Development and Application of a New Technique for Upscaling Miscible Displacements
- Mun-Hong Hui (Stanford U.) | Dengen Zhou (ChevronTexaco China Energy Co.) | Xian-Huan Wen (ChevronTexaco EPTC) | Louis J. Durlofsky (Stanford U./ChevronTexaco Energy Technology Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 2005
- Document Type
- Journal Paper
- 189 - 195
- 2005. Society of Petroleum Engineers
- 5.1.5 Geologic Modeling, 5.4.2 Gas Injection Methods, 5.8.7 Carbonate Reservoir, 5.3.2 Multiphase Flow, 5.5.3 Scaling Methods, 5.2.1 Phase Behavior and PVT Measurements, 4.6 Natural Gas, 4.3.4 Scale, 4.1.2 Separation and Treating, 5.4.9 Miscible Methods, 5.5 Reservoir Simulation
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To better design and manage miscible gas injection, a fast and accuratecoarse-scale miscible simulation capability is required. In this paper, wepresent a new technique for the upscaling of first-contact miscibledisplacements. The method comprises two components: effective flux boundaryconditions (EFBCs) and the extended Todd and Longstaff with upscaled relativepermeabilities (ETLU) formulation. The former accounts approximately for theeffects of the global flow field on the local upscaling problems, while thelatter modifies the way that effective fluid properties and upscaled relativepermeabilities are computed so that effectively residual oil is properlyrepresented.
For a sequence of partially layered, synthetic 2D permeability fields, thetechnique is shown to be successful in reproducing reference fine-scalesolutions. The method is also shown to outperform other upscaling techniquesover a wide range of coarsening factors. The upscaling procedure is thenapplied to a 3D simulation of a miscible gas-injection field study. A near-wellupscaling technique is also incorporated into the methodology. We show that thenew approach provides coarse-scale simulation results that match the referencesolutions closely. In addition, the technique is shown to be very efficientcomputationally.
In many oil fields with significant amounts of associated gas, miscible gasinjection is a potentially attractive recovery method because it can yield highlocal displacement efficiencies and may also offer a solution for gas handling.For an accurate estimation of the displacement efficiency, complex phenomenalike viscous fingering need to be modeled properly. There are two broadcategories of approaches to modeling miscible displacements: fullycompositional (FC) and limited compositional (LC).
For multicontact miscible processes, FC simulations are generally required.However, fine-scale FC simulations of miscible processes are prohibitivelytime-consuming. While compositional streamline techniques may eventuallyaddress many of the computational difficulties, several issues (e.g., gravity,compressibility, and streamline updating) have yet to be fully resolved. Whenfirst-contact miscibility is applicable, the LC formulation may be preferablebecause of its computational efficiency. The LC formulation allows thesimulator to model miscibility within a black-oil framework and empiricallyaccounts for viscous fingering by modifying the fluid properties of thepseudophases. However, because fine-scale LC simulations are stillcomputationally demanding, there remains a clear need for a robust miscibleupscaling technique.
In this work, we present a novel upscaling technique for the fast andaccurate coarse-scale simulation of first-contact miscible displacements. Ourmethod is an LC approach that has two components: the use of EFBCs for thecalculation of upscaled (pseudo-) relative permeabilities and the ETLUformulation. EFBCs incorporate some approximate global flow information intothe local upscaling calculations and appropriately suppress the flux throughhigh-permeability streaks that are not continuous throughout the domain. As aresult, EFBCs address the problem of premature breakthrough of injected fluid,which can occur because of the overestimation of flux that results from the useof standard boundary conditions. Our ETLU formulation extends the Todd andLongstaff method by accounting for the fact that, within reservoir-simulationlength scales, there exists an amount of oil that is practically immobile andnot available for mixing (Sorb). The computation of effective fluid propertiesand upscaled relative permeabilities, therefore, should not include this Sorb.This concept in fact leads to the improved behavior of the upscaled relativepermeabilities. Previous miscible upscaling approaches entailing upscaledrelative permeabilities neither included the Sorb concept nor used anyspecialized boundary conditions such as EFBCs.
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1. Todd, M.R. and Longstaff, W.J.: "The Development, Testing, andApplication of a Numerical Simulator for Predicting Miscible FloodPerformance," JPT (July 1972) 874.
2. Thiele, M.R., Batycky, R.P., and Blunt, M.J.: "A Streamline-Based 3D Field-ScaleCompositional Reservoir Simulator," paper SPE 38889 presented at the 1997SPE Annual Technical Conference and Exhibition, San Antonio, Texas, U.S.A., 5-8October.
3. Wallstrom, T.C. et al.: "Effective Flux Boundary Conditions for UpscalingPorous Media Equations," Transport in Porous Media (February 2002) 46, No. 2-3,139.
4. Zhang, H.R. and Sorbie, K.S.: "The Upscaling of Miscible andImmiscible Displacement Processes in Porous Media," paper SPE 29931presented at the 1995 SPE International Meeting on Petroleum Engineering,Beijing, 14-17 November.
5. Barker, J.W. and Fayers, F.J.: "Transport Coefficients forCompositional Simulation With Coarse Grids in Heterogeneous Media," SPEAdvanced Technology Series (April 1994) 103.
6. Jerauld, G.R.: "A Case Studyin Scaleup for Multi-Contact Miscible Hydrocarbon Gas Injection," paper SPE39626 presented at the 1998 SPE/DOE Improved Oil Recovery Symposium, Tulsa,19-22 April.
7. Hui, M., Durlofsky, L.J., and Wen, X.H.: "Application of a new upscalingtechnique to a miscible gas injection field study," Proc., 13th EAGE Symposiumon Improved Oil Recovery, Budapest, Hungary (25-27 April 2005).
8. Wallstrom, T.C. et al.: "Application of effective flux boundaryconditions to two-phase upscaling in porous media," Transport in Porous Media(February 2002) 46, No. 2-3, 155.
9. Christie, M.A. et al.: "Effective medium boundary conditions inupscaling," Proc., 7th European Conference on the Mathematics of Oil Recovery,Baveno, Italy (5-8 September 2000).
10. Stone, H.L.: "RigorousBlack Oil Pseudo Functions," paper SPE 21207 presented at the 1991 SPESymposium on Reservoir Simulation, Anaheim, California, U.S.A., 17-20February.
11. Hui, M.: "Upscaling of Multiphase Flow Parameters for Modeling Near-Welland Miscible Displacements," PhD dissertation, Stanford U., Stanford,California, U.S.A. (September 2005).
12. Durlofsky, L.J., Jones, R.C., and Milliken, W.J.: "A nonuniform coarseningapproach for the scale up of displacement processes in heterogeneous porousmedia," Advances in Water Resources (October-December 1997) 20, No. 5-6,335.
13. Wen, X.H., Durlofsky, L.J., and Edwards, M.G.: "Use of border regions forimproved permeability upscaling," Mathematical Geology (July 2003) 35, No.5, 521.
14. Mascarenhas, O. and Durlofsky, L.J.: "Coarse scale simulationof horizontal wells in heterogeneous reservoirs," J. Pet. Sci. & Eng.(March 2000) 25, No. 3-4, 135.