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Secondary Water Recovery by Air Injection: 2. The Implicit Simultaneous Solution Method
Author(s) -
Moridis George J.,
Reddell Donald L.
Publication year - 1991
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr01130
Subject(s) - classification of discontinuities , secondary air injection , mechanics , capillary action , discontinuity (linguistics) , saturation (graph theory) , capillary pressure , nonlinear system , boundary value problem , flow (mathematics) , atmospheric pressure , materials science , mathematics , geotechnical engineering , thermodynamics , geology , mathematical analysis , physics , meteorology , porous medium , combinatorics , quantum mechanics , porosity
The finite difference equations of air and water flow in air‐driven secondary water recovery define a multidimensional strongly nonlinear system with sharp pressure and saturation fronts, large differences in the magnitude of flow coefficients, physical and mathematical discontinuities, sudden flow reversals, and high injection rates. The implicit simultaneous solution (SS) method, which solves simultaneously for the unknown pressures and saturation changes, was the sole method capable of handling these problems. Instabilities were alleviated by introducing implicit flow coefficients, implicit capillary pressures, and implicit accumulation terms. The treatment of hysteresis was based on petroleum engineering models. The concept of two separate air‐water interfaces was introduced: (1) the “zero air saturatution interface,” which indicates the physical boundary of air discontinuity, and (2) the “zero capillary pressure interface,” defined as the upper boundary of a zero capillary pressure zone. A method for the numerical tracking of the two interfaces, necessary for the evaluation of the effectiveness of secondary water recovery, was also developed.