Analytical solution of a pressure transmission experiment

Abstract

Analytical solutions are derived for a pressure transmission experiment of a saturated charged compressible porous medium. The governing equations describe infinitesimal deformations of charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoupled introducing a set of normal parameters, being a linear combination of the eigenvectors of the diffusivity matrix. The magnitude of the eigenvalues of the diffusivity matrix correspond to the time scales for Darcy flow, diffusion of ionic constituents and diffusion of electrical potential.1 Introduction Shales exhibit swelling and shrinkage behavior induced by changes in external salt concentration. Swelling and shrinkage results from the interaction between the fixed charges on the solid and ions present in the fluid. Donnan-osmosis, electroosmosis, streaming potentials and streaming currents, (Mitchell 1993) are observed phenomena. Swelling of shales is of major concern for petroleum engineering during active drilling, (Heidug and Wong 1996) (Frijns et al. 1997). The solution procedure has been verified using an analytical solution of confined swelling and compression by (van Meerveld et al. 2003). While these biomechanical models in-