In this paper, Boundary Element (BEM) solutions were obtained for the transient flow of fluids through homogeneous, anisotropic porous media. The Greenís function method with Euler method of forward time differencing and Laplace transform method have been used by previous authors. Unlike these methods, this paper uses the fundamental solution to the differential equation and the convolution behavior of the resulting integrals to obtain an implicit and stable solution. This allows large time steps to be taken without significant loss in accuracy. Comparison with the Laplace transform method and Greenís function method with discrete time stepping, for two test cases, show that the method is very accurate. The computations however, become quite storage intensive owing to the dynamic increase in the number of stored matrices. It has been shown elsewhere that for certain problems with both Dirichlet and Neumann boundary conditions, asymptotic expression generated from exact solution is needed for starting the computational procedure. The present formulation alleviates this requirement. These solutions are developed for use in the analysis of pressure transients in complex reservoir problems.

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