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Approximate Solutions for Forchheimer Flow to a Well |
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| Authors: | Simon A. Mathias Adrian P. Butler Hongbin Zhan |
| Affiliation: | 1Lecturer, Dept. of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, U.K. E-mail: simon.mathias@imperial.ac.uk 2Reader, Dept. of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, U.K. E-mail: a.butler@imperial.ac.uk 3Associate Professor, Dept. of Geology and Geophysics, Texas A&M Univ., College Station, TX 77843-3115. E-mail: zhan@geo.tamu.edu |
| Abstract: | An exact solution for transient Forchheimer flow to a well does not currently exist. However, this paper presents a set of approximate solutions, which can be used as a framework for verifying future numerical models that incorporate Forchheimer flow to wells. These include: a large time approximation derived using the method of matched asymptotic expansion; a Laplace transform approximation of the well-bore response, designed to work well when there is significant well-bore storage and flow is very turbulent; and a simple heuristic function for when flow is very turbulent and the well radius can be assumed infinitesimally small. All the approximations are compared to equivalent finite-difference solutions. |
| Keywords: | Turbulent flow Wells Hydraulics Numerical models Finite difference method |