P0002-96

Hysteretic Relative Permeability Effects andReservoir Conformance - An Overview

D.Brant BennionF. Brent ThomasRonald F. Bietz

Hycal Energy Research Laboratories Ltd.

functions of such parameters as pore system geometry andtortousitf, wettabilityJ,4,S, initial phase saturations6,temperature1, viscmity of fluids', interfacial teosion9 andhysteresis effectslo,ll.12. The subject of hysteretic effects is thetopic of this paper.

Abstract

Hysteretic effects refer to the difference between relativepenneability and residual saturation values as a given fluidphase saturation is increased or decreased. The differencebetween initial, trapped, mobile and irreducible saturations areclarified. Hysteretic effects can impact a number of reservoirproduction scenari~ in both favourable and unfavourablefashions. Hysteretic effects can operate positively in suchprocesses as anti-water coning technology (A W AT), mobilitycootrol in cyclic projects. such as a water alternating gastreatment or cyclic thennal stimulation operation, or inheterogeneous carlxmates in a process known as the successivedisplacement process (SOP). Adverse effects include phasetrapping and critical vs trapped saturation hysteresis effects.Discussion on the favourable use of hysteretic effects forconformance control processes, such as gas or water shut-off,are also presented.

What ~ Hysteres~?

Hysteresis refers to the directional saturation phenomenaexhibited by relative permeability curves. In many porousmedia. relative permeability val~ are a non-unique functionof saturation, having different values when a given phasesaturation is being increased than when it is being reduced.This phenomena is illustrated for an oil-water case in Figure1. Commencing with a condition of 100% water saturation(" A-), an oilflood is conducted, reducing the water saturationto point "B- along relative permeability path A-B. In a water-wet porous media, this process is often referred to as primarydrainage (drainage referring to a process where the wettingphase saturation is being reduced). Reflooding with water,referred to as an imbibition process in a water-wet porousmedia (a situatioo where the wetting phase samratioo is beingincreased), we move to point "C" along relative permeabilitypath B-C. It can be seen that the initial condition of 100%water samration is not re-achieved due to capillary trapping,resulting in a residual oil saturation being obtained. Asubsequent drainage watertlood (C-B) results in differentrelative permeability paths being traced, in comparison to theequivalent imbibition process (B-C). This phenomena isknown as hysteresis. In general, hysteresis is morepronounced in the non-wetting phase than in the wetting phase,but may occur in both phases with up to two orders ofmagnitude difference in relative permeability at equivalent

Introduction

The concept of relative permeability was introduced to modifyDalCies Law, describing single phase flow in a porous media,for the extremely complex multiphase flow effects occurringwhen more than a single immiscible phase is present in aporous media. Relative permeability values strongly controlthe flow mechanics, pressure and production response ofvirtually every producing oil or gas property and, therefore, aproper undelStanding of how they are infl~nced is importantin the process of reservoir optimization. Relativepenneabilities are expressed as functions of water (for water-oil systems) or total liquid saturation (for gas-liquid systems),and have been well documented in the literature' to be strong

HYSTEREnC RELAnvE PERMEABllJ1Y EFFK'TS AND RESERVOIR CONFORMANCE - AN OVERVIEW rooo2-962

represent the i"educible saturation conditions with which theyare often confused. In some reservoirs, the initial water, gas,or condensate saturation may exist at some value which isconsiderably less than the irreducible or mobile valuelS(Figure 4).

saturatiom. In most cases, the relative penneability for a givenphase is greater when its saturation is being increased ratherthan decreased. This phenomena can be used advantageouslyin situations such as a cyclic steam injection process, since itwill enhance oil mobility and retard high water productionrates on a return flow cycle.

Critical Fluid Saturatioll,f. This represents the minimumphase saturation which must occur when the minimum phasesaturation is being increased the first time such thatconnectivity of the phase is established and finite relativepermeability exists, so that the phase can begin to flow in theporous media. This should not be confused with the trapped orirreducible saturation. Examples of a critical fluid saturationwould be the point of fust free gas mobility in a sub-bubblepoint ~pleted black oil system. the point of first liquidhydrocarbon condensate production in a sub-dewpointretrograde condensate gas system, or the point of first waterproduction as water saturation is increased in a desiccated orsubirreducible water saturation system (Figure 4).

Two dominant mechanisms came the saturation hysteres~. Inthe primary and secondary drainage case, a portion of thehysteres~ ~ due to the disparity between the initial conditionof 100% water saturation and the trapped irreducible oilsaturation. This ~ commonly referred to as trap hysteres~.The difference in relative pemleability curves caused by themotion between the same endpoint saturation ~ ~ due tomicroscale hysteretic effects, or sometimes called draghysteres~. It is believed to be primarily due to a phenomenaknown as contact angle hysteresis. Contact angle hysteresis ispictorially illustrated in Figure 2. It refers to the fact that, asimmiscible interfaces advance in a IX>lOUS media, the effectiveangle of the advancing interface, which ~ related by wettabilityand capillary dynamics to the relative ease of the fluiddisplacement in the porous media, ~ different betweenadvancing and receding phase conditions. This difference,which appears to be a strong factor of the degree of surfaceroughness and torblooty which exists in the system. ~ believedto be the root came of hysteretic microocale relativepermeability effects.

Trapped or Irreducible Fluid Saturation. This represents thesaturation value obtained when a fluid saturation is reducedfrom a large mobile value to an immobile value. This is alsothe i"educible saturation as is commonly detennined from aprimary drainage capillary pressure test or a waterflood toultimate Sm (Figure 4).

Mobile Fluid Saturation. ~ value is subtly different fromthe critical saturation as it is the value to which the saturationmust be increased after a trapped or irreducible saturation isobtained by a displacement process. The value is generallyidentical to (in an ideal situation) or larger than the trapped ori"educible saturation (Figure 4).

To further complicate the issue. not only is the relativepenneability value a function of the direction of the saturationcbang~. it is also a strong function of the tenninal saturationendpoint reached before the direction of the saturation reversaloccurs. This is illustrated in Figure 3. It can be seen that therelative penneability path, if a saturation reversal occurs at anintennediate saturation level (and not an endpoint saturation).will result in the relative penneability curv~ tracingintennediate paths between the secondary drainage andimbibition curves called a scanning curve. Since these curveshave virtually an infinite number of va1u~. measurementwould be expensive and technically difficult. They are muallydetennined using analytical models such as those developedby Killough').

How Hysteretic Effects Can Affect Reservoir Conformanceand Production

Hysteretic effects may positively or negatively influencereservoir perfonnance. Some examples of each situation aregiven for illusttative pu~.

Positive Effects

Saturation Definitions Mobility Control. Hysteretic relative penneability effects haveoften been used as a mobility control agent to preferentiallyreduce the mobility of one phase over another to achievesuperior confonnance control and ultimate sweep efficiency,particulary in the presence of adverse viscosity ratios. A primeexample of this techoology is the water alternating gastreatment or WAG process used to reduce the mobility ofinjected gas in a horizontal gas injection project. Theinterfering effects between the gas and liquid p~ are usedto selectively retard the speed of gas migration. Since thewater, due to its higher viscosity, tends to preferentiallychannel into the higher penneability channels of the reservoir

To provide a discussion on hysteretic effects, a properdefmition of a number of commonly confused saturationcooditions is necessary.

Initial Fluid Slduralions. This represents the true fraction ofthe rock actually occupied by oil, gas and water at initialreservoir conditions. There are a number of methods fordetennining fuese values I., which are crucial to properevaluation of relative penneability. It should be noted that theinitial saturation conditions do not, in many situations,

DB. BENNION, FB moMAs. R.F. BI£IZ

it tenm to screen off these better quality zones and selectivelyreduces the permeability to gas. Due to hysteresis andmobility effects, it is more difficult for the gas to displace thewater from this zone than to be preferentially redirected intozones of lower permeability. which tenm to improve theoverall conformance and sweep efficiency of a horizontal gasinjection project, particularly in thick pay zones or zonescontaining highly variable permeability or high permeabilitystreaks. This phenomena is pictorially illustrated as Figure 5.

in vertical displacements in heterogenous carbonate fonnationswith strong bottom water drives with immiscible gas injectionprojects for preaure support. The mechanism of the processis illmtrated as follows:

Figure 8(a) Initial saturation conditions. The oil wet carbonatemedia, generally a reef type structure with considerable verticalrelief, exhibits oil wet behaviour with a low initial watersaturation encapsulated in the central portion of the poresystem (i.e. 5% water, 95% oil).

Water Coning Reduction. Hysteretic relative permeabilityeffects are the basis of anti-water coning technology used insome heavy oil ~rvoir situations. Due to the extremelyadverse viscosity ratio between many heavy oils and activebottom water present in some of these systems, rapid waterconing, high water cuts and marginal or uneconomicproduction occurs. It bas often been found in such situationsthat the presence of a mobile gas phase saturation appears topreferentially reduce the water phase permeability over the oilphase permeability. This tends to selectively reduce the watercut, and may improve dle economics of a marginal well by thesimple injection of a slug of inert gas in the near wellboreregion. A particular application of this technology waspatented in the 1980's by the Alberta Oil Sands TechnologyResearch Authority (AOSTRA) under the trade name A W AT(Anti-Water Coning Technology). Figure 6 provides anillustrative set of gas-water relative permeability curvesshowing the basis for this technology.

Figure 8(b) Immiscible gas cap encroachment as gas injectionfor pressure support continues. This results in stable gravitydrainage of oil. in some cases down to fairly low oil saturationvalues of 20-25%. This establishes a zone of high gassaturation in the gravity drained zone.

Figure 8( c) Gascap blowdown and oil sandwich displacement.The depressurization of the gascap results in the active aquiferdisplacing up a sandwich of unrecovered oil from the base ofthe reservoir. As the oil bank penetrates the highly gassaturated zone, hysteretic saturation and relative permeabilityeffects result in a very high trapped gas saturatioo (generallyin excess of 50%) being retained in the oil encroached zone.

Figure 8(d) Aquifer Encroachment. Following the displacedoil sandwich ~ the active water front. Due to the high trappedgas saturation. the encroaching water appealS to be redirectedby hysteretic relative permeability effects to penetrate portionsof the pore space not previously accessed during the gasdrainage process. Th~ results in a measurable reduction in theresidual oil saturation (to perhaps as low as 10%) over thatobtained during the conventional gas drainage p~, andrepresents significant incremental recovery which may beobtained from what was thought to be a depleted reservoirduring the blowdown cycle.

Enhanced Cyclic Production. The me of a simulation modelwith hysteretic relative permeability capability is sometimes theonly method of accurately predicting the performance of somecyclic projects, particularly cyclic steamfloods in heavy oilapplicationsl6. This is illustrated in relative petmeability curvesas pictured in Figure 7. It can be seen that the higher waterphase relative permeability on the water injection cycle aids inincreasing the ease of injectivity of the hot water and steamcondensate into the formation. The lower oil phasepermeability, as its satUIation is being reduced, allows the hotwater!steam to b~ some oil and peneb'ate deeper into theformation which improves the contact and size of the heatedzone. Conversely, on the production cycle, oil production rateis enhanced as the water mobility is reduced, since itssaturation is being reduced, and the oil phase relativelypermeability may be significantly increased. This results inenhanced production of oil rather than rapid production of theless viscous water phase.

This phenomena bas been documented in a number of reservoirapplications in die literaturel7.

Negative Effects

Phase Trapping. Phase trapping has been well documented inthe literature as a me(;.hanism of substantially reducedproductivity in many reservoir applicatioos.I..9. Phase trappingis caused by a combination of both adverse saturationhysteresis effects and associated adverse relative penneabilityeffects ~ illtmtrated in Figure 9. Common situations wherephase trapping may occur are the use of water-based drilling,completion. stimulation or kill fluids in overbalancedconditions in low initial water saturation condition gasreservoirs or strongly oil wet oil reservoirs (both of whichexhibit extremely low initial water satUlations). Hydrocarbonphase traps may be established through the use of oil-baseddrilling, completion or stimulation fluicb in gas reservoir

Succesli.,e Displacement Process (SD/? The suc~vedisplacement process is a recently researched process whichappears to utilize saturation hysteresis effects as a basis forenhanced oil production as a by-product of an immiscible gasand water displacement process. The mechanism is notentirely \Dlderstood, but is pictorially illustIated in Figures 8(a)to 8(d). The prime application for the SDP has been observed

HYSTERImC RELAnvE PERMEABIU1Y ~6,;13 AND RESERVOIR CONFORMANCE - AN OVERVIEW4 POOO2-96

applicatioos or retrograde condensate dropout effects during theproduction of rich gas condensate reservoirs.

may, depending on the rock geometry and relative penneabilitycharacteristics, significantly reduce the inflow characteristics ofwater from the affected zone. The establishment of a trappedgas saturation in the oil saturated strata is obvio~lyundesirable and should be avoided as this may substantiallyaJso impair the permeability to oil. This process is illustratedschematically as Figure 12.

Massi" Critical and Trapp,d StlJuration Hysteresis. In somereservoirs, the difference between the initial critical mobilesaturation level, when the phases saturation is being increasedand the trapped saturation value, when that phases saturationis being reduced, can be significant. This is schematicallyillustrated as Figure 10. An example would be in a black oildepletion process where the reservoir p~ is dropped asignificant degree below the saturation pressure. This willresult in the liberation of a large amount of free solution gas.The critical gas saturation will rapidly be exceeded and gaswill begin to flow but, as pressure continues to drop, the valueof the mobile gas saturation will also tend to rise. If thepressure decline is then halted, and we attempt to flow backinto the highly gas saturated zone, a much higher -trapped- gassaturation than the initial critical value will usually beobtained. This may significantly reduce the mobility of the oilphase, resulting in a large loss in potential productivity.

Oil injection (although opposite of what we want to accomplishis most producing wells) may also be an effectual WaRreducing technique in certain situations where free bottomwater with an active drive in present. The objective of thistechnique is to inject produced oil, or some other low viscosityhydrocarbon, directly into the wet zone underneath theproducing zooe. Hysteretic effects will trap an irreducible oilsaturation in this zone which may reduce the effectivepermeability to water by as much as 95%, depending on therelative permeability characteristics of the porous media.

Conclusions

Using Hyst6retic R6lati"6 P6rmeability Eff6CU forConformanc6 Control PUrpOS6S. Some examples have alreadybeen presented as to how hysteretic relative permeabilityeffects may influence conformance control. Potentialapplications include:

A discmsion on cyclic hysteresis effects in dle exploitation ofoil and gas producing properties has indicated that:

Significant saturation and relative penneability hysteresisoccurs in many reservoir systems. The degree ofhysteresis is usually more pronoWlced in the non-wettingphase, but may be significant in both p~. Researcl1studies suggest that the degree of hysteresis is related tothe magnitude of contact angle hysteresis which is, inturn. a function of the amoWlt of surface roughness in agiven reservoir system. Therefore, tight, low permeabilityrocks with high surface roughness may exhibit morehysteresis than their more uniform higher penneabilitycounterparts, although specific detemlination on areservoir by reservoir system is required.

Gas Shill 0.0: Gas phase relative penneability may bepreferentially affected by selective treatments with animmiscible fluid The selective injection of water based fluid,possibly a surfactant. into the upper portion of a high gas cutweD may result in the hysteretic trap of a higher watersaturation in the zone of high gas saturation and penneability,and result in a ~ient or pe~nt reduction in gas-oil ratio.Inclusion of a surfactant may generate a high viscosity stablefoam system when contact is made with zones of high gassaturation. This will result in a large portion of the pole systemwhich is available for mobile gas to flow being occluded bythe immobile foam phase and, once again, result in apreferential reduction in the gas phase penneability. Treatmentsof this type tend to be somewhat transient in effect due togradual degradation of the foam system over time byadsorption (particularly in clastic fonnations) and dispersioneffects. This process is illustrated schematically as Figure 11.

2. The difference between initial, irreducible, critical, mobileand trapped fluid saturations has been defmed.

3. Hysteretic effects may be advantageous in reducing waterconing problems, gas coning problems, enhancingproduction from some cyclic projects (such as steaminjection) and reducing gas phase mobility in someprocesses such as water alternating gasfloods (WAG) orco-current injection projects. Residual oil satunttion maybe substantially reduced in some heterogenous carbooateformations due to hysteretic effects in what is known asthe successive displacement process (SDP).

Water Shut Q6: Hysteretic effects can also be used to aid inwater shutoff. Reference has already been made to the A W A Tprocess when non-condensible gas injection is ~ topreferentially reduce water cuts by a selective redoction in therelative permeability to water over the oil value. In zonescontaining pure water, which cannot be readily isolated bycasing and selective completion. a similar effect can beaccomplished by the direct zooe specific injection of animmiscible non condensible gas into the water saturated zone.This will establjsh a zooe of high trapped gas saturatioo and

4 Hysteretic effects may also reduce productivity andincrease problems with water and gas coning in certainsituations due to adverse effects associated with "trap"saturation hyste~ or what is more commonly referredto as "phase trapping".

DB. B~ON. f.B rnoMAs, R.f. BIETZ 5

Acknowledgments Displacement in Water Wet and Oil Wet Formatiom",SPE 3SSS, Presented at the 46th annual SPE fall meeting,New Orleans, Oct 3-6, 1971.The authors wish to express appreciation to Maggie Irwin and

Vivian Whiting for their assistance in the preparation of theman~pt and figures and to the management of HycalEnergy Researeh Laboratories for the fimding of this work andpermission to present the data.

13, Killough. J.E. et ai, -Reservoir Simulation With HistoryDependent Saturation Functions", Trans SPE of A/ME,261, pp. 37-45.

References 14. Bennion, D.B., et at, "Detennination of Initial fluidSaturations - A Key Factor in Bypassed PayDeterminatioo", ~ted at die PNEC 2nd annualconference on Profile Modification and ConfoID18DCeControl, August, 1996, Houston, Texas.

Hooarpour, M. et al, ~elative Penneability of PetroleumReservoirs", CRC Press, 1986, Boca Raton, Florida.

2 Alps. J.J., et aI, "The Effect of Relative PenneabilityRatio, the Oil Gravity and die Solution Gas-Oil Ratio ondie Primary Recovery from a Depletion Type Reservoir",Trans AlME, 204,120, 1955.

15. Katz, D.L. et ai, - Ab5eIlce of Connate Water in Michigan

Gas Reef Reservoirs-, AAPG Bulletin, Vol. 66, No. I,Jan. 1982..

3, Salathiel. R.A., .Oil Recovery by SUlfate Film Drainagein Mixed Wettability Rocks", SPE 4014 presented at theSPE 47th annual meeting, San Antonio, California, Oct 8,1972.

16. Bennion, D. W .. et at. ~ Effect of Relative Penneabilityon the Steam Stimulation Process", JCPT, 1985.

7. Irwin, D., et al, "Bonnie Glen", Presented at the 46thannual technical meeting of the Peb'oleum Society ofaM. June, 1995, Banff, Canada.Leach, R.O., et ai, "A Laboratory and Field Study of

Wettability Adjustment in Waterflooding", JPT, 44, 206,1962.

4.

18. Bennion. D.B., et ai, "Water and Hydrocarbon PhaseTrapping in Porous Media, Diagnosis, Prevention andTreatment", JCPT, September, 1996.s. Denenkas. N.D., ~e Eff~t of Crude Oil Compments on

Rock Wettability", Tram A/ME, 216,330, 1959.19. Bennion, D.B., et ai, "Reductiom in die Productivity of

Oil and Gas ReservoilS Due to Aqueous Phase Trapping",JCPT, 1994.

6. Caudle, B.H., et aI. -Further Developments in theLaboratory Detennination of Relative Permeability",Trans A/ME, 192,145, 1951.

7. Edmonson, T .A., '"The Effect of Temperature onWaterflooding", JCPT, 10,236, 1965.

8. Lefebvre du Prey, E,. Deplacements Non-Miscibles dansles MiUuex Poreux Influence des Parameters Interfaciaxsur les Permeabilities Relatives", C.R. IV Coloq, ARTFPPau. 1968.

9 Leverett, M.C.. "The Flow of Oil Water MixturesThrough Uncomolidated San~". Trans AIME, 132,149,1939.

10. Geffen, T.M., -Experimental Investigation of FactorsAffecting Laboratory Relative PermeabilityMeasurements", 1rans A/ME, 192,99,1951.

11 Osaba, J.S., ~e Effect ofWettability on Rock Oil-WaterRelative Permeability Relationships", Trans A/ME,192,91,1951.

12. ~-31dson, B.C., -Microscopic Observatiom of Oil-Water

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F1GURE1ILlUSTRATION OF HYSTERESIS EFFECTS

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