Effective fluid transport properties of deformable rocks

Abstract

Modern reservoir monitoring technologies often make use of diffusion waves in order to estimate the hydraulic conductivity and diffusivity of reservoir rocks. However, most theoretical descriptions for these effective uid transport properties assume that the host rock is elastically rigid. Inhomogeneous poroelastic continua described by Biot's equations of dynamic or quasi-static poroelasticity provide an adequate framework to study the dependence of uid transport properties on the elastic properties of the host rock. Analysis of diffusion wave elds in randomly inhomogeneous poroelastic structures provides new insight into how uctuations of the compressible constituents of the rock affect the effective diffusivity. Using the method of statistical smoothing we derive an effective wave number of the coherent diffusion wave eld. This wave number yields expressions for the effective conductivity and diffusivity of a deformable and inhomogeneous porous medium. These uid transport properties are frequency-dependent. Comparison of the hydraulic conductivity derived here with that estimated from unsteady ow through porous media based on Darcy's law shows that they are identical in the limits of low and high frequencies.