Distribution theory and transform analysis: an introduction to generalized functions, with applications
Analysis of a Finite Element Method--PDE/PROTRAN
Analysis of a Finite Element Method--PDE/PROTRAN
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This paper is aimed at developing a methodology for studying the transient pressure behavior of horizontal wells with any curvilinear trajectory in an isotropic/anisotropic arbitrarily shaped reservoir. This methodology employs generalized functions to represent the tortuous horizontal well. A particular way of removing the singularities involved in the partial differential equation is based on reducing the original problem to the conventional solution of the homogeneous diffusivity equation under any given initial and boundary conditions The Green function method and any standard numerical technique are combined in a single computational strategy to obtain the transient pressure response generated by a curved and twisted horizontal well in reservoirs with irregular boundaries. Analytical methods can be also used, whenever possible, to solve the reduced problem. This proposal can be easily broadened to analyze the performance of the pressure transient of any kind of reservoir sources or sinks that can be modeled using generalized functions. Some models are presented.