Semianalytical Approach to the Computation of the Laplace Transform of Source Functions

L. G. Thompson () and G. Zhao ()
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L. G. Thompson: The University of Tulsa
G. Zhao: University of Regina

A chapter in Integral Methods in Science and Engineering, 2011, pp 369-378 from Springer

Abstract: 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.

Keywords: Source Function; Laplace Transform; Horizontal Well; Heterogeneous Reservoir; Linear Conduction (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-8176-8238-5_34

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