Modeling Fluid Flow in Heterogeneous and Anisotropic Porous Media

Permeability distribution in reservoirs is very important for the flow ofwater or oil and gas. In this study, the effects of various heterogeneous permeability distributions on the flow field are simulated using the finite difference technique. We have simulated the flow for two types of heterogeneous distributions, one is Gaussian and the other is self-similar or fractal, the latter being much rougher than the former. The results show that the flow is not sensitive to the roughness of the distribution. In the case of lineated heterogeneities, anisotropy in the flow properties occurs. The anisotropy is not very significant if the lineated highly permeable regions are surrounded by less permeable regions. However, in the case of lineated fractures, where the background permeability is small, the flow is very sensitive to the direction of the lineation, such anisotropy can produce orders of magnitude difference in permeability. Furthermore, it is shown that the degree of anisotropy depends on the connectivity of the fractures. The anisotropy decreases with decreasing connectivity.