Abstract
We develop an Eulerian-Lagrangian numerical model for the simulation of fully miscible, highly compressible, multicomponent fluid flow processes through compressible porous media with multiple injection and production wells. We describe the numerical schemes, the treatment of the multiple injection and production wells, problems related to characteristic tracking, and other issues. We perform numerical experiments to investigate the performance of the numerical model. These results show that the numerical model generates robust, stable, and physically reasonable simulations without nonphysical oscillation or excessive numerical diffusion, even in the presence of multiple injection and production wells and the use of large time steps and coarse spatial grids. Finally, numerical experiments to well known test problems show that the numerical model does not generate noticeable grid orientation effect.
Similar content being viewed by others
References
Aziz, H., Settari, A.: Petroleum Reservoir Simulation. Applied Science Publishers, New York (1979)
Bouloutas, E.T., Celia, M.A.: An improved cubic Petrov-Galerkin method for simulation of transient advection-diffusion processes in rectangularly decomposable domains. Comp. Meth. Appl. Mech. Engrg. 91, 289–308 (1991)
Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics, vol. 15, Springer-Verlag, New York (1991)
Celia, M.A., Russell, T.F., Herrera, I., Ewing, R.E.: An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Advances in Water Resources 13, 187–206 (1990)
Douglas, J. Jr., Furtado, F., Pereira, F.: On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs. Computational Geoscience 1, 155–190 (1997)
Ewing, R.E. (eds.): The Mathematics of Reservoir Simulation. Research Frontiers in Applied Mathematics, vol. 1, SIAM, Philadelphia (1984)
Ewing, R.E., Russell, T.F., Wheeler, M.F.: Simulation of miscible displacement using mixed methods and a modified method of characteristics. SPE 12241, 71–81 (1983)
Finlayson, B.A.: Numerical Methods for Problems with Moving Fronts. Ravenna Park Publishing, Seattle (1992)
Firoozabadi, A.: m Thermodynamics of Hydrocarbon Reservoirs. McGraw-Hill, New York (1999)
Helmig, R.: Multiphase Flow and Transport Processes in the Subsurface. Springer Verlag, Berlin (1997)
Lax, P.D., Wendroff, B.: Systems of conservation laws. Comm. Pure Appl. Math. 13, 217–237 (1960)
Lohrenz, J., Bray, B., Clark, C.: Calculating viscosities of reservoir fluids from their composition. J. Pet. Tech. 16, 1171–1176 (1964)
Morton, K.W., Priestley, A., Süli, E.: Stability of the Lagrangian-Galerkin method with nonexact integration. RAIRO M2AN 22, 123–151 (1988)
Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15, 59–64 (1976)
Pironneau, O.: On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numer. Math. 38, 309–332 (1982)
Pollock, D.W.: Semianalytical computation of path lines for finite-difference models. Ground Water 26, 743–750 (1988)
Raviart, P.A., Thomas, J.M.: A mixed finite element method for second order elliptic problems. In: Galligani Magenes (eds.), Mathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics, vol. 606, pp. 292–315. Springer-Verlag, Berlin (1977)
Russell, T.F., Trujillo, R.V.: Eulerian-Lagrangian localized adjoint methods with variable coefficients in multiple dimensions. In: Gambolati, (ed.), Computational Methods in Surface Hydrology. pp. 357–363 Springer-Verlag, Berlin (1990)
Russell, T.F., Wheeler, M.F.: Finite element and finite difference methods for continuous flows in porous media. In: Ewing (ed.), The Mathematics of Reservoir Simulation. pp. 35–106 SIAM, Philadelphia (1984)
Schafer-Perini, A.L., Wilson, J.L.: Efficient and accurate front tracking for two-dimensional groundwater flow models. Water Resources Research 27, 1471–1485 (1991)
Wang, H., Dahle, H.K., Ewing, R.E., Espedal, M.S., Sharpley, R.C., Man, S.: An ELLAM Scheme for advection-diffusion equations in two dimensions. SIAM J. Sci. Comput. 20, 2160–2194 (1999)
Wang, H., Ewing, R.E., Qin, G., Lyons, S.L., Al-Lawatia, M., Man, S.: A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations. J. Comput. Phys. 152, 120–163 (1999)
Wang, H., Liang, D., Ewing, R.E., Lyons, S.L., Gin, G.: An approximation to miscible fluid flows in porous media with point sources and sinks by an Eulerian-Lagrangian localized adjoint method and mixed finite element methods. SIAM J. Sci. Comput. 22, 561–581 (2000)
Yanosik, J., McCracken, T.: A nine-point, finite difference reservoir simulator for realistic prediction of adverse mobility ratio displacements. Soc. Pet. Eng. J. 19, 253–262 (1978)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by: G. Wittum
Rights and permissions
About this article
Cite this article
Wang, H., Zhao, W. & Ewing, R.E. A numerical modeling of multicomponent compressible flows in porous media with multiple wells by an Eulerian-Lagrangian method. Comput. Visual Sci. 8, 69–81 (2005). https://doi.org/10.1007/s00791-005-0153-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00791-005-0153-8