Governing equations for the coupled electromagnetics and acoustics of porous media

TLDR

Porous media are modeled as solid grain packings saturated with electrolyte, exemplified by sedimentary rocks. The study derives the macroscopic governing equations for coupled electromagnetics and acoustics in porous media from first principles. The equations are obtained by volume‑averaging the fluid and solid phase equations and incorporating interface boundary conditions, with electrokinetic coupling arising from surface‑adsorbed excess charge balanced by mobile ions. The resulting equations resemble Maxwell’s equations coupled to Biot’s equations, with frequency‑dependent transport coefficients explicitly linked and Onsager reciprocity derived rather than assumed.

Abstract

The macroscopic governing equations controlling the coupled electromagnetics and acoustics of porous media are derived here from first principles. The porous material is assumed to consist of a packing of solid grains that is saturated by an electrolyte. A sedimentary rock is an example of such a material. The approach is to volume average the equations known to apply in the fluid and solid phases while allowing for the boundary conditions that exist on the fluid-solid interface. The coupling is due to a layer of excess charge adsorbed to the sufaces of the solid grains that is balanced by mobile ions in the fluid electrolyte; i.e., the coupling is electrokinetic in nature. The derived equations have the form of Maxwell's equations coupled to Biot's equations with coupling occurring in the flux-force (or transport) relations. The frequency-dependent macroscopic-transport coefficients are explicitly obtained and related to each other. Onsager reciprocity is derived and is not simply postulated.