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. A 122,137-148 (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^-9 for Bentheimer sandstone.