Efficient 3D Implementation of Local-Global Upscaling for Reservoir Simulation
- Xian-Huan Wen (Chevron Corp.) | Louis J. Durlofsky (Stanford University) | Yuguang Chen (Chevron ETC)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2006
- Document Type
- Journal Paper
- 443 - 453
- 2006. Society of Petroleum Engineers
- 5.5.3 Scaling Methods, 5.1.5 Geologic Modeling, 5.3.2 Multiphase Flow, 5.5 Reservoir Simulation, 5.1 Reservoir Characterisation, 4.3.4 Scale
- 0 in the last 30 days
- 625 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Upscaling is often applied to coarsen detailed geological reservoir descriptions to sizes that can be accommodated by flow simulators. Adaptive local-global upscaling is a new and accurate methodology that incorporates global coarse-scale flow information into the boundary conditions used to compute upscaled quantities (e.g., coarse-scale transmissibilities). The procedure is iterated until a self-consistent solution is obtained. In this work, we extend this approach to 3D systems and introduce and evaluate procedures to decrease the computational demands of the method. This includes the use of purely local upscaling calculations for the initial estimation of coarse-scale transmissibilities and the use of reduced border regions during the iterations. This is shown to decrease the computational requirements of the reduced procedure significantly relative to the full methodology, while impacting the accuracy very little. The performance of the adaptive local-global upscaling technique is evaluated for three different heterogeneous reservoir descriptions. The method is shown to provide a high degree of accuracy for relevant flow quantities. In addition, it is shown to be less computationally demanding and significantly more accurate than some existing extended local upscaling procedures.
Fine-scale heterogeneity can have a significant impact on reservoir performance. Because it is usually not feasible to simulate directly on the detailed geocellular model, some type of upscaling is often applied to generate the simulation model from the geological description. Here, we focus on the upscaling of single-phase flow parameters, particularly absolute permeability. The algorithms we consider can provide either coarse-scale permeability, designated k *, or coarse-scale transmissibility, designated T* . It is important to emphasize that the accurate upscaling of permeability (which can be studied within the context of single-phase flow) is essential for the development of accurate coarse models of two-phase or multiphase flow. Thus the applicability of the methods developed here is very broad and includes all types of displacement processes.
|File Size||1 MB||Number of Pages||11|
Aarnes, J. 2004. On the use of amixed multiscale finite element method for greater flexibility and increasedspeed or improved accuracy in reservoir simulation. Multiscale Modeling andSimulation 2: 421-439.
Abbaszadeh, M. and Koide, N.1996. Evaluation of PermeabilityUpscaling Techniques and a New Algorithm for Interblock Transmissibilities.Paper SPE 36179 presented at the SPE Abu Dhabi International PetroleumExhibition and Conference, Abu Dhabi, 13-16 October. DOI:http://dx.doi.org/10.2118/36179-MS.
Chen, Y. and Durlofsky, L.J. 2006a. Adaptive local-global upscaling forgeneral flow scenarios in heterogeneous formations. Transport in PorousMedia 62 (2): 157-185. DOI: http://dx.doi.org/10.1007/s11242-005-0619-7.
Chen, Y. and Durlofsky, L.J. 2006b. Efficient incorporation of globaleffects in upscaled models of two-phase flow and transport in heterogeneousformations. Multiscale Modeling and Simulation 5:445-475.
Chen, Y., Durlofsky, L.J., Gerritsen, M., and Wen, X.H. 2003. A coupledlocal-global upscaling approach for simulating flow in highly heterogeneousformations. Advances in Water Resources 26 (10): 1041-1060. DOI:http://dx.doi.org/10.1016/S0309-1708(03)00101-5.
Christie, M.A. and Blunt, M.J. 2001. Tenth SPE Comparative Solution Project: A Comparison ofUpscaling Techniques.SPEREE 4 (4): 308-317. SPE-72469-PA. DOI:http://dx.doi.org/10.2118/72469-PA.
Deutsch, C.V. and Journel, A.G. 1998. GSLIB: Geostatistical SoftwareLibrary and User's Guide. Second edition. New York: Oxford U.Press.
Ding, Y. 1995. Scaling-Up in the Vicinity of Wellsin a Heterogeneous Field. Paper SPE 29137 presented at the SPE ReservoirSimulation Symposium, San Antonio, Texas, 12-15 February. DOI:http://dx.doi.org/10.2118/29137-MS.
Durlofsky, L.J. 1991. Numerical calculation of equivalent grid blockpermeability tensors for heterogeneous porous media. Water ResourcesResearch 27: 699-708. DOI: http://dx.doi.org/10.1029/91WR00107.
Durlofsky, L.J., Milliken, W.J., and Bernath A. 2000.Scaleup in the Near-Well Region. SPEJ 5 (1): 110-117. SPE-61855-PA. DOI:http://dx.doi.org/10.2118/61855-PA.
Gautier, Y., Blunt, M.J., and Christie, M.A. 1999.Nested gridding and streamline-based simulation for fast reservoir performanceprediction. Computational Geosciences 3 (3/4): 295-320. DOI: http://dx.doi.org/10.1023/A:1011535210857.
Gómez-Hernández, J.J. and Journel, A.G. 1994. Stochastic Characterization ofGridblock Permeabilities. SPEFE 9(2):93-99.SPE-22187-PA. DOI: http://dx.doi.org/10.2118/22187-PA.
Holden, L. and Nielsen, B.F.2000. Global upscaling of permeability in heterogeneous reservoirs: theoutput least squares (OLS) method. Transport in Porous Media 40(2):115-143. DOI: http://dx.doi.org/10.1023/A:1006657515753.
Jenny P., Lee, S.H., and Tchelepi, H.A. 2003. Multi-scale finite-volumemethod for elliptic problems in subsurface flow simulation. Journal ofComputational Physics 187: 47-67.
King, M.J. and Mansfield, M. 1999. Flow Simulation of GeologicModels. SPEREE 2 (4): 351-367. SPE-57469-PA. DOI:http://dx.doi.org/10.2118/57469-PA.
Lee, S.H., Tchelepi, H.A., Jenny, P., and DeChant, L.J.2002. Implementation of a Flux-Continuous Finite-DifferenceMethod for Stratigraphic, Hexahedron Grids. SPEJ 7 (3): 267-277. SPE-80117-PA. DOI:http://dx.doi.org/10.2118/80117-PA.
Pickup, G.E., Jensen, J.L., Ringrose, P.S., and Sorbie,K.S. 1992. A method for calculating permeability tensors using perturbedboundary conditions. Proc., European Conference on the Mathematics ofOil Recovery, Delft, The Netherlands, 17-19 June.
Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. 1992.Numerical Recipes in C, The Art of Scientific Computing. Second edition.New York: Cambridge U. Press.
Ruge, J.W. and Stuben, K. 1987. Algebraic Multigrid (AMG). In MultigridMethods. S.F. McCormick (ed.), SIAM Frontiers in AppliedMathematics 3: 73-130.
White, C.D. and Horne, R.N. 1987. Computing Absolute Transmissibilityin the Presence of Fine-Scale Heterogeneity. Paper SPE 16011 presented atthe SPE Symposium on Reservoir Simulation, San Antonio, Texas, 1-4 February.DOI: http://dx.doi.org/10.2118/16011-MS.
Wu, X.H., Efendiev, Y.R., and Hou, T.Y. 2002. Analysis of upscaling absolutepermeability. Discrete and Continuous Dynamical Systems, Series B2: 185-204.