england 1987 petroleum migration

8/13/2019 England 1987 Petroleum Migration

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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 ofpetroleum fluids in the subsurfaceW . A .E NGL AND,A. S . MACKENZIE',D.M.MANN & T. M. QUIGLEY

Geochemistry Branch, BP Research Centre, Sunbury+n-Thames, Middlesex TW16 7LN, UKAbstract: This paper discusses the migration of petroleum from its formation in a source rock to itssubsequent possible entrapment in a reservoir. The chemical and physical properties of petroleumgases and liquids are stressed, particularly their phase behaviour under ubsurface conditions which isshown to be a very important factor in determining migration behaviour. Engineering correlations arepresented for estimating the propertiesof petroleum fluids under geologically realistic conditions . Thedirections ndmagnitudes of the orces acting on migrating petroleum rededuced rom hecombined effects of buoyancy and water flow n compacting sediments. These forces are combined,using a fluid potential description. This procedureallows the direction of migration to be defined. Therate of migration is thenestimated rom heproperties of the ediments nvolved, allowing adistinction to be made between 'lateral' and vertical' carrier beds. This simplified approach is suitablefor rapid predictive calculations n petroleum exploration. It is compared with the more complex 3-Dcomputer modelling approaches which are currently becoming available. Migration losses are relatedto the cumulative pore volume employed by the petroleum in establishing a migration pathway. Thepetroleum migration mechanism is shown to be predominantly by bulk flow, with a small diffusivecontribution for light hydrocarbons over distances less than c . 100m. The loss factors involved insecondary migration are estimated fromield evidence. Themechanism of reservoir filling is presentedas a logical extension o hose described formigration.This, ogether with the inefficiency ofin-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 describedby other workers.

B0

Symbols and units usedA Scaling constant in k , = A @ * ,mBG Gasormationolumeactor,or single-phase gas reservoir:

volume of gas + dissolved condensateunder subsurface conditions

volume of gas measured at STPOil formation volume factor:volume of oil + dissolved gas in subsurface

volume of oil at STPC Number of componentsc, Capillaryumber, pq/yc c Compaction coefficientC Coefficient of consolidationC G R Condensate:gasatio,elatingoetro-leum gas, kg kg-'d Grainiameter,D Diffusion coefficient, m s- lF Number of degrees of freedom; or force onFK Rate of enthalpyhangeaused by unitFP Force acting on unitolume of petroleumFw Forcecting on unitolume of water , N m-3

unit volume of fluid, N m-3 or Pa m-lvolume of kerogen breakdown, J m-3 sK1fluid, Nm-3 or Pa m-'or Pa m-'

'Presentaddress BP PetroleumDevelopment Norway)plc.,Forusbeen 35, P.O. Box 197, 4033 Forus, Norway.

Verticalorce acting onnitolume ofpetroleum, N m-3 or Pa m-'Acceleration due to gravity, 9.81 m-Surface gas:oilatio of petroleum fluidsexpelled from a source rock, kg kg-'Surface gas:ilatio of a subsurfacepetroleum liquid, kg kg-'height of sedimentary column, mCarrier bed thickness, mMaximum height of petroleum column hata seal can support, mCharacteristic segregation length for a givencompound, mIntrinsic permeability, m*Boltzmann constant, 1.38X 10-23JK-Molecular weight of ith component, kg (kgmol)-Subsurface mass of petroleum liquid or gas,kgSurface mass of petroleum liquid (oil orcondensate), kgSurface mass of petroleum gas, kgnumber of molesReynolds number, p q t l pPressure, Pa; or number of phases (for usewith phase rule)Darcy flux perunit cross-sectional area ofrock, m3 m-' s-lVertical component of Darcy flux, m3m-'S-1Lateral Darcy flux, m3s-lVertical Darcy flux, m3S-

327


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328 W . A . E N G L A N D E T A L .r, f

RSR ,tTVviWWXXiXYZz

(Y

B(YW

Pore throat radius, mean pore throat radius,mHydrodynamic radius of the ith component,mGas constant, 8.314 X Id JK-' (kg mo1)-'Rayleigh numberPetroleum saturation of pore space, m3 m-3Time, STemperature, KVolume, m3Molarvolume of ith omponent, m3 (kgmoI)-'Length scale for estimating Peclet numberHorizontal length of camer bed, mHorizontal dimension, mMole fraction of ith componentCompositionHorizontal width of carrier bed, mVertical dimension, mCompressibil ity actor ocorrect deal gaslaw f or non-ideal behaviour: PV = ZnR TDip of beds, degrees or radiansCoefficient of expansion for water, K-'Contact angle of petroleum-water nterfaceon pore wall, measured through petroleum,degrees, or radiansInterfacial tension, or energy, Nm-' or Jm-*Proportions of subsurfacepetroleum fluids,liquids orgases that are gas at the surface, kgkg-'Tortuosity factor, m m-'Dynamic viscosity, Pas or kg m-' sC1Density, kg m-3Subsurface petroleum gas density, kg m-3Surface petroleum gas density, kg m-3Subsurface petroleum liquid density, kg m-3Surface petroleum liquid (oil or condensate)density, kg m-3Subsurface petroleum fluid density, kg m-3Subsurface rock density , kg m-3Subsurface water density, kg m-3Total stress, effective stress, PaPorosity, average porosity, surface porosity,m3 m-3Fluid potential, Pa or J m-3Electrostaticotential,olts,echanicalpotential, JPetroleumpotential,waterpotential,Pa orJ m-3Vector ifferential of verticalndateralwater potential, N m-3or Pa m-'

Understanding the movement of petroleum fluids throughthe pores of sedimentary rocks is of enormous commercialimportance. Much has been written on he extraction ofpetroleum fluids from the pores of underground reservoirs(e.g. Dake 1978); but the understanding of how these fluidsmoved towards and accumulated in the reservoirs issomewhat superficial. An improved appreciation of thisprocess will help to plan extraction programmes, andincrease the precision of petroleum exploration. Petroleumis defined as both crude oil and natural gas; 'oil' and 'gas'are descriptions applied to petroleum fluids under surfaceconditions of pressure and temperature.A typical petroleum composition isshown in Table 1.The thousands of naturally occurring compounds have been

Table 1. Compositions of subsurface petroleum liquid from theBruce field, UK continental shev, reservoired at 40 MPa and 105 C;and surface gases and oils producedat STP COR = 0.3 kg kg-')Subsurface petroleumliquid Surfaceasurface oil

Com-ponents M(%) mol( ) M(%) mol( ) M(%) mol(%)1.10.110.93.33.43.02.52.84.86.35.13.73.02.92.93.02.72.62.31.91.40.90.90.70.40.30.20.10.10.070.040.0226.57 (MW. 450)100

1.90.349.98.15.83.82.52.33.54.02.91.91.41.21.11.10.90.80.70.50.40.20.20.20.090.060.040.020.020.010.0070.0034.2100

4.3.60.4 0.411.88.3

12.61.0.02.1 13.1.8.1 0.510.4.7.4.4 6.9.5.9.6 5.8 1.6.8.33.4.8.30.8 1.0.2.24.9 0.4.08.70.5 0.1 0.02 4.9.0

4.1 5.33.9 4.53.9 4.34.0 4.13.6 3.43.5 3.13.1 2.52.5 1.41.9 0.91.2 0.91.2 0.60.9 0.30.5 0.30.4 0.10.3 0.060.1 0.060.1 0.060.1 0.060.05 0.030.03 0.0136.26.0

10000 loo 100C, refers to a molecule with n carbon atoms.

grouped by carbon number. Thus, the C6 fraction includesnormal and branched hexanes (C,H,,) as wells theunsaturated compound benzene (C6&). The compoundswith carbon numbers of five or less are mainly found in thegaseous phase under surface conditions, while the heavierhydrocarbons are mostly found in the liquid state.Petroleum is formed in the subsurface in finegrainedsource rocks and its generation is well understood (e.g.Tissot & Welte 1984). Some fraction of the organic remainsof dead organisms deposited with the rocksmayepreserved to form a solid, insoluble constituent known askerogen (e.g. Durand 1980). Kerogen ischemically stableuntil c. lOO C, at which point some of the bonds withinkerogen are broken and mobile petroleum fluids areproduced; if their volume within the pores is adequate toform an inter-connected phase, expulsion may occur (Cooleset al. 1985). To create accumulations from which petroleummay be extracted economically, the petroleum must migrateinto the pores of coarser, more permeable 'reservoir' rocks.It is not uncommon for petroleum to migrate more than2 km vertically and 100km aterally from its origin to areservoir.Therere several procedures for quantifying the


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MOVEMENT O F PETROLEUM F L U I D S 329generation andexpulsion of petroleum fromsource rocks. Amass balance calculated fromhe decreasing kerogenconcentration and corresponding increasing petroleum fluidconcentration has been described by Cooles et al. (1985). Inaddition,here are kineticchemes which relateheconversion of kerogenoetroleum fluids andhetemperature history of the source rock (Tissot & Espitalie1975; A. S. Mackenzie & T. M. Quigley inpreparation).Hence the masses of petroleum fluids produced in a givensource rock may be estimated, if its volumeand initialkerogen concentration are known. A petroleum expulsionefficiency must also be estimated to compute the amount ofpetroleum expelled fromheourceock. An overallmigration efficiencymust be assigned to calculate theamount of petroleum whichfinally reaches a trap from agiven source rock.

This paper aims to explain the fate of petroleum fluidsafter expulsion, as they migrate towards and into reservoirrocks. To achieve this we need o: (a) develop a realisticphysical model of migration,ndb)makeccurateestimates of the properties of the subsurface fluids and therocks which contain hem.Case histories will be used toexamine the migration of petroleum and the osses involved.This will be related to predictions to produce a physicalmodeldetermining hedirectionand ange of petroleummigration.The entrapment of commercial quantities of petroleum,and the displacement of water from the eservoir rock poreswill be described.The ole of diffusivemixingwithin apetroleumaccumulation,and heproduction of composi-tional gradients by theEarth'sgravitational field will beanalysed, together with the effect of lateral pressuregradientsreated by formation water flow on theequilibrium configuration.The scope foralibrating rigorously the theoreticalmodels of the flow andnteraction of petroleum-watersystems through porous media on a geological timescale isgreat, given the largedatabase collected by drilling forpetroleum.The ncreasedunderstanding hat is emergingwill undoubtedly throw ight on a myriad of other geologicalprocesses where multiphase flow in porous media occurs.Properties of petroleum fluidsThe phase behaviour of subsurface fluids is one of the maindeterminants of their properties. The phase rule states:

P = C - F + 2where P is thenumber of phases, C is thenumber ofcomponents and F is the number of degrees of freedom,usually ~ 3 .ue to the very large number of componentspresent, see Table 1, the phase rule does not mpose anysevere constraint on the number of phases whichmay nprinciple coexist. Under usual subsurface conditions, up tothree phases may in fact be in equilibrium:(1) A gaseous phase, referred to as 'petroleum gas'.(2) A petroleum-poor liquid phase richn water,

(3) A petroleum-rich liquid phase,eferredo asBecause the mutual solubility of most petroleum speciesandwater is ery low, the etroleum phases will besaturated with respect to water. One need only thereforeconsider two phases: (water-saturated) petroleum iquid and

referred to as 'water'.'petroleum liquid'.

(water-saturated)petroleum gas. The gaseous phase willusually containredominately CH4 with other lighthydrocarbons, NZ O, and small quantities of H,S andH,O. The terms gas' and 'oil' will be reserved for describingpetroleum phases under surface conditions, following thesomewhat confusing practice of the petroleum industry.The next sections will discuss the generalized propertiesof petroleum phases and water, and how they are affectedby pressure temperatureand composition (P , T and X .Conclusions will be deduced from engineering correlations,rather than thermodynamic calculations. The correlationsare based on laboratoryexperiments(e.g. Standing 1952;G l a s ~ 980) and are accurate enough for he purposes ofthis overview, and have been validated by process and plantengineers.CompositionThe relationships between P, T and X for subsurfacepetroleum gases and liquids are first examinedand henused as a basis for defining subsurface fluid densities. Thegreatest compositional influence on subsurface liquid densityis thequantity of lighter hydrocarbons (generally thosewhich are gases at STP) dissolved in the liquid phase. Thisis quoted as the gas :oil ratio GOR) expressed in kg kg-',as measured at the surface.Figure 1 shows the processes involved ndefining theGOR. First,aquantity of subsurface petroleum liquid ofmass M l s taken o he surface and P-T are educed,usually resulting in heseparation of a gaseous phase ofmass M3 and a liquid phase of mass M,. he GOR is definedas the ratio of the surface masses of gas and oil:

GOR = M J M ,The corresponding volumes are defined in Fig. l as V,, V,and V,. Using the extensive oil industry database of fluidproperties, predictive correlations of parameters such sGOR, subsurface density etc. can be made. The correlationsuseypical surface densities of oil ndgas at tandardtemperatureandpressure(STP), p:' = 800kg r n p 3 andpEz = 0.8 kg m-3. Predictions from these correlations areshown nFig. 2a; GOR increases sharply with increasing

Stock Tank Stock Tank

SurfaceSubsurface

Su r f aceSubsurface

i M 4Liquld

(Liquid-Containing Reservoir) (Gas-Contaming R e w v o i r )

Fig. 1. Definition of terms to relate subsurface petroleumiquidsand gases to their surface properties. The reduction in- T , aspetroleum is bought to the surface, causes separation into crudeiland gas whose relative masses and volumes are importantparameters. NB: in practice, several separators are usedyengineers.


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M O V E M E N TFE T R O L E U MLUIDS 331The 'oil formationvolume actor' B. represents hereduction in volume observed when a volume V, ofsubsurface liquid is brought o surface conditions via agaslliquid separator-see Fig. 1. Thus, B. = V JV , andtypical values of B. are in he ange 1.1-2. A similarformula is derived for subsurface gaseous density:

( l + C G R ) STPPgas = P S =BGThe 'gas formationvolumefactor', BG may be calculatedfrom the modified ideal gas law, PIVl= ZlnR Tl , where 2, isthe empirical compressibility factor. Values for Z may beobtained from correlation tablesStanding 1952) if p i z , andP - T are known.From Fig. 1:

thusBG = 3352,- (assuming Z,= 1, P3= 0.1 MPa

1 and = 298 K) (4)Thevariationn poil and psaswith temperature ndpressure is shown in Figs 4a and 4b. As before p:fp and p Eare set to 800 kg m-3 and 0.8kg m-3 respectively.The most striking feature of the subsurface density ofpetroleum liquid is its decrease with increasing pressure(Fig. 4a). The dissolution of additional low molecular weightcomponents (expressed as an increasing G O R ) lowers theaverage molecular weight of the petroleum liquid, and thusalso lowers its density. Values of poi l may be asmuchas30% lower than those found at STP.The subsurface gas density behaves in a completelydifferent way-see Fig. 4b. Density increases with increasingpressure due to the normal PVT behaviour of gases, and to

the increase n C G R with pressure. Values of pgasay reachabout half that of liquid petroleum at pressures ofc . 40 MPa.Thus in thesubsurface,petroleum gasesmayhave properties approaching hose of petroleum liquids.

700 r

600

500

50C

4 0 0 ' ' ' 50 1Pressure (MPa)

Figures 5a & b show contours of pgas nd poi,on a P-Tplot; a typical geological, P-T gradient is shown. Clearly aspetroleum migrates upwards, the density of the liquid phaseincreases, whereas that of the gaseous phase decreases.Wa ter densityThe subsurface density of water isprincipallyaffected byP - T and salinity. Correlations have beeniven bySchowalter (1979) but the influence of dissolved gases hasnot been reported.Interfacial tensions and viscositiesAn appreciation of how these parameters varywith P, Tand X is essential when considering the mechanismandrates of petroleum migration. Berg (1975) has shown thatthe oil-water interfacialension, y , remains reasonablyconstant with increasing P - T (within the limits experiencedin sedimentary basins) at 20-40 X 10-3 Nm-l.Atdepths>2 kmgashas a similar density to that of oil, and thegas-water interfacial tension is similar to he oil-waterinterfacial tension; at depths


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332 W . A . E N G L A N D E T A L .

interface between two phases is related to the ratio of theirviscosities. A large difference in viscosity such as betweengas and water can cause fingers of the less dense phase tomove into moredense phase if the interface ismoving(Saffmann & Taylor 1958).Effects on composition and phase behaviour duringmovementTypical P - T ranges for sedimentary basins are shown nFigs 2-5: they illustrate thegeneral rends in behaviourexpected as gas or liquid-saturated petroleum fluidsmoveupwards. These trends are summarized as follows:

( 1 ) Petroleum liquids lose low molecular weight material( 2 ) Petroleum gases lose high molecular weight material(3) Petroleum liquids increase their density.(4) Petroleum gases reduce their density.(5) Petroleum gas and liquid properties become lessIt is currently not possible to model the more complexthree-phasepetroleum liquid-petroleum gas-water)e-haviour of real dynamic systems, that result from continuousvariations in P, T and composition. A further complicationis the characterof the surrounding matrix of porous rock asthis may cause changes in behaviour. The discussion abovehas only concerned systems in which gas and liquid phasesare always in equilibrium. Situations are possible in whichpetroleum gases and liquids become physically separated,which is the geological equivalent of a one-stage gaslliquid

separator.

to a gaseous phase.to a liquid phase.

similar.

Table 2. Approximate subsurface vbcositiesoffluids ( taken fro m Frick & Taylor 1962

However there ismuch that may be learnt from anexamination of equilibrium phase behaviour. The composi-tion, X , has only been described in terms of threeparameters, the surface density ofoil or condensate, thesurface density of gas, the G O R or CGR. In eality asshown in Table 1 petroleum has a very large number ofsignificant components,heir concentrations can have agreat effect on the phase behaviour of particular petroleumsystems,whichmay deviate widely from the typicalcorrelations used above.Wehave discussed elsewhere (A. S . Mackenzie & T.M. Quigley in preparation), he techniques for estimatingthe masses of petroleum expelled from a given volume ofsource rock ( M E )and the ratio of surface gas and oil of theexpelled petroleum CF.Defining M3 and M2 by analogy withFig. 1 , GF= M 3/M , . Surface mass balance requires thatME= Mz + M3. For a given P - T and GF it is possible tocompute the quantities andnature of the phases presentfrom ME and the subsurface G O R and CGR. Three possibleconditions exist, depending on he relative magnitudes ofGF, G O R and IICGR.If GF is less thanhe subsurface saturation G O R ,calculated from the correlations discussed above, then thepetroleum liquid is undersaturated with respect to gas, andno separate petroleum gas phase will be present.If GF s greater than1ICGR (i.e. the gas:oil ratio for thepetroleum gas phase), then the petroleum gas phase will beundersaturated with respect to oil, and no separatepetroleum liquid phase will be present.If, however, GF is greater than the C O R and less thanl ICGR, two phases will be present in equilibrium. They willboth be fully saturated with respect to the other phase. Therelative masses of the petroleum liquids and gasmaybecomputed from mass balance considerations.

Viscosity (Pa S )Gas 10-~-10-~Oil 5 X 10-4-5 X 10-Water 10-~-10-~

Gas viscosity increases with increasingdepth; Oil viscosity decreases with increasingdepth; Water viscosity increases with increas-ing depth.

Forces controlling petroleum movem entMigration s the process bywhich petroleum fluidsmovefrom the low porosity, fine-grained source rocks, where theyaregenerated, o higher porosity eservoir ocks, wherethey may (under suitable circumstances) form a highlyconcentrated hydrocarbon accumulation.Primary migration sdefinedas the movement of thenewly generated petroleum from the lowermeabilitysource rock to its first encounter with higher permeability


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M O V E M E N TFE T R O L E U ML U I D S 333beds-usually a sandstone or fractured imestone body. Thedistance involved is typically in the range up to1km.Secondary migration isheubsequentransfer ofpetroleumhrough higher permeability strata known ascarrier beds. If a suitable reservoir structures encounteredwithin theange of secondary migration, etroleumaccumulation may be formed.The distance involvednsecondary migration is usually up to 100km, but depends onthe volumes and types of petroleumand rocks involved;these factors will be discussed below. Figure 6 illustrates thedefinition of primary and secondary migration.Early attempts o explain the mechanism of migrationwere based on the dissolution of petroleum in pore waterandloron diffusion through water-wet rocks.However,attempts to quantify these mechanisms have shown that thesolubilities and diffusion constants are far tooow to accountfor the masses of petroleum transported, or the timescalesavailable (Jones 1980; Leythaeuser et al. 1982).This paper demonstrates that models based on the bulkflow of petroleum can quantitatively account forhemigration distances and timescales observed in nature (e.g.Durand 1981). The discussion of migration will be split intotwomain sections. First the origin and magnitudes of thedriving forces which controlpetroleum migration will bediscussed. Then these will be used, in conjunction with rockand fluid properties to estimate the rates at which primaryand secondary petroleum migration occur, and the distancescovered.Fluid potential: the driving forceIn many complicated physical situations a number of forcescompete to control a natural or artificial system. Instead ofresolving the force vectors at every point, it is often simplerto work with a scalar potential, Q, calculated for each point.This generalapproach opetroleummovement hasbeendescribed in more detail by Hubbert (1953); a summary ofhis work is given here and some alternative techniques andinterpretations are offered.In conventional mechanics, the motion of a mass restingon a frictionless surface may be examined mosteasily byassociating a mechanical potential QM at each point. QM isdefined as the work against gravity needed o bring unitmass from some datum level to the point of interest. Theforce experiencedby unit mass is then given by:

MigrationPrimary SecondaryMigrationFig. 6. Definitions of primary and secondary m igration after Tissot& Welte (1984).

The force vector F points along the steepest gradient of thecontours of @-the equipotential contours.In electrostatics the potential, QE, is defined as the workdone nransferring unit charge from atum point(usually infinity) to he coordinates of interest. The forcevector on unit charge is then given byF = -VQE

The negative sign shows that the forces point from areas ofhigh potential to those of low potential. Positions of stableequilibrium in any potential field are defined by:andi.e. zero force and positive curvature in Q.We will now define Q in a form applicable to petroleummigration, known as the petroleum potential QP. A similarpotential, Qw, maybe defined to describe the subsurfacemovement of water. Note, however, that a certain conditionmust be satisfied before any force field can be represented asa gradient of asuitablepotential, namely the curl of theforce must vanish. This is only strictly true for the fluid forcefield when the fluid density does not vary with horizontalposition. This is generally not the case during long distancepetroleum migration where oil and gas densities may varyconsiderably. Formore local considerations, however,whereheetroleum densities can be regarded asapproximately constant t is convenient to use the fluidpotential concept.The following sections will show methods for calculatingthe various contributions o QP. Sinceknowledge of Qppleads to an understanding of the driving forces acting onpetroleum, it leads to a escription of the factors controllingpetroleum migration. Table 3 compares he mechanical,electrostatic and fluid potentials.Definition of water and petroleum fluid potentialsThe fluid potential is defined as the worknecessary totransfer unit volume of fluid from reference conditions totheelevant (subsurface) conditions of interest.hereference condition is taken as bulk fluid at a depthof zo= 0and a gauge pressure of PO = 0 (NB, z increases, as depthincreases). The conditions atadepth z and pressure Pinclude any capillary pressure caused by petro1eum:waterinterfacial tension y in pores of radius r .The work done (assuming incompressible fluids)stherefore:

V Q=OV2Q 0 6)

[P PO]V -mg[z- 01 + 2y - vK1The first two terms are the work done against pressure andgravity respectively; the final term is the work done againstcapillary forces in transferring bulk fluid into a porous rockTable 3. Examples of the use of potentialields in scient@capplicationsApplicationotentialnitsorce, FMechanics Potentialnergyoules d%/&Electrostatics Potential Volts q d@,/&Hydrology Water potential Pascals (Nm-*) dQW/&


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334 W . . E N G L A N D E T AL .medium. (Strictly speaking the capillary pressure term houldbe multiplied by cos /3 where /3 is the angle thepetroleum-water meniscus makes with theore wall,measured hrough hepetroleum. In practice, p = 0-30:cosB will tend o unity and may be ignored.) Since thepotentials will be defined aswork per unit volume, andnoting that p p= m / V , P* = 0 and zo= 0:

@ p = P - p p g z + -Yrby analogy, the water potential is defined by:

@W = P - pwgz (8)Note he definitions introduced by Hubbert (1953) arefor unit mass of petroleum or water, and therefore differ bya factorof p from our definitions. The use of unit volumeasaeference results in potentials being measured inconvenient units of pressure. Our water potential s identicalto the overpressure, used byoil scientists, orhehydrologists piezometric pressure. Since @ the waterpotential, iswidely applied in hydrodynamics, is oftenrelated o by substitutingequation (7) intoequation (8):

@ P = @W + (Pw - P k Z + 2 y / r 9 )It isnlyn small-pored rocks-notably sourcerocks-that the 2 y l r term in equation (7) or (8) will besignificant. For example in a clay with 60nm pores it mayreach a value of 1MPa ( = l 0 atm), assuming an interfacialtension of y = 0.03N m-. However, in rocks with largerpores, such as sandstones, the capillary contributions to @pare insignificant, being


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M O V E M E N TFE T R O L E U ML U I D S 335

Gas-waterequipotentialcontour----- Gas-iquidquipotentialontour= Impermeable rockig. 8. Equipotential contours for petroleum liquid and petroleum

gas under hydrostatic a) and hydrodynamic(b) conditions.Equipotential contours are perpendicular to the forcescting on thefluids (see Fig. 7). Thus, to be at rest, a petroleum-water boundary(or contact) must be parallel to an equipotential surface.all petroleum-water contacts are horizontal. However, in ahydrodynamic environment, Fig. 8b, tilted contacts occur.The recognition of tilted contacts has been predicted andobserved for many years (Hubbert 1953).Direction, rates and ranges of petroleum movementHaving discussed the forces acting on petroleum, wewillshow how its rateof movement may be calculated from rockand petroleum properties.Flow through porous mediaFor single-phase flow through a porous rock, Darcys awhas been found to be an accurate description:

q =-V@k ,Pq is known as the superficial Darcy velocity, since it hasunits of ms-, but is better thought of as the volume flux offluid passing across unit area of the rock (m m- S - ) . V@ isthe fluid potential gradient discussed previously, and k , l pdefines the constant of proportionality between q and [email protected] , is the intrinsic permeability of the rock measured in m(1 Darcy = 9.689 X lO-I3 m). p is the dynamic viscosity ofthe fluid measured in Pas (1 centipoise = 10-3 Pas). Darcyslaw ssuccessful for single phase flow; unfortunately it sinadequate for describing multiphase flow.In single phase flow V@ only contains the fluid pressuregradient term of equation 7: i.e. the capillary term may beignored since no water-petroleum interfaces are present. Intwo-phase systems, the capillary term will become

important: consider an initially water-saturated rock,through which petroleum may flow. The rock will containpores, whose radii varyreatly in size. Thus as thepetroleum potential gradient, VaP,s increased across therock, petroleum will start o flow into hepore space.However, flow will occur nly along a iven tortuouspathway through the rock if the applied pressure is greaterthan the opposing capillary pressure 2 y l r . (i.e. flowwilloccur only if VcPp for a given pathway is always negative.)For relatively low pressures, no continuous pathway throughthe rock is possible, and no flow will occur. As the pressuredifference across the rock increases, a critical value will bereached at which continuous pathways through the rockoccur. This is the minimum pressure at which bulk flow canstart. This process is illustrated inFig.9. This type ofnon-linear behaviour is obviously inconsistent with Darcyslaw, whichonly llows for linear [email protected], in the absence of a better theory, modifiedversions of Darcys law will be used in the remainder of thispaper.For practical purposes, the intrinsic permeability of apore network filledwithmoving petroleum may beestimated from its mean pore radius f (Amyx et al. 1960)according to Pouisseilles law:

where 8 is the tortuosity of the network, defined as theaveraged ratio of the path-lengths travelled by petroleumfluid tohe geometrical length of the region of rockconsidered. Substitution into equation (13) yields:

where q now refers to the flux per m of the petroleum-fillednetwork. Thus the petroleum flux per square metre of rockmay be elated oequation (15) by including factors ofporosity, G, and the fraction of the porosity that is

Fig. 9. Sketch to how the nature of petroleum flow through a coreof porous water-filled rock.


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336 W . A. E N G L A N D E T A L .petroleum-filled, known as the petroleum saturation S:

r2q = 802p (16)Inorder oestimate he flux of petroleum flowing (i.e.migrating persquare metre of rock) one must have goodestimates of the quantities on theight hand side of equation

C and p are measured by standard techniques (see Amyxet al 1960). The tortuosity factor, 6, or most rocks is takento be about d 3 , the theoretical prediction for a looserandom oretructure (Li & Gregory 1974), andhedynamic viscosities of petroleum under subsurface condi-tions have been discussed above.S , the fractional oil saturationat which the sample ofrockirst contains interconnecting pathways,may beestimated using percolation theory (Stauffer 1979). Percola-tion theoryattempts to describe complex interconnectednetworks, such as the pore space of a rock. Calculations foridealized networks indicate that 20-30% of a rocks pores(on a number basis, as opposed to a volume basis) mustbecome petroleum-filled before petroleum can flow throughthe rock. Because of the effect of capillary pressure, whenconduction begins the petroleum will be contained in thelargest pores-i.e. only those with an entry radius abovesome value. Thus the critical volume saturation will exceed20-30%. Once interconnection is complete,breakthroughoccurs, and the aturation of the network will remainconstant.We have carried out experiments to investigate thiseffect, by studying oil breakthrough in laboratory cores oftypical reservoir rocks. Liquid petroleum at a fewatmospheres pressure was supplied toone end of a coresample and when breakthroughoccurred, he petroleumsaturation was calculated from knowledge of the porosityand volume of petroleum supplied. The results arepresented in Table 4: they confirm that S is always greaterthan 20%. The maximum values found reached 90%.The mean radius, F, of the petroleum-filled network maybe estimated by mercury porosimetry (e.g. Ritter & Drake1945). By injecting pressurized mercury into dried coreplugs, the relationship betweenressurend mercurysaturation may be obtained. Since the non-wetting mercurywill enter he largest pore hroatsfirst, he effective poreradius at hat pressure can be ascertained from P = 2 y /rthroat, he capillary term of equation (7). A distributionfunction, S ( r ) , which sdefined as the cumulative volumefraction of rock porosity occupied by pores whose radius is

(16).

Table 4. Pore space saturations ( S ) required for oil flowthrough rocksSample ( ) SYorkshire Deltaic 9. 29 .6series 1.0 3.9 56.0Millstone 5.3Cotswold Oolites 15.1 47. 8Bereaandstone (US) 20.09.0*St Bees Sandstone 18.04.5

*Average value of threeesults:7.6%,1.0%,38.4%.

greater than r , may be deduced from the mercuryporosimetry data.Figure 10 shows two typicalcumulative pore volume,versus poreentry radius curves. The average pore hroatradius for interconnected flow across a rockmay beestimated from the critical saturation, S . Since ourexperimental results (Table 4) suggest S = 50 on a volumebasis, the pores generally involvednulk flow arerepresented by the shaded areas. From these measurementsthe average pore throat radius F may be deduced after somemathematical computation. Equation (16) may then be usedto estimate the petroleum flux nprimary and secondarymigration.Variation in water fluid poten tial aused by sedimentcompaction and petroleum generationIn this section it is shown how the water potential may becalculated in a sediment whichs undergoing bothcompaction and petroleum generation. The principle of themethod, Terzaghi (1948), is to consider a volume element ofvariable size, which always contains the same mass of rock.Thus, as compaction occurs, the volume elements reducetheir size appropriately.Figure 11 defines the volumesnvolved: in thisone-dimensional model, onlyertical water f lux , q z(normalized to unit area of rock), need to be consideredwith any internal volume generating processes. The rate ofchange in volume may be written:

I d d- - ( A V - V )= - (qJv d t dzV is the resulting volume change in an element, and A Vrepresents the volume created by petroleum generation andthermal expansion. (In practice the effects of thermalexpansion are generally small and were ignored.)

The flows, qL were calculatedsingDarcys Law,equation (13).

a-. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . . . . . .::X*. . . . . .. . . . . .

5 10 15Pore throat radius ( r ) - Llm

Fig. 10. Cumulative plots of pore volume filled relativeo porethroat radius for two sandstones. Sandstone A hasa porosity of19.7% and a permeabilityof 5.1 X 1O-l m; for sandstone B thevalues are 20.3% and4.01 X l0-l m respectively. Since ourexperimental breakthrough results suggest thatS>0.5 forbreakthrough of petroleum o occur, pore throats between 5 and3 pm n sandstone A , and between 8 and 13 pm in sandstone B ,must be filledfor flow of petroleum to occur.


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M O V E M E N T O F P E T R O L E U ML U I D S 337

42+62

Petroleum

Expansion

4

Fig. 11. Definition of terms used in the calculationof waterpotential in compacting sediments. . is the vertical pore waterluinto a volume elementof variable size;q z + s r s the vertical flux outof the volume element; and V s the extra volume created y thegeneration of petroleum and the thermal expansion f water in thevolume element.Of course, in a compacting sediment,he intrinsicpermeability, k,, is itself a function of depth and time. Thisis modelled by taking the localvalues of porosity, G, asestimated for a given element, nd using a porosity-permeability correlation for shales and mudstones:

k = A @A is a lithology-dependent constant, for which 4 X 10-15m2for shales and 4 X 10-'' m' for siltstones were, taken, unlessotherwise stated.This correlation (Smith 1971) gives areasonable behaviour for k as a function of Cp. The ratherlow value of A = 4 X 1O-l' m was found to be necessary inorder o give agreement between calculated overpressuresand field measurements.For sandstones, the relationship reported by Berg (1975)was used:

k = 0.084d2G5.' (20)where d is the average grain diameter in metres. The rateofgeneration of petroleum from kerogen was calculated usingan Arrhenius law formalism developed for oil exploration(A. S. Mackenzie & T. M. Quigley in preparation).l /V(aV/at ) , the rateof change of sediment volume withrespect to time is, by definition, equivalent to the rate ofchange of linear strain in the z direction i.e.

where e is the base of thenatural logarithm and C, is aconstant known in soilmechanics as the compactioncoefficient. Typical values of C, are 0.42 for shale, 0.88 forchalk and 0.25 for sandstone.The effective vertical stress U' represents he pressuredue to the overlying rock supported by the sediment. Thetotal pressure due to rock and water is defined by U. Thusthe following definition of U' holds:u ' = u - @ w - p w g z ( 2 2 )

In other words the rock supports he otal weight of theoverburden less the weight supported by the pore fluids.

Equation (21) is written in terms of a d / , i.e. the rateof increase in effective stress with time. Sincehissprincipally caused by the extra loading of freshly depositedsediment, it s more convenient to workwith (dhldt) therate of increase in sediment thickness at the surface, i.e. theburial rate. U is the pressure due to the combined weight ofwater and rock.

where pR is the rock mineral grain density. Substituting Uinto equation (21), and differentiating with respect to timegives:

whichwill be used later o epresent do'/ n terms ofknown geological quantities.Experimentally it has been found that he equilibriumporosity can be calculated from the effective stress by theequation:1 - G 1-40o - c c l o g l o ( ~ )

where Go and U; re, respectively, the values of porosity andeffective stress at some reference level.For convenience this evel may te taken as a depth of10 m with the overlying sediment being normally pressuredand having an average porosity of 0.5. Thus 56 is given by:

The best fit to experimental data is given when Go= 0.55 forshales and 0.49 for sandstones.It isnowpossible to re-express equation (17) usingequation (18); the volume generated by kerogen breakdownFK is calculated as indicated above:

1

since u'/(Cc(l-G)logloe) is nearly constant. C . is a variablein time and z. It is known in soil mechanics as the coefficientof consolidation. Our studies have shown that FK is smallcompared to 3/az{G a@,, /az)} and may in most cases beignored.In order to solve equation (28) it is necessary to definethe initial conditions at the surface, in the rock column andat he bottom of the column, where the sediments makecontact with the basement. These assumptions andconstraints are known as boundary conditions, and play animportantole in determining the outcome of a pore-pressure calculation.The following boundary conditions have been assumed:(a)an initially hydrostatic environment (aw 0 at allpoints), (b) a zero-valued water potential at the surface atall times, and (c) either a constant basement overpressure,or an impermeable basement with no flow (i.e. V@,., = 0 atthe bottom of the sediment column).Equation (28) wasolvedsinginiteifferencenumerical methods; U and 9 are calculated from the


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338 W . A . ENGLAND E T AL .Bur ial rate (m Ma-'J 200 r

Depth (km)Fig. 12. Predicted present day variation in water potentialaw)sa function of depth, for a shaley sequence deposited onto animpermeable basement, currently buried to depths l0 km, atburial ratesof 10,35, 100,250 and loo0 Ma-'. The trends werepredicted using equation (28).equations throughout a compacting column of rock for smallincrements in sediment loading. The output consists of aW,4 and U as a function of both depth and time.Figure 12 shows the results of calculations based on thismethod for water potentials aW,hich result when shale isdeposited at between 10 and 1000 mper million years onto adeep impermeable asementat a depth reaterhan10 km). It is clear that at depths greater than c . 3 km theslope d@,/az is essentially independent of deposition rate.This can be explained in terms of equations (22) and (25).At reat epths, permeability and porosity have beenreduced by compaction to the point where water flow ratesare negligibly small compared to the deposition time scale.All the additional stress due to sediment deposition is thenborne by the pore water as a', he effective stress on therock matrix has become effectively constant. Rearrangingequation (22) and making use of equation (23)gives theslope d@,/dz:

In Figs 13 and 14 measured pore water pressures (i.e.cPw + pwgz) obtainedfrompetroleum exploration in theNorthSea and he Gulf of Mexico are shown.Assumingdeposition rates of 35 and 150m per million years

l2 150?3 1ma

I /

2 4 6 8Depth(km1

Fig.U Comparison of predicted variation in pore pressure as afunctionof depth with observed pressures for the North Sea, usingequation B ) ,nd a burial rateof 35m Ma-'.

2 4 6 8Depth(km)

Fig. 14. Comparison of predicted variation in pore pressure as afunction of depth, as for Fig.13, except the pressure data shown arefor the Gulfof Mexico Coast (taken from Dickenson 1953) and thepredicted trend is for deposition rateof 150 m Ma-'.respectively in the North Sea and the Gulf of Mexico, weused our model to predict the pressures expected as afunction of depth at the present-day. It can be seen thatalthough the model appears to fit the trend there are manysignificant deviations from it.This 'scatter' s attributable to the presence of dippinghigh permeability features, such as sand lenses notconsidered in ourone dimensional model. These porousbodies will have avery mall gradient in across them,which will disturb local water flows as sketched in Fig. 15.This may increase or decrease at a given depth from thetrend if shale alone were present.Since pressures in the field may be measured accuratelyonly n permeable rockssuch as sandstones, drilling intopoints A or C will give, espectively, over-estimates orunder-estimates of the undisturbed sediment pressure in theabsence of the sandstone lens. Only point B shows theundisturbed pressure of the low ermeability sediment.These considerations can explain the wideanges ofpressures measured in the North Sea of Gulf of Mexico andshown in Figs 13 and 14.Figure 16 shows the results of our calculation procedurefor the more complicated case of a petroleum source rocksandwiched between equal thicknesses of shales and with asandstone overburden. The geological column is assumed tohave a normally-pressured basement.

Fig. 15. Perturbation to water potentialsand water flows caused bya dipping sandstone lens within shaley sequence. This causesWat C to be lower than predicted y our model, which assumes onlyvertical flow. ConverselyaWt A will be higher than thatpredicted.


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MOVEMENT OF PETROLEUMLUIDS 339

v)

a-mv)c

C

rvJ(a) (b) C )

F%.16. Predicted variation in QW through threeshaley sequencesthat containa source rock. The water potential was calculatedyassumingthe sequences were buried o 3.5km at 100m Ma-' bysandstone with pore pressure close o hydrostatic; the sequences areunderlain by similar sandstones. See text for full explanation.

Figure 16a howshow the water potential attains amaximum value near the middle of the source rock portion,which is caused by the extra volume created by petroleumgeneration.huswater willlow both upwards anddownwards away from the centre of the source rock unit.Figure 16b was calculated for similar conditions as Fig.16a, except that he overlying shale is wice as thick:allwater flow through the source rock s now downwards. InFig. 16c the overlying shale in Fig. 16a has been replacedwith a morepermeable siltstone: more water can owescape upwards, and most of the water flowing through thesource rock will flow upwards.We have discussedmodelling of the flowf watervertically; however our previous discussion of the North Seaand Gulf of Mexico results suggested there is often asignificant lateral component, at least in sandstone. We musttherefore examine situations where it may be assumed thatwater flow is mainly vertical, and where it is mainly lateral.The competition between vertical flow and lateral flowmay be quantified using Darcy's law, equation (13), and Fig.17. The ateraland vertical lows, QLAT and Q m R T (inm3S- ) are estimated by multiplying the Darcy fluxes qLATand q W R T y the corresponding cross-sectional areas H Yand Wlcos a Y.

QLAT = -. H . Y V@bATL A T (30)P

V@, , ' isgivenby @2-@l)cos a / W while V@FRTsequal to (@z-@l)/zor (@+D, )/W tan a: Thus the ratio oflateral and vertical fluxes is estimated to be:QLATLAT Htan a-WVERT VERT-- --. (32)

Assuming realistic values of a = 2 , W = 300 km, H =

0.1 km and k = 10- m2 (i.e. typical value for a shale)equation (32) becomes:--LAT - 0 -15kLAT (33)QVERT

Therefore, if kLAT s greater than 10-15 m* ( = l mD), thenlateral flowswill be more mportant than vertical wherelaterallyxtensive carrier beds are present. Althoughpermeabilities measured on sandstone cores may substan-tially exceed l O - I 5 m', the presence of faults andhetortuosity of high permeability streaks within xtensivesandstone formations may decrease their overall effectivepermeability.Migration directionsHavingdiscussed the calculation of and hence the flowof water in compacting sediments; we will now describe howthe direction of water movement may be related to that ofpetroleum. First V@., must be related to VmP (whichdetermines the forces acting on petroleum) and (viapermeability) to migration rates.

Equations (11) and (12)define the forces acting onpetroleum and water; by substituting one into the other FPcan be related to Fw:FP=&+(Pp-Pw)g (34)

since: Fw= -V@., and (35)FP = -V@, + P P - w g

For vertical flows in rocks less permeable than 10-15 m'(this includes primary migration) petroleum will move in thesame direction as water provided that he buoyancy term(pp- pw)g isess than V Q W (or in the vertical aseV@, ). Taking pw= loo0 kg m-3, pp= 600 kg m-3 forpetroleum liquid and pp= 200 kg m-3 for petroleum gas, thebuoyancy term has value of c. 4000 Pa m-' and 8000 Pa m-lfor liquid and gaseous petroleum respectively.Figures 12,13, 14 and 16, suggest that in over-pressured sequences atdepths greater than2-3 km d@.,/dr exceeds 10,000 Pa m-',reaching 15,000 Pa m-'.Most petroleum is generated and expelled from sourcerocks below 2 km; therefore during vertical migration thebuoyancy term is smaller than the V@., term, and as seenfrom Fig. 7 petroleum will low n thesame direction aswater. Extrapolating from Figs 15 and 16 implies thatpetroleum will migrate out of the source rock, up or down,towards the nearest continuous horizon of permeabilitygreater han10-'5mZ; henceforth called a lateral carrier.However, if the overlying strata are relatively impermeable

Fig. 17. Competition between vertical nd lateral flows,Q W R T ndQLAT,hrough a sandstone embedded in shale.


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340 W . A . ENGLAND E T A L .compared to the underlying strata, a large gradient inwill produce a powerful force causing downward migrationof petroleum into more permeable lateral carrier beds.The buoyancy force acting updip on petroleum migratingin lateral carriers isiven by multiplying the verticalbuoyancy force by the sine of the dip of the beds. Taking atypical dip of 2O, and the above densities this yields140 Pa m-' for liquid and 280 Pa m-' for gas. Case history inthe North Sea suggests valuesof 500-1000 Pa m-' for V@&ATare common at depths >3 km. Both he water potentialgradient and the force due to buoyancy push petroleum (andwater) in the same direction-updip. At depths >3 km themajor force driving petroleum is water potential gradients;buoyancy takes over at shallower depths.Until this point, capillary effects have been ignored-the2 y / r term in equation (7). This term will generate significantforces only when there is a lithology change which causes agradient in r . This important effect will occur atheboundary between fine and coarse-grained rocks. In asimplified picture of capillary forces, there will be a largecapillary pressure difference which drives petroleum out ofsource rocks into carrier beds, e.g. Hubbert (1953).Bymakinggeochemical measurements on actively generatingsource rocks we have found (Mackenzie et al. 1986) thatsource rocks are more efficiently depleted of petroleumwithin 5 m of their margins which are in contact withsandstone strata. We attribute his to capillary effects.Nature of petroleum flowWe havesuggested that petroleum generated in a sourcerock will migrate vertically upr down towards aneighbouring horizon of high lateral permeability, i.e.permeability is more han 10-15m* (or 1 millidarcy). Thishorizon is called a lateral carrier.Petroleum will remain in the lateral carrier unless itovercomes the excesscapillary pressure that opposes itsentry into the smaller pores of the overlying seals. If thishappens, the petroleum will then move vertically into andthrough the overlying rock until another lateral carrier/sealsystem s encountered, inwhich case it will again migratelaterally updip. We have shown that the typical magnitudeof V@, for vertical migration is about 104Pam-';hemagnitude of V@, for lateral migration along carrier beds isabout 103Pa m-'.The variables required to solve equation (16) for q theflux of petroleum per m of rock, are now defined. Takingthe mean values of p@,S and f from Tables 2 and 5, and thetypicalvalues of 103Pa m-' and 104Pam-' determinedabove for V@kAT and V @ F R T respectively, the averagevalues for q may be calculated for lateral migration ofpetroleum liquids in sandstones and verticalmigration nshales. The values are given in Table 6.

A measure of the significanceof these flow rates is givenTable 5 . Typicalproperties of rocks important for migration(approximate burial depth of 3 k m )

Sandstones Shales9 (porosity) 0.2 0.1f (mean radius of petroleum-filledores in metres)0-6 10-8S (saturation) 0.5 0.5

Table 6. Petroleum liquid mean subsurface superjicial velocities anddimensionless numbers

4(m3-'s-') c NReVertical migrationLateral migrationin shales 4 X 1 0 - l ~ 7 X 10- l~. 5 X 10-l~

in sandstones 8 X 10-O 10-O0-0

Typical' values: S = 0.5; 9 = 0.2 (sandstones), 0.1 (shales);f = 10-6m (sandstones),10-8 m (shales); y = 0.03 Nm-': =650kg m-3; p = 5 X 10-3PaS- ; V @ ,= 103 am-l (LAT),104 Pam-' (VERT).

. , .

by the capillary number, C, = p q / y , which represents theratio of viscous to capillary (or surface tension) forces inestablishing pathways through pore networks. Experimentswithil-watermixtures in rocks have shown thattcapillary numbers greater than 10-4, viscous forces becomeimportant. Hinch (1985) has related the small value of thisnumber to thepore geometry: values in this range areexpected if the pores have throatsa tenth of the size of theirlengths. However, Table 6 shows that at geological flowrates he capillary number is never greater than 10-l :capillary forces therefore dominate at all times.The capillary numbers for our experiments, designed tocalculate the poresaturation required for petroleum flowthrough porous media, are about 10? capillary forces stilldominatend the measured values for saturation atbreakthrough will thus apply under geological timescales.The Reynolds number, NRe p q P / p , measures the ratioof inertial to viscous forces. Taking an arbitrary density forsubsurface petroleum liquid of 50 kgm-3, the valuescalculated range from 10-l' to 5 X 10-l6 (Table 6). Thesemay be regarded as small: they show that during petroleummigration, all lows occur in he 'laminar' (non-turbulent)regime.A third parameter of interest is the Peclet numberqw/D, Lerman (1979),hich measures the relativeimportance of bulk and diffusivemass transport over aparticular length scale defined by W. D is the effectivediffusionoefficient for a given component in thewater-filled rock: it is distinct from the molecular diffusionconstant measured in a single phase. If the Peclet number isc. 0.5 diffusive mass transport will be more significant thanbulk flow (Mackenzie et al. 1986).Estimates of the Peclet number, using Leythaeuser etal's. (1982)ield estimates of D inhales for Cl-C,hydrocarbons are shown in Table 7, which also shows thePeclet number for length scales of W = 10 m, 100m and1000m, using a value of q appropriate for liquidphasevertical migration in shales (Table 6).Table 7 suggests that, with the exception of methane andethane, diffusion is insignificant during vertical migration inshales over distances greater than 10-100m for all thecomponents of petroleum. The Peclet numbers (and hencethe diffusive length scale) for lateral migration in sandstoneswill behe same order of magnitude as for verticalmigration n hales: although q increases by about threeorders of magnitude for sandstones (Table 6), laboratoryexperiments (Krooss 1985) suggest a similar ncrease n D


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M O V E M E N T O F P E T R O L E U MLUIDS 341Table 7. Calculation of Pecletnumbers for verticalmigration ofpetroleum liquids

Peclet numbers (qw/D) for differentlength scales (W )(m2s- ' )D* w=10m=100m w=lOOOm

Methane 2 X 10-10 0.02 0.20 2.0Ethane 1 X 10-10 0.04 0.40 4.0Propane 6 X 10- 0.07 0.70 7.0Isobutane 4 X 10-11 0.10 1.0 10n-butane 3 X 10- 0.13 1.3 13n-pentane 2 X 10- 0.20 2.0 20n-hexane 8 X 10-'' 0.50 5.0 50n-heptane 4 X 10-'' 1.0 10 100n-decane 6 X 10-'3t 6.7 67 670n-tncosane 1 X 10-I3t 40 400 4Ooo

From Leythaeuser et al. (1982); t Extrapolated using log,, D= -0.283C,,- 10.39 wheresarbonumber. q = 4 X10-13 m3 m 2 -1S (Table 6).

fromshales tosandstones.Hence because petroleumcanmigrate more than lOOkm from its source rock (e.g. Tissot& Welte 1984), these results support our earlier assumptionthat diffusive transport isonly important or very shortdistance migration of light n-alkanesduring expulsion ofpetroleum and vertical migration. Otherwise bulk transportis the dominant process of migration.Losses during migrationThe migration rates reported in Table6 must be affected bythe rate at which petroleum may be supplied by a sourcerock. Typically source rocks for oil are 100 m thick and havepotential yields of petroleum fluid relative to rock weight of0.02 kgkg-'. Most of thispotential is realized between120-150C (Cooles er al. 1985). Geological heating atesrange mostly between 1 and 10 CMa-l. Assuming a rockdensity of 2400kgm-'nd a petroleum density of650 kg m-3, then the flux across the boundary of the sourcerock is about 8 X 10- to 8 X lO - I 4 m3m-' S- . This flux iscompared with the values for q inTable 6. If verticalmigration throughshales,relative to rock area, occurs at4 X 10-13m3m-'s-l (Table 6) then the cross-sectional areaof rock filled with flowingpetroleum must be greater than orequal to between two hundredths andwo tenths the areaofthesource rock interface.A similar argumentfor ateralmigration through sandstones at8 X 1O-I m3 m-' S- (Table6) suggests that the cross sectional area of rock filled withflowing petroleum must be greater than or equal to 10-' to10-4 the area of the source rock interface.The area of rock available for vertical migration will besimilar to the area of the source rock interface. The aboveanalysis suggests therefore that the petroleum must exploitat least two hundredths to two tenths of this area. In ourexperience, the ratio of the area of mature source rock tothe cross sectional area of a lateral carrier (perpendicular tothe direction of flow) isabout1000: 1. Therefore, heminimum area that must be petroleum-filled during lateralmigration will correspond to one hundredth to one tenth ofthe area available for petroleum flow.Perhaps a better approach to estimate the area of rockexploited by lowing petroleum s omakeuse of case

history from regions whose petroleum geology is wellunderstoodandwhere most accumulations of petroleumhave been discovered. By subtractinghe volumes ofdiscovered petroleum from the xpelled petroleum volumes,calculated using methods reported elsewhere (Cooles et al.1985; A. S . Mackenzie& T. M. Quigley in preparation), thelost petroleum volumes can be estimated. These volumescan be ratioed to the pore volume available for migration(the otal volume of rock along the migration pathwaymultiplied by the average porosity). Detailed results will bereported elsewhere (MacGregor & Mackenzie 1986; A. S .Mackenzie & T. M.Quigleyn preparation); hese willdemonstrate that theaverage ratio of lost petroleum to porevolume is of the order of a few percent.Our experiments on cores reported in (Table 4) suggestthat flowing petroleum onaverage exploits about 50% of theavailable porosity. In order to reduce the effective overallsaturation to a few percent, this implies that he flowingpetroleum usesess than 0% of the rock area. Thisobservation is in agreement with our analysis of the relativemigration fluxes, where t was concluded that migratingpetroleum exploits at least between l and 10% of the rockarea available for flow.The comparison betweenheorynd observationassumes thatpetroleum migrates by forging an intercon-nected path of petroleum-filled porosity leading away frommature source rock: petroleum will only migrate as far (andas fast) as the volume of petroleum expelled from the sourcerock can spread out, whilst remaining fully interconnected.

Fig.18. An example of an eroded migration pathway.Oil stains thecoarser partsof a turbidite sequence belongingo the SocorroFormation of Eo cen e Ag e. The picture taken by Martin Heffernannear the Ancon oilfields n the Santa Elena Peninsula, Ecuador;the hammer handle measures0.25m in length.


16/21


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MOVEMENT O F PETROLEUM F L U I D S 343-1 Areaovered b yfh>- f r l l

Waterearingand igrating Petroleum

Petroleum Bearing Sand hale

Fig.20 Proposed mechanism of trap-filling. a) Petroleumadvances into the reservoir fromhe source rock; a dendriticpathway of petroleum-filled pores connects the trap with the sourcerock. (b) Petroleum advances into the trap via series of fronts,that reflect the changing compositionf petroleum leaving thesource rock.(c) & (d) The fractionof petroleum filled poresincreasesby petroleum displacing water downwards, untilnlysmall amountsof low pore-size rock remain unfilled.(assuming that the reservoir is not already filled to spill)petroleum will flow into the seal and no further increase inpetroleum saturation within the trap is possible.

As shown by Schowalter (1979), the maximum height ofpetroleum which may be supported by a caprock or seal isgiven by:

If lateral updip transmission of pressure occurs throughthe reservoir, a positive pressure or potential difference mayexist between seal and reservoir; hence a term equivalent toVQw/r(p, - p g must be subtracted from the right handside of equation (36). Lateral transmission of pressure in thereservoir rock will cause the seal to fail under somecircumstances; this is predicted when the calculated h,, isnegative.

Figure 20d suggests the emergence of a transition zone atthe bottom of the petroleum accumulation. This is caused bythe reduced buoyant pressure of petroleum near the bottombeing increasingly unable to overcome the capillary pressureterm (2ylr) of the petroleum potential. Thus only the verylargest pores are oil-filled near the base of the trap.As petroleum continues to migrate into the reservoir, apoint will be reached when the petroleum saturation issufficiently great for he petroleum to behave in a moreliquid-like manner.From previous arguments this point is taken arbitrarilyas corresponding to an overall saturation of -50 . This willbe achieved when the petroleum column has sufficientheight so that the force due to buoyancy at the top of thecolumn exceeds the capillary pressure of the smallest poresthat must become petroleum-filled to achieve an overallsaturation 4 0 % . Equation (36) can be used to calculate theheight where r is the critical pore radius: the height requiredincreases with increasing petroleum density and decreasingcritical pore radius (broadly equivalent to reservoir quality).Most petroleums require heights


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344 W . A .N G L A N D E T AL .Oneoes, however, expect reservoir petroleumopreserve some lateral maturity differences, representing thehistory of the filling process, although mixing processes andthe possible overturning of density gradients will also causesome degree of smearing of the initial simpler picture. Inour experience these maturityifferences can be detected bygeochemical measurements made on petroleum amples.

Gravitation al and thermal segregationIn petroleum reservoirs, because of the often considerableheight of petroleum columns, the effect of the Earthsgravitational fieldmust be takenntoccount. Thissignificantly alters he equilibrium concentrations of thevarious hydrocarbons so that they vary systematically withdepth (assuming sufficient time for the petroleum reservoirto come to thermodynamic equilibrium). This results in thedenser (high molecular weight) components tending to bemoreconcentrated toward thebottom of thepetroleumcolumn.In the presence of ageothermalgradient (typically30Ckm-), thermally induced concentration gradientsmaybecome established: this is known as the Soret effect. Thiseffect has been estimated to be of a similar magnitude togravitational segregation (Holtet al. 1983), but has not beenwidely studied.The magnitude of the gravitationally induced concentra-tion gradient may be estimated rom chemical thermo-dynamics. If one assumes ideal mixingbehaviour-i.e.nointeractionsbetween he molecules, an exponential con-centration gradient is predicted, Hirschberg (1984).xi(hl)= x i h 2 ) e k l - k 2 ) h g (37)

whereR Th , =

( ~ r e s V ,- MThe mole fractions of the ith component at heights h land h2 above a reference height are related to the reservoirfluids average density prcs nd he molecular weight, Mi,and partial molar volume, V,.Thus concentrationdifferenceswill be greatestfor high molecular weight species in lowdensity reservoirs.In practice, however, real petroleum reservoirs oftenexhibit concentration gradients up to ive times greater thanpredicted by equation (37). This is a reflection of thenon-ideal behaviour of multi-component mixtures. This typeof system is best dealt with by using an equation of stateapproach in which an empirical mathematical model is usedto describe the non-ideal behaviour of the mixtures.Schulte (1980) for example found that improved (thoughnot complete) agreement with field resultpwas obtained byassuming non-ideal mixing. For example in the Brent field

(UK NorthSea) hemethane mole fraction changes by5 mole over 150 m, nd in theStatfjord reservoirgravitationally induced concentration changes mayavebeen sufficient to eliminate a sharp petroleumas-petroleumliquid interface in the reservoir.In-reservoir mass transport processesThere re two possible mechanisms which could causemovement of material within a petroleum reservoir; theseare molecular diffusion and thermal convection.

Diffusion. Molecular diffusion s a processwhich tendsto reduce and eventually eliminate chemical potentialgradients by the random motions of molecular species.Consider the case of a freshly filled reservoir with an initiallynon-uniform distribution of chemical components. Diffusionwill cause a edistribution of matter so that horizontalconcentrationgradients will be eliminated and vertical,gravitational or thermally induced gradients becomeestablished.In order to estimate the rates andimescales of diffusion,its essential to have accurate values for the diffusionconstants of hydrocarbons in rocks. Unfortunately these arenot available to better han order-of-magnitude estimates,so our analysiss based onmoreccurateaboratorymeasurements in pure liquids.A reasonable irst-ordercorrelation of diffusion con-stants with viscosity, temperature and molecular dimensionis given by the Stokes equation, Ghaiet al. (1973):

This implies that Di is proportional to absolute temperature,but inversely proportional odynamic viscosity-ri s thehydrodynamic radius of theth component. Since theviscosity of oil in an oil reservoir is approximately equal tothat of pure water at 20 C, one can make use of resultsfromexperimentscamedout in water at 20 C withoutcorrection, as only order-of-magnitude estimates of diffusionrates are required. Table 8 shows the values of Di estimatedfor various hydrocarbons in pure liquids (i.e. in the absenceof a rock matrix).The time necessary to achieve equilibration by diffusion,teq ay be estimated from the relation, e.g.Shulte (1980):

(39)l is the length scale over which diffusion is considered totakeplace. In an individual petroleum column, l will betaken as 100m for the purpose of estimating zeq or verticaldiffusion: l will be taken as 2000m for estimating tcqorlateral diffusion on a reservoir-wide basis. A factor of O 2 isincluded to account for the increased length through whichmatter must diffuse in a tortuous porous medium, comparedTable 8. Diffusion coefficients or petroleum components in rock-freeliquids and equilibration times (res) for selected components andlength scales (1)

res (Ma) from equation (39)Component* Di (pureiquid) 1 = 1 0 0 m 1 = 2 0 0 0 mCH4 1 X 1 0 - ~ m2 S-) 0.1 42

c 2 0.5 X 10-9 0.2 84t G m 1 X 10-10 1.0 422

Sahores &Witherspoon (1970)Interpolated

Balthus & Anderson(1983)C, refers to amoleculewithn carbon toms; t Typicalmolecularweightorighmolecularweightaturaletroleumconstituents known as asphatenes by the petroleum industry.


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M O V E M E N T O F P E T R O L E U ML U I D S 345with within a pure liquid. A value of 8 = v3 is assumed forrock matrices which is similar to values found experimen-tally by Li & Gregory (1974), and is based on that predictedtheoretically for a loose random pore structure. However, itis possible that when considering 8 over lengths measured nmetresorkilometres, dditional larger-scale tortuositiesoperate. t should also be remembered hat hydrocarbonmolecules will only be diffusing through that part f the totalpore network which s petroleum-saturated, this will alsoaffect e.The values for Di n pure liquids were calculated bymaking viscosity correlations, if needed, to data from heliterature. The results are shown in Table 8 which shows thetimes necessary forvariouscomponents o diffuse across100m or 2000 m. These distances are representative of thevertical and lateral extents of a typical petroleum reservoir.It is clear that molecules will, in general, have sufficient timeto equilibrate by diffusion to set p gravitationally orthermally induced concentration gradientswithin a reservoirinnyiven vertical petroleum column, provided nodisturbance to the reservoir occurs during = lMa. The caseis different, however, on the larger length scales associatedwith horizontal diffusion over 2000 m. It is very unlikely thata reservoir will exist without disturbance for sufficient timeto allow theydrocarbonomponentsoquilibratehorizontally, although this is often assumed to be the case.

Convection. Thermal convection may occur when abody of fluid experiences a heat flow across it. The Rayleighnumber, R , determines the onset of thermal convection: ifR , >40 for a body of fluid in a horizontal rock formation,convection currents will be established. It is important onote, that in contrast to diffusion, convection willcompletely homogenize a reservoir, removing any thermallyor gravitationally induced concentration gradients.Figure 21illustrates schematically the different effects of reservoir

mixing by convection or diffusion on lateral and horizontalconcentration gradients. Figure 21a shows the variation incomposition between wells, and within an individual columnof oil 'inherited' from the filling process shown in Fig. 20.Diffusion will rapidly cause thermodynamic equilibrationwithin individual wells on a geological timescale, but not ana well-to-well basis. Thus Fig. 21b shows that wells 1, 2 and3 have different average compositions. Given sufficient timefor diffusion to occur, the compositions of the different wellswould eventually approach each other, but thegravitationally induced compositional gradient wouldpersist. This is hown nFig.21c. If, however, thermalconvection occurs, thentire reservoir will becomehomogenized, Fig. 21d.Field evidence suggests thatpetroleum accumulationsdo not convect andhat most accumulations reach thestate exemplified by (b). However, in the absence of carefulwell testing and analysis, (b) may be hard o distinguishfrom (c).In practice, the Rayleigh number of a liquid petroleumreservoir is c . 0.1, so convection is not expected to occurexcept under exceptional conditions. This is in fact borneout by field observations, which show that significant lateraland vertical concentration gradients an occur in reservoirs.

Field evidence. Some of our studies of petroleumreservoir compositions have confirmed that they are indeednot well-mixed. This appears to be a new theoretical andobservational conclusion as far as the oil industry isconcerned.n previous studies of petroleum reservoirsapparent inconsistencies in analyses between wells n thesame reservoir, have often been ascribed to sampling andanalytical errors.As far as vertical gravitationally induced concentrationgradients are concerned,we have observed similar values tothose of Shulte (1980), Hirschberg (1984), Creek &

(bVertical Diffusione

Wel ls1 2 3

5 compositionInheritedvariations

I Composition (d) Wel ls 1,263

S

Convection

W l l S1,2 3

Composition

CompositionFig. 1. The effectsof various mass transfer processes on three dimensional reservoir composition for a hypotheticalpetroleum accumulation.


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M O V E M E N T OF P E T R O L E U ML U I D S 341We are grateful to Stephen W. Richardson and Dan P. McKenziefor helpful discussions. We thank Gary P. Cooles for donation ofthe results of his oil saturation experiments (Table 4) and BritishPetroleum p.1.c. for permission to publish.

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england 1987 petroleum migration

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