A parallel algorithm for two phase multicomponent contaminant transport. (English) Zbl 0833.65139

When trying to model complex chemical processes, like biological decontamination for instance, one comes across some troubles. The physical, chemical and geologic definition of the problem is a partial one only, and in addition, the chemical process involves interphase mass transfer as well as a host of interphase chemical reactions, including dissolution, ion exchange, adsorption, and so on.
It appears that parallel computation offers a useful alternative for simulating such processes, and the present paper shows how this can be made. In section three one describes the parallel implementation of the model (water phase, air phase, state equation, Darcy’s law, capillarity pressure, volume balance), and then section four displayes some simulation results.


65Z05 Applications to the sciences
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
80A22 Stefan problems, phase changes, etc.
35R35 Free boundary problems for PDEs
35Q80 Applications of PDE in areas other than physics (MSC2000)
80A32 Chemically reacting flows
76S05 Flows in porous media; filtration; seepage
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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[1] T. Arbogast, A. Chilakapati, and M. F. Wheeler: A characteristic-mixed method for contaminant transport and miscible displacement. Computational Methods in Water Resources IX, Vol. 1: Numerical Methods in Water Resources, Russell, Ewing, Brebbia, Gray, and Pindar (eds.), Computational Mechanics Publications, Southampton, U.K., 1992, pp. 77-84.
[2] T. Arbogast, C. N. Dawson, P. T. Keenan, M. F. Wheeler, and I. Yotov: Implementation of mixed finite element methods for elliptic equations on general geometry (submitted).
[3] T. Arbogast, C. Dawson, D. Moore, F. Saaf, C. San Soucie, M. F. Wheeler, and I. Yotov: Validation of the PICS transport code. Technical Report, Department of Computational and Applied Mathematics, Rice University, 1993.
[4] T. Arbogast, and M. F. Wheeler: A characteristics-mixed finite element method for advection dominated transport problems. SIAM J. Numerical Analysis (in press) (1995). · Zbl 0823.76044
[5] T. Arbogast, and M. F. Wheeler: A parallel numerical model for subsurface contaminant transport with biodegradation kinetics. The Mathematics of Finite Elements and Applications, Whiteman, J.R. (ed.), Wiley, New York, 1994, pp. 199-213. · Zbl 0828.76047
[6] T. Arbogast, M. F. Wheeler, and I. Yotov: Logically rectangular mixed methods for groundwater flow and transport on general geometry. Computational Methods in Water Resources X, Vol. 1, Peters, A., et al. (eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994, pp. 149-156.
[7] T. Arbogast, M. F. Wheeler, and I. Yotov: Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences (submitted). · Zbl 0880.65084
[8] C. Y. Chiang, C. N. Dawson and M. F. Wheeler: Modeling of In-situ biorestoration of organic compounds in groundwater. Transport in Porous Media 6 (1991), 667-702.
[9] C. N. Dawson: Godunov-mixed methods for advective flow problems in one space dimension. SIAM J. Numer. Anal. 28, (1991), 1282-1309. · Zbl 0741.65068
[10] C. N. Dawson: Godunov-mixed methods for advection-diffusion equations in multidimensions. SIAM J. Numer. Anal. 30 (1993), 1315-1332. · Zbl 0791.65062
[11] J. C. Evans, R. W. Bryce, D. J. Bates, and M. L. Kemner: Hanford Site Ground-Water Surveillance for 1989. PNL-7396, Pacific Northwest Laboratory, Richland, Washington, 1990.
[12] M. C. Hagood, and V. J. Rohay: 200 West area carbon tetrachloride expedited response action project plan. WHC-SD-EN-AP-046, Westinghouse Hanford Company, Richland, Washington, 1991.
[13] B. Herrling, J. Stamm, and W. Buermann: Hydraulic circulation system for in situ bioreclamation and/or in situ remediation of strippable contamination. In Situ Bioreclamation, Applications and Investigations for Hydrocarbon and Contaminated Site Remediation, Hinchee, R.E., and Olfenbuttel, R.F. (eds.), Butterworth-Heinemann Pub., Boston, 1991, pp. 173-195.
[14] P. T. Keenan, and J. Flower: PIERS Timings on Various Parallel Supercomputers. Dept. of Computational and Applied Mathematics Tech. Report #93-29, Rice University, 1993.
[15] G. V. Last, R. J. Lenhard, B. N. Bjornstad, J. C. Evans, K. R. Roberson, F. A. Spane, J. E. Amonette, and M. L. Rockhold: Characteristics of the volatile organic compound-arid integrated demonstration site. PNL-7866, Pacific Northwest Laboratory, Richland, Washington, 1991.
[16] J. C. Parker: Multiphase flow and transport in porous media. Reviews of Geophysics 27 (1989), 311-328.
[17] D. W. Peaceman: Fundamentals of Numerical Reservoir Simulation. Elsevier, Amsterdam, 1977.
[18] R. G. Riley: Arid site characterization and technology assessment: volatile organic compounds-arid integrated demonstration. PNL-8862, Batalle, Pacific Northwest Laboratory, 1993.
[19] R. S. Skeen, K. R. Roberson, T. M. Brouns, J. N. Petersen, and M. Shouche: In-situ bioremediation of Hanford groundwater. Proceedings of the 1st Federal Environmental Restoration Conference, Vienna, Virginia, 1992.
[20] J. M. Thomas, M. D. Lee, P. B. Bedient, R. C. Borden, L. W. Canter, and C. H. Ward: Leaking underground storage tanks: remediation with emphasis on in situ biorestoration. Environmental Protection Agency 600/2-87, 008, 1987.
[21] J. A. Wheeler, R. and Smith: Reservoir simulation on a hypercube, SPE 19804. Proceedings of the 64th Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Richardson, Texas, 1989.
[22] M. F. Wheeler, C. N. Dawson, P. B. Bedient, C. Y. Chiang, R. C. Borden, and H. S. Rifai: Numerical simulation of microbial biodegradation of hydrocarbons in groundwater. Proceedings of AGWSE/IGWMCH Conference on Solving Ground Water Problems with Models, National Water Wells Association, 1987, pp. 92-108.
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