SOCIETY (N? PETROLEUM ENGINEERS OF AIME ;?!%SPE 5808

The Sensitivity of Micellar F!oodingto Reservoir Heterogeneities

By

, C..A..Kossack and H..L. Biltiartz;Wi, Atlantic Richfield Co.. . .. ...,-

. .. ., ..@Copyright 1976

Ameriean Iristitiitggf,Miniag, Metallurgical,and PetroleumEngineers,Inc.

. . .. ..’i%IS PI@ER IS SUBJECT TO CORRECTIONThis paper was prepared for We Itiproved 0i2. Recovery Symposium of the Society

of Petroleum. Erig@e~r,~.of AIME, to be held in Tulsa, Okla., March 22-24, 1976.Permission to copy’is restricted to an abstract of not more than 300 words. Illu-strations may not be copied. The abstract should contain conspicuous acknowledg-ment of.where and by whom the paper is presented. Publication elsewhere afterpublication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUMENGINEERS JOURNAL is usually granted upon request to the Editor of the appropri-ate journal provided agreement to give proper credit is made.

Discussion of this paper is invited. Three copies of any discussion should besent to the Society of Petroleum Engineers offiae. Such discussion may be presen-ted at the above meeting and with the paper, may be considered for publication inone of the two SPE magazines.

ABSTRACT

.. .This paper provides a comparative that’for a heterogeneous reservoir the most’”

evaluation of the effect of reservoir hetero- econornical slug size maybe a very small

geneityon amiscible -tertiary micellar flood. surfactant slug that displaces only the easily

The sensitivityof slug size, preflushvolum-e, mobilized oil. This work also shows thata

surfactant loss, and miscibility saturation of reduction in the surfactant’s adsorption

this complex displacement process was evalu- praperties anda micellar fluid that mobilizesated for a homogeneous, randomly hetero- oil at low surfactant concentrations will, for

geneous, non-communicating layered and a micellar flood with a given slug size, both

partially communicating layered model substantially improve recovery.

reservoir. The five-component, finite-difference reservoir simulator used for this INTRODUCTION

study is described in detail.The o~jective ofthis work wasto stud)

The results show that reservoir the effectof reservoir heterogeneityon theheterogeneityis a dominant factor, adversely performance ofmicellar flooding using aaffecting the performance ofmicellar flooding numerical simulator. The four reservoir

to suchan extent that the process may notbe descriptions used in this study were homo-feasible in many non-homogeneous reservoirs. geneous, randomly heterogeneous! non-

Inth.e partiall ycommunicatin glayered model communicating layered, and partially com-reservoir, large volumes of preflush were municating layered models. Micellar floods

required; and even after adequate preflushing~ were simulatedto compare the effect of slug50 to70 percent of the post waterflood oil in size, surfactant loss, and critical slug satu-place was unrecoverable. The results indicate ration upon tertiary oil recovery in the four

References and illustrations at end of paper.

THE SENSITIVITY 03? MIGELLAR FLOODING* ●

ifi TO RESERVOIR HETEROGENEITIES sP17 5808. . — -.—- ..-

model reservoirs. These sensitivity studiesindicate where and under what conditions themice llar flooding concept might be applicable.

The performance prediction of amicellar flood in a complex reservoir requiresa numerical simulator that represents thereservoir features, chemical properties, anddisplacement mechanisms that affect the. floodperformance. To simulate this oil recoveryprocess the model described .below accountsf dr the flow of five separate components - -oil,water, surfactant, polymer, and pref lush. Inaddition, the simulator includes the adsorptionof surfactant and polymer, permeability re -

‘ duction, generation of miscibility, and themixing of miscible fluids.

THE MODEL

Previous finite -difference siinulatordevelopment, omitting stream tube modelsand incompressible models, in the field ofmiscible flooding has been very limited dueto numerical dispersion dissipating the smallsurfactant slug. The basic models in thisfield are not suited for micellar flooding but‘were designed for solvent and polymer floods.Todd and Longstaffl and Bondor, Hirasakiand Thom2 have developed four-component,miscible flood mode 1s for the simulation ofsolvent and ptilymer ‘displacement, - re spe’c -tively. These two papers describe methodsto simulate many of the important featuresin a miscible flood and a mobility controlledflood, such as the flow of miscible fluids, themixing of miscible fluids, adsorption, residualresistance (permeability reduction), arid non -Newtonian effects.

A numerical model approximating asystem of five nonlinear partial differentialequations, each representing conservationof fluids, is assumed to describe two-phase,multi -component compressible flow in rese r -voirs unclergoing water external micella rflooding. These equations, obtained bycombining Darc y’s law with continuity, arerepresented explicitly for the ith componentin Eq.1.

[.

Bi k kri piV*

1Vli +qw j=:(q BiSi)

eii=l,2,3,4,5 1

(1) I1..

5It is also required that Z S = 1 and the

ii=l

usual capillary pressure relationship beexpressed as a linear function of the aqueoussaturation.

?2 .c2-~ ‘sac/-pl=p (2)

The development and loss of misci-bilityy, permeability reduction, and surfactant10Ss are handled by placing auxiliary con-straints on the system of equations and aresatisfied explicitly to the pressure solution.The .imulator solves the pressure equationimplicitly using either Gaussian eliminationor the strongly implicit procedure. Thesaturations are then calculated explicitlyfollowing the standard IMPES (implicit pres -sure, explicit sat~. dtiOI’i)procedure.

The model contains an explicit calcu-lation in which the surfactant and polymerare removed from the flow to simulate lossof chemicals. The rat~s of reaction for thepolymer adsorption and surfactant loss areassumed to be infinite (an instantaneousreaction) until the predetermined quantityof the component has been either lost oradsorbed; at that time the rate becomes“2eroi ‘ The surfactant loss “rnechahism ‘ca’n “include true chemical adsorption, and pre -cipitation when in contact with multivalentions or the 10Ss of effectiveness when mixedwith a high salii~iity brine. The 10Ss isassumed known and inputted to the simulatorin terms of pounds of surfactant 10Ss peracre -foot of reservoir. Once a grid blockhas “lost” its specified amount of surfactant,no additional 10Ss is calculated for that cell,To maintain a material balance, lost surfac -tant and adsorbed polymer saturations becomepreflush brine saturation.

The amount of surfactant 10Ss ismodeled as a function of preflush eff icienc yjsee Fig. 1, where

preflush

[

saturation ofefficiency 1/=preflush brine

[

saturation saturationof preflush + of reser - 1(3)

brine voir brine

,,

SPE 5808 C, A. Kossack and H. L. Bilhartz, Jr. IL7-..

Therefore, in a given cell, at any time, the fraction in that phase, since the movementmaximum quantity of surfactant 10Ss allowed of one component through a porous mediumis dependent on the ‘ ‘pref lush efficiency. ‘‘ No is not impeded by the presence of otherdesorption of either component is currently components in the same phase except for aallowed in the model. reduction in the area available for flow.

Thus, in the two-phase region, S4 < ScThe miscibility mechanism currently

used in this model is a. first order approxi - Simation to many of the complex transition izone k

= r“kr (Saq)phase relationships that are currently being

r,1 aq aqinvestigated. 3$4 The switch f rorn immiscible ?two-phase flow to a single phase is achieved i=l,3,4,5 (4a)through fir st contact miscibility, * which iskeyed to the amount of the surfactant slug k = k (Saq) . (4b)present at any point. This critical satura - ‘2 ‘2tion** of the surfactant is a laboratorymeasured parameter which varies for different For miscible flow, S4 ~ Scmicellar fluids) crude oils, and salinity. Itsvalue represents the lowest concentration that k = Si for all i. (5)the micellar slug can be diluted to and still be

r.1miscible with the oil. Therefore, as long asthe micellar saturation at a given point is A mixing parameter model is used toabove the critical saturation, all five com- account for the creation of dispersed orponents are considered as miscible components mixing zones between miscible componentsof the mixed phase and the capillary pressure within a single phase. A description of the

P= is set equal to zero. Miscibility y, for one -fourth power fluidity mixing rule and2-1 the definitions of the effective viscosity are

this study, is not a function of pref lush effi - outlhed in Appendix A. .Yhe mechanism ofciency except through adsorption which de - permeability reduction due to polymer andcreases the iurfactant concentration. If the surfactant contacting reservoir rock can be.surfactant saturation is, less than this critical handled by the model, but it will not be

“+aiueDthen ‘miscibility’ between the aqu”eous discussed here because it was neglected forphase (reservoir brine solution, polymer this work.solution, surfactant solution, pref lush solu -tion) and the hydrocarbon phase is assumed To complete the mathematical formu-lost; i, e. , the flow is immiscible, and p ‘ lation of the model, in::ial and boundary

C2-1 conditions are needed.is non-zero. Even under this condition allfour aqueous components remain miscible Initial condition: @j = Ij (x, y, Z,O) (6)within the wetting phase. Each misciblecomponent assumes a fraction of the phase Boundary condition: ;“ ;(o,t) =0 (7)relative permeability equal to its volume

Where: u = boundary surface. .— ,H,

*Iu this paper the word “miscible” n = unit vector normal to uimplies a numerical state where all thecomponents in a cell are mobile. No Eqs. 1 through 7 describe completely theinference is intended concerning the flow of fluids under the assumed mechanisms inumber of phases or occurrence of fluid The se equations with unknowns of pressureinterfaces. and saturation constitute a set of nonlinear

differential equations which must be solved**The critical saturation (expressed numerically. The solution of this mathemat -

as a function of the cell’s pore volumes Sc - ical model is accomplished by reducing

is equivalent to the minimum surfactant the se difference equations to a single oilconcentration necessary to achieve misci - phase matrix problem through the use of thebility. ‘ IMPES solution technique.

. . ... ..-.— .——.

THE SENSITIVITY ‘OF MICELLAR FLOODING

Numerical Dispersion

The discretization error which occurswhen the first spatial derivative of a quanti-ty, c, is difference (first order accuratewith upstream weighting) has the form5 #6

Ax~z c

()Z-z

(8)

,.,J *

This error introduces added dispersion tothe partial differential equation; thus its “name, numerical dispersion. For example,in a porous medium, a flow with a frontalvelocity of one foot/day, a grid block lengthof 20 feet, a time step of one day, and singlepoint upstream weighting of relative pe rme -ability experiences a diffusivity of 9, 5 f t2/day. To reduce th@ to an average reservoirdiffusivity of one ft~ /day would require gridblocks of 3 feet in length (this would requireincreasing the number of grid blocks by afactor of seven).

The difference equations- used tosolve for the flow of miscible fluids in thismodel contain fir st order accurate differenceformulas; thus, using the results of Lantz, 6~he dimensionless numerical cliff usivit y, R*$created by the solution of Eqs. 1 through 7in a miscible region is given by Eq. 9.

AS-AT ‘KE*=T‘G (9)

Since it is infeasible to attempt to reduceR* to such a level that it is no longer asignificant factor in the flow, the only re -course is to use the numerical dispersionto simulate the real dispersion present inthe formation. The numerical diffusivity,R*, can be made to match the physicaldispersion, K, with the proper choices ofAx and At, ‘as surning a cor.stant f rentalvelocity, u. Thus, for a 1-D reservoirdisplacement simulation at unit mobility,.10-acre well spacing, frontal velocit of

1one f t/day, and a cliff usivit y of one ft /day,the numerical dispersion will match thephysical dispersion with any of the following(Ax, At) pairs: (3 feet, one day), (4, 2),(5, 3), etc. The use of two point upstreamweighting will replace the 2 in the denomina -tor of Eq. 9 with an 8; thus the (k, At) pairsbecome (9, 1), (10, 2), (11, 3), etc.

This match of dispersion applies inthe direction of flow when the frontal velocityis a constant throughout the reservoir; i. e. ,it is valid for 1-D and 2-D vertical, cross-sectional, homogeneous reservoirs. Theanalysis can be extended to 2 -D vertical,cross -sectional, heterogeneous reservoirsby making the following assumption:

If two-dimensional (cross -sect<onal) reser-voir A with constant velocity ii (specifiedinjection and production rates), length L,time step At, and block size Ax yields adiffusivity y K1 (corre spending to numericaldispersion of K* ● ii ● L), then the additionof certain heterogeneity (not requiring re -gridding) into the description of A does not‘increase the r.’~me.rical dispersion, Thus ,the additional diffusivity encountered by thefluid results from cross flowing and channel-ing which may be called mac~oscopic disper-sion and not be due to additional truncat&n-error in the mathematical formulation.

Implicit in this statement is that theaverage longitudinal velocity in homogeneousreservoir A is the same as a weighted verticalaverage of the veloci~ies of heterogeneousreservoir A, and that the longitudinal compo -nent of velocity is much greater than thetransverse component. Also, no attempt wasmade -to scale” the transverse. dispersion’.

Thus, it was assumed for this workthat micella r floods could be simulated incross-sectional (x-z strip) reservoirs witha fixed amount of numerical dispersion. Thisnumerical dispersion represents the intra -grid block microscopic dispersion (the dis -persion created by heterogeneities that areless than Ax in scale). When studying micellarflood performance in a reservoir with verticalheterogeneities, the total simulator dispersionwould be the sum of numerical dispersionfixed by Ax, At, and u and the additionalmacroscopic dispersion created by the in-hornogeneous fluid flew between grid blockswhere thm heterogeneity can be representedby a varying.pe rmeabilit y from grid block togrid block or fror.. layer to layer. Thismacrosco~ic dispersion is an approximationof the dispersion effect of real phenomenaof cross flow, channeling, ctc. ‘VW inherentassumption is that the numerical dispersionmatches the int rablock micr~copic .dis per-sion and the simulator’s r&-croscopic

,,

.=PE 5808 C. A. Kossack and H. L. Bilhartz. Jr. lb

—--

dispersion approximates gross fluid move -ments, and that their interaction in the simu-lator results in a total simulator dispersionequal to the total physical dispersion inreservoirs like the ones that were modeledin this study. (Refer to Fig. 2.)

THE SENSITIVITY STUDY

The re are limitations to our nume ri -cal reservoir simulator, to our uncler standingof certain micellar f 100ding mechanisms, andto the availability y of descriptive reservoirinformation on specific reservoirs. How-ever, a sensitivity analysis of the micellar.flooding concept using this simulator toevaluate the effect of various types of reser -voir heterogeneity, flooding parameters, andchemical properties upon oil recovery shouldgive us semi-quantitative insight as to theapplicability y of the process. This study pro-vides information on (1) the types of reser -voirs where micellar flooding is moreapplicable, (2) the effect of surfactant slugsize and critical saturation on recovery,(3) the preflush requirements needed undervarious reservoir conditions, and (4) theeffect of surfactant 10ss on recovery.

Model Reservoir Des criptions

. .Four reservoir’ deicriptio-ns W6re

constructed with average properties repre -senting a five spot with ten acre well spacing.A table of all the properties common to allfour reservoir models is given in Table 1.The grid was constructed with a variable Aygrid in an attempt to simulate a quprter fivespot with the two -dimensional, vertical crosssection; see Fig. 3. This alteration of a 2 -Dstrip gave a better approximation of the threedimensional case with respect to the velocitydistribution in the x direction and the timingof the volumetric sweep, especially whenmiscibility was lost before surfactant break-through. Since the frontal velocity variedwith x, the application of the assumptionsfor the match of numerical dispersion wasmore complex than previously discussed.

The total physical dispersion for thehomogeneous reservoir was chosen to be oneft2/day because (1) it is typical of many sand-stone reservoirs and (2) it is low enough notto be the dominant characteristic in the

micellar flood. A vertical cross sectior.

(constant Ly), homogeneous reservoir model(660 feet between wells) required 74 gridblocks for the simulator dispersion to matcha physical dispersion of one ft2/day. For thevariable Ay configuration, miscible simula -tions were run where the production concen -t ration was plotted against time. Eighty-eight grid blocks were required for theconcentration “profile’ to match that of a homo -geneous reservoir where K equaled one ftZ/day.

The four model reservoirs weredescribed by using various levels of permea -bility to represent heterogeneity. ReservoirNo. 1 was homogeneous; No. 2 was randomlyheterogeneous; No. 3 was non-communicatinglayered; No. 4 was a partially communicatinglayered reservoir with 10 percent of the cellshaving vertical communication. A des c riptiomof the assignment of permeabilities is givenin Table 2, and the procedure for the drawingof permeabilities from a log-normal distribu-tion is given in Appendix B.

The re suits from f I’ooding the homo -geneous reservoir were used as a comparisonstandard for the heterogeneous reservoirfloods . The randomly heterogeneous reser -voir was designed to show the effect of .lddi -tional dispersion created between grid blockswith -randomly assigned permeabilities ‘rangin~from 90 to 3200 md (from a log-nomrial distribution, mean 500 md, V = O.6). ReservoirNo. 3 had horizontal layer permeabilitiesvarying from 200 md to 1220 md. ReservoirNo. 4 was identical to No. 3 except a limitedamount of vertical communication was allowec

The four model reservoirs were waterflooded in the simulator at a rate of 300 B/Duntil a WOR of 30 was reached. This pointwas considered the economic limit of second-ary recovery, and the remaining oil in thereservoir was classified as ‘%ertiary oil. ‘1The recovery and rough saturation profilesfollowing the waterflood are given in Table 3.Reservoir heterogeneity had a very slighteffect on the recovery of oil because of thelack of areal sweep effects, the low viscosityof the oil, and the “effect of g“ra”vity on thevertical sweep in the homogeneous andrandomly heterogeneous reservoir. Thisresult minimized the effect of waterfloodperformance on the results of the micellarflood.

THE SENSITIVITY OF MICELLAR FLOODING—50 TO RESERVOIR HETEROGENEITIES sPl? 5801

1?’‘eflush Studies

Niwt micellar flood applicationsrequire preflushing with a particular brine.The purpose of this preflush is to act as abuffer between the reservoir brine in placeat the start of preflush and the micellar slug.The presence of high total dissolved salt con-

..centrations and/or divalent ions (Ca+ t ) in the—reservoir brine can cause “a loss of oil dis-placing ability and an increase in adsorptionupon mixing with the micella r slug. Thus, astudy of the quantity of preflush required inthe four model reservoirs was a necessarypart of this work.

The question posed was how large aslug of preflush is needed to separate thereservoir brine from the surfactant slug sothat only a specific fraction of the injectedmicellar slug (overlap volume) is renderedineffective by mixing with the reservoirbrine ? The overlap volume is defined asthe volume of the micellar slug that iscontacted (mixed) by the reservoir brineabove a “cutoff’ I brine saturation and abovea “cutoff” surfactant saturation. This isbest explained by using an example alongwith Figure 4. With a slug made up of15,000 mg/1 brine, O mg/1 Ca++, let usassume that the process could tolerate amaximum salinity increase of. 10 percent .

‘:” (to 16,500 mg/1)’ and a maxim’u Ca+ + &on-centration of 200 ppm before the activity ofthe micellar slug decreases to zero. There-fore, i~~., mixture of more than 5 percentrese; vtiiv brine would result in an ineffectiveSIUZ f:f wo used a reservoir brine salinity of50,900 mg/1 NaCl and 4,000 mg/1 Ca++ .This gave the definition of the “cutoff” brinesaturation of O. 05 in Fig. 4.

Also, we assumed that the micellarslug was ineffective at saturations below O. 051this defined the surfactant “cutoff 1’ saturationof 0.05 in Fig. 4. The total volume of poten-tially active surfactant in contact with re se r -voir brine between the O. 05 “cutoffs” iscrosshatched in Fig. 4; i. e. , this overlapregion contains surfactant made ineffectiveby contact with high salinity brine and Ca+ +ions. If a very high salinity reservoir brine

‘. were encountered, say 200, 000 mg/1 NaCland 20, 000 mg/1, Cat+, then the brine ‘~cut-off” saturation would be lowered to O. 01 and

.- the volume labeled (a) would be a’dded to the

,..

crosshatched overlap region in the casesketched in Fig. 4.

A series of twenty complete micellarfloods was simulated using varying amountsof preflush to determine the preflush require -ments for the four reservoirs. The previ -ously waterflooded reservoirs were treated,with an 8.8 percent pore volume micellarslug with a critical saturation for loss ofmiscibility of O. 05 and a baseline surfactantadsorption of a constant 1000 lb/acre -foot.The volume of surfactant overlapped wascalculated every four days throughout eachmicellar flood. The maximum overlap wasthen determined for each micellar displace -me nt. These maximum overlaps have beenexpressed as fractions of total injectedsurfactant and plotted in Fig. 5 against thevolume of preflush injected.

This figure shows the results of allfour reservoirs using the O. 05 “cutoff’! andof reservoirs 2 and 4 using the O. 01 “cutoff. “It is in’portant, in view of the assumptions,to study these curves in a comparative sense.The O. 01 “cutoff” curves demonstrate thesensitivity y of the pref lush process to in-creasing reservoir brine salinity; and forthe O. 05 “cutoff’! cases, approximately tentimes as much preflush was required for thepartially communicating layered reservoir ,. .than for the ‘other reservoirs when comparedat a low overlap value.

To minimize the impact of preflushefficiency on the following micellar floodingsensitivity y study, the four model reservoirswere treated with the preflush volume thatwould yield a O. 10 maximum surfactant over -lap. (See Figure 5.) This means that, inFig. 4, the crosshatched region was allowedto be a maximum of 10 percent of the totalinjected slug in each of the four reservoirs.This resulted in a 2.85, 3.7, 2.2, and 32percent of a pore volume preflush slug forreservoirs No. 1 to, No. 4, respectively,when the O. 05 “cutoff” was used.

Micellar Displacements

The standard micellar flood wasdesigned with typic~i values of the processvariables to establish a base performancefor the four reservoirs. The process wasconducted on the four reservoirs in an

. . . . .

SPE 5808 C. A. Kossack and H. L. E+ilhartz, Jr. 151—. - )

I

identical fashion so any difference in recov - ve rtic’al communication between layers

ery can be attributed to the cliff erences in usually exists. The partial communicating

reservoir heterog,eneity. The standard ,,.,~,case left an additional 20 percent of the

micellar flood included all of the data of tertiary oil in the reservoir compared toTable 1 and began after the preflmh injec - the non -communicating case.

tion. The surfactant slug vol.urne was 6.13‘percent of the total pore volume of the reser - A sensitivity y study of the process

voir which provided sufficient surfactant variables was made to further evaluate

“(!hemical to satisfy a 1000 lb/ac re.-foot micella r f 100ding in the four model re ser -

surfactaht “1os3 “for all of the rock in the entire voira. The study consisted of 28 micellar

quarter of a five spot. Thus, in a homogen - floods that were identical to the correspond-eous reservoir, in the absence of gravity$ ing standard micellar flood except that onewith piston -like displacement, and at a 100 variable in each simulation was altered. Thepercent efficient preflush, no surfactant sensitivity y study was developed around the

would be produced. The critical saturation perturbation of the following variables: (1)

of the micellar slug for the loss of misci - the slug size, (2) the amount of surf actant

bility was 0.05 (miscibility means 100 per- loss, and (3) the critical saturation of the

cent displacement of the oil was allowed). slug for 10Ss of miscibility, The surfactantThe standard surfactant loss curve was slug sizes injected were 4 percent and 12 per-

assumed to be linear with pref lush efficiency cen,t of the pore volume. The high and low

with end points of 1000 lbs/acre, -foot at a surfactant loss curves are plotted on Fig. 1.

preflush efficiency of 1.0 and 3000 lbs/acre - The critical saturations used were O. 10,foot at 0,0 efficiency, as shown in Figure 1. 0.025, and 0.001. The tertiary oil recoveryThe micellar slug was followed by a 40 per- efficiency for all the simulations in reservoircent pore volume slug of polymer solution, No. 1 are plotted against pore volumes of

Drive water was then injected into the for - fluid injected after preflush in Figs. 7a, 7b,

mation until the water/oil ratio in the pro- and 7c. The same efficiencies are plotted

ducer reached 30. for reservoirs No., 2, 3, and 4 on Figs. 8a,8b, 8c, Figs. 9a, 9b, 9c, and Figs. 10a,

We calculated the tertiary oil recovery 10b, 10c, respectively.

and oil/ surfactant ratios for the standardflood. Those re suits are labeled ‘! standard The sensitivities of the tertiary oil

micellar flood” in Tables 4 and 5. The ‘ ‘recovery and oil/ surfactant ratio are’ listed ~. -normalized tertiary oil recovery is plotted in Tables 4 and 5. The upper number in

against the pore volumes of fhid injected Table 4 is the fraction of the oil in place

after preflush in Fig. 6. A tertiary oil recovered by the tertiary process, whereas,recovery efficiency of 1.0 would mean that the upper number in Table 5 is the oil

the process recovered all the tertiary oil recovered- surfactant volume ratio. The(total oil in the reservoir at the end of the lower number is the sensitivity y (percentwaterflood). The results show that reser - change) of the parameter variation whenvoir heterogeneity y has a pronounced effect co~pa red to the standard micellar flood inon the tertiary oil recovery efficiency.’ The that reservoir. No special simulations toadditional dispersion caused by the randomly optimize any of the variables and no simula -heterogeneous reservoir resulted i,~ 18 per- tions with a combination of altered variablescent less oil recovery than that for the homo - were run..geneous reservoir. The layering of reservoirNo. 3 (with no vertical communication) caused DISCUSSIONthe production of 31 percent less than thehomogeneous case. When some vertical An overview of the sensitivity studycommunication was added to the layered case, reveals that reservoir heterogeneity andone -half of the recoverable tertiary oil was su.rfactant loss are major factors in theleft behind. The comparative results be- recovery of tertiary oil. A severely hetero -tween reservoirs No. 3 and No, 4:are signifi- geneous reservoir or’ a reservoir with a highcant because many micellar floodfield evalu- surfactant loss will leave as much as three-ations are ‘estimated from a non ~communi - fourths of the tertiary oil in the formation..eating laye’red model, wlien in reality some Specific- observations which. can be drawn .,

.

THE SENSITIVITY OF MICELLAR FLOODINGD-52 TO RESERVOIR H.

from Tables 4 and 5 concerning the effectsof heterogeneity and process variablesfollow.

~—~= (1) Increasing the surfactant slug—

size from 4 to 12 percent pore volume in-creased the oil recovery substantially asexpected. Yet the oil/ surfactant volumeratio, a measure of the worth of the process,decreases (with the exception of reservoirNo, 1). An economic analysis to determinethe optimum slug sizes should include aweighted combination of recovery (Table 4)and oil/ surf actant ratio (Table 5). Theseresults suggest that for expensive surfactantsthe injection of a small slug into a hete ro -geneous reservoir, displacing only the easilymobilized oil, may be more profitable.

(2) Decreasing the slug size had theleast effect on recovery for the reservoirNo. 4 case because a reduction in slugvolume means less slug is cycled throughthe reservoir and/or lost to tight layers.Decreasing the slug size had the largesteffect on recovery for the homogeneousreservoir No. 1 case since it directlyaffected the volume swept by active sur -factant.

(3) Increasing the slug size had thesmallest effect on recovery for the reser -.,voir No. “3 case” because ”th-e‘surfactant cycledthrough the more permeable layers. In-‘creasing the slug size had the largest effectfor the reservoir No. 2 case because disper-sion led to an earlier inactivation of a smallsurf actant slug.

(4) The high surfactant loss param-eter has the smallest effect for the reservoirNo. 4 case because ths heterogeneitiesreduced the surfactant contact with thereservoir to such an extent that high surfac -tant 10Ss had little effect on the recovery.The largest effect of high surfactant 10SCSoccurred for the reservoir No. 1 case,because the contact was the largest. A plotof the tertiary oil recovery efficiency vs.pore volume of fluid injected after preflushfor the four model reservoirs with high sur -factant loss (see Fig. 11) shows that the fourcurves are grouped very tightly. This indi -cates that a high surfactant. loss in a reser - .voi.r g“reatly reduces the effects of hetero -gene it y; i. e., the advantage of the slug to

rEROGENEITIES SPE 580$

contact a large portion of the reservoir wasnegated by ,the 10Ss of surfactant to the rock.Thus, the high surfactant 10Ss systems looked“equally bad” in all types of reservoirs.

(5) The effect of low surfactant lossis surprisingly constant in reservoirs No. 1,No. 2, and No. 3, where an additional 25 per-cent recovery was gained..’ Reservoir No. 4did not increase as much as the others, againbecause of the dominance of heterogeneity onthe process.

(6) The low value (O. 10) of criticalsaturation of the slug for 10Ss of miscibilityhad its largest effect for reservoirs No. 1and No. 2 because the formation was con-tacted by the slug more evenly and misci-bility was lost in all layers at some distancefrom the reservoir entrance. The locationin each layer when miscibility was lost isgiven, along with standard micellar floodrecoveries, in Table 3. Reservoirs No. 3and No. 4 showed little effect of this lowdilution as most of the surfactant enteredonly the most permeable layers where dilu-tion was not severe.

(7) The change of the critical satura -tion from O. 05 to O.025 (generally consideredthe most probable range) showed little effectfor any of the cases. The largest effect wasfetid for ‘the ‘No. 2 rese#voir case” because’dispersion of the slug dominated the behavior.

(8) The asymptote for the criticalsaturation of surfactant (O. 001) gives theresults of a completely miscible displace-ment; i. e. , if any surfactant is present, thenthe system is miscible. These recoveriesare the most optimistic for the reservoirswith the standard surf actant slug and sur -factant loss curve. The recovery resultsshow that the more homogeneous reservoirs(No. 1 and No. 3) had nearly. reached theirasymptote by the O. 025 simulations, yet themore heterogeneous reservoirs (No. 2 andNo. 4) showed significant increases inrecovery at O. 001. Thus, the developmentof micellar fluids effective at lower concen-trations of surf actant ne~ded to producemiscibility could have a favorable effect onthe micellar flooding of heterogeneous re ser -.voirs.

..I

SPE 5808 C. A. Kossackam

PROGRAM LIMITATIONS

h evaluating the model and the resultsp~esented, it is important to recognize thelimitations introduced by the assumptions andthe simplifications that were needed to con-struct a tractable solution. The model doesnot rigorously represent the thermod~amic’.and transport phenomena which are neces -sary to describe the mechanisms and detailsof the various processes. The model attemptto describe the pertinent features, as a firstorder approximation, so it can be used forthe evaluation of micella r floods in variousmodel reservoir types. The sensitivity studyshould be viewed in a comparative sense, notas the absolute performance. When viewedin the proper sense, the effects of hetero-geneity and chemical properties between,simulations give a semi-quantitative re suitfor the effects in a real reservoir. Certainassumptions and simplifications listed belowlead to higher oil recoveries than could beexpe’cted from real reservoirs.

(1) Transverse dispersion. 7

(2) Areal sweep effects.

(3) Stratification and gravity effectswithin a grid block.

,,. ;. ,.. _. . . ., . .

CONCLUSIONS

(1) The numerical simulator studyof tertiary micellar flooding showed thatreservoir heterogeneity has a pronounceddetrimental effect on the oil recovery effi-ciency. For example, in the standardmicellar flood the oil recovery of the partiall’communicating layered reservoir was lessthan one -half that of the homogeneous re ser -voir. The oil recovered-micellar fluidvolume ratio for this heterogeneous reser -voir was only 1.7 compared to 3; 3 for thehomogeneous reservoir.

(Z) The partially communicatinglayered reservoir required ten times theqgantity of preflush needed for the morehomogeneous reservoirs to provide “adequateseparation _between the reservoir brine. andthe micellar fluid. Despite the optimisticfluid flow mechanism built into the simulator,the result of this study showed that pref lush

H. L. Bilhartz 15:

quantities in excess of 50 percent of a porevolume will likely be required to be effectivein stratified reservoirs with communicationbetween the strata.

(3) The sensitivity analysis of thesurf actant slug size showed that as the slug

, siz’e increases the oil recovery, as expected,increases; but the oil produced/ surfactantinjected ratio (as a measure of process effi-ciency) decreases in the heterogeneous reser -voirs. Therefore, the optimum slug size fora heterogeneous reservoir is likely to be lessthan that for a homogeneous reservoir.

(4! For a 6.13 percent pore volumesurfactant slug, a reduction in the surfac -tantfs adsorption and other loss character-istics caused an increased oil recovery fromthe more homogeneous reservoirs but led toonly a slight increase in the partially com-municating la ye red reservoir.

(5) A micellar fluid that “mobilizesoil at much lower surfactant concentrationsthan can be achieved with eurf actants current-ly available will not substantially increaserecovery in homogeneous reservoirs. Yet,in heterogeneous reservoirs a micellar fluidthat is miscible at lower concentrations willgreatly increase the tertiary oil recovery

efficiency . ... ; . . ... ,. ..

NOMENCLATURE

Bi =

~a+ + .

K =

—*K =

k =

kr =

L =

P =

P= ‘2-1 “=

qj .=

formation volume factor, STB/RB

calcium ions

physical dispersion, (length)2 /time

dimensionless numerical diffusivity

absolute permeability, md

relative permeability, fraction

total system length, injector toproducer distance, length

pressure, psi

oil-water capillary pressure

strength of source or’ sink repre -‘senting wells, ST B/time

. .

THE SENSITIVITY OF MICELLAR FLOODING—54 TO RESERVOIR HETEROGENEITIES SPE 5808

RK3

RR3

RK4,

s.1

saq

t

u

v

v

v

v“

u‘i

b{

#~

.>”

~

P

A7

w

= polymer component to permeabilityreduction

= polymer residual resistance factor

RK4’ = micellar permeability reduc -tion factor, input value

saturation, fraction

total aqueous phase saturation

time, days

frontal velocity, V/q

darcy velocity, length/time

permeability y variation

gradient

dive rgence

effective viscosity, cp

dimensionless Jell size, Ax/L

Hubbert’s potential =

[1‘jJ *.L , heightP.. .: .. . .. .. . .‘“ o 1“

porosity, fraction

density

dimensionless time uAt/L, pv

the fluidity mixing parameterindicating-the degree of mixing

Subscripts

aq = aqueous

D = , standard deviation

e = effective

i = 1,2, 3,4,5, component: reservoirbrine, oil, polymer, surfactant,preflush

.

M = median

m = mixing

r = relative

REFERENCES

1.

2.

3.

4.

5*

6.

7.

8.

Todd, M. R. and Longstaff, W. J,:“The Development, Testing, andApplication of a Numerical Simulatorfor Predicting Miscible Flood Per -formance, “ J. Pet. Tech. (July, 1972)-——874.

Bondor, P. L. , Hirasaki, G. J. , andThorn, J. J. : “Mathematical Simulationof Polymer Flooding in Complex Reser -voirs, r’ Paper SPE’ 3524, presented atSPE -AIME 46th Annual Fall Meeting,New Orleans (Oct. 3-6, 1971).

Healy, R. N. and Reed, R. L.:“Physiochemical Aspects of Micro-emulsion Flooding, ‘‘ Sot. Pet. ~. ~.(October, 1974) 491.

Healy, R. N., Reed, R. L., andStenmark, D. G,: r!M~tipha se Micro -

emulsion Systems, “ Paper SPE 5565,presented at SPE-AIME 50th AnnualFall Meeting, Dallas (Sept. 28 -Oct. 1,1975).”” ‘“” ““” ““’

Todd, M. R. , O’Dell, P. M., andHirasaki, G, J.: “Methods for Increased

Accuracy in Numerical Reservoir Simu-lators, “ Trans. AIME (1975) &, 515.

Lantz, R. B.: “Quantitative Evolutionof Numerical Diffusion (TruncationError), II Sot. Pet. ~. ~. (September,1971) 315xo. —

Koonce, K. T. and Blackwell, R. J.:“Idealized Behavior of Solvent Banksin Stratified Reservoirs. “ Sot. Pet.~: J. (December, 19~5) ~8 -3~0

#-

Dykstra, H. and Parsons, R. L.: “ThePrediction of Oil Recovery by WaterFlo~di’ in: Secondary Recovery of Oil——in the’ United States, 2nd Edition, API,——— —New York, New York (1950).

,, i

SPE 5808 C. A. Kossack and H. L. Bilhartz, Jr. 155

APPENDIX A

Fluid Mixing and Effective Viscosity

A mixing parameter model was usedto account for the creation of dispersed ormixing zcnes between miscible components

1 If the dispersed zonewithin a single phase.completely occupied a cell in the model, thenthe effective viscosity. of each component wasthat defined by a one-fourth power fluiditymixing rule as given in Eq. A-1.

n

(A-1)

where L = set of components which can sharea dispersed zone

h = total number of components inset L

4 identified each component in set L.. . .-. -’.....,, .-, .,, , ,

On the other hand, when the size ofthe dispersed zone was small compared tocell size, the component viscositiess becamethose of the pure components. It is reason-able to expect the actual effective viscositiesto fall somewhere between the mixing limits;thus, the effective viscositiess are defined as:

(1 - u) U)iMe = Pi v 8

i ‘1,3,4,5

i= 1, 3, and 5 (for water, polymer,.and preflush)

(1 - W2)v = V2 v‘2 ‘2, 4

(2 = ‘oil, 4 = ‘micellar fluid)

(1 - W4) U)4IJ = V4 v‘4 ‘1,2, 3,4,5

(A-2)

where ~ is the one-fourth power fluid mix-ing rule (Eq. A-1) and @i is the mixing pa -,rameter indicating the degree of mixing.The limiting cases of no mixing and completemixing correspond to ~i = O and ~i = 1,respectively. The model included the optionof specifying separately the degree of mixingfor each component (when the componentsshare a dispersed zone).

APPENDIX B

Assignment of Permeabilitiesfrom a Log-Normal Distribution

The Dykstra -Parsons8 concept ofscaling the rock permeability to a log-normaldistribution with a permeability variationparameter measuring the degree of hetero-geneity provides an unbiased means of assign-ing permeability to layers or grid blocks.When the cumulative distribution is plottedon a log-probability scale, the location of the(assumed) straight line is fixed by two param-eters, the permeability y at the median kM andat one standard deviation (84. 1) above themean kD. ~ The slope is commonly called thepermeability variation, V; see Fig. B-1.The average value of 0,6 was used for thesimulations since most sandstone reservoirshave a macroscopic permeability variation of0.4 S V <0,8. Thus, given the mean (500md)and V = 0.6,” a straight line, Fig. B-1, canbe drawn. To obtain five pe rmeabilities fromthis log -normal distribution to be assigned tothe five reservoir layers as was done inreservoirs No. 3 and No. 4, the permeabil -ities at cumulative probabilities of 16.6, 33, 350.0, 66.7, and 83.3 are read from the graphThese five * ~lues were then assigned ran-domly to ti. five layers. For reservoirNo. 2, the J8 permeabilities at cumulativeprobabilities of 1.12, 2.24, 3.37, . . . . 97.8,98.9 are read from this graph. These 88values were then, drawn ra.ndo~y for eachgrid block- in a given layer. Each of the fivelayers was constructed from a separate ran-dom drawing in an attempt to create a trulyrandom (tibiased) reservoir description.

I

TABLE 1 - DATA FOR ALL 2-D VERTICAL CROSS SECTION SIMULATIONS/

System Dimension: 10 acre spacing, quarter 5-spot, 660 x Variable

Reservoir Data - before waterflood

Initial Oil SaturationConnate WaterResidual Oil to WaterfloodPore VolumeOriginal Oil in PlacePorosity, pAbsolute Permeability y, kRock Compre risibilityInitial Reservoir Pressure

0.700.300.25360 M bbl252 M bbl0.2500 md.000003 psi-i

2000 psia

Relative Permeability Table

Sw KR W

. 3 0

.4 0.01314

5 0.0555

:6 0.129

.7. 0.’2348

.75 0.30

1.0 1.0

“ Fluid Data ‘

Oil ViscosityWater ViscosityPreflush Viscosity

KRH

1.00.6280.33710.1310.01720.00.0

.. ,.. .

l.o.cp1.0 Cp1.0 Cp

Micellar Fluid Viscosity“Polymer ViscosityFormation Volume Factors (All Components)Polymer Content rationMaximum Polymer AdsorptionMixing Parameters (All)Aqueous Densities (at standard conditions)Oil Density (at standard conditions)

Water CompressibilityOil CompressibilitySurfactant Concentration

4.0 Cp4.0 Cp1.0 RB/STB1000 ppm

50 lb/ (acre -ft)1.0

62.4 lb/cu. ft.55.0 lb/cu. ft..0000004 psi- 1.00005. ,ps,i- 1

30,000 ppm

YX45

Capillary Pressure O at all, saturations “

Wi l.O i= 1,2, 3,4,5.

TABLE 2 - ASSIGNMENT OF PERMEABILITIES IN THE FOUR RESERVOIRS

.. .,

.-

Reservoir No. 1

Homogeneouspe rmeabilityof 500 md.-,

kv/\ = 0.1

Reservoir No. 2

Randamly heterogeneous permeability distribution

Mean permeability =500md

Permeability variation, V=O.6 (see Appendix B)

Permeability assigned randomly to each cell (one layer at a time)from 88 permeabilities from a log-normal distribution with V = 0.6.

Reservoir No. 3

Layered heterogeneous reservofz without vertical communication

Mean permeability = 500 md

Permeability variation, V = 0.6

Permeability varies among the layers onlfi each layer has aconstant permeability.

Ayes 1 (top) kx = 500

Layer 2 kx = 740

Layer 3 k= = 205

“Layer 4’ - kx- = ‘-.12z0

Layer 5 (bottom) kx = 340

kv/\ = 0.

Reservoir No. 4

Layered heterogeneous reservoir with some vertical communication.8ame a~ Reservoir No. 3 except vertical communication was per-mitted thrmgh periodic windowc spaced every eight cells in the xdirection staggered from layer to layer so vertical flow cannot trave~more than one cell up or down without flowing ltorizontelly four cells.

No.2

No. 3

No. 4

TABLE 3 - RECOVERY AND DISPLACEMENTRESULTS FOLLOWINGWATERFLOOD AND STANDARJMICELLAR FLOOD

Waterflood IncrementalSurfactant

252

252

252

-.. — .-Flood Recovery Loss of Miscibility**

atWORof 30 Location in Layers 1-5{% of initial (distance from

63.7

63.4

62.6

OilRecovery Unit Displacement*Initial Oil atWORof 30 Effect in Layers 1-5In Place (%ofinitial (distancefrom

Reservoir (Mbbls) oilinplace) injector, feet)

(layer)No. 1 252 63.8 1-450

2-4853-5254 -6085 - swept***

1-3832-4283-4504-5185-548

1 - swept

2 - swept3-2334 -swept5-428

1-4432 - swept3-2634 -swept5-345

23.9

20.2

15.2

oil ~ place) injector, feet)

(layer)28.8 1 -443

2 -4503 - 45a4-4655 -495

1 :4352 -4653 - swept4 -3045 - swept

1 -3832 - swept3 - 1954 - swept5 -278

1 -3152 -4733-3384 - swept5 -240

*’l’he location (feet from the injection well) where the waterflood left mobile oil at l~o above residual oilto waterflood.

#*~he location (feet from the injection well) where the surfactant slug lost miscibility with the oil and two-phaaeflow began.

#**Swept means the layer was swept clean of mobile oil.

TABLE4 - SENSITIVITY OF TERTIARY OIL RECOVERY(Barrels Produced/Barrels Tertiary Oil In Place)

Standard 4% Pv 12% Pv High Low 0.10Micellar

0.025 0.001Micellar Mcellsr Surfactant Surfs.xant Critical Critical Critical

Flood Flood Fkcd Leas Loo, fiaturation Saturation Saturation

Reservoir No. 1

Reservoir No. 2

Reservoir No. 3

Reservoir No. 4

*Lower f$gureg are percent change when compared to standard rnicellar flood in a particulm zeaervoir.

.

TABLE5 - SENSITIVITY OF TERTIARY OIL

Standa d 4% Pv 12% PvMicellar Micellar Micellez

Flood Flood Floodt

Reservoir No. 1 I 3“2813X ‘~,.Reservoir No. 2

2*7’ ‘x 2~3%

2.67/ 7

1.46 -Reservoir No. 3 2:30 ‘

I

PRODUCEDISURFACTANTINJECTED (B!)lS

High Low 0.10Surfactant Surf~ctant Critical

Loee ‘ Loss Saturation

~ ‘z,% ‘:X6%

Reeervoir No. 4~ ‘*70 z% X%.zo z% z%

.

Bbls)

0.025Critical

Saturation

/

3.45

+5%

‘.93

/ +0%

0.001Critical

Saturation

:...

/

3,56

+9%

3.25 ‘

/ + ‘0%

/

2.40

+4%

/

2.10

+24%

*Lower figures are percentchangewhen compared to standard micella r flood in a particular reservoir.

.

/

2.37

+ 3%

/

1.75

+3%

.

~... .i-o 0.25 0.50 0.75 1.0

PREFLUSH EFFICIENCYFig. I - Surfactant loss curvesvs pref lush efficiency.

SCALE: WELL TO WELL INTRAGRID BLOCK INTERGRID SLOCK

MACROSCOPIC

TOTAL SIMULATOR = NUMERICAL DISPERSIONEIMULATOR

DISPERSION DISPERSION + (MiXINGOUETOGROSS FLUIDMOVSMSNT)

FORCS THIS MATCH WITH APPROX_lMATSLYSOUALITY PROPER AX At EQUAL

MACROSCOPIC

TOIAt PHYSICAL = OISPSRSIONREAL RESERVOIR MICROSCOPIC

DISPERSION DISPERSION + (MIXING OUE1OGROS5 FLUIDMCtVEMSNT)

Fig. 2 - Relationships of longitudinaldispersion in the simulator and in thereal reservoir.

Fig. 3 - Variable AY configuration of aa quarter five spot.

●

.

1.0

r

——- ..- ... . —-—- ..- --- ..-_—

(o) ADDITIONAL VOLUME ADDED TOINTEGRAL WHEN CUTOFF IS 0.01 1

0

SURFACTANTSLUG

BRINE I CUTOFF SURFACTANTSAT. = 0.05/ -+

—.— .—_____ . - .—X, DISTANCE IN DIRECTION OF FLOW

Fig. 4- Definition of overlap reg”ion inpreflush study.

o RESERVOIR #1o RESERVOIR #2v RESERVOIR #3& RESERVOIR #4

/ f.

\ ‘—-+4

1 I # f+p++-0 2 4 6 8 10 12

1.0

o

VOLUME PREFLUSH INJECTED (% PV)

Fig. 5 - Resul ts of the pref lush study in thefour reservoirs.

I I 1 I 1 I I I I I I I I I I I

o RESERVOIR #1

o RESERVOIR #2

A RESERVOIR #4

I ~- 1 1 J 4-0 0.2 0.4 0.6 0.8 l.O, 1.2 I*4 1.6

PORE VOLUMES OF FLUID INJECTED AFTER PREFLUSH

Fig. 6 - Standard micel Iar floods.

1.0. I I IGz o STANDARD MICELLAR FLOODm (6.13% PV SLUG) ‘s 0.8 - 0 12% PV SLUG* A 4% PV SLUG

~ 0,6 -

:w; 0.4-

0*S 0.2-

;o 1 10 0.2 0.4 0.6 0.8 1.0 1.2 ‘.4 L6

PORE VOLUMES OF FLUID INJECTED AFTER PRE. “HFig. 7A - I - homogeneous reservoir sensto surfactant slug size.

1.0 -: 1 t I I I I 1 1

k

;o STANDARD MICELLAR FLOOO(O.05) ~❑ 0.10 CRITICAL SATURATION

~ 0.8 - A 0.02S CRITICAL SATURATION~v O.001 CRITICALIn

b SATURATION~ 0.6 ->~u \

u 0.4 -*o*z 0.2 -~w%

o I [ I 10 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

PORE VOLUMES OF FLUID INJECTED AFTER PRSFLUSH .Fig. 7C - I - Homogeneous ressrvoir sensitivityto critical slug saturation.

1.0 1 I 1 I I I I I

*

s o STANDARO MICELLAR FLOOOw o HIGH SU,RFACTANT LOSS~ 0.8 - a LOW SURFACIANT LOSS

.5w*~ 0.6 -*~w* 0.4-*o*z 0.2-s~ [SEE FIGURE I FOR SURFACTANT LOSSw

o~ 1 1 I 10 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

PORE VOLUMES OF FLUID INJECTSD AFTER PREFLUSHFig. 8B - 2 - Randomly heterogeneous reservoirsensitivity to the amount of surfaotant loss.

1.0 - I I I I ( , I I {

5~

o STANDARD MICELLAR FLOOD (6.13% PV SLUG)a 12ZPV SLUG

~ 0.8 - a 4% PV SLUG~uw~ 0.6 -

E

:0.4 -

3P:0.2 -~

so

0 0.2 0.4 0.6 0.8 l+o 1.2 1.4 1,6PORE VOLUMSS OF FLUID INJECTED AFTER PREFLUSH

Fig. 9A - 3 - non-communicating layered reservoirsensitivity to surfactant slug size.

●

c~ o STANDARO MICELLAR FLOODo HIGH SURFACTANI LOSS

G 0.8 -c

A LOW SURFACTANT LOSS~

●

~ 0.6 -

gu: 0.4 -

0●

~ 0,2 - (SEE FIGURE IFORsuRFACTANT LOSS -

&o

0 0.2 0.4 0.6 0.S 1.0 1.2 1.4 1.6PORE VOLUMES OF FLUID INJECTED AFTER PREFLUSH

Fig, 7B - I - homogeneous reservoir sensitivityto the amount of surfactant loss.

1.0 - 1 I I I I I●

zo STANDARD MICELLAR FLOGD

w (6.13% PV SLUG)G 0.8 -= ~ 12% PV SLUG

h A 4% PV SLUG

*:0.2 -F=*g

o- 1 I I 1 I I I0 0.2 0.4 0.6 0.8 1,0 1,2 1.4 1.6

PORE VOLUMES OF FLUID INJECTED AFTER PREFLUSHFig. BA - 2 - Randoml

%heterogeneous reservoir

sensitivity to surfac ant slug size.

1.0r I I I I I I I ( 15z Q STAhU3AR0 MICSLLAR FLOOD (0.0S)w G O.IO CRITICAL SATURATIONu 0.8

://; -

A 0.02S CRITICAL SATURATION~

v 0.001 CRITICAL’ SATURATIONIII*~ 0.6*o~

: 0.4

5*:0.2~~

o0 0.2 0.4 0.6 0.8 1.0 !!2 1.4 1.6

PORE VOLUMES OF FLUID INJECTED AFTER PREFLUSHFig. 8C - 2 - Randomly heterogeneous reservoirsensitivity to critical slug saturdon.

STANDARD MICELLAR FLOODHIGH SURFACTANT LOSSLOW SURFACTANT LOSS

Q

(SEE FIGURE 1 FOR SURFACTANT LOSS CURVES)

01 d“ t I I I 1 1 1 Io 0.2 0.4 0.6 0,8 1.0 1.2 1.4 1.6

?OREVOLUMES OF FLUID INJECTED AFTER PREFLUSHFig. 9B - 3 - non-communicating layered reservoirsensitivity to the amount of surfactant loss.

I 1 I I I I I I Io STANDARD MICELLAR FLOOD (0.0S)u 0,10 CRITICAL SATURATIONa 0.025 CRITICAL SATURATIONv O.001 CRITICAL SATURATION

1J

1 f

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6PORE VOLUMES OF FLUID INJECISD AFTER PRSFLUSH

g, 9C - 3-non-communicating layered reservoirssitivity to critical slug saturation.

I I I I I I I II

o STANDARD MICELLAR FLOOD(6.137S PV SLUG)❑ 12% Pv SLUG& /4~PVSLUE3

I

1 I I [ I I I 10.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

PORE VOLUMES OF FLUID INJECTED AFTER PREFLUSHIOB - 4 - partially communicating layered

-rvoir sensitivity to the amount o? surfactant3.

10 STANDARD MICELLAR FLOODo HIGH SURFACTANT LOSSA LOW SURFACTANT 10SS

I

—

(SEE FIOURSI FOR SURFACTANT LOSSCURVESI1 1 1

‘O 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6PORE VOLUMES OF FtUID INJECTED AFIER PREFLUSH

3. 1! - Influence of high surfactant loss on=covery from the four reservoirs.

1.0 [ I I 1 I I I I 1 I*!i

[

o STANDARD MICELLAR FLOOD (0.05)w ~ 0.10 CRITICAL SATURATIONc 0.8= a 0.02S CRITICAL SATURATION

v 0.001 CRITICAL SATURATION& 1

-191 I

gw

LfdJ?-’---

:0.4 -

5*w*.0.2-=mE

o0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

PORE VOLUMES OF FLUID INJECTED AFTER PREFLUSHFig, IOA - 4 - ~artially communicating layeredreservoir sensitivity to sdrfactant slug size.

(0~~:----5 0,8=

I

7 RESERVOIR #3: A RESERVOIR #4

7*~ 0.6

t

(SEE FIGURE I FOR THE HIGH SURFACTANT LOSS CIIRVE)

> I

i 2<: ~~LAo 0,2 0.4 0.6 0.8’ 1.0 1.2 1.4 1.6

PORE VOLUMES OF FLUID INJECTEO AFTER PREFLUSHFig. IOC - 4 - partially communicating layeredreservoir sensitivity to critical slug saturation.

3000I I , ) I ! I I I

1-CUM. PROB. k— -116.633.350.066.783.3

20s

/M

340500 o~740 &o

1220

v=kD-k

ko

,oL&&EYYl1 10 50 80 90 99

CUMULATIVE PROBABILITY DISTRIBUTIONFig. B-1 - The selection of five permeabil itiesfrom a log-normal distribution.