Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks |
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| Authors: | Chongbin Zhao Bruce E Hobbs Alison Ord Shenglin Peng Liangming Liu |
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| Institution: | (1) Computational Geosciences Research Centre, Central South University, Changsha, 410083, China;(2) CSIRO Division of Exploration and Mining, P.O. Box 1130, Bentley, WA, 6102, Australia |
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| Abstract: | In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical
coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions
to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried
inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical
solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long
axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are
expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively,
the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined
elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed
in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application
example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion
affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the
elliptic inclusion is of finite but nonzero values. |
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| Keywords: | Theoretical analysis Analytical solution Pore-fluid flow Buried inclined elliptic inclusion |
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