Fundamental Controls on Fluid Flow in Carbonates: Current Workﬂows to Emerging Technologies

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Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

SUSAN M. AGAR1,2* & SEBASTIAN GEIGER3 1ExxonMobil Upstream Research Company, PO Box 2189, Houston, TX 77252-2189, USA 2Present address: Aramco Research Center, 16300 Park Row, Houston, TX 77084, USA 3Institute of Petroleum Engineering, Heriot Watt University, Edinburgh EH14 4AS, UK *Corresponding author (e-mail: [email protected])

Abstract: The introduction reviews topics relevant to the fundamental controls on fluid flow in carbonate reservoirs and to the prediction of reservoir performance. The review provides research and industry contexts for papers in this volume only. A discussion of global context and frameworks emphasizes the value yet to be captured from compare and contrast studies. Multidisciplin- ary efforts highlight the importance of greater integration of sedimentology, diagenesis and structural geology. Developments in analytical and experimental methods, stimulated by advances in the materials sciences, support new insights into fundamental (pore-scale) processes in carbonate rocks. Subsurface imaging methods relevant to the delineation of heterogeneities in carbonates highlight techniques that serve to decrease the gap between seismically resolvable features and well-scale measurements. Methods to fuse geological information across scales are advancing through multiscale integration and proxies. A surge in computational power over the last two decades has been accompanied by developments in computational methods and algorithms. Devel- opments related to visualization and data interaction support stronger geoscience–engineering collaborations. High-resolution and real-time monitoring of the subsurface are driving novel sensing capabilities and growing interest in data mining and analytics. Together, these offer an exciting opportunity to learn more about the fundamental fluid-flow processes in carbonate reservoirs at the interwell scale.

This Special Publication grew from numerous study or technology development. While we recog- discussions related to a joint AAPG–SPE–SEG nize that these papers may lack the scientific and Hedberg Conference in July 2012 at Saint-Cyr sur technical rigour of a peer-reviewed manuscript, Mer, France (Agar et al. 2013), and manuscripts we feel that their inclusion is justified to represent were submitted 12–18 months after the conference. evolving frontiers in fields that are relevant to car- While these papers represent only a small pro- bonate reservoirs. Related and complementary per- portion of many strong conference contributions, spectives can be found in Geological Society they span several active research areas related to Special Publications and related journals (e.g. van flow prediction in carbonate reservoirs. Here, we Buchem et al. 2010; Hollis 2011; Garland et al. do not attempt a comprehensive review of all 2012; Agar & Hampson 2014). research areas related to carbonate reservoirs but At a time when unconventional reservoirs are discuss the themes represented by the papers in attracting much attention, discussions at the Hed- this volume in an industry context, considering the berg Conference reinforced that there remains much broad challenges addressed as well as the relevant exciting and important research to pursue in the advances. Much of the science and technology realm of carbonates. Some of the most significant discussed here can also be applied to other conven- advances are now emerging from a growth in multi- tional and unconventional reservoir types but our disciplinary research efforts (and, perhaps, a shift in primary aim is to highlight recent applications in the population of geoscientists to develop more the domain of carbonate reservoirs in a manner hybridized skill sets). As history shows, however, that is useful to non-specialists. To capture recent new knowledge to support efficient production from developments from industry as well as academia, carbonate reservoirs is likely to emerge from inter- we include references to extended abstracts from actions not only between different geoscience dis- industry conferences. In many cases, these publi- ciplines but at the interfaces with other fields, such cations are likely to be the only record of a case as materials science, fundamental physics and

From:Agar,S.M.&Geiger, S. (eds) 2015. Fundamental Controls on Fluid Flow in Carbonates: Current Workﬂows to Emerging Technologies. Geological Society, London, Special Publications, 406, 1–59. First published online November 12, 2014, http://dx.doi.org/10.1144/SP406.18 # The Geological Society of London 2015. Publishing disclaimer: www.geolsoc.org.uk/pub_ethics Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

2 S. M. AGAR & S. GEIGER chemistry, biotechnology, applied mathematics, and influence ‘styles’ of flow and recovery behaviours computational sciences. For this reason, scientists (flow/recovery types) for given reservoir con- from fields outside the traditional domains of geo- ditions, fluid types and well scenarios. Knowledge science were invited to the Hedberg Conference of the frameworks and evolutionary patterns that with a view to discussing and formulating novel give rise to distinct geological combinations can joint ventures. To reinforce the multidisciplinary provide early insights into the nature of distinct approach, this introduction is organized to reflect flow domains in the subsurface. Static and thematic areas that cut across multiple disciplines dynamic domains defined by separate model com- (Table 1). Topics covered in this volume include ponents can be radically different from those geophysics, structural geology, pore-scale pro- defined by a knowledge of: (a) the combined cesses, reactive transport modelling, geological impacts of geological elements on flow in a given modelling visualization and reservoir simulation. region v. their effects modelled separately and Accordingly, we start with examples that illustrate coupled across different grids; and (b) the signifi- the value of global context and multidisciplinary cance of knowing the relative impacts of geological studies. We then discuss advances in analytical elements on flow at different scales (in a given com- and experimental methods. This section is followed bination) and to determine which ones matter. There by a discussion of advances in subsurface imaging is certainly value in individual studies, such as and sensing methods. We then discuss inputs into in-depth investigations of carbonate fault zones models and the representation of multiscale data (Ferrill et al. 2011), studies of mechanisms, environ- as a challenge common to multiple geoscience dis- ment and timing related to fracture populations ciplines. A discussion of modelling techniques is (Amrouch et al. 2010; Jeanne et al. 2012), and con- then followed by a discussion of monitoring on pro- straints on reservoir architecture, physical proper- duction timescales or in real time. ties and fluid systems (Hausegger et al. 2010; Wolf et al. 2012) that yield valuable insights into processes and location-specific factors. Similarly, the last few years have seen a continuing publication Global context and frameworks of diagenetic studies in outcrops (Lo´pez-Horgue Background and challenges et al. 2010; Maliva et al. 2011; Palermo et al. 2012) as well as in the subsurface (Morad et al. One of the key challenges for translating academic 2012; Machel 2010). However, as recognized at geoscience research into industry applications is the Hedberg Conference, advances in these scienti- the need to place information and insights from fic areas could benefit substantially from broader, independent studies into a relevant framework or coordinated community efforts in a manner similar global context. For decades, geoscientists have to large integrated studies such as the Genome Pro- captured detailed data and interpretations from out- ject (Abecasis et al. 2010). crops, complemented by various theoretical, ana- Comparisons of myriad investigations per- lytical and modelling studies. But much of this formed independently on local outcrops can, in the work remains untapped by industry because it has right circumstances, offer insights far beyond those yet to be integrated into a form that provides gained through isolated studies. Given the chal- readily available, generic insights for subsurface lenges of (geological) model validation based on scenarios. While carbonate sedimentology and stra- limited access to subsurface data, regional-scale tigraphy have been developed in local, regional and insights can strengthen capabilities to link outcrop global contexts (Insalaco et al. 2000; Markello observations to inferences for the subsurface. Such et al. 2008; Garland et al. 2012), greater integration approaches can strengthen early reservoir distri- of this information into a post-depositional frame- bution and quality predictions during exploration work offers further uplift. We believe that there phases, and, together with production data, may remain significant opportunities to develop similar offer paradigm shifts for the evaluation of carbon- frameworks for diagenesis and deformation. By ate reservoirs. Comparative studies can further pro- global context, we do not simply mean ‘tectonic mote the identification of processes or associations setting’ or ‘depositional environment’ but, rather, common to given geological settings and/or his- a more sophisticated examination of the multiple, tories that support the development of algorithms interacting factors that impact reservoir quality, for deformation or diagenetic modelling tools. flow behaviours and recovery processes (Fig. 1). Even if they do not provide tight constraints, they Stratigraphic, diagenetic and structural elements in can help to reduce uncertainty, particularly if flow a carbonate reservoir are commonly evaluated in the simulation studies are combined with classical context of separate disciplines. Such approaches can outcrop analogue studies. We note, however, that obscure the importance of understanding how these comparative studies are limited by the wide variety different elements interact in the subsurface and of data acquisition methods, as well as by the levels Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 3 of detail. While rigorous direct comparisons of data- timescales (e.g. Wilkinson et al. 2010; Stewart sets from different outcrops or subsurface assets are et al. 2013; Teletzke & Lu 2013). unrealistic, value still resides in a broader community effort to interpret the signals from integrated Insights to deformation through compare and con- academic and industry legacy data. From a trast studies. Comparative studies of deformation broader perspective, many advances now sought in carbonate reservoirs or outcrop analogues appear by industry may require wider access to industry to be less common. On a regional scale, Fitz-Diaz datasets for academic researchers. et al. (2011) examined the influence of carbonate lithologies and their distributions on first-order Selected advances structural styles and the degree of penetrative deformation within thrust sheets, extending the earlier Regional perspectives on diagenesis. In recent work by Spratt et al. (2004). Following examples years, there have been several attempts to develop such as that of Mannino et al. (2010), we perceive a broader perception of the systems that drive dia- further opportunities to integrate numerous studies genesis and to explore common diagenetic themes of carbonate outcrops in central–southern Italy within given geographical regions (van Buchem (e.g. Agosta et al. 2010; Cilona et al. 2012; Petra- et al. 2010; Machel 2010; Coimbra & Olo´riz chinni et al. 2013; Antonellini et al. 2014). In this 2012; Wilson et al. 2013). Wilson (2012) promoted volume, Welch et al. (2014) compare fault and frac- an Earth Systems approach, identifying common ture systems in two distinct chalk outcrops. Their environmental, sedimentological and diagenetic approach offers a refreshing change in the pursuit factors as a means of identifying equatorial carbon- of a more broadly applicable framework for fracture ate systems. In this volume, Li et al. (2014) provide prediction. Instead of looking for intriguing fea- a preliminary demonstration of the value of com- tures or ‘special cases’, they seek characteristics that parative studies based on their analysis of the La may be applicable to other geological situations Molata outcrop, southern Spain. Their initial com- around the globe. parisons of the geological and hydrological settings and isotopic data for this location with those for the Dynamic simulations across multiple scales. Under- Nijar and Mallorca platforms (similar age, located standing and quantifying how multiscale geological on same isotopic trend) offer novel perspectives structures in carbonates impact flow behaviours, for regional controls on trends in dolomitization. displacement efficiency and residual oil saturation Through these comparisons, they are able to support under different production scenarios and fluid prop- broader applicability for their ascending fresh- erties remains an outstanding challenge. In recent water–mesohaline mixing model across the region, years, new modelling and simulation techniques while discounting the significance of basement have emerged that enable us to study these effects rock–freshwater interactions during dolomitization. from the pore scale up to the outcrop and interwell scale by comparing and contrasting different Predicting reservoir quality and reservoir processes types of geological structures, fluid properties and using reactive transport modelling. Reactive trans- well placements (e.g. Al-Kharusi & Blunt 2008; port modelling (RTM) is now a well-established Agar et al. 2010; Jackson et al. 2013a, b; Agada tool to study how the flow and transport of chemi- et al. 2014; Geiger & Matthaï 2014). The outcome cally reactive fluids alter porosity and permeability of these simulation experiments offers new ways (cf. Steefel et al. 2005). Although truly quantita- to interpret and quantify the large number of more tive predictions using RTM are still difficult to traditional laboratory and field-based geological achieve (e.g. Katz et al. 2011), compare and con- studies. Considering that there is a wealth of geo- trast studies allow us to link depositional environ- logical (analogue) data available for carbonate ments and climate variations to patterns of early reservoirs, a concerted effort of such simulation diagenesis (Whitaker & Xiao 2010; Whitaker studies could eventually lead to a database or catalo- et al. 2014) or to quantify how strata and structures gue that links generic flow behaviours to certain around three-dimensional (3D) faults influence geological structures and, therefore, allows us to resulting patterns of dolomite geobody charac- understand the relative impacts of geological ele- teristics (Corbella et al. 2014; Gomez-Rivas et al. ments on flow at different scales. Such a database 2014). The outcome of RTM models can then would have multiple practical applications for the guide the modelling of geobodies, porosity and industry, including providing new guidelines for permeability evolution in between wells, ensuring robust upscaling of static carbonate reservoir that the static geological model is self-consistent. models to dynamic reservoir simulation models, Similarly, RTM can be used to analyse and inter- steering the interpretation of dynamic production pret how Enhanced Oil Recovery (EOR) processes data or assisting in forecasting future reservoir can impact reservoir quality during production performance. 4 Downloaded from

Table 1. Organization of this introductory article listing the selected research and technology advances discussed and related workﬂows tools and techniques

Sections Selected advances Workﬂows, tools and techniques included Reference to papers in this volume http://sp.lyellcollection.org/

Global context and † Regional perspectives on diagenesis † Frameworks for global perspectives Li et al. (2014); Welch et al. (2014) frameworks † Reservoir quality, processes from RTM and patterns † Insights to deformation † Compare and contrast outcrop/

through comparisons modelling studies GEIGER S. & AGAR M. S. † Dynamic simulations across † Generic ﬂow behaviours, ﬂow multiple scales simlations, RTM

Multidisciplinary † Diagenesis and deformation † Integrated outcrop studies Cantrell et al. (2014); Sousa et al. (2014) collaboration † Sedimentation and deformation and modelling † Reservoir modelling and † LiDAR, hyperspectral imaging outcrop studies † Real-time data analysis on outcrops byguestonOctober1,2021

Insights into fundamental † Pore-scale imaging technologies † High-resolution 3D X-ray CT Chandra et al. (2014); Healy et al. processes † Experimental methods for † AFM (2014); Hebert et al. (2014); Hiemstra reservoir characterization † Analysis of competing & Goldstein (2014); Levenson et al. † Rock physics chemical–mechanical processes (2014); Li et al. (2014); Pal et al. † Novel experiments † Rock typing, diagenetic backstrippng (2014); Ramaker et al. (2014); † NMR, DIC, time-lapse analysis Skalinski & Kenter (2014); Vanorio of microcracks et al. (2014)

Subsurface imaging † Seismic acquisition methods † WAZ, FAZ, FWI, broadband Astratti et al. (2014); Gibson & Gao † Seismic attributes † Diffraction imaging, (2014); Shao et al. (2014) † Forward seismic modelling of scattering, inversion diagenetic overprints † Various attribute † Seismic anisotropy algorithms, workflows † Forward seismic modelling of diagenesis † Seismic anisotropy and wave guides Multiscale representations † Incorporating fine-scale structures in † Upscaling methods and uncertainty Cantrell et al. (2014); Chandra et al. Downloaded from and proxies reservoir characterization † Outcrop modelling, data (2014); Healy et al. (2014); Hebert † Multiscale geological impacts on flow acquisition, drones et al. (2014); Hiemstra & Goldstein † Upscaling methods † Numerical flow-simulation (2014); Li et al. (2014); Ramaker et al. † Scaling relationships in deformed experiments (2014); Welch et al. (2014) carbonate rocks † Multiscale proxies † Multiscale upscaling methods UDMNA OTOSO LI LWI CARBONATES IN FLOW FLUID ON CONTROLS FUNDAMENTAL

Modelling tools † Pore-scale simulations † Computational methods for pore- to Chandra et al. (2014); Sousa et al. http://sp.lyellcollection.org/ † Computational methods – ﬁeld-scale simulations (2014); Li et al. (2014); Hebert et al. unstructured grids † Fracture-ﬂow simulations (2014); Hiemstra & Goldstein (2014); † DFM modelling † SBIM Pal et al. (2014); Ramaker et al. † Parallel computing and † 3D printing (2014) ; Prodanovic´ et al. (2014); adaptive gridding Welch et al. (2014) † Reactive transport, geomechanical modelling † Visualization and interaction

Monitoring in real time or † Data mining and real-time † History matching, RTM Astratti et al. (2014); Sousa et al. (2014); † on production data analytics Data mining, sensors, AI Li et al. (2014); Vanorio et al. (2014) byguestonOctober1,2021 timescales † Dynamic behaviour of † TFI structural features † Time-lapse GPR, SP, EM † RTM on production timescales † Underground laboratories † Time-lapse seismic

AFM, Atomic Force Microscopy; AI, Artiﬁcial Intelligence; CT, Computed Tomography; DFM, Discrete Fracture Matrix; DIC, Digital Image Correlation; EM, Electromagnetic Monitoring; FAZ, Full Azimuth; FWI, Full Waveform Inversion; GPR, Ground Penetrating Radar; LiDAR, Light Detection And Ranging; NMR, Nuclear Magnetic Resonance; RTM, Reactive Transport Modelling; SBIM, Sketch- based Interface Modelling; SP, Spontaneous Potential; TFI, Tomographic Fracture Imaging; WAZ, Wide Azimuth. 5 Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

6 S. M. AGAR & S. GEIGER

Fig. 1. Stratigraphic, diagenetic and structural elements in a carbonate reservoir are commonly evaluated in the context of separate disciplines. Such approaches can obscure the importance of understanding how these different elements interact in the subsurface and influence ‘styles’ of flow/recovery behaviours (flow/recovery types) for given reservoir conditions, and for fluid and well scenarios. The left-hand column shows schematic representations of natural patterns or geometries in rocks created by sedimentological, diagenetic and structural processes. The upper centre diagram shows schematic combinations of these products. Each geological ‘type’ combines sedimentological, diagenetic and structural elements, reflecting a domain or subdomain for a given carbonate reservoir setting (defined by the cube schematically representing static parameters on the RHS). The lower centre diagram schematically represents the translation of the geological combinations into distinct types or domains of flow behaviours. In some cases, the geological combinations will differentiate the flow behaviour, while, in other cases, the geological details may not have that much impact. Knowledge of the frameworks and evolutionary patterns that give rise to distinct geological combinations can provide early insights into the nature of distinct flow domains in the subsurface. Static and dynamic domains defined by separate model components can be radically different from those defined by a knowledge of: (a) the combined impacts of geological elements on flow in a given region v. their effects modelled separately and coupled across different grids; and (b) the significance of knowing the relative impacts of geological elements on flow at different scales (i.e. in a given combination, which ones matter and at what scale?).

All of the developments outlined can support collaborations between those who study fracture stronger integrative frameworks that lead to broader populations in nature and those who develop perspectives on the patterns of geological character- models of their acoustic signatures have spurred istics and reservoir performance around the globe. the development of more sophisticated capabilities We argue that such perspectives are key to opening to interpret the geological significance of seismic new avenues of research (new hypotheses to test) anisotropy (Far et al. 2013). Similarly, studies that and vital to avoiding entrenchment so commonly integrate the geochemistry, diagenesis and low- rooted in isolated outcrop or reservoir studies. temperature deformation of carbonate rocks were relatively sparse until the last decade. There remain numerous further opportunities to integrate the role Multidisciplinary approaches of syndepositional faulting and the evolution of Background and challenges fault systems into an understanding of reservoir location, geometry, facies variations and transport There remain significant opportunities to strengthen routes (Quiquerez et al. 2013; Wu et al. 2014). In the multidisciplinary integration. For example, stronger context of this Special Publication, a significant Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 7 area for integration is that between studies of static Sedimentation and deformation. As a link between records of geology and a dynamic understanding carbonate sedimentology and structural geology, of the reservoir. There is still much that could the influence of syndepositional deformation on be done within university curricula and industry carbonate reservoir geometries and qualities con- training to develop geoscientists who are comfort- tinues to receive attention with a view to predicting able crossing the geoscience–reservoir engineer- reservoir potential, properties and flow behaviour ing divide. A common language that strengthens (Katz et al. 2010; Quiquerez et al. 2013). In the communication between engineering and geosci- Guadalupe Mountains, geomechanical modelling ence, while avoiding jargon, would help. Language has been used to investigate the interplay of synse- can also pose barriers in academic–industry dimentary deformation in the progradation of a relationships. Industry practitioners may dismiss steep-sloped carbonate margin (Resor & Flodin efforts by academics because results are not framed 2010). In the same area, Frost et al. (2012) demon- in a way that supports translation to the business strated how syndepositional fracturing has not only problem. influenced depositional patterns and stratal architecture but also the flow paths of early dolomitiz- Selected advances ing fluids. Studies of near-surface, normal faulting in chalk provide novel insights into the pressure Diagenesis and deformation. In terms of cross- solution–fracturing interactions that control the dis- disciplinary advances, a leading area of activity tribution of distinct permeability zones around a has been that of ‘structural diagenesis’. Coined by fault plane (Richard & Sizun 2011). Seismic-scale Laubach et al. (2010), it represents an attempt to investigations document remarkable examples of understand the links between deformation and dia- tall collapse structures in a carbonate platform (Sun genetic processes and offers potential advances for et al. 2013) and are complemented by studies of modelling open, partially or fully cemented frac- outcrop examples of sinkhole-related deformation tures in fracture-flow simulations. Several studies in a shallow-marine environment (Moretti et al. have now documented the interactions of brittle 2011). Studies of modern carbonate platforms are failure with fluid–rock interactions in carbonates: providing insights into the coupling between plat- by examining the relationships between fracture form developments and fault-system evolution (Lu opening rates and the style and extent of cementa- et al. 2013; Wu et al. 2014), while tighter integration tion, Gale et al. (2010) provided insights into of sedimentology, structure and geophysics con- mechanisms of fracture porosity and permeability tinues to advance new play concepts (Gao 2012). evolution in carbonate reservoirs. A new look at Together, such investigations are developing a the way that early-stage fractures may form and more sophisticated approach to the prediction of seal integrates studies of fluid flow, evaporation, variations in carbonate reservoir locations, geome- vapour transport and the localization of mineral tries and quality. precipitation with the microfracture network geometry (Noiriel et al. 2010). Investigations of defor- Reservoir modelling and outcrop studies. A further mation bands in a carbonate grainstone further example of multidisciplinary research involves the highlight the influence of syndeformation cementa- development of reservoir analogue models from tion on changes in deformation mechanisms (Rath outcrop studies and their subsequent use in numeri- et al. 2011). Others have explored the links between cal flow-simulation experiments. In this approach, facies, diagenesis and fracturing as a means to structural and architectural elements observed in strengthen frameworks for fracture-intensity pre- the outcrop are used as templates for a subsurface diction (Ortega et al. 2010). On a larger scale, stud- reservoir, while petrophysical properties (e.g. per- ies of fault-associated dolomitization have also meability, porosity, relative permeability and capil- expanded (Riva & Di Cuia 2013); although Vande- lary pressures) are substituted from actual reservoir ginste et al. (2012) provided a reality check, not- data. Numerical flow-simulation experiments can be ing the challenges of interpreting complex fluid used to test how structural features and reservoir flow and structural histories in carbonates in a architectures that are representative for a certain foreland fold-and-thrust belt. A related novel study reservoir type impact flow behaviours and recovery of injected fluids and their influence on fractures processes (e.g. Agar et al. 2010; Agada & Geiger highlights the importance of understanding the 2013, 2014; Agada et al. 2014; Fitch et al. 2014; impact of high-temperature fluids on deformation Geiger & Matthaï 2014; Shekhar et al. 2014; Whi- mechanisms over production timescales (Zadjali & taker et al. 2014). The combination of outcrop ana- Mohammed 2011). All of these studies are blurring logue models and flow-simulation experiments the boundaries between rock deformation, diagen- involves little additional cost given that the field- esis and geochemistry, and all of these fields are work to collect outcrop data is usually the most benefitting as a result. time-consuming step. Such an approach will have Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

8 S. M. AGAR & S. GEIGER

Fig. 2. (a) Application of conventional digital images and hyperspectral imaging to the wall of the Pozalagua Quarry, Cantabria, Spain (from Buckley et al. 2013, fig. 6). (i) Conventional digital image. (ii) Image classification used to highlight different dolomite types. (iii) Image classification used to highlight organic-rich limestone bodies using hyperspectral imaging (see the key for rock types). Original figure provided by S. Buckley. (b) Examples of LiDAR data that support the translation of outcrop data into reservoir simulations. (i) Textured (photographic overlay) LiDAR surfaces of Jurassic carbonates from a location near the village of Amellago, Morocco. LiDAR data acquired and processed by Gilan Survey. The LiDAR data were acquired from various vantage points in the area and compiled to Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 9 strong pedagogical value. It enables geoscientists Insights into fundamental processes and reservoir engineers to develop a mutual under- via advances in analytical and standing of how geological features impact recovery processes. In turn, the resulting knowledge inte- experimental methods gration will help to focus on the characterization Background and challenge of those geological features that are first-order controls on flow. Given the wealth of outcrop studies The geosciences are benefitting from the many for carbonate reservoirs, their future use in flow recent, rapid advances in materials science that are simulations can support the creation of a database underpinning a near-revolution in technology devel- of generic flow behaviours for typical carbonate opments and manufacturing, such as improvements reservoirs. Such a database can be readily leveraged in 3D X-ray Computed Tomography (CT) or 3D using efficient techniques to set up and analyse printing of materials with embedded sensors (Bogue simulation studies. These techniques include the 2013; Xu et al. 2014). Related developments in design of experiments and novel multiscale visu- analytical techniques and advances in measurement alization techniques that enable the fusion and capabilities may offer new opportunities for detect- blending of different data sources (e.g. LiDAR (light ing and quantifying rock properties, diagenesis and detection and ranging), petrophysical models and fluid distributions in the subsurface. Merged tech- saturation distributions) for multiple geological nologies may further support faster and better- models (Sousa et al. 2014) (Fig. 2). Results from integrated analyses of the types of data represented such interdisciplinary studies will not necessarily in this volume (e.g. isotopes, petrography and image tighten constraints on uncertainty in the subsur- analysis). face but they can certainly provide better guidelines Such advances have much to contribute to an and early predictions during exploration phases. understanding of the macroscopic properties (e.g. Ultimately, they may offer paradigm shifts for risk porosity, permeability, capillary pressure and acous- evaluation in carbonate reservoirs. tic properties) that quantify flow and transport In the future, one might envisage a ‘Google through reservoir rocks, and ultimately reservoir glass’-type device that feeds live observations from quality. These properties emerge from the chemical geoscience interpreters on the outcrop, perhaps with and physical interactions of fluids with each other, a view to training (even in the form of a game) or and between the fluids and minerals comprising capturing opinions from ‘the crowd’. Over the last the rock matrix. These interactions occur at the decade, each year has delivered bolder versions of scale of individual pores in the rock (e.g. adsorption outcrop virtual reality (Buckley et al. 2013; Ahmad- of a chemical component dissolved in the brine Zamri et al. 2014), supporting experience on the phase onto a mineral surface) and even at smaller outcrop with very high-resolution LiDAR imaging scales (e.g. molecular diffusion across the inter- and fly-throughs back at the office. Such models face between two fluid phases). Averaging these commonly surprise geoscientists in the different chemical and physical interactions over a rock perspectives they deliver for outcrop images: for volume that contains tens to hundreds of thousands example, revealing previously unseen faults and of pores yields the macroscopic (also called Darcy- 3D relationships not visible from the ground. The scale) properties (e.g. porosity, permeability and future offers augmented realities by which the geo- empirical correlations describing their changes). scientist automatically receives related geodetic These properties are used to model and quantify data or satellite image analyses superimposed live the static and dynamic processes in the reservoir at on the actual outcrop or by which the seismic inter- the field scale. preter might gain real-time, geological knowledge The network of connected pores in carbonate of the rock layers underpinning the seismic traces. rocks is susceptible to chemical and mechanical Similarly, results from related flow-simulation stud- changes over geological (e.g. diagenesis) and pro- ies or digital rock physics could be fused with the duction (e.g. mineral-scale formation) timescales. outcrop data in a virtual reality. Changes in the properties of the pore network in a

Fig. 2. (Continued) generate a 3D image viewable from all angles. White lines represent the locations of logged sections and coloured dots represent tracks along horizons in the 3D model (from Amour et al. 2013, fig. 10). (ii) & (iii) LiDAR images of the Frogs’ Point wall a few kilometres from the location in (i) (Agar et al. 2010). The cliff in (ii) is approximately 300 m long. The grey surface was generated from points acquired during LiDAR acquisition. The brown zone represents an area where an image of the rock texture has been draped over the LiDAR-generated morphology. The image in (iii) shows a close up of the same location revealing the high-resolution delineation of individual fractures and fine strata in the grey LiDAR surface. In some examples, the LiDAR resolution is sufficiently high to delineate individual stylolites. Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

10 S. M. AGAR & S. GEIGER carbonate rock – for example, when pore throats interfacial tension between the reservoir’s fluid widen as reactive fluids flow through the rock – phases (cf. Lake 1996); steam injection to reduce will inevitably change the rock’s macroscopic prop- the viscosity of (ultra)-heavy oil and bitumen (e.g. erties, and so alter flow behaviours and reservoir Naderi et al. 2013); or (miscible) water-alternating quality. A challenge in carbonate reservoir charac- gas injection that increases microscopic and macro- terization is to develop robust material laws that scopic sweep (e.g. Christensen et al. 2001). Other support the quantification of reservoir property EOR methods aim to trigger fluid–rock interactions evolution over both geological and production time- that cause a wettability alteration of the reservoir scales. Such laws can link property changes to the rock, from oil-wet to water-wet, liberating addi- emergent sedimentary, diagenetic and structural tional oil (e.g. Gupta & Mohanty 2011; Mohan textures observed in the reservoir. et al. 2011). One example of this alteration is Robust material laws can have far-reaching controlled-salinity water flooding, in which chemi- 22 2+ 2+ consequences. They could be used in reactive trans- cal species such as SO4 ,Mg and Ca dissolved port modelling (RTM) studies of diagenetic events in the brine phase interact with the surface of to predict reservoir quality away from wells. RTM carbonate minerals. The interaction is thought to is increasingly used to analyse the evolution of change wettability (e.g. Austad et al. 2008; Gupta reservoir quality in an attempt to predict porosity et al. 2011; Yousef et al. 2011; Romanuka et al. and permeability away from wells (e.g. Jones & 2012; Chandrasekha & Mohanty 2013). All of Xiao 2006, 2013; Whitaker & Xiao 2010; Xiao these processes represent chemical and physical et al. 2013; Corbella et al. 2014; Pal et al. 2014), interactions between fluid phases and fluid and adding value to studies that constrain porosity evol- solid phases that drive improvements in hydro- ution using geological and geochemical techniques carbon recovery from carbonate rocks. Hence, the (Ramaker et al. 2014; Hiemstra & Goldstein need for robust material laws that upscale the rel- 2014; Li et al. 2014). Yet, comparisons between evant pore-scale processes to the Darcy scale. well-calibrated laboratory experiments and numerical simulations in carbonate rocks have shown that Selected advances RTM is able to match experimental observations at best qualitatively (Katz et al. 2011). This is due Over the last decade, many analytical and exper- to our incomplete understanding as to how the fun- imental advances have found routes to geoscience damental chemical and physical interactions that applications relevant to carbonate reservoirs. occur at the pore scale should be quantified and upscaled to formulate more reliable macroscopic High-resolution micro X-ray computed tomography material laws. (X-ray CT). X-ray CT has enabled the observation Understanding how porosity and permeability of fluid–fluid and fluid–rock interactions in carbon- evolve during diagenesis is directly relevant to ate rocks at the pore scale. While this technology has reservoir rock typing. A wide range of rock-typing been applied to carbonate reservoir characterization methods has been proposed for carbonate reservoirs for several years and faces challenges in carbonates (e.g. Lucia 1999; Gomes et al. 2008; Hollis et al. owing to their multiporosity nature (Remeysen & 2010; Xu et al. 2012; Kazemi et al. 2012; van der Swennen 2008), recent progress now supports the Land et al. 2013; Chandra et al. 2014; Skalinski visualization and quantification of in situ fluid distri- & Kenter 2014). However, these methods are com- butions at reservoir conditions in heterogeneous monly more oriented towards practical industry 3D reservoir rocks at the pore scale (Blunt et al. workflows, such as defining empirical porosity– 2013; Wildenschild & Sheppard 2013) and the real- permeability transforms that translate porosities time visualization of 3D fluid-displacement pro- measured at the wireline scale to permeability cesses at the pore scale using synchrotron-based values in reservoir models. Usually rock typing is X-ray CT (Berg et al. 2013). Direct observations not based on a sound understanding of how the of the fundamental pore-scale flow and transport pore space of a carbonate rock evolves as reactive processes in carbonate reservoir rocks offer new fluids flow through it. insights into porosity, permeability and wettability Applications of porosity and permeability evol- evolution. A variety of techniques exist to numeri- ution during reactive transport at production time- cally simulate flow, transport and chemical reac- scales include acid stimulation (e.g. Davies & tions through the 3D pore space of reservoir rocks Kelkar 2007) and mineral-scale formation (e.g. (cf. Meakin & Tartakovsky 2009). Combining Sorbie & Mackay 2000). EOR technologies also observations from X-ray CT laboratory experiments rely on the chemical interaction between fluid with numerical simulations of reactive flow and phases. These include: polymer flooding, in which transport at the pore scale will enable the develop- the viscosity of the injected fluid increases (cf. ment of new material laws for carbonate rocks Sorbie 1991); surfactant injection to change the based on first principles. Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 11

Porosity and permeability evolution in carbon- quantify reaction rates in carbonates, a key par- ates has been quantified with X-ray CT. It is well ameter for RTM. known that pore-size distributions impact the rate of chemical reactions in sedimentary rocks owing Atomic force microscopy (AFM). AFM has been to the differences in available reactive surface used successfully to quantify mineral reaction rates area (Emmanuel & Berkowitz 2007; Emmanuel & for calcite growth and to develop macroscopic reac- Ague 2009). It is, therefore, critical to quantify tion rates for use in RTM studies (Bracco et al. how the topology of reactive surface area evolves 2013). However, these models also need to account during fluid–rock interactions and how this evol- for the heterogeneity of the crystal surface. Using ution impacts reaction rates (e.g. Noiriel et al. AFM, Levenson et al. (2014) found that, although 2009, 2010, 2012). Using X-ray CT, Luquot & the dissolution of carbonate minerals is strongly Gouze (2009) and Gouze & Luquot (2011) have dependent on the carabonate rock texture, the mac- shown how the evolution of the reactive surface roscopic reaction rates do not differ greatly. In a area – a key input parameter in Darcy-scale reactive related study, Levenson & Emmanuel (2013) fur- transport models – can be parameterized as a func- ther demonstrated that polished crystal surfaces tion of porosity in different dissolution regimes. react faster than surfaces that have been smoothed These results can also be extended to quantify the by prolonged fluid–mineral reactions. This implies evolution of permeability as a function of porosity that new fault zones or fractures where deformation in carbonates under different dissolution regimes has generated polished carbonate mineral surfaces (Luquot et al. 2014). Combining results from may be more prone to dissolution than other min- X-ray CT experiments with numerical simulations eral surfaces. This combination of direct experi- of reactive flow at the pore scale allows a more mental observations and numerical simulations at robust quantification of such dissolution regimes the pore scale (and below) now enables the quantifi- (Varloteaux et al. 2013). Overall, this approach pro- cation of the key chemical and physical controls for vides new characterization opportunities that lab- porosity and permeability evolution, and underpins oratory experiments alone cannot offer. Nogues empirical porosity–permeability transforms in car- et al. (2013) showed that permeability evolution bonate reservoir rock typing (Fig. 3). in carbonates tends to follow a counter-intuitive behaviour: brines that are far from chemical equili- Experimental techniques for reservoir characteriz- brium induce less permeability change compared ation. Detailed pore-scale imaging and simulations, to brines that are closer to chemical equilibrium, as well as AFM studies, are still too time-consuming even if both brines have the same pH. pH alone is for routine applications in reservoir characteriza- not necessarily a good proxy to interpolate perme- tion workflows but the outcome of such studies can ability and porosity away from wells using RTM. be used to guide reservoir rock typing (see also In another example, Molins et al. (2012) demon- Skalinski & Kenter 2014). Mousavi et al. (2013) strated that the non-uniformity of the pore-scale used pore-scale simulations to quantify perme- transport velocities leads to an overall decrease in ability and porosity evolution for different types fluid–rock reaction rates at the continuum scale. of sediment grains and cements in carbonates. Van This observation could explain, and quantify, the der Land et al. (2013) showed how ‘diagenetic frequently observed discrepancy between reaction backstripping’ could be combined with pore-scale rates measured in the laboratory and those observed simulations to quantify porosity and permeability at the Darcy scale. evolution in carbonate rocks, and relate them to The combination of X-ray CT visualization and reservoir rock types. Two-dimensional (2D) rock numerical modelling of (reactive) flow processes images, each corresponding to a different diage- at the pore scale has limitations, particularly for netic event for the same reservoir rock, were taken carbonate rocks. Hebert et al. (2014) demonstrate as input to stochastic algorithms that recreated the that porosity–permeability relationships that have 3D pore-space geometries from which permeabil- been identified in carbonates using X-ray CT are ity and porosity, as well as other rock properties, non-unique and depend on the resolution of the could be computed. While Li et al. (2014) use more X-ray CT scanner as well as the sample size. Fur- conventional analyses, their integrated approach thermore, they demonstrate how variability in achieves several insights into the processes under- connectivity at fine scales may be obscured by con- pinning the timing and distribution of multiphase nectivity measurements at larger scales. They rec- diagenesis. They develop conceptual models for ommend multiscale X-ray CT experiments to simultaneous dolomitization and dissolution (mix- quantify the spatial variability of porosity and ing of freshwater and evaporative brines), controls pore structure in order to overcome the limitat- on the timing and distribution of calcite cements ions in sample size. Multiscale X-ray CT exper- (proximity to palaeo-water table, different rock iments provide sufficient resolution to adequately types), correlations between increasing calcite Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

12 S. M. AGAR & S. GEIGER

Fig. 3. Typical steps involved in pore-network modelling. (a) A binarized 3D digital rock image is generated using X-ray CT. The black colour indicates the pore space, the grey colour the mineral grains. Note that the volume of the 3D sample typically ranges between 1 and 10 mm3.(b) The surface and topology of the pore space are identified from the binary image. (c) The network of connected pores is extracted, typically by identifying the centre lines through the pore-space topology. (d) The diameter and shape of the pore throats and pores are computed by measuring the distances from the centre line to the pore surface; typically, regular shapes such as triangles, n-cornered stars or quadrilaterals are used to represent the pore throats as such shapes allow the analytical calculations of capillary entry pressures, fluid volumes and conductivities in the pore throat. (e) Drainage is simulated by injecting oil (red) into the water-filled (blue) pore geometry; note that oil can only enter a pore if the capillary pressure exceeds the entry pressure of that pore. (f) Imbibition of water or gas (green) is simulated, and the evolution of residual oil, relative permeability and capillary pressure can be monitored while modelling the displacement processes such as piston displacement or snap-off in each pore throat.

cement and decreasing porosity and permeabil- Rock physics. Recent advances in analytical meth- ity, the relative impact of vadose-zone dissolu- ods and the design of experiments now enable tion and cementation, and the different degrees to the exploration of coupled processes in carbonate which heterozoan and photozoan carbonates react rocks, yielding new insights to rock physics. These with fluids. The study reinforces the continuing insights support the prediction of reservoir quality need for conventional geological studies that pro- from geophysical data. Experiments by Vanorio vide the data and context that enable us to con- et al. (2014) examine the coupling between chem- strain permeability–porosity distributions away ical dissolution, mechanical compaction, and the from wells using the novel experimental methods original rock compositions and textures. Their sim- discussed in this volume. A further advance that ulations of competing chemico-mechanical pro- may eventually provide tighter constraints on the cesses during diagenesis highlight the ways by timing of diagenesis is that of clumped isotope which the original rock texture (linked to pore applications in combination with d18O measure- stiffness and reactive surface area) may define dis- ments. Studies of core samples from fields in Oman tinct evolutionary paths for velocity and perme- and Kazakhstan used the distributions of O and ability for different carbonate rock types. Such C isotopes to identify distinct temperatures for experiments are complemented by research that cements and to differentiate the temperatures of links routine analyses to interpretations of the cement fill in factures v. the host rock (Bergmann geological controls on rock velocities. For exam- et al. 2011). This method is still developing, with ple, the distribution and timing of different cement continuing efforts being made to calibrate the phases can impact the evolution of acoustic method (Zaarur et al. 2013). properties. A wide scatter of velocity–porosity Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 13 relationships in Paris Basin carbonate core sam- differences in the mechanical response depending ples was attributed to patterns of early cementa- on whether the injected brine is NaCl or MgCl2. tion that influenced subsequent compaction paths The latter brine promotes dissolution of calcite (Brigaud et al. 2010). These impacts would not and silica that increases strain and weakens the be captured by standard time-average equations rock. This effect may need to be considered (Wyllie et al. 1956; Raymer et al. 1980) and offer when aiming to increase oil recovery from mechani- potential refinements of velocity–porosity trans- cally weak carbonate formations by controlling forms for carbonate successions. Toullec et al. the chemistry of the injected brine. Experiments (2012) found that the specific characteristics of related to acid fracturing have probed further into dolomitic texture have a greater impact than poros- the combined effects of effective stress and fluid ity values on Vp/Vs trends. parameters. Studies of the impact of fluid pH and Healy et al. (2014) extend combined textural effective stress on fracture aperture changes in lime- and rock physics research to structural features. stone have identified a transitional pH regime that, Their investigations of the impact of host-rock for a given effective stress, reflects a balance textures, fault-rock microstructure and fault dis- between the mechanism for free-face dissolution placement on acoustic velocities measured at the and pressure solution. At high pH values, the frac- laboratory scale demonstrate the factors and pro- ture aperture increases; however, at lower pH cesses that can lead to potentially large changes values, there is a decrease as stress effects become in Vp and Vs values. Broader engagement could more important (Ishibashi et al. 2013). These obser- develop global perspectives surrounding the veloc- vations may help to constrain elusive fracture ity structures of fault zones in carbonates while sup- aperture evolution, a process that is commonly porting industry advances for fault-zone imaging poorly constrained in fracture-flow simulations. Fur- and interpretation in the subsurface at seismic wave- ther studies have explored the rates of fracture lengths. All of these petrophysical approaches aperture opening related to CO2-acidified brine, help to move our understanding beyond empirical identifying factors that determine aperture evolution relationships (e.g. velocity–depth trends) by reveal- (surface roughness, constrictions, mineral depo- ing the set of interacting processes involved in sition and carbonate content of the host rock) (Ellis the modification of transport and elastic properties et al. 2011). of carbonates. Novel and insightful experiments have used Ongoing developments target the capture of nanometre-resolution methods to reveal the detailed continuous records of carbonate porosity and per- mechanisms involved in strain accommodation meability via downhole sensors. This has pro- and the influence of associated cracking on strain moted further investigations of Nuclear Magnetic rates (Croize´ et al. 2010). Digital Image Correlation Resonance (NMR) and its use as a complementary (DIC) has enabled multiscale analysis of images method to Mercury Injection Capillary Pressure of carbonate rock samples during uniaxial com- (MICP) and other petrophysical tools. Difficulties pression tests, enabling the quantification of both persist in differentiating NMR signals for different global and local strain fields during deformation carbonate rocks (e.g. micritized grainstone v. mud- (Dautriat et al. 2011). This method supports a stone–wackestone), low resolution and diffusional deeper understanding of controls on damage localiz- pore coupling that may interfere with permeability ation and local compaction mechanisms, and their calculations (Vincent et al. 2011). However, by relationship to structural heterogeneities in carbon- combining 3D NMR with dielectric logs, Abdul ate reservoirs. Aal et al. (2013) were able to show the variation Efforts to learn more of the interplay between in wettability with pore type, rock type and height multiple processes during carbonate compaction, above oil–water contact in carbonate reservoirs in and the relative importance of thermodynamic and onshore Abu Dhabi. petrophysical and fluid parameters (Zhang et al. 2011; Croize´ et al. 2013), provide a way to Novel experiments. Experimental advances are strengthen model algorithms incorporating both also providing insights into the role of fluids in car- strain rates and the formation and morphology of bonate deformation. Novel time-lapse monitoring stylolites (Angheluta et al. 2012). Combined exper- of subcritical crack propagation in calcite at room imental and outcrop observations have provided temperature indicates the presence of a threshold new insights into the role of multiscale heterogene- in fluid composition that determines whether the ities in limestones in localizing stylolites and their crystal weakens (cracks propagate) or strengthens influence on the distribution of pressure solution in (crack propagation is retarded) (Rostom et al. 2012). the surrounding reservoir rock (Ebner et al. 2010). Further studies in chalk have identified potential Further studies attempt to strengthen the case for causes of the weakness of chalk in the presence the use of stylolites to estimate palaeostress, as of seawater. Madland et al. (2011) recognized well as their absolute values of formation stresses Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

14 S. M. AGAR & S. GEIGER and compaction (Koehn et al. 2012). These studies impacts on carbonate reservoir performance by are supported by outcrop investigations of scaling subtle depositional, diagenetic and structural fea- relationships (Rolland et al. 2012). Strengthening tures calls for continuing efforts to improve seismic the link between experimental and field studies, characterization and the detection of fluid-flow Gratier (2011) emphasized the significance of the paths on production timescales. Improved imaging geological context in studies of pressure solution methods are critical to the identification of future that impacts rates of fault creep, sealing processes carbonate plays, which are likely to be found in and permeability changes over production time- increasingly challenging environments. Key chal- scales. Several groups are now pursuing the mech- lenges include: the delineation and characterization anisms that localize and grow deformation bands of individual faults and fracture corridors that may (Cilona et al. 2012), following a long period in promote water breakthrough or compartmentalize which few had even recognized that such structures the reservoir (Singh et al. 2008); methods to differ- existed in carbonate reservoirs. New insights from entiate first-order stratigraphic intervals from the studies of faults in outcrop have identified a new signatures of diagenetic overprints; the need to dis- brittle–ductile mechanism for nano-grain formation tinguish lithologies, and to quantify porosity and in carbonate rocks (Siman-Tov et al. 2013). permeability (Baechle et al. 2008; Xu & Payne With a view to the future, advances in materials 2009), as well as the need to monitor evolving fluid- science offer several possible avenues for develop- flow partitioning on production timescales. Activity ments in analytical and experiment methods. For in unconventional assets is now driving technologi- example, numerous incremental developments in cal advances that can also benefit conventional car- atom-probe tomography (McMurray et al. 2011; bonate reservoirs (Goodway et al. 2010; Trinchero Arey et al. 2013) may help to constrain reaction pro- et al. 2013). cesses in carbonate rocks, thereby helping to reduce Improvements in seismic data acquisition and a strong reliance on empiricism in current reactive- processing techniques offer improvements for transport models. Microfluidic methods, long used ‘seeing more’ and ‘seeing more accurately’ in car- in biology and chemical research, as well as by the bonate reservoirs (Fig. 4). This brief survey high- drug industry (Tabeling 2005), have also advanced lights just a few examples of benefits realized from for the benefit of the oil and gas industry (Schneider the exploitation of broadband and full-azimuth & Tabeling 2011; Schneider et al. 2011). In the seismic datasets, spectral analysis, diffraction imag- latter case, there is clear relevance to heteroge- ing and full-waveform imaging. Many of these neous wettability behaviours in carbonate rocks. It efforts are in their infancy and there remain signifi- is possible that developments in materials science cant hurdles: for example, it is not yet fully under- can enable constructs within microfluidic cells to stood how to stack and interpret full-azimuth support a rigorous analysis of wettability behaviour (FAZ) data (Hung & Yin 2012). The common prac- and potentially the combined impacts of micro- tice of summing FAZ data can result in image cracks that overprint the original rock pore space. deterioration (smearing) of structural details. FAZ At the opposite end of the spectrum, we perceive and long-offset data can be used for lithology pre- further opportunities to design experiments in the diction but this requires specialized processing subsurface or in large laboratory facilities to learn that has yet to mature (Hall et al. 2008). The use more about deformation and fluid–rock interaction of diffractions to image fractures and karst in car- behaviours over larger volumes. For example, bonate reservoirs has also advanced (Khaidukov McDuff et al. (2010) demonstrated the benefits et al. 2004; Fomel et al. 2007; Koren & Ravve from experiments on wormhole formation via the 2011). However, challenges for diffraction imag- non-destructive imaging of large (c. 0.5 m3) blocks ing require access to the diffracted wavefield, sepa- of carbonate rock. ration of the diffraction from the reflection and imaging of the diffracted wavefield (Reshef & Landa 2009; Klokov & Fomel 2012). The use of Subsurface imaging and sensing full-waveform inversion (FWI) to develop better Background and challenges velocity models (Virieux & Operto 2009; Plessix 2013) is also being tested in carbonate reservoirs. A detailed review of advances for seismic imaging Recognized challenges for FWI include the need and other geophysical methods applied to carbonate for algorithms that keep the computational costs as reservoirs is beyond the scope of this introduction. low as possible, spurious local minima, unrealistic In part, this is due to the fact that the area is solutions, as well as the limited accuracy of FWI rapidly evolving and many of the developments at depths greater than about 2 km (Nangoo et al. are held in confidentiality within companies as pro- 2012; Amazonas et al. 2013). prietary technology while the published literature Early applications of seismic attributes to car- lags behind. However, the potential for significant bonate reservoirs (Skirius et al. 1999) significantly Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 15

Fig. 4. Selected examples of recent application of seismic attributes in carbonate reservoirs. (a) Improvements resulting from full-azimuth (FAZ) broadband land data acquisition from Saudi Arabia (modified from Wallick & Giroldi 2013, fig. 7). The image compares absolute acoustic impedance from a previous dataset (left of the common well) with that generated from new FAZ broadband data (right of the common well). The base of the Khuff (predominantly a shallow-marine carbonate) is indicated by the white arrow. Carbonate v. clastic sections are broadly indicated by high v. low impedance, respectively, even though the relationship between impedance values and colour scale is different between the two images. (b) Examples from a study of seismic attributes extracted along the horizon located just below the Dhruma Shale, Saudi Arabia (modified from Sliz & Al-Dossary 2014, fig. 4). An attribute based on the difference between the Azimuthal Residual Moveouts computed in fast and slow directions (azRMO MAX-MIN) is used to interpret regions of higher fracture intensity. The black ellipses have high azRMO MAX–MIN values but no indication of fractures from the post-stack attributes. (c) Normalized difference between 50 and 20 Hz isofrequency volumes (modified from Li et al. 2011, fig. 4). The data were acquired from Carboniferous carbonates in the Pricaspian Basin. The use of spectral decomposition is used here to highlight high-frequency anomalies associated with higher quality carbonate reservoir encased in tight limestone (well A1). Well B1 intercepts a thinner and lower quality reservoir. changed perspectives on structural and stratigraphic might be manipulated to either enhance or retard heterogeneities, revealing dense populations of fluid flow would represent a key advance. In the fine-scale faults and details of stratal geometries case of ‘subseismic’ fault identification, analyses previously unseen. Advances continue to improve of seismically resolved fault lengths, heights and capabilities to interpret heterogeneities, many of orientations have been used to define characteristics which are at the threshold of seismic resolution. In of a given fault population, and to infer the density, carbonate reservoirs, it remains difficult to identify orientation and distribution of finer-scale faults ‘the’ fault or fracture corridor that would lead to (Kolyukhin & Torabi 2013; Verscheure et al. repositioning a well. An ability to identify the 2013). Neural network modelling approaches that content of fault zones and fracture corridors (fluid build on various seismic attribute volumes have types, cements) and the ways by which the system also been attempted (Cherazi et al. 2013), as have Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

16 S. M. AGAR & S. GEIGER various methods for automated fault extraction low-frequency shadows as hydrocarbon indicators (Souche et al. 2012; Tomaso et al. 2013). How- in carbonates (Wang 2006). The high-frequency ever, many published examples still fail to pass a anomalies, however, have been proposed as indi- test of being geologically reasonable. The same cators of carbonate reservoir quality (Li & Zheng can be said for applications of seismic anisotropy 2008). Diffraction-imaging methods have been to carbonate reservoirs. Even with decades of in- applied to shallow settings of carbonate rocks using dustry developments (Schoenberg & Sayers 1995; 3D Ground Penetrating Radar (GPR) (Pelissier Tsvankin et al. 2010), results from studies of et al. 2011; Grasmueck et al. 2012). These studies seismic anisotropy commonly represent a non- demonstrated the alignment of diffraction apices geological character. with vertical fractures and locations of karstic dis- One challenge is to ensure that all of the factors solution features. While the interpretation of karst affecting the anisotropic signature and the scales at collapse structures from subsurface data is not which they act have been considered. For carbonate new (e.g. Hardage et al. 1996), the interpretation reservoirs, anisotropic signatures need to be inter- of electrical resistivity and MRS methods could preted in the light of information on heterogeneities provide uplift to current practices (D. Astratti that occur on different scales. For example, karstifi- pers. comm.) and may offer improved methods to cation in the Idd el Shargi North Dome (Trice 2005) highlight and differentiate karst components from may impact the signatures of anisotropy maps in the other reservoir heterogeneities (Trice 2005). Fur- area (Angerer et al. 2006). In situ horizontal stress, ther applications of diffraction imaging in carbon- stratal architecture, diagenesis and structure can all ate reservoirs in the deeper subsurface also claim contribute to the signature of anisotropy. While to identify zones of fractures (Boelle et al. 2012; many have attempted to interpret a single array of Nicolaevich et al. 2013). fractures from seismic anisotropy, the signature may reflect the combined effects of layering, mul- Advances in seismic acquisition and processing. tiple sets of fractures, variations in fracture-fill Wide-azimuth (WAZ) data have been used to gener- cements and even stylolites. Even when methods ate azimuthal stacks with different illumination are applied to interpret the signature attributable to directions to improve the sharpness of subtle fault multiple fracture sets (Sayers & Den Boer 2012; and fracture images (Kong et al. 2012; Mahmoud Far et al. 2013), there remain large uncertainties in et al. 2012), and to infer the locations of fracture values of fracture compliance and the distributions corridors (Svetlichny et al. 2010). Furthermore, of fracture apertures and cements. Frequency- it has been proposed that scattering of seismic dependent fracture compliance has yet to be energy can be used, when full-azimuth seismic incorporated into fracture modelling (Liu & Marti- data are available, to identify subsurface locations nez 2013). with elevated fracture intensities (Willis et al. 2006; Burns et al. 2007). It is not unusual for the Selected advances importance of previously unrecognized, subtle features in the reservoir to become apparent dur- Advances in seismic imaging related to carbonate ing production. In such a case, Yin et al. (2010) reservoirs include studies of the low-frequency reinterpreted seismic volumes, using stochastic seis- content in broadband seismic data (Martin & mic inversion to improve the resolution of intra- Stewart 1994; Houston & Duval 2013). Wallick & reservoir surfaces, the distribution of coral-rich Giroldi (2013) used full-azimuth broadband data facies, 3D geometries of dense ponds and channels, to demonstrate the strong improvements (better and third-order maximum flooding surfaces, to signal-to-noise, critical velocity information) from improve the understanding of injected water move- extending low-frequency content down to 3 Hz, ment. Application of 3D full-waveform tomo- as well as the extra detail realized by including graphic inversion (FWI) to North Sea chalks has higher frequencies. Even in the absence of well now been used to obtain realistic velocity models data, it is now possible to generate much higher res- within a chalk reservoir down to depths of 4000 m olution images. The low-frequency content of (Kim et al. 2011; Nangoo et al. 2012). These seismic data gives a greater measure of confidence efforts used FWI with reverse time migration to in impedance results away from well control by achieve better imaging of carbonate reservoirs. reducing interpretational bias (Wallick & Giroldi Further applications in shallow settings of Saudi 2013). Further applications of spectral decompo- Arabia, as well as Oman, have also been published sition include: the improved resolution of a reef (Tonellot et al. 2013; Stopin et al. 2013). Combi- boundary (Nejad et al. 2009); the delineation of nations of FAZ with far-offset data elastic inversion strong amplitude, high-frequency events in pro- offer a more robust method to separate limestone, ducing areas of Brazilian deep-water carbonate dolomite and anhydrite, as well as fluid content reservoirs (de Matos et al. 2008); and the use of (Banik et al. 2009). Such capabilities are immature Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 17 but offer opportunities to delineate subtle variations medium representations for the acoustic responses in seismic character (especially amplitude) as a of fractured rock. For example, Wei et al. (2007) means to identify diagenetic features. recognized a decrease in shear-wave splitting with a decrease in fracture radius, while increasing frac- Seismic attributes. Applications of seismic attri- ture aperture thickness is associated with stronger butes to carbonate reservoirs have sought to shear-wave splitting. These results may help to dis- develop novel algorithms to compute new attributes, tinguish fracture populations dominated by thin as well as creative combinations of multiple attri- microcracks as opposed to large open fractures. butes to highlight specific features (Chopra & Tillotson et al. (2012) reported experiments on syn- Marfurt 2008, 2013; Nissen et al. 2009; Bravo & thetic rock samples to support theoretical predic- Aldana 2010; Yuan et al. 2013). Some studies tions that shear-wave splitting can be used as a have focused on methods to detect fracture corridors good estimate of fracture density. Further research (Arasu et al. 2010). Astratti et al. (2014) develop has highlighted the frequency- and scale-dependent this theme, arguing that most seismic attributes nature of fracture compliance (Hobday & Worthing- only highlight subsets of a desired solution. Their ton 2012), the use of scattered seismic energy to ‘seismic triple combo’ workflow combined three constrain fracture spacing and intensities (Vlastos individual attributes (amplitude, structural and et al. 2007), and advanced numerical methods to uncertainty attributes) into one aggregate fault attri- simulate seismic-wave propagation in discrete rep- bute. Their globally consistent dip estimation that resentations of fracture populations (Hall & Wang calculates both positive and negative dips in the 2012). Although by no means mature, improved inline and crossline directions achieves a theoreti- approaches to predict anisotropic permeability have cal lateral resolution that doubles that of any other been explored through the analysis of frequency- known methods of dip computation. This attribute dependent seismic amplitude v. angle and azimuth then provides the basis for an aggregate fault cube data (Ali & Jakobsen 2013). Constraints on fracture that combines complementary information for apertures have been sought through joint seismic structural dip, structural uncertainty and amplitude inversion combined with analysis of production variations, with recognized benefits for time-lapse data (Shahraini et al. 2011). Further efforts include analysis of seismic data. Nevertheless, this and those that provide links to geomechanics and pro- many other studies still struggle to resolve distinct duction data (Kozlov et al. 2007), as well as struc- generations of faults. tural analysis and fracture modelling (Liu et al. 2007a). Forward seismic modelling of diagenetic over- Gibson & Gao (2014) draw attention to the need prints. Recent publications highlight improvements to evaluate subsurface stress as well as fluid satur- in porosity prediction (Ras et al. 2012; Emang ations when analysing time-lapse seismic data. et al. 2013) and resolution of diagenetic overprints Their work adds to a sparse group of studies that (Maranu et al. 2013). These efforts are complemen- directly include stress-dependence in a theory for ted by forward seismic modelling of depositional effective elastic properties of fractured media. and diagenetic heterogeneities based on seismic- They test new and simplified solutions for stress- scale carbonate reservoir analogues (Schwab et al. dependent fracture compliances. Their results 2005; Goldberg et al. 2010; Fournier et al. 2011). demonstrate not only a fit with inverted anisotropic Toullec et al. (2012) emphasized that changes in seismic-velocity variations in rock samples but also the seismic signal do not necessarily correspond a potential method to predict anisotropic velocity directly to sequence boundaries and unconformi- data for different fluid-saturation conditions. In a ties. For example, it can be challenging to dif- related effort to constrain the fracture anisotropy ferentiate a lateral sedimentary/diagenetic facies signature for a carbonate reservoir in Abu Dhabi, variation from a toplap, and the true geological con- Ali & Worthington (2011) modelled the upper tinuity of the seismic signal is unclear. Overall, limit of fracture compliance. This was then used seismic methods do not yet provide adequate resol- to define an upper limit of the seismic velocity ution and differentiation to reliably delineate fine- anisotropy that would result from a specified set of scale diagenetic bodies. fractures and served to gauge confidence for interpreting seismic anisotropy as an indicator of fracture Seismic anisotropy. There have been numerous presence. advances that reflect more sophisticated approaches Shao et al. (2014) advance our understanding of to modelling and interpreting seismic anisotropy seismic anisotropy by investigating the impacts of (Liu & Martinez 2013) (Fig. 5). Although not all both layers and fractures on guided waves. Their advances are directly linked to carbonate reservoirs, experiments explore the relative roles of layer thick- relevant advances include deeper knowledge of the ness, fracture spacing and wavelength in the gener- ways that fracture characteristics impact equivalent ation of guided waves. Because the layers and the Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

18 S. M. AGAR & S. GEIGER

Fig. 5. A comparison of seismic-based intepretations of fracture orientations with core data (from Liu et al. 2011; Liu & Martinez 2013). The rose diagrams represent the azimuths of fracture strikes determined from well data (core and Formation Micro-Imager log (FMI)). Seismic anisotropy data were analysed after the migration of overburden effects. The anisotropy orientation is indicated by the black vectors with the interpreted fracture-strike azimuth as indicated by the coloured scale bar, which also shows the orientation of the source and the receiver. There is a qualitative correlation with the orientation of the anisotropy at three of the five wells (E, G, H). fractures generate competing scattering mechan- seismic signatures. Oversimplified interpretations isms, their combined effects can obscure or enhance of seismic anisotropy and other seismic attributes compressional-mode wave guiding. By understand- can lead to substantial misrepresentations of natural ing the impacts of layering and fractures in situ- fracture populations. ations when layer thickness is either smaller or greater than a seismic wavelength, Shao et al. (2014) develop insights into source, layer and frac- Modelling: multiscale integration and ture configurations that enable the use of guided modes to assess the presence and mechanical proxies properties of fractures. Their method also offers Background and challenges a less complex approach for the interpretation of compressional-wave data. Overall, this study There are significant uncertainties in predicting the emphasizes the importance of understanding the geology of, and recovery from, carbonate reservoirs. interactions of distinct geological heterogeneities This uncertainty falls into two separate but linked in the reservoir and their combined impacts on categories: first, the spatio-temporal distribution of Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 19 facies and their associated petrophysical properties can be used with sea-level curves, and with palaeo- is uncertain, largely due to the complex and abruptly climate and drainage data, to constrain forward changing nature of the rock fabric and the intrinsic models of carbonate accumulations (Whitaker lack of a method to quantify these changes in the et al. 2014). subsurface through direct measurements. Secondly, The approaches above focus on modelling the the dynamic interactions between the fluids and car- carbonate rock matrix. However, the common bonate rock are uncertain, both on geological time- occurrence of natural fractures in carbonate reser- scales (e.g. chemical alteration during diagenesis voirs also indicates a potential need to model a and resulting porosity–permeability changes) and network of connected fractures, and to quantify during production (e.g. wettability changes during their hydraulic properties in the form of fracture enhanced oil recovery). porosity, fracture permeability and shape factor To address these uncertainties, two types of (Bourbiaux 2010). For this purpose, it is common models are needed: the static model that describes to use discrete fracture network (DFN) modelling the spatial variability of geology (present day) and to create single or multiple realizations of the the associated rock properties; and a dynamic network of connected fractures based on the fracture model that describes the flow processes. For static statistics collected from wells, outcrop analogues modelling, it has become standard to use geostatis- and proxies, such as the curvature of the sedimen- tical methods to interpolate facies, reservoir rock tary layers or distance to faults (Dershowitz et al. types and petrophysical data, including their spa- 2000). The hydraulic properties of a DFN can tial variability, between wells, guided by seismic be calculated using analytical methods (e.g. Oda data. By using statistical methods, it is relatively 1985) or numerical simulations (e.g. Matthaï& straightforward to generate multiple realizations Belayneh 2004). of a geological model, and to generate probability Many geoscience disciplines wrestle with the distributions of the spatial distribution of facies, problem of linking observations and processes reservoir rock types and petrophysical properties. across multiple scales (time/rates, space). A combi- This probabilistic approach can capture some of nation of analytical and modelling methods has the geological uncertainty. A range of geostatistical- proven to be critical in realizing the integration of simulation approaches includes object-based knowledge across scales and disciplines. Advances modelling, variograms, kriging and co-kriging, co- in this area will have broad and significant impacts variance functions, or multipoint statistics. A both in terms of knowledge and as industry appli- detailed review of the advantages and disadvantages cations. The last decade has seen significant efforts of these methods is beyond the scope of this paper to capture and represent the multiscale properties but see works by authors including Deutsch & of rocks. This need is particularly relevant for car- Journel (1998), Jensen et al. (2000), Deutsch (2002) bonate reservoirs in which components of the pore and Daly & Caers (2010). Geostatistical modelling structure can range from nanometres to metres in of reservoir properties is complemented by pro- size with large spatial variability. A key challenge cess-based models that simulate the sedimentation is how to quantify and integrate the variety of and compaction of carbonate rocks. Such simu- matrix pore structures and associated deformation lations enable us to explore the nature and controls features in a way that provides a reasonable rep- of spatial heterogeneities typically observed in car- resentation of their hydrodynamic impacts on the bonate stratigraphy over a variety of scales (e.g. Darcy and reservoir scale. Paterson et al. 2006, 2008; Hantschel & Kauerauf Analytical and modelling techniques are based 2009; Hill et al. 2009) and the impact of these on assumptions and assumed data input. Inaccurate heterogeneities on production behaviour (Chandra assumptions and inadequate information can lead et al. 2014; Whitaker et al. 2014). An area for to erroneous results. When modelling the spatial future development is the design of efficient meth- variability of facies and associated rock properties, ods to couple process-based models more closely a fundamental assumption is that the variability to subsurface data (e.g. seismic geometries, pore measured along the 1D trajectory of a well is sta- pressure and present-day rock properties) as a tionary (i.e. its probability distribution remains means to constrain the final model state but also constant) and can be extrapolated into three dimen- to constrain intermediate evolutionary steps. In sions. Yet, there are many examples in carbonate geomechanical modelling, for example, final and reservoirs where this is not the case because of intermediate time geometries for strata can be used abrupt changes in carbonate rock properties caused to constrain the strain evolution of originally unde- by diagenesis, fracturing and faulting. The con- formed layers, with assigned material properties tributions by Healy et al. (2014), Chandra et al. and boundary conditions controlling stress evol- (2014), Ramaker et al. (2014), Hiemstra & Gold- ution (Pande & Pietruszczak 2004). Similarly, seis- stein (2014), Li et al. (2014) and Hebert et al. mic and well constraints on the facies distributions (2014) provide excellent illustrative examples. The Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

20 S. M. AGAR & S. GEIGER Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 21 statistical properties that are measured along a well carbonate reservoir properties are exacerbated if can also be biased due to under- or oversampling of the formation contains fractures because fracture certain facies, which may lead to fundamentally networks are normally not stationary and, hence, incorrect static models. do not possess an REV (Berkowitz 2002). This Once a static geological model (or an ensemble fact can lead to significant uncertainties when of models) has been created, it can be subjected to computing effective fracture properties from DFNs dynamic modelling of the relevant fluid-flow pro- (Dershowitz et al. 2000; Ahmed Elfeel & Geiger cesses (Fig. 6). Typically, this occurs on a grid 2012) that cannot necessarily be recalibrated or that is coarser than the grid of the static model to reduced by history matching (Ahmed Elfeel et al. reduce computational costs, requiring upscaling 2013c). (averaging) of the rock properties from the fine In the context of pore-scale investigations, static grid to the coarser dynamic grid. Various further advances are needed to streamline multiscale upscaling methods have been tested and applied imaging and analysis of pore structure so that they successfully to heterogeneous (carbonate) reser- can be effectively used to support an understanding voirs, including (semi-) analytical and numerical of flow behaviours. These types of investigations methods (e.g. Li & Beckner 2000; Pickup et al. provide important, fundamental insights that link 2000; Christie 2001; Christie & Blunt 2001; miscroscropic properties to the intrinsic variability Farmer 2002; King et al. 2006; Ringrose 2007; and hierarchy of the pore organization. In the con- Zhang et al. 2008; Hui et al. 2013) that can be vali- text of rock deformation, a key challenge for fault dated with streamline simulation (e.g. Samier et al. and fracture data is the understanding and repre- 2002; Ates et al. 2003; Elsaid et al. 2006). If the sentation of brittle–low-temperature deformation property distribution in a carbonate reservoir is processes and products (e.g. cementation) over not stationary, a well-defined representative ele- multiple scales. Common questions revolve around mentary volume (REV) cannot be defined for the the appropriate levels of detail to analyse, how fea- property, which renders upscaling difficult. When tures in distinct size ranges relate to each other, if upscaling a static model, or constructing the static at all, and how pre-existing structures influence model, it is implicitly assumed that each grid later phases of deformation. Can we, for example, block is at the REV scale and, hence, an average move beyond basic statistical analyses of fracture property can be assigned to a grid block. Yet, populations and concepts of scale dependency and there are numerous examples where the average fractals, and evaluate mechanisms that control asso- property changes as the observation scale changes ciations and interactions between structures on (e.g. grid block size) and, hence, upscaling of the different scales? With respect to flow prediction in static model to the dynamic model is challenging. carbonate reservoirs, such knowledge may offer The validity of the upscaling should, therefore, routes to new proxies for multiscale impacts of always be confirmed (e.g. Li & Beckner 2000; Ates structures (and potentially other features) on flow et al. 2003; Elsaid et al. 2006; King et al. 2006; (e.g. Correia et al. 2013). Novel proxies may also Agada et al. 2014). The challenges for upscaling assist in the identification of those features that

Fig. 6. Workflow for multiscale modelling and flow simulations through geological structures identified in a carbonate outcrop reservoir analogue. (a) Reservoir architectures are identified in the outcrop analogue. (b) Fractures are modelled with DFNs using the fracture statistics from the outcrop. The impact of different fracture systems (e.g. fault v. bedding-related fractures) can be tested by generating different DFNs. Km (mD) is the matrix permeability. (c) Matrix permeability and porosity are distributed deterministically or statistically for the observed reservoir architectures using data from subsurface reservoirs to exclude the impacts of meteoric diagenesis. The impact of different matrix properties for the same reservoir architectures on flow behaviours can be analysed. (d) Fracture permeability and porosity are computed from the DFN through upscaling. The impacts of different DFNs and different upscaling methods on resulting fracture properties are explored. Kf (mD) is the fracture permeability. (e) Relative permeability and capillary pressure curves are distributed in the model (each colour represents a domain with a unique relative-permeability–capillary pressure curve). Different rock typing approaches can be tested in this step to understand how assumptions about reservoir rock typing impact the predicted flow behaviours. (f) Wells are placed in the reservoir simulation model and production is simulated. This step can be used to test how fluid properties, well completion, well location and production strategies impact flow behaviours and reservoir performance. So is the oil saturation. (g) The key sensitivities are identified (here using tornado diagrams, although other diagrams are also possible) and linked back to the assumptions made about reservoir architecture, matrix/fracture properties, fluid properties, well location, and completion and production strategies. Large parameter spaces can be explored efficiently using efficient simulation strategies such as design of experiments techniques where only a subset of the parameter space is explored and results are interpolated in-between. Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

22 S. M. AGAR & S. GEIGER have the greatest impact on flow in a given geologi- reservoir models in industrial workflows. A num- cal/production scenario. ber of workflows exist that aim to define rock In the context of RTM, there are two challenges: types with unique hydraulic properties for car- as discussed above, the first challenge resides in bonate reservoirs (e.g. Lucia 1999; Gomes et al. upscaling reaction rates robustly from the scale of 2008; Hollis et al. 2010; Xu et al. 2012; Kazemi individual mineral surfaces within single pores to et al. 2012). However, as mentioned before, these the Darcy scale. Better upscaling procedures are workflows are not based on first principles. Instead, needed to explain the frequently observed differ- they employ empirical relationships that may ences between reaction rates measured in the labo- work well for a given reservoir but are not neces- ratory and observed at the field or Darcy scale. sarily widely applicable. Work such as that of The second challenge is to quantify adequately the Chandra et al. (2014) can underpin the traditional mixing of two brines with different chemical carbonate reservoir rock-typing workflows because compositions (Dentz et al. 2011). To solve the math- it incorporates efficient, yet robust, porosity– ematical models describing the transport of chemi- permeability transforms of small-scale geological cally reactive fluids through a rock formation, structures, which can impact reservoir quality. At RTM usually uses grid cells that are tens of metres even smaller scales, pore-scale studies such as wide and high (and therefore contain tens of thou- those of Mousavi et al. (2013) or Van der Land sands of tons of rock and thousand of tons of et al. (2013) can be used to quantify how individual fluids). Flow and chemical reactions in each grid diagenetic events impact reservoir quality and cell are, hence, described by volume-averaged prop- change reservoir rock types. erties. RTM assumes that chemical reactions occur uniformly everywhere in the grid block, predicting Multiscale geological impacts on flow. Outcrop- a uniform change in composition, mineralogy, and, modelling studies enable us to understand the subsequently, porosity and permeability at the scale relative impacts of specific multiscale geological of tens of metres. Yet, such uniformity is rarely features (including fractures and faults) on reser- observed in nature where there is ample evidence voir performance (Agada & Geiger 2013, 2014; that fluid–rock interactions are commonly restricted Agada et al. 2014; Shekhar et al. 2014; Whitaker to narrow regions, such as halos surrounding frac- et al. 2014). Such studies have been able to deliver tures or dissolution seams around stylolites. Both guidelines such as the significance of matrix het- of these challenges indicate a need to use RTM at erogeneity in obscuring a unique signature from the pore scale to constrain behaviors in upscaled subtle diagenetic or structural features in well tests models. (Agada et al. 2014) and the dominant, competing pathways along high-permeability layers and Selected advances fracture corridors (Agar et al. 2010). Some have explored the interplay of these factors with engin- Incorporating fine-scale structures in reservoir eering solutions, such as well placement or selec- characterisation. Chandra et al. (2014) show how tion of injection fluid (Agada & Geiger 2013, sampling bias for petrophysical properties can lead 2014). It is now also possible to capture geologi- to the generation of inadequate carbonate reservoir cal data from larger areas into outcrop-analogue rock types and the subsequent construction of a simulation studies: after years of kites, blimps and static model that is very difficult to calibrate using balloons, drones now offer the field geologist long- production data. For example, the undersampling sought-after images from tens of metres above plat- of core plugs from a poorly recovered and mechani- form exposures (Bertotti et al. 2013) and are used by cally weak reservoir zone comprising numerous the United States Geological Survey for monitoring dissolution seams, tension gashes and stylolites in the Earth-surface processes. New software tools a giant carbonate reservoir has led to the construc- allow us to collect, categorize and analyse massive tion of a reservoir model that was biased towards amounts of data acquired with these techniques, the low-permeability rocks. They demonstrate, such as fracture networks, in only a short time however, that careful upscaling of small-scale, (e.g. Hardebol & Bertotti 2013). high-permeability structures using process-based Numerical experiments have been used to test modelling of diagenetic carbonate structures can suitable proxies for subseismic features and the enable us to correct for the bias and create more impact of reduced permeability in deformation robust reservoir rock types that include geological bands on pressure draw-down (Antonellini et al. heterogeneities well below the scale of a reservoir 2014). Further tests of statistical proxies for the simulation grid block. Overall, the heterogeneous impact of deformation bands in subseismic fault- and multiscale nature of carbonate rocks renders relay zones on reservoir performance have also the application of reservoir-rock typing difficult. been explored (Fachri et al. 2013). Some cases, Yet, this approach remains a crucial step in building studies have shown where the simplification of Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 23 models can be justified. In other cases, they reveal Scaling relationships in the deformation of car- situations in which it becomes critical to understand bonate rocks. Efforts by structural geologists to the level of structural heterogeneity in a reservoir constrain multiscale characteristics include: the and related uncertainties for significant economic recognition of scale-dependent fault-displacement impacts (Hillgartner et al. 2011). Methods to scaling relationships in a specific tectonic setting upscale structural heterogeneities in reservoir sim- (Bergen & Shaw 2010); the quantification of dis- ulations (Jonoud et al. 2013), to constrain fracture tinct scaling relationships for different categories corridor locations in models (Ozkaya 2010) and of structures that form on similar scales (fractures, workflows demonstrating iterative calibration and deformation bands) (Schultz et al. 2013); new validation of production and geological data in sub- fractal geometry methods that offer alternative surface models (Al-Azri et al. 2013) are support- views on scaling, inhomogeneity and anisotropy ing closer geoscience–engineering integration. Such (Kruhl 2012); and stronger insights into strati- models allow us to query the assumptions and sim- graphic and diagenetic controls on multiscale frac- plifications that are made when modelling and sim- turing (Barbier et al. 2012). Further studies of ulating carbonate reservoirs. It is important to scaling relationships in fault systems attempt to understand which assumptions and simplifications reconcile the processes that drive a wide scatter in are valid, and which distort the results and interpret- the overlap and separation distances of relay zones ations of flow behaviours and the geological influ- with a strong power-law relationship that persists ences upon them. over eight orders of magnitude (Long & Imber 2011). Distinct scaling relationships have also been Multiscale upscaling methods. Multiscale flow- identified for zones of faults accommodating dif- modelling methods provide an alternative to tra- ferent intensities of strain (Putz-Perrier & Sander- ditional upscaling techniques. These methods are son 2010). Others have examined the interaction now well established but are not yet applied on a of stratigraphic layering with the development regular basis in commercial workflows (e.g. Jenny of a fault system, and the consequent departures et al. 2006; Kippe et al. 2008; Popov et al. 2009; from expected fault length–height scaling relation- Fossum Gulbransen et al. 2010; Lie et al. 2012). ships (so-called flat-topped faults) (Roche et al. The principal idea of a multiscale method is to 2012). Scaling studies related to fault zones in- establish a hierarchy of grids and to compute the clude the use of a truncated power law as a means different physical processes occurring in a reservoir to constrain the most reliable range of data for on different levels of grid refinement. Mathemati- the statistical approximation of fault-zone attri- cal operators, constructed for a given reservoir butes (Kolyukhin & Torabi 2013) and to provide simulation model, upscale and downscale the com- insights into distinct displacement–thickness rela- puted results between the different grids. The main tionships in low-displacement faults in carbon- advantage is computational efficiency and physical ate v. clastic rocks (Bastesen et al. 2013). Distinct accuracy. This efficiency arises because computa- scaling relationships for fracture spacing in dif- tionally expensive operations, such as computing ferent carbonate facies have also constrained the pressure distribution in a reservoir, are per- controls on spatial relationships between different formed on a coarse grid where the permeability fracture sets in shallow-water carbonate outcrops has been upscaled. Computationally less expensive with inferred impacts on fracture permeability operations, such as computing the saturation distri- (Larsen et al. 2010). Scaling investigations have bution in a reservoir, are performed on a finer grid extended to pressure-solution cleavage, identifying without any upscaling; the flow field on the fine a relationship between the host-rock stratal thick- grid is reconstructed using the pressure distribution nesses and the spacing between pressure-solution of the coarse grid and suitable mathematical down- seams, as well as the role of existing pressure- scaling operators. Hence, channelling through high- solution seams on the location of new dissolution permeability layers, the bypassing of hydrocarbons surfaces (Tavani et al. 2010). Investigations of and other complex flow processes can be modelled deformation bands in carbonate grainstones reveal accurately. For example, Jenny et al. (2006) demon- distinct length, thickness and displacement ranges strated a 10-fold increase in computational effi- that change during their evolution (e.g. from defor- ciency using a multiscale method for a reservoir mation bands to a localized fault) (Tondi et al. model that contained over six orders of variation 2012). All of these studies serve to constrain rela- in permeability; the multiscale method gave essen- tionships between deformation features that form tially identical results as the reference simulation. on different scales, as well as between deforma- Theoretically, it would even be possible to couple tion features and diagenetic and/or sedimentologi- pore-scale modelling with multiscale methods to cal characteristics. These results offer potentially upscale pore-scale physics directly to the reservoir smarter ways to incorporate structural heterogene- scale (e.g. Sun et al. 2012). ities into flow simulations. 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24 S. M. AGAR & S. GEIGER

Modelling: tools carbonate rocks, from RTM to EOR. It is therefore to be expected that any results from field-scale simu- Background and challenges lations of reactive-transport processes in carbonate reservoirs, from geological to production time- The classical advection–dispersion–reaction equa- scales, are biased because of the limitations of the tion (ADRE – see the Appendix) aims to model ADRE. the advective and dispersive transport of reactive The field of hydrology has long recognized the solutes at the reservoir scale, and forms the core of limitations of the ADRE, and has, for the past two commercial and research-grade simulators. Exper- decades, developed and refined alternative proba- imental evidence shows that macroscopic changes bilistic models to simulate the (reactive) transport in permeability and porosity during carbonate dis- of chemical components during miscible single- solution are intrinsically linked to changes in tortu- phase flow (cf. Berkowitz et al. 2006). While these osity, a parameter that quantifies the spreading of models can be used to robustly upscale transport solutes that are dissolved in the fluid phases (e.g. processes from the pore scale to the reservoir scale Luquot et al. 2014). This observation is consistent (Rhodes et al. 2008), they have hardly permeated with theoretical observations by Bijeljic et al. into the fields of reservoir engineering and pet- (2013a, b) and Mostaghimi et al. (2012). These roleum geoscience where mixing and spreading of authors showed that the centre of a chemical com- chemical components is still approximated using ponent plume remains increasingly stagnant, while dispersion tensors and volume-averaged proper- dispersion (spreading) increases with increasing ties. A key reason that the limitations of the heterogeneity. This behaviour cannot be modelled ADRE are not a significant problem for hydrology with the ADRE but it has been observed at the is that probabilistic models in hydrology consider pore scale, both in laboratory experiments and in single-phase flow only, a major simplification that field studies (e.g. Berkowitz et al. 2006; Dentz is impractical for hydrocarbon reservoirs. et al. 2011). Any type of dynamic modelling requires solv- What may appear as a trivial point has funda- ing the ADRE numerically on a given reservoir mental consequences for any field-scale simula- geometry, for the modelled reservoir properties tions, from reactive transport modelling over and the appropriate boundary conditions (e.g. well geological timescales to simulating EOR methods: locations, inflow from aquifers and groundwater the ADRE cannot capture miscible displacement recharge). The ADRE can be solved numerically processes observed at the pore scale unless the using a number of approaches – finite volumes, complete flow field at the pore space is resolved. finite differences, finite elements or streamline As a consequence, the ADRE will predict very methods (e.g. Helmig 1997; Chen et al. 2006). different concentration gradients due to mixing Finite-difference methods remain the most com- and dispersion compared to what has been observed mon numerical technique used in commercial sim- in nature. This immediately impacts the predicted ulators as these are computationally efficient, are chemical disequilibrium between fluid and rock, tailored to the underlying grid structure of the and, hence, the rate and location at which per- static models (and vice versa) and provide some meability and porosity change, even for the most moderate geometrical flexibility to represent reser- basic bimolecular reactions of the type A + B voir structures. Well-defined (commercial) work- C (e.g. Edery et al. 2010). When solving the flows exist to build static models, to upscale them ADRE in reactive transport modelling studies, and to dynamic models and to calibrate them during more generally for reservoir simulation, the coef- history matching. However, it is well known that ficients of the ADRE are taken as the average finite-difference methods work best if the under- across a single-reservoir simulation grid block. lying grid is orthogonal, and numerical errors can This implies that the flow field at scales below a be significant if the grid is deformed to match reservoir simulation grid block is not resolved, and complex reservoir structures (e.g. Heinemann et al. spreading and mixing are approximated by the dis- 1991; Aziz 1993; Aavatsmark 2002; Lie et al. persion tensor (physically incorrect). Hence, the 2012). In addition to solving the ADRE, specific ADRE does not model the spreading and mixing constitutive relationships are needed to model of solutes correctly, and any subsequent chemical the physico-chemical problem of interest. These reactions are going to be estimated incorrectly include the fluid properties (e.g. an equation of (Dentz et al. 2011). This probably helps to explain state, the Black Oil model and the compositional why Katz et al. (2011) were not able to properly model), the relevant material laws describing match well-calibrated laboratory experiments of fluid–rock interactions (e.g. mineral precipitation/ reactive transport through carbonates using RTM, dissolution for RTM or wettability alterations and so limits the predictability of any simulation during EOR) and the fluid–fluid interactions (e.g. studies that involve fluid–rock interactions in hysteresis due to the trapping of the non-wetting Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 25 phase or viscosity changes in the injected fluid that leads to hysteresis and the trapping of the non- during polymer injection). wetting phase. Hysteresis needs to be modelled A wide range of commercial but also highly accurately to obtain reliable recovery predictions. advanced (open source) research simulators exists. Yet, the many different empirical trapping and hys- Some of these simulators serve more well-defined teresis models that are available in modern reservoir purposes, for example RTM (Saaltink et al. 2004; simulations yield very different recovery forecasts Steefel et al. 2005; Xu & Pruess 2010; Xu et al. (Spiteri & Juanes 2006). Although the effect of hys- 2011; Lichtner et al. 2013), while others can be teresis decreases with increasing reservoir hetero- viewed as general-purpose simulators that can geneity in carbonate reservoirs, it is not negligible model a wide range of so-called THMC (thermal– (Agada & Geiger 2014). A final example where hydraulic–mechanical–chemical) processes (e.g. the lack of macroscopic material laws hinders the Cao 2002; Pruess 2004; Matthaï et al. 2007; Fle- accurate predictions during reservoir simulation is misch et al. 2011; Kolditz et al. 2012; Lie et al. controlled water flooding in carbonate reservoirs. 2012; Finsterle et al. 2014). Controlled water flooding has been observed to A particular challenge for all of these simula- yield attractive incremental oil recoveries in labora- tors is to model flow through fractured forma- tory experiments. However, the underlying physico- tions. Simulation of fractured carbonate reservoirs chemical effects are not yet fully understood (e.g. traditionally employs a dual-continua model that Austad et al. 2008; Gupta et al. 2011; Yousef comprises two domains: the mobile fractures that et al. 2011; Romanuka et al. 2012; Chandrasekha have little storage but provide the main flow paths; & Mohanty 2013) and, hence, conceptual models and the immobile or low-permeability matrix that remain mechanistic to date in that they adjust rela- provides the main storage (Warren & Root 1963; tive permeability curves as a function of brine sal- Kazemi et al. 1976). At the heart of the dual- inity (Wu & Bai 2009; Aldasani et al. 2012; continua model lies a transfer function that mod- Fjelde et al. 2012; Korrani et al. 2013; Al-Shalabi els the fluid exchange between fractures and the et al. 2014; Masalmeh et al. 2014). matrix due to gravitational and capillary forces. In addition to the lack of appropriate constitutive Several transfer functions exist and are routinely models for fluid–fluid and fluid–rock interactions applied in reservoir simulators (Kazemi et al. in reservoir simulation models, industry capabilities 1976; Gilman & Kazemi 1983; Quandalle & Saba- to predict the characteristics and impacts of diagen- thier 1989). A major problem is that these transfer esis in the subsurface using RTM are limited by functions do not capture the actual physics seen several factors. Software tools available for RTM in experiments or high-resolution simulations of (Saaltink et al. 2004; Steefel et al. 2005; Xu & fracture–matrix transfer (Abushaikha & Gosselin Pruess 2010; Xu et al. 2011) have limitations in car- 2008; Lu et al. 2008; Geiger et al. 2013; Ahmed bonate reservoirs. Ongoing debates address: the via- Elfeel et al. 2013a, b). Not surprisingly, this funda- bility of different concepts and models (Ehrenberg mental shortcoming poses major difficulties in the et al. 2012; Xiao et al. 2013; Li et al. 2014); the history matching of fractured carbonate reservoirs. lack of effective integration of RTM tools with Further simulation challenges include concep- other geological simulation tools; a lack of quanti- tual models for fluid–fluid interactions during three- tative constraints for physico-chemical processes phase flow and hysteresis. Water-alternating gas during diagenesis; the use of empirical material injection is now considered to enhance microscopic laws that link porosity and permeability evolu- and macroscopic sweep in many carbonate reser- tion to chemical reactions; the limitations of the voirs (Kalam et al. 2011; Pizarro & Branco 2012; ADRE, as noted above; Darcy-scale reaction rates Rawahi et al. 2012). The available empirical three- from fluid–rock interactions that occur at the pore phase relative permeability models – such as the scale and below; and relatively infrequent (pub- Stone I and Stone II models – that aim to predict lished) attempts to validate models or concepts the mobility of the gas, water and oil phases are against relevant laboratory experiments or subsur- not necessarily suitable for this purpose (Blunt face data. In addition, relatively few RTM models 2000): they assume a water-wet rock (carbonates have published results from 3D simulations, which are mixed to oil-wet) and gas to be the least non- remain challenged by their computational expense wetting phase (gas can be the intermediate wetting (Xiao & Jones 2006; Gomez-Rivas et al. 2010). phase). Empirical models tend to overpredict the Despite its challenges, RTM still offers a plat- relative permeability to oil at low oil saturations, form to strengthen communication between geo- and yield overly optimistic recovery scenarios and scientists and engineers by demonstrating the inaccurate residual oil saturations (Blunt 2000; potential value of conceptual models for carbonate Al-Dhahli et al. 2013a, b). Another issue for three- diagenesis in evaluations of reservoir performance. phase water-alternating gas injection is the constant This engagement can also ensure that ‘diagenesis’ decrease and increase in water and gas saturation is considered equally with other geological factors Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

26 S. M. AGAR & S. GEIGER as a potential control on reservoir issues and per- the distribution and timing of mechanisms involved formance (e.g. super-K zones, unconformities), and at different stages of burial and compaction (Croize´ in the capture of relevant statistics for the design et al. 2013). of geological models (Farzaneh et al. 2013). Such Even with improved modelling capabilities, the efforts may, in turn, stimulate the development of value of these capabilities resides in the develop- novel logging devices and techniques for RTM on ment (and possible standardization) of modelling local scales. RTM models will also benefit from methods and experiments to explore an appropriate fully unstructured grid simulations and more 3D spectrum of model sensitivities. Only through modelling because the combined impacts of faults, rigorous evaluation of model sensitivities can guide- fractures and matrix on patterns of flow and diagen- lines for use by the broader community be devel- esis can be significantly different from those rep- oped. For example, are there certain conditions resented in 2D. (thresholds) for which significant changes in the While the primary focus of RTM in carbonate distribution and style of dolomitization occur? reservoirs has been in the geological time domain, Under what circumstances might we expect to see there is potential to realize further value by linking extreme impacts on porosity and permeability by knowledge and expertise from this area to that of deformation? Are there multiple sets of conditions reservoir engineering on production timescales. that can lead to similar outcomes? Even with inevi- Fluid–rock interaction studies related to the effects table gaps in data and model approximations, it of injection fluids with different composition may still be possible to develop first-order guide- on recovery have benefited from RTM applica- lines to constrain scenarios in geological models. tions: for example, in the area of controlled-salinity For example (e.g. Hiemstra & Goldstein 2014; water flooding. There remain opportunities to Ramaker et al. 2014), can diagenesis in carbonate broaden impacts of RTM on production decisions reservoirs be categorized by levels of complexity by strengthening links to pore-scale processes. of diagenesis? When is it important to include Pore-scale modelling in combination with X-ray diagenetic details or when can they be readily CT visualization and other microscale experiments, ignored in representations of reservoir quality in such as AFM, enable the development of constitu- reservoir simulations? The need to develop sys- tive relationships and material laws that offer tematic ways to incorporate the appropriate scale more robust modelling at the Darcy scale. and density of data into models is essential for In the area of geomechanics, realistic modelling industry. There is also value in knowing when cer- of carbonate rocks requires an in-depth understand- tain modelling will not work due to data limitations ing of the physico-chemical mechanisms involved or model assumptions. and the incorporation of time-dependent mechan- Overall, research efforts related to model- ical properties or, at least, an evaluation of the ling could benefit from integrated modelling plat- different outcomes they may drive. Numerical mod- forms that can couple forward sedimentological elling of the evolution of individual faults and frac- modelling, diagenetic/RTM and geomechanical tures is extremely challenging in any rock type, modelling, underpinned by probabilistic models let alone carbonates. Even if an initial set of frac- that quantify the heterogeneity in the flow field tures can be generated, their impact on local stress and chemical reactions across scales. Furthermore, fields, and on the localization and propagation of there may be opportunities to link RTM on local subsequent fractures, is rarely captured in a realistic and regional scales, taking advantage of multiscale manner. Few have attempted to capture interactions modelling strategies, with regional-scale models between fracture apertures and pressure-solution providing boundary conditions for the local models. creep on production timescales, with most geome- Currently, no such platform exists. chanical models focusing on elastic responses. Common, polyphase diagenetic and fluid-flow his- Selected advances tories in carbonate rocks alter porosity and stiffness, as well as connectivity, but none of these is com- Recent advances in visualizing and modelling mul- monly represented in geomechanical models of car- tiphase flow processes across a wide range of scales bonate rocks. More sophisticated material models now put us on the brink of revolutionizing the way are needed to capture the brittle-failure processes, that we can quantify multiphase flow processes in pressure-solution creep and volume losses associ- hydrocarbon reservoirs from first principles rather ated with stylolite formation. The influence of pres- than using volume-averaged dispersion tensors and sure solution on carbonate reservoir quality and relative permeability and capillary pressure curves. fault-zone properties and the potential role of stylolites as local baffles or sites of porosity and Pore-scale simulations. Pore-scale simulations of permeability enhancement are widely recognized. fluid flow are no longer restricted to single-phase However, there is continuing debate concerning reactive-flow processes. It has long been possible Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 27 to compute physically consistent relative per- developed in hydrology for single-phase flow, the meability and capillary curves for two-phase flow quantitative insights from pore-scale studies can displacements (cf. Blunt 2001; Blunt et al. 2002; also be used to develop probabilistic models for Sorbie & Skauge 2011). Simulations can be per- multiphase flow that link the variability in pore- formed for two-phase displacements in complex scale physics to the Darcy scale. This approach pro- 3D porous structures with mixed-wet pores, which vides a novel simulation approach that accounts are common in carbonate rocks (e.g. Valvatne & for the pore-scale physics directly by reformulating Blunt 2004; Al-Kharusi & Blunt 2008; Ryazanov the ADRE as a stochastic partial differential equa- et al. 2009, 2014). Extensions are well underway tion rather than using (incorrectly) averaged multi- to perform similar calculations in 3D pore struc- phase flow physics (Tyagi et al. 2008; Tyagi & tures during three-phase flow (e.g. Piri & Blunt Jenny 2011). 2005a, b; Al-Dhahli et al. 2013a, b) and for dynamic displacement processes (e.g. Prodanovic´ & Computational methods – unstructured grids. It is Bryant 2006; Raeini et al. 2014). While relative now increasingly recognized that classical finite- permeability and capillary pressure curves from difference methods are no longer adequate to pore-scale simulations cannot replace special core simulate flow processes in structurally complex analysis (SCAL) experiments, they allow us to reservoirs. Many so-called ‘next-generation’ simu- analyse how these flow properties evolve during lators, developed commercially or academically, EOR in order to identify shifts in relative per- have successfully implemented fully unstructured meability and capillary pressure, and the resulting grids that can be adapted to complex geological changes in residual oil saturation (e.g. Bolandtaba structures using the appropriate discretization tech- & Skauge 2011). Simulators now offer the possi- nique, such as finite-element or multipoint flux bility of modelling EOR by shifting the relative per- methods (e.g. Lee et al. 2002; Karimi-Fard et al. meability curves from oil- to water-wet as a function 2004; Matthaï et al. 2007; Flemisch et al. 2011; of salinity and/or the concentration of (adsorbing) Kolditz et al. 2012; Lie et al. 2012; Jackson et al. cations in the brine. Laboratory experiments can 2013a, b; Moog 2013; Mallison et al. 2014). These be readily matched using this approach (Wu & Bai simulators have been applied to reservoirs, either 2009; Aldasani et al. 2012; Fjelde et al. 2012; as a standalone simulator or to augment the upscal- Korrani et al. 2013; Al-Shalabi et al. 2014; Masal- ing of heterogeneous and fractured carbonate meh et al. 2014). It remains to be seen how predic- reservoirs (e.g. Gong et al. 2008; Hui et al. 2008, tive these empirical mechanistic models can be for 2013; Karimi-Fard & Durlofsky 2012a, b). Fully real field applications but pore-scale modelling unstructured grids offer a completely new reservoir offers, at least, the possibility of quantifying the modelling approach in which any geological het- magnitude of the changes in permeability curves erogeneity, be it faults, fractures, stratigraphic, sedi- during EOR. mentary or diagenetic boundaries, are represented Another emerging possibility is to use pore- as a hierarchy of surfaces that bound volumes scale modelling to quantify changes in relative per- (domains) of equal or similar petrophysical proper- meability and capillary changes due to the evolution ties. This approach explicitly captures the key reser- of the pore space, during production or geological voir architectures, producing reservoir models that timescales. Prodanovic´ et al. (2014) show how instantly look geologically realistic such that the cementation, dissolution and the amount of micro- impact of stratigraphic, sedimentological and diage- porosity in carbonates cause distinct shifts in capil- netic heterogeneities on recovery can be assessed lary pressure and relative permeability. A similar (Matthaï et al. 2007; Paluszny et al. 2007; Jackson approach was followed by Van der Land et al. et al. 2013a, b). For example, Fitch et al. (2014) (2013), who used pore-network modelling to quan- showed that rock property contrasts between tify how capillary pressure and relative permeability sequence boundaries in a carbonate ramp setting curves evolve over geological time as carbonate and the properties of the environment of deposition rocks experience different diagenetic events. In belts (e.g. interfingering, anisotropy and rock prop- particular, the amount of microporosity and the erties) control recovery, independent of fluid prop- way that micro- and macroporosity are connected erties and well placement. Although surface-based in carbonates appears to impact capillary pres- reservoir modelling is in stark contrast to the use sure and relative permeability curves (Jiang et al. of geostatistical means to represent key reservoir 2013a, b). It is now possible to quantitatively architectures, geostatistics can still be applied combine pore-scale modelling studies, such as within a volume (domain) of equal or similar petro- those of Prodanovic´ et al. (2014) or Jiang et al. physics to model localized petrophysical variations. (2013a, b), with multiscale X-ray CT imaging of The bounding surfaces can be generated directly carbonates, as represented by Hebert et al. (2014). in the geological model, either deterministically or By analogy to probabilistic model concepts stochastically between wells. Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

28 S. M. AGAR & S. GEIGER

For completeness, we also note simulators based Parallel computing and adaptive gridding. Simu- on perpendicular bi-sector (PEBI) grids. PEBI grids lators now routinely perform calculations in parallel are also commonly referred to as ‘unstructured using multicore processors or clusters. The first grids’ but it should be pointed out that PEBI grids promising results have been demonstrated for accel- provide geometric flexibility mainly in areal dimen- erating reservoir simulation with graphical proces- sions. PEBI grids were first applied in the context of sing units (GPUs) and report run-time reductions reservoir simulation originally over two decades of up to a factor of 100 (Bayat & Killough 2013; ago (Heinemann et al. 1991), and are now used reg- Fung et al. 2013). Computing power is no longer a ularly in some proprietary industry simulators (e.g. limitation for reservoir simulation, which is of par- Liu et al. 2007a, b; Dogru et al. 2009; Verma ticular interest for giant carbonate reservoirs. Mas- et al. 2009) and research simulators (e.g. Lie et al. sively parallel computing with hundreds or even 2012; Moog 2013). thousands of processors enables grid refinement and, hence, better resolution of geology and flow Discrete fracture matrix modelling. Fully unstruc- physics in simulations of giant carbonate reservoirs tured simulators have been used to disentangle the with many decades of production data (e.g. Dogru complex flow processes in sector- or grid-block- et al. 2008, 2009). Although such large-scale simu- scale models of fractured carbonate reservoirs, lations require novel ways to interact with the reser- typically using reservoir architectures from out- voir simulation, visualize results, and manage the crop analogues (e.g. Matthaï & Belayneh 2004; input and output data (Dogru et al. 2011), they also Belayneh et al. 2006, 2007, 2009; Sternlof et al. enable the investigation of old concepts that were 2006; Agar et al. 2010; Geiger et al. 2013; Geiger not previously possible. & Matthaï 2014). These are a special class of While parallel computing is becoming the norm, unstructured grid simulations, the so-called Discrete alternative and computationally efficient techniques Fracture Matrix (DFM) models, which represent to refine the grid and resolve the flow physics are both the fracture network and the rock matrix, in a also available. In some simulators, it is possible reservoir simulation using fully unstructured grids for the grids to adapt to evolving physical processes (e.g. Karimi-Fard et al. 2004; Reichenberger et al. over the course of a simulation by refining the grid 2006; Matthaï et al. 2007; Hoteit & Firoozabadi dynamically and automatically in certain regions 2008a, b; Sandve et al. 2012; Schmid et al. 2013; of interest (e.g. Jackson et al. 2013a, b; Faigle Geiger & Matthaï 2014). Results from such DFM et al. 2014) (Fig. 7). This capability now opens the simulations (Ahmed Elfeel et al. 2013c; Geiger door to multiphysics–multiscale simulations: that et al. 2013), in combination with theoretical and is, reservoir simulations in which different physics mathematical analysis of fracture–matrix transfer are modelled on grids with different resolution. processes (Schmid et al. 2011, 2012; Schmid & The grids change their resolution automatically as Geiger 2012, 2013), have recently led to a new needed to capture the spatio-temporal evolution of transfer function for dual-continua models in which the relevant physical processes with minimum the transfer processes are computed using exact error (Helmig et al. 2013). This simulation approach analytical solutions of the underlying physical pro- expands the aforementioned multiscale methods to cesses. This new transfer function can be extended a dynamic framework, providing efficient, yet accu- to account for complex matrix heterogeneity in rate, simulations of complex recovery processes terms of matrix block sizes, wettability or permea- in carbonate reservoirs. For example, in EOR stud- bility, and employed in unstructured grid reservoir ies, it is commonly necessary to resolve in detail simulators (Di Donato et al. 2007; Maier & Geiger regions in which physical and chemical processes 2013; Maier et al. 2013). Other DFM simulation lead to a reduction in residual oil saturation in results have suggested an empirical approach to order to provide better predictions about incre- compute upscaled relative permeability curves in mental oil recovery. These regions are commonly fractured porous media (Matthaï & Nick 2009). concentrated in a small part of the reservoir (i.e. Within such models of fractured rock masses, where the fluids mix), and evolve in space and time. however, it needs to be recognized that diagenetic Modelling these processes by adequately refining or hydrothermal fluids are not only modifying the the reservoir simulation grid uniformly throughout matrix but are also modifying fracture apertures the reservoir may be computationally prohibitive, through the precipitation and/or dissolution of frac- even with parallel computing. However, since ture cements. DFM models provide the geometrical these processes are normally restricted to localized flexibility to capture geologically realistic fracture regions in the reservoir, it seems natural to refine geometries and aperture variations. They offer a the grid only in these regions and to keep it coarse way to explore the impacts of cemented fractures everywhere else. This technique increases the on production during multiphase flow, overcoming resolution of flow fields where two brines mix the limitations of existing fracture-flow simulations. and, hence, improves the resolution of important Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 29

Fig. 7. (a) LiDAR image of a Jurassic carbonate ramp outcrop containing fractures, fracture corridors and several sedimentary layers (see also Fig. 3b). (b) Unstructured finite-element grid representation of the outcrop geometry where each sedimentary layer is represented by a different colour and each fracture by a thicker black line. The black box in (a) shows the location of the finite-element grid. (c) Numerical simulation of water flooding through two adjacent sedimentary layers with high (yellow) and low (brown) permeability. Note how the finite-element grid is adapted as the waterfront propagates from left to right (red colour indicates high water saturation; blue indicates low water saturation). (a) is modified from Agar et al. (2010); (b) and (c) are modified from Geiger & Matthaï (2014) and Jackson et al. (2013), respectively. processes such as mixing, dispersion and reactions. underpinning the simulations (Kaczmarek & The adaptive grid refinement within a multiscale– Sibley 2011; Paster et al. 2013). Developments in multiphysics framework could overcome some of approaches to modelling RTM are as significant as the intrinsic challenges of the ADRE by capturing the changes to algorithms. Mangione et al. (2013) the mixing, dispersion and chemical reactions via explored iterative modelling methods to inter- a locally refined grid and sufficiently resolved face outputs from finite-element basin models flow field. An alternative could be to augment the with RTM. Doligez et al. (2011) explored different ADRE with a stochastic forcing term so that fluid– modelling workflows suited to distinct geological fluid (Tyagi et al. 2008; Tyagi & Jenny 2011) settings. Increasingly sophisticated approaches are and fluid–rock (Geiger et al. 2012) interactions now also linking depositional environments and below the grid block scale are modelled in a prob- climate variations to patterns of early diagenesis abilistic way rather than using volume-averaged (Whitaker & Xiao 2010; Whitaker et al. 2014). parameters. While Li et al. (2014) seek to identify the systems controlling dolomitization through outcrop studies, Reactive transport modelling. In the last 5 years, Pal et al. (2014) seek to test the plausibility of long- RTM research has progressed to offer new insights proposed dolomitization mechanisms through into the distribution of dolomite and anhydrite, numerical modelling. Their use of a code for multi- with implications for reservoir connectivity and physics modelling enables solutions for coupled subsurface correlation strategies (Xiao et al. 2013). systems for cases of brine reflux and geothermal Incremental improvements in RTM software con- convection. Even though their models remain in tinue (Xu & Pruess 2010) and have been sup- the realm of 2D, they have been able to generate ported by advances that improve the algorithms similar scales and patterns of dolomitization to Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

30 S. M. AGAR & S. GEIGER those in published outcrop studies. The application deformation. These links offer novel proxies for use of RTM to fault systems in 3D remains limited but in geomechanical modelling: for example, the style is critical to understanding the ways by which the and extent of deformation within a carbonate fault combined impacts of strata and structures influence zone can be improved by integrating data related the resulting patterns of dolomite geobody charac- to facies, rock strength and mud content within a teristics. A few 3D studies have provided insights sequence stratigraphic framework (Zahm et al. into the rock types and structural associations that 2010). In this area, we believe that the development strongly influence reservoir quality trends around of probabilistic numerical modelling approaches faults (Corbella et al. 2014; Gomez-Rivas et al. offer potential uplift (Pereira et al. 2012). Such 2014) (Fig. 8). models can explore sensitivities to stratal and struc- Even with the advances above, it is important tural geometries, as well as material properties and to consider the most effective way to use the boundary conditions. These approaches can accel- results from various modelling efforts (Teletzke & erate the exploration of key uncertainties. Welch Lu 2013; Xiao et al. 2013). Results are being used et al. (2014) explore the mechanical modelling of increasingly to steer broad insights to diagenetic chalk. Recognizing the common patterns of faults processes and to provide first-order guidelines for and fractures that occur in different rock types and scenarios in the subsurface. For example, brine geological settings, this work explores the impacts reflux modelling by Al-Helal et al. (2012) shed of pre-existing structures and pore-fluid pressure light on why in some settings reflux preferen- on fracture development. To date, very few mechan- tially dolomitizes muddy sediments but elsewhere ical models that explore processes on geological favours grainstones. In a study of fault-associated timescales attempt to incorporate pore-fluid effects dolomitization, Gomez-Rivas et al. (2014) was in simulations of fracture generation and propa- able to define a minimum difference in permeabil- gation. Comparisons between two distinct chalk ity to control fluid-flow paths into specific layers. outcrops and the simulation of their fracture popu- This enabled the authors to differentiate preferred lations by elastic-dislocation and finite-element scenarios for fluid fluxes and heat flow to achieve models may help to constrain guidelines for the cat- observed patterns and characterization of dolomiti- egorization of fractures, the conditions that favour zation. Previously, Consonni et al. (2011) demon- their generation and their relative impacts on flow strated the influence of permeability assumptions (when open). and the presence of fault zones on the final predicted geometry of dolomite bodies. While Pal Visualization and interaction. The work by Sousa et al. (2014) have been able to generate results et al. (2014) shows how novel interactions can that at least look similar to patterns of dolomitiza- be facilitated using interactive display surfaces to tion in outcrop, they recognize that further progress explore and visualize reservoir simulation mod- is needed to evaluate the model to boundary con- els in a collaborative environment. For example, ditions, parameters, other model assumptions and rather than using mouse-based operations, intuitive full 3D modelling. touch-based operations allow us to display different reservoir properties, to rotate and zoom into reser- Geomechanical modelling. Geomechanics research voir models or to create cross-sections through continues to advance modelling for carbonate reser- models (Fig. 9). It also becomes increasingly poss- voirs. Numerical modelling offers insights into ible to store different and multiscale data sources controls on fracture and fault populations (Caputo in such environments (e.g. the static model, results 2010), while geomechanical modelling of reservoirs from dynamic simulations, seismic data, outcrop has advanced capabilities to simulate permeability analogue data, borehole images or X-ray CT changes related to reservoir deformation (Dutta images) and to fuse and blend the different types et al. 2011). Combined modelling and outcrop stud- of data interactively. The touch-based approach ies have advanced more sophisticated approaches allows us to overlay reservoir simulation output for characterizing the effects of fracture patterns, on the original geological data that underpinned connectivity and clustering (Larsen et al. 2010). the construction of the reservoir model. Links Although not new, studies continue to highlight between geological structures, flow behaviour and the risks of directly attempting to link macroscopic production performance can, hence, be explored in geometries (curvature) in carbonate structures intuitive ways. Interactive display surfaces can to fracture populations (Claringbould et al. 2013), communicate with smart phones, tablets and other and to offer more informed guidance for the rela- mobile devices so that data can be readily trans- tionship between fractures and dip domains in ferred between different hardware systems and carbonate rocks (Bazalgette et al. 2010). Multidisci- user groups: for example, linking field teams with plinary research is also supporting advances by laboratory teams in real time. The collaborative strengthening the links between sedimentology and nature of this emerging technology cannot be Downloaded from UDMNA OTOSO LI LWI CARBONATES IN FLOW FLUID ON CONTROLS FUNDAMENTAL http://sp.lyellcollection.org/ byguestonOctober1,2021

Fig. 8. Outcrop image and 3D model of stratiform and fault-associated dolomitization in the Benica`ssim area, NE Spain showing the results of a dolomitizing fluid- and heat-flow simulation. (a) Image of the Benica`ssim outcrop showing dolomitized strata dissected by low-offset and seismic-scale faults. Field of view is approximately 1.2 km. (b) The 3D model shows the distribution of temperature around multiple vertical faults after 15 500 years of model run time. (c) Cross-section showing fluid velocity and streamlines with two hypothetical and vertical faults (f). High-temperature dolomitizing fluids flow upwards along fault zones and invade high-permeability layers. This example represents a rare demonstration of 3D RTM in a system representing both faults and strata. The model incorporates infinite volume blocks on the top and bottom layers with near-zero permeabilities to maintain constant boundary temperatures. Neumann boundary conditions specified: 60 mW m22 of heat flux into the model at the base and the same heat flux out of the system at the top layer. See Corbella et al. (2014) for further information. (c) provided by E. Gomez-Rivas, S. Stafford and A. Lee (see also Xiao et al. 2013). 31 Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

32 S. M. AGAR & S. GEIGER

Fig. 9. The use of interactive multitouch displays for collaborative visualization and analytics in exploration and production. (a) Multitouch displays can be placed and integrated with existing working environments, including offices, labs and visualization rooms. (b) Multitouch displays facilitate interrogation of modelling and simulation results in post-processing phases. In this example, the user is able to literally pull the geological model apart to see property values ‘inside’ the model and then put the model back together again (Sultanum et al. 2010, 2011). (c) Multitouch displays in large tabletop tablets facilitate the display and manipulation of multidimensional data. In this example, maps of hydrocarbon seeps generated at different scales are integrated with geochemical data and geological surface data at one scale and can be manipulated in 3D (Seyed et al. 2013). (d) Use of a tablet with a multitouch display to interact with geological information (carbonate strata in a cliff face) represented by LiDAR data. In this example, the interpreter is tracing stratal surfaces which can then be extrapolated into 3D surfaces and digitized as input to a geological model (Sultanum et al. 2013). overemphasized. It allows geoscientists and engin- simulation, has the potential to revolutionize the eers to query different types of data across multiple static and dynamic modelling of structurally com- scales when analysing static and dynamic reservoir plex carbonate reservoirs, replacing the conven- models, comparing reservoir performance with tional geostatistical reservoir modelling workflows simulated reservoir behaviour and planning future and finite-difference simulations. reservoir development. We perceive an exciting future for modelling Further developments are supporting the rapid tools and techniques: at the Hedberg Confer- capture of geological concepts into models, enabl- ence, the potential benefits of additive manufac- ing greater transfer of geological experience and turing (3D printing) for geological modelling were perspectives for multiple scenarios into the model- recognized as a possible avenue for uplift. Today, ling process. As Sousa et al. (2014) show, there a house has been ‘printed’ in Amsterdam (Bogue are intuitive and interactive approaches to rapidly 2013; Rutkin 2014). In the same way, geological generate and modify geological surfaces from a models from nanometre to decametre scales could variety of input data including seismic data, out- be programmed remotely to be ‘printed’ at a remote, crops, wells or even blank screens, the so-called centralized facility (R. Gibson pers. comm.: see sketch-based interface modelling (SBIM) (Fig. Agar et al. 2013). Advances in materials science 10). Using tabletop and surface PCs, SBIM supports that deliver ‘bespoke’ material properties may even- the creation, augmentation or refinement of geo- tually enable robust approaches to scaling the flow logical surfaces by sketching simple lines that or rheological properties of such models, as well trace, for example, a bed boundary on an outcrop as the wettabilities (Torrez-Sanchez & Corney image or a fault in a seismic cross-section. The 2D 2009). It may be that these capabilities offer a new surface is then generated automatically from these lease of life to the realm of physico-chemical mod- sketches and geological rules can be implemented elling of the Earth that has diminished significantly to ascertain that the resulting geometries are con- over the last decade. Knowing the full 3D properties sistent: for example, that cross-cutting relationships of such materials and being able to rapidly construct are obeyed. SBIM, together with surface-based configurations of the fine-scale heterogeneities in reservoir modelling and unstructured grid reservoir carbonate reservoirs (pores, fractures and stylolites) Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 33

Fig. 10. Reservoir modelling interfaces. Current high-end Windows, Icons, Menus, Pointer (WIMP)-based modelling tools are suitable for modelling tasks involving accurate and detailed parameter adjustments over a reservoir model. Sketch-based interfaces and modelling (SBIM) (Olsen et al. 2009) are suitable for supporting interactive, intuitive, interpretive visual geometric and topological data modelling leading to conceptual, prototype structural model of the reservoir. Ultimately, SBIM tools should be able to leverage existing modelling tools and workflows. SBIM allows the use of personal computers and tabletops (centre) to draw lines on the existing surfaces (right) where modifications are needed. Geological rules can be implemented that ensure that geological concepts (e.g. cross-cutting relationships) are obeyed when modifying the surface, that constraints in the form of hard data (e.g. well locations) are honoured or that hierarchies of surfaces are created automatically from predefined templates (e.g. foresets). This illustration of SBIM is for a seismic image but SBIM works for other types of data such as outcrop models (Figure provided by M. C. Sousa.) could help to address many flow-related questions. (e.g. production rates, bottom-hole pressures, tracer Furthermore, developments in medical imaging data and fluid ratios). This history matching process and sensing may promote methods to ‘look inside’ requires a large number of additional simulations physical models or to use embedded sensors to that explore multiple possible geological scenarios, monitor processes during model runs. Concepts and adapts them by altering the static and dynamic related to imaging in complex media have long model parameters until the simulated model been translated to or exchanged between medical response matches the observed production data. and geophysical fields (Fink 1992; Fink et al. The term ‘history matching’ is somewhat mislead- 2002; Mosk et al. 2012). With the development of ing in that the primary aim is not to simulate histori- new avenues for physical modelling, similar tech- cal production but to use the mismatch between niques may also find application to live 3D render- simulated model responses and production data to ing of actively deforming or flowing physical understand flow behaviours and geological struc- models. These approaches complement advances tures in the reservoir. History matching is an that have been realized for various tomographical inverse problem with a non-unique answer: that is, and fluid imaging of core samples during defor- an infinite number of possible geological models mation experiments, even though applications to that match the past production history exist in higher density carbonate rocks pose challenges theory. Hence, using a single well-calibrated geo- (Viggiani & Hall 2004; Hall et al. 2012). logical model to forecast future production behaviours is inadequate, especially if the model is uncertain, as is the case for many carbonate reser- Monitoring in real time or on production voirs. For all that, we know that the model could be wrong despite being calibrated to the production timescales data, giving the ‘right answer for the wrong reason’ Background and challenges and therefore yielding incorrect future production estimates. It is, hence, pertinent to use an ensem- To validate static and dynamic reservoir models, ble of likely geological models that all match it is common practice to calibrate the reservoir the past production history within a given toler- simulation model using dynamic production data ance to robustly quantify the uncertainty bounds Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

34 S. M. AGAR & S. GEIGER for future production (cf. Oliver et al. 2008). Gener- production data to geological and fluid information. ating such an ensemble of well-calibrated but also We suggest that there is an opportunity for industry diverse yet likely geological models and using to be more proactive in the design of subsurface them for robust uncertainty quantification and opti- experiments, building on the strengthening plat- mization of future hydrocarbon production in a forms for real-time reservoir monitoring in digital computationally efficient way is an active field of oilfields (Dogru et al. 2011; Gomez et al. 2013; research. Algorithms that originated in other disci- Al-Jasmi et al. 2014; Sousa et al. 2014). There plines (e.g. evolutionary algorithms, machine learn- will always be an argument that each experiment ing and particle swarms) are continuously adapted is a special case that cannot be applied elsewhere to reservoir simulation, and industry workflows and will generate more questions than answers. for uncertainty quantification have been updated Nevertheless, in an age of burgeoning sensor tech- accordingly (e.g. Hajizadeh et al. 2011; Abdollaza- nology with strong scientific and technical inte- deh et al. 2013; Arnold et al. 2013; Ashraf et al. gration, such efforts may deliver benefits beyond 2013; Dehdari et al. 2013; He & Durlofsky 2013; those previously envisaged. Park et al. 2013; Peters et al. 2013; El-Sheikh While time-lapse studies are not new, there et al. 2014). However, it is not clear how readily remains much to learn about their optimal imple- those new algorithms, which are commonly de- mentation in carbonate reservoirs. A key challenge veloped for well-known and sometimes slightly for time-lapse studies in carbonates arises from the idealized benchmark problems comprising clastic fact that the acoustic response of carbonates can reservoir models, can be applied to carbonate reser- be highly variable and the applicability of Gass- voirs. Building static models and running dynamic mann’s equation for predicting the impact of models for giant fractured carbonate reservoirs changes in saturation on the acoustic properties of that contain hundreds to thousands of millions of carbonates is debatable (Misaghi et al. 2010; Li & grid blocks, decades of production data and hun- Chen 2013). This point is highlighted by Yee et al. dreds of wells, and are operated by surface facilities (2012), who performed 4D studies of carbonate that serve multiple fields is not trivial from a com- gas fields of offshore Sarawak. They note that Gass- putational point of view, even for a single model man’s equation would predict that water influx into realization (e.g. Fung & Dogru 2008; Hui et al. a gas reservoir would produce a relatively minor 2008; Dogru et al. 2009; Carrillat et al. 2010; Ais- acoustic response but two of the six repeated 2D saoui & Moreno 2013; Clara et al. 2013). New tech- seismic lines showed a strong, coherent ampli- niques are required to visualize and analyse the tude response at the gas–water contact. Continuing overwhelming amounts of input and output data challenges for time-lapse studies include finding (Dogru et al. 2011; Sousa et al. 2014). Another chal- opportunities to validate interpretations through lenge is to use different data sources (e.g. tracers, carefully designed well experiments or the installa- 4D seismic and produced-water chemistry) as they tion of (semi-) permanent downhole monitoring become available, and to update the static and stations. Even then, sampling, scaling and resolution dynamic models accordingly. There is also the issues limit capabilities to cross-validate seismically intrinsic danger of replacing the intuition of experi- derived fracture attributes with geological obser- enced production geologists and reservoir engineers vations of fractures. Expanded efforts are needed with computing power, a process that has been to validate seismic interpretations and bulk-volume referred to as ‘Nintendo engineering’ at various attributes and to link them to data obtained at well conferences in recent years. The history matching and interwell scales. Overall, time-lapse objectives process should be used to query the concepts that would benefit from improved velocity models, underpin the construction of static and dynamic rooted in robust knowledge of physical property models, and to develop insights that establish links evolution of carbonate rocks, which include more to the ways in which geology impacts reservoir per- sophisticated representations of physico-chemical formance and that guide the decision-making changes during burial/uplift and diagenesis process during reservoir development. Instead, we (Vanorio et al. 2014). Further advances require a are tempted to rely exclusively on the outputs of a full understanding of the physics, as well as the large number of computer simulations. limitations and complementary nature of tools Augmenting history matching with results from and techniques, used to acquire information on the outcrop-scale flow-modelling studies discussed different scales. above represents significant progress in linking knowledge of geological impacts on flow to carbon- Selected advances ate reservoir performance. However, relevance to the subsurface has largely emerged from fortui- Data mining, pattern recognition and real-time data tous connections. The right people just happened analytics. Parallel computing and vastly expanded to be in the right place at the right time to link computational capacities are impacting many areas Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 35

Fig. 11. Visualizing and analysing multidimensional data. This example shows plots of outputs from reservoir simulations that are being used to test five different algorithms applied to a history matching exercise (Hajizadeh et al. 2012, fig. 3). The five algorithms are: Ant Colony Optimization (ACO), Differential Evolution (DE Rand and DE Best), Neighbourhood Algorithm (NA) and Particle Swarm Optimization (PSO). Each set of iterations traces a path (projected into 2D) from the first to last iteration (blue to red). The cloud-like patterns indicate that a given algorithm is not converging. The PSO algorithm follows a more discrete path to convergence of the simulation. Each iteration point contains information about the 45 parameters input into the simulation. Future developments could provide capabilities that link to further representations of the parameter space by selecting a given iteration. in the modelling and inversion realms. Ensem- their systems based on real-time monitoring of bles of static and dynamic models with produc- vast data streams (Batty et al. 2012), while our tion data using history matching and uncertainty homes can already learn our habits and modify our quantification workflows leads to ‘Big Data’: that environments accordingly (Robles et al. 2010). is, high-dimensional parameter spaces that can- Service and technology companies have quickly not be explored by traditional means. Although the recognized related opportunities for the industry, visualization and analysis of huge quantities of pursuing novel sensor designs for the subsurface multiscale data remain a challenge, new, interactive (Al-Mohanna et al. 2013; Faichnie et al. 2013; Hal- techniques have emerged that enable geoscientists dorsen et al. 2013; Kabir et al. 2014). With these and reservoir engineers to work together in a truly developments have come the growth of commu- collaborative environment (Sousa et al. 2014) nities that focus on handling rapid and large data (Fig. 11). In the context of history matching, uncer- streams from the oil and gas fields with a view to tainty quantification and production optimization strengthening real-time optimization (Gomez et al. that link static and dynamic data, such interactive 2013; Knabe et al. 2013). Large datasets from vast techniques project the parameter space that will be arrays of wells in unconventional fields and novel explored in an interactive environment. End users sensor development are also driving an intense can interfere with reservoir simulations in real focus on Big Data and tools for data analytics time by querying the parameter space visually: (Barron et al. 2010). for example, to test a diverse range of geological Closely coupled to developments in sensors and models and manipulate the parameter space based large data streams are developments in artificial on such analysis (Dos Santos Amorim et al. 2012; intelligence (AI). Machine learning and pattern Gundersen et al. 2012; Hajizadeh et al. 2012). recognition are not new to the geosciences but Developments in the realm of sensors represent advances in AI (and related advances in robotics) a further area of strong research activity. Advances have a significant potential to impact future work- in the areas of materials science and electronics flows. Systems that are being developed to assist have decreased the size of sensors and computers the blind through computer visualization and sensor to the micrometre–millimetre scales (or less), and data fusion (Rivera-Rubio et al. 2013), security increased their tolerance for harsh environments. monitoring systems (Choi & Savarese 2014) and We are told that cities of the future will adjust biomedical imaging (Mudry et al. 2013; Toews & Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

36 S. M. AGAR & S. GEIGER

Wells 2013) are all advancing technologies of inter- transferred to the subsurface (e.g. Bastesen & est to geoscience: for example, pattern recogni- Braathen 2010; Elvik 2012). tion of images can support quantitative, multiscale Integrated approaches involving outcrop stud- analyses of 3D core images and real-time com- ies, numerical simulation, sandbox modelling and parisons with core data from other fields. Similarly, seismic data offer strong platforms for the develop- machine learning algorithms can use production ment of conceptual geometrical models of faults, as data to fuse different geological scenarios into a well as static and dynamic fault-seal properties self-consistent reservoir modelling during history (Agosta et al. 2010). One novel approach identified matching (Demyanov & Christie 2011). Related a correspondence between fluid flow and patterns techniques can be used on outcrops and with seis- of damage in fault zones based on observations of mic data, and offer significant acceleration in data stalactites in carbonate caves (Kim & Sanderson acquisition and analysis (real time), as well as 2010). A subsurface experiment imaged fluid flow greater data integration. Artificial intelligence is through a fault zone via electrical tomography to now reaching the point where machines can gen- explore the detailed hydraulic property impact erate novel scenarios based on their experience resulting from alteration on fluid flow through a (He´lie & Sun 2010). There is the potential for ma- fault zone in carbonate rock (Jeanne et al. 2012, chines to learn from geoscience datasets (or ‘smart 2013). These insights into the dynamic properties analogues’), and to envisage new opportunities of fault zones in carbonates have been matched by and processes in the carbonate reservoirs that may a rapidly expanding group of studies related to not be readily apparent to humans. understanding the detailed impacts of fracture popu- While the benefits from these developments may lations on flow (e.g. Dorn et al. 2013). be a decade or more away, they offer new insights Reactive transport modelling on production time- into potential exploration opportunities and pro- scales. Published applications of RTM on productivity of carbonate reservoirs based on broader duction timescales are growing with expanded and better integrated views of all the data (see the modelling efforts related to CO sequestration and earlier section on ‘Global context and frameworks’), 2 EOR (Wilkinson et al. 2010; Stewart et al. 2013; with possibly less human bias than at present. Some Teletzke & Lu 2013). Advances that link model may dismiss data analytics as simply plotting data results to observations in the subsurface offer as geoscientists and engineers have always done. support for the ability of RTM modelling to simu- However, we suggest that key changes, particularly late trends in chemical data from enhanced oil in the areas of visualizing and analysing large vol- recovery projects involving CO injection into car- umes of data, are influencing geoscience research. 2 bonate reservoirs (Holubnyak et al. 2011; Sheva- These include a stronger emphasis on systems think- lier et al. 2012). At the Hedberg Conference, one ing (as opposed to local studies of a fault zone or study discussed 2D RTMs used to simulate the facies pattern) and the ability to analyse the coup- impact of steam injection on dissolution and pre- ling or links between different processes across a cipitation on production timescales (Champenoy wide range of scales that lead to emergent beha- et al. 2012). A key point here was the need for appro- viours. Greater data integration within these frame- priate measurements and monitoring to determine works may stimulate paradigm shifts, enabling which, of a wide array of engineering and geological practitioners to see things differently. factors, have the most significant impacts. Factors such as well deliverability, historical operations, Dynamic behaviour of structural features. Studies completions, facility constraints and reactivity may of fault zones in carbonate rocks have historically not be at the front of a geologist’s mind when con- lagged behind those in clastic rocks. However, sidering controls on flow. This work highlights over the last decade, many more investigations of an important area for future RTM research: spe- fault zones in carbonates have emerged, encouraged cifically, the potentially significant modification of by the high-resolution seismic imaging of carbonate fluid pathways on production timescales by fluid– reservoirs that revealed large populations of subtle rock interaction during EOR/IOR. Observational faults. For example, Corona et al. (2012) discussed studies that are bringing knowledge of reactive dynamic data for multiple fault zones within the transport and deformation processes closer together Zechstein carbonates, representing a rare quantifi- also signal opportunities for an expanded suite of cation of flow properties in subsurface fault zones complementary experiments to address changes in with sufficient data to support broader inferences. fracture permeability during production (Huerta Other large datasets of fault damage zones in et al. 2012; Ishibashi et al. 2013). outcrops in the NW German Basin also enabled Reyer et al. (2012) to develop rules of thumb for Seismic time-lapse and (semi-) permanent monitor- the mechanical behaviour of, and fluid flow in, car- ing. Time-lapse studies are helping to promote inte- bonate faults in a region that might be usefully grated investigations of geological and engineering Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 37 controls on flow paths. Early, simple models that volume, Astratti et al. (2014) introduce time-lapse attributed geological controls to a single struc- seismic data as a means to capture information on tural conduit or a super-K zone are evolving with the connectivity of fracture networks on production deepening appreciation of the combined impacts timescales in chalk reservoirs. Integration of the of environmental conditions (e.g. stress), geological production history with the comparisons of repeated heterogeneity and fluid–rock interaction during surveys was used to link changes in fault images production (Xu & Gui 2013; Grochau et al. 2014). to qualitative interpretations of changes in fault- While passive seismic time-lapse applications in flow behaviour (e.g. fingering parallel to faults, carbonates lag behind those in clastics, pilot stud- possible role as barriers). Their study demonstrates ies in the Middle East led Soroka & Al-Jenaibi that petrophysical and geomechanical properties (2009) to suggest improved geophysical sensing of the South Arne reservoirs (North Sea) respond via a combination of passive seismic monitoring, rapidly to water injection and production. After 10 time-lapse 3D, vertical seismic profile (VSP) and years, they were able to extract 12% more fault sur- reflection-seismic data. In their case, however, they faces (better definition and greater lateral extent) found that results were commonly inconclusive from the 4D fault cube as a consequence of ident- owing to difficulties in surface conditions, well ified impacts of water injection. This observation, integrity and equipment availability, and in finding as well as clear amplitude anomalies related to an appropriate situation to demonstrate value from complex changes and fluid saturation and com- passive seismic. Studies that monitored CO2 injec- paction, has been related to the possible dynamic tion over a 7 year period in a carbonate reservoir response of the fault network to production. The (Weyburn, Saksatchewan, Canada) confirmed a response may have modified the connectivity of reasonable match between reservoir simulations the fault network, influencing fault-controlled pre- and time-lapse-based interpretations of the move- ferential pathways for flow. Nevertheless, there ment of the CO2 plume (White 2009). Another remain acknowledged uncertainties related to the CO2 storage study demonstrated time-lapse feasi- velocity model as well as the different acquisi- bility in a Devonian reef environment in Canada tion technologies used for the two 3D surveys that (Sodagar & Lawton 2010). To circumvent the were separated by a decade. Further studies empha- issues of low sensitivity to pressure changes in car- size the value obtained from integrating multiple bonate rocks, Zadeh et al. (2011) used a long-offset datasets: Colombo et al. (2010) explored a comp- time-lapse seismic approach at Valhall (in the North lementary approach, combining anisotropic resis- Sea). Time-lapse cross-well electromagnetic (EM) tivity distribution, seismic and reservoir simulation surveys have also been used to monitor changes in to explore the sensitivity of the EM field to fluid sat- fluid saturation during water injection in a Mid- urations in in-situ reservoir conditions. In shallow dle East carbonate reservoir (Clerc et al. 2010). settings, Grasmueck et al. (2012) have applied time- Time-lapse joint inversion of geophysical data has lapse GPR in carbonate rocks. In this case, the 4D been used as a way to reduce the non-uniqueness approach highlighted structural baffles (deforma- of inverse modelling and to monitor changes in tion bands) and their impacts on the near-surface partial saturation during oil production from car- flow of water. In addition, 4D seismic developments bonate reservoirs. For example, Revil et al. (2012) in other areas are promoting advances for perma- and Torres-Verdıń et al. (2012) employed two nent monitoring. Once more, advances in unconven- inversion methods (active time-constrained (ATC) tional reservoirs may offer benefits to carbonate and structural time-lapse inversion) to simulate the settings. A new passive seismic method, Tomogra- inversion of cross-hole resistivity and seismic phic Fracture Imaging (TFI), was recently used to data. The technique is well suited to rocks with vari- image factures in two unconventional reservoirs able fluid saturation (i.e. carbonates). Not only does and a fractured carbonate reservoir (Lacazette the method reduce spatial artefacts in the tomo- et al. 2013) (Fig. 12). Their results suggest promis- grams relative to other inversion methods but it ing insights into hydraulically active fractures, ‘illu- also offers ways to improve the time-lapse inversion minating’ fluid pathways, some of which have been of seismic and resitivity data performed indepen- independently identified by chemical tracers and dently. This approach has been complemented by pressure monitoring. software development designed specifically to han- At the Hedberg Conference, Jackson et al. dle the time-lapse resistivity problem for cross-well (2012) discussed the use of spontaneous potential tomography during enhanced oil recovery (Karaou- (SP) during waterflooding to detect and monitor lis et al. 2013). water encroaching on a well through the use of Efforts to use 4D seismic to improve history SP and electrodes installed permanently downhole matching in reservoir simulations (Osdal et al. (Fig. 12) (Saunders et al. 2012). The technique has 2006) and to provide insights to controls on water the potential to detect increasing water satura- movement (Pires et al. 2013) continue. In this tion several metres to hundreds of metres away but Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

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Fig. 12. Examples of advances in real-time monitoring in carbonate reservoirs. (a) Tomographic fracture imaging (TFI) of a fractured carbonate anticline (from Lacazette et al. 2013). Reservoir depth slice of the ambient TFI derived from the sum of microseismic activity over 4 days. Symbols indicate productivity: 0, no productivity, S, some productivity; E, excellent productivity. The best productivity occurs in the location with the highest microseismic activity. (b) Exploring the potential use of spontaneous potential to detect water encroachment (from Saunders et al. 2012). The two plots represent results from a simulation of a heterogeneous reservoir model at two different times, showing water moving towards a horizontal well. The plotted line traces the value of SP along the well profile. The grey tones show the variation in water saturation along the well. As water approaches the well (high saturation in the lower plot), but is still several tens of metres away, the SP signal increases (lower plot). Modelling and experiments by Saunders et al. (2012) suggest that this method can be used for several monitoring objectives, including: early detection of a waterfront approaching a well; mapping a moving waterfront from multiple wells; identifying and tracking injected fluids during EOR processes and monitoring steam flooding. still needs appropriate hardware and interpreta- Summary tion methods, and a better understanding of the coupling coefficients involved (these relate gradi- Many areas of geoscience and engineering appli- ents in water-phase pressure, salinity and tem- cable to carbonate reservoirs today might be con- perature to gradients in electrical potential). Gosh sidered ‘mature’ in that most recent research et al. (2014) have used a time-lapse pulsed neutron advances have been largely incremental and few capture log to track the history of water encroach- step changes have occurred in the last two decades ment in a carbonate reservoir. Other advances are or more. The discussion in this paper has highlighted being realized through the use of underground lab- advances in geophysical imaging, larger and faster oratories. The low-noise underground laboratory reservoir simulations supported by very large-scale at Rustrel (southern France) has hosted numerous computing, and real-time monitoring and sensing experiments related to the acoustic and flow proper- of reservoirs as among the fastest moving areas ties of carbonate rocks that form the Aptian type today. However, this does not imply that research section (Gaffet et al. 2010; Derode et al. 2013), in other areas lacks significance. Some areas seem and offers many further opportunities for multidi- to have reached a point of diminishing returns but sciplinary collaboration for industry and academic these and other areas may simply be waiting for researchers. Discussions at the Hedberg Confer- the next scientific or technology development in ence reinforced that community efforts involv- fields outside the geosciences to enable further ing academic–industry collaboration are likely to advances. In this respect, the geosciences are no dif- lead to more significant uplift for the industry as ferent from other fields of scientific research that a whole. encounter periods of relatively slow development Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

FUNDAMENTAL CONTROLS ON FLUID FLOW IN CARBONATES 39 interspersed with periods of rapid advance. As attributes to delineate subtle faults, diagenetic recent history has shown, simply connecting to overprints or karst features. Advances in established technology (such as fracking) can have seismic anisotropy now enable more sophisti- a dramatic impact on a resource base. cated interpretations of anisotropic signatures In our introduction we have attempted to high- but there remain significant limitations in abil- light areas of promising research and research ities to isolate distinct sets of subseismic faults advances as represented by papers in this volume or fractures. and elsewhere, and the concepts, tools and tech- † Modelling: multiscale integration and proxies – nologies that might offer new avenues and uplift. developments related to the content and design These can be summarized as follows: of geological and process models are driving efforts to streamline the capture and integra- † Global context and frameworks – there exist tion of information from subsurface/other data many opportunities to bring isolated outcrop directly into models. Such approaches can studies together, particularly in the realm of support rapid iterations with data updates or carbonate deformation, for greater insights. faster experimentation with more scenarios. Regional perspectives can be strengthened Novel approaches to upscaling and simulation through more ‘compare and contrast’ studies studies are yielding deeper insights into the supported by collaborative, community research impacts on flow of geological features that efforts in areas such as RTM and deforma- form at different scales. Nevertheless, there are tion processes over multiple scales. Dynamic many opportunities to close the gap between modelling of outcrop examples could support geological studies of scaling relationships in the development of a catalogue of examples to rocks and the development of suitable proxies support the common understanding of generic in reservoir models. A stronger emphasis on flow behaviours and comparisons with the the need to integrate across multiple scales is subsurface. driving the development of hierarchical gridding † Multidisciplinary approaches – while multidis- and increases in computational efficiencies, ciplinary studies have strengthened consider- although these approaches have not yet fully ably, research still tends to reflect disciplinary entered the commercial arena. organization as opposed to the organization † Modelling tools – developments in pore-scale of researchers around a problem. Recent devel- simulations are now able to quantify changes in opments highlight a stronger integration of relative permeability and capillary changes due diagenesis and deformation, the interaction of to the evolution of pore space, during production sedimentation with deformation and tectonic or on geological timescales. Novel approaches processes, as well as the use of outcrops to pro- are also developing probabilistic models for mote collaboration between geoscientists and multiphase flow to link variability in pore-scale engineers. Developments in sensing and visual- physics to the Darcy scale. Capabilities to rep- ization technologies offer closer links between resent increasingly complex geological geo- the outcrop and the office. metries in models are being complemented by † Insights to fundamental processes via advances the development of tools for unstructured gridd- in analytical and experimental methods – the ing. This approach has supported DFM model- development of new tools and techniques in ling simulations, as well as a much-needed materials science is bringing great benefits alternative to dual-continua methods. Adaptive for the geosciences and reservoir engineering. gridding now supports multiphysics–multiscale Advances in imaging tools and novel experi- simulations and may overcome recognized chal- mental methods are pushing frontiers, reveal- lenges associated with solutions for the ADRE. ing the details of coupled processes at the pore Much modelling research stands to benefit from scale. These developments are improving algor- advances in pre- and post-processing visualiza- ithms for pore-scale simulations that can sup- tion, and novel capabilities to interrogate models port sophisticated modelling approaches to link and data. pore-scale processes to field-scale performance. † Monitoring in real time and on production time- † Subsurface imaging and sensing – develop- scales – burgeoning interest in data mining, ments in subsurface imaging represent one pattern recogntion and data analytics supports of the fastest moving areas. New acquisition the exploration of high-dimensional parameter and processing technologies are enabling high- spaces and, in turn, geoscience–engineering col- resolution imaging of the numerous hetero- laborations. In combination with developments geneities that exist in carbonate reservoirs. in sensors, these approaches offer opportunites Practitioners continue to develop novel work- to design novel subsurface experiments to flows and algorithms for seismic imaging and monitor flow and to learn more about flow Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

40 S. M. AGAR & S. GEIGER

behaviours between wells. Such experiments can dispersion (the third left-hand-side term) and chemical bring multiple technologies together (e.g. RTM reactions (the fourth left-hand-side term) modelling on production timescales, time-lapse ∂(wr S Xi ) seismic, AI and new downhole monitoring tech- a a a +∇(r v Xi ) −∇(r S D∇Xi ) − r G = 0 niques) while driving stronger collaboration and ∂t a a a a a a a a integration. (A1)

Finally, while there are many promising advances, where w is the porosity of the rock, r and S are the density their translation into industry applications is by no and saturation of phase a, respectively, X is the mass frac- means straightforward. Challenges include achiev- tion of chemical component i in phase a, v is the Darcy vel- ing recognition for the ways in which academic ocity, and G is a reaction term for component i in phase a work can contribute, communicating results from (e.g. adsorption). D is the dispersion tensor, which models academic studies in a framework and a common the spreading and mixing of the chemical component, and language that strengthens connections to industry, yields symmetric and Gaussian plumes, which are rarely and the need for courageous champions within observed in nature (cf. Berkowitz et al. 2006). oil and gas companies to manage the academic– industry divide, recognizing the need to experiment as a means to reduce uncertainty, and the time References it typically takes to displace established industry Aavatsmark, I. 2002. An introduction to multipoint flux methods while achieving widespread penetration approximations for quadrilateral grids. Computational of new ones. The Hedberg Conference focused Geosciences, 6, 405–432. not only on scientific and technical contributions Abdollazadeh, A., Reynolsd, A., Christie, M. A., but also on the behaviours that can help to over- Corne, D., Williams,G.&Davies, B. 2013. Esti- come such hurdles, emphasizing the importance of mation of distribution algorithms applied to history ‘boundary spanners’ in promoting paradigm shifts. matching. SPE Journal, 18, 508–517. We hope that this introduction will encourage Abdul Aal, A. F., Al Daghar,K.A.et al. 2013. Inte- more geoscientists and engineers to cross disci- gration of dielectric dispersion and 3d NMR character- izes the texture and wettability of a Cretaceous plinary boundaries, to explore beyond traditional carbonate reservoir. Paper SPE 164150-MS presented industry arenas and to bring new perspectives to at the SPE Middle East Oil and Gas Show and Confer- old problems. ence, Manama, Bahrain, 10–13 March 2013, http:// dx.doi.org/10.2118/164150-MS We would like to recognize all those who enthusiasti- Abecasis, G. R., Altshuler, D., Auton, A., Brooks,L. cally participated in and supported the Hedberg Confer- D., Durbin, R. M., Gibbs,R.A.&Shefler, E. 2010. ence, and who helped to shape many of the concepts and A map of human genome variation from population- ideas represented here while generously sharing their scale sequencing. Nature, 467, 1061–1073, http:// research. All of the academic and ExxonMobil mem- dx.doi.org/10.1038/nature09534 bers of the (FC)2 Alliance are thanked for their input and Abushaikha,A.S.A.&Gosselin, O. 2008. Matrix– guidance (2007–2013). Thanks to all those who contribu- fracture transfer function in dual-medium flow simu- ted papers to the volume, and to all the reviewers for their lation: review, comparison, and validation. SPE diligence and support in improving the overall content. Paper 113890 presented at the Europec/EAGE Confer- Further thanks to J. DeGraff, A. Tscherch, G. Jones, ence and Exhibition, Rome, Italy, 9–12 June 2008. S. Buckley, E. Liu, M. C. Sousa, M. Jackson, D. Astratti, Agada,S.&Geiger, S. 2013. Optimising gas injec- E. Gomez-Rivas, S. Stafford and A. Lee for providing tion in carbonate reservoirs using high-resolution and/or suggesting improvements to the figures. D. Astratti, outcrop analogue models. SPE Paper 166061 pre- R. Gibson, S. Stafford and Y. Xiao are thanked for pro- sented at the SPE Reservoir Characterisation and viding pre-submission reviews. S. Geiger thanks Foun- Simulation Conference, Abu Dhabi, UAE, 16–18 Sep- dation CMG for supporting his Chair in Carbonate tember 2013. Reservoir Simulation. S. Agar thanks ExxonMobil for Agada,S.&Geiger, S. 2014. Wettability, trapping and the opportunity to pursue the GSL Special Publication fracture-matrix interaction during WAG injection in and for permission to publish. fractured carbonate reservoirs. SPE Paper 169054 presented at the SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, 12–16 April 2014. Appendix Agada, S., Chen,F.et al. 2014. Numerical simulation of fluid-flow processes in a 3D high-resolution carbon- Advection–Dispersion–Reaction Equation ate reservoir analogue. Petroleum Geoscience, 20, 125–142, http://dx.doi.org/10.1144/petgeo2012-096 (ADRE) Agar, S., Geiger-Boschung,S.et al. 2010. The impact of hierarchical fracture networks on flow partition- Fundamentally, the ADRE aims to describe the spatio- ing in carbonate reservoirs: examples based on a temporal evolution of a chemical component i in phase a Jurassic carbonate ramp analog from the High Atlas. due to advection (the second left-hand-side term), Paper SPE 135135, presented at the SPE Annual Downloaded from http://sp.lyellcollection.org/ by guest on October 1, 2021

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Technical Conference and Exhibition, Florence, Italy, carbonate reservoirs. SPE Paper 155560 presented at 19–22 September 2010, http://dx.doi.org/10.2118/ the SPE EOR Conference at Oil and Gas West Asia, 135135-MS Muscat, Oman, 16–18 April 2012. Agar,S.M.&Hampson, G. J. 2014. Fundamental con- Al-Dhahli, A., Geiger,S.&van Dijke,M.I.J. trols on flow in carbonates: an introduction. Petroleum 2013a. Three-phase pore-network modelling for res- Geoscience, 20, 3–5, http://dx.doi.org/10.1144/ ervoirs with arbitrary wettability. SPE Journal, 18, petgeo2013-090 285–295. Agar, S. M., Geiger,S.et al. 2013. Summary of Al-Dhahli, A., van Dijke,M.I.J.&Geiger, S. 2013b. the AAPG–SPE–SEG Hedberg Research Confer- Accurate modelling of pore-scale film and layer flow ence on ‘Fundamental Controls on Flow in Carbon- for three-phase flow processes in clastic and carbonate ates’. American Association of Petroleum Geologists rocks with arbitrary wettability. 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permeability and performance in a mature carbo- seismic data for characterization, monitoring and nate field using near-wellbore upscaling. In: Agar, dynamic modelling of water injection in a hetero- S. M. & Geiger, S. (eds) Fundamental Controls geneous carbonate reservoir. AAPG Search and Dis- on Fluid Flow in Carbonates: Current Workflows covery Article #90105 presented at the AAPG GEO to Emerging Technologies. Geological Society, Middle East Conference & Exhibition, Manama, London, Special Publications, 406. First published Bahrain, 7–10 March 2010. online June 23, 2014, http://dx.doi.org/10.1144/ Coimbra,R.&Olo´riz, F. 2012. Contrast comparison SP406.11 of differential diagenetic pathways of Lower Tithon- Chandrasekha,S.&Mohanty, K. K. 2013. Wettability ian carbonate materials from the Betic Cordillera alteration with brine composition in high-temperature (S. Spain): evidence for physico-chemical paleo- carbonate reservoirs. SPE Paper 166280 presented at seawater properties. 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