REAL-SPACE RENORMALIZATION ESTIMATES FOR 2-PHASE FLOW IN POROUS-MEDIA

We present a spatial renormalization group algorithm to handle immisci ble two-phase flow in heterogeneous porous media. We call this algorit hm FRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Alg orithm for Correlated Transport in Anisotropic Media, and the R stands for relative permeability. Originally, FRACTAM was an approximate ite rative process that replaces the L x L lattice of grid blocks, represe nting 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 su ch a way that finding the solution of the two-phase flow equations bec omes trivial. This triviality translates in practice into computer eff iciency. For N = L x L grid blocks we find that the computer time nece ssary to calculate fractional flow F(t) and pressure P(t) as a functio n 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 simi lar to N-2.3. The solution we find in this way is an acurate approxima tion to the direct solution of the original problem.