Time-Dependent Shape Factors for Uniform and Non-Uniform Pressure Boundary Conditions |
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Authors: | Edgar R Rangel-German Anthony R Kovscek Serhat Akin |
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Institution: | (1) Department of Civil and Environmental Engineering, University of Alberta, School of Mining and Petroleum, 3-112 Markin CNRL-NREF, Edmonton, AB, Canada, T6G 2W2; |
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Abstract: | Matrix–fracture transfer functions are the backbone of any dual-porosity or dual-permeability formulation. The chief feature
within them is the accurate definition of shape factors. To date, there is no completely accepted formulation of a matrix–fracture
transfer function. Many formulations of shape factors for instantly-filled fractures with uniform pressure distribution have
been presented and used; however, they differ by up to five times in magnitude. Based on a recently presented transfer function,
time-dependent shape factors for water imbibing from fracture to matrix under pressure driven flow are proposed. Also new
matrix–fracture transfer pressure-based shape factors for instantly-filled fractures with non-uniform pressure distribution
are presented in this article. These are the boundary conditions for a case for porous media with clusters of parallel and
disconnected fractures, for instance. These new pressure-based shape factors were obtained by solving the pressure diffusivity
equation for a single phase using non-uniform boundary conditions. This leads to time-dependent shape factors because of the
transient part of the solution for pressure. However, approximating the solution with an exponential function, one obtains
constant shape factors that can be easily implemented in current dual-porosity reservoir simulators. The approximate shape
factors provide good results for systems where the transient behavior of pressure is short (a case commonly encountered in
fractured reservoirs). |
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