Abstract
A new algorithm is introduced for upscaling relative permeabilities, and tested in simulations of two-dimensional reservoir displacement processes. The algorithm is similar to existing algorithms for computing upscaled relative permeabilities from subgrid simulations, but uses new boundary conditions for the pressure field. The new 'effective flux boundary conditions' were introduced in a previous paper and provide a more accurate estimate of flux through high permeability channels. The algorithm was tested in conjunction with uniform grid coarsening and upscaled absolute permeabilities for a broad range of coarsenings. The permeability fields were highly heteroge-neous and layered, and were obtained from synthetic data and from conditioned realizations of actual oil reservoirs. The algorithm was tested for a wide variety of grid aspect ratios, and for both viscous-and gravity-dominated flow. Typical fine grids were of the order of 100×100 cells; the coarsest scaled-up grids were on the order of 5×5 cells. The quality of scale up was evaluated by comparing oil cut curves for the fine and coarse grid simulations. We consistently obtained excellent agreement, even at the coarsest levels of scale up.
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Christie, M. A., Mansfield, M., King, P. R., Barker, J. W. and Culverwell, I. D.: 1995, A Renormalisation-based upscaling technique for WAG floods in heterogeneous reservoirs, Paper SPE 29127 presented at the 1995 SPE Symposium on Reservoir Simulation, San Antonio, Feb. 12–15, SPE 29127, 353–361.
Durlofsky, L. J.: 1991, Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resource Res. 27(5), 699–708.
Durlofsky, L. J., Jones, R. C. and Milliken, W. J.: 1997, A nonuniform coarsening approach for the scale up of displacement processes in heterogeneous porous media, Adv. Water Resour. 20, 335–347.
King, P. R.: 1989, The use of renormalization for calculating effective permeability, Transport in Porous Media 4, 37–58.
King, P. R., Muggeridge, A. H. and Price, W. G.: 1993, Renormalization calculations of immiscible flow, Transport in Porous Media 12, 237–260.
Malik, M. A.: 1996, Geostatistical reservoir characterization and scale-up of permeability and relative permeability, Ph.D. thesis, University of Texas at Austin.
Muggeridge, A. H.: 1991, Generation of effective relative permeabilities from detailed simulation of flow in heterogenerous porous media, in: Reservoir Characterization II, Academic Press, pp. 197–225.
Peaceman, D. W.: 1977, Fundamentals of Numerical Reservoir Simulation, No. 6 in Developments in Petroleum Science. Elsevier, Amsterdam.
Stone, H. L.: 1991, Rigorous black oil pseudo functions, SPE proceedings (SPE 21207), 57–68. Presented at 11th SPE Symposium on Reservoir Simulation, Anaheim, CA, Feb 17–20.
Wallstrom, T. C., Christie, M. A., Durlofsky, L. J. and Sharp, D. H.: 2001, Effective flux boundary conditions for upscaling porous media equations, Transport in Porous Media (to appear).
Wallstrom, T. C., Hou, S., Christie, M. A., Durlofsky, L. J. and Sharp, D. H.: 1999a, Accurate scale up of two phase flow using renormalization and nonuniform coarsening, Comput. Geosci. 3, 69–87. (Also available as Los Alamos Technical Report LA-UR-98-2507).
Wallstrom, T. C., Hou, S., Christie, M. A., Durlofsky, L. J. and Sharp, D. H.: 1999b, Application of a new two-phase upscaling technique to realistic reservoir cross sections, in: SPE Symposium on Reservoir Simulation, pp. 451–462, SPE 51939. (Also available as Los Alamos Technical Report LA-UR-98-5397).
Wallstrom, T. C., Hou, S., Christie, M. A., Durlofsky, L. J., Sharp, D. H. and Zou, Q.: 1999c, Effective medium boundary conditions for upscaling relative permeabilities, Technical report, Los Alamos National Laboratory, LAUR 99-6488. Also presented at Upscaling Downunder, Melbourne, February 2000.
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Wallstrom, T., Hou, S., Christie, M. et al. Application of Effective Flux Boundary Conditions to Two-Phase Upscaling in Porous Media. Transport in Porous Media 46, 155–178 (2002). https://doi.org/10.1023/A:1015003527103
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DOI: https://doi.org/10.1023/A:1015003527103