Dynamic Fluid Flow in Heterogeneous Porous Media and through a Single Fracture with Rough Surfaces

This study investigates the frequency-dependence of fluid flow in heterogeneous porous media using the theory of dynamic penneability and a finite-difference method. Given a penneability distribution, the dynamic penneability is applied locally to calculate the frequency-dependence of fluid flow at each local point. An iterative Alternating Direction Implicit finite-difference technique is applied to calculate the flow field in the frequency domain. We compare the flow through a 2-D heterogeneous porous medium and that through an equivalent homogeneous medium and find that the two media do not behave equivalently as a function of frequency. At very low-frequencies, the heterogeneous medium is less conductive than the homogeneous medium, However, in the transition region from quasi-static to dynamic regimes, the fonner medium becomes more conductive than the latter medium, with the ratio of the fonner flow over the latter flow reaching a maximum in this region. The larger the scale, or the higher the degree of the heterogeneity, the higher this maximum is. This finding is important for studying the interaction of a borehole stoneley wave with a heterogeneous porous fonnation. The finite-difference technique is also applied to simulate frequency-dependent flow through a single fracture with rough surfaces. It is shown that the fiow exhibits strong frequency-dependence even for small fractures with contacting surfaces. The amount of flow through the fracture is reduced by the surface roughness .