Modeling reactive transport using exact solutions for first-order reaction networks

Transport in Porous Media

Volumn 71, Issue 2, 2008, Pages 217-231

  Sun, Yunwei ^a   Buscheck, Thomas A ^a   Hao, Yue ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Analytical solution; First order reaction; Numerical modeling; Operator splitting; Reactive transport

Indexed keywords

ALGEBRA; COMPUTATIONAL EFFICIENCY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS;

ADVECTION-DISPERSION-REACTION EQUATIONS; OPERATOR SPLITTING; REACTIVE TRANSPORT;

ADVECTION;

ADVECTION; ALGEBRA; COMPUTATIONAL EFFICIENCY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS;

ADVECTION; ALGORITHM; DISPERSION; NUMERICAL MODEL; REACTIVE TRANSPORT;

EID: 38649135762     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-007-9121-8     Document Type: Article

References (39)

1. Ataie-Ashtiani B. and Hosseini S.A. (2005). Error analysis of finite difference methods for two-dimensional advection-disperion-reaction equation. Adv. Water Resour. 28: 793-806
2. Barry D.A., Bajracharya K. and Miller C.T. (1996a). Alternative split-operator approach for solving chemical reaction/groundwater transport models. Adv. Water Resour. 19(5): 261-275
3. Barry D.A., Miller C.T. and Culligan-Hensley P.J. (1996b). Temporal discretisation errors in non-iterative split-operator approaches to solving chemical reaction/groundwater transport models. J. Contam. Hydrol. 22: 1-17
4. Barry D.A., Bajracharya K., Crapper M., Prommer H. and Cunningham C.J. (2000). Comparison of split-operator methods for solving coupled chemical non-equilibrium reaction/groundwater transport models. Math. Comput. Simu. 53(1-2): 113-127
5. Bear J. (1979). Groundwater hydraulics. McGraw-Hill, New York
6. Carrayrou J., Mosé R. and Behra P. (2004). Operator-splitting procedures for reactive transport and comparison of mass balance errors. J. Contam. Hydrol. 68: 239-268
7. Chen D.J.Z. and MacQuarrie K.T.B. (2005). Investigation of a modified sequential iteration approach for solving coupled reactive transport problems. Int. J. Numer. Analy. Methods Geomech. 136: 113-136
8. Cheng H.P., Li M.H. and Cheng J.R. (2003). An assessment of using predictor-corrector technique to solve reactive transport equations. Int. J. Numer. Meth. Eng. 56: 739-766
9. Clement T.P., Hooker B.S. and Skeen R.S. (1996). Numerical modeling of biologically reactive transport near nutrient injection well. J. Environ. Eng. 122(9): 833-839
10. Clement T.P., Sun Y., Hooker B.S. and Petersen J.N. (1998). Modeling multi-species reactive transport in groundwater aquifers. Ground Water Monit. Remediat. 18(2): 79-92
11. Clement T.P. (2001). Generalized solution to multispecies transport equations coupled with a first-order reaction network. Water Resour. Res. 37(1): 157-163
12. Geiser J. (2001). Numerical simulation of a model for transport and reaction of radionuclides. Lecture Notes Comput. Sci. 2179: 487-496
13. Hammond G.E., Valocchi A.J. and Lichtner P.C. (2004). Application of Jacobian-free Newton-Krylov with physics-based preconditioning to biogeochemical transport. Adv. Water Resour. 28: 359-376
14. Harada, M., Chambré, P.L., Foglia, M., Higashi, K., Iwamoto, F., Leung, D., Pigford, T. H., Ting, D.: Migration of Radionuclides Through Sorbing Media: I - Analytical Solutions. Lawrence Berkeley National Laboratory, LBL-10500 (1980)
15. Kaluarachchi J.J. and Morshed J. (1995). Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 1. First-order reaction. Adv. Water Resour. 18: 89-100
16. Lanser D. and Verwer J.G. (1999). Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling. J. Comput. Appl. Math. 111: 201-216
17. Lu W., Hansson P., Barry D.A., Miller C.T. and Culligan-Hensley P.J. (1996). Temporal discretisation errors in non-iterative split-operator approaches to solving chemical reaction/groundwater transport models. J. Contam. Hydrol. 22(1): 1-17
18. Lu X., Sun Y. and Petersen J.N. (2003). Analytical solutions of TCE transport with convergent reactions. Transp. Porous Med. 51: 211-225
19. MathWorks: MATLAB High-performance Numeric Computation and Visualization Software, Web site: www.mathwroks.com. Natick, MA, USA (2000)
20. Miller C. and Rabideau A. (1993). Development of split-operator Petrov galerkin methods to simulate transport and diffusion problems. Water Resour. Res. 29(7): 2227-2240
21. Morshed J. and Kaluarachchi J.J. (1995). Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 2. Monod kinetics and coupled transport. Adv. Water Resour. 18: 101-110
22. Press W.H., Teukolsky S.A., Vetterling W.T. and Flannery B.P. (1996). Numerical Recipes in C. Cambridge University Press, Cambridge
23. Prommer H., Barry D.A. and Zheng C. (2003). MODFLOW/MT3D-based reactive multicomponent transport modeling. Ground Water 41: 247-257
24. Robinson B.A., Viswanathan H.S. and Valocchi A.J. (2000). Efficient numerical techniques for modeling multicomponent ground-water transport based upon simultaneous solution of strongly coupled subsets of chemical components. Adv. Water Resour. 23(4): 307-324
25. Radhakrishnan, K., Hindmarsh, A.C.: Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations. Lawrence Livermore National Laboratory, report UCRL-ID-113855 (1993)
26. Samper-Calvete, J., Yang, C.: A semi-analytical solution for linearized multicomponent cation exchange reactive transport in groundwater. Transp. Porous Med. DOI 10.1007/s11242-006-9065-4 (2006)
27. Schulz H.D. and Reardon E.J. (1983). A combined mixing cell/analytical model to describe two-dimensional reactive solute transport for unidirectional groundwater flow. Water Resour. Res. 19: 493-502
28. Schäfer D., Schäfer W. and Kinzelbach W. (1998). Simulation of reactive processes related to biodegradation in aquifers: 1. Structure of the three-dimensional reactive transport model. J. Contam. Hydrol. 31: 167-186
29. Simpson M.J., Landman K.A. and Clement T.P. (2005). Assessment of a non-traditional operator split algorithm for simulation of reactive transport. Math. Comput. Simu. 70: 44-60
30. Sportisse B. (2000). An analysis of operator splitting techniques in the stiff case. J. Comput. Phys. 161: 140-168
31. Sun Y. and Clement T.P. (1999). A decomposition method for solving coupled multi-species reactive transport problem. Transp. Porous Med. 37: 327-346
32. Sun Y., Petersen J.N. and Clement T.P. (1999a). Analytical solutions for multiple species reactive transport in multiple dimensions. J. Contam. Hydrol. 35: 429-440
33. Sun Y., Petersen J.N., Clement T.P. and Skeen R.S. (1999b). Development of analytical solutions for multi-species transport with serial and parallel reactions. Water Resour. Res. 35(1): 185-190
34. Sun Y., Lu X., Petersen J.N. and Buscheck T.A. (2004). An analytical solution of tetrachloroethylene transport and biodegradation. Transp. Porous Med. 55: 301-308
35. Steefel, C.I., MacQuarrie, K.T.B.: Approaches to modeling of reactive transport in porous media. In: Lichtner, P.C., Steefel, C.I. (ed.) Reviews in Mineralogy vol. 34: Reactive Transport in Porous Media. Mineralogical Society of America (1996)
36. Valocchi A.J. and Malmstead M. (1992). Accuracy of operator splitting for advection-dispersion-reaction problems. Water Resour. Res. 28: 1471-1476
37. Yabusaki S.B., Carl C.I. and Wood B.D. (1998). Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: Code verification using an advective reactive streamtube approach. J. Contam. Hydrol. 30: 299-331
38. Yeh G.T. and Tripathi V.S. (1989). A critical evaluation of recent developments in hydrochemical transport models of reactive multichemical components. Water Resour. Res. 25: 93-108
39. Zheng, C., Wang, P.P.: MT3DMS: A Modular Three-dimensional Multi-species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems. U.S. Army Engineer Research and Development Center, Vicksburg, MS, SERDP-99-1 (1999)