Modeling fluid flow in heterogeneous and anisotropic porous media

Abstract

Permeability distribution in reservoirs is very important for the flow of water 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.

Solute Transport in the Element of Fractured Porous Medium with an Inhomogeneous Porous Block

“…j+1 are indeterminate coefficients. When using ( 39) from (31), we obtain the following recurrence formulas for determining the coefficients α…”

“…The inhomogeneity of the porous block in terms of porosity and permeability leads to heterogeneity of the medium and in the sense of diffusion solute transport in it. In [30,31], the behavior of solute transport in inhomogeneous media was numerically studied with emphasis on the influence of permeability inhomogeneities. There are two main mechanisms that control the solute transport process-diffusion and advection.…”

“…The dispersion effect promotes diffusion and mechanical mixing during the solute transport due to advection of the liquid. The effects of heterogeneity on the processes of solute transport were studied using various permeability distributions, which are characterized as continuous and discontinuous models [31]. For continuous distribution models, numerical simulations show that the tracer distribution is distorted by a local change in permeability, but the global distribution behavior still resembles a uniform distribution behavior.…”