Connection between formation factor for electrical resistivity and fluid‐solid coupling factor in Biot’s equations for acoustic waves in fluid‐filled porous media

Abstract

The coefficient of inertial coupling between fluid and solid for elastic waves in fluid‐filled porous media is shown to be equal to or greater than the porosity times the low‐frequency electrical‐resistivity formation factor, being equal to this product when effects of fluid viscosity are minimal, as they may be for high‐frequency measurements on porous materials of high permeability and porosity. At sufficiently low frequencies, the coupling is due primarily to viscous forces. At intermediate frequencies, viscous forces increase inertial coupling, and inertial forces increase viscous coupling. Thus, porosity and formation factor measurements provide lower limits to coupling coefficients that can be used in the interpretation of acoustic data.