Pressure dependence of permeability: a model for cracked rocks

Abstract

We assume that permeability in crystalline rocks is mainly controlled by interconnected cracks. Following Dienes (1982), statistical distributions of cracks are introduced (crack aperture and radius distributions, spatial distribution). Percolation theory is used to describe the interconnection of cracks. At first, we assume that cracks are smooth and close elastically under pressure. In that case, permeability evolution results from both variations of crack aperture and interconnection. In a second step, crack roughness is taken into account: when asperities of rough‐walled cracks make contact, the evolution of cracks is controlled by asperities indentation. Two different possibilities are then considered: modification of the flow tortuosity or modification of the crack aperture. Calculations are performed for both of these situations and we compare theoretical models with experimental results. It appears that the tortuosity effect is negligible and that the second model gives the best results and describes well the permeability decrease. Values of microstructural parameters introduced are realistic, so that it seems possible to predict the permeability evolution from the observation of microstructural parameters. Copyright © 1989, Wiley Blackwell. All rights reserved