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An Analytical Approach to the Hot Water Drive
Author(s) -
Gilbert R. P.,
Jeffrey A.,
Meek P.
Publication year - 1984
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19840641202
Subject(s) - mathematics , algebraic equation , nonlinear system , work (physics) , representation (politics) , saturation (graph theory) , viscosity , numerical integration , algebraic number , numerical analysis , mathematical analysis , thermodynamics , physics , quantum mechanics , combinatorics , politics , political science , law
In this work, a hybrid scheme, analytical and numerical, is devised to solve the one‐dimensional hot water drive for secondary oil recovery problems. In our model capillary pressure and gravity are ignored. It is shown how when the oil viscosity variation as a function of temperature is specified the oil and water saturations may be found by numerical integration of a first‐order nonlinear hyperbolic equation which involves the fluid temperature. The numerical scheme makes use of ideas due to Meek and Norburry [8] and leads to a system of algebraic equations where only a single iteration is necessary to obtain a second‐order accurate (in time) approximation to the solution of the saturation equation. It is then shown that the fluid and also the solid temperature may be found analytically in terms of the solution to a Goursat‐problem. The integral representation of this problem is then evaluated numerically and used in the saturation equation.