Real-space renormalization estimates for two-phase flow in porous media

被引:14
作者
Hansen, A
Roux, S
Aharony, A
Feder, J
Jossang, T
Hardy, HH
机构
[1] Univ Oslo, Dept Phys, N-0316 Oslo, Norway
[2] Fracton AS, N-0873 Oslo, Norway
[3] Norges Tekn Nat Vitenskapelige Univ, Inst Fys, N-7034 Trondheim, Norway
[4] Ecole Super Phys & Chim Ind, Lab Phys & Mecan Mat Heterogene, CNRS, URA 857, F-75231 Paris 05, France
[5] Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Phys & Astron, IL-69978 Tel Aviv, Israel
[6] Conoco Inc, Geosci & Reservoir Res, Ponca City, OK 74603 USA
关键词
effective properties; relative permeability; renormalization numerical algorithm; heterogeneity; simulation;
D O I
10.1023/A:1006593820928
中图分类号
TQ [化学工业];
学科分类号
0817 ;
摘要
We present a spatial renormalization group algorithm to handle immiscible two-phase flow in heterogeneous porous media. We call this algorithm FRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithm for Correlated Transport in Anisotropic Media, and the R stands for relative permeability. Originally, FRACTAM was an approximate iterative process that replaces the L x L lattice of grid blocks, representing the reservoir, by a (L/2) x (L/2) one. In fact, FRACTAM replaces the original L x L lattice by a hierarchical (fractal) lattice, in such a way that finding the solution of the two-phase flow equations becomes trivial. This triviality translates in practice into computer efficiency. For N = L x L grid blocks we find that the computer time necessary to calculate fractional flow F(t) and pressure P(t) as a function of time scales as tau-N-1.7 for FRACTAM-R. This should be contrasted with the computational time of a conventional grid simulator tau similar to N-2.3. The solution we find in this way is an acurate approximation to the direct solution of the original problem.
引用
收藏
页码:247 / 279
页数:33
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