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- W96575619 abstract "The method of “Sources and Sinks” has has found wide application to the solution of the diffusion equation for linear conduction of heat in infinite, semi-infinite and finite solids; see, for example, (Carslaw and Jaeger, 1988). Since reservoir flow of a slightly compressible, constant viscosity fluid is governed by the diffusion equation, fundamental solutions of the one-dimensional diffusion equation are routinely used to build solutions to three-dimensional flow problems using the Newmann product method (Newmann, 1936). These solutions can be rapidly generated for constant-rate production (or injection) to a uniform-flux line or plane in an anisotropic homogeneous reservoir; (see for example, (Gringarten and Rame, 1973)). However, for variable-rate, variable-flux or complex-geometry (heterogeneous reservoir) problems, solutions are most easily generated by manipulating Laplace transforms of the product solutions and inverting to the time domain using a numerical inversion procedure such as the Stehfest algorithm (Stehfest, 1970). Raghavan and Ozkan (1994) presented complete analytical expressions for the Laplace transforms of the 3-D source functions. For flow in rectangular parallelepiped reservoirs, their expressions involve triple infinite series." @default.
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- W96575619 date "2011-01-01" @default.
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- W96575619 title "Semianalytical Approach to the Computation of the Laplace Transform of Source Functions" @default.
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