A microscopic model of fluid transport in porous rocks

NMR measurements of water velocity flowing through two different porous rocks, Bentheimer and Clashach, have been made using the PEPI sequence. Random changes of localised velocity occur in both materials even though the average velocities across the core cross-sections follow Darcyʹs Law. The velocity distributions are approximately Gaussian and the velocity variance follows a linear relationship with mean velocity as predicted in the stochastic theory of Mansfield and Issa. The origin of the large fluctuations in localised velocity is thought to be hydrodynamic and a detailed theory of intervoxel coupling is presented, which accounts for such behaviour in a coupled voxel array. In this work the intervoxel coupling is restricted to isolated voxel pairs.