Effective Diffusivity of Heterogeneous Porous Rocks

Modern reservoir monitoring technologies often make use of diffusion waves <br>in order to estimate the hydraulic conductivity and diffusivity of reservoir rocks.<br>Analysis of diffusion wave fields in randomly inhomogeneous poroelastic structures<br>provides new insight how fluctuations of the compressible constituents of<br>the rock affect the effective diffusivity.<br>Based on the method of statistical smoothing an effective wave number of the <br>coherent diffusion wave field is computed. <br>From this wave number both an effective conductivity and diffusivity are<br>identified.<br>The correspondence between this conductivity and that estimated from unsteady<br>flow through porous media based on Darcy's law is elucidated. <br>It is shown that in the limits of low and high frequencies these effective<br>conductivities are identical.