Forward and inverse problems in modeling of multiphase flow and transport through porous media

Computational Geosciences

Volumn 8, Issue 1, 2004, Pages 21-47

  Hazra, S B ^a   Class, H ^b   Helmig, R ^b   Schulz, V ^a  

^a UNIVERSITY OF TRIER   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Multiphase flow; Multiple shooting; Numerical parameter identification; Porous media; Reduced Gauss Newton technique

Indexed keywords

FLOW MODELING; MULTIPHASE FLOW; POROUS MEDIUM; SOLUTE TRANSPORT;

FLOW MODELING; MULTIPHASE FLOW; POROUS MEDIUM;

EID: 2542621422     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:COMG.0000024445.39048.21     Document Type: Article

References (42)

1. Y. Bard, Nonlinear Parameter Estimation (Academic Press, New York, 1974).
2. P. Bastian, Numerical computation of multiphase flows in porous media, Habilitationsschrift, Technische Fakultät der Christian-Albrechts-Universität Kiel, Kiel (1999).
3. P. Bastian and R. Helmig, Efficient fully-coupled solution techniques for two-phase flow in porous media: Parallel multigrid solution and large scale computations, Adv. in Water Resour. 23 (1999) 199-216.
4. H.G. Bock, Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, Bonner Mathematische Schriften 183 (1987).
5. A. Brooks and A. Corey, Hydraulic properties of porous media, in: Hydrol. Pap., Colorado State University, Fort Collins, 1964.
6. N. Burdine, Relative permeability calculations from pore-size distribution data, Technical Report, Petroleum Transactions, AIME (1953).
7. J. Carrera and S.P. Neuman, Estimation of aquifer parameters uder transient and steady state conditions, 1. Maximum likelihood method incorporating prior information, Water Resour. Res. 22(2) (1986) 199-210.
8. G. Chavent, J. Jaffré, S. Jegou and J. Liu, A symbolic code generator for parameter estimation, in: Proc. of the SIAM Workshop on Computational Differentiation, SIAM, 1996, pp. 129-136.
9. H. Class, Theorie und numerische Modellierung nichtisothermer Mehrphasenprozesse in NAPL-kontaminierten porösen Medien, Ph.D. thesis, Mitteilungsheft 105, Institut für Wasserbau, Universität Stuttgart (2001).
10. H. Class, R. Helmig and P. Bastian, Numerical simulation of nonisothermal multiphase multicomponent processes in porous media, 1. An efficient solution technique, Adv. in Water Resour. 25 (2002) 533-550.
11. Th. Dreyer, B. Maar and V. Schulz, Multigrid optimization in applications, J. Comput. Appl. Math. 120(1/2) (2000) 67-84.
12. R.E. Ewing, R.D. Lazarov and Y. Lin, Finite volume element approximations of nonlocal in time one-dimensional flows in porous media, Computing 64 (2000) 157-183.
13. A. Faerber, Wärmetransport in der ungesättigten Bodenzone: Entwicklung einer thermischen in-situ Sanierungstechnologie, Dissertation, Institut für Wasserbau, Universität Stuttgart (1997).
14. I. Fatt and W.A. Klikoff, Effect of fractional wettability on multiphase flow through porous media, AMIE Transactions 216 (1959) 246.
15. S. Finsterle, Multiphase inverse modeling: An overview, in: Proceedings, DOE Geothermal Program Review XVI, Berkeley, CA, 1-2 April 1998, pp. 3-3-3-9.
16. S. Finsterle and K. Pruess, Solving the estimation-identification problem in two-phase flow modeling, Water Resour. Res. 31(4) (1995) 913-924.
17. S.B. Hazra and V. Schulz, Numerical parameter identification in multiphase flow through porous media, J. Comput. Visual. Sci. 5 (2002) 107-113.
18. S.B. Hazra and V. Schulz, On efficient computation of the optimization problem arising in the inverse modeling of nonstationary multiphase multicomponent flow through porous media, Comput. Opt. Appl. (2004) to appear.
19. R. Helmig, Multiphase Flow and Transport Processes in the Subsurface - a Contribution to the Modeling of Hydrosystems (Springer, Berlin, 1997).
20. R. Helmig, H. Class, R. Huber, H. Sheta, J. Ewing, R. Hinkelmann, H. Jakobs and P. Bastian, Architecture of the modular program system MUFTE for simulating multiphase flow and transport processes in heterogeneous porous media, Math. Geologie 2 (1998).
21. R. Helmig, H. Class, A. Faerber and M. Emmert, Heat transport in the unsaturated zone - comparison of experimental results and numerical simulations, J. Hydr. Reas. 36(6) (1998).
22. International Formulation Committee, A formulation of the thermodynamic properties of ordinary water substance, Technical Report, IFC Sekretariat, Düsseldorf, Germany (1967).
23. P. Knabner and B. Igler, Structural identification of nonlinear coefficient functions in transport processes through porous media, in: Lectures on Applied Mathematics, eds. Bungartz, Hans-Joachim et al. (Springer, Berlin, 1999) pp. 157-175.
24. J.B. Kool, J.C. Parker and M.Th. Van Genuchten, Parameter estimation for unsaturated flow and transport models - A review, J. Hydrology 91 (1987) 255-293.
25. R. Lenhard, J. Parker and S. Mishra, On the correspondence between Brooks-Corey and Van Genuchten models, J. Irrigation Drainage Engrg. 115(4) (1989) 744-751.
26. K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math. 2 (1944) 164-168.
27. M.C. Leverett, Capillary behaviour in porous solid, AMIE Transactions 142 (1941) 152.
28. D.W. Marquardt, An algorithm for least squares estimation of nonlinear parameters, J. Soc. Ind. Appl. Math. 11(2) (1963) 431-441.
29. Y. Mualem, A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res. 12 (1976) 513-522.
30. J. Parker and R. Lenhard, A model for hysteretic constitutive relations governing multiphase flow, 1. Saturation-pressure relations, Water Resour. Res. 23(12) (1987) 2187-2196.
31. J. Schlöder, Numerische Methoden zur Behandlung hochdimensionaler Aufgaben der Parameteridentifizierung, Bonner Mathematische Schriften 187 (1988).
32. V. Schulz, Solving discretized optimization problems by partially reduced SQP methods, Comput. Visul. Sci. 1 (1998) 83-96.
33. V. Schulz, Constrained programming for optimization problems in PDE, in: ENUMATH 97, Proc. of the 2nd European Conf. on Numerical Mathematics and Advanced Applications, eds. H.G. Bock, G. Kanschat, R. Rannacher, F. Brezzi, R. Glowinski, Y.A. Kuznetsov and J. Periaux (World Scientific, Singapore, 1998) pp. 580-587.
34. V. Schulz, Mehrgittermethoden für Optimierungsprobleme bei partiellen Differentialgleichungen, Habilitationsschrift, Universität Heidelberg (2000).
35. V. Schulz, A. Bardossy and R. Helmig, Conditional statistical inverse modeling in groundwater flow by multigrid methods, Comput. Geosci. 3 (1999) 49-68.
36. V. Schulz, H.G. Bock and M. Steinbach, Exploiting invariants in the numerical solution of multipoint boundary value problems for DAEs, SIAM J. Sci. Comput. 19(2) (1998) 440-467.
37. V.H. Schulz and G. Wittum, Multigrid optimization methods for stationary parameter identification problems in groundwater flow, in: Multigrid Methods V, eds. W. Hackbusch and G. Wittum, Lecture Notes in Computational Science and Engineering, Vol. 3 (Springer, New York, 1998) pp. 276-288.
38. H. Sheta, Einfluss der Hysterese bei Infiltrations- und Ausbreitungsvorgängen in der gesättigten und ungesättigten Bodenzone, Ph.D. thesis, Universität Stuttgart, Institut für Wasserbau (1999).
39. F. Stauffer, W. Kinzelbach, K. Kovar and E. Hoehn, eds., ModelCARE'99, Internat. Conf. on Calibration and Reliability in Groundwater Modelling, Vol. 265 (IAHS Publication, 2000).
40. K.S. Udell and J.S. Fitch, Heat and mass transfer in capillary porous media considering evaporation, condensation and non-condensible gas effects, presented at: 23rd ASME/AIChE National Heat Transfer Conference, Denver, CO, August 1985.
41. M.T. van Genuchten, A closed form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Amer. J. 44(5) (1980) 892-898.
42. W.G. Yeh, Review of parameter estimation procedures in groundwater hydrology: The inverse problem, Water Resour. Res. 22 (1986) 95-108.