New Method of Incorporating Immobile and Nonvaporizing ...s-skj/Knutsen.Stian/Residual... · gas injection, S orm, defined by Spence and Watkins (1980). In this paper, the concept

New Method of Incorporating Immobileand Nonvaporizing Residual Oil

Saturation into Compositional ReservoirSimulation of Gasflooding

T. Hiraiwa,* SPE, and K. Suzuki,** SPE, Japan Oil Development Co. Ltd.

SummaryIn compositional simulation of gas-injection processes, it is oftenobserved that gridblock oil saturations decrease far beyond theuser-defined residual oil saturation, even under immiscible condi-tions. This numerical phenomenon occurs because oil componentsare allowed to vaporize into the gas phase as much as the phaseequilibrium obtained with an equation of state (EOS) permits.Especially in the vicinity of gas injectors, an oil saturation of zerois sometimes predicted. On the other hand, such significant low oilsaturation is rarely seen in laboratory data such as coreflood ex-periments and slimtube tests.

The reason for the discrepancy between the simulation resultsand the laboratory results described above is that bypassed oillocated in dead-end pores or caused by subgrid-scale heterogene-ities is not considered in the current compositional-simulationpractice. To overcome this, we developed an innovative method ofincorporating laboratory-based residual oil saturations. The pro-posed method can restrict the excessive vaporization and maintainthe prescribed residual oil by accommodating a novel applicationof the transport coefficient (Barker and Fayers 1994).

IntroductionIncorporation of the “true” residual oil saturation into the gasfloodcompositional simulation has been a critical problem in the indus-try. On the other hand, most compositional simulators allow oilsaturations to be as low as an EOS predicts, but no rigorousmethod has been proposed to honor laboratory observations usu-ally indicating nonzero residual oil saturations. This is why im-miscible gas injection is predicted to achieve a good recoveryfactor despite the fact that even miscible coreflood experimentresults rarely show 100% recovery.

Not only laboratory experiments but also field observationsindicate that bypassed oil occurs even after the miscible injectantpasses through above the minimum miscibility pressure (MMP), asstated by Stalkup (1983) and McGuire et al. (1995). Dead-end porevolume and precipitation can cause such bypassed oil under gasinjection with no prior waterflood history. Although the masstransfer in microscopic scale like molecular diffusion can partiallyrecover such bypassed oil, as described by Burger et al. (1996),there still remains the oil behind the miscible front.

For this reason, even under the miscible-flooding condition, theresidual oil saturation will not reach 0% in the real heterogeneousreservoir. This residual oil is referred to as miscible flood residualoil saturation (Spence and Watkins 1980). In the conventionalcompositional simulation, there is no facility to actively define“true” residual oil (nonvaporizing oil) and, hence, the excessivevaporization of oil components into the gas phase is predicted.

Consequently, the miscible flood residual oil saturation could notbe represented in the simulation model. This frequently has causedoptimistic results in which all the oil in the gridblock can bestripped by the injected gas.

The first attempt to restrict the excessive vaporization de-scribed above was made by Fayers et al. (1992), who proposed theconcept of dual-zone mixing. In this concept, the phase equilib-rium is established between the hydrocarbon trapped in dead-endspace (uncontacted oil) and that in the permeable portion of asimulation block. Analogous to a dual-porosity model, uncon-tacted oil is allowed to disperse only when it is vaporized into thecontacted oil or gas. The concept of the transport coefficient(Barker and Fayers 1994) was adopted to incorporate the compo-nent dependence in mass transfer. However, the work of Fayerset al. (1992) has not been used widely, primarily because of thecomplexity of the theory and, hence, special coding was requiredto accommodate the dual-zone mixing.

In a coreflood simulation, considering and modeling the het-erogeneity inside the core sample could yield a residual oil satu-ration along with the laboratory experiments. However, it is dif-ficult to convey such insight derived from the core-scale hetero-geneity to a simulation block size. Besides, it is widely known thatpseudofunctions or upscaled relative permeability, especially forgas/oil two-phase flow, do not always work well because the re-sultant large-scale saturation functions are extremely limited to theassumed pressure and velocity conditions.

In this paper, we present a simple and robust method of incor-porating nonvaporizing residual oil saturations, in which the labo-ratory-based residual oil saturations can be respected exactly. Theresults of the case studies are also shown where the sensitivity ofthe residual oil saturations will be discussed.

Explanation of the Developed MethodOverview. This method consists of three elements: the partitioningof the fluid-component system, an innovative application of thetransport coefficient, and relative permeability modificationcaused by the inclusion of the transport coefficient. We partitionthe fluid system so that each component has a mobile portion andan immobile portion. This is controlled by assigning differenttransport coefficients (alpha factors) to each of the mobile andimmobile portions as described later.

Partitioning of the Fluid-Component System. In the real reser-voir, there must be residual oil saturation even under the misciblegas injection, Sorm, defined by Spence and Watkins (1980). In thispaper, the concept of Sorm is defined as the residual oil saturationthat does not decrease less than physically acceptable values underboth miscible and immiscible conditions.

To model the Sorm in the framework of an equation of state, wedouble the fluid-component system over the originally defined one(see Fig. 1). The additional components are dedicated to model theSorm and assigned with the EOS parameters identical to the origi-nally defined components. Kim assigned the independent compo-nents for injection-gas components (Kim 1993), but we make simi-lar assignments for the immobile components. In other words, theEOS was split, and two sets of identical EOS parameters anddifferent compositions coexist.

* Now seconded to Abu Dhabi Marine Operating Co.** Now seconded to Zakum Development Co.

Copyright © 2007 Society of Petroleum Engineers

This paper (SPE 88719) was first presented at the 2004 SPE Abu Dhabi InternationalPetroleum Exhibition and Conference, Abu Dhabi, UAE, 10–13 October, and revised forpublication. Original manuscript received for review 7 December 2004. Revised manuscriptreceived 30 May 2006. Paper peer approved 10 October 2006.

60 February 2007 SPE Reservoir Evaluation & Engineering

For the component i of the original EOS, after the componentsplitting, we prepare component iA as a mobile component andcomponent iB as an immobile component. The overall mole frac-tion of component i is referred to as zi. The mobile portion is zi,A,and the immobile portion is zi,B. In the initial condition, theseinitial mole fractions are referred to as z*i, z*i,A, and z*i,B.

At the model initialization, it is assumed that no vapor phaseexists in the system. This allows us to further assume that liquid-phase mole fractions (x*i, x*i,A, and x*i,B) are identical to those ofoverall mole fractions (z*i, z*i,A, and z*i,B). Thus, the mole ratiobetween z*i,A and z*i,B is set to be identical to the ratio between themobile oil and the residual oil. In a process of gas injection, itis known that the remaining oil changes from the initial composi-tion because of the mass transfer; however, we simply assumedthat the residual oil remained the same because no contact by theinjection gas is assumed due to dead-end pores. In addition, nomass transfer is assumed between the hydrocarbon componentsand the water component.

This relationship can be expressed in the following equations:

x*i,A: x*i,B = z*i,A:z*i,B = �Soi − Sorm�: Sorm. . . . . . . . . . . . . . . . . . . . . (1)

z*i,A + z*i,B = z*i. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

Transportation-Coefficient Setup. The concept of the transportcoefficient was introduced by Barker and Fayers (1994). This con-cept has been used to upscale compositional models (Christie andClifford 1998; Ballin et al. 2002; Jerauld 1998). The transportcoefficient relates the composition of the fluid flowing out of agridblock to that within the block.

The mass-balance equation for hydrocarbon component i in aconventional compositional-simulation model can be written asfollows for cells without sink or source:

�

�t��Fzi� + �•�uo�oxi + ug�gyi� = 0, . . . . . . . . . . . . . . . . . . . . . . (3)

where F indicates the total hydrocarbon moles in a cell of interest.When we adopt the concept of transport coefficients, this equa-

tion is modified by introduction of transport coefficients (�) in theflow terms as follows:

�

�t��Fzi� + �•��oiuo�oxi + �giug�gyi� = 0. . . . . . . . . . . . . . . . . . (4)

As a result, the transport coefficients determine the relative veloc-ity of a particular pseudocomponent in a simulation model.

In our new method, we use the transport coefficients to immo-bilize a particular component of an EOS system. By assigning thetransport coefficient of zero to an immobile portion of a certaincomponent, that portion is immobilized from a gridblock. On theother hand, the transport coefficient of unity makes no change inthe flow velocity of the component. By this method, any molefraction of any component can be completely immobilized fromthe gridblock. These can be summarized as follows.

�� = �0 for dedicated immobile portion, iB

1 for mobile portion, iA

. . . . . . . . . . . . . . . (5)

Then, substituting Eq. 5 into Eq. 4 yields

�

�t��Fzi� + �•�uo,A�o,Axi,A + ug,A�g,Ayi,A� = 0. . . . . . . . . . . . . . . (6)

Due to the assumption of Eq. 5, immobile residual oil remains inthe initial composition, z*i,B (i=1,2, . . . ,n).

Relative Permeability Modification. Because the transport coef-ficient modifies the convection term of each component as shownin Eq. 4, the total velocity of the oil phase is also inevitablychanged. Consequently, the history-matching result (or a periodbefore the start of gasflooding) will be changed. In other words,the use of the transport coefficient requires the modification of theoil relative permeability to maintain the same flow rate.

Under waterflooding conducted in the undersaturated conditionwith no solubility of hydrocarbon components into the aqueousphase, there exists only a liquid phase in a hydrocarbon system.Comparing a liquid-phase convection term for component i be-tween Eq. 3 and Eq. 6 yields

uo�oxi = uo,A�o,Axi,A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

It is required to maintain the viscosity, density, and pressure dis-tribution of the liquid phase by use of Sorm; hence,

uo,A

uo=

kro,A

kro=

xi

xi,A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)

If we introduce the correction factor C, the modified relative per-meability of oil can be written as follows by use of Eq. 1:

From Eq. 8, we put the correction factor C to be

C = kro,A�kro = xi�xi,A = So��So − Sorm�, . . . . . . . . . . . . . . . . . . . . (9)

where x i,A is the mole fraction of movable oil and Sorm is theresidual oil saturation by miscible flooding.

Then, the relative permeabilities are adjusted as follows:

krog,mod = C krog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10)

krow,mod = C krow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

Testing the Developed Method by Use of a 1DModelModel Description. The developed method was tested by use of a1D compositional-simulation model of coreflooding (1×1×50cells) for the validation (see Fig. 2). In this test, three types ofinjectants were assumed: water, lean gas, and CO2. For each case,four different Sorm values (0, 0.1, 0.2, and 0.3) were assumed to seethe sensitivity of Sorm. It should be noted that a Sorm of 0.0 stands

Fig. 1—Partition of the fluid-component system to accom-modate the concept of immobile and nonvaporizing residualoil saturation.

Fig. 2—One-dimensional coreflooding model used to test thedeveloped method.

61February 2007 SPE Reservoir Evaluation & Engineering

for the conventional simulation. The Sorw and Sorg were both as-sumed as 0.348 for method-validation purposes.

Water-Injection Case (Displacement Without Oil Vaporiza-tion). Using the 1D coreflood model described above, the water-flooding experiment was simulated. As shown in Fig. 3, the de-veloped method reproduced the result that was simulated with theconventional model (Sorm�0) in all cases. In addition, no spreadof results between different sets of Sorm was observed in the wa-terflooding cases. Thus, we confirmed that the developed methoddoes not affect the simulation results of water injection.

Gas-Injection Case (Displacement With Oil Vaporization). Wetested the developed method against two gas-injection schemes:pure CO2 and lean gas (C1: 75%). In contrast to the water-injectioncase, the sensitivity of Sorm was observed as the spread in theoil-recovery profiles among different sets of Sorm caused by thevaporization of oil (see Figs. 4 and 5). When Sorm is increased, thevaporization effect of oil by gas is suppressed. Consequently, wesaw less recovery.

Requirement of Sorm in Coarse-Scale ReservoirSimulation of Gas InjectionThe use of Sorm in coarse-scale reservoir simulation is requiredbecause oil that cannot be contacted easily by the miscible gas is

bypassed and, hence, not displaced. This bypassing is due to res-ervoir heterogeneity and preferential flow paths that prevent theinjected gas from reaching such oil. It also implies that, as thereservoir characterization becomes more and more homogeneousas the grid becomes coarser and coarser, a larger Sorm is needed toreproduce the “heterogeneous” results.

To prove the discussion above, we carried out a numericalexperiment using two different models: a coarse homogeneousmodel and a fine heterogeneous model. This coarse model is iden-tical to the 1D coreflooding model used in the previous section(Fig. 2). The corresponding fine model was obtained by refiningthe coarse model with the dimension and the permeability distri-bution shown in Fig. 6. It should be noted that the average per-

Fig. 3—Predicted waterflooding performance insensitive toSorm by adjustment of oil-phase relative permeability where fourdifferent curves overlap each other among Sorm values of 0%,10%, 20%, and 30% (rcc=reservoir condition cm3).

Fig. 5—Sensitivity of Sorm on lean-gas flood production perfor-mance by use of the coreflooding model.

Fig. 6—Dimension and permeability distribution of the coarsemodel and the fine model.

Fig. 4—Sensitivity of Sorm on CO2 flood production performanceby use of the coreflooding model.

62 February 2007 SPE Reservoir Evaluation & Engineering

meability is common between the coarse model and the finemodel, while an Sorm of zero was assumed in the refined model. Asshown in Fig. 7, the recovery profile in the fine model was almostidentical to that of the coarse model, with an Sorm of 10%. Thisexperiment clearly indicates that for field simulations, Sorm isan upscaling parameter that would change with grid resolutionand heterogeneity.

Application to the Real Reservoir ModelAfter the evaluation by use of a 1D simulation model, this methodwas applied to a sector model of a real reservoir to compare CO2

injection and lean-gas injection while Sorm is varied along with thelaboratory results. The overview of the sector model without de-fining Sorm is shown in Fig. 8. It can be seen that the vicinity of gasinjectors shows oil saturation much lower than the prescribed Sorg

(30% in this case). This is because of the lack of restriction on thevaporization of oil from liquid phase to vapor phase.

In this model, a gas-injection scheme is started using horizontalgas injectors and horizontal producers after approximately 20years of natural depletion. No gas was liberated during the primarydepletion period because the oil is highly undersaturated. The natu-ral-depletion period was already history matched.

With the new method, Sorm was varied among 15%, 20%, 25%,and 30%. The simulated production performances under the natu-ral depletion and water injection almost have not changed irre-spective of the varied Sorm.

In the prediction of the gas-injection scheme, we observed thedistinct impact of the immobile oil incorporated by our newmethod. Fig. 9 shows the prediction result of production profiles

under the CO2 injection scheme. It clearly can be seen that thehigher Sorm causes the lower oil-production rate and the highergas/oil ratio with time. The lean-gas injection scheme showed asimilar tendency with the increased Sorm.

In the laboratory coreflooding experiments using core samplesfrom the real reservoir at pressures similar to the simulation de-scribed above, the Sorm obtained by CO2 flooding was measured asapproximately 15%, while the Sorm obtained by the lean-gas flood-ing was measured as approximately 30%. To evaluate the CO2

injection case and the lean-gas injection case accounting for thelaboratory results, we assumed these laboratory results as repre-sentative Sorm in this sector model. The results are shown in Fig.10. Both injection schemes show a similar reduction in the recov-ery factor.

It should be noted that, in this sector-model simulation, wesimply applied the laboratory coreflood results. However, it issuggested that Sorm be estimated by adopting past theoretical work[e.g., by Fayers (1988), who proposed the approximate method ofmiscible viscous fingering].

DiscussionWe have shown that our method successfully differentiated recov-ery performance along with the several Sorm values (see Fig. 9). Inthis paper, we made a simple assumption that the residual oilremains at the initial oil compositions as if the oil in the dead-end pore never contacts the injected gas. Hence, the transportcoefficient of zero for the immobile components in Eq. 1 causes

Fig. 7—Comparison in recovery performance between thecoarse model and the refined model shown in Fig. 6.

Fig. 9—Prediction results of the CO2 flood case with severalSorm by use of the sector model.

Fig. 10—Prediction by use of the sector model with Sorm basedon laboratory results.

Fig. 8—Oil-saturation distribution predicted in the lean-gasflood with a real field sector model where Sorm proposed in thispaper was not defined and oil saturation decreased far beyondthe prescribed Sorm (30%).

63February 2007 SPE Reservoir Evaluation & Engineering

no compositional change in the residual oil and fulfills the as-sumed condition.

On the other hand, a flash calculation is conducted for anyhydrocarbons contained in a simulation block, whether they aremobile or immobile. It cannot be avoided that a simulation blockacts like one pressure/volume/tempereature (PVT) cell. This alsohappens in our new method. Thus, the mobile and immobile por-tions are flashed together. Strictly, “uncontacted oil” is not exactlyrepresented, though “immobile oil” can be modeled.

As studied by Cockin et al. (2000) and McGuire et al. (1995),nonzero residual oil saturation exists in gas injection, even undermiscible conditions, as a result of bypassed oil or dead-end pores,namely those caused by reservoir heterogeneity. In the field scalecompositional model adopting coarse cells, it is necessary to havereasonable residual oil saturation, while it is expensive to upscalefine-cell models. Because of this requirement, upscaled residual oilsaturation in coarse cells was represented by the concept of Sorm

featured as nonvaporizing immobile oil saturation. This was dem-onstrated in this paper, as shown in Figs. 6 and 7.

It is also possible to define the composition of Sorm as a spatialvariable, although we assume that the composition of Sorm remainsthe same as the initial oil composition in this paper. The compo-sition of Sorm is a consequence of mass transfer and phase equi-librium between different fluid systems. The light-intermediatecomponents tend to transfer even from dead-end pores and, hence,Sorm can be dominated by heavy components. When the residualoil is made up of different compositions from the initial oil (e.g.,due to vaporization of the light components), each component canhave its specific transport coefficient. In such a condition, wewould have to further generalize the relative permeability modifi-cation shown in Eqs. 10 and 11 because the correction factor in Eq.9 is unique throughout the gas phase and the oil phase.

In addition, the prescribed Sorm obtained by partitioning of thefluid component can be spatially variable. Although Sorm was setconstant throughout the model in this paper, Sorm can be a functionof the composition of injectant, capillary number, temperature, andpressure provided that such source code is available. There shouldbe sufficient database content regarding Sorm from laboratory andfield data to describe Sorm as a function of those parameters above.Such a data library would allow us to assign variable Sorm by cellsand even as a function of pressure and capillary numbers. Forinstance, in the vicinity of wellbore, Sorm can be different from thatin other portions of the reservoir owing to higher fluid velocityand, hence, is less dominated by capillary forces.

Regarding the application of local grid refinement (LGR) in thevicinity of injectors, the effect is expected to depend on howsubgrid scale heterogeneity is honored. LGR simply dividingcoarse cells without assigning heterogeneity to refined cells willstill decrease oil saturation less than unphysical values.

This method can be applied to both miscible and immiscibleconditions. Because of the ability to restrict vaporization, thismethod can be powerful in field-scale models made up of coarsecells, though calculation time will be increased owing to a doubledfluid-component system. In our case, the calculation time and re-quired memory were increased by approximately two times theoriginal case. It also should be noted that this method theoreticallyrequires the condition when Sorm is lower than Sorg and Sorw,though such a relation is unlikely to be violated in real data.

ConclusionsWe developed a novel method of incorporating and honoring re-sidual oil saturation obtained in laboratory coreflood experiments.This residual oil was made nonvaporizing and immobile, applyingthe concept of the transport coefficient. The developed method hasbeen tested for CO2 and lean-gas injection. The results of thisstudy can be summarized as follows:1. The newly developed method is able to restrict vaporization

beyond the prescribed residual oil saturation. Thus, the accurateevaluation of gasflooding is made available, reflecting the residualoil saturation derived from laboratory coreflood experiments.

2. A novel application of the transport-coefficient approach wasdeveloped, in which it was found that the adjustment of oil-

phase relative permeability was required to correctly simulatethe model performance before gas injection.

NomenclatureA � mobile phaseB � immobile phaseC � correction factor for krow and krog

F � total hydrocarbon present (mol/unit pore volume)krg � gas relative permeability

krog � oil relative permeability to gaskrog,mod � modified oil relative permeability to gas

krow � oil relative permeability to waterkrow,mod � modified oil relative permeability to water

krw � water relative permeabilityn � number of components in the hydrocarbon systemS � saturation

So, Sg � oil- and gas-phase saturationsSoi � initial oil saturation

Sorm � residual oil saturation by miscible floodingSorw,Sorg � residual oil saturations by water and gasSwir � irreducible water saturation

uo, ug � darcy velocity of oil and gas phasesxi � liquid-phase mole fraction of component i

x*i � initial liquid-phase mole fraction of component iyi � vapor-phase mole fraction of component i

y*i � initial vapor-phase mole fraction of component izi � overall mole fraction of component i

z*i � initial overall mole fraction of component izi,A � mobile-phase mole fraction of component i

z*i,A � initial mobile-phase mole fraction of component izi,B � immobile-phase mole fraction of component i

z*i,B � initial immobile-phase mole fraction of component i�oi, �gi � oil- and gas-phase transport coefficients for

component i� � porosity

�o, �g � oil- and gas-phase densities�• � divergence

AcknowledgmentsThe authors are grateful to Abu Dhabi National Oil Co. for per-mission to present this paper. It should be noted that this paperdoes not necessarily reflect their opinions. Japan Oil DevelopmentCo. Ltd. is also acknowledged.

ReferencesBallin, P.R., Clifford, P.J., and Christie, M.A. 2002. Cupiagua, Modeling

of a Complex Fractured Reservoir Using Compositional Upscaling.SPEREE 5 (6): 488–498. SPE-81409-PA. DOI: 10.2118/81409-PA.

Barker, J.W. and Fayers, F.J. 1994. Transport Coefficients for Composi-tional Simulation With Coarse Grids in Heterogeneous Media. SPEAdvanced Technology Series 2 (2): 103–112. SPE-22591-PA. DOI:10.2118/22591-PA.

Burger, J.E., Springate, G., and Mohanty, K.K. 1996. Experiments onBypassing During Gasfloods in Heterogeneous Porous Media. SPERE11 (2): 109–115. SPE-28626-PA. DOI: 10.2118/28626-PA.

Christie, M.A. and Clifford, P.J. 1998. Fast Procedure for Upscaling Com-positional Simulation. SPEJ 3 (3): 272–278. SPE-50992-PA. DOI:10.2118/50992-PA.

Cockin, A.P., Malcom, L.T., McGuire, P.L., Giordano, R.M., Sitz, C.D.2000. Analysis of a Single-Well Chemical Tracer Test To Measure theResidual Oil Saturation to a Hydrocarbon Miscible Gas Flood at Prud-hoe Bay. SPEREE 3 (6): 544–551. SPE-68051-PA. DOI: 10.2118/68051-PA.

Fayers, F.J. 1988. An Approximate Model With Physically InterpretableParameters for Representing Miscible Viscous Fingering. SPERE 3 (2):551–558. SPE-13166-PA. DOI: 10.2118/13166-PA.

64 February 2007 SPE Reservoir Evaluation & Engineering

Fayers, F.J., Barker, J.W., and Newly, T.M.J. 1992. Effects of Heteroge-neities on Phase Behavior in Enhanced Oil Recovery. In The Math-ematics of Oil Recovery, ed. P.R. King. Oxford, U.K.: Clarendon Press.

Jerauld, G.R. 1998. A Case Study in Scaleup for Multicontact MiscibleHydrocarbon Gas Injection. SPEREE 1 (6): 575–582. SPE-53006-PA.DOI: 10.2118/53006-PA.

Kim, J.S. 1993. Tracking Injected Components in Fully CompositionalReservoir Simulations. Paper SPE 26638 presented at the SPE AnnualTechnical Conference and Exhibition, Houston, 3–6 October. DOI:10.2118/26638-MS.

McGuire, P.L., Spence, A.P., Stalkup, F.I., and Cooley, M.W. 1995. CoreAcquisition and Analysis for Optimization of the Prudhoe Bay Mis-cible-Gas Project. SPERE 10 (2): 94–100. SPE-27759-PA. DOI:10.2118/27759-PA.

Spence, A.P. Jr. and Watkins, R.W. 1980. The Effect of Microscopic CoreHeterogeneity on Miscible Flood Residual Oil Saturation. Paper SPE9229 presented at the SPE Annual Technical Conference and Exhibi-tion, Dallas, 21–24 September. DOI: 10.2118/9229-MS.

Stalkup, F.I. Jr. 1983. Miscible Displacement. Monograph Series, SPE,Richardson, Texas, 8.

Takeshi Hiraiwa joined Japan Oil Development Co. (JODCO)in 1996 as a reservoir engineer and is presently seconded toAbu Dhabi Marine Operating Co. (ADMA-OPCO) in the UAE.Since joining JODCO, Hiraiwa has worked on field-development planning optimization, reservoir management,and simulation studies. He holds a BS degree in petroleum en-gineering from the U. of Tokyo. Koichi Suzuki is currently work-ing as Upper Zakum Field Development Planning Leader ofZakum Development Co. (ZADCO) in Abu Dhabi, UAE, sec-onded from JODCO. His work experience includes optimiza-tion of integrated field development planning, reservoir mod-eling and simulation, theoretical development of pressure-transient anaylsis, and time-lapse reservoir monitoring. Suzukiholds BE and ME degrees from the U. of Tokyo and a PhDdegree from Stanford U., all in petroleum engineering.

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