In a preceding paper [P. Mansfield and B. Issa, J. Magn. Reson. the constraint that a small and constant fraction of the applied A 122, 137-148 (1996)], a stochastic model of fluid flow in porous pressure difference across the selected slice was responsible rocks based upon the experimental observation of water flow for creating a random velocity distribution about the mean through a Bentheimer sandstone core was proposed. The flow value of velocity. maps were measured by NMR-imaging techniques. The stochastic
This approach has led to a prediction that the flow distributheory led to a Gaussian velocity distribution with a mean value in tion variance is proportional to the mean flow velocity, the soaccord with Darcy's law. Also predicted was a linear relationship called Mansfield-Issa equation. This was first proposed (2) as between flow variance and mean fluid flow through rock, the an empirical relationship but has now been placed on a theoreti-Mansfield-Issa equation, originally proposed as an empirical relacal basis in Part I. However, in deriving this expression, as tionship. In the present work a flow coupling mechanism between stated earlier, hydrodynamic energy conservation principles voxels is proposed. Examination of the flow coupling between isolated voxel pairs leads to a complementary explanation of the were used without reference to the detailed interaction mecha-Gaussian velocity distribution, and also gives further details of the nism responsible for the stochastic behavior.
Mansfield-Issa equation. These details lead to a new expression
In this paper we propose a model for flow coupling befor the connectivity, ยปCโฆ, between voxels with an experimental tween isolated voxel pairs and we show that this leads to value of ยปCโฆ ร
5.64 1 10 09 for Bentheimer sandstone. แญง 1996 both the Gaussian velocity distribution and the details of the Academic Press, Inc.
Mansfield-Issa equation. While it is not based on standard finite-element analysis, our approach could be regarded as modeling the finite element itself. It is, of course, still neces-