Similarity Analysis of Instability Phenomenon in Porous Media with Mean Capillary Pressure
Keywords:
Non-Linear Ordinary Differential Equation, Homogeneous Medium, Linear FunctionalAbstract
In the present paper, we analytically discussed the phenomenon of instability in polyphasic flow through porous media with the assumption of mean pressure. We consider that water is injected at a uniform rate into an oil-saturated porous medium, and at the interface between the two fluids, there arise protuberance of water into oil zone at relatively greater speeds, compared to the average movement of the interface. In this paper, we have applied a continuous group transformation technique of a similarity analysis, which reduces the governing non-linear partial differential equation to a non-linear ordinary differential equation. The existence and uniqueness of solution of this reduced solution is indicated. A perturbation solution of equation is obtained using the method of composite expansions.
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