Abstract
Elliptical flow is common in the near vertical fracture area and in anisotropic reservoirs. However, the classical radial flow models cannot provide a complete analysis for elliptical flow. This article presents a new mathematic model for gas elliptical flow in tri-porosity gas reservoirs. The differential equation of the new model is written in Mathieu equation, so that the solution can also be expressed by Mathieu functions. The numerical solution of the corresponding Mathieu functions ce2n(ξ, −q), Ke2n(ξ, −q) and their derivatives are obtained to derive the dimensionless pseudo pressure drop in Laplace space. The sensitivities of tri-porosity systems, including the parameters related to anisotropies CDe2S and ξw, the storativity ratios ωf and ωm, and the interporosity flow coefficients λvf and λmf, are studied using Laplace numerical inversion. The new solution includes not only the factors considered in classic solutions in previous articles, but also incorporates the effect of reservoir anisotropy.
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