Fluid transport in porous rocks. I. EPI studies and a stochastic model of flow

The velocity of water flowing through a Bentheimer sandstone core has been measured by NMR-imaging techniques. The localized pixel values of velocity indicate a random distribution centered around the mean value corresponding to Darcy's law. When the same flow state is repeated, the velocity map changes but the general characteristics of the velocity distribution remain unchanged. The random nature of the irreproducibility of the flow maps has led us to propose a stochastic theory of flow in porous rocks. The theory leads to a Gaussian velocity distribution which approximates well to the data. Also predicted is a linear relationship between flow variance and mean fluid flow through the rock, the Mansfield-Issa equation, originally proposed as an empirical relationship.