Abstract
An implicit diffusive numerical procedure is formulated for computing the mole fraction distribution in a slightly compressible multicomponent single phase miscible displacement problem in a porous medium. This scheme has several desirable features including a substantial reduction of the "grid orientation" effect often observed with other methods. Theoretical convergence analyses for rectangular regions and computational results for this method are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aziz, K., and Settari, A., Petroleum Reservoir Simulation, Applied Science Publishers Ltd., London (1979).
Bavly, D., Harris, C. D., and Sheldon, J. W., "A method for general reservoir behavior simulation on digital computers, SPE, Paper 1521G presented at the 35th SPE Annual Fall Meeting, Denver, Colorado Oct. 2–5 (1960).
Bell, J. B., Shubin, and Wheeler, M. F., "Analysis of a new method for computing the flow of miscible fluids in a porous medium (to appear).
Bird, R. B., Lightfoot, W. E., and Stewart, E. N., Transport Phenomenon, John Wiley and Sons, New York (1960).
Bramble, J. and Hilbert, S., "Estimation of linear functionals on Sobolev space with application to Fourier transforms and spline interpolation, SIAM, J. Numer. Anal., 7, No. 1, 112–124 (1970).
Buckley, S. E. and Leverett, M. C., "Mechanism of fluid displacement in sands", Trans. AIME, 146, 107–110 (1942).
Coats, K. H. and Ramesh, A. B., "Effect of grid type and difference scheme on pattern steamflood simulation results", SPE, Paper 11079 presented at the Sixth SPE Symposium on Reservoir Simulation, New Orleans, La. (1982).
Darlow, B. D., Ewing, R., and Wheeler, M. F., "Mixed finite element method for miscible displacement problems in porous media", SPE, Paper 10501 presented at the Sixth SPE Symposium on Reservoir Simulation, New Orleans, La. (1982).
Douglas, J. Jr. and roberts, J. E., "Numerical methods for a model for compressible miscible displacement in porous media" (to appear).
Nitsche, J. A., "L∞ — convergence of finite element approximation", Proc. of the Second Conference on Finite Elements, Rennes France (1975).
Peaceman, D. W., Fundamentals of Numerical Reservoir Simulation, Elservier Scientific Publishing Co., New York (1977).
Peaceman, "Interpretation of well block pressures in numerical reservoir simulations with nonsquare grid blocks and anesotropic permeabilitys", SPE, Paper 10528 presented at the Sixth Symposium on Reservoir Simulation, New Orleans, La. (1982).
Potempa, T. C., Finite Element Methods for Convection Dominated Transport Problems, Ph. D. Thesis, Rice University (1982).
Potempa, T. C., "A numerical model of two dimensional, two component, single phase flow in a porous media" (to appear).
Potempa, T. C., "The effect of the definition of fractional flow upon grid effects in a numerical model of thermal processes" (to appear).
Potempa, T. C., "Three dimensional simulation of steam displacement processes with minimal grid orientation", SPE, Paper 11726 presented at the SPE California Regional Meeting, Ventura Calif. (1983).
Scott, R., "Optimal L∞ estimates for the finite element method on irregular meshes", Math Comp. 30, 681–697 (1976).
Young, L., "A finite element method for reservoir simulation", SPE Journal, Trans. AIME, 21, 115–128 (1981).
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Potempa, T.C., Wheeler, M.F. (1984). An implicit diffusive numerical procedure for a slightly compressible miscible displacement problem in porous media. In: Griffiths, D.F. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099528
Download citation
DOI: https://doi.org/10.1007/BFb0099528
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13344-5
Online ISBN: 978-3-540-38881-4
eBook Packages: Springer Book Archive