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Some theoretical results concerning the displacement of a viscous oil by a hot fluid in a porous medium

Published online by Cambridge University Press:  28 March 2006

F. J. Fayers
F. J. Fayers
Affiliation:
California Research Corporation, La Habra, California
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Abstract

Two simultaneous first-order non-linear equations are derived to give a ’high-flow-rate’ model for the displacement of oil by hot water in a porous medium. The solution of these equations is analysed by the method of characteristics and it is shown that in problems for which thermal capacity dependence on temperature is neglected, the solution will have the properties of a simple wave. The simple wave behaviour gives a rapid method for solving practical systems. When temperature dependence is included in the thermal capacities, it is found that a simultaneous shock in temperature and saturation develops, but the solution will usually approximate quantitatively the simple wave result. Decoupling the equations by using an average saturation in the heat transport equation gives results in reasonable agreement with the coupled case.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 13 , Issue 1 , May 1962 , pp. 65 - 76
Copyright
© 1962 Cambridge University Press

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References

Buckley, S. E. & Leverett, M. C. 1942 Mechanism of fluid displacement in sands. Trans. AIME, 146, 107.Google Scholar
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. New York: Interscience.
Scheidegger, A. E. 1957 The Physics of Flow Through Porous Media, Ch. VIII. London: MacMillan.
Von Mises, R. 1958 Mathematical Theory of Compressible Fluid Flow. New York: Academic Press.