Society of Petroleum Engineer'S

SPE 1...... "' ...........

Fifth Comparative Solution Project: Evaluation of MiscibleFlood Simulators

Inst. of Technologyr"m'u\.l I.lll , ARCO Oil & Gas Co., and C.A. Kossack,by J.E.

SPE Members

Copyright 1987, Society 01 Petroleum Engineers

This paper was prepared for presentation at the Ninth SPE Symposium on Reservoir Simulation held in San Antonio, Texas, February 1-4, 1987.

review of information contained in an abstract submilled by the01 Petroleum and are SUbject to correction by the

of Petroleum its or members. Papersof Engineers. to is

The contain 01Box 833636, Richardson, TX Telex,

ABSTRACT

This paper presents the results of comparisonsbetween both four-component miscible flood simulatorsand fully compositional reservoir simulation modelsfrom seven different participants for a series ofthree test cases. These cases varied from scenariosdominated by immiscible conditions to scenarios inwhich minimum miscibliity pressure was maintained orexceeded throughout the simulations. In general,agreement between the models was good.

For a test case in which reservoir pressure wasmaintained above the minimum miscibility pressure,agreement between simulators, with theassumption of complete miXing of solvent and oil, andcompositional simulators was excellent based oncumulative oil production as a function of cumulativewater injection. For cases in which immiscibleconditions dominated, the four-component modelstended to be pessimistic compared to fullycompositional models because condensible liqUids werenot considered to be carried in the gaseous phase inthe four-component simulations. Relativepermeability treatment, especially near the injectionwell, tended to the timing of recovery and

. injectant br'eakt:hI-murlJ..

The simulation of gas or solvent injection intoa volatile oil reservoir can be modeled byapproximating the phase behavior with four components- oil, water, free/solution gas, and injection gas

(solvent)- as described by Todd and Thisprocess can also be modeled by accurately simulatingthe phase behavior with n-components whose K-valuesare complex functions of pressure, temperature. andcomposition. A precise set of rules of when one mayapproximate the displacement process with fourcomponents and when one must use the fully

and i lustrations at end of Paper.

compositional formulation is not generally available.There is much discussion in the technical communityof exactly this problem. but all too often thedecision of which model is used comes from time,money, computer, or data availability or purelysubjective reasons. Thus, this comparative solutionproject has attempted to present an opportunity forthe petroleum simulation community to investigatesome aspects of this question and at the same timeprovide an attempt to validate two types of reservoirsimulators under certain conditions. Aswas said in the Fourth SPE Solution

Project,2 "good agreement between results fromdifferent simulators for the same problem does notinsure validity of any of the results, (but) a lackof agreement does give cause for some concern."

This paper represents the fifth in a series ofcomparative solution problems which have been openfor participation by oil companies, researchinstitutes, and consult~ts_ The first study was

conducted by and consisted of athree-dimensional, two-phase, black-oil simulation.

Chappelear and a study ofthree-phase. single weI radial cross-sectionalconing simulations. A compositional, three-phasestudy of gas cycling in a retrograde gas condensatereservoir comprised the third comparative solution

project organized by Kenyon and Behie. 5 The mostrecent comparative solution problem conducted by

Aziz. Ramesh, and was a two-dimensional radialsteam injection (thermal) simulation.

The object of this paper is to present thesimulation problems and selected results as submittedby the participants and to discuss any largedifferences which exist in the results. Sevenparticipants were involved in this project. Anattempt has been made to describe the problems andthe input to the simulators in such a fashion thatall of the appropriate variables for each participant

55

2 FIFTH COMPARATIVE SOLUTION PROJECT: EVALUATION OF MISCIBLE FLOOD SIMULATORS SPE 16000

(1) For scenario one the average reservoirpressure declined rapidly below theinitial saturation pressure for mostof the simulation.

For scenario two the average reservoirpressure was maintained well above theoriginal saturation pressure and in thevicinity of the minimum miscibilitypressure for the entire simulation.

The oil contained the following mole percents:50% , 3% 7% 20% 15% and 5%

( See Appendix. ) ObViously, these compositionsrepresent an extremely light oil. The injectantgas/solvent contained 77% , 20% and 3%

component was added to the

Figure 2 depicts the typical average reservoirpressure response for the three scenarios. As shownin figure 2, the main difference between scenariosone and three is the rapidity in which averagereservoir pressure is raised from natural depletionconditions to minimum miscibility conditions. Theminimum miscibility pressure is in the range of 3000to 3200 psia, depending on the definition used, andthe initial saturation pressure for the reservoir oilis 2300 psia. A detailed description of thereservoir and fluid properties and the scenarios isgiven in the Appendix and in Tables 1-9.

For scenario three the average reservoirpressure initially declined below thesaturation pressure. Rapid overinjectionrepressured most of the reservoir to apoint near the minimum misciblitypressure.

The four-component fluid description containeddetails necessary to simulate the three scenarioswith a standard four-component. mixing parameter

model as described by Todd and Togenerate the "black-oil" PVT properties thatcorrespond with thePeng-Robinson equation-of-statecharacterization, constant composition expansions anda differential liberation were simulatedfor both the reservoir fluid 1) and the injectiongas/solvent. In Tables 6 through 8 these results are

C~~ULCU as if they were experimental results from alaboratory. The participants generated the

required PVT data for their model fromthese tables. An example of ARCO's four-componentmodel PVT data ( Table 9 ) was included as referenceto aid the particiPants.

The fluid description was a sixcomponent (PR) characterization.

See Tables 4 an 5. ) All acentricL"ictnr~, binary interaction , andequations coefficients were given. The specificationof all equation-or-state parameters eliminateddifferences in charaterization and phase matches inthe phase behavior results.

injection gas so the fluid system would reach acritical point and become single phase as might beexpected in a condensing gas drive mechanism.Without the in the gas, this system, in a linear

displacement, exhibited the combined

condensing/vaporizing mechanism described by Zick.6

( See Table 5. ) The

have been well defined. The hope was then that anydifferences seen in the simulation results would becaused by differences in the simulators or bydifferences in the input data that were intentionallyleft to the discretion of the engineer making thesimulation.

Three injection and production scenarios weredesigned to test the abilities of theand compositional models to simulate the WAG wateralternating gas) injection process into a Ieoil reservoir. One reservoir desciption was used inall simulations. The problem did not necessarilyrepresent a real field application or real fluids. A7 by 7 by 3 finite difference grid was used as shownin Figure 1. Both the coarse grid and the extremely

reservoir oil were chosen to allow the problemto simulated in a reasonable amount of computertime with a fully-compositional simulator. Thecoarseness of the grid produced significant numericaldispersion and/or grid orientation errors for all ofthe models which were compared. Obviously, for amore realistic simulation, grid refinement ororientation studies might be necessary to betterquantify these errors. During the develOPment of theproblem, a comparison of results from more finely

four-component models was considered;hOl~e,rer, for between the four-componentand composi models it was decided to use asingle coarse grid, ignoring numerical dispersioneffects.

Three production/injection scenarios were givenfor the comparative problem. The discussion of theresults for each scenario includes a comparison ofresults submitted from both four-component andcompositional simulations. These comparisons give usa look at the validity of the models for a givenscenario. COmParisons of typical four-componentresults with compositional results show us thedifferences between the two types of simulators forthe various scenarios. A complete set of graphicaland tabular results from all of the participants forthe three scenarios can be obtained from the authors.

Each participant was requested to submitsimulations of each scenario from a four-componentsimulator and/or from a compositional simulator.Along with each simulation result, the participantwas requested to explain, in a few sentences, whichsimulator he would choose for each scenario. Sincethis was an engineering judgement. there is no rightor wrong answer to the choice of simulator or thereason for the choice.

The three scenarios involve one WAG injectionwell located in the grid block with i:1. j:l. andk:1, and one production well located in grid blocki=7, j:7, and k=3. The production well isconstrained to produce at a maximum oil rate of 12000SIBID. The minimum bottom hole pressure for theproduction well was varied among the scenarios. Alimiting COR of 10 MCF/SfB and a WOR limit of 5SIB/SIB were used for the shut-in criteria for thesimulations. The WAG injection schemes andproduction constraints were altered to give thefollowing properties:

56

SPE 16000 J. E. KILLOUGH, CHARLES A. KOSSACK 3

In most four-component models there are 3 to 5parameters or switches which must be set by the userto control the model's calculation of the change fromimmiscible to miscible conditions. The selection ofthese parameters affects the ability of thefour-component model to emulate the immisciblelmiscible process. Participants were required tospecify the miscibility parameters for theirparticular model based on the recoveryversus pressure data given in the appendix for theslim tube . ( See Figure 3. ) A furtherdiscussion these parameters is given in thesection on the description of the participants'models.

The fol sections describe the reservoirsimulators were used by the forthe comparative solution project.four-component or miscible flood simulators werebased on the original work by Todd and Longstaff.The compositional simulation models with theexception of the TDC model used an internalPeng-Robinson equation-of-state for phasecalculations. Further information aboutsimulators is available from the participants."Five-point" finite differences were used by allparticipants.

The ARCO miscible flood reservoir simulator isbased on a formulation. (SeeReference 7. ) This formulation allows for thetreatment of condensation or vaporization of liqUidsin gas condensate or volatile oil systems. The modelhas options for either IMPES or fully-implicittreatment of the finite difference Formiscible gas injection situations Todd-Longstaffmixing parameter formulation is used to account forvicous For the cases reported here theIMPES was employed. Three phase oilrelative permeabilities were based on a normalized

version of Stone's method I.S For pressures abovethe "miscibility" pressure, the oil relativepermeability from the water-oil two phase data ( k

row) was used for the solvent and oil phases. Singlepoint upstream weighting of phase transmissibilitieswas used, although other schemes are available. Apreconditioned generalized conjugate residual methodwas used for the linear equations solution.

The ARCO compositional simulator is a modifiedversion of s COMP II

The convergence of the phase eqUilibriacalculations is based on the use of the GeneralDominant Eigenvalue Method for nonlinear

For the comparative solution cases,

Stone's method 11 11 was used for three phase oilrelative permeabilities. A maximum trapped gassaturation of twenty percent was used for imbibitiongas relative permeabilities. Single point upstreamweighting is used for transmissibilities. D4 Gausswas used for all cases for the linear equationsolutions.

57

British Petroleum used a modified version ofScientific Software-Intercomp's COMP II reservoirsimulator for the solutions. Two modifications whichwere used included the extended Todd-Longstafftreatment and an associated modification to therelative permeabilites.

For the extended Todd-Longstaff model thehydrocarbon phase existing in each grid block ispartitioned into two , "oil" and"solvent", The phases are assumed to flow asindependent miscible phases wi their densities andviscosities given not by their composition. butthe mixing rules proposed by Todd and Longstaff. Thesaturations of the pseudo phases are found by

that the composition of the pseudo oil isknown usually the initial oil composition) andthat one of the components acts as a tracer of thepseudo-oil saturation. Any remainingafter the pseudo-oil phase been subtractedcomprise the With two components ina simulation formulation reduces to preciselythe original Todd and Longstaff model.

The parameters for the extended Todd-Longstafftreatment are the mixing w and thepseudo-oil composition. the comparativesolutions the pseudo-oil c(J,m-PK)siition is assumed to bethe initial oil composition component C20 is usedas the tracer.

For the comparative solution cases D4 Gauss andsingle point upstream weighting of phasetransmissibilities were used.

The results from BP were reported for twosimulations: standard treatment of compostionalphenomena ( "BP COMP I") and the extendedTodd-Longstaff approach ( "BP roMP

For the four-component cases Computer ModelingGroup's lMEX. four-component, adaptive-implicit,black-oil model was used with the pseudo-miscibleoption. This option assumes that solvent maydissolve in water but not in the oil phase similar tomost of the other four-component-type models in thispaper. The Todd-Longstaff mixing parameter approachis used.

The compositional runs were performed usingCMG's adaptive-implicit model GEM. Asemi-analytical approach was used to decouple theflow equations from the flash equations. Aquasi-Newton methed ( QNSS ) was used to solve theresultant flash equations. To insure rapidconvergence, the fully coupled well equations weresolved simultaneously with flow equations using aNewton Raphson procedure.

Preconditioned generalized conjugate gradientsand single point upstream weighting were used for thesolutions given in this paper. A modification toStone's three phase oil relative permeabilitytreatment was used.

Chevron

The Chevron miscible flood simulator ("four-component simulator" is a fully-implicitthree-component model on the concepts outlined

4 FIFTH COMPARATIVE SOLUTION PROJECT: EVALUATION OF MISCIBLE FLOOD SIMULATORS SPE 16000

by Todd and Longstaff. As opposed to the othermiscible flood models in this paper, the Chevronsimulator does not include a free gas component. TheChevron compositional model is a fully-implicit.equation-of-state model. For both miscible flood andcompositional simulations. banded gaussianelimination and single point upstream weightedtransmissibilities were used. For the miscible floodsimulation Stone's method II was used for three phaserelative permeabilities: for the compositionalsimulations a modification to Stone's method wasused.

The simulations by Energy Resource ConsultantsLimited and Atomic Energy Research Establishment,Winfrith, were performed on a four-component versionof the PORES black-oil simulator. PORES has bothIMPES and fully-implicit options available. TheTodd-Longstaff mixing parameter approach is used forsimulation of miscible conditions.

precipi tate.

The mode1 uses an IMPES approach enhanced wi th astabilized Runge-Kutta time discretization. Animplicit saturation option in thcx-, y-, and/or z­directions is also available. Two-point upstreamweighting of the transmissibilities and D4 Gauss wereused for the comparative solutions. weregenerated as a function of pressure. and Cl and C3concentrations.

For the fully compositional simulations, theK-values for the five volatile components, and molarvolumes for all components were generated usingHagoort and Associates' equation-of-state basedprogram "PvrEE". For the four-componentrepresentation. the stock-tank oil and the separatorgas are represented by two pseudo in thenormal black-oil fashion except that solutiongas-oil ratios, formation volume factors, densities,and viscosities are represented with K-values, molardensities. mol-weights, z-factors. etc.

SORM4

0.3000.2300.1100.0380.000

1800.2400.2800.3000.3400.

PRESSURE

The comparisons of results for the variousscenarios are presented in the follOWing sections inthree manners. First. the results from thefour-component f simulators arecompared. Next. compositional model results areexamined. Finally, a brief comparison is madebetween typical four-component and compositionalresults.

Several different treatments were used formiscibility conditions in the various Todd-Longstaffformulations presented here. The AROO model used asingle value of the miscibility pressure equal to3000 psia for the switch to miscibility conditions.A "ramp" condi tion was available but not used. )mixing parameter w was set to a value of 1.0corresponding to complete mixing of oil and solvent.CMG also used a parameter equal to 1.0. ForCMG. miscibility tions were allowed to vary withpressure in a linear fashion from completelyimmiscible conditions at 2300 psia to fullmiscibility at 3000 psia. Chevron used an w equal to0.7 for miscible flood simulations. The Chevronresidual oil to solvent flood SORM4) was variedwith pressure according to the lOWing table:

ERC used a miscibility pressure of 2800 psia. Themixing parameter for ERC was set equal to 0.5 for allruns. The TDC miscible flood simulator used amiscibli ty pressure linear "ramp" from 1500 to 3200psia with a mixing parameter of 0.6 .

As indicated above. scenario one involved a WAGinjection case in which the reservoir pressureremained substantially below both the initialsaturation pressure and "miscibility" pressure for

Todd. Dietrich. and Chase used their Multiflood

Simulator13 for the comparative solution cases. Thissimulator has been designed to reproduce the effectsof major mass transfer and phase transport phenomenaknown to be associated with the miscible floodprocess with particular emphasis on enhanced oil

recovery. For immiscible conditions, phaseeqUilibria may be input to the simulator to representenhanced oil recovery mechanisms of oil phaseswelling with condensed solvent, and vaporization ofhydrocarbon fluids into the solvent-rich phase.

For the comparative solution cases thefully-implicit option was used. Gas relativepermeability hysteresis and three oil relativepermeabilities by Stone's method were employed.

Reservoir Simulation Research Corp. incorporatedan IMPES-type equation-of-state compositional modelfor the simulations. Single point upstream weightingand redlblack line SOR were used in the resultspresented here. Reference 12 gives further detailsof this simulator.

Although multiple contact miscibile displacementmay be represented explicitly with the programthrough the use of appropriate equilibriumdata, the philosophy of the program for simulatingmiscible displacement processes is to maintainsegregated solvent-rich and oil-rich regions. Thedegree of segregation is controlled by a mixingparameter approach to account for viscous fingeringphenomenon.

The simulator treats seven components which maypartition among three phases: liquid hydrocarbon. gasor solvent rich phase. and aqueous phase. The brinecomponent is confined to the aqueous phase. Five ofthe six remaining components are allowed to partitionbetween the non-aqueous phases as determined by theinput K-values. In addition to pressure. K-valuescan depend on key component concentrations. Onecomponent may partition into the aqueous phase. Oneof the components is non-volatile. but may

58

SPE 16000 J. E. KILLOUGH. CHARLES A. KOSSACK 5

almost the entire simulation. qualitatively similar.

is the oil relative permeability from the

Comparison of Results for Scenario Two

Scenario two represents a case in which thereservoir pressure was maintained near or above theminimum miscibility conditions.

these treatmentsinjectivi ty andtimings for

where krowwater-oil two phase data. Each ofleads to a substantially differentcan cause the major differences in

The large variation of water injection rate bythe participants is probably the result of differentgas/solvent relative permeability treatment near theinjection well. There are at least two possibilitiesfor injection well permeabilities. First. an"upsteam" relative permeability could be assumed inwhich all nearwell saturations are assumed to be at100% of the injected phase saturation or at residualsaturations. For the other possibility, a totalmobility of phases in the injection grid block couldbe used. For the total mobility treatment therelative permeabili used for the gas/solvent hasthree possibilities: 1 drainage gas relativepermeability, tion gas relativepermeability, imbibition for gas/solvent.

Figure 13 gives the results for the cumulativeoil production versus time for the four-componentmodels in scenario two. As shown in this figure.there is a marked deviation between the TDC model andthe other participants. The ARCO and CMG results aresimilar to one another. and the ERC and Chevronresults are higher than the others. Thesedifferences in results can be easily resolved. Aplot of cumulative oil prodution versus cumulativewater injection as shown in figure 14 shows that thefour-component models fall into two groupings. TheCMG and AROO results are still close to one anotherbut higher that the other particiPants. Thedifferences in results can now be explained in aconsistent manner by the value of w which was used bythe participants. Both CMG and AROO used values of1.0 for w in an attempt to obtain a comparison withcompositional model results. Chevron, ERC, and TDCused values of 0.6. 0.5, and 0.7. respectively. toshow the effect of possible viscous fingering onrecovery. The differences in miscibility n~·~~e"r~

treatment as described above appears to a minoreffect on results since a higher value of w for theChevron model resulted in a slightly lower recoverythan predicted by IDe. The TDC model used thehighest value of pressure for complete miscibilty tooccur. This resulted in lower overall recovery.Figures 15 and 16 show GOR and WOR as a function oftime. Implicit in this is the fact that

- timing of high WOR and is dependent on theinjection volumes. Since both Chevron and ERCinjected substantially greater volumes of water at agiven time than the other • waterbreakthrough and high GOR occurred earlierin their simulations compared to the others. Theaverage reservoir pressures shown in Figure 17indicate the effect of the greater volumes ofinjection for Chevron and ERe resulting in higherpressures for their simulations. As shown in Figure17 the average pressures for all participantsexceeded the minimum misiciblity conditionsthroughout the simulations of scenario two.

The scenario one compositional simulator resultsfor all participants compared somewhat better thanthe four-component models. Figure 9 comparescumulative oil production for the compositionalmodels. As shown, the results were quite similar forall participants with deviations of only ±3%. TheChevron and RSR models do tend to produce slightlylonger than other participants' models beforereaching the maximum GORIWOR limits, although all hadcomparable total oil recoveries. Figures 10 and 11show WOR and GOR behavior for the compositionalmodels for scenario one. These figures indicate thereason for the longer period for the RSRand Chevron models. water breakthrough andhigh GOR production occurred at approximately thesame time for all models, both the RSR and Chevronmodels show a slower rise in both GOR and WOR withtime. Again, this may be the result of a differentoil relative permeability treatment at the productionwell for these two models. As shown in Figure 12,average reservoir pressure for all models behavedsimilarly.

Figure 4 compares the cumulative oil productionfor all of the four-COmponent models. Two things areevident from this figure. First, cumulative oil

for the Chevron model is substantiallythe results for the other particiPants. This

can be explained the inability of that model tocorrectly account the evolution and production ofdissolved gas. The second point is the continued oilproduction of the CMG model after the other threemodels have ceased production due to excessiveproducing gas-oil ratio. An analysis of the GOR andWOR behavior for this case as shown in Figures 5 and6 gives a clearer indication of the differences inthe results. The GOR behavior shown in Figure 5indicates that the Chevron of ignoringdissovled gas results in a lower GORfor the early time period of the simulation. It isinteresting to note that the Chevron results do showgas breakthrough at about the same time as most ofthe other models. Figure 6 shows that the CMGfour-component model had water breakthrough at theproducer at about the same time as the other models.The slower increase in both WOR and GOR for the CMGmodel after breakthrough may result from the use of adifferent oil relative permeability treatment fromthe other participants since oil saturation variationwith time at the center of the top layer is similarin the different models. ( See Figure 7. ) As shownin Figure 8 the average reservoir pressures for allof the models were similar with the exception of theChevron results.

Figures 9-12 also show a comparison of a typicalfour-component model ( ARCO limited-compositionalmiscible flood simulator) with the compositionalmodels for scenario one. In general. thefour-component models tend to be somewhat pessimisticin oil recovery compared to the compositional modelsdue in part to the assumption that the four-componentmodels cannot carry an oil component in the gasphase. Because some oil vaporization oil did occur inscenario one in the compostional simulations, thefour-component GOR behavior is somewhat higher thanthe compositional models especially after solventbreakthrough. Water breakthrough. high GOR behavior.and average reservoir pressures for bothcompositional and four-component models tend to be

59

FIFTH COMPARATIVE SOLUTION PROJECT: EVALUATION OF MISCIBLE FLOOD SIMULATORS6

results as discussed above.

For scenario two the cumulative oil productionsversus time for compositional models ( Figure 18 )showed a substantial deviation for all of theparticipants. Again, cumulative oil production as afunction of cumulative water injection removes mostmajor differences in the results as shown in Figure19. The deviation of the TDC results from the otherparticipants is probably due to the differenttreatment of behavior in the TDC model comparedto the equation-of-state models for theother In the TDC model, as descibedabove, heaviest component is not allowed tovolatilize. In addition, K-values are table lookupsas a function of pressure and key-campon.en.tcompositions. As shown in Figure the BP modelwith the extended Todd-Longstaff approach ( "BP mMPII" ) gives somewhat lower recoveries due to theincomplete mixing of "solvent" and "oil"phases. The standard treatment by BP ( mMP I" )gave results similar to the other participants.

The marked deviation of the timings of theresults is again likely due to the near welltreatment of gas/solvent relative permeability. Boththe BP and RSR results use drainage gas relativepermeabilities for calculation of near-wellinjectivity. ARm used a combination of k

rowand

imbibition gas relative permeabilities depending oninterfacial tensions, and CMG used k for the

rownear-injection well conditions. Each of thesetreatments leads to substantially differentinjectivities. Figures 20 and 21 show that the GORand WOR behavior for the scenario two compositionalcases. As shown in 22 the average reservoirpressure of the BP, and RSR models wassomewhat higher due to the larger volumes of waterinjected. of oil saturations at center ofthe top layer Figure 23 ) indicates the differencein results caused by the approximate phase behaviortreatment in the TDC model.

SPE 16000

the results. For the other • the lengthof the simulations differs somewhat todifferences in GOR behavior. Oil production for theCMG case continues longer than any of the otherparticipants. Figures 26 and 27 indicate that themain reason for the differences may be a minordifference in relative permeability treatment at theproducer for the CMG case. Both GOR's and WOR'sbegan increasing at the same time for all modelsexcept the Chevron model. The WOR climbed somewhatmore slowly for the CMG model in turn causing the GORmaximum to be reached well after the other models.As shown in Figure 28, average reservoir pressureshowed a somewhat more erratic behavior due to theseverity of the injection rates in this case.

Compositional results for scenario threecumulative oil versus time showed a substantialdeviation among the participants ( See 29. )The plot of cumulative oil production versuscumulative water as shown in Figure 30shows that the from all participants arecomparable. The main difference among the models wasthe of time until the GOR limit criterion wasmet. shown in Figure 31, GOR's for all modelsbegan to climb above 2 MCF/STB at approximately thesame time; however, GOR for the CMG and TDC modelsappeared to rise at a slower rate than the othermodels. Again, this may be the result of the use ofdifferent treatments. As shown in Figure32, WOR for all models was similar withbreakthrough occurring at about the same time.Average reservoir pressure results for thecompositional models were again erratic as shown inFigure 33.

As shown in Figure 31, the main difference inthe results for scenario three between thefour-component and compositional models is the higherCOR for the four-component models during years 2-8.Again, this is probably the result of the simplisticphase behavior assumptions of the four-componentmodels for this comparative solution project.

The comparison of simulator efficiencies isbased on three criteria reported by theNumber of time steps,. number of nonlineariterations, and CPU time. Since the total number of

to simulate a given case varied widelyespecially for scenario two) , the length of the

simulation should be taken into account whencomparing results.

Table 10 compares the CPU time for the differentcases. As shown in this table, a variety ofcomputers were used. For the cases which employedthe Cray computer, a reasonable comparison of CPUtimes can be made.

Figures 18,20-23 show a compari son of ARm'sfour-component results with compositional results forscenario two. The results appear qualitativelysimilar; the CMG compositional and AROOfour-component results are almost the same. Figure24 is a plot of cumulative oil production versuscumulative water injection for scenario two for theAROO and CMG four-component and compositional models.As shown in this figure the results are almostidentical. The small deviation that does exist isthe result of a slighlty smaller volume of solventinjection in the ARCO model. The useof complete mixing ( w = 1.0 in both the AROO andCMG four-component models does give solutions thatare comparable to the compositional results.

Four-component model results for scenario threereflect a behavior similar to the results forscenario one since immiscible conditions dominate theproduction behavior for this case.

As shown in Figure 25 cumulative oil productionfor the cases was similar with the exception of theChevron model. Again. the inability of the Chevronmodel to handle the production of gas which hasevolved from solution causes the major differences in

Tables 11 and 12 compare total number of timesteps and outer iterations for eachparticipant for all of the cases. In general, thenumber of outer Newtonian iterations varied betweentwo to four for each time step for all participants.The lower totals for the number of time

to fully-implicit treatments whi thelarger number is more representative of the IMPESmodels.

These results do not necessarily represent

60

SPE 16000 J. E. KILLOUGH. CHARLES A. KOSSACK 7

1. C. S. van den BergheBritish Petroleum Research CentreChertsey RoadSunbury-on-ThamesMiddlesex TW16 7LN

2. Aziz, K.• Ramesh, B., and Woo, P. T., "Fourth SPEComparative Solution Project: A ofSteam Injection Simulators", SPE presentedat the Eighth SPE on ReservoirSimulation, Dallas,

3. Odeh, A. S., "Comparison of Solutions to a Three­Dimensional Black Oil Reservoir SimulationProblem, ,. ~et. '!leek .. pp 13-25 1981).

4. Chappelear, J. E., and Nolen, J. ,"SecondComparative Solution Project: A Three-PhaseConing Study", Proceedings of the Sixth SPE

on Reservoir Simulation, New Orleans31-February 3,

5. D. E., and BeMe. A., "Third SPEComparative Solution Project: Gas cycling ofRetrograde Condensate Reservoirs." Proceedings ofthe Seventh on Reservoir Simulation.San Francisco 15-18.

6. Zick. A. A., Combined Cond'en!sirlglVapoJriMechanism in the Displacement of Oil by EnrichedGases", SPE 15493 presented at the 60th AnnualSPE Fall Conference and Exhibition, New Orleans,October 5-8, 1986.

7. Bolling, J. D., "Development and Application ofa Limited-Compositional Miscible FloodSimulator". SPE 15998 presented at the Ninth SPE

on Reservoir Simulation, February 1-4.

8. Stone, H. L. "Probability Model for Estilnait;irlgThree-Phase Relative Permeability", Trans.249 (

9. Coats, K. ,"An Equation-of-State tionalModel", SPE 8284. presented at the 54thFall Conference and Exhibition of SPE, AlME. LasVegas. Nevada, 23-26, 1979.

10. Crowe, C. M. and M. "ConvergencePromotion in the Simulation of Chemical Processes- The General Dominant Eigenvalue Method," AlatE,. 21 , 528-533.

11. Stone, • "Estimation of Three-Phase RelativePermeability and Residual Oil Data," ,. ~alL '!I'et.'!leek., 12), No.4, pp 53-61 (

12. Young, C., "Equation-of-State tionalon Vector Processors," SPE 16023

presente,d at the Ninth SPE Symposium on ReservoirSimulation. New Orleans, February 1-4,1987.

13. Chase, C. A.• and Todd, M. R., "NumericalSimulation of Flood Performance,"

December, 1984, 596-605.

The authors would like to express theirappreciation to the fol participants whoprovided the data used in paper:

Compositional results were similar for allparticipants for scenario one. For scenarios two andthree, differences existed among the compositionalresults primarily due to differing solvent and waterinjectivi ties.

The results presented in this paper showed thatsimulations for scenarios one and three gavecomparable results among the various participants forfour-component models. For scenario twofour-component results show deviations in recoveryversus time due to different injection volumes andmiscibility parameters for the participants.

Comparisons of four-component and compositionalresults showed that for scenario two the mbdels werein good agreement. For the cases dominated byimmiscible conditions ( scenarios one and three ),the four-component models tended to be somewhatpessimistic due to asumptions concerning the phasebehavior in the four component models.

The discussion of the previous section indicatesthat for scenario two, in which minimum miscibilityconditions were exceeded during the entire simulationfor most grid blocks, four-component results withcomplete mixing gave excellent agreement withcompositional results. If viscous fingering is adominant mechanism, the use of a Todd-Longstaffapproach ( or extension may give more realisticanswers in these situations.

CDNCLUSIONS

simulations as far as efficiency isconcerned. The emphasis for the comparative solutionwas on the accuracy of results rather thanefficiency.

Based on the results given above it is possibleto comment on the appropriate model for a givensimulation case. The compositional formulationappears to give somewhat more accurate results forthe cases in which some of the reservoir oil isvolatilized into the gaseous phase ( scenarios oneand three). The presence of oil in the gas phaseresults in a more realistic recovery for theco>mplQs;itional case. A four-component model which

some form of volatile component in the gasphase could produce results similar to those for the

models; however, this was notinvestigated in this paper.

These results indicate that for situations inwhich injection rates are limited by bottomholepressure constraints, care should be taken in thecalculation of near-well phase mobilities andrelative permeabilites. Three phase relative...",rnlO":Olhi Ii ty treatments near the producer may haveaffected the results of the four-component models toa lesser extent.

REFERENCES

1. Todd, M. R. and Longstaff, W. J., "TheDevelopment, Testing, and Application of aNumerical Simulator for Predicting Miscible FloodPerformance", ,. ~et. '?Jeck., July, 1972.

2. W. ChenChevron Oil Field Research CompanyP. O. Box 446La Habra, California 90631

61

8 FIFTH COMPARATIVE SOLUTION PROJECT: EVALUATION OF MISCIBLE FLOOD SIMULATORS SP!!: 16000

0.0 to <91.25 Days Water Inj. plus

3. Yau-Kun LiComputer Modelling Group3512 - 33 Street N. W.

Alberta T2L 2A6Canada

4. C. D. FernandoEnergy Resource Consultants Limited15 Welbeck StreetLondon WIM7PFEngland

Oil production at 12000 STB oil perminimum bottomhole ofinjection at time on acycle. Injection Bottomhole Pressuremaximum, Gas Rate::: 20,000 MCF/D,Water Rate:::: 45,000 STB/D.

day with aBegin WAG

month WAG4,500 psia

5. L. C. YoungReservoir Simulation Research Corp.1553 East Nineteenth StreetTulsa, Oklahoma 74120

6. M. R. ToddTodd, Dietrich, and Chase, Inc.16000 Memorial DriveSuite 220Houston. Texas 77079

We especially thank Mike Todd for his helpfuldiscussions and comments.

The three cases used for both the four-componentand compositional comparisons were based on the 7 by7 by 3 finite difference grid sbown in Figure 1. Thegrid and reservoir description are similar to thatused in the first comparative reservoir simulation

project by Odeh. 3 Two wells, one for production andone for injection, were located in te cornersof the grid. For compositional sixcomponents were used for the hydrocarbon fluids. Thethree cases all involved alternate of waterand an enriched methane solvent. 1-9 presentthe details of the model input data.

Scenario One

Oil production at 12ooo.STB oil per day with aminimum bottomhole pressure of 1000 psia for twoyears wi th no injection. At year 2. begin WAGinjection with a one year cycle. Maximum InjectionBottomhole Pressure::: 10,000 psia.Gas Rate::: 12,000 MCF/D • Water Rate: 12000 STB/D.

0.0 to {2.0 Years Production only2.0 to {3.0 Years Water Inj. plus

Production.3.0 to (4.0 Years Gas Inj. plus

Production.4.0 to <5.0 Years Water Inj. plus

Production.5.0 to (6.0 Years Gas Inj. plus

Production.6.0 to <7.0 Years Water Inj. plus

Production.7.0 to <8.0 Years Gas Inj. plus

Production.~ ~ .................... e ......

62

91.25 to <182.5 Days Gas Inj. plusProduction.

182.5 to (273.75 Days Water Inj. plusProduction.

273.75 to <365.0 Days Gas Inj. plusProduction.

365.0 to <456.25 Days Water Inj. plusProduction.

456.25 to <547.5 Days Gas Inj. plusProduction.

................

.............. ..

Oil production at 12000 STB oil per day with aminimum bottomhole of 1000 psia. Productiononly for one year, production plus waterinjection only for one year. Begin WAG ;o.~~;·~~

time 2.0 years on a standard three monthInjection Bottomhole Pressure: 4,500 psia maximum.Gas Rate::: 30,000 MCFID, Water Rate::: 45,000 STB/D.

0.0 to (365.0 Days Production Only365.0 to (730.0 Days Water Inj. plus

Production.730.05 to (B21.25 Days Water Inj. plus

Production.821.25 to (912.5 Days Gas Inj. plus

Production.912.5 to <1003.75 Days Water Inj. plus

Production.1003.75 to <1095.0 Days Gas Inj. plus

Production... a ~ ..........

.. ~ .. .. .. ......

TABLE IReservoir Data. for the Model Problems

16000TABLE 2

Reservoir Data By Layers

Water Compressibi 1 i ty

Rock Co''l'r'essibi 1UoyWaterWater Viscosi ty

Reservoir Temperature

with 3= 62.4"'" 38.53 Ib/cuft= 68.64 Ib/MCF

:: 3.3 x 10-6 psi-1

-6= 5.0 x 10Factor = 1.000

=0.70cl'

"F

Layer

500.0

50.0

200.0

50.0

50.0

25.0

0.30

0.30

0.30

20.0

30.0

50.0

Reference Depth :::; 8400.0 ft

Oil Formation Volume Factor=:; -21.85 x 10-6 RB/STB/PSISlope Above Bubble Point

lni tial Pressure at ReferenceDepth = 4000,0 psia

Separator Condi tions (FlashTemperature and Pressure)

Reservoir OilSaturation Pressure

OF

psia

:;;; 2302.3 psia

TABLE 2 (Continued)Reservoir Data By Layers

Layer Initial InitialS

w S0

8335. 3984.3 0.20 0.80

8360. 39!.lO.3 0.20 0.80

8400. 4000.0 0.20 0.80

Initial Water Saturation '= 0.20OU Saturation ::::: 0.80

Grid Block Dimensions "" 500 ft ftReservoir Data by Layers (See TableNo

Gas Saturation

Wellbore Radius ::::: 0.25 ftWell Kh = OO.0סס1 md/ftWell Located in Center of Grid Cells.Production Well In layer 3 Only.WAG at In Layer 1 Only.

Conditons:COR Limi t of 10.0 MCFISTBWOR Limit of 5,0 MCF/STBMaximum Time of Simulation:::::: 20 Years

TABLE 3Relative Permeabili ty and Capillary Pressure Data

Sw Pcow krw krow0.2000 46.0 0.0 ooסס.1

0.2899 19.03 0.0022 0.67690.3778 10.07 O.OlSO 0.41530.4667 4.90 0.0607 0.21780.S556 1.80 0.1138 0.08350.6444 0.50 0.2809 0.01230.7000 0.05 0.4009 0.00.7333 0.01 0.4855 0.00.82:'.2 0.0 0.7709 0.00.9111 0.0 ooסס.1 0.0ooסס.1 0.0 ooסס.1 0.0

Llq.Sat. k rllq k rg0.2000 0.0 ooסס.1

0.2889 8.000 0.0 0.56000.3500 4.000 0.0 0.39000.3778 3.000 0.0110 0.35000.4667 O.BOO 0.0..170 0.20000.S556 0.030 0.0078 0.10000.644.4 0.001 0.1715 0.05000.7333 0.001 0.2963 0.03000.8222 0.0 0.4705 0.01000.9111 0.0 0.7023 0.00100.9500 0.0 0.8800 0.0ooסס.1 0.0 ooסס.1 0.0

TABLE 4Peng-Robinson Fluid Description

Component Pc(psia) M1f Accen.Fac Critz

CI 667.8 343.0 16.040 0.0130 0.290C3 616.3 665.7 14.100 0.1524 0.217a3 436.9 913.4 B6.IBO 0.3007 0.264CIO 304.0 1111.8 142.290 0.4885 0.257CI5 200.0 1270.0 206.000 0.6500 0.245(:20 162.0 1380.0 282.000 0.8S00 0.235

For all components: n~:::::: 0.4572355

~ = 0.0777961

For single components, the Peng-Robinson parameters A and Bare given by:

[ 1+k ( 1-

T

where.

+ 1.54226<.> - 0.26992",2 _..,(0.4.9.

+0.016666<,,3 . ..,,0.19

All binary interaction coefficients are zero EXCEPT:

Between Cl and CI5 0.05CI and C20 0.05C3 and CI5 0.005C3 and C20 0.005

Residual Oil to Gas Flood"" 0.15Critical Gas S3.turation :;;:: O.C15

Fluid densi ties atthe Peng-Robinson

condi tions were obtained using

TABLE 5Composi tional Fluid Description

TABLE 6

Pressure-Volume Relations at(Constant Composi tion

Reservoir Fluid C.omposition (Mole Fractions):

Cl 0.50C3 0.03C6 0.07ClO 0.20C15 0.15C20 0.05

Injection Cas/Solvent C.omposi tion (Mole Fractions):

Cl 0.77C3 0.20C6 0.03C10 0.00C15 0.00C20 0.00

Pressure.

4500.04000.03500.03000.02600.02302.32000.01800.01600.01200.01000.0500.0

14.714.7 @ 600 F

63

RelativeVolume0.96130.96490.97150.97880.98690.9960ooסס.1

1.066S1.12621.25001.44.731.65092.9317

164..088077.5103

LiquidSaturation

ooסס.1

1.0000ooסס.1

ooסס.1

ooסס.1

ooסס.1

ooסס.1

0.90770.81280.73150.62030.53440.?.B83OOסס.0

0.0100

SPf 1 6 0 0 ifTAJlLE 7

DIFFERENTIAL VAPClUZATION OF OIL JJ 16C'F

Ga. Ga. Gas Oil Oil Ga. Dev.Pressure Rela. tive Volume Molecular Viscosity Pac tor

(PSIA) Volume Pac tor ""ight (CP) Z

17.4217.42

4000. .1115 .01703500. .1115 .0170

.0170 572.8

.0170 572.8

1800. I. 2350 .6578 .0851BOO. 1.1997 .5418 .06981200. .42661000. .3508

14.7 1.0000 .00473 .0011 30.93 .6174 .414 .0107 .9947

(1) Barrels of oil at indicated pressure and teJIperature per barrel of residual oil at 6O°F~

(2) Mer of gss at 14.7 psia and 60 ....' per 1 RVB of gas at temp and pressure (c.alculated)"

(3) SCF of gas at tel'llP and pressure per barrel at 14,,1 p81a and WOF.

TAlILE 8

l'RESSUl.E-VOLIME RELATOllS OF SOLVENT GAS AT 160'P(COIISTANT CCIll'OSITIOll EXPANSION)

(1) (2)

Gas Foma tionVolwe Factor

DeviationFactor

ZGas Viscosity

(CP)

Gas(3)

Volatile

4000.3500.3000.2500.2302.32000.1800.1500.1100.1000.

14.7 @ 60'7

1.10531.20211.34201.56121.68501.94122.1756Z.6812

304.5530

1.0201.8853

.00600 .0010 .9946

.027

.023

.010 23.76

o.o.o.o.o.o.o.o.O.o.o.o.o.O.o.

(1) VolUdle relative to volume of the original charge at 4800 1>81a and loo-F.

(2) MCF of gas at 14.7 psia .and 60"17 per 1. RVR of gas at reap and pre.\H'It)'r'e (calculated) ~

(3) Stock tank barrels of 011 per MSCF at 160"'1' ~

TABLE 9

FOUR COOPOIlENT P1!T TABELAllffiTlONAL PIIT TilLE (llEl'RE:5S1JRI:!ATIOIl DATA)

Formation Volume Factor Viscosity

SolutionOil

(Rs/STll)Oil(CP)

14.7500.0

1500.01800.0

1.199701.235001.260001. 30100

1.559301. 26570

0.010700.01270

O.QUOD0.01200

0.016000.01000

64

40004000

TABLE 11 TABLE 12Comparison of Total Number of Time Steps Comparison of Total Number of Outer Itera-cions

Scenario 3 Scenario 1 Scenario 2 Scenario 3

AROO 372 874 692 ARCO H2o 1748 1407Chevron 239 6469 321 Chevron 813 2059 1112CMG 258 553 451 CllG 971 1926 1652ERC 137 221 118 ERC 465 888 449me 237 722 531 roc 972 2978 2522

Scenario 1 3 Scenario 1 Scenario 2 Scenario 3

ARCO 641 ARCO 1875BP I 914 BP I 2183BP II 900 BP II 2583Chevron 224 Chevron 953OIG 157 CllG 733RSR 898 RSR 920TDC 715 TDC 2170

TABLE 10Comparison of CPU Times

Scenario 1 Scenario 2 Scenario 3

ARm1

7.1 20.1 13.2

Chevron1 75.0 186.0 102.0

CMC2 3062.0 5263.0 4933.0

ERc3 1191.0 1282.0 1230.0

TOC4

75.0 221.0 298.0

Scenario 1 3

ARC01

532.1 1045.0 860.5

SP II 500.0 525.0 960.0

BP III 670.0 650.0 890.0

Chevron1 740.0 1700.0 10B8.0

CMC2 21177.0 32965.0 33279.0

RSR1 17.4 28.7 17.7

me'! 237.8 344.5 349.0

1 CRAY XlMP

2. HONEYWELL lruLTICS DPS817

3 NORSK DATA ND 570/CX

'1 mAY IS

o20

I-'

0'

1500

500

2500

2000

1000

3000

3500

15

.. ------

SCENARIO ONE

SCENARIO TWO--------SCENARIO THREE

105

-- ---_ ...

"",... .. _._wafl!JlJJflllll"­~4'

-- ..... , ...... -1\

\

oo

3500

3000

2500

2000

1500

1000

500

INJECTOR~

GRID FOR<l1(]I

Fig. 1-Three-dimensional finite dillerence grid lor comparative solution problems. Fig. 2-Comparison 01 average reservoir pressures lor comparative solulion Scenarios One, Two, and Three.

oo

2000 2500 3000 Fig. 4-Scenario One: comparison 01 cumulative oil production for ff.)l.ll'~component models.

25000

5000

30000

35000

15000

10000

-. 20000

o201510

TIME5

f/I"---­.......". ... '

... """,'",,,

II

II,,.

o r ,

o

COMP'ARISCIN OF vUIVIUIl..M.!

FOUR COiMP~:lNE='NT

35000 ..., -------------------,

z 30000og 25000 ~­:JCo 20000II:Q.

d 15000oW2: 10000

'<:5 5000'­:E:Jo

0.5 +------,-- -,------,1500

0.9

1

SPE FIFTH

0.6

>I:L

o01 0.8

~)0­0:::~ 0.7oUw0:::

ru....:l..:lUf\L, PSIAFig. 3-S1~m~tube oil recovery YS. pressure.

ill

COMPARISON OF PRODUCING GAS-Oil RATIOSSCENARIO ONE

FOUR COMPONENT MODELS

COMPARISON OF WATER-Oil RATIOS

FOUR COMPONENT MODELS

I-"

0'

C.Jc::>

4

5

.4 2

-. 3

o20155 10

TIME

AROO 401"

-TOC 4CP

CHEVRON 4CP

e I·5 , I•I·,·I·I•I•

I,Io

o

4

o 3

~II:

d 2oI

II:W

~~

4

2

10

-4 6

-, 8

o20

I·,•I·I·,·I.I.

.. J

1510TIME lYEARlS\

5

ARCO 4CP

CHEVRON------G

TOC 4CP... '" ... ... ... .. .. ...

o • I ,

o

10

8

o 6

EiII:..J 4(5,(fJ

~ 2

Fig. S-Scenario One: comparison of producing gasJoil ratios for four-component models. Fig. 6-Scenario One: comparison of producing waterfoil ratios for fouN:omponent models.

COMPARISON OF Oil SATURATIONS COMPARISON OF AVERAGE RESERVOIR PRESSURESSCENARIO ONE ONE

FOUR COMPONENT MODELS FOUR MODELS1.0 i , 1.0 4000 4000

3500 35000,6 ---, ~ 0.8 "-Z I, . w 3000 -l 3000, .

0 , ' , a::~ 2500

ERC 4CPF- , I , - - - - - - - II. -i 2500~ 0.6 ? ,

, , 0.6 (fJ TDe ._-. . . . . w ~

::> , I , If 2000 .."".J .. -l 2000tc ~ ..

en 0.4 0.4 a::1500 t- -- - ..... 'fIIIJ fIIIIII"- -l 1500...l g0 .... -,.., ---- a:: 1000 I:- -l 1000w

0.2 l- i . - "- 0.2 (fJWa:: 500 I- -l 500

0.0 0.0 o ' ! 0

0 5 10 15 20 0 5 10 15 20

TIME TIMEfig. 7-Scenario One: comparison of oil saturations In location 1:= 4, J:: 4, K =: 1, for four-component model$. Fig. a-Scenario One: comparison of average pore-volume weighted pressures for four-component models,

'"-.J

I--'

:.::J'

ooC.:>

o201510

TIME IVCADI::n

5

COMPARISON OF PRODUCING GAS-Oil RATIOS~LiI:::""I'I,"UU ONE

Cnl~p()Srr'!nNAI MODELS

Fig. 10-Scenario One: comporillion of producing gas/oil ratios for compositional models.

35000 10 , ; I - • 10

•30000 ,8 • I -l 8

25000 I It ...I, .20000 6 I : I -l 6

0 I 1/~ •15000 , •a::<4 ,'/ -I 4...l ARea 4CP •

10000 aI

en« 2 I- 8X.. /'.,.:.../ ....·...'..-.~/J. VA+P\..1 -l 25000 (!:l

o2015

­,...

COMP----_ .... _... ~

TOe.......... _.... _-~ARCO oliOI'

10

TIME5

o ' !

o

Fig. 9-Scenario One: comparison of cumulative 011 production for compositional models.

COMPARISON OF CUMULATIVE Oil PRODUCTIONSCENARIO ONE

COMPOSiTIONAL MODELS35000 r,------------------,

30000 -­zo~ 25000 .-:Joo 20000a::Q.

~ 15000oW2: 10000

tc:5 5000'­~:Jo

4000

2500

4500

2000

5000

-. 3000

150020

I _J 3500I

1510TIME {VY;;:A~I~\

ARCO CaMP

ARCO 4CP------- .......

SP COMP I-_ ..... _---_.SP CaMP II_ ... _---_ ....CHEVRON CaMP- -- .......... --CMG COMP

." .. .. ... ~ '" '" ..

5

1500 L~~g~~o

3500

3000

4500

2500

4000

2000

COMPARISON OF AVERAGE RESERVOIR PRESSURESSCENARIO ONE

COMPOSITIONAL MODElS5000

wa::::JWWWa:a..a:~a:wwwa:w~a::w~

5

2

-. 4

-< :3

-- 1

o201510

TIME5

ARCO COMP

ARCO 40F'

4 t- 5f' COMP I_ ..... _-----~BP II_.... ----- ..CHEVRON CaMP-- - ---CMG CaMP....... '" ...

COMP

5 i II I I ,

o ! , I

o

COMP'ARISC~N OF PRODUCING RATIOSSCENARIO ONE

COMPOSITIONAL MODELS

o :3 .-

~a::::::! 2oa:w~ 13:

Fig. 11-Scenario One: comparison of producing water/oil ratios for compositional models. Fig. 12-Scenario One: comparison of average poreMvo!ume weighted pressures for compositional models.

gj

OF CUMULATIVE OIL PRODUCTION COMPARISON OF CUM OIL PROD. VS CUM WATER INJ.SCENARIO TWO SCENARIO TWO

FOUR COMPONENT MODELS FOUR COMPONENT MODELS35000 35000 35000 I i 35000

z 30000 30000Z 30000 f ~ ... -l 30000

0 Q _ _ _ ~c~_

t5 25000 b 25000 -E~G ______ -I 25000:> :::J ERC 4Cp0 o TDC4CP- -

-l 20000o 20000 20000 ~ 20000 .•......a:Q. Q.

:::::! 15000 15000 d 15000 -l 150000 0W w2: 10000 - 10000 2: 10000 10000

~ ~..J ..J

5000:::J 5000 5000 :::J 5000 i-':::2: :::2: 0'::J :::J0 n 0 0 0 0

5 10 15 20 5000 10000 15000 20000 25000 30000 35000 0TIME CUMULATIVE WATER INJECTION

Fig. ~.. ... _____l_ ......_. ------,--- -" _ .. _" .• _ .., .. _. _" ----'..-~:_- ..- _ .. __ .• _~,_.- ... _ .._- ,-,--~,.- - ~-- ,,_ .. - - - ------~ 4.Fig. l3-Scenarlo Two: comparison of cumulative oil production for four~component models.

COMP'ARISCIN OF PRODUCING GAS-Oil RATIOSSCENARIO TWO

FOUR COMPONENT MODELS

COMPARISON OF PRODUCING WATER-Oil RATIOSSCENARIO TWO

FOUR COMPONENT MODELSI) 5.,

ARCO 4CP I4 CHEVRON 4CP • -I 4

-------- •-- •- •o 3 • -I 3

~,

a: •...I

,(5 2 , -I 2, •a: ,

w~ 1

,s: 'I•J

oLe"" ,!,?,', . ,1,1"",1 00 5 10 15 20

TIME

4

6

e

:2

10

o2015

II " .. • 111. .

10TIME

5

~~ ..............................

ARCO ",ep

CHEVRON 4CP-_ ...... _----CMG 4CP_ ... _ ... _--ERe- -TOC 4CF'

o

8

6

10

o

o~a:...I 4(5,UJ

<3 2

Fig. i5-Scenario Two: comparison of producing gas/oil ratios for four~component mode!s. Fig. 16-$cenario Two: comparison of producing water/oll ratios for four~cClmponent models.

'"'"

COMPARISON OF AVERAGE PRESSURESSCENARiO

FOUR COMPONENT MODELS

ARCO 4CP

COMPARISON OF Oil PRODUCTIONTWO

COMPOSITIONAL MODELS35000 35000

Z 30000 30000

0§ 25000 -I 25000::JCo 20000 -I 20000II:Il.

:::! 15000 -l 150000w~ 10000 CMGCOMP - 10000 I-.. ... ... .. ... .. - ... ..

~ RBA CaMP 0"----_ .... __ .....I

5000 roc CaMP::J _ ................. _--_ .. 5000 C~ ARCO 4CP c::J

--_ ....... __ ..... _..

0 0 0 <;:>0 5 10 15 20

TIME

4000

500

2500

:2000

1000

3000

3500

1500

o20

/.."

15

CHEVRON

10TIME

5

...... IJIIJIIIlI'tI ~ lfiIIIIIIIIIIJ. .....,. rr--. :--.

.. ..........................................

o

4000

w 3500II:::J~ 3000w[ 2500II:(5 2000>a:w 1500UJwa: 1000w(!'« 500II:w~ a

Fig. 17-Scenario Two: comparison of average pore~volume weighted pressures for four-component models. Fig. is-Scenario Two: comparison of cumulative oil production for compositional medels.

COMPARISON OF PRODUCING GAS-Oil RATIOSTWO

MODElS10 10

:~I• f 1-1 8

0CMG COMP ; J: o- f --I 6

~a::..J 4 I- AFICO 4CP .•• ..:...t',.;~-- -I 4a,w< :2 1- -'J/,/!.. - ... ----- -I 2(!I

o . , 00 5 10 15 20

TIME

Fig. 20-Scenario Two: comparison of producing gas/oil ratios for compositional models.

5000

25000

15000

20000

10000

30000

35000

AReo COMP

BP COMP I

SF........._... _-~CHEVRON COMP

"",,~ .../"

"",,"/"

."",,"

. ,,/./

.'/

o5000 10000 15000 20000 25000 30000 35000CUMULATIVE WATER INJECTION

oo

COMPARISON OF CUM OIL PROD. VS CUM WATER INJ.QI\A~:~~I~·:bR~i~ITWOCI MODElS

Fig. 19-5cenario Two: comparison of cumulative 011 production V$. cumulative water injection for compositional

35000

Z 30000

o§ 25000 .­=>Co 20000a::Il.

::::! 15000 .­ow> 10000 .-

~:5 5000:E:Jo

.....a

COMPARISON OF PRODUCING WATER-OIL RATIOS PRESSURESSCENARIO TWO

COMPOSITIONAL MODELS5 5 4000 4000

I.. 'l:i:""_~

I ~ 3500 - 3500dIl::'':.~_IIII'':':.==-_.':':'.~.___ :''''':_._·-

4 4 :J

I ~ 3000 -l 3000w

0 3I - 3 g: 2500 -~ 2500

COMP

~" '" .. .. .. zo " I a::

COMP a 2000 :WOOa:: -----_ ..TOC I >

-J 2---- ---" 2 a::a - ARCO 4CP W 1500 1500, -------_ ..

I wa:: w 1--'W a:: 1000 1000!;( 1 I 1 w J.....

s: (!I 0) < 500 -_ .... _---_ .. 500a:: .::Jw -_ ........

o hr' ...... ",,1 M"W'"1'feel!"nmnm.·nmmm'p' . , 0 ~ 0 00 5 10 15 20 0 5 10 15 20

TIME TIMEFig. 21-Scenario Two: comparison 01 producing waterfoll ratios for compositional models. fig. 22-Scenarlo Two: comparison of average porEl~volume weighted pressures for compositional models.

Fig. 23-Scenario Two: comparison of all saturations in location 1=4, J=4, K-= 1, for compositional models.

COMPARISON OF OIL PROD. VS CUM WATER INJ.TWO

FOUR COMPONENT AND COMPOSITIONAL MODELS35000 35000

30000 -j 30000cwg 25000 -I 250000

~ 20000 -1 2000011.....J(5 15000 r T -I 15000w~ 10000 r .I!' ARCO 4CP -I 10000«....J::> 5000 r ,,- ....:.'~~ :::'~''.: _ -I 5000~::>(.) o If , 0

0 5000 1000ll 15000 20000 25000 30000 35000CUMULATIVE WATER INJECTED

Fig. 24-Comparison of cumulative oil production vs. cumulative water Injection for compositional and four~

1.0

COMPARISON OF OIL SATURATIONS II.........J..• .... I".....

SCENARIO TWOCOMPOSITIONAL MODElS

1.0 i ,

0.8 , _fl.! ~~M~ 1___ . l 0.8Z0i=

-j~ 0.6 I- ICOMP 0.6,'" .... '" ..

::>~~ 0.4 ,- I ARCO 4CP --- - ---I 0.4

I . . -------_ ..0

0.2 0.2

..0.00.0

I) 5 10 15 20TIME

j

......0"

oo

4

6

10

-. :2

o20

-. 8

10TIME 15

5

6 >-

10 , . I I

.I !

COMP'AR,ISCl,N OF PRODUCING RATIOSSCENARIO THREE

FOUR COMPONENT MODELS

8

o~a:....J 4-(5,00

C3 2

35000

30000

5000

25000

20000

15000

10000

o2015

ARCO 4CP

- - --CMG 4CP

1/)~".

10TIME

I)

FOUR COMPIDNI::NT35000 , •

Z 30000

o§ 25000::>Co 20000a:11.

:::! 15000ow2: 10000

~:5 5000~::>(.)

Fig. 25--Scen3rio Three: comparil.wu Q1 cumulative oil production for four-oompanent models. Fig_ 26-Scenaric Thn.e: comparison of producing gas/oil ralio$ for fOl.lr~eompon.ntmodels_ .,A,

4000

3500- I4CP3000

2500

2000

1500

1000

500

0201510

TIME IVJ=4R!~'

5

COMPARISON OF AVI.. HJl~l"i'" RI=~I=I~Vi"IR PRIES~)UftES

FOUR COMPIONI=NT4000 L •

~ 3500:;:)

~ 3000wg: 2600

II:5 2000>II:m1500wII: 1000w(!J

« 500II:w~ Ol..------J... .l.- -.l.. ---'

o

WATER-OilTHREE

FOUR COMPONENT MODELS5 5

4 r -I 4

-o :3 I- TDO 4CP -I 3

tiII:

:::::! 2 l- I -I 20,II:W

~;::

0 00 5 10 15 20

TIME

Fig. 27-Scenatio Three: comparison of producing water/oil ratios for four..component models. Fig.. :'la-Scenario Three: comparison of average porevvolume weighted pressures 10r four-component models.

"'"

COIMPJl~RI~tON OF CUM Oil PROD. VS CUM WATER INJ.OI\llSp~~~~~~I~~lTHREE(:1 MODELS

35000 , , 35000

30000 l- ..~' -l 30000awo 25000 I- ~" --I 25000;:)a~ 20000 - 20000ll...J5 15000 15000

w l--"

~ 10000 10000 0"

« 0..J;:) 5000 5000 0~

- _.....;:)0 ......-

0 I)

0 5000 10000 . 15000 20000 25000 30000 35000

CUMULATIVE WATER INJECTED

Fig.

20000

5000

15000

25000

10000

30000

35000

o2015

ARCO COMP

I

SF'

.. .. .....

10TIME

5

Fig. 29-Scenario Three: comparison of cumulative oil production for compositional Model,..

COMPARISON OF vU'MULI'\ISCENARIO

COMPOSITIONAL MODELS35000 ..., ------------------.,

Z 30000

ot5 25000;:)ao 20000a::ll.

:::::! 15000ow> 10000

ti:5 5000~;:)o

4

2

3

5

-~ 1

o2015

fI•

_I

I•,

10TIME iVr;:AI:l:~\

5

ARCO COMP

Sf> I-- ...... ---~

Sf II__ ... _ .... __ 8

CHEVRON COMP........... - -- ..........

CMG.. .... .. ......R- -_ ...... - ..

COMPARISON OF PRODUCING WATER-Oil RATIOSSCENARIO THREE

COMPOSiTIONAL MODELS5

oo

4

o 3

~a:d 2o

I

a:

~ 1 .-­~

10

COMPARISON OF GAS-Oil RATIOSCE:NARIO THREE

COMPOSITIONAL MODELS10

a t- •• I • I -l 8

6 J- -l 60

~. .

a:-l 4...J 4

0,(f)0(

2 -l 2C)

0 00 5 10 15 20

TIMEFig. 31-Scenario Three: comparison of producing gas/oil ratios for compositional mOdels. fig. 32-Scenario Two: comparison of producing water/oil ratios for compositional models.

'"OJ

5000 5000

4500 4500

-_ ..... _...... ---~

4000 1- ~~~~~ ___ . --I 4000COMP

3500 1\ • ~M~ • ~ .. .. u -I 3500

3000 H ~':~ ~~ - - - . . 3000. ..2500 1--' . I 2500. # I--". a-2000 1-- - 2000

0<:)

1500 15000 5 10 15 20

TIME

COMPARISON OF AVERAGE RESERVOIR PRESSURESSCENARIO THREE

COMPOSITIONAL MODELS

UJa:::>(f)(f)wa:a.a:o::>a:UJfI)UJa:w~a:UJ

~

Fig. 33-Scenario Two: comparison of average pore~volume weighted pressures for compositional models.