Do cracks improve the conductive ability of porous rocks?

Abstract

AbstractCracks widely exist in rocks and are important in various geophysical applications. However, although electrical methods are conventionally employed for the detection and characterization of cracks, the fundamental question whether cracks improve the conductive ability of porous rocks (a quantification of their electrical conductivity if their porosity and saturant are the same) remains largely unaddressed. We address this knowledge gap through theoretical models with confirmed validity. We show that the conductive ability of a rock containing non‐interacting penny‐shaped cracks with random orientation will be improved only in the case when the aspect ratio of the cracks is below a certain value, which is referred to as the critical crack aspect ratio. We also show that the critical crack aspect ratio is uniquely determined by the porosity and electrical conductivity (or cementation exponent) of the porous rock where the cracks reside. We further demonstrate that the critical crack aspect ratio is some representation of the pore structure, and using two times the critical crack aspect ratio as the pore geometry can give rise to a reasonable agreement between modelled and measured P‐ and S‐wave velocities. The critical crack aspect ratio offers a consistent microstructure for the joint elastic–electrical modelling for the improved characterization of cracks through integrated seismic and electrical surveys.