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Journal of the Geological Society, London, Vol. 144, 1987, pp. 327-347, 21 figs, 8 tables. Printed in Northern Ireland

The movement and entrapment of fluids in the subsurface

W. A.ENGLAND, A. S. MACKENZIE',D. M. MANN & T. M. QUIGLEY Geochemistry Branch, BP Research Centre, Sunbury+n-Thames, Middlesex TW16 7LN, UK

Abstract: This paper discusses the migration of petroleum from its formation in a to its subsequent possible entrapment in a reservoir. The chemical and physical properties of petroleum gases and liquids are stressed, particularly their phase behaviour undersubsurface conditions which is shown to be a very important factor in determining migration behaviour. Engineering correlations are presented for estimating the propertiesof petroleum fluids under geologically realistic conditions. The directionsand magnitudes of theforces acting on migrating petroleumare deduced from the combined effects of buoyancy and water flow in compacting sediments. These forces are combined, using a fluid potential description. This procedureallows the direction of migration to be defined. The rate of migration is thenestimated from the properties of thesediments involved, allowing a distinction to be made between 'lateral' and'vertical' carrier beds. This simplified approach is suitable for rapid predictive calculationsin petroleum exploration. It is compared with the more complex 3-D computer modelling approaches which are currently becoming available. Migration losses are related to the cumulative pore volume employed by the petroleum in establishing a migration pathway. The petroleum migration mechanism is shown to be predominantly by bulk flow, with a small diffusive contribution for light over distances less than c. 100m. The loss factors involved in secondary migration are estimated fromfield evidence. Themechanism of reservoir filling is presented as a logical extensionto those described formigration. This, together with the inefficiency of in-reservoir mixing by diffusion or convection, is shown to tend to cause significant lateral composi- tional gradients in reservoirs over and above the gravitationally induced vertical gradients described by other workers.

Symbols and units used Verticalforce acting onunit volume of A Scaling constant in k, =A@*,m' petroleum, N m-3 or Pa m-' Acceleration due to gravity, 9.81 mS-' BG formationGas volumea factor, for single- phase gas reservoir: Surface gas:oilratio of petroleum fluids expelled from a source rock, kg kg-' volume of gas + dissolved condensate Surface gas:oilratio of a subsurface under subsurface conditions petroleum liquid, kg kg-' volume of gas measured at STP height of sedimentary column, m Carrier bed thickness, m B0 Oil formation volume factor: Maximum height of petroleum column that volume of oil + dissolved gas in subsurface a seal can support, m volume of oil at STP Characteristic segregation length for a given compound, m C Number of components Intrinsic permeability, m* c, number,Capillary pq/y Boltzmann constant, 1.38X 10-23JK-' cc coefficient Molecular weight of ith component, kg (kg C" Coefficient of consolidation mol) - CGR Condensate:gaspetro- a relatingratio, to Subsurface mass of petroleum liquid or gas, leum gas, kg kg-' kg d m diameter, Grain Surface mass of petroleum liquid (oil or D Diffusion coefficient, m' s-l condensate), kg F Number of degrees of freedom; or force on Surface mass of petroleum gas, kg unit volume of fluid, N m-3 or Pa m-l number of moles FK Rate of enthalpychangecaused by unit Reynolds number, pqtlp volume of breakdown, J m-3 sK1 Pressure, Pa; or number of phases (for use FP Force acting onvolume unit of petroleum with phase rule) fluid, Nm-3 or Pa m-' Darcy flux perunit cross-sectional area of Fw Forceacting on unitvolume of water, N m-3 rock, m3 m-' s-l or Pa m-' Vertical component of Darcy flux, m3m-' S-1 'Presentaddress BP PetroleumDevelopment (Norway) plc., Lateral Darcy flux, m3 s-l Forusbeen 35, P.O. Box 197, 4033 Forus, Norway. Vertical Darcy flux, m3S-' 327

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r, f Pore throat radius, mean pore throat radius, Table 1. Compositions of subsurface petroleum liquid from the m Bruce field, UK continental shev, reservoired at 40 MPa and 105 "C; Hydrodynamic radius of the ith component, and surface gases and oils produced at STP (COR = 0.3 kg kg-') m R Gas constant, 8.314 X Id JK-' (kg mo1)-' Subsurface petroleum R, Rayleigh number liquid Surface gas Surface oil S Petroleum saturation of pore space, m3 m-3 Com- ponents M(%) mol(%) M(%) mol(%) M(%) mol(%) t Time, S T Temperature, K 1.1 1.92.6 4.3 V Volume, m3 0.1 0.3 0.4 0.4 vi Molarvolume of ithcomponent, m3 (kg 10.9 49.9 68.3 11.8 moI)-' 3.3 0.1 0.028.1 11.0 12.6 W Length scale for estimating Peclet number 3.4 0.1 5.8 7.8 13.1 0.5 W Horizontal length of camer bed, m 3.01.4 0.4 3.84.7 10.4 2.52.6 0.9 2.52.5 6.9 X Horizontal dimension, m Mole fraction of ith component 2.8 2.3 4.3 5.81.8 1.6 Xi 4.810.8 5.3 3.5 0.8 3.4 X Composition 6.314.9 8.2 4.0 0.2 1.0 Y Horizontal width of carrier bed, m 5.1 10.5 6.72.9 0.08 0.4 z Vertical dimension, m 3.7 1.9 0.1 0.027.0 4.9 Z Compressibilityfactor to correct ideal gas 3.0 1.4 4.1 5.3 law for non-ideal behaviour: PV = ZnRT 2.9 1.2 3.9 4.5

(Y Dip of beds, degrees or radians 2.9 1.1 3.9 4.3 3.0 1.1 4.0 4.1 (YW Coefficient of expansion for water, K-' B Contact angle of petroleum-water interface 2.7 0.9 3.6 3.4 on pore wall, measured through petroleum, 2.6 0.8 3.5 3.1 2.3 0.7 3.1 2.5 degrees, or radians 1.9 0.5 2.5 1.4 Interfacial tension, or energy, Nm-' or Jm-* 1.4 0.4 1.9 0.9 Proportions of subsurfacepetroleum fluids, 0.9 0.2 1.2 0.9 liquids orgases that are gas at the surface, kg 0.9 0.2 1.2 0.6 kg-' 0.7 0.2 0.9 0.3 Tortuosity factor, m m-' 0.4 0.09 0.5 0.3 Dynamic viscosity, Pas or kg m-' sC1 0.3 0.06 0.4 0.1 Density, kg m-3 0.2 0.04 0.3 0.06 Subsurface petroleum gas density, kg m-3 0.1 0.02 0.1 0.06 0.1 0.02 0.1 0.06 Surface petroleum gas density, kg m-3 0.07 0.01 0.1 0.06 Subsurface petroleum liquid density, kg m-3 0.04 0.007 0.05 0.03 Surface petroleum liquid (oil or condensate) 0.02 0.003 0.03 0.01 density, kg m-3 26.57 (MW. 450) 4.2 16.0 36.2 Subsurface petroleum fluid density, kg m-3 100 100100 100 loo 100 Subsurface rock density, kg m-3 Subsurface water density, kg m-3 C, refers to a molecule with n carbon atoms. Total stress, effective stress, Pa , average porosity, surface porosity, m3 m-3 grouped by carbon number. Thus, the C6 fraction includes Fluid potential, Pa or J m-3 normal and branched hexanes (C,H,,) as wellas the Electrostaticpotential, volts, mechanical unsaturated compound benzene (C6&). The compounds potential, J with carbon numbers of five or less are mainly found in the Petroleumpotential, water potential, Pa or gaseous phase under surface conditions, while the heavier J m-3 hydrocarbons are mostly found in the liquid state. Vectordifferential of verticaland lateral Petroleum is formed in the subsurface in finegrained water potential, N m-3 or Pa m-' source rocks and its generation is well understood (e.g. Tissot & Welte 1984). Some fraction of the organic remains Understanding the movement of petroleum fluids through of dead organisms deposited with the rocksmay be the pores of sedimentary rocks is of enormous commercial preserved to form a solid, insoluble constituent known as importance. Much has been written onthe extraction of kerogen (e.g. Durand 1980). Kerogen ischemically stable petroleum fluids from the pores of underground reservoirs until c. lOO"C, at which point some of the bonds within (e.g. Dake 1978); but the understanding of how these fluids kerogen are broken and mobile petroleum fluids are moved towards and accumulated in the reservoirs is produced; if their volume within the pores is adequate to somewhat superficial. An improved appreciation of this form an inter-connected phase, expulsion may occur (Cooles process will help to plan extraction programmes, and et al. 1985). To create accumulations from which petroleum increase the precision of petroleum exploration. Petroleum may be extracted economically, the petroleum must migrate is defined as both crude oil and ; 'oil' and 'gas' into the pores of coarser, more permeable 'reservoir' rocks. are descriptions applied to petroleum fluids under surface It is not uncommon for petroleum to migrate more than conditions of pressure and temperature. 2 km vertically and 100 kmlaterally from its origin to a A typical petroleum composition isshown in Table 1. reservoir. The thousands of naturally occurring compounds have been Thereare several procedures for quantifying the

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generation andexpulsion of petroleum fromsource rocks. A (water-saturated)petroleum gas. The gaseous phase will mass balance calculated fromthe decreasing kerogen usually containpredominately CH4 with other light concentration and corresponding increasing petroleum fluid hydrocarbons, NZ,CO, and small quantities of H,S and concentration has been described by Cooles et al. (1985). In H,O. The terms 'gas' and 'oil' will be reserved for describing addition,there are kineticschemes which relatethe petroleum phases under surface conditions, following the conversion of kerogenpetroleumto fluids andthe somewhat confusing practice of the . temperature history of the source rock (Tissot & Espitalie The next sections will discuss the generalized properties 1975; A. S. Mackenzie & T. M. Quigley inpreparation). of petroleum phases and water, and how they are affected Hence the masses of petroleum fluids produced in a given by pressure temperatureand composition (P, T and X). source rock may be estimated, if its volumeand initial Conclusions will be deduced from engineering correlations, kerogen concentration are known. A petroleum expulsion rather than thermodynamic calculations. The correlations efficiency must also be estimated to compute the amount of are based on laboratoryexperiments (e.g. Standing 1952; petroleum expelled fromthe source rock. An overall Glas~1980) and are accurate enough for the purposes of migration efficiencymust be assigned to calculate the this overview, and have been validated by process and amount of petroleum whichfinally reaches a trap from a engineers. given source rock. This paper aims to explain the fate of petroleum fluids Composition after expulsion, as they migrate towards and into reservoir The relationships between P, T and X for subsurface rocks. To achieve this we need to: (a) develop a realistic petroleum gases and liquids are first examinedand then physical model of migration,and (b) make accurate used as a basis for defining subsurface fluid densities. The estimates of the properties of the subsurface fluids and the greatest compositional influence on subsurface liquid density rocks which containthem. Case histories will be used to is thequantity of lighter hydrocarbons (generally those examine the migration of petroleum and thelosses involved. which are gases at STP) dissolved in the liquid phase. This This will be related to predictions to produce a physical is quoted as the gas : oil ratio (GOR) expressed in kg kg-', modeldetermining the direction and range of petroleum as measured at the surface. migration. Figure 1 shows the processes involvedin defining the The entrapment of commercial quantities of petroleum, GOR. First,a quantity of subsurface petroleum liquid of and the displacement of water from thereservoir rock pores mass Ml is takento the surface and P-T arereduced, will be described.The role of diffusivemixing within a usually resulting inthe separation of a gaseous phase of petroleumaccumulation, and the production of composi- mass M3 and a liquid phase of mass M,. The GOR is defined tional gradients by theEarth's gravitational field will be as the ratio of the surface masses of gas and oil: analysed, together with the effect of lateral pressure gradientscreated by formation water flow on the GOR = MJM, equilibrium configuration. The corresponding volumes are defined in Fig. l as V,, V, The scope forcalibrating rigorously the theoretical and V,. Using the extensive oil industry database of fluid models of the flow andinteraction of petroleum-water properties, predictive correlations of parameters suchas systems through porous media on a geological timescale is GOR, subsurface density etc. can be made. The correlations great, given the largedatabase collected by drilling for usetypical surface densities of oiland gas atstandard petroleum.The increased understanding that is emerging temperatureand pressure (STP), p:' = 800 kg rnp3 and will undoubtedly throwlight on a myriad of other geological pEz = 0.8 kg m-3. Predictions from these correlations are processes where multiphase flow in porous media occurs. shownin Fig. 2a; GOR increases sharply with increasing

Properties of petroleum fluids Stock Tank l Stock Tank The phase behaviour of subsurface fluids is one of the main determinants of their properties. The phase rule states: P=C-F+2 where P is thenumber of phases, C is thenumber of components and F is the number of degrees of freedom, usually ~3.Due to the very large number of components Surface Surface present, see Table 1, the phase rule does not impose any Subsurface Subsurface severe constraint on the number of phases whichmay in principle coexist. Under usual subsurface conditions, up to three phases may in fact be in equilibrium: Liquld (1) A gaseous phase, referred to as 'petroleum gas'. iM4 (2) A petroleum-poor liquid phase richin water, (Liquid-Containing Reservoir) I (Gas-Contaming Rewvoir) referred to as 'water'. (3) A petroleum-rich liquid phase,referred to as Fig. 1. Definition of terms to relate subsurface petroleumliquids 'petroleum liquid'. and gases to their surface properties. The reductionP-T, in as Because the mutual solubility of most petroleum species petroleum is bought to the surface, causes separation into crudeoil andwater isvery low, thepetroleum phases will be and gas whose relative masses and volumes are important saturated with respect to water. One need only therefore parameters. NB: in practice, several separators are usedby consider two phases: (water-saturated) petroleumliquid and engineers.

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200°C

U) 9 0 , 50 100 100 200 Pressure (MPa) Temperature I'CJ Fig, 2. (a) VariationA, in the saturation gas:oil ratio of petroleum liquid as a functionof pressure, at 50 and 200 "C, calculated using Glasa's (1980) correlations, pzy = 800 kg m-3 and p:? = 0.8 kg The trends above 30 MPa are extrapolated. (b) Curves of constant gas:oil ratio (GOR) of petroleum liquid in P-Tspace, calculated as describedfor Fig. 2a. The stippled region delimits theP-T range encountered in the subsurface. (Note: oilis chemically unstable above 160 "C on a geological time scale.) pressure but decreases slightly with increasing temperature. CGR measurements by Price et al. (1983) for The relationship between the variables P, T and GOR can gas are shown in Fig. 3a, and demonstrate therapid increase be treated as a conventional phase diagram, in which GOR in CGR with temperatureand pressure. Using a phase is contoured in P-T space (Fig. 2b). For a given GOR it diagram representation (Fig. 3b) it can beshown how a shows the equilibrium pressures and temperatureswhich are condensate-rich petroleum gas at depth (high P-T) loses its possible assuming both liquid and gaseous petroleum phases heavier components with upwards migration. are present. For liquid petroleum migrating along a typical The relative compositions of subsurface gases and liquids P-T line, defined by the geothennal and pressure gradients, arethus liable tocontinuous adjustment asmovement thechange in GOR can be estimated.Note that the occurs along geological gradients of P-T. In particular this calculations to give Fig. 2 are for an arbitrary stock tank oil explains the field observation thatthe richest condensate density of 800 kg m-3 and must be recomputed in order to accumulations are generally found at the greatest depths. describe particular field situations. Subsurface petroleum gaswill also have physical properties-- which are strongly influenced by composition, Density since it always has a finite amount of heavier hydrocarbons The densityof a subsurface petroleum fluid in equilibrium (i.e. C, andabove) in solution. At STPthe amount is with gas or liquid will influence greatly its direction of but at pressures and temperaturesmigration. The subsurface densityof gas-saturated oil may the amount may be large* When subsurface gas is brought to be calculated fromthe GOR and oil formation STP a liquid phase may separate and is known by petroleum factor B0 from the mass balance Ml = M2+ M3. This gives: engineersas a gas condensate.The condensate: gas ratio (CGR) is defined in Fig. 1: CGR = MJM3

2.0 I /

... 50 100 100 200 Pressure (MPa) Temperature ("CJ Fig. 3. (a) Variation in the saturation condensate: gas ratio (CGR) of petroleum gas at 50, 150 and 200°C with pressure, as reported by Price et al. (1983) for mixturesof methane (PE: = 0.68 kg m-') and an oilof surface density 806 kg m-3. (b) Location of curves of constant condensate: gas ratio (CGR)in P-T space, as described for Fig. 3a. The stippledregion delimits the P-Trange encountered in the subsurface. Because the condensate components arethermally unstable at temperatures greater than 160 "C on a geological timescale, itis unlikely that the high CGRs predicted at these temperatures are ever achieved.

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The 'oil formationvolume factor' B. representsthe Figures 5a & b show contours of pgasand poi, on a P-T reduction in volume observed when a volume V, of plot; a typical geological, P-T gradient is shown. Clearly as subsurface liquid is broughtto surface conditions via a petroleum migrates upwards, the density of the liquid phase gaslliquid separator-see Fig. 1. Thus, B. = VJV, and increases, whereas that of the gaseous phase decreases. typical values of B. are inthe range 1.1-2. A similar formula is derived for subsurface gaseous density: Water density (l + CGR) STP The subsurface density of water isprincipally affected by Pgas = BG PS= P-T and salinity. Correlations have beengiven by The 'gas formationvolume factor', BG may be calculated Schowalter (1979) but the influence of dissolved gases has from the modified ideal gas law, PIVl = ZlnRTl, where 2, is not been reported. the empirical compressibility factor. Values for Z, may be obtained from correlation tables(Standing 1952) if piz, and Interfacial tensions and viscosities P-T are known. An appreciation of how these parameters varywith P, T From Fig. 1: and X is essential when considering the mechanismand rates of petroleum migration. Berg (1975) has shown that the oil-water interfacialtension, y, remains reasonably thus constant with increasing P-T (within the limits experienced in sedimentary basins) at 20-40 X 10-3 Nm-l.At depths >2 kmgas has a similar density to that of oil, and the BG = 3352, - (assuming = 1, P3 = 0.1 MPa Z, gas-water interfacial tension is similar tothe oil-water '1 and = 298 K) (4) interfacial tension; at depths <2 km the rapidly decreasing Thevariation in poil and psaswith temperatureand density and water solubility of gas causes y to rise to pressure is shown in Figs 4a and 4b. As before p:fp and pE 70 X lOP3 Nm-' at the surface (Berg 1975). are set to 800 kg m-3 and 0.8 kg m-3 respectively. The interfacial tension between gas-saturated petroleum The most striking feature of the subsurface density of liquid andcondensate-saturated petroleum gas decreases petroleum liquid is its decrease with increasing pressure from 3 Nm-' at STP to 0.02 Nm-' at 40 MPa and 120°C, (Fig. 4a). The dissolution of additional low molecular weight the two phases approach one another in their properties. components (expressed as an increasing GOR) lowers the The low interfacial tension at high P-T implies that if two average molecular weight of the petroleum liquid, and thus phases separate from a single petroleum-rich phase at high also lowers its density. Values of poil may be asmuch as P-T the physical unmixing of the two phases may be slow: 30% lower than those found at STP. thesegregated petroleum phases will continueto migrate The subsurface gas density behaves in a completely together, possibly as a foam (Katz et al. 1943). different way-see Fig. 4b. Density increases with increasing The viscosities of the three phases have been measured pressure due to the normal PVT behaviour of gases, and to in the laboratory for different compositions and ranges are the increase in CGR with pressure. Values of pgasmay reach given in Table 2. Viscosity increases in the order petroleum about half that of liquid petroleum at pressures of gas << water = petroleum' liquid. Hence viscous fingering of c. 40 MPa.Thus in thesubsurface, petroleum gasesmay petroleum gas into water, and water into liquid petroleum have properties approaching those of petroleum liquids. may occur. This in part explains why the stability of an

700 r 50°C B 600

f 500 2 500 ' a 0 (D r 2 , , , , , , , 400' ' ' ' :/G 50 100 9 50 100 "I Pressure (MPa) Pressure (MPa)

Fig. 4. (a) Subsurface density of petroleum liquid, when saturated with petroleumgas, as a function of pressure at 50 and 200"C, calculated using equation (1). COR was estimated from Fig. 2a; the oil formation volume factors were calculatedusing Glase's (1980) correlations. Surface densities were as for Fig. 2a. The trends above 30 MPa are extrapolated. (b) Variation in the subsurface density of petroleumgas, when saturated with condensate, as a function of pressure50 at and 200 "C,calculated using equation (2). CGR was estimated from Fig. 3a; the gas formation volume factors were calculated usingGlas~i's (1980) correlations. Surface fluid densities were as for Fig. 2a. The trends above 30 MPa are extrapolated.

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interface between two phases is related to the ratio of their However there ismuch that may be learnt from an viscosities. A large difference in viscosity such as between examination of equilibrium phase behaviour. The composi- gas and water can cause fingers of the less dense phase to tion, X, has only been described in terms of three move into moredense phase if the interface ismoving parameters, the surface density ofoil or condensate, the (Saffmann & Taylor 1958). surface density of gas, the GOR or CGR. Inreality as shown in Table 1 petroleum has a very large number of Effects on composition and phase behaviour during significant components,their concentrations can have a movement great effect on the phase behaviour of particular petroleum systems,which may deviate widely from the ‘typical’ Typical P-T ranges for sedimentary basins are shownin correlations used above. Figs 2-5: they illustrate thegeneral trends in behaviour Wehave discussed elsewhere (A. S. Mackenzie & T. expected as gas or liquid-saturated petroleum fluidsmove M. Quigley in preparation), the techniques for estimating upwards. These trends are summarized as follows: the masses of petroleum expelled from a given volume of (1) Petroleum liquids lose low molecular weight material source rock (ME)and the ratio of surface gas and oil of the to a gaseous phase. expelled petroleum CF.Defining M3 and M2 by analogy with (2) Petroleum gases lose high molecular weight material Fig. 1, GF = M3/M,. Surface mass balance requires that to a liquid phase. ME = Mz + M3. For a given P-T and GF it is possible to (3) Petroleum liquids increase their density. compute the quantities andnature of the phases present (4) Petroleum gases reduce their density. from ME and the subsurface GOR and CGR. Three possible (5) Petroleum gas and liquid properties become less conditions exist, depending onthe relative magnitudes of similar. GF, GOR and IICGR. It is currently not possible to model the more complex If GF is less thanthe subsurface saturation GOR, three-phase(petroleum liquid-petroleum gas-water)be- calculated from the correlations discussed above, then the haviour of real dynamic systems, that result from continuous petroleum liquid is undersaturated with respect to gas, and variations in P, T and composition. A further complication no separate petroleum gas phase will be present. is the character of the surrounding matrix of porous rock as If GFis greater than 1ICGR (i.e. the gas:oil ratio for the this may cause changes in behaviour. The discussion above petroleum gas phase), then the petroleum gas phase will be has only concerned systems in which gas and liquid phases undersaturated with respect to oil, and no separate are always in equilibrium. Situations are possible in which petroleum liquid phase will be present. petroleum gases and liquids become physically separated, If, however, GF is greater than the COR and less than which is the geological equivalent of a one-stage gaslliquid lICGR, two phases will be present in equilibrium. They will separator. both be fully saturated with respect to the other phase. The relative masses of the petroleum liquids and gasmay be Table 2. Approximate subsurface vbcosities computed from mass balance considerations. offluids (taken from Frick & Taylor 1962)

Viscosity (Pa S) Forces controlling petroleum movement Migrationis the process bywhich petroleum fluidsmove Gas 10-~-10-~ from the low porosity, fine-grained source rocks, where they Oil 5 X 10-4-5 X 10-’ Water 10-~-10-~ aregenerated, to higher porosityreservoir rocks, where they may (under suitable circumstances) form a highly Gas viscosity increases with increasing concentrated accumulation. depth; Oil viscosity decreases with increasing Primary migrationis defined as the movement of the depth; Water viscosity increases with increas- newly generated petroleum from the lowpermeability ing depth. source rock to its first encounter with higher permeability

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beds-usually a or fracturedlimestone body. The The force vector F points along the steepest gradient of the distance involved is typically in the range up to 1km. contours of @-the equipotential contours. Secondary migration isthe subsequent transfer of In electrostatics the potential, QE, is defined as the work petroleumthrough higher permeability strata known as doneon transferring unit charge fromadatum point ‘carrier beds’. If a suitable reservoir structureis encountered (usually infinity) to the coordinates of interest. The force within therange of secondary migration,apetroleum vector on unit charge is then given by accumulation may be formed.The distance involvedin secondary migration is usually up to 100 km, but depends on F = -VQE the volumes and types of petroleumand rocks involved; The negative sign shows that the forces point from areas of these factors will be discussed below. Figure 6 illustrates the high potential to those of low potential. Positions of stable definition of primary and secondary migration. equilibrium in any potential field are defined by: Early attempts to explain the mechanism of migration were based on the dissolution of petroleum in pore water VQ=O and (6) andloron diffusion through water-wet rocks.However, V2Q 3 0 attempts to quantify these mechanisms have shown that the solubilities and diffusion constants are far toolow to account i.e. zero force and positive curvature in Q. for the masses of petroleum transported, or the timescales We will now define Q in a form applicable to petroleum available (Jones 1980; Leythaeuser et al. 1982). migration, known as the petroleum potential QP. A similar This paper demonstrates that models based on the bulk potential, Qw, maybe defined to describe the subsurface flow of petroleum can quantitatively account forthe movement of water. Note, however, that a certain condition migration distances and timescales observed in nature (e.g. must be satisfied before any force field can be represented as Durand 1981). The discussion of migration will be split into a gradient of asuitable potential, namely the curl of the twomain sections. First the origin and magnitudes of the force must vanish. This is only strictly true for the fluid force driving forces which controlpetroleum migration will be field when the fluid density does not vary with horizontal discussed. Then these will be used, in conjunction with rock position. This is generally not the case during long distance and fluid properties to estimate the rates at which primary petroleum migration where oil and gas densities may vary and secondary petroleum migration occur, and the distances considerably. Formore local considerations, however, covered. wherethepetroleum densities can be regarded as approximately constantit is convenient to use the fluid potential concept. Fluid potential: the driving force The following sections will show methods for calculating In many complicated physical situations a number of forces the various contributionsto QP. Sinceknowledge of Qpp compete to control a natural or artificial system. Instead of leads to an understanding of the driving forces acting on resolving the force vectors at every point, it is often simpler petroleum, it leads to adescription of the factors controlling to work with a scalar potential, Q, calculated for each point. petroleum migration. Table 3 comparesthe mechanical, This generalapproach to petroleum movement hasbeen electrostatic and fluid potentials. described in more detail by Hubbert (1953); a summary of his work is given here and some alternative techniques and Definition of water and petroleum fluid potentials interpretations are offered. In conventional mechanics, the motion of a mass resting The fluid potential is defined as the worknecessary to on a frictionless surface may be examined mosteasily by transfer unit volume of fluid from reference conditions to associating a mechanical potential QM at each point. QM is therelevant (subsurface) conditions of interest.The defined as the work against gravity neededto bring unit reference condition is taken as bulk fluid at a depthof zo = 0 mass from some datum level to the point of interest. The and a gauge pressure of PO = 0 (NB, z increases, as depth force experiencedby unit mass is then given by: increases). The conditions ata depth z and pressure P include any capillary pressure caused by petro1eum:water interfacial tension y in pores of radius r. The work done (assuming incompressible fluids)is therefore: [P- PO]V - mg[z - 201 + 2y K1- v The first two terms are the work done against pressure and gravity respectively; the final term is the work done against capillary forces in transferring bulk fluid into a porous rock

Table 3. Examples of the use of potentialfields in scient@c applications

A pplication Potential Units Force, UnitsPotential Application F, Primary Secondary Migration Migration Mechanics JoulesenergyPotential d%/& Electrostatics Potential Volts q d@,/& Fig. 6. Definitions of primary and secondary migration after Tissot Hydrology Water potential Pascals (Nm-*) dQW/& & Welte (1984).

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medium. (Strictly speaking the capillary pressure termshould HYDROSTATICENVIRONMENT be multiplied by cos /3 where is the angle the /3 PetroleumWaterliquidgas petroleum-water meniscus makes with thepore wall, measuredthrough the petroleum. In practice, p= 0-30”: cosB will tendto unity and may be ignored.) Since the potentials will be defined aswork per unit volume, and noting that pp= m/V, P* = 0 and zo= 0:

@p=P-ppgz+-2Y r

by analogy, the water potential is defined by: HYDRODYNAMICENVIRONMENT

W ater PetroleumWaterliquidgas @W = P - pwgz (8) Note the definitions introduced by Hubbert (1953) are for unit mass of petroleum or water, and therefore differ by a factor of p from our definitions. The use of unit volume as a referencea results in potentials being measured in convenient units of pressure. Our water potentialis identical to the ‘overpressure’, used bysoil scientists, orthe hydrologists’ ‘piezometric’ pressure. Since @,, the water potential, iswidely applied in hydrodynamics, is often Fig. 7. The forces acting on unit volumes of water, petroleum liquid and petroleum gas may be obtained from the vector equations (11) relatedto by substitutingequation (7) intoequation (8): and (12). The resultant force FP or F, acting on petroleum or water is that given by vector summation of the pressure gradient, VP, and @P = @W + (Pw - PPkZ + 2y/r(9) the appropriate density-relatedterm ppg or pwg. It onlyis in small-pored rocks-notably source rocks-that the 2ylr term in equation (7) or (8) will be representation. Differentiating equations (7) and (8) gives: significant. For example in a clay with 60 nm pores it may reach a value of 1MPa (=l0 atm), assuming an interfacial tension of y = 0.03 N m-’. However, in rocks with larger pores, such as , the capillary contributions to @p Fw = -VP + pwg (12) are insignificant, being <0.01MPa (-0.1 atm). This behaviour of the capillary contributionto fluid potential Figure 7 shows these force components and the resultant FP means that capillary effects can be safely ignored in rocks and Fw for hydrostatic andhydrodynamic environments, with large pores such as sandstones, butwill be significant in ignoring the capillary term 2yV(l/r)which is small except at clays. Since many source rocks are organic-rich clays or silts, lithological boundaries involving fine-grained rocks. primary migration will be influenced by capillary effects. In In a hydrostatic environment there is no flowof water contrast, capillary effects will be negligible for secondary and Fw = 0. Since VP= pwg, theresultant force l$ = migration because of the large pores found in the camer (pw- ppg) and is known as the buoyant force. The beds. The ‘seals’, which prevent petroleum ‘leaking’ out of resultant forces on migrating petroleumare thus always reservoirs areoften fine-grained rocks which generate vertical: petroleum gases and liquids will migrate in the sufficient capillary pressures to present a barrierin (Pp which same direction. Because of their lower density, petroleum prevents further movementof petroleum. gases experience larger values of FP. Thus once a free gas In orderto interpret petroleum and water potentials, phase separates it will migrate considerably faster than its consider the water potential and itsbehaviour in hydrostatic associated liquid phase, particularly since the relative andhydrodynamic systems. Ina ‘normally’ pressured permeability of petroleum gases through water-wet rocks is (hydrostatic)environment, the pressure is given by the usually greater than that for petroleum liquids. equivalent columnof water; thus P = pwgz and equation (8) In a hydrodynamic environment, water will experience shows that = 0 at any position.There will be no driving an additional force G.This force may be in any direction, forceto cause movement of water in any direction since depending onthe nature of the flow involved. Figure 7 VaW is everywhere zero. However, petroleum oil or gas, illustrates that the resultant forces on petroleum fluids and will experiencea strong upward force on a unit volume water will be in different directions. Thus petroleum liquids given by (neglecting capillary effects): and gasesmay migrate in different directions. This has important consequences for petroleum exploration, where it is vital to assess the migration pathways of petroleum in order to compute drainage areasand potential reserves. If contours orthogonal toFP are drawn, migration occurs This is knownas the buoyant force, and is largerfor only at right angles to these ‘equipotential’ contours, along petroleum gases than petroleum liquids since pgas< pail. lines of steepest descent. If a suitable rock structure, with a In a hydrodynamic regime, WW# 0 at all points, and ‘seal’ or cap rock is present, migrating petroleum fluids will the forces experienced by petroleum will no longer only be accumulate in such a way that the tilt of their oil-water or vertical. One wayof visualizing the interplay of forces gas-water ‘contacts’ are along an oil or gas equipotential experienced by migrating petroleum, is by using a vector surface. Figure 8a shows that in a hydrostatic environment,

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important: consider an initially water-saturated rock, through which petroleum may flow. The rock will contain pores, whose radii varygreatly in size. Thus as the petroleum potential gradient, VaP,is increased across the rock, petroleum will startto flow intothe pore space. However, flow will occuronly along agiven tortuous pathway through the rock if the applied pressure is greater than the opposing capillary pressure 2ylr. (i.e. flowwill occur only if VcPp for a given pathway is always negative.) For relatively low pressures, no continuous pathway through the rock is possible, and no flow will occur. As the pressure difference across the rock increases, a critical value will be reached at which continuous pathways through the rock occur. This is the minimum pressure at which bulk flow can start. This process is illustrated inFig. 9. This type of non-linear behaviour is obviously inconsistent with Darcy’s law, whichonly allows for linear flux-V@relationships. However, in the absence of a better theory, modified versions of Darcy’s law will be used in the remainder of this paper. For practical purposes, the intrinsic permeability of a pore network filledwith moving petroleum may be Gas-waterequipotential contour estimated from its mean pore radius f (Amyx et al. 1960) ----- Gas-liquid equipotential contour according to Pouisseille’s law: = - Impermeable rock Fig. 8. Equipotential contours for petroleum liquid and petroleum gas under hydrostatic (a) and hydrodynamic (b) conditions. where 8 is the tortuosity of the network, defined as the Equipotential contours are perpendicular to the forcesacting on the averaged ratio of the path-lengths travelled by petroleum fluids (see Fig. 7). Thus, to be at rest, a petroleum-water boundary (or ‘contact’) must be parallel to an equipotential surface. fluid tothe geometrical length of the region of rock considered. Substitution into equation (13) yields: all petroleum-water contacts are horizontal. However, in a hydrodynamic environment, Fig. 8b, tilted contacts occur. The recognition of tilted contacts has been predicted and observed for many years (Hubbert 1953). where q now refers to the flux per m’ of the petroleum-filled network. Thus the petroleum flux per square metre of rock Direction, rates and ranges of petroleum movement may berelated to equation (15) by including factors of Having discussed the forces acting on petroleum, wewill porosity, G, and the fraction of the porosity that is show how its rateof movement may be calculated from rock and petroleum properties.

Flow through porous media For single-phase flow through a porous rock, Darcy’slaw has been found to be an accurate description:

q =-V@-k, P q is known as the superficial Darcy velocity, since it has units of ms-’, but is better thought of as the volume flux of fluid passing across unit area of the rock (m’ m-’ S-’). V@ is the fluid potential gradient discussed previously, and k,lp defines the constant of proportionality between q and V@. k, is the intrinsic permeability of the rock measured in m’ (1 Darcy = 9.689 X lO-I3 m’). p is the dynamic viscosity of the fluid measured in Pas (1 centipoise = 10-3 Pas). Darcy’s lawis successful for single phase flow; unfortunately itis inadequate for describing multiphase flow. In single phase flow V@ only contains the fluid pressure gradient term of equation 7: i.e. the capillary term may be ignored since no water-petroleum interfaces are present. In Fig. 9. Sketch toshow the nature of petroleum flow through a core two-phase systems, the capillary term will become of porous water-filled rock.

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petroleum-filled, known as the petroleum saturation S: greater than r, may be deduced from the mercury r2 porosimetry data. q = Figure 10 shows two typicalcumulative pore volume, 802p (16) versus poreentry radius curves. The average porethroat Inorder to estimate the flux of petroleum flowing (i.e. radius for interconnected flow across a rockmay be migrating persquare metre of rock) one must have good estimated from the critical saturation, S. Since our estimates of the quantities on theright hand side of equation experimental results (Table 4) suggest S = 50% on a volume basis, the pores generally involvedinbulk flow are (16). represented by the shaded areas. From these measurements C#J and p are measured by standard techniques (see Amyx et al. 1960). The tortuosity factor, 6,for most rocks is taken the average pore throat radius F may be deduced after some to be about d3, the theoretical prediction for a loose mathematical computation. Equation (16) may then be used randompore structure (Li & Gregory 1974), andthe to estimate the petroleum fluxin primary and secondary dynamic viscosities of petroleum under subsurface condi- migration. tions have been discussed above. S, the fractional oil saturationat which the sample of Variation in water fluid potentialcaused by sediment rockfirst contains interconnecting pathways,may be compaction and petroleum generation estimated using percolation theory (Stauffer 1979). Percola- In this section it is shown how the water potential may be tion theoryattempts to describe complex interconnected calculated in a sediment whichis undergoing both networks, such as the pore space of a rock. Calculations for compaction and petroleum generation. The principle of the idealized networks indicate that 20-30% of a rock’s pores method, Terzaghi (1948), is to consider a volume element of (on a ‘number’ basis, as opposed to a ‘volume’ basis) must variable size, which always contains the same mass of rock. become petroleum-filled before petroleum can flow through Thus, as compaction occurs, the volume elements reduce the rock. Because of the effect of capillary pressure, when their size appropriately. conduction begins the petroleum will be contained in the Figure 11 defines the volumesinvolved: in this largest pores-i.e. only those with an entry radius above one-dimensional model, onlyvertical water flux, qz some value. Thus the critical volume saturation will exceed (normalized to unit area of rock), need to be considered 20-30%. Once interconnection is complete,‘breakthrough’ with any internal volume generating processes. The rate of occurs, and thesaturation of the network will remain change in volume may be written: constant. We have carried out experiments to investigate this Id d --(AV - V)=- (qJ effect, by studying oil breakthrough in laboratory cores of v dt dz typical reservoir rocks. Liquid petroleum at a few atmospheres pressure was supplied toone end of a core V is the resulting volume change in an element, and AV sample and when breakthroughoccurred, the petroleum represents the volume created by petroleum generation and saturation was calculated from knowledge of the porosity thermal expansion. (In practice the effects of thermal and volume of petroleum supplied. The results are expansion are generally small and were ignored.) presented in Table 4: they confirm that S is always greater The flows, qL, were calculatedusing Darcy’s Law, than 20%. The maximum values found reached 90%. equation (13). The mean radius, F, of the petroleum-filled network may be estimated by mercury porosimetry (e.g. Ritter & Drake 1945). By injecting pressurized mercury into dried core plugs, the relationship betweenpressure and mercury saturation may be obtained. Since the non-wetting mercury will enter the largest porethroats first, the effective pore radius atthat pressure can be ascertained from P = 2y/ rthroat,the capillary term of equation (7). A distribution function, S(r), whichis defined as the cumulative volume fraction of rock porosity occupied by pores whose radius is -a Table 4. Pore space saturations (S) required for oil flow through rocks

...... Sam ple Porosity Sample (%) S ...... \ ...... :::X* . Yorkshire Deltaic 59.6 9.2 5 10 15 Pore throat radius (r)- Llm series sandstone series 91.0 6.5 3.9 56.0 Fig. 10. Cumulative plots of pore volume filled relativeto pore M illstone Grit Millstone 65.3 6.7 throat radius for two sandstones. Sandstone A hasa porosity of Cotswold Oolites 15.1 47.8 19.7% and a permeability of 5.1 X 1O-l’ m’; for sandstone B the Berea SandstoneBerea (US) 29.0* 20.0 values are 20.3% and 4.01 X l0-l’ m‘ respectively. Since our St Bees Sandstone 24.5 18.0 experimental breakthrough results suggest that S > 0.5 for breakthrough of petroleumto occur, pore throats between0.5 and *Average value of threeresults: 17.6%, 31.0%, 3 pm in sandstone A, and between 8 and 13 pm in sandstone B, 38.4%. must be filledfor flow of petroleum to occur.

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42+62 Equation (21) is written in terms of ad/&, i.e. the rate of increase in effective stress with time. Sincethis is principally caused by the extra loading of freshly deposited Petroleum sediment, itis more convenient to workwith (dhldt) the rate of increase in sediment thickness at the surface, i.e. the burial rate. U is the pressure due to the combined weight of water and rock.

where pR is the rock mineral grain density. Substituting U into equation (21), and differentiating with respect to time Expansion gives:

42 whichwill be used laterto represent do'/& in terms of Fig. 11. Definition of terms used in the calculation of water known geological quantities. potential in compacting sediments.q. is the vertical pore waterflu Experimentally it has been found that the equilibrium into a volume element of variable size;qz+sr is the vertical flux out porosity can be calculated from the effective stress by the of the volume element; andAV is the extra volume createdby the generation of petroleum and the thermal expansionof water in the equation: volume element. 1-GG 1-40Go - -ccloglo(~) Of course, in a compacting sediment,the intrinsic permeability, is itself a function of depth and time. This where Go and U; are, respectively, the values of porosity and k,, effective stress at some reference level. is modelled by taking the localvalues of porosity, as G, For convenience this level may te taken as a depth of estimated for a given element,and using a porosity- 10 m with the overlying sediment being normally pressured permeability correlation for shales and mudstones: and having an average porosity of 0.5. Thus 56 is given by: k, =A@

A is a -dependent constant, for which 4 X 10-15m2 The best fit to experimental data is given when Go = 0.55 for for shales and 4 X 10-'' m' for siltstones were, taken, unless shales and 0.49 for sandstones. otherwise stated.This correlation (Smith 1971) gives a reasonable behaviour for as a function of The rather It isnow possible to re-express equation (17) using k, Cp. equation (18); the volume generated by kerogen breakdown low value of A = 4 X 1O-l' m' was found to be necessary in order to give agreement between calculated overpressures FK is calculated as indicated above: and field measurements. For sandstones, the relationship reported by Berg (1975) was used: k, = 0.084d2G5.' (20) 01 where d is the average grain diameter in metres. The rate of generation of petroleum from kerogen was calculated using an Arrhenius law formalism developed for oil exploration since u'/(Cc(l - G)logloe) is nearly constant. C,. is a variable (A. S. Mackenzie & T. M. Quigley in preparation). in time and z. It is known in soil mechanics as the coefficient l/V(aV/at), the rate of change of sediment volume with of consolidation. Our studies have shown that FK is small respect to time is, by definition, equivalent to the rate of compared to 3/az{G(a@,,/az)} and may in most cases be change of linear strain in the z direction i.e. ignored. In order to solve equation (28) it is necessary to define the initial conditions at the surface, in the rock column and at the bottom of the column, where the sediments make where e is the base of thenatural logarithm and C, is a contact with the basement. These assumptions and constant known in soilmechanics as the compaction constraints are known as boundary conditions, and play an coefficient. Typical values of C, are 0.42 for shale, 0.88 for importantrole in determining the outcome of a pore- chalk and 0.25 for sandstone. pressure calculation. The effective vertical stress U' representsthe pressure The following boundary conditions have been assumed: due to the overlying rock supported by the sediment. The (a)an initially hydrostatic environment (aw= 0 at all total pressure due to rock and water is defined by U. Thus points), (b) a zero-valued water potential at the surface at the following definition of U' holds: all times, and (c) either a constant basement overpressure, or an impermeable basement with no flow (i.e. = 0 at u'=u-@w-pwgz (22) V@,., the bottom of the sediment column). In other words the rock supports the total weight of the Equation (28) wassolved using finite difference overburden less the weight supported by the pore fluids. numerical methods; U' and 9 are calculated from the

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Burial rate (m Ma-'J 200 r

2 4 6 8 Depth (km) Depth(km) Fig. 12. Predicted present day variation in water potential(aw) as a function of depth, for a shaley sequence deposited onto an Fig. 14. Comparison of predicted variation in pore pressure as a impermeable basement, currently buried to depths>l0 km, at function of depth, as for Fig. 13, except the pressure data shown are burial ratesof 10,35, 100,250 and loo0m Ma-'. The trends were for the Coast (taken from Dickenson 1953) and the predicted using equation (28). predicted trend is fora deposition rateof 150 m Ma-'. equations throughout a compacting column of rock for small respectively in the and the Gulf of Mexico, we increments in sediment loading. The output consists of aW, used our model to predict the pressures expected as a 4 and U as a function of both depth and time. function of depth at the present-day. It can be seen that Figure 12 shows the results of calculations based on this although the model appears to fit the trend there are many method for water potentials aW,which result when shale is significant deviations from it. deposited at between 10 and 1000 mper million years onto a This 'scatter' is attributable to the presence of dipping deep impermeablebasement (at a depthgreater than high permeability features, such as sand lenses not 10 km). It is clear that at depths greater than c. 3 km the considered in ourone dimensional model. These porous slope d@,/az is essentially independent of deposition rate. bodies will have avery small gradient in across them, This can be explained in terms of equations (22) and (25). which will disturb local water flows as sketched in Fig. 15. Atgreat depths, permeability and porosity have been This may increase or decrease at a given depth from the reduced by compaction to the point where water flow rates trend if shale alone were present. are negligibly small compared to the deposition time scale. Since pressures in the field may be measured accurately All the additional stress due to sediment deposition is then onlyin permeable rockssuch as sandstones, drilling into borne by the pore water as a', the effective stress on the points A or C will give,respectively, over-estimates or rock matrix has become effectively constant. Rearranging under-estimates of the undisturbed sediment pressure in the equation (22) and making use of equation (23)gives the absence of the sandstone lens. Only point B shows the slope d@,/dz: undisturbed pressure of the lowpermeability sediment. These considerations can explain the wideranges of pressures measured in the North Sea of Gulf of Mexico and shown in Figs 13 and 14. Figure 16 shows the results of our calculation procedure In Figs 13 and 14 measured pore water pressures (i.e. for the more complicated case of a petroleum source rock cPw + pwgz) obtainedfrom petroleum exploration in the sandwiched between equal thicknesses of shales and with a NorthSea and the Gulf of Mexico are shown.Assuming sandstone overburden. The geological column is assumed to deposition rates of 35 and 150 m per million years have a normally-pressured basement. - l 2 150 I- / I ?! 3 100 m aE

2 4 6 8 Depth(km1 Fig. 15. Perturbation to water potentialsand water flows caused by a dipping sandstone lens withina shaley sequence. This causesQW Fig. U. Comparison of predicted variation in pore pressure as a at C to be lower than predictedby our model, which assumes only function of depth with observed pressures for the North Sea, using vertical flow. Conversely aWat A will be higher than that equation (B),and a burial rateof 35 m Ma-'. predicted.

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0.1 km and k,, = 10-" m2 (i.e. typical value for a shale) equation (32) becomes:

--QLAT - 10-15kLAT (33) Q VERT Therefore, if kLATis greater than 10-15 m* (=l mD), then lateral flowswill be moreimportant than vertical where laterallyextensive carrier beds are present. Although permeabilities measured on sandstone cores may substan- tially exceed lO-I5 m', the presence of faults andthe tortuosity of high permeability streaks withinextensive

v) C sandstone formations may decrease their overall effective permeability. a -m c v) Migration directions rvJ Havingdiscussed the calculation of and hence the flow of water in compacting sediments; we will now describe how

(a) (b) (C) the direction of water movement may be related to that of petroleum. First V@., must be related to VmP (which F%. 16. Predicted variation in QW through three shaley sequences determines the forces acting on petroleum) and (via that contain a source rock. The water potential was calculatedby permeability) to migration rates. assuming the sequences were buried to 3.5 km at 100 m Ma-' by Equations (11) and (12)define the forces acting on sandstone with pore pressure closeto hydrostatic; the sequences are petroleum and water; by substituting one into the other FP underlain by similar sandstones. See text for full explanation. can be related to Fw: Figure 16ashows how the water potential attains a FP=&+(Pp-Pw)g (34) maximum value near the middle of the source rock portion, since: Fw = -V@., and (35) which is caused by the extra volume created by petroleum generation.Thus water willflow both upwards and FP = -V@, + (PP - Pw)g downwards away from the centre of the source rock unit. For vertical flows in rocks less permeable than 10-15 m' Figure 16b was calculated for similar conditions as Fig. (this includes primary migration) petroleum will move in the 16a, except thatthe overlying shale istwice as thick:all same direction as water provided that the buoyancy term water flow through the source rock is now downwards. In (pp- pw)g isless than VQW (or in the verticalcase Fig. 16c the overlying shale in Fig. 16a has been replaced V@,""). Taking pw = loo0 kg m-3, pp= 600 kg m-3 for with a morepermeable siltstone: more water cannow petroleum liquid and pp = 200 kg m-3 for petroleum gas, the escape upwards, and most of the water flowing through the buoyancy term has value of c. 4000 Pa m-' and 8000 Pa m-l source rock will flow upwards. for liquid and gaseous petroleum respectively.Figures 12, We have discussedmodelling of the flowof water 13, 14 and 16, suggest that in over-pressured sequences at vertically; however our previous discussion of the North Sea depths greater than2-3 km d@.,/dr exceeds 10,000 Pa m-', and Gulf of Mexico results suggested there is often a reaching 15,000 Pa m-'. significant lateral component, at least in sandstone. We must Most petroleum is generated and expelled from source therefore examine situations where it may be assumed that rocks below 2 km; therefore during vertical migration the water flow is mainly vertical, and where it is mainly lateral. buoyancy term is smaller than the V@., term, and as seen The competition between vertical flow and lateral flow from Fig. 7 petroleum willflow in thesame direction as may be quantified using Darcy's law, equation (13), and Fig. water. Extrapolating from Figs 15 and 16 implies that 17. Thelateral and verticalflows, QLAT and QmRT (in petroleum will migrate out of the source rock, up or down, m3 S-') are estimated by multiplying the Darcy fluxes qLAT towards the nearest continuous horizon of permeability and qWRTby the corresponding cross-sectional areas H Y greaterthan 10-'5mZ; henceforth called a lateral carrier. and Wlcos a Y. However, if the overlying strata are relatively impermeable

~LAT QLAT = -. H.Y * V@bAT (30) P

V@,",^' isgiven by (@2-@l)cos a/W while V@FRTis equal to (@z-@l)/zor (@+D,)/W tan a: Thus the ratio of lateral and vertical fluxes is estimated to be:

QLAT kLAT QLAT H -- --. tan a- (32) QVERT VERT W Fig. 17. Competition between verticaland lateral flows, QWRTand Assuming realistic values of a = 2", W = 300 km, H = QLAT,through a sandstone embedded in shale.

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compared to the underlying strata, a large gradient in Table 6. Petroleum liquid mean subsurface superjicial velocities and will produce a powerful force causing downward migration dimensionless numbers of petroleum into more permeable lateral carrier beds. The buoyancy force acting updip on petroleum migrating 4 in lateral carriers isgiven by multiplying the vertical m-'s-') (m3 c, NRe buoyancy force by the sine of the dip of the beds. Taking a typical dip of 2O, and the above densities this yields Vertical migration in shales 4 X 10-l~ 7 X 10-l~. 5 X 10-l~ 140 Pa m-' for liquid and 280 Pa m-' for gas. Case history in Lateral migration the North Sea suggests values of 500-1000 Pa m-' for V@&AT in sandstones 8 X 10-'O10-'0 10-'O are common at depths >3 km. Boththe water potential gradient and the force due to buoyancy push petroleum (and water) in the same direction-updip. At depths >3 km the major force driving petroleum is water potential gradients; Typical' values: S = 0.5; 9 = 0.2 (sandstones), 0.1 (shales); buoyancy takes over at shallower depths. f = 10-6 m (sandstones),10-8 m (shales); y = 0.03 Nm-': . ,.= Until this point, capillary effects have been ignored-the 650 kg m-3; p = 5 X 10-3 Pa S-'; V@,= 103 Pam-l (LAT), 2y/r term in equation (7). This term will generate significant 104 Pam-' (VERT). forces only when there is a lithology change which causes a gradient in r. This important effect will occur atthe by the capillary number, C, = pq/y, which represents the boundary between fine and coarse-grained rocks. In a ratio of viscous to capillary (or surface tension) forces in simplified picture of capillary forces, there will be a large establishing pathways through pore networks. Experiments capillary pressure difference which drives petroleum out of withoil-water mixtures in rocks have shown thatat source rocks into carrier beds, e.g. Hubbert (1953).By capillary numbers greater than 10-4, viscous forces become makinggeochemical measurements on actively generating important. Hinch (1985) has related the small value of this source rocks we have found (Mackenzie et al. 1986) that number to thepore geometry: values in this range are source rocks are more efficiently depleted of petroleum expected if the pores have throatsa tenth of the size of their within 5 m of their margins which are in contact with lengths. However, Table 6 shows that at geological flow sandstone strata. We attributethis to capillary effects. ratesthe capillary number is never greater than 10-l': capillary forces therefore dominate at all times. The capillary numbers for our experiments, designed to Nature of petroleum flow calculate the poresaturation required for petroleum flow We havesuggested that petroleum generated in a source through porous media, are about 10? capillary forces still rock will migrate vertically upor down towards a dominateand the measured values for saturation at neighbouring horizon of high lateral permeability, i.e. breakthrough will thus apply under geological timescales. permeability is more than 10-15 m* (or 1 millidarcy). This The Reynolds number, NRe= pqP/p, measures the ratio horizon is called a lateral carrier. of inertial to viscous forces. Taking an arbitrary density for Petroleum will remain in the lateral carrier unless it subsurface petroleum liquid of650 kgm-3, the values overcomes the excesscapillary pressure that opposes its calculated range from 10-l' to 5 X 10-l6 (Table 6). These entry into the smaller pores of the overlying seals. If this may be regarded as small: they show that during petroleum happens, the petroleum will then move vertically into and migration, allflows occur in the 'laminar' (non-turbulent) through the overlying rock until another lateral carrier/seal regime. systemis encountered, inwhich case it will again migrate A third parameter of interest is the Peclet number laterally updip. We have shown that the typical magnitude qw/D, Lerman (1979),which measures the relative of V@, for vertical migration is about 104Pam-';the importance of bulk and diffusivemass over a magnitude of V@, for lateral migration along carrier beds is particular length scale defined by W. D is the effective about 103Pa m-'. diffusioncoefficient for a given component in the The variables required to solve equation (16) for q, the water-filled rock: it is distinct from the molecular diffusion flux of petroleum per m' of rock, are now defined. Taking constant measured in a single phase. If the Peclet number is the mean values of p@, S and f from Tables 2 and 5, and the c. 0.5 diffusive mass transport will be more significant than typicalvalues of 103Pa m-' and 104Pam-' determined bulk flow (Mackenzie et al. 1986). above for V@kAT and V@FRT respectively, the average Estimates of the Peclet number, using Leythaeuser et values for q may be calculated for lateral migration of al's. (1982)field estimates of D inshales for Cl-C, petroleum liquids in sandstones and verticalmigration in hydrocarbons are shown in Table 7, which also shows the shales. The values are given in Table 6. Peclet number for length scales of W = 10 m, 100 m and A measure of the significance of these flow rates is given 1000m, using a value of q appropriate for liquidphase vertical migration in shales (Table 6). Table 5. Typicalproperties of rocks important for migration Table 7 suggests that, with the exception of methane and (approximate burial depth of 3 km) , diffusion is insignificant during vertical migration in shales over distances greater than 10-100m for all the Sandstones Shales components of petroleum. The Peclet numbers (and hence the diffusive length scale) for lateral migration in sandstones 9 (porosity) 0.2 0.1 will bethe same order of magnitude as for vertical f (mean radius of petroleum- filled poresfilled in10-6 metres) 10-8 migrationin shales: although q increases by about three S (saturation) 0.5 0.5 orders of magnitude for sandstones (Table 6), laboratory experiments (Krooss 1985) suggest a similar increase in D

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Table 7. Calculation of Pecletnumbers for verticalmigration of history from regions whose is well petroleum liquids understoodand where most accumulations of petroleum have been discovered. By subtractingthe volumes of Peclet numbers (qw/D) for different discovered petroleum from theexpelled petroleum volumes, length scales (W) calculated using methods reported elsewhere (Cooles et al. 1985; A. S. Mackenzie & T. M. Quigley in preparation), the (m2s-')D* w=10mw=100m w=lOOOm lost petroleum volumes can be estimated. These volumes can be ratioed to the pore volume available for migration Methane 2 X 10-10 0.02 0.20 2.0 (thetotal volume of rock along the migration pathway X 0.04 Ethane 1 10-10 0.40 4.0 multiplied by the average porosity). Detailed results will be 6 X 10-" 0.07 0.70 7.0 Propane reported elsewhere (MacGregor & Mackenzie 1986; A. S. Isobutane 4 X 10-11 0.10 1.0 10 Mackenzie & T. M.Quigley in preparation);these will n-butane 3 X 10-" 0.13 1.3 13 demonstrate that theaverage ratio of lost petroleum to pore n-pentane 2 X 10-" 0.20 2.0 20 n-hexane 8 X 10-'' 0.50 5.0 50 volume is of the order of a few percent. n-heptane 4 X 10-'' 1.0 10 100 Our experiments on cores reported in (Table 4) suggest n-decane 6 X 10-'3t 6.7 67 670 that flowing petroleum onaverage exploits about 50% of the n-tncosane 1 X 10-I3t 40 400 4Ooo available porosity. In order to reduce the effective overall saturation to a few percent, this implies that the flowing * From Leythaeuser et al. (1982); t Extrapolated using log,, D petroleum usesless than10% of the rock area. This = -0.283C,,- 10.39 whereisncarbon number. q = 4 X observation is in agreement with our analysis of the relative 10-13 m3 m-2 -1 S (Table 6). migration fluxes, whereit was concluded that migrating petroleum exploits at least between l and 10% of the rock fromshales tosandstones. Hence because petroleumcan area available for flow. migrate more than lOOkm from its source rock (e.g. Tissot The comparison betweentheory and observation & Welte 1984), these results support our earlier assumption assumes thatpetroleum migrates by forging an intercon- that diffusive transport isonly importantfor very short nected path of petroleum-filled porosity leading away from distance migration of light n-alkanesduring expulsion of mature source rock: petroleum will only migrate as far (and petroleum and vertical migration. Otherwise bulk transport as fast) as the volume of petroleum expelled from the source is the dominant process of migration. rock can spread out, whilst remaining fully interconnected.

Losses during migration The migration rates reported in Table6 must be affected by the rate at which petroleum may be supplied by a source rock. Typically source rocks for oil are 100 m thick and have potential yields of petroleum fluid relative to rock weight of 0.02 kgkg-'. Most of thispotential is realized between 120-150°C (Cooles er al. 1985). Geological heatingrates range mostly between 1 and 10 "CMa-l. Assuming a rock density of 2400 kgm-'and a petroleum density of 650 kg m-3, then the flux across the boundary of the source rock is about 8 X 10-" to 8 X lO-I4 m3 m-' S-'. This flux is compared with the values for q inTable 6. If vertical migration throughshales, relative to rock area, occurs at 4 X 10-13 m3 m-'s-l (Table 6) then the cross-sectional area of rock filled with flowingpetroleum must be greater than or equal to between two hundredths andtwo tenths the areaof thesource rock interface.A similar argumentfor lateral migration through sandstones at8 X 1O-I' m3 m-' S-' (Table 6) suggests that the cross sectional area of rock filled with flowing petroleum must be greater than or equal to 10-' to 10-4 the area of the source rock interface. The area of rock available for vertical migration will be similar to the area of the source rock interface. The above analysis suggests therefore that the petroleum must exploit at least two hundredths to two tenths of this area. In our experience, the ratio of the area of mature source rock to the cross sectional area of a lateral carrier (perpendicular to the direction of flow) isabout 1000: 1. Therefore,the minimum area that must be petroleum-filled during lateral Fig. 18. An example of an eroded migration pathway.Oil stains the migration will correspond to one hundredth to one tenth of coarser parts of a turbidite sequence belongingto the Socorro the area available for petroleum flow. Formation of Eocene Age. The picture taken by Martin Heffernan Perhaps a better approach to estimate the area of rock near the Ancon oilfieldson the Santa Elena Peninsula, Ecuador; exploited byflowing petroleumis to make use of case the hammer handle measures0.25 m in length.

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It also assumes, after migration, a volume of petroleum will vicinity of a hypothetical trap, together with the associated remain in the sequence. This residual volume will be similar contours of @’p.The much higher capillary forces acting on to that necessary to connect both sides of the sequence with petroleum in the fine-grained caprock causes a very sharp flowing petroleum. There are two supporting arguments for gradient to occur in QPpat the reservoirrock-caprock these assumptions: the dominance of capillary forces implied interface. The relevant contribution to isgoverned by by low capillary numbers (see above) and the field evidence 2ylr as shown in equation (7). The caprock provides a of petroleum-stained rock. potential energy barrier to petroleum leakage, the capacity Because capillary forces dominate over viscous forces, of this barrier may be estimated from rock properties as water is unlikely to displace petroleum after the supply of shown later. Equation (11) also shows how the forces acting petroleum from the source rock has dried up. The amount on petroleum (h)depend on the hydrological environment of petroleum left behind in a bed after migration will be and the density of the liquid or gaseous petroleum phases approximately equal to the amount necessary to form an present. The forces experienced by petroleum in hydro- interconnected pathway initially. dynamic environments may cause verysignificant shifts in Migration pathways may be examined either by drilling, the positions of petroleum liquid and gasaccumulations or by analysis of uplifted anderoded pathways. Inboth compared with predictions made assuming hydrostatic cases there is strong circumstantial evidence that migration conditions (see Fig. 8). Fuller details are given by Dahlberg involves considerable losses. The frequency withwhich (1982), who considers in more detail its importance to stained rockis encountered suggests that petroleum petroleum exploration. occupies between 1 and 10% of the rock along the migration We have previously shown that secondary migration may pathways. Figure 18 showssuch an observation; migrating be thought of as involving two levels of focusing into (a) the petroleum seeksout the larger poresand coarser-grained beds with the largest average pore entry radii and (b) the regions of the rock. most accessible pores of the beds described in (a). Figure 20a illustrates the situation envisaged by this model when migrating petroleum first encounters aregion which may Entrapment, filling and mixing of petroleum fluids subsequently become a . The final stages of migration, in which an initially water-wet The migrating petroleum will movealong a dendritic reservoir rock is transformed into a petroleum accumulation network from the source rockwhich demarcates the is nowis considered.The initial trapping and filling coarser-grained parts of the carrier bed.The three- mechanisms, and the mechanical and chemical adjustment dimensional structure of the migration pathway will of petroleum to its new reservoir environment is described. obviously dependon the depositional environment of the The effects of convective and diffusive mass transport as well rocks involved. From our experiments reported above, the as gravitational segregation are considered. petroleum saturation of the dendritic network itself will be c. 50% whichis thesaturation level at which petroleum Entrapment and filling entersthe trap for the first time. Within thetrap itself, petroleum will not behave as a continuous fluid. One There are no characteristic physical properties to distinguish therefore expects thatthe petroleum will initially fill the petroleum reservoir rocks fromcarrier beds or migration reservoir at the crest of a trap as an advancing ‘front’-in pathways. It is only the behaviour of the forces acting on rather the same way as a chromatographic ‘front’ advances petroleum whichdefines the location of possible a alonga chromatographic column. This first stage of petroleum reservoir or trap. A trap may be loosely thought reservoir filling is shown in Fig. 20b. of as a dead-end or cul-de-sac; it is a regionwhere the forces Because the pore sizes of the various layers of a reservoir controlling petroleum migration converge. A trap is always rock are not uniform, migrating petroleum will enter first associated withfine-graineda caprock, which prevents the layers with the largest pores. This situation is shown in vertical movement by capillary forces. The capacity of Fig. 20b, in which several layers with the highest pore sizes caprock will be discussed below. have filled with petroleum. The oil saturation within a layer Figure 19 shows the directions of the forces in the is 40%but the overall saturation on a reservoir-wide basis is about, say, 2%. Since exit from the trap is prevented by an overlying seal, fresh petroleum arriving from the source will be forced into successively smaller and smaller pores. Thus new bands of reservoir rock will become petroleum- filled (Fig. 20c). As more and more petroleum fills the trap, the buoyant pressure exerted by the petroleum increaseswith the I growing height of the inter-connected petroleum stringers. This increasing pressure will be able to overcome the larger capillary pressure of the smallerwater-filled pores, and petroleum will displace water from these pores. This can continue until the height of interconnected petroleum exerts sufficient buoyant pressure at its uppermost point to overcome the capillary pressure acting Fig. 19. The direction of forces acting on petroleum fluids in the between the reservoir rock andthe overlyingwater- vicinity of a trap (after Dahlberg 1982). The combination of water saturated seal. The seal must, of course, have a significantly potential, capillary pressure andbuoyancy forces petroleum towards smaller pore size than the reservoir rock so that 2y/r is much the reservoir in the crest of the structure. greaterfor the seal thanthe caprock. At this point,

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, -1‘covered Area by Figure 20d suggests the emergence of a transition zone at fh>-frll the bottom of the petroleum accumulation. This is caused by the reduced buoyant pressure of petroleum near the bottom being increasingly unable to overcome the capillary pressure term (2ylr) of the petroleum potential. Thus only the very largest pores are oil-filled near the base of the trap. As petroleum continues to migrate into the reservoir, a point will be reached when the petroleum saturation is sufficiently great forthe petroleum to behave in a more liquid-like manner. From previous arguments this point is taken arbitrarily as corresponding to an overall saturation of -50%. This will be achieved when the petroleum column has sufficient height so that the force due to buoyancy at the top of the column exceeds the capillary pressure of the smallest pores that must become petroleum-filled to achieve an overall saturation 40%. Equation (36) can be used to calculate the height where r is the critical pore radius: the height required increases with increasing petroleum density and decreasing critical pore radius (broadly equivalent to reservoir quality). Most require heights

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Onedoes, however, expect reservoir petroleumto Diffusion. Molecular diffusion is a processwhich tends preserve some lateral maturity differences, representing the to reduce and eventually eliminate chemical potential history of the filling process, although mixing processes and gradients by the random motions of molecular species. the possible overturning of density gradients will also cause Consider the case of a freshly filled reservoir with an initially some degree of ‘smearing’ of the initial simpler picture. In non-uniform distribution of chemical components. Diffusion our experience these maturitydifferences can be detected by will cause aredistribution of matter so that horizontal geochemical measurements made on petroleumsamples. concentrationgradients will be eliminated and vertical, gravitational or thermally induced gradients become Gravitational and thermal segregation established. In order to estimate the rates andtimescales of diffusion, In petroleum reservoirs, because of the often considerable itis essential to have accurate values for the diffusion height of petroleum columns, the effect of the Earth’s constants of hydrocarbons in rocks. Unfortunately these are gravitational fieldmust be takeninto account. This not available to better than order-of-magnitude estimates, significantly altersthe equilibrium concentrations of the so our analysisis based onmore accurate laboratory various hydrocarbons so that they vary systematically with measurements in pure liquids. depth (assuming sufficient time for the petroleum reservoir A reasonablefirst-order correlation of diffusion con- to come to thermodynamic equilibrium). This results in the stants with viscosity, temperature and molecular dimension denser (high molecular weight) components tending to be is given by the Stokes equation, Ghai et al. (1973): moreconcentrated toward thebottom of thepetroleum column. In the presence of ageothermal gradient (typically 30 “C km-’), thermally induced concentration gradientsmay become established: this is known as the Soret effect. This This implies that Di is proportional to absolute temperature, effect has been estimated to be of a similar magnitude to but inversely proportionalto dynamic viscosity-riis the gravitational segregation (Holt et al. 1983), but has not been hydrodynamic radius of theith component. Since the widely studied. viscosity of oil in an oil reservoir is approximately equal to The magnitude of the gravitationally induced concentra- that of pure water at 20 “C, one can make use of results tion gradient may be estimatedfrom chemical thermo- fromexperiments camed out in water at 20 “C without dynamics. If one assumes ideal mixingbehaviour-i.e. no correction, as only order-of-magnitude estimates of diffusion interactionsbetween the molecules, an exponential con- rates are required. Table 8 shows the values of Di estimated centration gradient is predicted, Hirschberg (1984). for various hydrocarbons in pure liquids (i.e. in the absence of a rock matrix). xi(hl) = xi(h2)e(kl-k2)’hg (37) The time necessary to achieve equilibration by diffusion, teq,may be estimated from the relation, e.g.Shulte (1980): where RT h, = (39) (~resV,- M& The mole fractions of the ith component at heights hl l is the length scale over which diffusion is considered to and h2 above a reference height are related to the reservoir takeplace. In an individual petroleum column, l will be fluid’s average density prcsand the molecular weight, Mi, taken as 100 m for the purpose of estimating zeqfor vertical and partial molar volume, V,.Thus concentrationdifferences diffusion: l will be taken as 2000m for estimating tcqfor will be greatestfor high molecular weight species in low lateral diffusion on a reservoir-wide basis. A factor of O2 is density reservoirs. included to account for the increased length through which In practice, however, real petroleum reservoirs often matter must diffuse in a tortuous , compared exhibit concentration gradients up tofive times greater than predicted by equation (37). This is a reflection of the Table 8. Diffusion coefficientsfor petroleum components in rock-free non-ideal behaviour of multi-component mixtures. This type liquids and equilibration times (res) for selected components and of system is best dealt with by using an ‘equation of state’ length scales (1) approach in which an empirical mathematical model is used to describe the non-ideal behaviour of the mixtures. res (Ma) from equation (39) Schulte (1980) for example found that improved (though not complete) agreement with field resultpwas obtained by Component* Di liquid)(pure 1=100m 1=2000m assuming non-ideal mixing. For example in the Brent field (UK NorthSea) the methane mole fraction changes by CH4 1 X 10-~(m2 S-’) 0.1 42 5 mole % over 150 m,and in theStatfjord reservoir Sahores & gravitationally induced concentration changes mayhave Witherspoon (1970) c12 0.5 X 10-9 0.2 84 been sufficient to eliminate a sharp petroleumgas-petroleum Interpolated liquid interface in the reservoir. tGm 1 X 10-10 1.0 422 Balthus & Anderson In-reservoir mass transport processes (1983) Thereare two possible mechanisms which could cause * C, refers to amolecule with n carbonatoms; t Typical movement of material within a petroleum reservoir; these molecularweight for high molecular weight natural petroleum are molecular diffusion and thermal convection. constituents known as ‘asphatenes’ by the petroleum industry.

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with within a pure liquid. A value of 8 = v3 is assumed for mixing by convection or diffusion on lateral and horizontal rock matrices which is similar to values found experimen- concentration gradients. Figure 21a shows the variation in tally by Li & Gregory (1974), and is based on that predicted composition between wells, and within an individual column theoretically for a loose random pore structure. However, it of oil 'inherited' from the filling process shown in Fig. 20. is possible that when considering 8 over lengths measuredin Diffusion will rapidly cause thermodynamic equilibration metresor kilometres, additional larger-scale tortuosities within individual wells on a geological timescale, but not an operate.It should also be rememberedthat hydrocarbon a well-to-well basis. Thus Fig. 21b shows that wells 1, 2 and molecules will only be diffusing through that partof the total 3 have different average compositions. Given sufficient time pore network whichis petroleum-saturated, this will also for diffusion to occur, the compositions of the different wells affect e. would eventually approach each other, but the The values for Diin pure liquids were calculated by gravitationally induced compositional gradient would making viscosity correlations, if needed, to data from the persist. This isshown in Fig. 21c. If, however, thermal literature. The results are shown in Table 8 which shows the convection occurs, theentire reservoir will become times necessary forvarious components to diffuse across homogenized, Fig. 21d. 100 m or 2000 m. These distances are representative of the Field evidence suggests thatpetroleum accumulations vertical and lateral extents of a typical petroleum reservoir. do not convect andthat most accumulations reach the It is clear that molecules will, in general, have sufficient time state exemplified by (b). However, in the absence of careful to equilibrate by diffusion to setup gravitationally or well testing and analysis, (b) may be hardto distinguish thermally induced concentration gradientswithin a reservoir from (c). inany given vertical petroleum column, provided no In practice, the Rayleigh number of a liquid petroleum disturbance to the reservoir occurs during =l Ma. The case reservoir is c. 0.1, so convection is not expected to occur is different, however, on the larger length scales associated except under exceptional conditions. This is in fact borne with horizontal diffusion over 2000 m. It is very unlikely that out by field observations, which show that significant lateral a reservoir will exist without disturbance for sufficient time and vertical concentration gradientscan occur in reservoirs. to allow thehydrocarbon components toequilibrate horizontally, although this is often assumed to be the case. Field evidence. Some of our studies of petroleum reservoir compositions have confirmed that they are indeed Convection. Thermal convection may occur when a not well-mixed. This appears to be a new theoretical and body of fluid experiences a heat flow across it. The Rayleigh observational conclusion as far as the oil industry is number, R, determines the onset of thermal convection: if concerned.In previous studies of petroleum reservoirs R, > 40 for a body of fluid in a horizontal rock formation, apparent inconsistencies in analyses between wellsin the convection currents will be established. It is important to same reservoir, have often been ascribed to sampling and note, that in contrast to diffusion, convection will analytical errors. completely homogenize a reservoir, removing any thermally As far as vertical gravitationally induced concentration or gravitationally induced concentration gradients.Figure 21 gradients are concerned,we have observed similar values to illustrates schematically the different effects of reservoir those of Shulte (1980), Hirschberg (1984), Creek &

(b WllS Vertical Diffusion 1,2&3

eac0a

Wells 123

Inherited 5 composition variations Composition

I Wells 1,263 Composition (d)

S

Convection

Composition Fig. 21. The effects of various mass transfer processes on three dimensional reservoir composition for a hypothetical petroleum accumulation.

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Schrader (1985),Monte1 & Gouel (1985), and Riemens & Allfluids in rockswith effective permeabilities >10-’5m2 de Jong (1985). will move chiefly laterally; uncemented fractured lime- We have also observed significant lateral differences in stones, and partially cemented sandstones fall in this the composition of samples from different parts of a category. Fluids in rocks witheffective permeabilities reservoir. The petroleum which is in regions of the reservoir lO-” m* are they diverted laterally. in more distant parts. This ispowerful evidence that Intheory these models could be extended tothree petroleum reservoirs arenot well-mixed or homogenized dimensions and coupled to models of the thermal history of laterally. This non-uniformity clearly has important a compacting sequence (e.g. McKenzie1981) and of the repercussions in deciding on the best methods to extract the kinetics of kerogen to petroleum conversion (e.g. Tissot & petroleumfrom the reservoir, as wellas on reserve Espitalie 1975), so as to predict the location of petroleum estimates. Because of the greater lateral extentof reservoirs accumulations, their volumes and composition (e.g. Chenet compared with theirheight, reservoirs will usually be in et al. 1984). We feel thatatour present stage in vertical (gravitational andthermal) equilibrium, but understanding thiswould not be sensible. We believe our horizontal dis-equilibrium. simplified treatment is more useful (A. S. Mackenzie & T. M. Quigley in preparation). Increased knowledge of the distributions of pore sizes and permeability in sedimentary sequences is required before more complex models would Discussion and conclusions be justified. In particular, we have deliberately not Wehave demonstrated that the migration of petroleum considered therole of faults and fractures. Most of the fluids in compacting sediments can be described adequately joints and fractures that formduring the burial of siliciclastic by the physics and chemistry of multiphase fluid flow. The sediments are compressional and do not help flow (Price separation of this movement by previous authorsinto & Cosgrove in press): the situation may be different for different processes, called primary migration, secondary carbonates. Although there is strong evidence that the faults migration and accumulation, artificial.is Nearly all have low intrinsic permeability parallel to the plane, petroleum flow in the subsurface occurs by the same the permeability and capillary pressures indirectiona mechanism-bulk transport driven by gradients in petro- sub-perpendicular to the plane are in our experience, highly leum fluid potential. Capillary forces dominate over viscous variable.Solving the controls on thisvariability is crucial forcesand the flowis notturbulent. Diffusionis only before wecan attempt to model flow across faults, and significant in the immediate vicinity of the source rock, and hence in three-dimensions within a . within a petroleum accumulation where it is important for As petroleum fluids migrate, vertical movement will mixing petroleums of different composition on a c. 100 m generally lead to changes in pressure and temperature: this length scale. will cause changes in the relative volumes of petroleum Thenature of the flowitself is non-turbulent,and is liquid and gas. Our physical understanding is not at present dominated by capillary forces in the rock pore network. sufficient to describe accurately the complex three-phase Thus the migrating petroleum exploits the larger rock pores flowsinvolving petroleum gases and liquids through in preference theto smaller pores, which remain water-saturated rocks. However, muchcan be learned by water-filled. The petroleum must fill c. 50% of the available constructing two-phase modelsinvolving water and one rock pore volume in orderto create an interconnected other petroleum gas or liquid phase. pathway, allowing movement to occur. Because of natural The final stage of petroleum movementis its variations in theaverage pore sizes of the rocks involved, on accumulation in a reservoir ortrap, overlain by a a 10 m length scale petroleum movement is concentrated, or finer-grainedlithology known as a seal, whichholds the ‘focused‘, intobetween 1 and 10% of the cross-sectional petroleum within the reservoir by virtue of the capillary area of the rocks through which if passes: i.e. in the pressure difference across the lithological boundary. Unless coarser, larger-pored beds. sufficient petroleum fills the reservoir to produce a The direction in which petroleum movesmay be significant column height, its buoyant pressure will not conveniently described in terms of fluid potential. It is overcome the capillary pressure of the majority of the pores defined in such a way that petroleum fluids move from high in the reservoir, and a poorly-filled accumulation will result. to low fluid potential. Fluid potential gradients are caused Once a petroleum accumulation has achieved mechanical by: variations in excess water pressures, thenatural stabilization, it canonly mix by diffusion or thermal buoyancy of the less dense petroleum ina medium convection. However, in liquid petroleum accumulations, otherwise filled with denserwater, and capillary pressure convection is not significanta process. Thus the only differences. Insedimentary basins, excess water pressures availablemixing mechanism diffusion.is Except for (pressures greaterthan those needed tosupport the distances less than c. loom, diffusion is too slow to cause overlying water column) are induced by the finite rates at compositional mixing in geologically accepted time-scales. which sediments dewater in response to compaction forces. Thus in mostcommercial petroleum reservoirs lateral This is the dominant mechanism controlling fluid potentials compositional variations acquired during the filling process at depths greater than 3 km. In contrast, buoyancy effects will be retained. However, since the columnheights of predominate at shallower depths. Capillary pressure typical reservoirs are measured in tens to hundreds of differences encourage the petroleum fluids to move from metres, the vertical compositions may reach thermodynamic small pores to large pores, at lithological boundaries. equilibrium in a reasonably short time. Thus petroleum We have chosen to investigate petroleum movement reservoirs are ina state of lateral disequilibrium, but are usingsimple models. Two classes of rocks have emerged. vertically equilibrated.

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Received 30 April 1986; revised typescript accepted 12 September 1986.

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