GENERALIZATION OF THE POISEUILLE LAW FOR ONE-PHASE AND 2-PHASE FLOW IN A RANDOM CAPILLARY NETWORK

Study of single-phase fluid flow in a three-dimensional (3D) random ca pillary network on a regular cubic lattice has established a simple ge neralization of the Poiseuille law for the total flow. Results are dis cussed in the light of effective-medium theory and percolation theory. Detailed examination of the behavior of such networks near percolatio n threshold leads to an extended model which is appropriate for phase conductivities in two-phase flow. The simple expression for conductivi ty when combined with pore phase occupancy distributions from a rule-b ased percolation approach can be used to calculate relative permeabili ties in 3D networks.