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Foamy-Oil FlowFoamy-Oil FlowBrij B. Maini, SPE, U. of Calgary

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SummaryFoamy-oil flow is a non-Darcy form of two-phase flow of

gas and oil encountered in many Canadian and Venezue-lan heavy-oil reservoirs during production under solution-gas drive. Unlike normal two-phase flow, which requires afluid phase to become continuous before it can flow, itinvolves flow of dispersed gas bubbles. This paper is aimedat acquainting the readers with this type of flow and its rolein heavy-oil production.

The paper starts with a discussion of what the termfoamy-oil flow means and how it evolved. Then a briefreview of the Canadian field practices is presented. This isfollowed by a discussion of the pore-scale mechanismsinvolved and the interplay between capillary and viscousforces. A discussion of the strengths and weaknesses of var-ious mathematical models proposed for numerical simula-

tion of this type of flow is also included. The paper endswith a brief discussion of issues that remain unresolved.

IntroductionThe term foamy oil originated from observations of sta-ble foams in samples collected at the wellhead from manyCanadian and Venezuelan heavy-oil wells that produceunder solution-gas drive. The oil produced from thesewells was in the form of thick oil-continuous foam. It wasnoticed that, very often, a sample container that was over-flowing with oil at the time of collection at the wellheadwas nearly empty; less than 20% of its volume was filledwith oil when opened in the laboratory a few days later, bywhich time the foam had collapsed. Many of these reser-

voirs also exhibit anomalous production behavior, both interms of higher-than-expected well productivity andremarkably high primary recovery factors,1 and this obser-vation was not the result of metering errors caused byfoam. Over the years, this anomalous production behaviorbecame closely associated with the foamy nature of theproduced oil, and it was suggested that perhaps the two-phase flow behavior of this type of oil in a reservoir rock isdifferent from that of a normal oil/gas mixture. The termfoamy-oil flow was coined to distinguish the two-phaseoil/gas flow in a porous medium of such heavy oils fromthe normal two-phase behavior. This overview attempts toacquaint the reader with recent developments related tothis topic, then provides some insight into the mecha-

nisms involved.Smith1 appears to be the first to publish a detailed analy-

sis of such unusual production behavior. He attributed it tothe flow characteristics of heavy oil containing a large vol-

ume fraction of very small gas bubbles. He suggested thatthe mobility of a dispersion of very small bubbles in the

heavy oil could be several-fold higher than the single-phase oil mobility. Maini et al.2 attempted to verify thisassertion of high dispersion mobility in the laboratory butfound that the presence of freshly nucleated gas bubblesactually decreased the oil mobility. However, they foundthat the dispersed flow of gas was indeed possible undersolution-gas-drive conditions. Since then, the flow behav-ior of such gas-in-oil dispersions has become a subject ofseveral investigations315 and considerable speculation,but it remains controversial and poorly understood.Nonetheless, it is well accepted that solution-gas drive infoamy-oil reservoirs involves some unusual effects. Itshould be mentioned that such dispersed flow of gas undersolution-gas-drive conditions in the laboratory was noted

by Handy16 in 1958 in high decline rate experiments.However, he concluded that, at the low pressure declinerates in the field, the dispersed flow would not be a signif-icant factor.

Although there is still debate on the suitability of thephrase foamy-oil flow to describe the anomalous flow ofthe oil/gas mixtures in cold production of heavy oil, theexpression has become a part of petroleum engineering ter-minology. To some, the term foamy-oil flow suggeststwo-phase flow in the form of oil-continuous foam, andthey find it to be a misnomer because the actualmicrostructure may not resemble foam. To others, includ-ing this author, it only denotes the flow of a gas-in-oil dis-persion, which is what appears to be involved. However,

the full meaning of the term is still evolving, and for nowit can be treated as a catchall phrase for representing thecontribution of nonequilibrium processes in solution-gasdrive in heavy-oil systems.

There are two types of nonequilibrium processesinvolved in solution-gas drive in heavy oils. There is thenonequilibrium between solution gas and free gas thatleads to a possibility of significant supersaturation of dis-solved gas in the oil phase. The ramifications are delayedrelease of solution gas and an apparent bubblepoint that islower than the true thermodynamic bubblepoint. Thisnonequilibrium process is affected by the kinetics of bub-ble nucleation and gas diffusivity. Because bubble nucle-ation is a stochastic process driven by supersaturation, the

degree of supersaturation required before nucleationoccurs depends on the time available for nucleation.Therefore, this type of nonequilibrium is likely to be moresignificant in laboratory experiments, which are run on amuch smaller time scale compared with the field case.

The other nonequilibrium is related to fluid distributionin the rock. Traditionally, in two-phase-flow situations in areservoir, the ratio of viscous to capillary forces is low, andthe capillary forces govern the fluid distribution. There-fore, it is permissible to assume that the fluids distributethemselves in such a way that the surface free energy for

Copyright 2001 Society of Petroleum Engineers

This is paper SPE 68885. Distinguished Author Series articles are general, descriptiverepresentations that summarize the state of the art in an area of technology by describingrecent developments for readers who are not specialists in the topics discussed. Written byindividuals recognized as experts in the area, these articles provide key references to moredefinitive work and present specific details only to illustrate the technology. Purpose: toinform the general readership of recent advances in various areas of petroleum engineering.

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fluid/fluid and solid/fluid interfaces is minimized. Oneconsequence of this assumption is that the fluid distribu-tion is the same under static and flowing conditions, andit is not affected by the local pressure gradient. Anotherconsequence is that the gas phase must become continu-ous before it can start flowing, with isolated gas bubblesremaining trapped by capillary forces. However, thisassumption may not be valid in solution-gas drive inheavy-oil reservoirs. Because of the high oil viscosity andhigh drawdown pressure used in cold production, the

local capillary number (k/og) can be high enough tomobilize isolated bubbles. This leads to dispersed flow.This type of nonequilibrium is affected by the surface ten-sion of the oil, the absolute permeability, and the valueof the gradient of flow potential in the vicinity of the iso-lated bubbles.

Both types of nonequilibrium processes play a role infoamy solution-gas drive. As stated earlier, the nonequilib-rium related to nucleation and growth of bubbles becomesless significant when the time scale moves from a fewhours or a few days in the laboratory to years in the field.However, the other nonequilibrium process is not directlyaffected by the time scale, but depends mostly on the cap-illary number. Hence, it can be equally important in the

laboratory and the field, provided similar rock/fluid prop-erties and pressure gradients are involved.

It is believed that the second type of nonequilibriumprocess is more important in causing the observed anom-alous production behavior in the field. The nonequilibri-um processes related to nucleation and growth of bubblesplay a role and need to be understood, but the key tounderstanding foamy-oil flow is in understanding the two-phase flow at a high capillary number with a very large dif-ference in viscosity of the two phases.

Field ObservationsThis section attempts to distill the experience of heavy-oiloperators in Canada into a few important observations

concerning cold production. The most notable field ob-servation is that some unconsolidated-sand heavy-oilreservoirs, exploited with vertical wells under primarydepletion conditions, perform better when sand is allowedto flow freely into the wells. Both the oil production rateand the oil recovery factor are much higher when the sandis produced into the wells and transported to sur-face with the oil. Oil production rates have beenreported to be more than 10 times the flow ratepredicted by Darcys law. It is believed that sandproduction increases the fluid mobility in the near-well zone by increasing the permeability in theaffected zone. Also, conventional wisdom predictsthat the solution-gas-drive recovery factor in these

viscous oil reservoirs should be in the range of 1 to3% of original oil in place (OOIP). The actual andprojected recovery factors are in the range of 5 to15% OOIP. Typical reservoir characteristics asso-ciated with successful applications of cold produc-tion are listed in Table 1. It should be noted that itmight be possible to apply the cold-productiontechnology to reservoirs that do not fall within therange of characteristics in Table 1. At present, thethreshold reservoir characteristics have not beenclearly established.

New cold-production wells go through a startup phase,during which the sand cut and fluid rate change in a char-acteristic manner. Immediately upon starting production,the sand cut is very high. The reported volume fraction ofsand in this phase is 10 to 50%.1719 As production fromthe well continues, the fluid rate increases slowly while thesand cut declines rapidly. After some time of uninterrupt-ed production, the sand cut stabilizes at a lower value thatseems to be a function of viscosity of the crude oil. Thereported values of sand cut in this phase are in the range

of 0.1 to 5 vol%.1719

The oil rate continues to increase for2 to 5 years, then starts a slow decline as reservoir-deple-tion effects begin to dominate inflow performance. Thetotal volume of sand produced from cold-production wellsover their productive life can range from 500 to 1000 m3

for wells that typically produce 10 to 20 m3/d of oil. Pro-gressing-cavity pumps are used to handle this volume ofsand production. Usually, the wells are operated at or nearatmospheric backpressure (i.e., the drawdown is kept nearthe maximum). The oil/water/sand/gas mixture is pro-duced as a foamy mass, which goes to a stock tank forgravity segregation.

It is believed that the sand production increases thefluid mobility in the near-well zone by increasing the

permeability in the affected zone.20 Continuing sandproduction generates a growing zone of enhanced per-meability that could be considered a growing negative-skin effect. The actual morphology of the affected sandis not well understood; two plausible models are net-works of wormholes and uniformly dilated sand. Worm-holes have been observed in the laboratory by use ofcomputer-aided-tomography imaging,21 and their exis-tence in the field has been inferred from tracer tests. It islikely that the continued production of sand more orless eliminates permeability damage in the near-wellzone that could have occurred by fines migration orasphaltenes precipitation.

Past field experience shows that similar reservoirs that

were produced earlier with sand control yielded muchlower recovery factors. Without sand production, thereservoir pressure declined more rapidly, and the gas/oilratio (GOR) increased much more rapidly. With sand pro-duction, the GOR increases very slowly throughout thedepletion process.

Characteristics Value

Reservoir rock Unconsolidated sand

Depth, ft 1,3002,600

Net pay, ft 1380Reservoir pressure, psi 350850

Reservoir temperature, F 5075

Porosity, % 3034

Permeability, md 50010,000

Oil saturation, % 6787

Oil gravity, API 1116

Oil viscosity (in situ), cp 1000100,000

Solution gas/oil ratio, scf/bbl 2575

Primary drive mechanism Solution gas

TABLE 1RESERVOIR CHARACTERISTICS ASSOCIATEDWITH SUCCESSFUL APPLICATIONS OF COLD PRODUCTION

IN CANADA

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in micromodels that show the bubble size to be larger thanthe pore size. The conditions required for this type of flowto occur can be summarized as follows.

Viscous forces acting on growing bubbles shouldexceed the capillary trapping forces.

Gravitational forces should not be capable of inducingrapid gravity segregation of the two phases.

Interfacial chemistry effects that hinder bubble coales-cence also may be needed.

Whether these requirements are met depends on the

rock/fluid properties and the operating conditions. Thefirst requirement is fulfilled when the pressure gradient ishigh enough to mobilize isolated gas ganglia. The secondrequirement is related to the role of gravitational forces inproducing segregated flow. If the pore structure is suchthat isolated gas ganglia can move under the influence ofgravity, then the flow is likely to become segregated. Thethird point is not well established, but it is likely that theinterfacial chemistry plays a role.

In terms of reservoir characteristics, dispersed flow ismore likely to occur when the permeability is high, the oilis viscous, and the interfacial tension between the oil andthe released solution gas is low. To generate the requiredviscous force, a high drawdown pressure is required. The

viscous trapping force decreases when the pore-body/pore-throat aspect ratio becomes low. Therefore, the foamy-oil-type dispersed flow is more likely to occur in well-sortedunconsolidated sands.

Field ImplicationsIf the premise is accepted that foamy-oil flow is a form ofnon-Darcy two-phase flow in which the viscous forceshave become comparable with or stronger than the capil-lary forces, then the implications in terms of field opera-tions are not difficult to determine. Promoting this type offlow requires conditions that generate high pressure gradi-ents in the reservoir. The required pressure-gradient mag-nitude depends on the sand characteristics and the interfa-

cial tension between the oil and the released gas. When anew well is put on production, the initial pressure gradientwould be sufficient in the vicinity of the well in all heavy-oil reservoirs if a high drawdown pressure were used.However, as the depletion propagates deeper into thereservoir, the pressure gradient becomes smaller and mayno longer be sufficient to generate the dispersed flow. Thedrainage area that can sustain dispersed flow woulddepend on the reservoir properties.

When sand is produced with the oil and increases thefluid mobility in the zone from which sand was removed,the reach of high pressure gradients needed for foamy flowbecomes much longer. Because mobility becomes high inthe near-well zone, the zone of high pressure gradient

moves deeper into the reservoir. Thus, sand production ishelpful in sustaining the dispersed flow in reservoirs thatwould otherwise exhibit this type of flow only during theinitial production period. It is apparent that even withsand production, the drainage area that can be producedwith foamy flow is not boundless. The required pressuregradient would be available only up to a certain radial dis-tance away from the well, beyond which dispersed flowwould not be generated.

As mentioned above, sand production is not a necessarycondition for the existence of foamy-oil flow. If the pressure

gradient is sufficient to mobilize gas ganglia, dispersed flowwill occur with or without sand production. Sand produc-tion is needed in Canadian wells primarily to make the pro-duction rates economically viable. The benefit in terms oflonger maintenance of foamy flow is a bonus.

The foregoing also suggests that the foamy flow is lesslikely to occur when the reservoirs are exploited with hor-izontal wells at low drawdown pressures. In Canadianreservoirs, the production rates obtained with horizontalwells (without sand production) are similar to those

obtained with sand-producing vertical wells, even whenhigh drawdown pressures are used in horizontal wells. Theproductivity of these horizontal wells is several times high-er than the productivity of vertical wells that do not pro-duce sand. The sand production improves the productivi-ty of vertical wells and makes it comparable with that ofhorizontal wells. Under these conditions, horizontal wellsoffer no significant economic advantage over the sand-pro-ducing vertical wells. The increased operating cost of sandproduction is more than compensated by the lower capitalcost of the vertical wells. In reservoirs that do not producesand, horizontal wells are generally superior.

Numerical Simulation of Foamy-Oil Flow

Numerical simulation of primary depletion in foamy-oilreservoirs is still based primarily on empirical adjustmentsto the conventional solution-gas-drive models. The two-phase flow of oil and gas mixtures is described by relativepermeability relationships, with some adjustment to the rel-ative permeability curves and/or to other fluid properties toaccount for the effects of foamy flow. The rock/fluid prop-erties that have been adjusted in such simulations includethe critical gas saturation, oil/gas relative permeability, fluidand/or rock compressibility, pressure-dependent oil viscos-ity, absolute permeability, and the bubblepoint pressure.23

Some of the more interesting attempts to model the foamysolution-gas drive are based on assumed mechanistic mod-els of how the gas comes out of solution and what happens

to the released gas. Such models can be divided into twobroad categories: equilibrium and kinetic models.

Equilibrium ModelsThe motivation for developing such models comes fromtheir ease of implementation by use of existing reservoirsimulators that assume complete local equilibrium betweendifferent phases. Most simulators also assume that themobility of fluids is independent of the capillary number.Consequently, such models of foamy flow are inherentlyincapable of accounting for the thermodynamically unsta-ble nature of foamy dispersions and, generally, cannot pre-dict the effect of operating conditions on solution-gas-driveperformance. However, such models have been successful

in attracting considerable attention in the literature andcontinue to be used in reservoir simulation studies. Someof these are briefly described in the following paragraphs.

Pseudobubblepoint ModelKraus et al.24 described a pseudobubblepoint model forprimary depletion in foamy-oil reservoirs. In this model,the pseudobubblepoint pressure is an adjustable parameterin the fluid property description. All of the released solu-tion gas remains entrained in the oil phase until the reser-voir pressure drops to the pseudobubblepoint pressure.

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Below this pseudobubblepoint pressure, only a fraction ofthe released gas remains entrained; and the gas fractiondecreases linearly to zero with declining pressures. Theentrained gas is treated as a part of the oleic phase, but itsmolar volume and compressibility are evaluated withthose of the free gas. Equilibrium ratios from the conven-tional pressure/volume/temperature (PVT) data are modi-fied according to the pseudobubblepoint. An example ofprimary depletion in a volumetric reservoir shows thatwhen foamy-oil fluid properties are used in a reservoir

simulator, the predicted results could show three anom-alous production characteristics observed for foamy-oilreservoirs, namely high oil recovery, low producing GOR,and natural pressure maintenance.

Modified Fractional-Flow ModelsSuch models attempt to match the production behavior bymodifying the fractional-flow curve or the gas/oil relativepermeability curves. Lebel25 described a model thatassumes that all released solution gas remains entrained inthe oil phase up to a certain system-dependent limiting-volume fraction. Consequently, as the gas saturationincreases from zero, the fractional flow of gas increases lin-early with saturation until the limiting entrained gas satu-

ration is reached. Beyond this limiting volume fraction ofdispersed gas, further increase in gas saturation results infree gas. The effective viscosity of the foamy oil wasassumed to decrease marginally as the volume fraction ofgas increases. The density of the foamy oil was taken as avolume-weighted average of the densities of the oil and gascomponents. The equilibrium gas-in-oil PVT relationshipwas assumed to be applicable. This model is equivalent toa manipulation of the gas relative permeability curve,which, up to a certain adjustable gas saturation, becomes afunction of oil viscosity and oil relative permeability.

A similar relative permeability-based approach has beenadvocated by Firoozabadi and Pooladi-Darvish.2627 Theirmain thesis is that the improved recovery results primari-

ly from reduced relative permeability of gas, whichdecreases as the oil viscosity increases. Assuming that therelative permeability concept can be applied to dispersedgas flow, the decrease in gas relative permeability withincreasing oil viscosity is expected when it is the pressuregradient in the oil that is causing the dispersed bubbles tomove. However, it is unlikely that a predetermined gas/oilrelative permeability curve can describe the field situationin which the capillary number varies with time and posi-tion in the reservoir.

Reduced Viscosity ModelsClaridge and Prats,28 in an attempt to explain the higher-than-expected inflow rates, suggested that the asphaltenes

present in the crude oil adhere to the gas bubbles while thelatter are still very tiny. This coating of asphaltenes on the bub-ble surfaces stabilizes the bubbles at a small size. The bubblescontinue to flow through the rock pores with the oil. The keyelement that differentiates this model from the others dis-cussed above lies in the net effect of asphaltenes adsorptiononto the bubble surfaces on the viscosity of the crude oil.They suggest that the oil viscosity decreases dramaticallybecause of the removal of the dispersed asphaltenes. It is dif-ficult to see why this transfer of asphaltenes to bubble surfaceswould have a large effect on the dispersion viscosity because

the asphaltenes adsorbed on the bubble surfaces are still a partof the dispersed phase. Moreover, attempts to verify suchreduction in dispersion viscosity in laboratory tests generallyhave shown opposite results.

Shen and Batycky29 formulated the theory of lubricationin an attempt to show that the apparent viscosity of oil/gasmixture at a low gas fraction is decreased because of thelubrication effect of gases coming out of solution. The gas-lubrication effect requires existence of microbubblesattached to the walls of pores, which has not been con-

firmed by direct experimental evidence.

Kinetic ModelsIt is readily apparent that a dispersion of gas in oil is not athermodynamically stable species. Given sufficient timeand a helpful environment, the dispersion will separateinto free gas and oil phases. Although the natural tenden-cy of the dispersion is to move toward segregation of phas-es, such segregation can be arrested by imposing flow con-ditions that favor regeneration of the dispersed bubbles.Therefore, the flow behavior of foamy oil can be expectedto be a function of time as well as of the imposed flow con-ditions. Kinetic models attempt to capture the time-depen-dent changes in the flow behavior of foamy oil.

Coombe and Maini30 described a model that accountsfor the kinetics of physical changes occurring in the mor-phology of the gas-in-oil dispersion. It defines three non-volatile components in the oil phase: dead oil, dissolvedgas, and gas dispersed in the form of microbubbles. Thedissolved gas changes to dispersed gas by means of a rateprocess that is driven by the existing local supersaturation.The dispersed gas changes into free gas by a second rateprocess. The model was implemented in the ComputerModeling Groups Stars31 simulator by use of existingchemical-reaction routines. Both rate processes were mod-eled as chemical reactions with specified stoichiometryand reaction-rate constants. The rate constants must bedetermined by history matching.

Although this model accounts for the time-dependentchanges in dispersion properties, it fails to consider theinfluence of time and the position-dependent capillarynumber. Therefore, it is not useful for predicting the influ-ence of operating conditions.

A similar approach was used by Sheng et al.,12 who mod-eled the rate of release of solution gas by exponential decayof the local supersaturation and assumed that the gasevolved from solution remained initially dispersed in theoil. The dispersed gas disengages from the oil to becomefree gas at a rate that is proportional to the volume fractionof the dispersed gas in the dispersion. Thus, the kinetics ofthe process involved in transfer of the solution gas to thefree-gas phase was described by two sequential-rate

processes with associated rate constants. This model wasused successfully for history matching laboratory solution-gas-drive experiments. However, it was found that the rateconstants depended on the depletion rate used in the tests.

Both of the kinetic models mentioned above account fortime-dependent changes in the dispersion characteristicsby use of simple rate processes. This method represents animprovement over the equilibrium models. However, therate processes involved in foamy solution-gas drive appearto be controlled by the rock/fluid properties and by thecapillary number. Therefore, the rate constants inferred by

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history matching a known depletion scenario are not validfor predicting the outcome of a new scenario involving dif-ferent flow conditions.

Other noteworthy models have been presented by Josephet al.,32 who treat the flowing gas-in-oil dispersion as apseudosingle-phase fluid, and by Arora and Kovscek,33

who use a bubble-population balance framework.A simulation model capable of predicting the perform-

ance under different operating conditions is unavailable.However, there are two promising routes that can be taken

for developing such a model. The first is an extension of thekinetic models to include the dependence of the rate con-stants on flow conditions. The second route is to make therelative permeability in equilibrium models functions of thecapillary number. Egermann and Vizika34 have recentlyreported on experimental verification of the differences inrelative permeability in the far field and the near-wellboreregion. A model based on capillary-number-dependent rel-ative permeability would not account for the changes indispersion properties with time, but may be a reasonableapproximation for fully developed flow in the field.

ConclusionsThe past decade has seen a remarkable increase in research

effort in this area, and considerable progress was achievedin understanding the mechanisms involved. It is clear thatthe pressure gradient, rather than the decline rate of aver-age reservoir pressure, is the driving force for foamy-oilflow. However, several fundamental questions remainunanswered. It still is not clear whether the interfacialproperties of the oil play a large role and what interfacialproperties (other than surface tension) are important. Therole of rock properties, such as pore geometry and pore-size distribution, also is not completely understood. Therheological properties of such foamy dispersions also arenot well characterized.

In practical field terms, answers to the following severalbasic questions are being sought.

What reservoir characteristics make foamy solution-gas drive possible?

What operating conditions are needed to maintainfoamy solution-gas drive?

How do we optimize the well spacing in foamy-oilreservoirs?

Does foamy-oil flow occur in steam stimulation ofgassy heavy-oil reservoirs?

What are the effects of foamy primary production onsubsequent secondary and tertiary recovery processes?

Several research groups are active in this area, and it islikely that answers to these questions will be forthcomingin the near future.

Nomenclaturek= permeability, m2

= gradient of flow potential, Pa/mog= surface tension, N/m

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33. Arora, P. and Kovscek, A.R.: Mechanistic Modeling of SolutionGas Drive in Viscous Oils, paper SPE 69717 presented at the2001 SPE International Thermal Operations and Heavy Oil Sym-posium, Porlamar, Margarita Island, Venezuela, 1214 March.

34. Egermann, P. and Vizika, O.: Critical Gas Saturation and Rel-ative Permeability During Depressurization in the Far Fieldand the Near-Wellbore Region, paper SPE 63149 presentedat the 2000 SPE Annual Technical Conference and Exhibi-tion, Dallas, 14 October.

Brij B. Maini,SPE, is Professor of Chemical and PetroleumEngineering at the U. of Calgary. Previously, he was groupleader for heavy-oil recovery research at the PetroleumRecovery Inst. Maini holds a BTech degree in chemical engi-neering from the Indian Inst. of Technology and a PhDdegree in chemical engineering from the U. of Washington.