Abstract
An Eulerian-Lagrangian localized adjoint method (ELLAM) is presented for compressible flow occurring in compressible porous media with wells. The ELLAM scheme symmetrizes the governing transport equation, greatly eliminates non-physical oscillation and/or excessive numerical dispersion present in many large-scale simulators widely used in industrial applications, and conserves mass. Computational experiments show that the ELLAM scheme can accurately simulate incompressible and compressible fluid flows in porous media with wells, even though coarse spatial grids and very large time steps, which are one or two orders of magnitude larger than those used in many numerical methods, are used. The ELLAM scheme can treat large mobility ratios, discontinuous permeabilities and porosities, anisotropic dispersion in tensor form, and wells.
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, H. and Settari, A., Petroleum Reservoir Simulation, Applied Science Publishers, 1979.
Bear, J., Hydraulics of Groundwater, McGraw-Hill, New York, 1979.
Celia, M. A., Russell, T. F., Herrera, I., and Ewing, R. E., An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation, Advances in Water Resources 13 (1990), 187–206.
Douglas, J., Jr., Ewing, R. E., and Wheeler, M. F., A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, RARIO 17 (1983), 249–265.
Ewing, R. E. (ed.), The Mathematics of Reservoir Simulation, Research Frontiers in Applied Mathematics, 1, SIAM, Philadelphia, 1984.
Ewing, R. E., Russell, T. F., and Wheeler, M. F., Simulation of miscible displacement using mixed methods and a modified method of characteristics, SPE 12241 (1983), 71–81.
Healy, R. W. and Russell, T. F., A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation, Water Resources Research 29 (1993), 2399–2413.
Herrera, I., Ewing, R. E., Celia, M. A., and Russell, T. F., Eulerian-Lagrangian localized adjoint methods: the theoretical framework, Numerical Methods for Partial Differential Equations 9 (1993), 431–458.
Peaceman, D. W., Fundamentals of Numerical Reservoir Simulation, Elsevier, Amsterdam, 1977.
Wang, H., A family of ELLAM schemes for advection-diffusion-reaction equations and their convergence analyses, Numerical Methods for Partial Differential Equations 14 (1998), 739–780.
Wang, H., Ewing, R. E., Qin, G., Lyons, S. L., Al-Lawatia, M, and Man, S, A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations, J. Comput. Physics 152 (1999), 120–163.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, H., Liang, D., Ewing, R.E., Lyons, S.L., Qin, G. (2000). An Accurate Approximation to Compressible Flow in Porous Media with Wells. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_27
Download citation
DOI: https://doi.org/10.1007/3-540-45467-5_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67566-2
Online ISBN: 978-3-540-45467-0
eBook Packages: Springer Book Archive