Effects of inhomogeneities in flow and wave transmission in porous media
Abstract
We study the effect of inhomogeneities in two different problems. In the first part of this work we examine, by means of numerical experiments, the effect of heterogeneous material on the Type II wave of Biot theory. An existing model due to Douglas, Santos, et. al., is adapted and used to study the effects of local inhomogeneities on the order of the wavelength of the Type II wave. We have varied the permeability in the porous medium, adjusted the porosity in accordance with a Kozeny-Carman relation, and recomputed the elastic coefficients. Both random and periodic variations are considered, including the insertion of randomly placed impermeable zones. Significant scattering of the Type II wave is observed when the spatial scale of the permeability variations is correlated with the wavelength of the Type II wave and does not occur if the variations are more rapid or less so. In the second part of this work we examine the effect of inhomogeneous matrix blocks on oil recovery during a waterflood of a naturally fractured petroleum reservoir. The Tall Block model, which has been developed by Douglas, Arbogast, et. al., is modified to handle heterogeneous matrix blocks. The results of numerical simulations are discussed. These results show that heterogeneity can have a significant effect on the oil recovery.
Degree
Ph.D.
Advisors
Douglas, Purdue University.
Subject Area
Mathematics|Petroleum production
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