Fluid Transport in Porous Rocks. II. Hydrodynamic Model of Flow and Intervoxel Coupling

In a preceding paper [P. Mansfield and B. Issa,J. Magn. Reson. A122, 137–148 (1996)], a stochastic model of fluid flow in porous rocks based upon the experimental observation of water flow through a Bentheimer sandstone core was proposed. The flow maps were measured by NMR-imaging techniques. The stochastic theory led to a Gaussian velocity distribution with a mean value in accord with Darcy's law. Also predicted was a linear relationship between flow variance and mean fluid flow through rock, the Mansfield–Issa equation, originally proposed as an empirical relationship. In the present work a flow coupling mechanism between voxels is proposed. Examination of the flow coupling between isolated voxel pairs leads to a complementary explanation of the Gaussian velocity distribution, and also gives further details of the Mansfield–Issa equation. These details lead to a new expression for the connectivity, 〈C〉, between voxels with an experimental value of 〈C〉 = 5.64 × 10⁻⁹for Bentheimer sandstone.