulative leakage in m3/compartment.

160 4.0E+07 Cum.Leakage 3) ) 140 3.5E+07 (m 0y Leak-rate

120 3.0E+07 e 00 g a 10 100 2.5E+07 k 3/ a e

m 80 2.0E+07 l e ( 60 1.5E+07 ve ti at r a - 40 1.0E+07 l u ak e 20 5.0E+06 m L u 0 0.0E+00 C 6 5 4 3 2 1 0 Time (Ma)

Figure 6 Modelled cumulative leakage (m3) and leakage rate (m3/10000y) for compartment K during the last 6 Ma. Note that leakage occurs in one major pulse.

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Hydraulic 500 leakage 450 400

350 ) ar

300 b Overpressure ( e 250 r sig_3' 200 sig_1' essu r

150 P 100 50 0 6 5 4 3 2 1 0 Time (Ma)

Figure 7 Modelled overpressure (bar), effective minimum horizontal stress (bar) and effective vertical stress (bar) for compartment K. Note rapid pressure build-up around 5 Ma. Hydraulic leakage is modelled to occur around 1.9 Ma (see Fig. 6).

a) b)

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Figure 8 a) Leakage volumes in different pressure compartments. Grey scale shows cumulative leakage to present day (m3). b) Timing of leakage from the different compartments in the study area. The earliest leakage event from compartments WK, EK and K is marked.

The significance of coefficient of internal friction and frictional sliding Pressure generation processes started to become effective during the last 5 Ma in the basin. This is mainly due to rapid late burial and the associated quartz cementation in the reservoir unit (Dalland et al. 1988, Teige et al. 1999). In the simulator, two failure criteria were used, first the Griffith-Coulomb and secondly the frictional sliding criterion (Figure 3). To test which parameters control the amount and timing of hydraulic fracturing and leakage, the coefficients of internal friction (µ) and frictional sliding (µ’) were varied (Figure 9). In the base case µ= 0.6, and µ’=0.7 (Figure 6). Figure 10 shows results from such simulations where the coefficients are varied, from

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µ=0.3 and µ’=0.7, to µ=0.6 and µ’=1.0. These simulations gave minor changes in the leak-rate, cumulative leakage (2.2-2.5·107 m7) and the timing (<150 Ka) for the failure (see also Lothe et al. in press). The largest changes were found in the peak leakage rates at failure for very high values for µ’ (1.0), which result in lower peak leakage rates (Figure 10b).

Shear stress (τ)

µ’ = 1.0 µ’ = 0.7 µ = 0.6

µ = 0.3

Normal stress (σn) σ 3 σ1

Figure 9 The coefficients of internal friction and frictional sliding used in two different simulations (µ=0.3 and µ’=0.7, and as µ=0.6 and µ’=1.0). a) b)

160 4.0E+07 160 4.0E+07 3) 140 3.5E+07 3) 140 3.5E+07 m e ( 120 3.0E+07 e (m 120 3.0E+07 10000y) 10000y) 100 2.5E+07 100 2.5E+07 3/ 3/ eakag eakag m m 80 2.0E+07 80 2.0E+07 l l e ( e ( ve ve

60 1.5E+07 60 1.5E+07 i t ti a a l 40 1.0E+07 40 1.0E+07 l u u eakag eakag m m L 20 5.0E+06 L 20 5.0E+06 u u C 0 0.0E+00 0 0.0E+00 C 6 4 2 0 6 4 2 0 Time (Ma) Time (Ma) Figure 10 Cumulative leakage (m3) and leakage rate (peak)(m3/10000y) in compartment K in runs with a) µ=0.3 and µ’=0.7 and b) µ=0.6 and µ’=1.0.

Significance of the permeability across major faults Sensitivities of the timing of failure and amount of leakage to fault permeability was also tested (Figure 11). The fault permeability curve used is discussed in Borge & Sylta (1998), where kinks in curves are supported by Loosveld & Franssen (1992). The fault permeability curves are based on empirical data (see discussion) and also on the calibration between simulated pressures and measured pressures in the basin. The permeability values were applied in a low, base and high case for all the master faults that define pressure compartments (Figure 12). Using low fault permeabilities resulted in a pressure build-up that takes place at an earlier stage. More compartments therefore suffer from hydraulic fracturing and leakage compared to runs using higher

-90- permeabilities (base and high case) (Figure 12). Using high permeabilites resulted in some compartments that did not fail at all. The timing of failure in compartments WK, EK and K, in the northern part of the study area, differed with only a few hundred thousand years when the low and the base case were compared (Figure 12b & d). Comparing the base case and the high case however, a marked delay in the timing of the hydraulic fracturing for compartments WK and EK, from 3.3 Ma to 1.8 Ma is observed, and there is no leakage from compartment K (Figures 12d & f). In the southern area compartment P fails approximately 1 Ma earlier in the low case compared to the high case. For the neighbouring compartment WP, no leakage is observed in the high case.

For the same three cases, the cumulative leakages for the respective compartments have been calculated (Figure 13). The results for the base case show that the highest cumulative leakage took place from compartment EK in the northern area and compartment P in the southern area. Because the amounts of leaked fluid from the two compartments were much larger than from the neighbouring compartments, the two would control the amount and also the timing for the leakage in the neighbouring cells. Compartment K is as an example of this effect (Figures 7 & 8). There is a progressive reduction in the total amount of cumulative leakage due to the time-dependency when comparing the leakage from compartment EK in the low, base and high cases (Figure 13). This is also observed for other compartments, except for compartment P, which displays an increase in cumulative leakage in the high case compared to that of the base case. This is because the neighbouring compartment to the south (compartment S) does not fail in the high case (Figures 12e & 13c). Accordingly, higher fluid pressures are developed in compartment P and the cumulative leakage is much higher relative to those in the low and base cases. This effect overrules the effect of timing on the cumulative leakage in this example.

A strong dependence on fault permeability for both the timing of hydraulic failure and hydraulic leakages rates noted from the previous descriptions. To quantify the uncertainty in the simulations, fault permeabilities have been systematically varied to investigate their effect on the timing and amount of leakage in selected overpressured compartments. As shown in Figure 11, the permeability across the faults varies according to depth of burial. To be able to compare the different cases, the permeability typical for a burial depth of 4 km was used. Figure 14 shows how the timing of leakage varies versus fault permeability for results for compartment K analysed in isolation. Figure 15 shows the same sensitivity for other overpressured compartments in the study area. The data points on the curves show at which time a particular compartment fails in different permeability runs when the permeabilities of the fault zones are varied.

The simulations show a strong dependency of the permeability across the major faults on the timing of hydraulic fracturing in overpressured areas. An early and significant build-up of overpressure was displayed in the simulation runs where a low permeability was applied. However, deviations between the simulated pressures and pressures measured in wells are large (Figure 15). This is because the early hydraulic fracturing gives too high leakage rates and too low simulated pressures for the present situation. When high fault permeabilities are used few compartments, and in the extreme case no compartments, will fail. A marked jump in the timing (from 5 Ma back to greater than 20 Ma) of the hydraulic failure in the different compartments for varying permeability models is observable in Figure 15. It changes from a very early failure using low permeability input, to late failure using higher permeabilities. Studying the changes

-91- during the last 5 Ma in more detail, we observe less change in timing of leakage from around 4 to 3.5 Ma and from 1.9 Ma to 1.7 Ma (Figure 16). This is typical for all of the studied compartments, except for compartment P, which fails in all cases.

When cumulative leakage versus permeability is studied, two compartments with higher leakage rates are observed; compartment EK in north and compartment P in south (Figure 17). These two compartments show high cumulative leakage in the runs when they go to failure using low permeability faults, but a rapid decrease in leakage approaching no failure with high permeability faults. The deviations between simulated pressures and those measured in the calibration wells for the varying permeability runs increase when the permeability is either very low and an early leakage occurs or permeabilites are very high and no failure occurs (Figure 17).

In the northern area, the first leakage is observed for compartments EK and WK followed by compartment K for all simulated fault permeabilities (Figure 18a). Cumulative leakage versus permeability curves are used to distinguish between compartments EK and WK (Figure 18c). Leakage is markedly higher for compartment EK at low fault permeabilities, because a larger fluid pressure has built up in this compartment due to its deep burial and to the relative size of the compartment. This compartment controls the leakage in the smaller, neighbouring compartments. There is also a relative decrease in the leakage from compartment EK in the runs where compartment K has a larger leakage at a permeability of 1·108 mD (Figure 18c). Studying the cumulative leakage in the three different compartments and the uncertainty in the runs, we see that compartment WK will most likely go to failure, but at low leakage rates (Figures 18a & c). Compartment K will have a low leakage rate if the compartment goes to failure using low permeabilities (<1·107 mD). Using high permeabilities, the compartment will not fail (Figure 18c).

In the southern area, the timing of leakage does not show such a clear trend for varying permeability runs as in the north. Compartment WP is an exception, in that it has the same plateaus in the timing of failure as the northern compartments (between 1.8-2 Ma, and between approx. 4.5 -3.6 Ma; Figures 18a & b). For compartments P and S, the timing is more linearly linked to the permeability (Figure 18b). This is because S is the largest compartment in this area, with high hydraulic leakage rates at low fault permeabilites (Figure 18d). Therefore it influences the leakage from compartment P, where an increase in the cumulative leakage is observed for lower permeability runs when compartment S is still intact (Figures 18b & d). The amounts of hydraulic leakage vary significantly for the low, base and high cases, especially for the two largest compartments in the northern and southern areas, compartment EK and compartment P, respectively (Figures 18c & d).

When plotting the timing of hydraulic fracturing versus cumulative leakage for all the compartments, a linear trend in each compartment between 5 Ma and Present emerges (Figure 19a). When failure occurs before 5 Ma, extreme values for cumulative leakage are observed. A similar situation is seen for runs with large mean deviations (>15 bar; Figure 15). A linear trend between timing and amount is observed for the small compartments during the last 5Ma (Figure 19b). The two larger compartments (P and EK) are characterized by a more complex relationship between timing and cumulative leakage.

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Fault permeability (mD)

1.E-09 1.E-07 1.E-05 1.E-03 0

1000

) 2000 pth (m e 3000 D

Low case 4000 Base case High case 5000

Figure 11 Depth dependent fault permeabilities used for three different cases; low, base and high case used as modelling input for all faults in the study area.

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a) b) Low fault permeability case

) 3 0y

00 2300 0 1 250 EK P

3/ 2

K ) m WP

( 200

EK e t

WK a g( 150 K e r 100 WK ag k

a 50 e

WP L 0 P 4 3.5 3 2.5 2 1.5 1 0.5 0 Time (M a)

10 km c) d) Base fault permeability case

300

K 10000y) 250 P 3/ EK K 200 EK (m e WK t 150 WP a WK e r 100

50

WP eakag L 0 P 4 3.5 3 2.5 2 1.5 1 0.5 0 Time (M a)

10 km e) f) High fault permeability case

300

10000y) EK

/ 250 P 3 EK 200 (m e t 150 WK a

e r 100 WK 50 eakag L 0 4 3.5 3 2.5 2 1.5 1 0.5 0 P Time (M a)

S 10 km

Figure 12 Fault permeabilities varied in the low, base and high cases. Maps a, c, and e) present cumulative leakage in the different compartments. (Colour scale as in Figure 8; m3). Graphs b, d and f) show the variation leakage throughout the last 4 Ma. Note that enhanced permeability causes delay in the timing of the hydraulic fracturing.

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a) Low fault permeability case

1.0E+08

8.0E+07 EK P 6.0E+07 WP 4.0E+07 WK 2.0E+07

K 0.0E+00 Cumulative leakage (m3) 4 3.5 3 2.5 2 1.5 1 0.5 0 Time (M a)

b) Base fault permeability case

1.0E+08

8.0E+07

EK 6.0E+07 P 4.0E+07 ve leakage (m3) K WK 2.0E+07 WP 0.0E+00 Cumulati 4 3.5 3 2.5 2 1.5 1 0.5 0 Time (M a)

c) High fault permeability case

1.0E+08

8.0E+07

6.0E+07 EK P 4.0E+07 WK 2.0E+07

0.0E+00 Cumulative leakage (m3) 4 3.5 3 2.5 2 1.5 1 0.5 0 Time (M a)

Figure 13 The cumulative leakage with time in the three fault permeability cases for different compartments.

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35 ) a

M 30 (

e

r 25 u il

a 20 f l

ia No t 15 i hydraulic in

f 10 failure o 5 me i T 0 1.0E-09 1.0E-08 1.0E-07 1.0E-06 Fault permeability (mD)

Figure 14 Time of hydraulic failure for compartment K versus fault permeability at 4 km depth. The data points show results from different runs. The highest fault permeability gives no pressure build-up and, hence, no hydraulic fracturing in the compartment.

50 25 Base ) 45 a Low High K M Me

( 40

e 20

an WK r

u 35 d il

a EK 30 e v l f i at ia 25 15 P it io in n 20 f

WP ( b o ar e 15 10 Mean dev m ) i 10 T 5 0 5 1.0E-09 1.0E-08 1.0E-07 1.0E-06 Fault permeability (mD)

Figure 15 Timing of failure in different compartments depending on the fault permeability at 4 km depth. The right y-axis shows the mean deviations between measured and simulated pressures in the whole basin in the different runs. The fault permeabilities used in the low, base and high cases are marked.

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5 25 Base

Low High )

a 4 Me M

( 20 K e an r d

ilu WK

3 e a viat l f EK ia 15 io it n

in 2

( P f b o ar e WP )

m 10 i

T 1 Mean dev

0 5 1.0E-09 1.0E-08 1.0E-07 1.0E-06 Fault permeability (mD)

Figure 16 Illustration of the fault permeability at 4 km depth versus timing of hydraulic leakage in the different compartments for the last 5 Ma. The right y-axis shows the mean deviations in the different runs. The fault permeabilities used in the low, base and high cases are marked.

1.2E+08 25 Base Low High

) 1.0E+08 3 Me

m 20 a

e ( K 8.0E+07 n de

ag WK

v EK i ati leak 6.0E+07 15 P on ve i WP (ba lat Mean dev u 4.0E+07 r m )

u 10 C 2.0E+07

0.0E+00 5 1.0E-09 1.0E-08 1.0E-07 1.0E-06 Fault permeability (mD)

Figure 17 Cumulative leakage (m3) versus permeability (mD) for the simulated fault at 4 km burial depth. Note the high cumulative leakage simulated for compartments EK and P. The right y-axis shows the mean deviations in the different runs. The fault permeabilities used in the low, base and high cases are marked. Note that the base and high case give mean deviation <13 bar.

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a) b) Northern area Southern area ) ) a a

M 5 M

5 ( e e ( r

r 4 u l u 4 P i l

K a 3 WP 3 WK l f S ia

EK it

itial fai 2

2 n n i i f f

1 o 1 o e e m m i

i 0 0 T T 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-09 1.0E-08 1.0E-07 1.0E-06 Fault permeability (mD) Fault permeability (mD)

c) d) Northern area Southern area

1.2E+08 1.2E+08 ) ) 3 3 m m ( 1.0E+08 ( 1.0E+08

e e 8.0E+07 K 8.0E+07 P kag kag a a WP e WK e 6.0E+07 6.0E+07 S ve l EK ve l ti 4.0E+07 ti 4.0E+07 la la u u m 2.0E+07 m 2.0E+07 u u C C 0.0E+00 0.0E+00 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-09 1.0E-08 1.0E-07 1.0E-06 Fault permeability (mD) Fault permeability (mD)

Figure 18 Timing of hydraulic fracturing versus permeability across faults in a) northern study area and b) southern study area. Cumulative leakage versus fault permeability in c) the northern and d) southern area. The largest amounts of leakage are simulated for EK and S.

a) b)

50 5 45 ) ) a 40 a 4

M K ( e (M 35 e r r u l

K u WK i

30 il a 3 a f WK EK 25 l f a i

itial EK it

in P

20 n 2 f P i

f o

e 15 WP WP o m i me T

10 i 1 T 5 0 0 0.0E+00 4.0E+07 8.0E+07 1.2E+08 0.0E+00 4.0E+07 8.0E+07 Cumulative leakage (m3) Cumulative leakage (m3) Figure 19 Time of hydraulic failure versus cumulative leakage for all the compartments during a) the last 50 Ma and b) the last 5 Ma. The smallest compartments (WK, K and EK) show a linear relationship in the last 5 Ma.

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Discussion Uncertainty is an important issue to address in order to evaluate the quality of the simulations. Therefore, well measurements of present reservoir pressure were used to calibrate the simulations. Unfortunately pressure data are not available for the caprock. Furthermore, not only the pressure measurement would be of interest to estimate, but also the possibilities for hydrocarbon shows. However, many of the highly overpressured compartments that have been simulated in this study, have not yet been drilled and calibration is therefore not possible. Using the predictions from the present simulations, however, better estimates may be obtained.

We start out assuming that hydrocarbons have accumulated in the highly overpressured compartments. The preferred situation from an exploration point of view would be that the caprocks for these compartments did not fail. However, if one or more of the compartments did fail, the timing and the amount of leakage are important factors to evaluate. One scenario is that the pressure build-up may have lead to very early fracturing, but that the caprock subsequently became chemically healed, and the compartment could be refilled. This, however, does not appear to be the case in the study area, because hydraulic fracturing and leakage is predicted during the last 5 Ma. Late leakage may be optimal for accumulations of hydrocarbons, since only small amounts of fluid would have time to escape.

To rank the possibilities of hydraulic fracturing and leakage in the compartments we have studied three important factors; the timing, the amount of leakage and the size of the accumulation. As an example we can compare the timing and amount of leakage in compartments WP and WK (Figure 16). In this dataset, WP is the first compartment that does not go to fail when the permeability is increased in the simulations (Figure 16). However, by using lower permeabilities, the cumulative leakage for compartment WP increases rapidly due to earlier failure (Figure 17). Compartment WK may therefore contain a more preferable prospect for hydrocarbon exploration, even though modelling suggests leakage at high permeabilities (Figure 16). More important perhaps, is that the cumulative leakage in compartment WK seems to be small when low permeabilities are used (Figure 17). In such a case, the size of the field will be the controlling factor: for a large field it would be best for the hydrocarbon accumulation that a low, but steady leakage occurs. As seen directly from the cumulative leakage versus permeability plot (Figure 17), the large compartments, in this case EK and P, would have too large cumulative leakages to be good exploration targets. Thus, the smaller compartments with either late fracturing or early, but low leakage rates are more favourable.

The uncertainty assessment can be used to evaluate the predictability of the simulations. In Figures 16 and 17 show the mean deviation between measured and simulated pressures in all compartments where wells exists calculated. Large mean deviations are observed when very high or low fault permeabilities are used in the simulations. If one define a mean deviation of 13 bars to be acceptable, then the uncertainties in the simulations of the timing and cumulative leakage for one compartment like K can be considered. If a mean deviation of 13 bars is acceptable, then late leakage from compartment K is predicted from 1.9 Ma to Present day. The cumulative leakage is estimated not to exceed 29·106 m3. The runs with lower deviations do not fail (Figure 16). Compartment P most likely fails, except using high permeability values. The timing of the failure in compartment P is simulated between 2.5 to 0.6 Ma, with cumulative leakage in the scale of 280·106 m3 to 78·106 m3, respectively. An uncertainty limit of 15

-99- bar, gives more or less the same results for most compartments (Figure 17). Differences are observed when low permeabilities are used and the rate of leakage increases rapidly. A relatively large change in the modelled timing of hydraulic leakage and cumulative leakage is seen for compartments K and WP, when changing the “acceptable” deviation from 13 to 15 bars. Both fail from 1 to 1.5 Ma earlier, with higher leakage rates resulting (Figure 16 & 17).

Effects on hydrocarbon migration Different effects have to be taken into account when the probability of hydrocarbon leakage is evaluated. In the simulations, we assume leakage from the highest point in the structure, with less or no leakage down dip. Still, hydrocarbons may be trapped down dip in compartments that have expired hydraulic leakage at the crest. To be able to evaluate the probability for hydrocarbon reserves, more detailed studies of smaller areas, incorporating more faults, need to be carried out. The presence of internal minor faults in the compartments will influence fluid flow. Furthermore, assuming leakage from the highest point of the structure, time-delays in the leakage should be taken into account.

Comparison of permeabilities used in modelling with measured permeabilities Faults in clastic sequences often represent significant barriers to fluid flow. Fisher & Knipe (2001) measured the permeability of faults within siliciclastic rocks in the North Sea and the Norwegian Continental Shelf. Faults typical in impure sandstones (vshale 15-40%) have a permeability of ~0.001 mD at depths > 4 km. While, clay-rich sediments (vshale >40%) deform to produce clay smears with very low permeability (< 0.001 mD; Fisher & Knipe 2001). Sperrevik et al. (2002) observed a relationship between the permeability and the mineralogical composition of the faulted rock, the effective stress conditions, and the history of the reservoir prior to, during and after deformation. They measured very low permeabilities (< 10-7 mD) in faults with clay smears at depths (> 3.5 km). This is in accordance with the permeability values used in our simulations, which resulted in hydraulic failure in the simulations (Figure 20). With less clay content in the fault zones, the data from Sperrevik et al. (2002) gave too high permeabilities in the fault, and the pressure barriers are not effective enough to simulate hydraulic fracturing. According to this data set, lower permeabilities should be used when simulating the shallow part of the faults. However, since overpressure is unlikely to occur at this shallow depth of burial, this is probably not critical for the timing and amount of hydraulic leakage modelled. On the other hand, clay smear is probably not the controlling sealing factor in all the faults with deeper burial depths in the study area. Diagenesis and quartz cementation in the fault zones are processes that contribute to fault sealing at large depths. Therefore, better control on the lateral leakage would be gained by integrating the clay content of the faults during subsidence into the simulator.

In addition to the initiation of hydraulic fracturing, the continuation of fluid flow and leakage should be considered. Gutierrez et al. (2000) presents results from laboratory tests of extensional fractures in shales. The tests show a decrease in permeability during increasing normal stress across the fracture and after shearing of the fracture under constant high normal stress. However, the fractures never completely closed. This indicates that fractures once created are difficult to close by mechanical loading. Then, as long as sufficient hydraulic gradients are obtained, fluid can still flow along fractures even in the absence of large overpressures. The results from Gutierrez et al. (2000) are

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in accordance with the simulation of continuous leakage done by us, as long as the pressure compartment is fractured and is at the leakage pressure gradient.

In this article we have presented a type of analysis that can be carried out using a coupled pressure and stress simulator to evaluate hydraulic fracturing and leakage. The simulator itself is described in Borge (2002), Borge & Sylta (1998) and Lothe et al. (in press). Other input parameters than the ones discussed by us can influence the timing of fracturing. Lothe et al. (in press) shows a large influence of the geo-mechanical parameters used for the caprock (Poisson’s ratio and Young’s modulus). The handling of stresses in the simulator has room for significant improvements. Nevertheless, by varying the input parameters in different runs, the uncertainty in the simulations can be found with a larger confidence than we could before.

Fault permeability (mD)

1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 0 Too early 1000 caprock failure.

) Poor 2000 Caprock m match failure. h (

pt Good No e 3000 D match caprock failure. 4000 Poor match 5000

Figure 20 Variations in fault permeability used in the simulations giving hydraulic fracturing and leakage. Matches to the pressure measurements with wells outlined.

Conclusions The main conclusion from this work is that the transmissibilites across faults between overpressured compartments will have a major impact on the timing and amount of hydraulic fracturing and leakage and this can be simulated. Low fault permeabilities cause restricted lateral flow, overpressure build-up and early hydraulic fracturing, and the resultant simulated pressures, give then large deviations compared to the measured pressures in wells. High permeabilities give later failure and in some cases no failure in some compartments. The hydraulic leakage in one compartment will influence the amount and timing of leakage in the neighbouring pressure compartments. The largest compartments in an area will control the timing and amount of leakage in the smaller ones. The uncertainty in the simulations can be estimated by comparing the simulated pressures with the measured pressures in the wells, and thereby be able to improve risk prediction of hydrocarbon shows in undrilled traps.

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Acknowledgement We would like to thank Norsk Hydro ASA for their funding to Lothe’s PhD thesis on hydraulic fracturing, providing data, and giving permission to publish. Colleagues at SINTEF Petroleum Research are thanked for useful discussions. Roy H. Gabrielsen has kindly corrected an early version of the manuscript.

References Berg, T., Berge, K., Cecchi, M. Ekeli, C, Hansen, L., Norvik, O., Waters, D. 2000. Fault seal and overpressure analysis of Halten Terrace. Hydrocarbon Seal Quantification, Norwegian Petroleum Society. Extended abstract only. Blystad, P., Færseth, R. B., Larsen, B. T., Skogseid, J. & Tørudbakken, B. 1995. Structural elements of the Norwegian continental shelf, Part II. The Norwegian Sea Region. Norwegian Petroleum Directorate Bulletin, 8. Borge, H. 2000. Fault controlled pressure modelling in sedimentary basins, An thesis for the degree of Doktor Ingenør of the Norwegian University of Science and Technology, 148 pp. Borge, H. 2002. Modelling generation and dissipation of overpressure in sedimentary basins: an example from the Halten Terrace, offshore Norway. Marine and Petroleum Geology, 19, 377-388. Borge, H. & Sylta, Ø. 1998. 3D modelling of fault bounded pressure compartments in the North Viking Graben. Energy, Exploration and Exploitation, 16, 301-323. Bour, O., Lerche, I & Grauls, D. 1995. Quantitative models of very high fluid pressures: The possible role of lateral stresses. Terra Nova, 7, 68-79. Chapman, R. E. 1980. Mechanical versus thermal causes of abnormally high pore pressures in shales. AAPG Bulletin, 64, 2, 179-183. Cosgrove, J. W. 1998. The role of structural geology in reservoir characterization. In: Coward, M. P., Daltaban, T. S. & Johnson, H. (eds) Structural Geology in Reservoir Characterization. Geological Society Special Publications, London, 127, 1-13. Darby, D. Haszeldine, R. S. & Couples, G. D. 1996: Pressure cells and pressure seals in the UK Central Graben. Marine and Petroleum Geology, 13, 865-878. Dalland, A. G., Worsley, D. & Ofstad, K. 1988. A lithostratigraphic scheme for the Mesozoic and Cenozoic succession offshore mid- and northern Norway. Norwegian Petroleum Directory. Fisher, Q. & Knipe, R. J. 2001. The permeability of faults within siliciclastic petroleum reservoirs of the North Sea and Norwegian Continental Shelf. Marine and Petroleum Geology, 18, 1063-1081. Grauls, D. 1996. Minimum Principal Stress as a Control of Overpressures in Sedimentary Basins. Proceeding of the8th Conference on Exploration and Production. IFP Report No43313, IFP Ruil-Malmaison. Gauls, D. 1998. Overpressure assessment using minimum principal stress approach. Overpressure in Petroleum Exploration, Proc. Workshop, Bull. Centre Rech. Elf Explor. Prod., Pau, France, 22, 137-147. Gutierrez, M., Øino, L. E. & Nygård, R. 2000. Stress-dependent permeability of a de- mineralised fracture in shale. Marine and Petroleum Geology, 17, 895-907. Hermanrud, C. & Bolås, H. M. N. 2002. Leakage from overpressured hydrocarbon reservoirs at Haltenbanken and in the northern North Sea. In: Koestler, A. G. & Hunsdale, R. (eds) Hydrocarbon Seal Quantification. NPF Special Publication 11. Elsevier Science, Amsterdam, 221-231.

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Horsrud, P, Sønstebø, E.F. & Bøe, R. 1998. Mechanical and Petrophysical Properties of North Sea Shales. International Journal of Rock Mechanical Mining Science, 35, 1009-1020. Hunt, J.M. 1990. Generation and Migration of Petroleum from abnormally pressured fluid compartments. AAPG Bulletin, 78, 12, 1811-1819. Koch, J.-O. & Heum, O. R. 1995. Exploration trends of the Halten Terrace. In: Hanslien, S. (ed) Petroleum Exploration and Exploitation in Norway. NPF Special Publication. Elsevier, Amsterdam, 4, 235-251. Lothe, A. E., Borge, H. & Gabrielsen, R. H. in press. Modelling of hydraulic leakage by pressure and stress simulations and implications for Biot's constant: An example from the Halten Terrace area, offshore Norway. Accepted for publication in Petroleum Geoscience. Loosveld, R. J. H. & Franssen, R. C. M. W. 1992. Extensional vs. Shear Fractures: Implications for Reservoir Characterisation. SPE 25017. Miller, T.W. & Luk, C.H. 1993: Contributions of compaction and aquathermal pressuring to geopressure and the influence of environmental conditions: Discussion. AAPG Bulletin, 77, 2 6-10. Morrow, C. A., Shi, L. Q. & Byerlee, J. D. 1984. Permeability of fault gouge under confining pressure and shear stress. Journal of Geophysical Research, 89, 3193-3200. Revil, A. & Cathles, L. M. 1999. Permeability of shaly sands. Water Resources Research, 35, 651-662. Skar, T., Balen, R. T. v., Arnesen, L. & Cloetingh, S. 1999. Origin of overpressures on the Halten Terrace, offshore mid-Norway: the potential role of mechanical compaction, pressure transfer and stress. In: Aplin, A. C., Fleet, A. J. & Macquaker, J. H. (eds) Mud & Mudstones: Physical and Fluid Flow Properties. Geological Society of London, London, 158, 137-156. Sperrevik, S., Gillespie, P. A., Fisher, Q. J. & Knipe, R. J. 2002. Empirical estimation of fault rock properties. In: Koestler, A. G. & Hunsdale, R. (eds) Hydrocarbon Seal Quantification. NPF Special Publication. Elsevier Science B.V., Amsterdam, 11, 109- 125. Swarbrick, R. E. & Osborne, M. J. 1998. Mechanisms that generate abnormal pressures: an overview. In: Law, B. E., Ulmishek, G. F. & Slavin, V. I (eds) Abnormal Pressures in Hydrocarbon Environments, AAPG Memoir, 70, 13-34. Teige, G. M. G., Hermanrud, C., Wensaas, L. & Bolås, H. M. N. 1999. The lack of relationship between overpressure and porosity in North Sea and Haltenbanken shales. Marine and Petroleum Geology, 16, 321-335. Verbeek, E. R. & Grout, M. A. 1993. Geometry and structural evolution of gilsonite dikes in the eastern Uinta basin, Utah. U.S. Geological Survey Bulletin, 1787, 42. Walderhaug, O. 1996. Kinetic modelling of quartz cementation and porosity loss in deeply buried sandstone reservoirs. AAPG Bulletin, 80(5), 731-745. Wiprut, D. & Zoback, M. D. 2002. Fault reactivation, leakage potential, and hydrocarbon column heights in the northern North Sea. In: Koestler, A. G. & Hundale, R. (eds) Hydrocarbon Seal Quantification. NPF Special Publication. Elsevier Science B.V., Amsterdam, 11, 203-219. Zhang, S., Tullis, T. E. & Scruggs, V. J. 2001. Implications of permeability and its anisotropy in a mica gouge for pore pressures in fault zones. Tectonophysics, 335, 37- 50.

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1.1.1.1.1 Appendix A Values of parameters used in the simulations (see Borge (2000) for explanation of parameters and nomenclature)

Description Symbol Value Unit Pressure generation and accumulation

Accumulating depth zA 2500 m

Generating depth zS 4100.0 m Salinity s 50000 ppm Accumulating exponent A 3.45 Shale drainage thickness γ 100.0 m

Minimum reservoir thickness zmin 0.10 m Minimum net/gross ratio N/Gmin 0.050 Maximum shale compaction depth zshale 10000.0 m Hydrostatic gradient 0.1030 bar/m ρw g Lithostatic gradient ρg 0.220 bar/m Time step ∆t 10000 years Diameter of quartz grain size D 0.0003 m Fraction of detrital quartz f 0.65 Molar mass of quartz M 0.06009 kg/mole Density of quartz 2650.0 -3 ρquartz kg ⋅ m D Temperature at which quartz cementation starts TC0 80.0 C D Temperature at which quartz cementation is TC1 175.0 C completed 2 Quartz precipitation rate factor r1 1.98e-18 mole/m s D -1 Quartz precipitation rate exponent r2 0.022 C Sand porosity at seabed 0.45 φS 0 Sand porosity constant 1 2400 m η1 Sand porosity constant 2 0.50 η2 D Temperature at seabed T0 4.0 C Temperature gradient ∂Tz/ ∂ 0.035 D Cm-1 Irredusible water saturation (Garn Formation) 0.040 φC1 Clay coating factor (Garn Formation) C 0.50 3 Minimum dissipation volume Vmin 1.0e+06 m Hydraulic leakage Poisson’s ratio (shales) at surface ν 0.40 z0 Poisson’s ratio (shales) at accumulating depth ν 0.27 zA Poisson’s ratio (shales) at sealing depth ν 0.20 zS Poisson’s ratio (shales) at max. shale comp. depth ν 0.02 zshale Young’s modulus (shales) at surface E 600 bar z0 Young’s modulus (shales) at accumulating depth E 20000 bar zA Young’s modulus (shales) at sealing depth E 40000 bar zS Young’s modulus (shales) at max. shale comp E 90000 bar depth zshale Coefficient of thermal expansion 1.00e-05 αT

Bulk modulus (shale) Ks 170000.0 bar

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Coefficient of internal friction µ 0.6 Coefficient of sliding friction µ ’ 0.7 Lateral transmissibility Lateral transmissibility 0.00069 Percent transmissibility remaining at no overlap p 0.05 Width of fault blocks b 20.0 m Porosity at seabed 0.45 φ0 Rate of change in porosity versus depth c 0.00039 m-1 Porosity where the K - curve changes between 0.1 φ φb deep and shallow relationships Permeability where the K - φ curve changes Kb 0.00001 mD between deep and shallow relationships -1 Rate of change in fault zone permeability (log) δ 5.0 mDm versus depth (log) for shallow faults sh -1 Rate of change in fault zone permeability (log) δ 7.0 mDm versus depth (log) for deep faults de

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Chapter 5

Sub-seismic faults and their possible influence on overpressure and hydraulic leakage - examples from offshore Mid-Norway

Lothe, A.E.1, 2, Borge, H.1 & Gabrielsen, R.H.2

1Sintef Petroleum Research, N-7465 Trondheim, Norway, 2Geological Institute, University of Bergen, Allêgaten 41, N-5007 Bergen, Norway

Abstract______

The sealing properties of the major fault in a sedimentary basin are potentially important, time-variable parameters in the evaluation of lateral fluid flow. The sealing capacity of fault depends on lithology, burial depth, diagenesis and throw. Though, large uncertainties are associated with the interpretation of hardly detectable faults where such occur in the continuation of larger fault zones on seismic. Such sub- seismic faults can contribute to the establishment of pressure compartments in sedimentary basin.

The study utilizes a seismic dataset from the Halten Terrace, offshore Mid-Norway. A fault map at the top of the reservoir unit (top Garn Formation) was constructed and is used to define the pressure and stress compartments. The pressure distribution and lateral pressure variance were simulated for the reservoir unit during the last 90 Ma. The transmissibilites across fault zones depends on the throw and width of the fault zones. Griffith-Coulomb and frictional sliding criteria are used to simulate hydraulic fracturing from the top points of the overpressured compartments.

Simulations show that the transmissibilities across individual fault situated in highly to intermediate overpressured areas in the sedimentary basin, have a major influence on the pressure distribution in the neighbouring compartments. The higher transmissibility the major fault has, the larger are the neighbouring areas, which are influenced. In the whole basin, the changes in pressure are minor. Changing the transmissibilites in low-pressured areas gives minor changes in the simulated pressure distribution. Several runs where sub-seismic faults are removed as pressure barriers have been carried out. Predictions have been carried out to quantify the uncertainty regarding timing and amount of hydraulic leakage from these areas. The results can be used in basin modelling to estimate hydrocarbon fills in undrilled prospects.

Keywords: hydraulic fracturing, hydraulic leakage, overpressure, basin modelling____

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Introduction Fault seal prediction has become one of the most important considerations in petroleum exploration in recent years. The sealing potentials of major faults are of special importance in overpressured sedimentary basins, sometimes controlling the pressure distribution in an area. The sealing capacity of a fault depends mainly on the lithology, juxtaposition, burial depth, diagenesis and throw (Knipe 1992). Knipe et al. (2002) discuss the uncertainty of the estimates of sealing capacity of faults, including sedimentary architecture, fault zone geometry, trap geometry, fault rock properties and upscaling. Townsend (2002) emphasises that fault geometry is on of the most important aspects for the sealing properties of such. However, from reflection seismic data, only information about the faults above seismic resolution can be obtained (i.e. commonly with dip-slip displacement of more than 20 m), because faults with displacement less than approximately one-quarter of the seismic wavelength would not be detectable. Furthermore, faults that appear continuously in the strike-dimension may in reality be segmented due to sub-seismic relay structures. Hence, there is particularly large uncertainties associated with the interpretation of smaller faults where such occur in the continuation of the strike of larger faults. Fossen & Hesthammer (2000) show that such “process zones” rarely will be visible in reflection data.

Fault interpretations based on reflection seismic data are usually a single deterministic realisation: Different interpretations of the data are often possible, but alternative realisations are rarely produced. In accordance to an accurate interpretation of fault traces, which may be merged into surfaces, the interpretations of the seismic horizons have to be realistic. In the vicinity of fault zones, the quality of the seismic data is usually poor, and interpretations of geological surfaces are accordingly difficult to quantify. Auto tracking and/or manual interpretation can be used to constrain horizons around faults, but errors in the order of >10m when a fault displacement is concerned is not unusual (Townsend 2002). Sometimes this causes highly variable displacement recordings along strike of individual faults.

Still, sub-seismic faults and faults which are near the seismic resolution can contribute to the establishment of pressure cells in overpressured parts of basins. Childs et al. (2000) report a large pressure difference (128 bar) across a fault with a small dip-slip displacement (~50 m) which juxtaposes high permeability reservoir rocks in the Viking Graben. They conclude that the low fault transmissibilites are connected either to shale smear or, less likely, to extensive quartz cementation in the fault rock. Lescoffit & Townsend (2002) found that in reservoir modelling, the fault populations play an important role on the resulting production forecast. By introducing sub-seismic faults, the recovery estimate changed markedly.

Compartmentalization of pressure can be simulated, defined by the fracture pattern at the top of the reservoir unit in a sedimentary basin (Borge & Sylta 1998, Borge 2002, Lothe et al. in press & prep). Such compartmentalisation of the pressure is supported by studies at the Halten Terrace (Skar et al. 1999, Borge 2002, Lothe et al. in press & prep) and from observations from the UK Central Graben where the pre-Cretaceous fault pattern controls the magnitude and distribution of overpressure (Darby et al. 1996). Grauls et al. (2002) tried to quantify fault seal in compartmentalised structures using fluid pressure data in different areas (Caspian Sea, South China Sea, Gulf of Mexico and North Sea, UK). The pressure-generating mechanisms itself, as discussed in Osborne & Swarbrick (1997), will not be further outlined here. However, when

-107- overpressure is generated and dissipated, it is important to have an understanding of how large parts is related to lateral fluid flow alone. Bjørlykke (1993) described how compaction-driven fluid flow is controlled by the depositional and structural history of a basin: The continuous of sandstone facies control the pore water flow, and faults offsetting the continuous sandstones may have a major effect on the pressure distribution. Yardley & Swarbrick (2000) presented fluid flow models that show that the effect of an inclined aquifer ranges from being a minor to a significant contributor (>10 MPa).

In Lothe et al. (in press) the possible hydraulic fracturing and leakage is discussed in connection to the use of failure criteria and geo-mechanical properties to the overlying caprock unit. This is followed by Lothe et al. (in prep), where it is discussed how the lateral fluid flow is controlled by the transmissibility across the large faults in a sedimentary basin. This will have a direct effect on the timing and amount of hydraulic leakage. The same data set are used, in these two previous papers as in this work. But now, instead of varying the transmissibility across all faults in an area, the sensitivity varying the transmissibility across individual faults are carried out.

In making realistic simulations of pressure distribution and possible hydraulic leakage in a sedimentary basin, single deterministic realisations of seismic horizons and fault zones should be avoided. Considering the errors discussed above different scenarios with alternative, realistic fault patterns supported by the reflection seismic data should be tested. In this work, the main topic will be the study of continuations of fault along strike and the potential influence of sub-seismic faults on the pressure. Such faults are typically interpreted to have a small dip-displacement at top reservoir level in the reflection seismic data. Seismic lines across fault zones with low throw are presented as examples. The transmissibilites across these individual fault zones, situated in different part of the studied sedimentary basin are varied. The uncertainty limits to the transmissibility across the fault zones are large, and the pressure changes in the rest of the basin will be tested. In the end, runs are carried out varying the transmissibilites across many fault zones with low throw in the study area.

Methods and data The fault traces mapped on top of the reservoir formation defines the lateral extent of the pressure (Borge 2000) and stress compartments in a pressure and stress simulator (Lothe et al. in prep & press). The flux between the pressure compartments, and not the flow within the compartment itself, is modelled. The overlying shale unit form top seals of the compartments. Depth-converted maps of the overlying sediments are used to construct a decompacted burial history through time. The development of pressure and stresses are reported for a series of time steps. Time steps are correlated to the depositional ages of the stratigraphic horizons that are used to build the model. The porosity-depth relation in the shales is used to model mechanical compaction and a kinetic model for quartz cementation (Walderhaug 1996) is used to model the chemical compaction of the sands. The geo-mechanical properties for the caprock will vary through time with burial depths (Lothe et al. in press). The pressure modelling is calibrated to pressure measurements from exploration wells in the study area. Isotropic horizontal stresses in the simulations are assumed. The minimum horizontal stress is estimated using an empirical formula (Grauls 1996). The vertical stress varies through time depending on the sedimentary loading. No strain or deformation is included and a

-108- passive sedimentary margin is assumed. The permeability in the fault zones is defined as depth dependent. The transmissibility across the fault zones depends on the throw and width of the fault zones (Borge & Sylta 1998). Juxtaposition faults have high transmissibilites, while faults with no overlaps have lower transmissibilites (Figure 1). The permeability versus depth is set for all major fault zones in the basin. The transmissibility across individual fault zones can be set independently if special cases should be tested. Griffith-Coulomb and frictional sliding criteria are used to simulate hydraulic fracturing from the overpressured compartments.

The data used are a present-day depth-converted map of the top reservoir unit, the present-day thickness of the reservoir, and a fault map at top reservoir level. From the fault map, pressure and stress compartments are defined. Drill stem tests and formation integrity tests are used for the pressure measurement in the different wells. The pressure data from 43 well in the area are taken at the top reservoir level, and are used to calibrate the model. Paleowater-depth in the area through time is set constant to 200 m. Poisson’s ratio and Young’s modulus are varied with depth (Lothe et al. in press). The other input parameter used is defined in Lothe et al. (in press). The simulations are carried out for the last 90 Ma.

Figure 1 In the simulations the lateral transmissibility (T) across a fault zone is defined by the overlap/offset (θ) of the reservoir unit. Reworked from Borge (2000).

Study area and regional geology The study area is located on the western part of the Halten Terrace, offshore Mid- Norway (Figure 2). The Halten Terrace is highly block-faulted, and the major extensional activity took place during the Late Jurassic to Early Cretaceous (Bøen et al. 1984, Blystad et al. 1995). The fault systems are oriented NE-SW, N-S and NW-SE. In west, the Klakk Fault Complex delineates the terrace, whereas the Bremstein Fault Complex defines the margin towards the east (Figure 2). The Halten Terrace area has undergone continuous subsidence since Paleozoic time. The subsidence history in Mesozoic corresponds to moderate to high sedimentation rates (Olstad et al. 1997), and in Late Pleistocene time a rapid subsidence took place (0.5 mm/year; Dalland et al. 1988). Today, the Garn Formation, which makes up the upper part of the Fangst Group

-109- is buried to depths between 2.0-3.5 km in the western part of the terrace. The rapid, late burial led to an increased pressure in the western part of the Halten Terrace (Teige et al. 1997). This was influenced by an increased quartz cementation in the Fangst Group. The major fault zones of the western part of the area are assumed to be sealing due to quartz cementation and diagenesis (Olstad et al. 1997). H

4° 6° 8° 10°

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x Trondheim NORWAY Møre Trøndelag Fault Complex 50 km 10 km Figure 2 Right map shows the study area situated at the western part of Halten Terrace, offshore Mid-Norway. Left map reworked from Blystad et al. (1995). Results In this work we aim to study the changes in pressure distribution and the time-related amount of hydraulic leakage when changing the transmissibilites across individual faults. When building a model with pressure compartments, sub-seismic faults frequently are interpreted to be present along strike in the continuation of major fault. The uncertainties associated with such sub-seismic and hardly detectable faults, are therefore large when sealing properties are concerned. Most likely single deterministic realisations of seismic horizons and faults are used as input from the seismic interpreter. To be able to draw some general trends, we want to study individual fault with low throw. In addition to the throw we want to check the effect of

a) location of the faults in the sedimentary basin, b) pressure difference, c) size of pressure compartments

One would expect larger changes in the pressure distribution to occur when the transmissibility across a fault in an overpressured area is increasing, as compared to that of an intermediately or hydrostatically pressured area. Also, larger impact on the pressure distribution should be expected in cases when a fault zone holds large pressure

-110- differences. However, it is clear that the effect of these different features would also depends on the size of the pressure compartments.

The significanse of transmissibilities across one individual fault zone The sensitivity of the transmissibility across individual fault zones in the basin was tested. The transmissibilities were varied for three fault zones, with small displacement. These were situated in overpressured, intermediately pressured and hydrostatically pressured parts of the sedimentary basin. The calculated throw for all the major fault zones in the study area is shown (Figure 3). The fault zones, where the transmissibilites are tested, have all throw interpreted to less than 25 m (Figure 4). A base case is carried out, to have an understanding of the pressure distribution, which is simulated in the study area (Figure 5a). In the base case the western part of the basin is highly overpressured. The simulator shows that this caused due to deep burial, rapid subsidence in this area and extended quartz cementation in the reservoir unit (Borge 2000, Lothe et al. in press). Due to the high overpressure, hydraulic leakage is simulated in westerly situated pressure compartments (Figure 5b). As Figure 5b shows, the simulated cumulative hydraulic leakage varies between the different compartments. This can particularly be seen for some key compartments, which will be studied in more detail. In the simulations, most of the compartments failed between 3.5 Ma and Present (Figure 6). The amount of leakage varies, depending on the size of the compartment and the overpressure generated and the amount of fluids that dissipated into the compartment before failure.

Figure 3 Map with calculated dip-slip extensional displacement (m) for the major fault zones in the study area. Faults marked with a ring, is discussed in the paper.

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Figure 4 Fault zones as interpreted from seismic at top Garn Formation horizon. The single lines are sub-seismic faults, which are interpreted to join up and form pressure compartments. Seismic lines presented in the paper are marked. (

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a) Base case (run211) b)

K EK WK

S

Figure 5 a) Todays overpressure simulated in the base case. High overpressure is simulated in the western area. Colours scale in bars. b) Logarithmic cumulative leakage (log m3). The pressure compartments that fail are marked with colours.

Figure 6 Cumulative leakage from different compartments situated in different parts of the basin, see location in Figure 5b. Early hydraulic fracturing and leakage are simulated from compartment EK and S. The neighbouring compartments to EK; WK and K fail at a later stage and with lower amount of fluids.

Overpressured area The aim is to test how sensitive the pressure simulations are, when the transmissibility across a fault zone between two pressure compartments are varied. In the first simulations a fault between compartments K and EK in the north-western part of the study area was assesed (Figures 3 & 4). The N-S trending border fault zone between compartment K and EK, is most clearly defined in reflection seismic data in the south. Towards north, the dip-slip is less than 25 m (Figure 3). The WNW-ESE oriented seismic line, crossing the fault shows a small displacement at the top Garn Formation horizon, and no displacement at base Cretaceous (Figure 4 & 7). The small

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displacement in this area, may be compatible with extended lateral leakage across the fault.

In the base case, large overpressure is simulated in this area. The compartments hold a present simulated pressure of 402 bar in compartment K and 363 bar in compartment EK, which is a difference of 39 bar. The base case simulation suggest a different cumulative leakage due to hydraulic fracturing in the two compartments varying from 24·106m3 in K to 82·106m3 in EK. The leakage rates are relatively high in this case, compared to neighbouring compartments to the east. In the neighbouring compartments to the west some leakage is simulated. Using the base case as reference, we varied the permeability across the fault zone separating the compartments (K and EK). We want to test the effect on the whole basin, when the permeability is increased. Figure 8a) - d) presents the changes in the simulated overpressure, when the transmissibilites between the compartments are increased by a factor of one order at time. A small increase in the transmissibilites with a factor, 10 and 100 give small changes for the pressure distribution. According to this, one observes an increase in the simulated pressure in compartment EK, and a decrease in K. Even though there are small changes in the pressure distribution a change in pattern of leakage is visible in the corresponding map for cumulative hydraulic leakage in these two runs (Figure 8e & f). In the base case leakage took place from both compartment K and compartment EK, but in this casd only compartment EK fails. By additional increase in the transmissibilites by a factor of 1000, changes in pressure distribution in a larger area become evident (Figure 8c). For this case an increase in the pressure took place for compartment EK, K and one compartment further to the south. The cumulative leakage map indicates that the leakage has changed from compartment EK to compartment K, and that leakage occurd earlier in compartment K and compartment WK (Figure 8d). It seems like the small forward time-shift for the failure in compartment K and compartment WK and also the increase in the pressure in the compartment to the south, prevent failure in compartment EK. The highest transmissibilites used (factor 1000), seems to cause increased pressure in a large area southwards (Figure 8d). The cumulative leakage map, shows leakage in compartment E occuring at approximately 3 Ma (see Discussion for assessement of this). Using the mean deviation in all the wells in the area as reference, the run using 0.001 gives the lowest mean deviation with 8.7 bar, compared to the base case with 11.3 bar.

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Figure 7 Fault F between compartment K and EK is marked. White line marks top Garn Formation and grey line marks base Cretaceous unconformity.

Trans missibility across individual fault zone *10 *100 *1000 *10000 a) (run 231) b) (run232) c) (run 233) d) (run 234)

F F F F K EK

e) f) g) h)

EK EK K EK

Mean dev. 12.2 bar Mean dev. 12.9 bar Mean dev. 8.7 bar Mean dev. 12.9 bar

i) j) k) 3) 3) 1.E+08 3) 1.E+08 1.E+08 m m m ( ( (

e e 8.E+07 e 8.E+07 8.E+07 g ag EK ag 6.E+07 K 6.E+07 6.E+07 eaka eak eak EK l l e 4.E+07 e 4.E+07 4.E+07 ve l v v i i i t t t WK a a a l l WK 2.E+07 l 2.E+07 WK 2.E+07 mu mu mu u 0.E+00 0.E+00 0.E+00 u C C Cu 3 2 1 0 3 2 1 0 3 2 1 0 Time (Ma) Time (Ma) Time (Ma)

Figure 8 Transmissibility between compartment K and EK situated in a overpressured area, is multiplied by a factor a) *10, b) *100 c) *1000 and d) *10000. e-h) Cumulative leakage in the same runs, varying the transmissibility between compartment K and EK (log m3). i-j) Cumulative leakage versus time for compartment EK, K and WK.

Intermediate pressure area From the intermediate pressure area, a fault in south-western part of the study area was selected for further analysis. This fault generally has a small displacement (Figure 3).

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From the seismic data the reflections below the base Cretaceous unconformity are poorly defined Figure 9a). Also the faults in this area are difficult to interpret. A NNE- SSW striking fault is identified in this area (Fault A, Figure 9b), but large uncertainties are connected to its characteristics. Therefore, the sensitivity of decreasing the sealing potential is particularly useful for this fault.

The base case simulations show overpressure in the two neighbouring compartments from 329 (compartment S) to 291 bar (compartment N), corresponding to a difference of 38 bar (Figure 10). The transmissibilites across the fault zone was increased with a factor (10 to 10000) in the runs. Studying the changes in overpressure in the different runs compared to the base case, we see small changes when low transmissibilites are utilized (Figure 10a & b). The pressure increase is mainly connected to compartment N, where the fluid is flowing from the more strongly overpressured compartment S. Minor pressure changes are also seen for the small neighbouring compartments. Increasing the transmissibilites even further with a factor 1000 across the individual fault, an increase in overpressure is seen both in compartment N, as previous, but to a less extent since also an increase in overpressure occurred in compartment S and P (Figure 10c). Using the highest transmissibility (10000), gives an increase in overpressure in compartment N, and also in neighbouring compartment in a wider area (Figure 10d).

On the scale of the basin, it is mainly the same compartments that go to failure, as in the base case (Figure 5b, 10e-g). However, on the local scale, varying the transmissibilites of fault A, have a major effect on the location of the leakage. In the base case, compartment S fails around 1.7 Ma. Increasing the transmissibilites slightly (10 to 100), give no changes in the leakage pattern in general. Actually, only some minor changes in a small compartment north of compartment S is observed (Figure 10e & f). Higher transmissibilites give increased fluid flow from compartment S to compartment N. In Figure 10c we see that the high fluid flow between compartment S and N, leads to a rapid pressure build up in compartment N and hydraulic fracturing in this compartment (Figure 10g). Since this compartment is now leaking, less pressure build up takes place in compartment S, which accordingly does not fail. After increasing the transmissibility even further, we see an increase in overpressure in a larger area. Since the increase in pressure is more widespread, no hydraulic leakage is takes place in compartment N, whereas leakage occurs in compartment S.

The mean deviation between the simulated pressure and the pressure measured in wells in the basin, varies only from 11.1 to 11.6 bar. Changing the transmissibility across one large fault in the overpressured and the intermediate pressured area, has a major effect on the pressure in the neighbouring compartments and the potential hydraulic leakage.

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Figure 9 Seismic line from the intermediate pressured area in south. a) without interpretation and b) with interpretation. Fault zone A between compartment N and S is marked. Yellow line marks top Garn Formation horizon and blue line mark base Cretaceous unconformity.

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Transmis sibility across a individual fault zone *10 *100 *1000 *10000 a) run 229) b) (run227) c) (run 224) d) (run 226)

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Mean dev. 11.6 bar Mean dev. 11.1 bar Mean dev. 11.6 bar Mean dev. 11.2 bar

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1.E+08 1.E+08 1.E+08 3) 3) 3) m m m 8.E+07 ( 8.E+07 ( 8.E+07 ( e e e

6.E+07 6.E+07 6.E+07 eakag eakag eakag S 4.E+07 4.E+07 4.E+07 ve l ve l ve l

i N i i t t S t 2.E+07 la 2.E+07 la 2.E+07 la u u u m m m 0.E+00 u 0.E+00 u 0.E+00 u C C C 3 2 1 0 3 2 1 0 3 2 1 0 Time (Ma) Time (Ma) Time (Ma)

Figure 10 a, b, c and d) The pressure changes in different runs where the transmissibility between cell A and B is varied compared to base case (Colour scale in bars). The transmissibility across fault A is multiplied by a factor a) *10, b) *100 c) *1000 and d) *10000. e-g) Logarithmic cumulative leakage simulated for the same runs as presented in a-d)(log m3). i-j) Cumulative leakage versus time for some compartments.

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Low-pressured area Increasing the transmissibilites across a fault in a low-pressured area, does not have the same effect on the pressure distribution as in overpressured. In such a case the transmissibility across the fault between two compartments with low pressure is varied. The compartments in the base case, have an overpressure of 34 and 72 bar, with a difference of 38 bar. Figure 11a) shows the changes in overpressure with increased transmissibility by a factor of 1000, compared to the base case. This results in minor changes in the cumulative leakage rate, compared with the base case (Figure 11b).

Figure 11 Transmissibility in a fault situated in the low-pressured area is increased by a factor 1000. a) Changes in simulated pressure compared to base case, measured in bars. b) Simulated logarithmic cumulative leakage (log m3).

The effect of varying the transmissibilites across several faults The transmissibility was varied for six faults in the study area. In accordance to the three fault already presented, three others were selected in the intermediately pressured area. Two of these, fault B, which strikes N-S and fault D, striking NNE-SSW were studied in some detail in reflection seismic sections (Figure 4). Fault B is clearly distinguished in its southern, but is more poorly defined on the seismic data in its northern part. This fault is characterized by a minor dip-slip separation, but because smaller faults are overlapping in the area, it is regarded that the fault is sealing (Figure 12). Fault D is a sub-seismic to small fault with a small dip-slip separation defined on top Garn level (Figure 13). The fault dips towards the west.

Different runs have been performed; increasing the transmissibilities across first, fault A, then fault A & B and so forth (Figure 14). The transmissibilites across the faults are increased with a factor 1000, and the changes in pressure distribution are compared to the base case. There is a major change in the pressure distribution, and subsequent opening up fault B for fluid flow. This causes an increase in the pressure in the northeastern part of the study area (Figure 14c). When studying the cumulative hydraulic leakage in a situation when the faults become opened one after another, it is seen that the changes are mainly in the southern area. In the base case (Figure 15a), compartment S fails at approximately 1.7 Ma. Changing the transmissibility across fault A, compartment N fails at 1.9 Ma. Increasing the

-119- transmissibility across more faults, no one of these two large compartments fail (Figure 15c-g). This, since less sealing faults northeastwards, give fluid flow is this direction. The result is that compartment N and S will not fail. In the last case, the fault F between compartment K and EK is opened. Then, compartment K does not fail, while a slightly higher leakage is seen from the neighbouring compartment EK (Figure 15g).

Figure 12 Fault B, with a small dip-slip displacement. Yellow line marks top Garn Formation and blue line marks the base Cretaceous unconformity.

Figure 13 Fault D, with a small dip-displacement.

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Figure 14 Changes in simulated overpressure when the transmissibilites across six faults zones are increased with a factor of 100. a) Base case (colour scale as in Figure 5a) b) 1 fault c) 2 faults, d) 3 faults, e) 5 faults, f) 6 faults. Positive and negative changes in pressure compared to base case measured in bars.

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Figure 15 Maps showing cumulative hydraulic leakage from the different compartments in the study area. a) Base case, then increase transmissibility by a factor of 100 in b) 1 fault zone, c) 2 faults, d) 3 faults, e) 4 faults, f) 5 faults and g) 6 fault zones.

Discussion Spatial continuity and linkage of faults may substantially affect fluid flow either by compartmentalizing the sedimentary basin or by increasing the tortuosity of flow pathways. This is the case whether the faults act as seals or as conduits. Often it can be a difficult task to constrain 3D fault continuation and linkage using reflection seismic data (Childs et al. 1997). Nevertheless, pressure differences are observed across faults with small dip-slip displacement (Childs et al. 2000). Olstad et al. (1997) discussed how petroleum migration in the Smørbukk Field area, offshore Norway, cannot be interfered from the present pressure distribution, because the permeability has changed continuously due to diagenesis processes. Hydrocarbons of different oil to gas ratios in the Smørbukk field, indicate stratigraphic and structural compartments, and perhaps even existence of diagenetic seals due to quartz cementation.

The uncertainty in the seismic data and the fault interpretation, should be kept in mind when the fault map at a horizon level, should be used to construct pressure

-122- compartments in pressure simulations. The uncertainty in the pressure compartments will be linked to the interpretation faults with low seismic resolvable fault throws and their sub-seismic continuations. In this work, the fluid flow across individual fault zones in both overpressured, intermediate pressured and low-pressured part of the basins was analysed. The fluid flow was varied systematically by changing the transmissibilites across faults. Darcy’s law gives the fluid flow:

kP∆ Q = µ ∆Z where Q is the flux (m3/m2 per s), k is the permeability (m2), ∆P/∆Z is the pressure gradient (bar/m) and µ is the viscosity of the fluid. In this work, the transmissibilites between two pressure cells are varied. This implies that when k is increased the pressure difference (∆P) between the two compartments decrease (Figure 16). By increasing the transmissibility across one fault, the fluids will flow from the high pressured area, to the low pressured area. An example is seen for the fluid flow between compartment K and EK. In the base case, both compartment EK and K fail at 3.1 Ma and 1.8 Ma, respectively. When the transmissibility between the two compartments is increased by a factor of 10 to factor 100, the fluid flow from the overpressured compartment K to compartment EK increases, and compartment EK fails approximately 3.2 Ma. This means that the initiation of leakage from compartment EK, does not change much as compared to base case. The amount of fluids, however changes from 82·106 m3 in the base case to 112·106 m3 using factor 100. The increased leakage from compartment EK does not cause compartment K to fail.

By increasing the transmissibility across the fault even more (by a factor 1000), the increase in fluid pressure spread to a larger area. The pressure builds up rapidly in compartment K, which fails at ca. 3.4 Ma. Also compartment WK fails earlier at 3.3 Ma. The early leakage in these compartments prevents compartment EK from failure. One should expect to see the same picture for even higher transmissibilites (factor 10000). However, in this case compartment EK fails, and not compartment K. Subsequently, an increase in pressure is noted for the larger neighbouring area. The reason to this pressure behaviour is that the transmissibilites are very high, and the fault was therefore nearly open. This results in very low fluid flow between the compartments. The compartments act as one large unit, and since compartment EK have a lower leak-off pressure than compartment K, compartment EK fails instead of compartment K. Thus, this would be an artefact due to the simulator used, since such high transmissibilites would be unrealistic. The sensitivity of a fault zone should then be tested using a sealing fault zone, and increase the transmissibilites up to a factor 1000. The probability of the different runs, should be found studying the measured pressure in wells compared to simulated pressure in the area.

The simulations show that the leakage in one compartment is dependent on the sealing properties in the bordering faults, but also on the pressure difference towards the neighbouring compartments. On a local scale, the assumed sealing properties have large influence on the neighbouring compartments during pressure build-up and possible hydraulic leakage. This effect would be most significant in overpressured areas, where the faults are assumed to hold large pressure differences. Grauls et al. (2002) give an example from a gas field from the UK side of the Viking Graben where a strong hydraulic potential or a ‘water drive effect’ is observed between neighbouring

-123- compartments. These observations would be in line with our simulations. Grauls et al. (2002) observe an empirical relationship between fault seal efficiency (E) and fault dip slip separation (R). A log-log linear relationship is established between these two parameters. In our simulations, the relationship is linear. Grauls et al. (2002) also points to the importance of the nature of fault gouge, with clay smear as an important factor. This is not taken into account in the present paper.

The timing and the amount of hydraulic leakage from an overpressured compartment seem to change rapidly if the transmissibilites are varied at some key fault zones in a basin. However, it is mostly the closest neighbouring compartments that are mainly effected. Also the amount of hydraulic fluid flow, are more or less the same. It is more a question of which compartments that are most likely to fail first. The timing seems to vary with only 1-2 Ma in the basin studied. To keep in mind from this sensitivity study on individual fault zones, is that the timing and amount of leakage is steady. Then, analysis of the seismic and how the fault zones are interpreted should be taken into account.

A way to map the uncertainties would be to vary the transmissibilites across many fault zones in different runs, to see how the overall pressure distribution is changed. Then the deviation from measured pressure from wells and simulated pressure can be used as a guide to quantify the uncertainty regarding timing and amount of hydraulic leakage from these areas.

250 bar 20 bar P r e

*10 230 bar s s es 100 bar u r ilit e b

i d s i s f i f e m r e s n n *100 c

a 180 bar r e

T 150 bar

*1000 175 bar 175 bar

Figure 16 The fluid flow between two compartments depends both on increase in transmissibility, here increased by a factor; one order of magnitude, and by pressure difference between the two cells.

Conclusions The sealing potential of sub-seismic fault or faults interpreted with low throw on reflection seismic would by nature be assessed with large uncertainties. In simulations the limits for the effect of varying the sealing potential on individual fault zones were tested. Varying the transmissibilites across individual fault zones situated in highly to intermediate pressured areas in a sedimentary basin, these have major influence on the pressure distribution in the neighbouring compartments. The larger transmissibilites

-124- used, the larger part of the basin were influenced. Also the timing and amount of hydraulic leakage would be affected depending on the transmissibilites used. In the surrounding part of the basin, only minor changes in the pressure should be expected. Varying the transmissibilites in low-pressured part of the basin, would have minor changes in the pressure distribution. Several runs were carried out to test the effect of changing the transmissibilites in many fault zones, situated in different part of the sedimentary basin. The deviation between simulated overpressure and measured pressure in wells, were used to quantify the simulations. The results can be used in basin modelling to estimate hydrocarbon fills in undrilled prospects.

Acknowledgement I would like to thank Norsk Hydro ASA for the data, financial support and scientific discussions during the work with my PhD thesis on hydraulic fracturing and leakage. Specially I would like to thank Geir Mørk for his help with the seismic dataset. Also my colleagues on SINTEF Petroleum Research and Øyvind Sylta in particular are thanked for useful discussions.

References Bjørlykke, K. 1993. Fluid flow in sedimentary basins. Sedimentary Geology, 86, 137-158. Blystad, P., Færseth, R. B., Larsen, B. T., Skogseid, J. & Tørudbakken, B. 1995. Structural elements of the Norwegian continental shelf, Part II. The Norwegian Sea Region. Norwegian Petroleum Directorate Bulletin, 8. Borge, H. 2000. Fault controlled pressure modelling in sedimentary basins. An thesis for the degree of Doktor Ingenør of the Norwegian University of Science and Technology, Trondheim, Norway, 148 pp. Borge, H. 2002. Modelling generation and dissipation of overpressure in sedimentary basins: an example from the Halten Terrace, offshore Norway. Marine and Petroleum Geology, 19, 377-388. Borge, H. & Sylta, Ø. 1998. 3D modelling of fault bounded pressure compartments in the North Viking Graben. Energy, Exploration and Exploitation, 16, 301-323. Bøen, F., Eggen, S. & Vollset, J. 1984. Structures and basins of the margin from 62 N to 69 N and their development. In: Spencer. A. M. et al. (eds). Petroleum Geology of the North European Margin, Graham & Trotman, London, 253-270. Childs, C., Manzocchi, T., Nell, P., Walsh, J. J., Heath, A. E. & Lygren, T. H. 2002. Geological implications of a large pressure difference across a small fault in the Viking Graben. In: Koestler, A.G. & Hunsdale, R. (eds.) Hydrocarbon Seal Quantification, NPF Special Publication, Elsevier Science, Amsterdam, 187-201. Childs, C., Walsh, J. J. & Watterson, J. 1997. Complexity in fault zone structure and implications for fault seal prediction. In: Møller-Pedersen, P. & Koestler, A. G. (eds) Hydrocarbon Seals: Importance for Exploration and Production, NPF Special Publication, Elsevier, Singapore, 7, 61-72. Dalland, A. G., Worsley, D. & Ofstad, K. 1988. A lithostratigraphic scheme for the Mesozoic and Cenozoic succession offshore mid- and northern Norway. Norwegian Petroleum Directory. Darby, D., Haszeldine, R. S. & Couples, G. D. 1996. Pressure cells and pressure seals in the UK Central Graben. Marine and Petroleum Geology, 13.

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Fossen, H. & Hesthammer, J. 2000. Possible absence of small faults in the Gullfaks Field, northern North Sea: implications for downscaling of faults in some porous sandstones. Journal of Structural Geology, 22, 851-863. Grauls, D. 1996. Minimum Principal Stress as a Control of Overpressures in Sedimentary Basins. In: Proceeding of the 8th Conference on Exploration and Production. IFP Report No43313, IFP Ruil-Malmaison. Grauls, D., Pascaud, F. & Rives, T. 2002. Quantitative fault seal assessment in hydrocarbon-compartmentalised structures using fluid pressure data. In: Koestler, A. G. & Hunsdale, R. (eds) Hydrocarbon Seal Quantification. NPF Special Publication. Elsevier Science B.V., Amsterdam, 11, 141-156. Knipe, R. J. 1992. Faulting processes and fault seal. In: Larsen, R. M., Brekke, H., Larsen, B. T. & Talleraas, E. (eds) Structural and Tectonic Modelling and its application to Petroleum Geology. Elsevier, Stavanger, 1, 325-342. Knipe, R. J., Fisher, Q. J., Jones, G., Needham, D. T., Davies, R. K., Edwards, H. E., Ellis, J., Freeman, S., Harris, S. D., Kay, M., Li, A., Lickorish, H., Phillips, G., Porter, J. R., Condliffe, D., Jones, P., O'Connor, S., Odling, N. & Barnicoat, A. C. 2002. Fluid flow behaviour of faults: critical variables, uncertainty limits and prediction. In: AAPG Hedberg Research Conference, Barossa Valley, South Australia. Lescoffit, G. & Townsend, C. 2002. Quantifying the impact of the fault modelling parameters on production forecasting from clastic reservoirs. In: AAPG Hedberg Research Conference, Barossa Valley, South Australia. Lothe, A. E., Borge, H. & Sylta, Ø. in prep. Evaluation of late caprock failure and hydrocarbon entrapment using a linked pressure and stress simulator. Submitted to AAPG Hedberg Research Conference, Special Publication. Lothe, A. E., Borge, H. & Gabrielsen, R. H. in press. Modelling of hydraulic leakage by pressure and stress simulations and implications for Biot's constant: An example from the Halten Terrace area, offshore Norway. Accepted for publication in Petroleum Geoscience. Olstad, R., Bjørlykke, K. & Karlsen, D. A. 1997. Pore water flow and petroleum migration in the Smørbukk field area, offshore mid-Norway. In: Møller-Pedersen, P. & Koestler, A. G. (eds) Hydrocarbon Seals: Importance for Exploration and Production NPF Special Publication, Elsevier, Singapore, 7, 201-217. Osborne, M. J. & Swarbrick, R. E. 1997. Mechanisms for generating overpressure in sedimentary basins: a reevaluation. AAPG Bulletin, 81(6), 1023-1041. Skar, T., Balen, R. T. v., Arnesen, L. & Cloetingh, S. 1999. Origin of overpressures on the Halten Terrace, offshore mid-Norway: the potential role of mechanical compaction, pressure transfer and stress. In: Aplin, A. C., Fleet, A. J. & Macquaker, J. H. (eds) Mud & Mudstones: Physical and Fluid Flow Properties. Geological Society, London, 158, 137-156. Teige, G. M. G., Hermanrud, C., Wensaas, L. & Bolås, H. M. N. 1999. The lack of relationship between overpressure and porosity in North Sea and Haltenbanken shales. Marine and Petroleum Geology, 16, 321-335. Townsend, C. 2002. Realistic fault description for reservoir modelling. AAPG Hedberg Research Conference: Evaluating the hydrocarbon sealing potential of faults and caprocks, Barossa Valley, South Australia. Walderhaug, O. 1996. Kinetic modelling of quartz cementation and porosity loss in deeply buried sandstone reservoirs. AAPG Bulletin, 80(5), 731-745. Yardley, G. S. & Swarbrick, R. E. 2000. Lateral transfer: a source of additional overpressure? Marine and Petroleum Geology. 17, 523-537.

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Chapter 6

Influence of pore pressure on secondary hydrocarbon migration - a case study from the Tune area, Viking Graben

Lothe, A.E.1,2, Sylta, Ø. 1, Lauvrak, O. 3 & Sperrevik, S. 3

1SINTEF Petroleum Research, N-7465 Trondheim, Norway, 2Geological Institute, University of Bergen, Allégaten 41, N-5007 Bergen, Norway, 3Norsk Hydro ASA, P.O. Box 7190, N-5020 Bergen, Norway.

Abstract______

Pressure and hydrocarbon migration modelling has been carried out in the Tune Field area, Viking Graben, offshore Norway. The pressures are considered to be controlled by compartments bounded by mapped faults. Two different interpreted fault maps at the top reservoir level (Brent Group) are used as input to the modelling. First, a low-resolution fault map is used, with only the large faults interpreted, and next, both large and small faults are included.

The simulations show high overpressures generated in the western area, in the deeper part of the Viking Graben, and hydrostatic in the eastern areas. The sharp transition zone results from using the low-resolution fault map in the simulations. Small N-S striking faults situated in between the wells have to have higher sealing capacity than expected from juxtaposition analysis alone, to be able to match the overpressures measured in well 30/5-2 and 30/8-1S in the Tune Field, and well 30/8-3 east of Tune. The intermediate pressure in the western part is probably in connection with the lower part of the sedimentary column in the compartment, where well 30/8-3 is situated. The secondary oil migration models show that the overpressures have major effect on the migration pathways of the hydrocarbons. The level of detail in the fault interpretation is important for the simulation results, both for pressure distribution and for hydrocarbon migration.

Keywords: pressure simulation, fault pattern, hydrocarbon migration______

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Introduction Faults may control lateral water flow and hydrocarbon migration in sedimentary basins. They can act as barriers to flow, but also as conduits or partial-conduits, depending on the involved lithologies and the geohistory. The flow transmissibility of faults is an important parameter when the pressure distribution and compartmentalization is modelled in a basin (Borge & Sylta 1998, 2000). Generally, large pressure differences across faults are observed when the dip-slip displacement of a fault is large at km to hundred-meter scale (Heppard et al. 1998). However, also smaller faults, with dip-slip displacements of approximately 50 m, can hold large pressure differences. This is described to be the case in the Tune Field in the Viking Graben, northern North Sea, where a small fault is assumed to hold a pressure difference of 150 bar (Childs et al. 2002). The ability to hold pressure differences is also seen at smaller scales, where deformation bands are nearly sealing (e.g. Antonellini & Aydin 1994, Fisher & Knipe 2001, Lothe et al. 2002). Such features may display permeabilities more than seven orders of magnitude less than the undeformed host rock (Antonellini & Aydin 1994). Deformation bands often are observed in association with to larger faults, thus contribute to the sealing capacity of the fault zone (Aydin & Johnson 1978, Antonellini & Aydin 1994, 1995). However, the main controlling mechanisms for fault seals are 1) shale gouge or smears in the fault zone or 2) juxtaposition of reservoir against non-reservoir lithologies (Davies & Handschy 2003). Sperrevik et al. (2002) combined knowledge of the burial depth at time of deformation, maximum burial depth and the fault zone clay content to estimate fluid flow properties of faults from a empirical relationship.

As noted above, the fluid flow properties of each fault is of importance when calculating lateral fluid flow in sedimentary basins. The fault interpretations from reflection seismic data of the dip-slip displacement and fault pattern are crucial for the pressure simulations (Townsend 2002, Lothe et al. in prep.). This implies that the level of details that the fault interpretations are carried out affect the pressure simulations strongly. Understanding which fault map resolution is needed to get a satisfying simulation of the pressure distribution will help in designing interpretation strategies. Probably, hydrocarbon migration modelling needs a higher resolution in the input data than simulations of the pressure distribution. The detail level needed of the input fault pattern, both to do pressure simulations and hydrocarbon migration, is one of the things this article aim to answer.

The present study was carried out using a dataset from the Viking Graben, in the northern North Sea. The data set covers both Oseberg South and the Tune Field, but the analysis was particularly focused on the intermediately overpressured Tune Field (Figure 1). The study area was chosen for three main reasons: (1) To test how different interpreted fault maps, will influence on the lateral pressure distribution. Will the detail level of the fault interpretation have special importance in the Tune Field, since this is situated in the pressure transition zone, between the deeper and higher overpressured part of the Viking Graben and the hydrostatic pressured Horda Platform? (2) It is obvious in highly overpressured areas like the Halten Terrace area, Gulf of Mexico and the Northern Viking Graben, that the overpressure has a large impact on hydrocarbon migration. However, will the pressures also influence migration, when the pressure is low to moderate as is the case in the Tune area? (3) Large pressure differences are sometimes supported by faults with small dip-slip displacements (Childs et al. 2002). It needs to be investigated whether it is possible to simulate the pressure differences in such cases with more accuracy.

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In this paper we aim to reproduce the large pressure differences observed across single faults by simulating the lateral fluid flow in a larger area, rather than simulate flow across the single fault itself (Figure 1). It is realised that the pressure distribution in an area, is not only controlled by a single fault, but is controlled by the product of the dip-slip displacements and the orientations of the faults in the area.

Figure 1 Overview map from the northern North Sea. Main oil and gas fields and faults are shown. Large frame marks our study area, while small frame mark simulated area in Childs et al. (2002).

Structural setting The northern North Sea sedimentary basin is a fault bounded, N-trending zone of extended crust. The composite fault pattern results from Late Permian - Early Triassic and Jurassic extensional episodes (Færseth 1996). The area is characterized by N-, NE- and NW-striking large normal faults, which define tilted blocks that are 15-50 km in width. They are generally assumed to be established during Permo-Triassic stretching and reactivated in subsequent Jurassic stretching (Badley et al. 1984, 1988, Roberts et al. 1995). Færseth (1996) and Færseth & Ravnås (1998) argue that most large major faults of Permo-Triassic origin show some Jurassic reactivation, but there is often an inverse relationship regarding the amount of dip- slip displacement related to the rifting episodes. These two episodes may have little spatial relationship.

The Tune Field consists of one north-south elongated structure approximately 2.5 km wide and 20 km long. The field is located in a structurally complex area down-faulted to the west from the Oseberg South area. Towards west and east the field is delimited by large scale N-S striking normal faults dipping towards west. These faults were active in Late Bajocian-Early Bathonian time (Færseth & Ravnås 1998). The Tune reservoir sequence consists of the Middle Jurassic Tarbert Formation and the Triassic Statfjord Formation. The Tarbert

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Formation has a constant thickness of around 150 m in the Tune Field area, indicating faulting postdating the deposition of the formation.

Methods The pressure simulator used (“Pressim”; Borge 2000, Lothe et al. in press), was developed to simulate pressure dissipation and migration at basin scales. The pressure compartments are defined by fault patterns interpreted at top reservoir level using reflection seismic data. The flux between the compartments and not the flow within the compartment itself was modelled. The shales above and below the reservoir form seals of the compartments. Fault transmissibility properties depends on the burial depth, the length, width and dip-slip displacements of the faults, thickness of the reservoir layers and the permeability inside the fault block (Borge & Sylta 1998, Table 1). The most controlling factor for the transmissibility is the dip-slip displacement as illustrated in Figure 2. Juxtaposition faults (faults were the reservoir is self-juxtapost) have high transmissibilites, while faults with no overlap have lower transmissibilites. The permeability versus depth is defined for all faults in the basin. However, the transmissibility across individual faults can be varied if local effects in the basin should be tested. In this work, the word “corrected” is used, if the transmissibility across individual faults has been changed to match measured pressures in particular wells (Table 1).

The simulator calculates mechanical compaction of shales (Baldwin & Butler 1985) and mechanical and chemical compaction of sand (Walderhaug 1996). Hydraulic fracturing and leakage from the reservoir unit is estimated using the Griffith-Coulomb failure criterion for the first failure, and a frictional sliding criterion for reactivation of faults (Lothe et al., in press). The minimum horizontal stress is formulated as an empirical relationship versus depth (Grauls 1996). The vertical stress was varied as a function of time, depending on sedimentary loading. No strain or deformation was included in the simulator, and a passive sedimentary margin was assumed.

In the secondary hydrocarbon migration modelling the “Semi” modelling software was used (Sylta 1993, Sylta & Krokstad 2003). Semi employs a ray tracing modelling approach, assuming that hydrocarbons migrate along the top of a permeable carrier bed and upwards along the most steeping dipping rock surface, and governed by buoyancy. Hydrocarbon charge from a source layer within the model area or from injection points at the edges of the model at locations defined from regional migration studies is assumed. Burial histories, hydrocarbon maturation, expulsion and secondary migration are calculated at discrete time- steps. The fault sealing potential is related to the percentage shale within the part of the sequence that has moved past a point on the fault surface; termed the Shale Gouge Ratio (Yielding 1997). The SGR concept is incorporated in the migration modelling software by calculating entry pressures from the SGR values (Childs et al. 2002b, Sylta et al. 2003; Figure 3). The SGR values on the fault surfaces are calculated from the dip-slip displacement to the faults and Vclay logs at the fault interpolated from Vclay-logs from nearby wells (Childs et al. 2002b, Sylta et al. 2003). The empirical estimations of fault rock properties presented by Sperrevik et al. (2002) are incorporated in the Semi modelling software (Sylta et al. 2003; Table 1). Fault rock entry pressures are estimated from the clay content, maximum burial depth and depth at time of deformation. These properties are simulated to affect hydrocarbon migration, but not the water fluid flow modelled in the presented simulator (Table 1). Sylta et al. (2003) used a multi-carrier model, while the present study is less complex, with only one carrier modelled.

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Table 1 Definitions of terms used in the simulations Use of terms Pressim Semi - water flow simulations - hydrocarbon migration Flow fault properties The fault transmissibility depends on the SGR along faults used to calculate burial depth, the length, width and dip-slip entry pressure (Childs et al. 2002, displacements of the faults, thickness of the Sylta et al. 2003). The fault rock entry reservoir layers and the permeability inside pressures from mercury (Sperrevik et the fault blocks (Sylta & Borge 1998). al. 2002) are recalculated to entry pressures for oil and gas. “Correction” The transmissibility across individual faults is reduced/increased to match well data Upscaling Transmissibility summed up between two No upscaling. Flow calculated in all compartments (Borge 2000) cells across fault zones.

Figure 2 Juxtaposition faults have a linear relationship between dip-slip displacement and transmissibilites, while the faults with offset have very low transmissibilities. From Borge & Sylta (1998).

SGR vshale 0 0 0 1 4 ) h (m pt e

D 100 00 43

Carrier 00 Interval 45 00 47

0200400600 Throw (m) Figure 3 Sketch presenting the calculation of Shale Gouge Ratio used. The calculation of fault properties is based on sequence/dip-slip displacement juxtaposition diagram constructed from well logs. From Childs et al. (2002b).

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Input data To build the pressure simulator model, different input parameters are needed: a fault trace map at top reservoir level, depth-converted horizons for different time steps, paleo-water depths to the corresponding time steps, isopach map of the reservoir unit and measured pressure data from wells (Table 2). In accordance, oil and gas expulsion maps and Vclay-logs from wells are needed to do the hydrocarbon migration modelling. Different paleo-pressure maps made in the present study using the pressure simulator, are used as input in the hydrocarbon migration carried out (Table 2).

The fault trace maps are interpreted from seismic at the top Brent Group horizon in this study (Figure 4). Data from different seismic surveys are combined in the two fault map versions: • Low-resolution fault map: Interpretation carried out on 2D lines, 125 m grids (Figures 4a & b). • High-resolution fault map: Combined grids with low resolution in some areas, and high resolution in central areas (15.625 m grids), partly interpreted from 2D lines and partly from 3D lines (Figures 4c & d). In the low-resolution fault map most of the faults have dip-slip displacement larger than 50m, but also faults with smaller dip-slip displacements are interpreted (Figures 4a & b). Few faults are interpreted in the western and southern part of the study area. This is due to sparse data of low quality in the area, since no oil fields are located in these deeply situated areas. In the high-resolution fault map many small-scale faults are incorporated in the model, especially south of well 30/8-3, but also in the whole southern area (Figures 4c & d). The interpretation of the large faults are more or less the same in the two fault maps, though the large fault west of the Tune Field in the low-resolution fault map, is interpreted as two separate large faults in the high-resolution fault map (west of well 30-5-2, Figure 4b & d). The low-resolution fault map is defined by 39 pressure compartments, while the high-resolution fault map is defined by 236 pressure compartments. All the input parameters are kept constant using the two fault maps, except the permeabilities to the faults versus depth, and the sealing depth to the caprocks (Figure 5).

The isopach map of the reservoir unit in the area is used to calculate the fluid volumes in the Brent Group. Paleo-waterdepth maps are used as input in the five modelled time steps: 71 Ma, 34 Ma, 5 Ma, 2 Ma and Present day. RFT pressure data from wells in the study area are used to calibrate the simulations (Table 2). The wells are mainly situated in the eastern part of the basin, but some wells are also situated in the western deeper part of the Viking Graben (Figure 4). Hydrostatic to low overpressure is observed in wells in the eastern part of the study area. Moderate overpressure is observed in the Tune Field area. An overpressure of 163 bar is measured in well 30/5-2 in the northern part of Tune (Figures 4 & 5). The pressure increases southwards to 169 bar in the 30/8-1S well. A very low overpressure of 22 bar is observed in the neighbouring well to the east (well 30/8-3). If these observations were correct, a pressure difference of 147 bar would be observed across one fault. However, higher pressures have been measured at larger depth in well 30/8-3, but with large uncertainties (Figure 6).

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Table 2 Input data used in the simulations Input data Pressim - water flow Semi - hydrocarbon migration simulations modelling

Depth-converted seismic Five time-steps; 71 Ma, 34 Ma, 5 In five time-steps horizons Ma, 2 Ma and Present Isopach map reservoir Brent Group (164 Ma - 155 Ma) Brent Group (166 Ma - 155 Ma) Paleo-water depth maps In five time-steps In five time-steps Oil and gas expulsions In five time-steps maps Vclay logs Vclay logs from nearby wells to calculate SGR in the fault zones. The 19 wells are 30/5-2, 30/8-1S, 30/8-3, 30/9-1, 30/9-2, 30/9-3, 30/9-4, 30/9- 5S, 30/9-6, 30/9-7, 30/9-8, 30/9-9, 30/9-11, 30/9-12, 30/9-13S, 30/9-14, 30/9-15, 30/9-18, 30/9-19. Fault maps High- and low-resolution fault High-resolution fault map at top maps at top Brent Group horizon Brent Group horizon Pressure data Pressure measurements in Brent Group from 36 wells used to calibrate the simulations. The wells are 30/10-6, 30/9-5S, 30/9- 9, 30/9-11, 30/7-7, 30/9-3,30/9- 4S,30/9-8,30/9-10,30/9-13S, 30/9-6, 30/9-7, 30/9-14, 30/8-3, 30/8-1S, 30/7-6, 30/5-2, 30/6-18, 30/6-9, 30/9-2, 30/6-13,30/6- 15,30/6-16,30/6-17,30/6-21,30/6- 24S,30/6-3,30/6-4,30/6-6,30/6- 7,30/6-8,30/9-12, 30/6-14, 30/6- 23, 30/6-5, 30/6-19. Pressure maps 8 different pressure maps generated from Pressim in five timesteps. 2 using low-resolution fault map and 6 using high-resolution fault maps in the pressure simulations.

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a) b)

Dip-slip displacement (m) c) d)

Dip-slip displacement (m) Figure 4 Low-resolution fault map interpreted from 2D lines at the top Brent Group horizon. Most of the faults have dip-slip displacement larger than 50 m, but also smaller faults are shown. a) All study area and b) Tune Field area. High- resolution fault map c) All study area and d) Tune Field. a) b) Fault zone permeability (mD) Accumulating factor 1.E-09 1.E-07 1.E-05 1.E-03 00.51 0 0 Coarse grid 1000 1000 Fine grid ) ) m m h ( 2000 h ( 2000 pt pt e e D Coarse grid D 3000 3000 Fine grid 4000 4000 Figure 5 a) Permeability versus depth used for all faults in the pressure simulations. b) Sealing depth used to the caprocks. The accumulation depths using the high- resolution fault maps are varied in the three different cases presented in Figure 11.

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3300 1A30/5-2 water 1A30/5-2 3350 30/8-1s water 30/8-1s 30/8-3 water 3400 30/8-3 waterzone overpressure: 22 bar 30/8-3 uncertain 30/8-3HC1 30/8-3HC2

) 3450

m 30/8-3HC3 ( h

t Hydrostatic p

De 3500

3550 30/8-1S waterzone overpressure: 169 bar

30/5-2 waterzone overpressure: 163 bar 3600

3650 355 375 395 415 435 455 475 495 515 535 Overpressure (bar)

Figure 6 Overpressures measured in different wells in the Tune Field area (bar).

Results of the pressure simulations To investigate the effect of the resolution of the fault interpretations on the lateral pressure distribution, two different fault maps, with low- and high-resolution, have been used in the simulations. In addition, some fault transmissibilites have been corrected, compared to the standard transmissibility model used, to match the observed pressure differences in wells. This, to better compare with the results from Childs et al. (2002). The resulting simulated pressure build up versus time in wells 30/8-3 and 30/8-1S, are presented.

To evaluate what effect the pressure distribution and history will have on the hydrocarbon migration, simulations have been carried out including pressure histories obtained using; a) low- and high-resolution fault maps with and without correcting the fault transmissibilites to match the observed pressure from wells and b) by varying the sealing properties of the cap rock using the high-resolution fault map in the pressure simulations. The different resulting pressure distribution simulations are used as input in the hydrocarbon migration modelling.

Simulate lateral pressure distribution using low- and high-resolution fault maps Figure 7 shows the simulated present day pressure distribution maps for the area, using the two different fault map patterns at top reservoir level as input. Using the high-resolution fault map, the simulations show a clear subdivision into a highly overpressured western area, and a low pressured eastern area (Figure 7a). Major N-S trending faults control the sharp boundary in the pressure distribution. The Tune Field is situated in the pressure transition zone. A

-136- gradual decrease in the simulated overpressure can be seen when going northwards in the Tune Field area (Figure 7b). The fault marked on Figure 8a holds most of the pressure difference south of well 30/8-3. In this particular well, an overpressure of only 22 bar is measured. The simulation gives an overpressure of 52 bar in this well, but with better match to the wells within the Tune Field area (Table 3, Figure 7b). In order to reproduce the nearly hydrostatic pressure in well 30/8-3, the fault marked on Figure 8a has to be more sealing than what should be expected from the dip-slip displacement and thickness interpreted from seismic data. The fault transmissibility must be reduced by a factor of 0.001, to obtain the high pressure differences between the wells. Lowering the transmissibility of the fault gives a simulated overpressure in well 30/8-3 of 32 bar, 12 bar higher than measured in the well (Table 3, Figure 8a). The large pressure difference between well 30/8-3 and well 30/8-1S, will be discussed in more detail later.

The same overall pressure distribution was obtained when the high-resolution fault map was used. High overpressures are simulated in the western area, a narrow transition zone with intermediate overpressures in the central area and low-overpressured to hydrostatic pressured compartments in the eastern area (Figure 7c). As shown, using the low-resolution fault map, the Tune Field is situated in the transition zone that is intermediately overpressured (Figure 7b). When comparing with the simulation using the high-resolution fault map, the pressure distribution is less rapid across faults due to much more higher detail level of the fault interpretation and faults with less dip-slip displacement interpreted (Figure 7d). A network of smaller faults controls the pressures in accordance to the larger N-S striking faults. Medium to high overpressures are simulated in both well 30/8-1S and well 30/8-3, using the high- resolution fault map, without correction of the transmissiblities (Figure 7d, Table 3). In the nearly hydrostatic well 30/8-3 (22 bar overpressure measured), an overpressure of 125 is simulated. The mismatch is fare to high, and to be able to match the low overpressure measured in this well, the transmissibilities of most faults in the transition zone, marked on Figure 8b, must be reduced. A network of small faults trending mainly NNW-SSE must be capable to hold pressure differences. Otherwise the fluids can easily flow southwards and around the fault, if only one fault has decreased permeability. The faults have reduced the transmissibility by a factor *0.001. To avoid pressure build up in well 30/8-3, some of the eastern small faults have increased transmissibility compared to the standard.

Differences in the pressure distribution between models with and without transmissibility corrections on the smaller faults are shown in Figure 9 and in Table 3. Reducing the transmissibility results in that the pressure decreases with ~90 bar in the compartment where well 30/8-3 is situated using the high-resolution fault map. The difference in pressure distribution between models with reduced and not reduced transmissibilities is only ~20 bar using the low-resolution fault map (Figure 9).

Pressure measurements from wells in the area are used to calibrate the simulations. The wells are mainly located in the eastern part of the Oseberg area (Figure 1). Figure 10 shows the difference between modelled and measured pressures in the different pressure compartments where wells exist, with corrected simulations. Too low overpressure (-240 bar) is generated in the deep eastern area when simulating the overpressure using both fault maps (Figures 10a & c). The reason for this is lack of interpreted faults in the deeply buried area, resulting in too few pressure compartments to make reliable pressure simulations. In the eastern area, the simulated pressure is hydrostatic, whereas a small amount of overpressure has been observed in wells.

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The agreement between simulated and measured overpressure using the low-resolution fault map, is acceptable in the Tune Field, with slightly too high simulated overpressure in the western area (34 bar in well 30/8-1S, and 7 bar in well 30/5-2; Figure 10b). The mismatch is 12 bar between measured and simulated overpressure in the low-pressured well 30/8-3. The mismatch would have been 30 bar without correction across one individual fault south of well 30/8-3. These results indicate that faults south of Tune are more sealing, have lower transmissibility than what should be expected from the measured dip-slip displacements and thickness relationship to the fault. The same trends are seen, as described for the low- resolution fault map using the high-resolution fault map. In models where the transmissibilities have been corrected, a quite good match is observed in the western part of the Tune Field area (deviation -5 bar in well 30/8-1S and -33 bar in well 30/5-2). An overpressure of 45 bar is simulated in well 30/8-3 (22 bar measured; Figure 9d and Table 3). In models where the transmissibilities have been calculated by the program, and not later corrected, the deviation is 113 bar.

Comparing the runs using low- and high-resolution fault maps, the overall pressure distribution is the same (Figures 10a & c). Thus, lower fault permeabilites are needed using the low-resolution fault map to build up the observed pressures (Figure 4a). With only few large compartments, it seems like the faults must be more sealing to accumulate pressures.

Table 3 Deviation between measured overpressure in wells and simulated overpressure in different runs with and without lowered transmissibility to certain faults. Wells Mean 30/5-2 30/8-1S 30/8-3 deviation Measured overpressure (bar) 163 169 22 in all wells Deviation from measured overpressure (bar) Low- K (23) -6 17 30 49 resolution With corrections K’ (22) 7 34 12 48 fault map High- A (24) -40 -17 113 54 resolution With corrections A’ (18c) -33 -5 24 47 fault map B (32) -25 -8 121 50 With corrections B’ (18b) -17 5 44 45 C (31) -3 6 136 46 With corrections C’ (30) -1 4 62 42

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Over- pressure (bar) c) (run A) d) (run A)

Over- pressure (bar)

Figure 7 Map showing the overpressure distribution using the a-b) low-resolution fault map and c-d) high-resolution fault map (coloured scale in bar). White areas are inside of faults, or eroded part of the Brent Group used in the simulations. The simulations are carried out without corrections.

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Over- pressure (bar)

Figure 8 Simulated overpressure distribution today, using lowered transmissibilites across faults marked on the; a) low-correction and b) high-resolution fault maps. a) b)

Overpressure difference between runs with and without correction (bar)

Figure 9 Difference in simulated overpressure in the runs with and without corrected transmissibilites for a) low- and b) high-resolution fault maps. The high- resolution fault map gives a decrease in pressure with 90 bar in well 30/8-3 using corrections. Also in the neighbouring compartments changes are seen in the simulated overpressure.

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Deviation between measured and simulated overpressure (bar) c) d)

Deviation between measured and simulated overpressure (bar) Figure 10 Deviation maps that show the compartment differences between simulated and measured overpressure in wells (coloured compartments), using low-resolution fault map with corrections a) whole basin and b) Tune area, and high- resolution fault map with corrections c) whole area and d) Tune area. a) and c) Colour scale stops at -40 bar, but a deviation up to -240 bar is simulated in the western area. The high mismatch is due to very few interpreted faults in the area where high overpressures are generated due to deep burial. b) and d) Good fit between observed and measured overpressure in the low pressured well 30/8-3.

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Pressure simulations in individual pressure compartments Different timing of the overpressure is noticed if we study the pressure changes through time in well 30/8-1S and well 30/8-3, (Figure 11a & b). The pressure starts to increase around 15 Ma to 12 Ma in well 30/8-1S, and then later between 5 Ma and Present day. When the pressure increases, the effective stresses decrease. In the models, the overpressures are mainly generated from pore quartz cementation and some from shale compaction. A marked increase in shale compaction due to mechanical compaction can be observed from 5 Ma in well 30/8- 1S (Figure 11c). The increase in overpressure starts much later, around 5 Ma in the low- pressured well 30/8-3, and the overpressure increase is more moderate than in well 30/8-1S (Figure 11d). At present, the pore quartz cementation and the shale compaction have reached the same stage in 30/8-3 as in 30/8-1S, but in shorter time, during the last 8 Ma (Figure 11d).

Well 30/8-1S Well 30/8-3 a) b)

350 350 Overpressure Overpressure sig_3' 300 sig_3' 300 ) sig_1' sig_1' ) ar 250 250 ar b b ( ( e e r 200 200 r su su es 150 150 es r r p p r r e e v 100 100 v O O 50 50

0 0 20 18 16 14 12 10 8 6 4 2 0 20 18 16 14 12 10 8 6 4 2 0 Time (Ma) Time (Ma) c) d)

1 1 PSC PSC PQC 0.8 PQC 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0 20 15 10 5 0 20 15 10 5 0 Time (Ma) Time (Ma)

Figure 11 a & b) Pressure builds up in well 30/8-1S around 17 Ma, while in the well 30/8-3 the pressure build up started around 8 Ma. c-d) The simulations show a that the pressure is controlled by quartz cementation and shale compaction.

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Pressure simulations using the high-resolution fault map and varying the sealing depth to the caprock

To calibrate the simulations, the depth where the caprock start to seal has been varied from 2.6 km (case A & A’), 2.5 km (case B &B’) to 2.3 km (case C & C’; Figure 12). The simulations are carried out with transmissibility corrections (case A’, B’ and C’), and without correcting the transmissibility calculated from the fault maps. These models are named A, B and C. The cases without corrections (A, B & C) give large deviations between modelled and measured overpressures in the eastern area, with too high pressures simulated (Table 3).

In case A’, the caprock starts to seal below 2.6 km (Figure 12). This model results in a relatively low pressure build up in the basin. The simulated pressure is too low in the Tune Field area, but correcting the transmissibilities across some of the small faults as marked in Figure 5, the results correspond quite well with measured pressures in well 30/8-3 (case A’, Figure 12a). The measured overpressure should be approximately 22 bar, while an overpressure of 46 bar results from the simulations.

The sealing depth is set to 2.5 km in case B’. It results in higher accumulation of overpressure in the Tune Field, compared to case A’, with a better match to the measured overpressure in well 30/5-2 and well 30/8-1S (Table 3; Figure 12b). A larger deviation in overpressure is obtained in well 30/8-3 in case B’, compared to case A’.

In case C’ the cap rock starts to seal at shallower depths (2.3 km). This model gives higher overpressure in the reservoir today compared to case A’ and case B’ described above (Figures 12a & b). This is because using a shallower sealing depth to the caprock in the simulations, gives a later increase in pressure in the reservoir layer in case C’ (Figure 12c). Case C’ gives a good match between simulated and observed overpressure in the Tune Field area (deviation in well 30/5-2 ~ -1 bar and well 30/8-1S ~4 bar), but an overpressure of 84 bar in well 30/8-3 is too high (measured 22 bar). However, higher pressures have been measured in deeper intervals in this particular well, though some uncertainties are connected to the measurements (pers. com Norsk Hydro; Figure 5). One explanation is that in reality the fluids flow from deeper buried parts to the west across the fault and into a deeper layer than the Tarbert Formation, such as the Ness Formation. The Pressim model is only a single carrier model, and the fluids from the west will be distributed into the Tarbert formation to the east in the simulations. We can therefore not expect very low overpressures to be modelled in this area. Overpressures around 80 bar should then be excepted. This would be in line with the simulated pressures in case C’, with a good match between simulated and measured pressures both in the Tune Field area and in well 30/8-3.

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Accumulation factor

00.51 2000

A ) 2500

m B

h ( 3000 C

pt e

D 3500

4000 a) (run A’ ) b) (run B’) c) (run C’)

Over- pressure (bar)

Figure 12 Shallow increase in caprock sealing properties, gives higher pressure accumulations in the Tune Field area. Cases A’, B’ and C’ have corrected transmissibilities.

Secondary oil migration modelling

In order to test how different pressure histories will influence the simulated migration, the different pressure maps at time steps were used as input for the secondary oil migration modelling. In six cases is the high-resolution fault map used. Simulations were carried out with pressure cases A’, B’ and C’ with corrections first, and cases A, B and C were simulated without corrections. Finally, two simulations have been carried out using the low-pressured fault maps; with and without corrections (Figure 13).

The results of all the different cases are presented in map view in Figure 14. The figure contains histograms of the hydrocarbons trapped through time. The histograms show the amounts of oil, condensate, solution gas and free gas. A major gas trap is simulated to occur west of Tune, and also some smaller amounts in the Tune Field area.

Different models have been carried out using the different pressure cases presented as input. The first three histograms from the left in Figure 13 show the resulting hydrocarbon columns in case A, B and C. The three next show the results from A’, B’ and C’. The two last histograms to the right show the results using the low-resolution fault map to model the

-144- pressure distribution. The cases using the high-resolution fault map show small variations in simulated hydrocarbon column. Starting out with the high-resolution fault map with corrections, there are some variations in the resulting gas columns depending on the depth where the cap rock starts to seal. Case A’ has a thicker gas column developed (Figure 14) and lower pressure build (Figure 12a) up than case B’ and C’. If one compares case A’ and case C’, the difference in simulated pressure is mainly seen in the eastern part of the area (Figure 15a). In the southwestern part, however, there is a small compartment, which experience a small pressure change between the two runs (A’ & C’; Figure 15b). This small pressure change (3 bar) also changes the oil migration in the area (Figure 16a). A profile is made across the structure to illustrate the oil-and gas distribution in the area (Figure 16b). The gas- water contact is situated directly on the fault, with oil on the other side. A small increase in the simulated fluid pressure in this compartment marked x on Figure 16, will influence the simulated gas column in the prospect.

Case A, B and C (without corrections) show the same trend in oil and gas accumulations as described for case A’, B’ and C’. The reason to this is probable that the main pressure changes between, for example case A and A’, is in the eastern part of the area with generally lower pressure. Also, the hydrocarbon modeling shows that the oil migrates from west towards east. Then, the pressure changes in west become the most critical for the hydrocarbon migration.

Secondary oil migration modelling has also been carried out, keeping the high-resolution fault map for the hydrocarbon migration simulations, but using the pressure distribution history simulated using the low-resolution fault map runs presented. Figure 14 shows the filling history, using the low-resolution fault map, with and without corrections. Run K (without correction) gives the lowest pressure in the western area, including Tune, and therefore more gas is dissolved in oil in this case. The free gas cap therefore fills less of the pore space and more oil can be trapped before spill starts.

High- Low- resolution resolution

A B C A’ B’ C’ K’ K

Figure 13 The different pressure distribution runs have been used in hydrocarbon migrations. The histogram shows the modelling, carried out with pressure cases: using high-resolution fault maps, with corrections (A’, B’, C’) and without corrections (A, B, C). The two last histograms show expected hydrocarbon columns using the low-resolution fault maps, with and without corrections (K’ and K).

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Depth (m)

Figure 14 Histograms shows expected hydrocarbon-columns using the high- and low- resolution fault maps, with and without corrections of the transmissibilites (see nomenclature Figure 8). The largest changes between the simulations are seen, using low-resolution fault map without correction, which gives a smaller gas column in the prospect west of Tune. White frame mark maps shown in Figures 12 and 13.

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a) b)

X

Figure 15 a) Difference in the simulated pressure between case A’ and C’ (colour scale in bar). b) The changes in one pressure compartment marked X, seems to have a major influence on the hydrocarbon column in the nearby traps, see Figure 12.

a) b) A A’ A

X

Depth A’ (m) X

Figure 16 a) Map showing the gas-flow rate in a smaller area marked on Figure 10. b) Profile A-A’ shows that the oil-gas contact is situated on the fault in this area. Then, changes in pressure in compartment X changes the migration path in to the prospect west of Tune.

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Discussion

The effect of using different resolution of fault maps in pressure modelling has been investigated in this work. The sensitivity to the fault maps are important for the lateral pressure distribution and will possible effect of the hydrocarbon migration histories. The simulations of the observed pressure barrier across small faults in the area are discussed below.

The effect of using different resolution of fault maps on the pressure distribution In this study we have carried out pressure simulations in the Viking Graben area using two different fault maps: with only large faults and with large and smaller faults. These simulations give mainly consistent large-scale pressure distribution results. High to intermediate high overpressure is simulated in the western part of the study area, in the deeper parts of the Viking Graben. The pressure is simulated to be nearly hydrostatic in the shallower eastern part of the study area. The differences between the two fault map datasets are mainly seen, when looking at the pressure in the transition zone between the two pressure areas to the east and west. The Tune Field is a good place to illustrate this, since in this area there is a lateral gradual change in the overpressures. The pressure can be modelled in more detail using a more detailed fault pattern. Such detailed studies of the fault distribution are probable more required in transition zones between high and low pressured compartments than in the more low or high-pressured zones. This is supported by Lothe et al. (in prep.), who show, using data from the Halten Terrace area, that the interpretation of the faults are of major importance when the pressure distribution is simulated. The fluid flow is not only dependent on the fault transmissibility, but also on the pressure difference across the faults. Regional areas in the basin will be influenced if the transmissiblities across one fault in overpressured to intermediate pressured areas were changed (Lothe et al. in prep.). Difference in simulated pressure distribution resulting from using different fault patterns, can also be seen in studies on the Halten Terrace area (Borge 2002, Lothe et al. in press). The differences were mainly observed in the intermediately pressured transition zone, between the highly overpressured western area and the hydrostatic eastern area. Ottesen & Townsend (2002) tested the effect of varying the fault population in reservoir scale models from the southern Viking Graben. Their simulations showed that by increasing the number of faults, the recovery in the reservoirs was reduced.

Pressure difference simulations Childs et al. (2002) model the pressure difference between well 30/8-3 (~20 bar overpressure) and well 30/5-2 (~150 bar overpressure) using an Eclipse flow model. Their model was centred on an interpreted relay zone between the two large N-S striking faults dipping westwards in the area. Childs et al. (2001) simulated an area of 6 km * 10 km, compared to 53 km * 70 km in our study (Figure 1). The relay zone is interpreted in the low-resolution fault map model used. In the high-resolution fault map, no explicit relay zone is interpreted; instead many small faults have taken up the deformation in a larger area.

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If we compare the results, Childs et al. (2001) find that the fault rock permeabilities are very low and/or the thickness of the fault zone is higher than what should be expected from published data. When using the low-resolution fault map we obtain the same trend and to match the observed pressure data the transmissibility of one fault situated in the relay zone must be reduced. Using the high-resolution fault map the transmissibilities must be reduced across many of the small faults, to match the known pressure data. Even then, it is difficult to obtain the low pressure that is observed in well 30/8-3, because too high pressures are simulated in the Tune area in this case.

Different scenarios that may result in the low transmissibilities can be argued for: Development of a continuous clay/shale smear along the fault plane. An 8 m thick mudstone unit is observed in the central parts of the Tarbert unit. This shale layer may have been smeared. But, since the high-resolution fault map shows that many small faults in the area need to have increased sealing, this model is may not be so likely for all these small faults. Another explanation is that the relay zone is characterized by a large number of sub-seismic faults. From the work by Antonellini & Aydin (1994, 1995), we know that an increase in the number of deformation bands can be expected in the step between two slip planes.

A third possibility would be that the nearby overpressured western part of the area, is in direct contact with the older carriers to the east. Higher overpressure is measured in well 30/8-3 in the deeper buried part of the sedimentary package. The sealing shale layer internally in Tarbert Formation could be sealing off the vertical fluid flow along the fault plane (Figure 4). To be able to test this hypothesis fully, a multi-layer model would have to been carried out. Finally, there is a chance for the pressure recordings in the Tarbert formation of the 30/8-3 to be erroneous.

Hydrocarbon migration The timing of the overpressure build up in the western part of the area in the Viking Graben, and in the Tune Field area, is early, as seen from the simulation results around 15 Ma (Figure 10). The work by Borge (2000) shows that the overpressure increases gradually from around 35 Ma, with a rapid increase during the last 5 Ma. This Quaternary increase is also observed in the present study. The same mechanisms controls the pressure build up, first quartz cementation in the Tertiary, and then shale compaction in the late phase of burial (Borge 2000). The simulations show that the pressures build up has mainly taken place the last 5 Ma. These results in some local variations in the lateral pressure distribution depending on e.g. the sealing depth used for the caprocks. However, the paleo-pressures are mainly the same, though the simulated Present pressure distribution in the area may vary laterally.

Buhring (1989) divided the pressure domains of the Brent Group at the east flank of the Viking Graben into three; a closed system in the western area, a transition zone and an open system. These pressure domains were not defined directly by the fault pattern, but were defined as large-scale systems from pressure observations in wells. The expulsion modelling is controlled by the regional pressure regimes. The modelling by Skjervøy & Sylta (1993) predicted a deeper prospect that contained gas and a shallower prospect that contained gas with an oil lag. The later drilled wells (well 30/8-1S, 30/5-2 and 30/8-3) showed a consistent between the observed and modelled hydrocarbon columns (Skjervøy et al. 2000). In this study we have tried to investigate how the pressure

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increase and distribution influence on the hydrocarbon migration. Pressure models with the high-resolution fault map shows that the pressure increase and distribution have some impact on the migration of the hydrocarbons, but as seen from Figure 14, the low- resolution fault map has an even larger influence on the migration pattern. Resulting low pressure in the prospect area give space for more gas, and more oil can be trapped before spill starts. Using the low-resolution fault map gives disproportionate large pressure compartments, which will give large effect on the simulated pressure in the area. The conclusion from this is that the resolution of the input fault map will be critical to the pressure distribution, and thereby to the hydrocarbon migration. Only small changes in pressure in “key” compartments can influence on the migration as shown using the high-resolution fault maps. The simulations show that even in an intermediate pressured area of a basin, will the faults have major control on the pressure distribution and on possible hydrocarbon migration paths.

Further work This paper suggests that a single layer model is not good enough to be able to explain large pressure differences measured from wells on both side of a small fault in time. A better understanding is obtained of the lateral pressure distribution, since a much larger area is simulated than what was carried out by Childs et al. (2002). They used a very restricted area, but on the other side, they had a multi-layer model. It is suggested that future approach would be to simulate the overpressure and the hydrocarbon migration with multi-layer carrier over a large area. Then, hopefully we could better answer whether models for fault transmissibility is wrong (i.e the faults are more sealing than we model), or whether the Tune Field area is a special case due to the relay zone between the larger faults.

Conclusions The key observations from the results of this study can be summarized as follows: 1. Simulations using a low-resolution fault map give a large-scale understanding of the major trends in the pressure distribution throughout the sedimentary basin. 2. In the Viking Graben study area large overpressures are simulated in the deepest western part of the basin, and close to hydrostatic pressures in the eastern area. In the intermediate zone, a rather narrow zone with intermediate pressure is simulated. 3. To be able to match the overpressures measured in well 30/5-2 and 30/8-1S in the Tune Field, and well 30/8-3 east of Tune, small N-S striking faults have to have higher sealing capacity for fluids than expected. 4. Even with extremely low accommodation depths for the caprock and simulating with increased sealing capacity to small faults, the simulated overpressures are 22 bar higher, than measured in well 30/8-3. 5. The intermediate pressures in the western part may be in connected with lower parts of the sedimentary column in the compartment where well 30/8-3 is situated. In the underlying Ness Formation, higher overpressures are observed, while the shallower Tarbert Formation has nearly hydrostatic conditions. 6. The modelled pressures have a controlling effect on the hydrocarbon migration even in intermediate pressured areas.

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Acknowledgement Thanks to the Tune licence and Norsk Hydro ASA for providing the data. Many thanks also to our colleagues at SINTEF for all help and support, especially Are Tømmerås and Hans Borge for useful discussions. We would also like to thank Prof. Roy H. Gabrielsen for correcting the manuscript and helpful support.

References

Antonellini, M. & Aydin, A. 1994. Effect of Faulting on Fluid Flow in Porous Sandstone: Petrophysical Properties. AAPG Bulletin, 78, 355-377. Antonellini, M. & Aydin, A. 1995. Effect of Faulting on Fluid Flow in Porous Sandstone: Geometry and Spatial Distribution. AAPG Bulletin, 5, 642-671. Aydin, A. & Johnson, A.M., 1978. Development of faults as zones of deformation bands and as slip surfaces in sandstones. Pure and Applied Geophysics, 116, 931-942. Badley, M.E., Egeberg, T. & Nipen, P. 1984. Development of rift basins illustrate by the structural evolution of the Oseberg structure, Block 30/6, offshore Norway. Journal of the Geological Society of London, 141, 639-649. Badley, M.E., Price, J.D., Dahl, C.R. & Agdestein, T. 1988. The structural evolution of the northern Viking Graben and its bearing upon extensional modes of graben formation. Journal of the Geological Society of London, 145, 455-472. Baldwin, B. & Butler, C.O. 1985. Compaction curves. AAPG Bulletin, 69, 622-662. Borge, H. 2000. Fault controlled pressure modelling in sedimentary basins. An thesis for the degree of Doktor Ingenør of the Norwegian University of Science and Technology, Trondheim, 148 pp. Borge, H. & Sylta, Ø. 1998. 3D modelling of fault bounded pressure compartments in the North Viking Graben. Energy, Exploration and Exploitation, 16, 301-323. Buhrig, C. 1989. Geopressured Jurassic reservoirs in the Viking Graben: modelling and geological significance. Marine and Petroleum Geology, 6, 31-48. Childs, C., Manzocchi, T., Nell, P., Walsh, J. J., Heath, A. E. & Lygren, T.H. 2002. Geological implications of a large pressure difference across a small fault in the Viking Graben. In: Koestler, A.G. & Hunsdale, R. (eds), Hydrocarbon Seal Quantification. NPF Special Publication, Elsevier Science, Amsterdam, 187-201. Childs, C., Sylta, Ø., Moriya, S., Walsh, J.J. & Manzocchi, T. 2002b. A method for including the capillary properties of faults in hydrocarbon migration models. In: Koestler, A.G. & Hunsdale, R. (eds), Hydrocarbon Seal Quantification. NPF Special Publication. Elsevier Science, Amsterdam, 127-139. Fisher, Q. & Knipe, R.J. 2001. The permeability of faults within siliciclastic petroleum reservoirs of the North Sea and Norwegian Continental Shelf. Marine and Petroleum Geology, 18, 1063-1081. Færseth, R.B. 1996. Interaction of Permo-Triassic and Jurassic fault-blocks during the development of the northern North Sea. Journal of Geological Society, 153, 931-944. Færseth, R.B. & Ravnås, R. 1998. Evolution of the Oseberg Fault-Block in context of the northern North Sea structural framework. Marine and Petroleum Geology, 15, 467- 490. Grauls, G. 1996. Minimum Principal Stress as a Control on Overpressures in Sedimentary Basins. Proceeding of the 8th Conference on Exploration and Production. IFP, Rueil-Malmaison, 9-10 Desember, IFP Report No. 43313.

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Heppard, P.D., Cander, H.S. & Eggertson, E.B. 1998. Abnormal Pressure and the Occurrence of Hydrocarbons in Offshore Eastern Trinidad, West Indies. In: Law, B.E., Ulmishek, G.F. & V.I. Slavin (eds), Abnormal Pressures in Hydrocarbon Environments. AAPG Memoir, 215-246. Lothe, A.E., Borge, H., & Gabrielsen, R. H. in prep. Sub-seismic faults and their possible influence on overpressure and hydraulic leakage - examples from offshore Mid-Norway. Lothe, A.E., Borge, H. & Gabrielsen, R.H. in press. Modelling of hydraulic leakage by pressure and stress simulations: An example from the Halten Terrace area, offshore Mid-Norway. Submitted to Petroleum Geoscience. Lothe, A.E., Gabrielsen, R.H., Hagen, N.B. & Larsen, B.T., 2002. An experimental study of the texture of deformation bands: effects on the porosity and permeability of sandstones. Petroleum Geoscience, 8, 195-207. Roberts, A.M., Yielding, G., Kusznir, N.J., Walker, I.M. & Dorn-Lopez, D. 1995. Quantitative analysis of Triassic extension in the northern Viking Graben. Journal of the Geological Society of London, 152, 15-26. Skjervøy, A. & Sylta, Ø. 1993. Modelling of expulsion and secondary migration along the southwestern margin of the Horda Platform. In: A.G. Dore (ed.), Basin Modelling: Advances and Applications. NPF Special Publication, Elsevier, Amsterdam, 3, 499- 537. Skjervøy, A., Sylta, Ø. & Weissenburger, K.S. 2000. From basin modelling to basin management: reuse of basin-scale simulations. In: K. Ofstad, J.E. Kittelsen & P. Alexander-Marrack (eds), Improving the Exploration Process by Learning from the Past. NPF Special Publication, Elsevier Science B.V., Amsterdam, 9, 141-157. Sperrevik, S., Gillespie, P.A., Fisher, Q.J. & Knipe, R.J. 2002. Empirical estimation of fault rock properties. In: A.G. Koestler & R. Hunsdale (eds), Hydrocarbon Seal Quantification. NPF Special Publication. Elsevier Science B.V., Amsterdam, 109- 125. Sylta, Ø. 1993. New techniques and their application in the analysis of secondary migration. In: Doré, A.G. (eds), Basin Modelling: Advances and Applications. NPF Special Publications, Amsterdam, 385-398. Sylta, Ø. & Krokstad, W. 2003. Estimation of oil and gas column heights in prospects using probabilistic basin modelling methods. Petroleum Geoscience, 9, 243-254. Sylta, Ø., Childs, C., Sperrevik, S. & Tømmerås, A. 2003. On the use of multi-carrier hydrocarbon migration modelling with clay-smearing in faults. EAGE Conference: Fault and Top Seals. What do we know and where do we go?, Montpellier, France. Abstract only. Townsend, C. 2002. Realistic fault description for reservoir modelling, AAPG Hedberg Research Conference: Evaluating the hydrocarbon sealing potential of faults and caprocks, Barossa Valley, South Australia. Walderhaug, O. 1996. Kinetic modelling of quartz cementation and porosity loss in deeply buried sandstone reservoirs. AAPG Bulletin, 80, 731-745. Yielding, G., Freeman, B. & Needham, D.T. 1997. Quantitative fault seal prediction. AAPG Bulletin, 81, 897-917.

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Chapter 7

An experimental study of the texture of deformation bands: effects on the porosity and permeability

Lothe, A. E.1, 3, Gabrielsen, R.H.3, Bjørnevoll Hagen, N.2 & Larsen, B.T 4

1Sintef Petroleum Research, N-7465 Trondheim, Norway, 2Phillips Petroleum Company Norway, Industriveien, 4056 Tananger, Norway, 3Geological Institute, University of Bergen, Allêgaten 41, N-5007 Bergen, Norway, 4Norwegian Geological Survey (NGU) Oslo Office, P.O. Box 5348 Majorstua, 0304 Oslo, Norway.

Abstract We investigated the texture and formation of deformation bands, in accordance to the permeability and porosity. Video image analysis of the Brumunddal sandstone showed a decrease in the number of large pores in the deformed zones. The frequency of small pores is increasing in the intermediate zone, compared to the undeformed rock and the central zone of a deformation band.

Tri-axial compression tests were performed on Red Wildmoor sandstone with constant confining pressure (8 MPa). Axial P- and S-wave velocities measured during loading showed structural changes in development of a deformation band: Stage I and II closure of micro-cracks and pores and tighter grain packing parallel to the maximum stress direction and simultaneously dilation perpendicular to the maximum stress direction. Stage III both the P- and the S- wave are decreasing, reflecting tighter grain packing and development of micro-fractures. These observations are supported by permeability measured before, under and after tri-axial compression, with recovering of permeability due to elastic effect and static reduction due to tighter packing and ultimately grain size reduction. NMR images of oil saturated samples after loading to failure shows stage III, grain size reduction, stage IV secondary fracturing, and stage IV, development of a slip plane.

Keywords: deformation bands, porosity, permeability, NMR images

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1. Introduction

The present work aims at investigating the processes associated with the development of deformation bands, with particular emphasis on the earliest stages of deformation. The study addresses these processes on both micro- and macros-scale. We also study the change in petro-physical parameters (porosity and permeability) associated with these processes. Deformation bands are faults in porous sandstones (Aydin & Johnson 1978) that may create flow barriers and have strong effect on the communication in porous siliciclastic hydrocarbon reservoirs. In fact, permeability reduction by up to three orders of magnitude has been reported across deformation bands (Antonellini & Aydin 1994). The magnitude of the permeability reduction depends on strain intensity associated with the development of deformation bands (e.g. Gabrielsen & Koestler 1987) and on the degree of lithification during deformation (e.g. Fossen & Hesthammer 2000; Fisher & Knipe 1998).

Deformation bands are planar and take up shear by grain compaction and, with continued stress, grain size reduction by micro-fracturing and cataclasis (e.g. Aydin, 1978; Underhill & Woodcock 1987; Antonellini et al. 1994; Gabrielsen et al. 1998). Thus, the central zone1 of deformation bands may be characterised by tight grain packing, reorientation of grain and grain-size reduction (e.g. Gabrielsen & Aarland 1990; Gabrielsen et al. 1998)(Figure 1). A deformation band can then be sub-divided into a central zone, taking up most of the deformation, and an intermediate zone at the rim to the undeformed rock. Deformation bands are often localised near each other, parallel or sub-parallel oriented in swarms (defined as a zone of deformation band e.g. Aydin, 1978; Aydin & Johnson 1983), which by further deformation can develop into a slip plane. Deformation bands accommodate small amount of offset (millimetre to centimetre), whereas slip planes are surfaces of large displacement discontinuity in the order of >1m. This has been taken as an indication that strain hardening and, hence, widening into a swarm is common in the more advanced stages of deformation (Rudnicki & Rice 1975; Mandl et al. 1977; Aydin, 1978). This view is supported by Mair et al. (2000) and Main et al. (2001), who reported experimental evidence for sequential development of increasing numbers of discrete deformation bands by increasing strain. With lasting strain a discrete slip plane commonly develops (Aydin, 1978; Aydin & Johnson 1978; Fossen & Hesthammer 1998).

The development of a deformation band depends on several physical parameters, such as tectonic stress, confining pressure, fluid pressure, temperature and strain rate, but also intrinsic properties like mineralogical composition, porosity, grain-size and sorting. In densely packed granular materials such as siliciclastic sediments, shearing starts in narrow bands, which are only a few grain diameters thick. The interlocking resistance of the particles is overcome by dilation (Mandl et al. 1977; Sperrevik et al. 2000) and grain breakage. Dilation occurs when the compressive stress is sufficiently low so that the grains can override each other. In such cases, breaking is restricted to abrasive rounding of grains. With greater stress grain crushing will occur (Mandl et al. 1977). Low porosity and low confining pressure favour the formation of dilation bands without

1 Aydin (1978) and Aydin & Johnson (1978) used the term “zone” for a spatially related group of deformation bands as well as for the internal style of one band. To avoid confusion, we follow Aydin (1978) and Aydin & Johnson (1978); “zone” when it comes to the internal architecture and Koestler & Gabrielsen (1987); “swarm” for a group of such structures.

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grain size reduction, whereas high porosity and high confining pressure support compaction and grain-crushing (Antonellini & Aydin 1994).

Zhang et al. (1990) and Yin et al. (1993) preformed experiments with glass beans and sand to investigate whether or not the final style of deformation depends on grain radii. They observed that large grains have few contact points, leading to larger stress concentration and resulting in enhanced grain size reduction in coarse sandstone. Other experiments (Dunn et al. 1973) confirm that porosity and sorting are also controlling factors in the development of deformation bands. A granular material, where the grains display great variation in radius and/or loose packing, will be more easily deformed than a granular material with uniform grain-size distribution and/or dense packing (Antonellini & Pollard 1995).

The present work aims at investigating the processes associated with the development of deformation bands, with particular emphasis on the earliest stages of deformation. We also studied the change in petro-physical parameters (porosity and permeability) associated with these processes. To accomplish this, deformation bands two types of samples were investigated. First, natural deformation bands in samples from the Early Permian Brumunddal sandstone of southern Norway were studied in the field and the laboratory. The field study included mapping, description and classification of deformation bands, as well as analysis of spatial distribution and frequency. This was accompanied by detailed structural and sedimentological investigations of the study area (Lothe, 1998; Haugan, 1998; Haugan et al. in prep.). The laboratory studies included detailed porosity and permeability measurements, which were compared with textural analyse.

The results of the study of the naturally deformed samples were correlated to those obtained by the investigation of deformation bands generated in the laboratory, using a tri-axial deformation cell. To avoid using material in which natural deformation bands already existed, the late Triassic Red Wildmoor sandstone from Bromsgrove, England, was selected. In addition to being almost undeformed, this sandstone has the advantage of being free from clay minerals. It has been frequently used in rock mechanics studies and its mechanical properties are therefore well known. For these samples, the laboratory investigations included registration of P- and S-wave velocities, textural analysis and measurements of porosity and permeability. In addition to light- microscope study of thin sections, Scanning Electron Microscope (SEM) and Nuclear Magnetic Imaging (NMI) techniques were used in to investigate texture. The textures created in the experiments were compared to those observed in the naturally deformed Brumunddal sandstone.

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Figure 1 Schematic architecture of a “complete” deformation band. A zonation of a deformation band is common, although a complete set, as displayed here is rare. UD= Undeformed rock, 1= zone of compaction, 2=zone with reorientation of grain and grain size reduction, 3=zone with mineralization, CJ= central open fracture. From Gabrielsen & Aarland (1990).

2. The Brumunddal sandstone

The Early Permian Brumunddal sandstone is found in Brumunddal, 150 km north of Oslo (Figure 2), in the northern part of Oslo Graben. The fine to coarse-grained sandstones occur in an 800 m thick succession with subordinate mudstone and calcrete horizons. They are exposed in a 6.5 km by 2.5 km area (Rosendahl, 1929; Olaussen et al. 1994; Lothe 1998) in a half-graben, delineated to the east by the NNE-striking and WNW-dipping Brumunddal fault (Figure 2). The total extensional dip-slip across the fault varies between 0.8 and 3 km. The hanging-wall fault block is rotated up to 40° towards ESE. This fault block is further subdivided into minor compartments by WNW-ESE, NNW-SSE and N-S striking faults. The dip-slip displacement along these 2nd order faults is less than 50 m.

The configuration of the deformation bands varies from simple planar (Figures 3a & b), to swarms. Also, the texture of the deformation bands shows a variation from those with reorientation of grains and none or moderate grain-size reduction, to deformation bands with a central zone with pronounced grain-size reduction (Figures 3c & d). The different types of deformation bands co-exist in the present study area.

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Figure 2 Location of the Brumunddal sandstone, 150 km north of Oslo. From Lothe (1998) and Haugan (1998).

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Cross bedding Deformation bands Deformation bands

a) b)

1.3 mm

c) d)

488 µm

e) f)

Figure 3 Examples of deformation bands from the Brumunddal sandstone. a) Deformation band displacing cross bedding (east of the river Leira), b) Weathered planar deformation bands (Hersetbekken), c) Thin section showing a thin deformation band (plug 3)(arrows), d) Thin section showing a crosscutting deformation band, where one deformation band is off-set by the other in 1.3 mm. Sample from Gåskvern. e) SEM-picture showing an approximately 500 µm wide deformation band oriented NE- SW. f) The pores on the SEM-pictures have different colours depending on size: diameter <200 µm (yellow), <100 µm (blue), <50 µm (green), <20 µm (pink), <10 µm (violet). The size of a pore is measured as average of all triangle altitudes drawn between pixels on the convex perimeter.

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3. Measurement of porosity and permeability

Three standard methods were utilised to measure the porosity. Determination using the compressibility of helium gas was performed on rock plugs with lengths and diameters of 25 mm. This method gives the bulk porosity of the sample, including the undeformed rock and the deformation bands (Figure 4 & Table 1). To distinguish the porosity of the undeformed rock from that of the deformation bands, 2-D measurements of porosity were read by point counting thin sections of the deformation band and the undeformed rock. In each point counting, 300 points were measured dividing between different grains, cement and type of porosity. A problem with this method is that the transition between the deformation bands and the undeformed rock is commonly diffuse. Furthermore, the accuracy of the point counting method is reduced in cases where deformation bands are extremely thin. The third method utilised video image analysis (Voyage EDS-Microanalysis) and a JSM-6300 scanning electron microscope study of thin sections. In these analyses the images were segmented to distinguish pore space from mineral grains, using a comb filter on the grey levels of the pixels, and porosity was determined by automatic pixel counting. After the auto-segmentation, the intensity for registration was set to measure the primary porosity. Permeability was measured using the rock plugs oriented parallel or transverse to the deformation band and was also measured in undeformed plugs.

Porosity was measured using the helium gas method on 17 rock plugs taken from outcrops east of Prestsætra and east of the river Leira in northern Brumunddal (see location on Figure 2 & Table 1). Point counting was used on thin sections from six plugs and SEM- analyse on four of the plugs. In plug 3, two SEM- images of the undeformed rock taken from both sides of the deformed zone were analysed and one image was taken in the central zone, covering both the intermediate zone and the central zone of the deformation band (Figures 3e & f). In plug 17, one picture in the undeformed rock, one in the intermediate zone and the centre of the deformation band were analysed. For plugs 10 and 14, five SEM-pictures were analysed, two of which were taken in the undeformed rock, two in the intermediate zone, and one in the central zone of the deformation band.

From the porosity and permeability measured in the undeformed rock in the intermediate zone and in the central zone to the deformation bands, two different patterns can be distinguished, reflecting dilation and reduction of the porosity in the central zone, respectively.

A typical single, planar deformation band with a width of 0.6 mm displays grain size reduction and reorientation of grains in its central zone (Table 2 & Figure 3c). The permeability is reduced from 195 mD in the undeformed rock to 32 mD perpendicular to the deformation band. Porosity determined by He-gas gives a minor decrease in the plug with the deformation band (19%), compared to the plug without the deformation band (20%)(Figure 5a). The band is too thin for point counting in the central zone to be applicable, video image analysis was performed. This SEM analysis demonstrated a small increase in porosity in the central and intermediate zones as compared to the undeformed rock, suggesting that a zone of dilation is preserved. This analysis also revealed that no pores with diameter >100 µm exist in the central zone (Figures 3e & f). It is concluded that there is a pronounced increase in the number of small pores in the central and intermediate zones compared to outside the deformation band. The

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deformation band is asymmetrically zoned: porosity is higher on one side than on the other side (Figure 5b).

Wider deformation bands (2-7.5 mm) are characterised by suppressed bulk permeability and porosity in the central zone (Figure 5c-h). For the widest deformation bands the permeability is reduced by nearly three orders of magnitude from 65 mD in the undeformed rock, to 0.091 mD in a plug oriented perpendicular to the deformation band. This deformations band is almost completely sealing. The lowest permeability value (0.008 mD) was measured perpendicular to a deformation band that had calcite cement in its central zone (Figure 5e & Table 2).

The widest deformation band (plug 14) shows a reduction in porosity from 14% (gas method) in the undeformed rock, to 6% (point counting) in the central zone. SEM- analysis gives 1% porosity in the central zone (Figure 5g). Five SEM-images were used to construct porosity profiles across the deformation bands. All of these display a symmetrical architecture, with a low porosity/low permeability central zone and a transitional zone of intermediate porosity and permeability.

Video image analysis also gives the pore size distribution. For the widest deformation bands, the smallest pores (<20 µm) are less frequent within the deformation band as compared to the undeformed rock, but in the border zone no clear correlation is seen. The larger pores (>20 µm) are less frequent in the border zone and in the central zone of the deformation band, than in the undeformed rock (Figure 5h). Deformation bands with reduced porosity show a decrease in the number of large pores in the intermediate and central zones, compared to the undeformed rock (Figures 5d, f, & h): the frequency of small pores increase from the undeformed rock to the intermediate zone. As expected, there is also a reduction in the number of small pores in the central zone. For the wider deformation bands destruction of larger pores in the border zone seems to be accompanied by a decrease of large pores and an increase of small pores. In the central zone, however, there is lower frequency of both small and large pores as compared to the undeformed rock. The frequencies of different pores are symmetrically distributed in these deformation bands (Figures 5d, f & h).

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Table 1 Porosity and permeability measured using the He-gas method in plugs oriented parallel to and at a right angle to deformation bands and in undeformed rocks. Orientation of Width of the Plug Permeability Location deformation band in deformation Porosity (%) No. (mD) plugs band 1 perpendicular* (band A) 1.5 mm 19 10 2 North of parallel* (band A) 18 48 3 Prestsætra perpendicular (band B) 0.6 mm 19 32 4 parallel (band B) 19 107 5 no band 20 195 16 perpendicular 6.3 mm, 12 0.008 “ 17 parallel 13 56 15 no band 24 53 6 East of perpendicular 2.0 mm 15 1.1 7 Leira parallel 14 12 8 no band 17 77 9 “ perpendicular 4.5 mm 14 0.012 10 “ perpendicular 2.0 mm 14 0.13 11 parallel 14 47 12 no band 17 112 14 “ perpendicular 7.5 mm 15 0.091 13 “ no band 17 65 *Perpendicular or parallel to long axis of the plug

Table 2 Description of the undeformed rock and the deformation band analysed. Plug Location Description of the sandstone Description of the deformation band No. 3. North of The yellow sandstone is medium to Some grain size reduction and Prestsætra coarse grained, well sorted and has reorientation in the central zone (0.6 sub-rounded to rounded grains. It is mm wide). 17. loosely packed, and has high Well-defined central zone (6.3 mm) primary porosity. Thin sections with grain size reduction and calcite show poikilotopic grains, and quartz cementation between the grains. The and feldspar overgrowth. central zone has less mono and polycrystalline quartz and feldspar and an increase of calcite cementation compared to the undeformed rock. 6. East of The red sandstone is medium to Reorientation of grains in the central Leira coarse grained, with sub-rounded to zone (2.0 mm wide). There is an rounded grains, and high primary increase of mono crystalline quartz porosity. Thin section shows from the undeformed rock to the pressure solution, feldspar deformation band. 9. overgrowth and hematite coatings Intense grain size reduction in the 4.5 around quartz grains. mm wide central zone, and a sharp border from deformed to undeformed rock. 10. A red, 2.0 mm wide, deformation band. Graded transition from the undeformed rock to the deformed rock. It has grain size reduction and iron hydroxide precipitation between the grains.

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14. A broad 7.5 mm wide central zone with iron hydroxide and feldspar deformed between angular quartz grains. There is a sharp border between the undeformed and the deformed rocks. In the deformation band Ridel shear is observed.

1000 0,6mm 1,5mm 2,0mm 2,0mm 6,3mm 4,5mm 7,5mm 100

10 Kn 1 Kp 1 3 17 6 9 10 14 Khr 0.1 Permeability (mD)

0.01

0.001

Figure 4 Examples of the variation of permeability in samples containing or lacking a deformation band. Samples are from location north of Prestsætra (plug 1,3 and 17) and from location east of Leira. Kn, Kp and Khr are the permeabilities measured normal and parallel to the deformation band and in the undeformed rock. The number above the column is the width of the deformation band and the number underneath is the plug number.

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<5 um b) Porosity (SEM) Plug 3 5-<10 um Porosity (point counting) 600 10-<20 um Porosity (plug) 550 20-<50 um Permeability (plug) 500 >50 um 450 400

y 350 a) Plugs 3,4 and 5 nc 300

30 1000 que e

250 Fr

25

D)

) 100

m 200 20 10 150 15 ility ( sity (%

o 1

r 100

o 10 eab P m 50 5 0.1 r

e

P 0 0 0.01 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6

c) Plugs 10, 11 and 12 d) Plug 10 30 1000 300

25 D) 250

) 100 y % 20 ( 200 nc

y 10 ty (m t i

15 ue ili s 150 1 q ro e

10 r 100 eab F Po m 5 0.1 r 50 e 0 0.01 P 0 -6 -4 -2 0 2 4 6 -6-4-20246 e) f) Plugs 15, 16 and 17 Plug 17 30 1000 300

25 ) 100 250 ) y % 20 200 ( nc

y 10 t i 15 ility (mD s 150 que 1 b ro 10 e 100 ea Fr Po 5 0.1 m 50 0 0.01 Per 0 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 g) h)

Plugs 13 and 14 Plug 14 30 1000 300

D) 25 250

) 100 y % /m 20 c 200 ( y 10 n t ty i

15 ili

s 150 b 1 que a ro e 10 e 100 Fr Po m 5 0.1 r e 50 P 0 0.01 0 -6 -4 -2 0 2 4 6 -6-4-20246

Figure 5 a, c, e & g) Porosity and permeability measurements based on SEM, point counting and flow of He-gas showing variations across deformation bands (see Table 2 for description of samples and each deformation band, respectively). Undeformed rock tested close to the deformation bands - horizontal parts of curves. A drop in both permeability and porosity in the central zones (corresponding to zone 2 and/or zone 3 in Figure 1) is seen. The drop in the permeability is up to 5 orders of magnitude. b, d, f & h) shows the frequency of pores of different size measured in µm across the same deformation bands. Note that an increase in the number of small pores (<20 µm) is common in the intermediate zone of the deformation bands (zone 1 in Figure 1).

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4. Experimental development of deformation bands

The aim of the experimental work was to identify textural changes in siliciclastic sandstones during loading and to investigate the relation between textural changes and porosity and permeability. Techniques using acoustic velocities, optical microscopy, SEM and NMI were employed.

The MTS 815 Rock mechanics test system at Norsk Hydro Research Centre, Norway was used in the tri-axial shear strength tests. Each sample was jacketed in a rubber sleeve to isolate it from the confining fluid. A circumferential and an axial extensiometer measured changes in width and length of the sample during testing. The tests were executed under room temperature conditions and with zero pore pressure. Two experimental series were performed. In the first series dry samples were applied to determine the shear strength and to investigate deformation mechanisms. In the second series, samples were saturated with oil and permeability was measured during different stages of loading. The oil used in the tests is the standard EMO 4000.

In the first test series, the confining pressure was kept constant (8 MPa). The maximum compressional stress was increased at a constant rate (deformation rate 0.001%). One sample (S4) was loaded until failure occurred, whereas three other samples were exposed to stress less than the shear strength (Table 3). For sample S4 ultrasonic transducers were employed at the top and bottom pistons and acoustic wave velocities were measured along the maximum stress axis. The piezo ferroelectric components of the ultrasonic transducer were used to generate and receive high frequency ultrasonic vibrations. The frequency was kept constant at 600 kHz.

In test series 2 the samples were saturated with oil (EMO 4000) at 21.4°C/atm, density 0.8077 g/ml and viscosity 2.74 cp. The permeability was measured before, during and after stress was applied. When measuring the permeability before loading, the hydrostatic pressure was kept at 2 MPa. The confining pressure was then raised to 8 MPa, before the compressional axial stress was increased at a constant rate (deformation rate 0.001%). The permeability was measured once under maximum loading. When testing different samples, the maximum axial stresses were varied. The cores were then reloaded to 2 MPa hydrostatic pressure, to measure the permeability again. During the different stages of loading, the permeability was measured with three different pump rates (1, 2 and 4 ml/min).

The porosity of the undeformed samples was measured using oil (EMO 4000), which gave the effective bulk porosity. The porosity in the samples after loading was not quantified directly, but can be evaluated indirectly by NMR images (Appendix). The output presented in this work is in the form of M0 and T1 pictures. The M0 picture represents the total magnetisation, which is proportional to the number of protons, e.g. the porosity. The T1 (relaxation time) picture depends on the pore size of the rock sample. In the analysis of thin sections a Scanning Electron Microscope JSM 6300 coupled to a Voyager 2 Microanalyse System was used (second electron and backscatter electron).

The sample rock-type used in the experimental part was the Red Wildmoor sandstone, a late Triassic sandstone from Bromsgrove, England (Table 4). This quartz-rich (90%) sandstone has well-rounded grains, with some angular feldspar (6%) and rock

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fragments (4%). No clay is present, but hematite exists as a coating on the grains. Secondary porosity and pressure solution is observed. Using He-gas the measured porosity is 27% in the tested samples. Cylinders of 37.5 mm diameter were cored from blocks, then cut and polished in the ends to produce right-angled planes. All sample preparation was carried out at room temperature. The samples marked H in the figures have horizontally oriented sedimentary layers (perpendicular to the cylinder axis), while in the samples marked LV, the layers are low angled. In the samples marked S there are no visible sedimentary layers.

The aim of the tri-axial compression test is to identify structural changes in the core sample during loading (Figure 6a), by continuously measuring the axial compressional and shear wave velocities. Figure 6b shows how, with increasing strain the P- and S- wave velocity-variation can be divided into three stages. In the first stage the P-wave velocity rapidly increased up to 4 %. In stage II from 4 to 5 % the P-wave velocity varied, with the maximum velocity (1980 m/s) at 5 %. In the last stage the P-wave velocity gradually decreased to 1934 m/s. The S-wave velocity displays a similar general pattern, but with smaller changes in values, but reached its maximum at 4 % (1180 m/s). In stage II and III the velocity slowly decreased to a value 20 m/s less than the initial measured S-wave velocity.

The increase in P- and S-wave velocities with increasing axial strain up to 4 % probably reflects the closure of micro-cracks and micro-pores. With increasing axial stress the grains become more tightly packed, giving higher acoustic velocities. Between 4 and 5 % the P-wave velocity still increased, indicating continuous tightening of the grain packing in the vertical direction. The decrease in S-wave velocity implies pre- opening/dilation of micro-cracks perpendicular to the axial stress direction, because the shear wave velocity reflects horizontally particle motion perpendicular to the wave propagation direction. In stage III both the P- and S- wave velocities decreased, reflecting tighter grain packing, which was followed by the development of micro- cracks.

The shear strength of the rock samples averages 33.5 MPa. In a previous study using Red Wildmoor sandstone under similar stress conditions and confining pressure (8 MPa), a shear strength of 36.7 MPa was obtained (Ringstad & Fjær 1990, unpubl.). Hence, deformation without fracturing could be expected for the cores that were loaded to maximum stresses of 25, 27 and 31 MPa. This is reflected in the stress-strain curve in the first experiment where the graph started to become less steep at around 33 MPa suggesting that elastic deformation prevailed up to that stress level (Figure 6a).

To measure the permeability as a function of strain in the elastic regime (before failure) the permeability was measured for six cores prior to and after loading under a confining pressure of 2 MPa (Figure 7). During loading, confining pressure was kept at 8 MPa for all the samples, while the axial compressive stress was varied from 30 MPa to 39 MPa. Except for one sample (H1), which failed at 41.7 MPa, all samples remained cohesive during the experiments.

Figure 7 shows how the permeability varied at the different stages of the test series. For all the samples tested, the permeability decreased during loading. The permeability reduction varied between 78% and 45%, with an average loss of 67%. Generally, the cores recovered part of the permeability after deloading, indicating that the bulk of the

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porosity loss was associated with elastic deformation. The recovery varied from 102% to 117%. One sample (H6) did not recover any permeability after de-loading, but lost 47% permeability compared to the one measured during deformation. For this sample, however, when measuring after loading under hydrostatic pressure, the permeability varied unsystematically, probably because cohesion was lost due to incipient cataclasis, so that loose grain fragments blocked the flow.

In summary, the permeability fluctuation recorded during the tests reflects the dynamic and static components in the deformation process. When the samples were loaded, the permeability became reduced due to tighter grain packing, closure of micro-cracks oriented perpendicular to maximum compressive stress, elastic deformation of grains, and ultimately grain size reduction. However, a large part of the permeability was recovered, reflecting that elastic deformation is dominant in the early stage of deformation. The results suggest that the development of deformation bands includes simultaneous elastic and permanent deformations. It is suggested that these processes are spatially separated so that they take place in different zones within a deformation band.

Table 3 Confining pressure, axial loading, length and diameter of the dry samples tested in the triaxial cell. Sample No. Confining Start End length Start End diameter Axial pressure length (mm) diameter (mm) loading (MPa) (mm) (MPa) (mm) S 3 8.0 76.3 76.1 37.6 37.6 25.0 S2 8.0 76.3 76.2 37.5 37.5 27.0 S1 8.0 76.3 76.0 37.6 37.6 31.0 S4 8.0 75.8 (fracture) 37.5 (fracture) 33.5

Table 4 Description of the Red Wildmoor sandstone used in this work. From Bjørnevoll (1996) General Micro Chemical XRF analysis Youngs Poissons ratio description description (n=1)(%) modulus (GPa) min max min max Late Triassic Bimodal grain SiO2 78.48 5.01 5.16 0.209 0.214 sandstone from size distribution, Al2O3 11.19 the Red Wildmoor with very fine to K2O 3.47 sand pit in fine grains Fe3t 1.70 Bromsgrove, dominating Na2O 0.74 England. The medium grains. MgO 0.62 sandstone is fine The grains have CaO 0.36 to coarse grained, high sphericity, TiO2 0.34 partly cross- are subrounded, P2O5 0.10 stratified and with MnO 0.042 partly horizontally occasionally S 0.026 layered. subangular and rounded grains. Zr (ppm) 131 Cr (ppm) 35

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a) b) 40 1980 1180 ) ) ) s

35 1970 1170 s a / / P m 30 1960 1160 m M ( ( y

y (

25 t t

1950 1150 i ci c ess 20 o I II III o r l 1940 1140 Vp 15 e st l 1930 1130 vel Vs a e

i 10 v x ave v 1920 1120 a A 5 w w - 1910 1110 - 0 S P 012345678910 1900 1100 012345678910 Axial Strain (%) Axial Strain (%)

Figure 6 Results from a tri-axial compression test of a Red Wildmoor sandstone sample at 8 MPa confining pressure. a) Axial strain vs. axial stress and b) axial strain vs. axial P- and S-wave velocities. Roman numbers indicates stages in the P- and S-wave velocity development. See text for more detailed explanation.

39.0 500 35.0 35.1 36.6 33.1 400 30.1 Permeability before loading 300 Permeability under loading 200 Permeability 100 after loading Permeability (mD)

0 H2 H3LV1H5 H6LV2 Sample No.

Figure 7 Permeability measured before, during and after loading in the tri-axial test. During loading the confining pressure was 8 MPa, whereas a confining pressure of 2 MPa was applied when measuring the unloaded samples. The number above each column cluster gives the maximum stress (in MPa) applied in each experiments.

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5. The texture of deformation bands

The study of six cores was expanded using a scanning electron microscope, supplemented by light microscopy and MRI. For three of these samples, loading was terminated before fracturing occurred, while the three others were loaded until failure (Table 5).

Two oil-saturated cores (LV1 and LV2) were loaded to 35 MPa and 39 MPa in the tri- axial test. The shear strength of horizontally layered samples was 42 MPa. The samples LV1 and LV2 were loaded to 84% and 94% of the rock strength respectively and MRI of the cores pre- and post loading were acquired. These images display no open fractures. In the M0 image an area of weak dark traces can be observed, indicating zones with low porosity (Figure 8a), whereas no clear effect was observable in the T1-recording (Figure 8b).

Another pair of oil-saturated cores (H1 and H9) was loaded in the tri-axial cell until failure occurred and a shear failure developed. Figure 8c shows a M0 recording where a darker thin zone, probably due to low hydrogen content, is seen. If the cores were fully saturated with oil, a dark thin zone indicates an area with low porosity. This zone is surrounded by a shadow that probably represents a zone of low porosity. In the cases when the sample was not fully saturated by oil, the dark colour could indicate an open fracture that was not filled with fluid.

The corresponding T1 image from the same core, representing the pore distribution, shows a broader area around the zone displayed as a bright area (Figure 8d). This zone is interpreted to represent a zone of dilation. It is also possible to identify smaller fractures situated near the larger fault in the NMR aperture imagery (Baldwin pers. com.).

From the recordings, it is clear that the deformation at the fracture surface is concentrated in zones separated by undisturbed areas. Figure 9a & b show a SEM- mosaic of one sample, which has been brought to rupture in a tri-axial cell without and with our interpretation, respectively. The main fracture plane coincides with the upper surface. Two fracture sets are observed: one set is oriented sub-parallel to the main fracture surface and is restricted to a zone 0.1 mm from it. The other set, which is believed to represent Riedel-shears, is oriented with an angle 20° to the fracture plane, indicating a dextral movement, which is in accordance with the recorded slip direction (Figure 9b). The picture covers a zone of approximately 1.2 mm thickness, as measured from the main fracture surface, but it cannot be ruled out that the deformed zone originally was wider because parts of the sample may have been lost in the preparation. Outside the crushed zone an approximately 0.5-1 mm wide zone with tighter grain packing is found and beyond this the grains are mainly undeformed except for some intra-granular cracks. Here, the bulk of the grains are reoriented with the longest axes parallel with the main fracture.

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Table 5 Variation in the permeability under different loading for the different cores. Sample Parameters Meas. 1 Meas. 2 Meas. 3 Comments No. Confining pressure (MPa) 2 - Fracture developed at H1 Axial stress (MPa) 2 41.7 - 41.68 MPa axial Permeability (mD) 383 - - stress Confining pressure (MPa) 2 8 2 H2 Axial stress (MPa) 2 30.1 2 Permeability (mD) 346 213 243 Confining pressure (MPa) 2 8 2

H3 Axial stress (MPa) 2 33.1 2 Permeability (mD) 394 291 296 Confining pressure (MPa) 2 8 2 During time the permeability H5 Axial stress (MPa) 2 35.1 2 192 decreased on measure Permeability (mD) 423 222 (116) station 2 Confining pressure (MPa) 2 8 2 Meas. 3 the perm. H6 Axial stress (MPa) 2 36.6 2 never stabilised on 4 Permeability (mD) 417 281 ca. 133 ml/min Confining pressure (MPa) 2 8 2 LV1 Axial stress (MPa) 2 35 2 Permeability (mD) 449 351 410 Confining pressure (MPa) 2 8 2 LV2 Axial stress (MPa) 2 39 2 Permeability (mD) 497 374 432

a) b)

c) d)

Figure 8 Nuclear Magnetic Images displaying fractures and fracture swarms (white arrows) generated during experimental tri-axial loading of Red Wildmoor sandstone cores. a) and b) show Mo and M1 imagery of core LV1. c) and d) are similar imagery for core H9. See text for more details.

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a) Slip plane

1 mm b)

Figure 9

Figure 9 SEM-imagery mosaic a) with and b) without interpretation, oriented perpendicular to the fault plane in the rock sample, showing cracks parallel to and with an angle approximately 20˚ with the slip plane. The micro-cracks are believed to represent Riedel shears. Note that the micro-fractures fade away from the slip-surface.

6. The development of deformation bands

Several previous studies of deformation bands have suggested that their development can be divided into distinct phases. Aydin & Johnson (1983) identified three. The first stage is the initiation of single deformation band, which displacement of the order of millimetres. The second stage, which occurs with continued displacement, involves strain hardening caused by the packing of grains and grain crushing (Rudnicki & Rice 1975; Hirth & Tullis 1989). This will prevent further shear along this particular deformation band and a new, sub-parallel one becomes initiated. By multiple repetitions of this process a zone of deformation bands develops, which can accumulate bulk strains of the order of a centimetre or decimetre. The third stage is characterised by strain softening and occurs when displacement is transferred to one single surface. This would be the last stage of the development and the accumulated strain may range from decimetres (Fossen & Hesthammer 1998) to many tens of meters or more. This scheme was modified and expanded by Mair et al. (2000) who, based on tri-axial laboratory tests, identified a sequence of seven stages in the development of deformation bands and zones of deformation bands.

Gabrielsen & Aarland (1990) and Gabrielsen et al. (1998), based on a textural microscope study, suggested a zoned architecture of deformation bands (Figure 1). A core, which is occasionally mineralised and where a linked system of fractures is sometimes developed, is flanked by parallel layers of cataclasite or fault gouge and distal zones where porosity is lost and grains are reoriented, but where no grain-size

- 171 - reduction has taken place. This type of zonation is not necessarily symmetrical. Combining these models with the present observations, a sequence of events can be identified all distinguishable by characteristic textures. Each stage also seems to be have a certain characteristics when porosity and permeability are concerned. It should be emphasised that the development described by Mair et al. (2000) includes the sequential initiation of and interaction between several single deformation bands within a zone. This makes the process more complex and variable than that described below, which considers the deformation within one single deformation band only.

6.1 Stage I Dilation

Stage 1 is related to the incipient stage of strain. Dilation is commonly experienced in the earliest stage of low-stress (5–600 kPa) ring-shear experiments with sand (Mandl et al. 1977; Sperrevik et al. 2000; Clausen & Gabrielsen 2001). It is ascribed to volume adjustments associated with rotation and reorientation of angular to sub-rounded grains. Sperrevik et al. (2000) observed that this process was heralded by a minor contraction, followed by decrease in shear stress and dilation. This suggests that new weak zones of loose grain packing, which accommodate continued shear, are generated (Rudnicki & Rice 1975; Mandl et al. 1977). Tri-axial experiments performed using sandstone show that positive dilation may occur at low values of confining pressure, with peak values just before shear band localisation (e.g. Bernabe & Brace 1990).

The zone of dilation would be characterised by expansion of the primary single pores as well as bulk pore volume in the incipient deformation band. This is a mechanically unstable configuration that would collapse with continued strain and increased loading stress, suggesting that the preservation potential for this type of texture is small. Still, zones of enhanced porosity are sometimes found as halos around deformation bands, perhaps representing preserved remnants of the dilational stage (Figure 8d). Thus, it is of interest to note that Mair et al. (2000) reported enhanced pore volume along the walls of deformation bands in experiments performed under confining pressure as high as 34 MPa, speculating that this was due to an early stage of dilation. Also Heiland & Raab (2001), who measured the permeability variation during tri-axial loading at a confining pressure of 10 MPa, reported that an increase in the permeability occurs prior to the development of deformations band, indicating a dilation stage. Wong & Zhu (1999), on the other hand, show in their experiments that the permeability would actually decrease while the pore space dilates as a sample is stressed to brittle failure. Since the permeability measurements in our study were carried out before and after loading, the variation in permeability in this early stage has not been recorded.

It is noted that NMI-recordings from fractured cores in our experiments reveal mode I- fractures oriented subparallel to σ1, as well as fractures oriented in the theoretical plane of maximum shear (Figure 8a). Of particular interest is the M0 and T1-imagery (Figures 8c & d), where a wider halo of enhanced porosity and presumably deformation surrounds the latter fracture system. It is unclear whether this is a zone of dilation (“process zone” in the nomenclature of Dunn et al. 1973) or a “wake of destruction” (Friedman & Logan 1970), but we think that the wide halo argues in favour of a zone of dilation.

Increasing porosity will cause P- and S-waves to slow down, which agrees with observations at an early stage in the present experiments. However, at the very

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beginning of loading, pre-existing flaws are closed, giving an increase in the velocities followed by a decrease in the velocities due to dilation (Figure 6b). Analysis of acoustic emissions suggests that the initial stage of deformation affects a wider area of the deforming rock and that the activity gradually concentrates in the plane of maximum shear, as is also reported from non-porous rocks (Lockner et al. 1991).

6.2 Stage II Pore collapse

This stage is characterised by collapse of the pores in the incipient deformation band. In low-stress (shallow) regimes, this process is probably associated with the stabilisation of the grain matrix following the dilational reorganisation of stage 1. Hence, it is commonly accompanied by strain hardening (Aydin & Johnson 1978, 1983; Gabrielsen & Koestler 1987; Sperrevik et al. 2000).

The deformational process zone developed in stage 2 seems mainly to affect a narrower area than that of stage 1. The zone is often observed at the rim of well developed deformation bands (Figure 10a-e).

Grain compaction should increase acoustic velocity, which would be consistent with the early phase of increasing P- and S-wave velocities on macroscopic scale observed in our experiments (Figure 6). The acoustic velocities measured during tri-axial deformation of dry siliciclastic sandstone in the present study show dependency on strain, with a greater increase in axial P-wave velocity compared to axial S-wave velocity. This is probably due to the closure of micro-cracks oriented perpendicular to the largest stress axis and to the tighter grain packing. Fjær et al. (1989) and Holt et al. (1991) described a similar effect. At low confining pressure (σr = 5 MPa), they detected an increase in axial P-wave velocity (and axially polarised S-wave velocity) resulting from the closing of pre-existing horizontal micro-cracks. This leads to an increase in vertical P-wave velocity, leaving horizontal P-wave velocity unaltered. At higher confining pressure (σr = 50 MPa) this behaviour is much less prominent (Holt et al. 1991). One mechanism for closure of micro-cracks is internal grain-sliding within the deformation band as described by Mandl et al. (1977).

The present permeability measurements suggest that an elastic component accompanies this deformation stage, because between 2% and 10% of the lost permeability is recovered when the samples are de-loaded (Figure 7).

In low stress (shallow) regimes, this process is probably associated with the stabilisation of the grain matrix following the dilatational reorganisation of stage 1. In cases where deformation takes place at deeper levels of burial, stage 1 will not develop, so that the first identifiable stage would be stage 2.

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a) b) c)

UD UD 1 1 1 2 1 2&3 UD 2 1 1 UD

1 mm 1 mm 1 mm

d) e) f) 1 CJ& 2 2 1 1

1 mm 1 mm 1 mm

Figure 10 Textures of deformation bands in naturally deformed sandstones. Examples are taken from the late Jurassic Sognefjord Formation, northern North Sea, except figure 10a) which is from the xxx. a) Thin section of deformation band with zone 2; reorientation of grain an grain size reduction and zone 3; mineralization developed in the central zone (see Figure 1 for reference). On the edge of the deformation band, tighter grain packing (zone 1) is observed. b) SEM-imagery of a deformation band with zone 2 developed in the central zone, and zone 1 in the intermediate zone. Note the sharp border between the undeformed host rock and the deformation band and the fine fracture network in the central zone. c) SEM-imagery of a deformation band with grain size reduction in the central zone (zone 2). d) SEM-imagery of internal structure with shear lenses of zone 2 with grain size reduction. The lenses are separated by zones of weak material, which are partly eroded, perhaps due to leaching. e) SEM-imagery showing a central joint with lenses of deformed rock in grain-size reduction (zone 2). f) SEM- imagery of terminal zone of deformation band, characterized by tailing at the tip line of deformation band.

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6.3 Stage III Grain-size reduction

The grain-size reduction stage heralds increasing strain and is associated with the on-set of fault-parallel shear. Brittle grain-size reduction becomes the prominent deformation process, probably nucleating on high-stress grain-grain boundary contacts (Gallagher et al. 1974). A considerable reduction of grain-size (> 1-2 orders of magnitude) is frequently recorded in deformation bands that display displacement on the mm- or cm- scale (Gabrielsen & Koestler 1987), suggesting that the process of grain-size reduction is most efficient before shear becomes significant (see also Engelder 1974). Detailed analysis of grain-size distribution in fault gouge (Biegel et al. 1989; Marone & Scholz 1989) shows that granulation frequently leads to a fractal, bimodal (Mair et al. 2000) grain-size distribution. The observation that the active deformation band commonly becomes even narrower at this stage suggests that strain softening is takes place within each deformation band at the transition from the pore collapse stage. With continuing strain, however, strain hardening takes over, commonly terminating the movement along the actual deformation band and activating another. This will cause the zone to widen (Aydin 1978; Aydin & Johnson 1978, 1983).

The texture of the deformation band changes dramatically during the grain-size reduction stage. In the scanning electron microscope, a central zone is seen as a homogeneous, tight band (Figure 10b & c). With continued deformation this zone breaks up into tiny, lozenge-shaped fragments or “micro-horses” (Gabrielsen & Koestler 1987) (Figure 10d). These features are oriented with the longest axes sub- parallel to the fault zone and may consist of micro-brecciaed fragments or country-rock, which is fractured to various degrees (Figure 10e).

Thin sections taken across deformation bands from the Brumunddal sandstone display a decrease in the number of pores in the central zone. In the intermediate zone, however, an increase of small and partly intermediate pores can be observed, but there is a bulk lowering of the porosity. The increase in small pores in the intermediate zone is probably due to crushing of larger grains that take place by continued strain. An interesting question is whether deformation bands are asymmetrical, as proposed by Mandl et al. (1977). From our work this seems likely.

The grain-size reduction stage is accompanied by a significant reduction in the permeability and the porosity. The data from the Brumunddal sandstone are in accordance with the observation of e.g. Antonellini et al. (1994), that permeability reduction amount to three orders of magnitude perpendicular to the deformation band and one order of magnitude parallel with the band. However, it is important to distinguish between deformation bands with and without cementation (zone 3; see Figure 1)(Fisher & Knipe 1998). One example of a deformation band with such characteristics is seen in plug 17, which is almost sealing.

In the tri-axial compressional test, where acoustic velocity and strain were compared, a rather low confining pressure (8 MPa) was used. This is significantly lower than stress applied in the experiments by Mair et al. (2000)(34 MPa) and in examples reported from other studies (e.g. Antonellini et al. 1994). However, the decrease in P- and the S- wave velocities in the last stage in the present experiments indicate that micro-cracks both parallel and oblique to σ1 were generated. Depending on the strength of the cement

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and the grains, some minor grain size reduction would be expected and such effects are indeed seen in thin sections using the electron microscope.

The permeability measurement using oil was also carried out with a confining pressure of 8 MPa, demonstrating that permeability reductions between 91% and 32% occurred when the measured values under hydrostatic conditions before and after deformation are compared. No clear relation between the reduction in permeability and the maximum axial stress has been documented in these experiments.

Stage IV Secondary fracturing The present study included experiments to investigate the deformation, which followed the grain-size reduction and the establishment of a central, homogeneous zone. From electron microscope images (Figure 9 & 10b) it is evident that this stage includes the initiation of tiny fractures with orientations parallel to those to be expected for Riedel- and Y-shears. The possible Riedel-shears are seen to extend beyond the zone of grain- size reduction, hence widening the zone of deformation compared to that of the grain- size reduction stage.

Previous workers have reported fracturing associated with the formation of deformation bands in laboratory experiments. It has been debated whether these represent the formation of a “process zone”, which is active prior to shear (Dunn et al. 1973; Menedez et al. 1996), a “wake of damage” (Figure 10e), which is active after the establishment of the shear fracture (Friedman & Logan 1970), or both (Mair et al. 2000). The experiments performed were demonstrated that fractures develop after the establishment of the non-porous gouge-zone of the deformation band, thus supporting the “wake of damage”-theory. However, our observations do not contradict the existence of mode I-fractures generated at the initial stage of the deformation band, as observed by (Mair et al. 2000); such fractures would be destroyed by later strain and would only be preserved in “pods” or lozenges separating deformation band branches. This type of structure was not studied by us.

Although no systematic study was performed to test the effect on porosity and permeability associated with the fracturing stage, it is reasonable to assume that a modest increase in porosity takes place. SEM images suggest that fracture-parallel permeability is enhanced, and increases even more with continued strain, including the development of a continuous Y-shears and the link-up of Riedel fracture strands.

It is reasonable to correlate this stage of deformation to the decrease in acoustic velocities recorded towards the end of the experiments, since the deformation disrupts the central zone and causes loss of cohesion (Figure 6).

6.4 Stage V Single fault plane

The single fault plane stage was not reached in the present experiments. Nevertheless, the concentration of strain on to one continuous fault strand is commonly observed in faults consisting of swarms or zones of deformation bands in low p,T-regimes (Aydin & Johnson 1978). Such coalescence of strain along one single surface is the ultimate sign of strain softening and would be accompanied by enhanced fault-parallel transmissibility. Alternatively, in situations where strain-hardening processes are active,

- 176 - the deformation band will widen (Aydin & Johnson 1978, 1983) and depress permeability both along and across the fault.

It is realised that a complete set of zones in deformation bands as proposed by Gabrielsen & Aarland (1990) and Gabrielsen et al. (1998) is rarely observed. This is because the initial deformation products such as the zone of dilation, may not be developed at higher confining pressures and, if developed, are commonly destroyed in by further strain. Nevertheless, the identification of different zones, when present, is important because the contrasting textures affect the relation between transverse and parallel permeability.

7. Conclusions

The development of deformation bands can schematically be subdivided into five stages distinguished by their unique texture. Each of these stages also has its particular influence on porosity and permeability, which change considerably from one stage to another:

• Stage I; Dilation perpendicular to the maximum stress direction. Heiland & Raab (2000) reported an increase in permeability prior to development of deformation bands. • Stage II; Pore collapse is shown by closure of micro-cracks and pores, and tighter grain packing parallel to maximum stress direction. • Stage III; Grain size reduction is reflected by a decrease in P- and S-wave velocities and a significant reduction in the permeability and porosity. Permeability measured before, during and after tri-axial compression shows recovering of permeability due to elasticity and static reduction due to tighter grain packing and grain size reduction. In a fully developed deformation band, the number of small pores in the intermediate zone, compared to the central zone of a deformation band and the undeformed rock. For large pores there is a decrease in the pore size in the intermediate and central zone as compared to undeformed rock. • Stage IV; Secondary fracturing can be seen by electron microscopy as Riedel shear and Y-shears. • Stage V; Single fault plane take up all the deformation along a slip plane.

Still, a number of holes in our understanding of the physical processes exist, like the role of micro-fracturing and details related to the influence of systematically increasing differential and efficient stress with depth. In this context, the influence of diagenesis, introduction of fluids and other lithological units also need to be studied in much more detail before we are able to predict characteristics of deformation bands in nature.

Acknowledgements We would like to thanks Johannes Stavrum and Geir Torkilsen at the Norsk Hydro ASA Laboratory for measuring the variation in pore sizes, Arne Graue, University of Bergen for help with measuring permeability and Dr. B.A. Baldwin at Phillips Research Laboratories, Houston for providing NMI-recordings. Norsk Hydro for financial support.

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References: Antonellini, M.A., Aydin, A. & Pollard, D.D. 1994: Microstructure of deformation bands in porous sandstones at Arches National Park, Utah. Journal of Structural Geology, 16, 941-959. Antonellini, M.A. & Aydin, A. 1994: Effect of Faulting on Fluid Flow in Porous Sandstones: Petrophysical Properties. American Association of Petroleum Geologists Bulletin, 78, 355-377. Antonellini, M.A. & Pollard, D.D. 1995: Distinct element modeling of deformation bands in sandstone. Journal of Structural Geology, 17, 8, 1165-1182. Attard, J., Hall, L., Herrod, N. & Duce, S. 1991: Materials mapped with NMR. Physics World, 41- 45. Aydin, A. 1978: Small faults formed as deformation bands in Sandstone. Pure and applied Geophysics, 116, 913-930. Aydin, A. & Johnson, A.M. 1978: Development of faults as zones of deformation bands and as slip surfaces in sandstone. Pure and Applied Geophysics, 116, 931-942. Aydin, A. & Johnson, A.M 1983: Analysis of faulting in porous sandstones. Journal of Structural Geology, 5, 19-31. Baldwin, B.A. & Yamanashi, W.S. 1989: Detecting fluid movement and isolation in reservoir core with medical NMR imaging techniques. Society of Petroleum Engineers, 4, 207-212. Bernabe, Y. & Brace, W.F. 1990: Deformation and fracture of Berea sandstone. In: Duba, A.G., Durham, W.B., Handin, J.W., Wang, H.F. (ed.) The brittle-ductile transition in rocks. American Geophysical Union Monograph, 56, 91-101. Biegel, R.L., Sammis C.G. & Dieterich, J.H. 1989: The frictional properties of a simulated gouge having a fractal particle distribution. Journal of Structural Geology, 11, 827-846. Bjørnevoll, N. 1996: Eksperimentell utvikling av brudd i porøse sandsteiner, og effekten slike brudd har på permeabiliteten. Cand. Scient. Thesis, University of Bergen. Clausen, J.A. & Gabrielsen, R.H. 2002: Parameters that control the development of clay smear at low stress states: an experimental study using ring-shear apparatus. Journal of Structural Geology. Dunn, D.E., LaFountain, L.J. & Jackson, R.E. 1973: Porosity dependence and mechanism of brittle fracture in Sandstones. Journal of Geophysical Research, 78, 2403-2417. Engelder, J.T. 1974: Cataclasis and the generation of fault gouge. Geological Society of America Bulletin, 81, 1515-1522. Fisher, Q.J. & Knipe, R.J. 1998: Fault sealing processes in siliciclastic sediments. In: Jones, G., Fisher, Q.J. & Knipe, R.J. (ed.) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publication, 147, 117-134. Fjær, E., Holt, R.M., Raaen, A.M. 1989: Rock Mechanics and Rock Acoustics. In: Maury, V. & Fourmaintraux, D. (ed.) Rock at great depth. Balkema, Rotterdam, 355-362. Fossen, H. & Hesthammer, J. 1998: Deformation bands and their significance in porous sandstone reservoirs. First Break 16, 21-25. Fossen, H. & Hesthammer, J. 2000: Possible absence of small faults in the Gullfaks Field, northern North Sea: implications for downscaling of faults in some porous sandstones. Journal of Structural Geology, 22, 851-863. Friedman, M. & Logan, J.M. 1970: Lüders bands in experimentally deformed sandstone and limestone. Geological Society of American Bulletin, 84, 1465-1476. Gabrielsen, R.H. & Aarland, R.-K. 1990: Characteristics of pre- and syn-consolidation structures and tectonic joints and microfaults in fine to medium-grained sandstones. In: Barton, N. & Sephansson, O. (ed.) Rock Joints, Balkerma, Rotterdam, 45-50.

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Gabrielsen, R.H., Aarland, R.-K. & Alsaker, E. 1998: Identification and spatial distribution of fractures in porous, siliciclastic sediments. In: Coward, M.P., Daltaban, T.S. & Johnson, H. (ed.) Structural Geology in Reservoir Characterization. Geological Society, London, Special Publications, 127, 49-64. Gabrielsen, R.H. & Koestler, A.G. 1987: Description and structural implications of fractures in late Jurassic sandstones of the Troll Field, northern North Sea. Norsk Geologisk Tidsskrift, 67, 371-381. Gallagher, L.L., Friedman, M., Handin, J. & Sowers, G.M., 1974: Experimental studies related to macrofracture in sandstone. Tectonophysics, 21, 203-247. Harper, T.R. & Lundin, E.R. 1997: Fault seal analysis: reducing our dependence on empiricism. In: Møller-Pedersen, P. & Koestler, A. (ed.) Importance for Exploration and Production, NPF Special Publication, Elsevier, Amsterdam, 7, 149-165. Haugan, M.H. 1998: Avsetningshistorie og diagnetisk utvikling i Brumunddalsandsteinen og relaterte avsetninger. Cand. Scient. Thesis, University of Bergen. Haugan, M.H., Lothe, A.E., Gabrielsen, R.H., Talbot, M., Olaussen, S. & Larsen, B.T. in prep: Structural and sedimentological aspect of the Early Permian Brumunddal Sandstone and associated sedimentary rocks, northern Oslo Graben. Heeremans, M. Larsen, B.T. & Stel, H. 1997: Paleostress reconstruction from kinematic indicators in the Oslo Graben, southern Norway: new constraints on the mode of rifting. Tectonophysics, 266, 55-79. Heiland, J. & Raab, S. 2001: Experimental investigation of the influence of differential stress on permeability of a Lower Permian (Rotliegend) sandstone deformed in the brittle deformation field. Physical Chemical Earth (A), 26, 33-38. Hirth, G. & Tullis, J. 1989: The effects of pressure and porosity on the micromechanics of the brittle-ductile transitions in quartzite. Journal of Geophysical Research, 29, 399-412. Holt, R.M., Fjaer, E., Raaen, A.M. & Ringstad, C. 1991: Influence of stress states and stress history on acoustic wave progradation in sedimentary rocks. In: Hovem, J.M. et al. (ed.), Shear Waves in Marine Sediments, 167-174. Lockner, D.A., Byerlee, J.D., Kuksenko, V., Ponomarev, A., Sidorin, A. 1991: Quasi-static fault growth and shear fracture energy in granite. Nature, 350, 39-42. Lothe, A.E. 1998: Den strukturelle utviklingen av Brumunddalsandsteinen: forkastningsgeometrier, tilpasningsstrukturer og deformasjonsbånd. Cand. Scient. Thesis, University of Bergen. Main, I., Mair, K., Kwon. O., Elphick, S. & Ngwenya, B. 2001: Experimental constraints on the mechanical and hydraulic properties of deformation bands in porous sandstones; a review. In: Holdsworth, R.E., Strachan, R.A., Magloughlin, J.F. & Knipe, R.J. (ed.), The Nature and Tectonic Significance of Fault Zone Weakening, Geological Society of London Special Publication, 186, 43-63. Mair, K., Main, I. & Elphick, S. 2000: Sequential growth of deformation bands in the laboratory. Journal of Structural Geology, 22, 24-42.1111 Mandl, G., de Jong, L.N.J. & Maltha, A. 1977: Shear Zones in Granular Material. Rock Mechanics, 9, 95-144. Marone, C. & Scholz, C.H. 1989: Particle size distribution and microstructures within simulated fault gouge. Journal of Structural Geology, 11, 799-814. McEachran, D.B. 1986-1992: StereoTM v. 5.21 Orientation Analysis fore the Macintosh. Menendez, B., Zhu, W., & Wong, T.-F. 1996: Micromechanics of brittle faulting and cataclastic flow in Berea sandstone. Journal of Structural Geology, 18, 1, 1-16. Olaussen, S., Larsen, B.T., & Steel, R., 1994: The upper Carboniferous-Permian Oslo Rift: basin fill in relation to tectonic development. Pangea: Global Environments and Resources. Canadian Society of Petroleum Geologists, 17, 175-197.

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Ramberg, I.B. & Spjeldnæs, N. 1978: The tectonic history of the Oslo Region. In: Ramberg, I.B. & Neumann, E.-R. (re.) Tectonics and Geophysics of Continental Rifts. Reidel Publishing Company, Dordrecht, 167-194. Ringstad, C. & Fjær, E. 1990: Scaling effects in hollow cylinders. Internal IKU report no. 33.0529.00/01/90. Rosendahl, H. 1929: Brumunddalens porfyr-sandstein-lagrekke. Norsk Geologisk Tidsskrift, 10, 367-448. Rudnicki, J.W. & Rice, J.R. 1975: Theory of inelastic deformation for strain hardening (or softening) materials. Journal of Mechanical Physical Solids, 23, 371-394. Sperrevik, S., Færseth, R. B. & Gabrielsen, R.H. 2000: Experiments on clay smear formation along faults. Petroleum Geoscience, 6, 113-123. Sundvoll, B. & Larsen, B.T. 1994: Architecture and early evolution of the Oslo Rift. Tectonophysics, 240, 173-189. Underhill, J.R. & Woodcock, N.H. 1987: Faulting mechanisms in high porosity sandstones; New Red Sandstone, Arran, Scotland. In: Jones, M.E., Preston, R.M.F. (ed.) Deformation of sediments and sedimentary rocks. Geological Society of London Special Publication, 29, 91- 105. Yin, H., Marvko, G. & Nur, A. 1993: Grain size effects on porosity, permeability and acoustic velocities in granular materials. Eos 74, 43, 568. Wong, T.-F. & Zhu, W. 1999: Brittle faulting and permeability evolution: hydromechanical measurement, microstructural observation, and network modeling. Faults and subsurface fluid flow in the shallow crust, Geophysical monograph, 113, 83-99. Zhang, J., Wong, T.F., & Davis, D.M. 1990: Micromechanics of pressure-induced grain crushing in porous rocks. Journal of Geophysical Research, 95, 341-352.

Appendix NMR images of fluid in porous rocks The Nuclear Magnetic Resonance (NMR) image technique (also called magnetic resonance image (MRI)), is a useful way to image fluids in porous rocks (e.g. Baldwin & Yamanashi 1989; Attard et al. 1991). The nuclear magnetic resonance refers to a physical principle - response of a nuclear particle to a magnetic field. Hydrogen has a relatively large magnetic momentum and is abundant both in water and hydrocarbons in the pore space of rocks. During the imaging samples were placed in a Teflon shrink tubing, with ceramic frit in the ends that allowed for flow to take place. The core was then put in a sample coil (receiver) surrounded by a magnetic field (B0). This magnetic field influences the protons, which will align the Bo field. After a certain time period, a second magnetic field (B1) is applied perpendicular to the initial static field B0, reorienting the spinning protons. This change induces a spin echo in the receiver, and by changing the size of the magnetic field, the whole sample can be scanned. The output presented in this work is M0 and T1 pictures, where the M0 picture represents the total magnetisation, which is proportional to the number of protons, e.g. the porosity. The T1 (relaxation time) picture depends on the pore size of the rock sample.

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Chapter 8

Discussion and Conclusions This dissertation deals with simulations of hydraulic fracturing and leakage of fluids from overpressured reservoirs though the cap rock. Borge (2000) describes how generation and dissipation of pressure is a continuous lateral fluid flow process. Hydraulic leakage due to hydraulic fracturing on the other hand, is a discontinuous vertical fluid flow process that again will affect the lateral flow. Borge (2000) used empirical depth-dependent leak-off pressure curves to calculate hydraulic leakage from overpressured compartments. Mechanisms for fracturing were not considered. In this work I wanted to include a more process-based understanding of hydraulic failure and leakage in the simulator, by introducing stresses and failure criteria. The overall aim of the work was to predict where hydraulic fracturing and leakage will occur, and the amount and the durability of the leakage.

It is debated how hydraulic fractures occur and to what extent (e.g. Cosgrove 1998). Does the leakage occur along one individual fault or does a fracture network develop? In the simulations presented in this thesis, this problem is not fully solved since it is difficult to identify the different fracture models from field observations. We assume that most compartments that fail will develop a fracture network, but the simulator does not distinguish between single faults and fracture networks. Failure is defined by the Griffith-Coulomb failure criterion. When the rock body loses cohesion, the frictional sliding criterion is used. The leakage from one compartment is then characterized with a peak followed by steady state flow. The results are in line with observation from manmade hydraulic leakage in reservoirs.

The effect of different factors on the timing and amount of hydraulic leakage are discussed in the thesis and the most important factors are a) fault transmissiblities, b) stress-strain relationship, c) caprock geo-mechanical parameters and d) resolution of fault maps. a) Fault transmissiblities One of the hypotheses is that the fluid flow is mainly controlled by the interpretation of faults and the fault transmissiblities. The simulations show that low fault permeabilities, will give early leakage in many compartments, and that high permeabilites will result in late or no leakage. Uncertainties in the timing and amount of leakage can be estimated using pressure measurements from wells. The results should be used as guidelines for possible hydrocarbon leakage risks. Another important result is that large compartments will control possible leakage from smaller compartments in the surrounding areas. This will also be useful information in risk evaluation. The interpretations of faults are very important for the resulting pressure distribution. Large uncertainties have been

- 181 - associated with the interpretation of hardly detectable faults, where such occur in the continuation of larger faults on reflection seismic data. The simulations show that changing the transmissiblities across faults situated in highly to intermediately overpressured areas have large influence on the pressure distribution locally. The fluid flow will depend on both the transmissibility across the fault, but also on the pressure differences between the different compartments. b) Stress-strain relationship Another hypothesis was that the stress and pressure are interrelated because pressure build-up and differential stress will control hydraulic failure. It was therefore necessary to incorporate stress in the simulator. Different approaches were tested to simulate the minimum horizontal stress through time. The best and most realistic simulations of both the present day minimum horizontal stresses and pressures in the basin, were obtained using Grauls empirical equation for the minimum horizontal stress (Grauls 1996). Important understanding of the complex three-dimensional effects of fluid flow, and its influence on hydraulic fracturing and leakage were studied using this empirical formula for the minimum horizontal stress. c) Caprock geo-mechanical parameters Different failure criteria were included for the initiation of hydraulic fractures in the caprocks. High values for the coefficient of internal friction (µ) and the coefficient of sliding friction (µ’) in the failure criteria, resulted in a time-delay in failures, and thereby less leakage from overpressured compartments. Probably, an even lower coefficient of internal friction should be used, in accordance with the experimental work presented by Dewhurst & Henning (2003). Sensitivity analysis of Young’s modulus and Poisson’s ratio, which control Biot’s constant, showed an effect on the accumulations of overpressures. d) Resolution of fault maps In this thesis, faults at different scales have been discussed ranging from deformation bands on micro-scale to large faults with dip-slip displacement of more than 1 km. Faults at different scales have different properties and will play a role in defining the pressure and stress distribution. Around large faults, a pattern of small-scale faults should be expected. All these small structures cannot be taken into account in the simulations. Certain simplifications have to be made, but it is important to understand how they will affect the results. As the Tune field case shows, increasing the resolution of the fault maps will have an impact on the results. Such extra information would be of large importance in certain areas, particularly for hydrocarbon migration modelling. It is a challenge to combine laboratory and the field observations. One of the strengths of the simulations is that different models can be tested e.g. for lateral fluid flow. The simulations from the Tune area are not sufficient to determine whether the pressure differences observed between wells are due to decreased fault transmissibilities, unreliable well measurements or a lacking understanding of the fault seal properties. Multi-layer simulations are a way to be able to answer these questions in the future.

The simulations give a good platform, and are suitable for evaluating hydraulic fracturing and leakage from overpressured compartments. Some general conclusions are drawn from the work:

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• Simulations where the minimum horizontal stresses are calculated using Grauls (1996, 1998) empirical equations, give realistic results calibrated to the measured overpressures and the minimum horizontal stresses from wells. • The Elastic Theory is not well suited to simulate pressure and stress changes over geological time scale, since it gives too low estimates for the minimum horizontal stresses. The simulation results in too early hydraulic failure, with too high leakage and thereby too low pressure build up compared with measured pressure at present. The same trend is seen using the Zoback & Healy (1984) equation to simulate minimum horizontal stress. • Breckels & van Eekelen (1982) empirical relationship, that depends on the overpressure, gives too large simulated minimum horizontal stress, and thereby too late hydraulic failure and too high overpressure. • The coefficient of internal frictional and the coefficient of frictional sliding would have a minor impact on the timing and amount of hydraulic leakage. This will mainly be controlled by the lateral fluid flow and in turn by the transmissibility across the larger faults in a study area. • The timing of hydraulic fracturing and amount of fluid leakage can be estimated for the different compartments. • The largest compartment in an area will control the timing and amount of leakage in smaller neighbouring compartments. • Varying the permeability across faults, low fault permeabilities give early leakage, while high permeabilities result in no or late hydraulic fracturing and leakage. • Simulations show that the transmissibilities across individual faults situated in highly to intermediately overpressured areas will have a major influence on the pressure distribution in neighbouring compartments. The higher transmissibilites used, the larger parts of the basin were affected. • Changing the transmissibilities across individual faults in low-pressure areas would have minor effect on the surrounding pressure distribution. • Detailed fault pattern interpretations are important to make high quality pressure distribution simulations and hydrocarbon migration modelling. • On small scale, the development of deformation bands can be subdivided into five different stages: Stage I and II - closure of microcracks and pores and tighter grain packing parallel to, and dilation perpendicular to maximum stress direction. Stage III - both P- and S-wave velocities decrease, due to tighter grainpacking and development of micro-fractures. Stage IV - secondary fracturing and Stage V - development of a slip plane. • Video image analysis of deformation bands from the Brumunddal area, southern Norway, showed a decrease in the number of large pores in the deformed zone. An increase in the frequency is seen for small pores, in the intermediate zone, compared to the central part of the deformation band and the undeformed rock.

More specific results, using the Halten Terrace as the study area: • Hydraulic fracturing and leakage should most likely be expected in the western areas. • The Presidenten compartment most likely fails, except using very high fault permeabilites in the basin. The timing of failure is simulated to be between 2.5 Ma to 0.6 Ma, with cumulative leakage between of 78·106 m3 and 280·106 m3.

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• The Kristin compartment will have late leakage, occurring between 1.9 Ma and present day. The cumulative leakage is estimated not to exceed 29·106 m3. High permeabilities across the faults give possibly no hydraulic failure.

Future perspective In this thesis, both pressure and horizontal stress were controlled by the faults in the study area. This is a good approximation for the pressure distribution. Only the pressures in the top-points of the compartments were calculated in the simulations. However, when discussing the stress, a higher lateral resolution in the stress distribution than what is obtained today using the simulator, would be critical in describing the stresses around and along faults. Present status of the simulator is that the minimum horizontal and the vertical stresses are calculated in the top-point of each compartment. Probably, a conventional stress simulator applying distinct element method can be used to solve the time-dependent stress-strain changes. Then, a stress-simulator coupled to the pressure simulator could work interactively and will probably give a better understanding of the pressure-stress development. If this could be realised, one would have a tool to simulate where in the basin hydraulic fracturing and leakage should be expected. Today, the top-points in overpressured compartments are candidates for hydraulic fracturing. However, it is also possible that hydraulic leakage could develop in connection with reactivation of existing large faults.

Another part of the simulation method that may need further improvement is the understanding of the minimum horizontal stress. As shown, different empirical and theoretical formulas have been incorporated in the simulator. A major hope was connected to the use of Elastic Theory and that this equation should be useful in the simulator. On basin scale and over geological time scale, this resulted in too low minimum horizontal stress, and consequently too low pressures were simulated. However, the idea of expressing the horizontal stress by the vertical stress, the relation to pressure and to a minor extent to temperature, should still be valid.

References Borge, H. 2000. Fault controlled pressure modelling in sedimentary basins. Thesis for the degree of Doktor Ingenør of the Norwegian University of Norway, Trondheim, Norway, 148 pp. Breckels, I. M. & Eekelen, H. A. M. v. 1982. Relationship between horizontal stress and depth in sedimentary basins. Journal of Petroleum Technology, 34, 2191-2199. Cosgrove, J. W. 1998. The role of structural geology in reservoir characterization. In: Coward, M. P., Daltaban, T. S. & Johnson, H. (eds) Structural Geology in Reservoir Characterization, Geological Society Special Publications, London, 127, 1-13. Dewhurst, D. N. & Henning, A. L. 2003. Geomechanical properties related to top seal leakage in the Carnarvon Basin, Northwest Shelf, Australia. Petroleum Geoscience, 9, 255-263. Grauls, D. 1996. Minimum Principal Stress as a Control of Overpressures in Sedimentary Basins. In: Proceeding of the8th Conference on Exploration and Production. IFP Report No43313, IFP Ruil-Malmaison. Grauls, D. 1998. Overpressure assessment using a minimum principal stress approach. In: Overpressures in petroleum exploration; Proc. Workshop Bull. Centre Rech. Elf Explor. Prod., Pau, France, 22, 137-147. Zoback, M. D. & Healy, J. H. 1984. Friction, faulting, and "in situ" stress. Annales Geophysicae, 2(6), 689-698.

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