Multimodel framework for characterization of transport in porous media

Water Resources Research

Volumn 51, Issue 5, 2015, Pages 3384-3402

  Ciriello, Valentina ^a   Edery, Yaniv ^b   Guadagnini, Alberto ^c,d   Berkowitz, Brian ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c POLITECNICO DI MILANO   (Italy)

^d UNIVERSITY OF ARIZONA   (United States)

Author keywords

global sensitivity analysis; model calibration; multimodel framework; polynomial chaos expansion; porous media; reactive transport

Indexed keywords

CHEMICAL ANALYSIS; COST BENEFIT ANALYSIS; POROUS MATERIALS; SOLUTE TRANSPORT; UNCERTAINTY ANALYSIS;

GLOBAL SENSITIVITY ANALYSIS; MODEL CALIBRATION; MULTI-MODEL; POLYNOMIAL CHAOS EXPANSION; REACTIVE TRANSPORT;

SENSITIVITY ANALYSIS;

CALIBRATION; CHAOTIC DYNAMICS; DATA INTERPRETATION; EXPERIMENTAL STUDY; MODEL VALIDATION; POROUS MEDIUM; REACTIVE TRANSPORT; SOLUTE TRANSPORT; SPATIOTEMPORAL ANALYSIS; THEORETICAL STUDY;

EID: 84932648518     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2015WR017047     Document Type: Article

References (91)

1. Abramowitz, M., and, I. Stegun, (1970), Handbook of Mathematical Functions, Dover, N. Y.
2. Akaike, H., (1974), A new look at statistical model identification, IEEE Trans. Autom. Control, 19, 716-723.
3. Ashraf, M., S. Oladyshkin, and, W. Nowak, (2013), Geological storage of CO2: Application, feasibility and efficiency of global sensitivity analysis and risk assessment using the arbitrary polynomial chaos, Int. J. Greenhouse Gas Control, 19, 704-719.
4. Barth, G. R., and, M. C. Hill, (2005a), Numerical methods for improving sensitivity analysis and parameter estimation of virus transport simulated using sorptive-reactive processes, J. Contam. Hydrol., 76, 251-277.
5. Barth, G. R., and, M. C. Hill, (2005b), Parameter and observation importance in modeling virus transport in saturated systems-Investigations in a homogeneous system, J. Contam. Hydrol., 80, 107-129.
6. Berkowitz, B., and, H. Scher, (1995), On characterization of anomalous dispersion in porous and fractured media, Water Resour. Res., 31 (6), 1461-1466.
7. Berkowitz, B., and, H. Scher, (1997), Anomalous transport in random fracture networks, Phys. Rev. Lett., 79, 4038-4041.
8. Berkowitz, B., H. Scher, and, S. E. Silliman, (2000), Anomalous transport in laboratory-scale, heterogeneous porous media, Water Resour. Res., 36 (1), 149-158.
9. Berkowitz, B., A. Cortis, M. Dentz, and, H. Scher, (2006), Modeling non-Fickian transport in geological formations as a continuous time random walk, Rev. Geophys., 44, RG2003, doi: 10.1029/2005RG000178.
10. Beven, K. J., and, A. M. Binley, (1992), The future of distributed models: Model calibration and uncertainty prediction, Hydrol. Processes, 6, 279-298.
11. Beven, K. J., and, J. Freer, (2001), Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, 11-29.
12. Bianchi Janetti, E., I. Dror, M. Riva, A. Guadagnini, and, B. Berkowitz, (2012), Estimation of single-metal and competitive sorption isotherms through maximum likelihood and model quality criteria, Soil Sci. Soc. Am. J., 76, 1229-1245.
13. Bromly, M., and, C. Hinz, (2004), Non-Fickian transport in homogeneous unsaturated repacked sand, Water Resour. Res., 40, W07402, doi: 10.1029/2003WR002579.
14. Cao, J., and, P. K. Kitanidis, (1998), Pore-scale dilution of conservative solutes: An example, Water Resour. Res., 34 (8), 1941-1949.
15. Carrera, J., and, S. P. Neuman, (1986a), Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information, Water. Resour. Res., 22 (2), 199-210.
16. Carrera, J., and, S. P. Neuman, (1986b), Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms, Water Resour. Res., 22 (2), 211-227.
17. Ciriello, V., and, V. Di Federico, (2013), Analysis of a benchmark solution for non-Newtonian radial displacement in porous media, Int. J. Non-Linear Mech., 52, 46-57.
18. Ciriello, V., A. Guadagnini, V. Di Federico, Y. Edery, and, B. Berkowitz, (2013a), Comparative analysis of formulations for conservative transport in porous media through sensitivity-based parameter calibration, Water Resour. Res., 49, 5206-5220, doi: 10.1002/wrcr.20395.
19. Ciriello, V., V. Di Federico, M. Riva, F. Cadini, J. De Sanctis, E. Zio, and, A. Guadagnini, (2013b), Polynomial chaos expansion for global sensitivity analysis applied to a model of radionuclide migration in a randomly heterogeneous aquifer, Stochastic Environ. Res. Risk Assess., 27, 945-954.
20. Cirpka, O. A., and, P. K. Kitanidis, (2000), An advective-dispersive stream tube approach for the transfer of conservative-tracer data to reactive transport, Water Resour. Res., 36 (5), 1209-1220.
21. Crestaux, T., O. Le Maître, and, J. M. Martinez, (2009), Polynomial chaos expansion for sensitivity analysis, Reliab. Eng. Syst. Safety, 94 (7), 1161-1172.
22. Cushman, J. H., and, T. R. Ginn, (1993), On dispersion in fractal porous media, Water Resour. Res., 29 (10), 3513-3515.
23. Dagan, G., and, S. P. Neuman, (1991), Nonasymptotic behavior of a common Eulerian approximation for transport in random velocity fields, Water Resour. Res., 27 (12), 3249-3256.
24. Doherty, J., (2002), PEST: Model Independent Parameter Estimation, User Manual, 4th ed., Watermark Numer. Comput., Corinda, Queensland, Australia.
25. Edery, Y., H. Scher, and, B. Berkowitz, (2010), Particle tracking model of bimolecular reactive transport in porous media, Water Resour. Res., 46, W07524, doi: 10.1029/2009WR009017.
26. Edery, Y., A. Guadagnini, H. Scher, and, B. Berkowitz, (2014), Origins of anomalous transport in heterogeneous media: Structural and dynamic controls, Water Resour. Res., 50, 1490-1505, doi: 10.1002/2013WR015111.
27. Esfandiar, B., G. Porta, S. Perotto, and, A. Guadagnini, (2015), Impact of space-time mesh adaptation on solute transport modeling in porous media, Water Resour. Res., 51, 1315-1332, doi: 10.1002/2014WR016569.
28. Fajraoui, N., F. Ramasomanana, A. Younes, T. A. Mara, P. Ackerer, and, A. Guadagnini, (2011), Use of global sensitivity analysis and polynomial chaos expansion for interpretation of nonreactive transport experiments in laboratory-scale porous media, Water Resour. Res., 47, W02521, doi: 10.1029/2010WR009639.
29. Formaggia, L., A. Guadagnini, I. Imperiali, V. Lever, G. Porta, M. Riva, A. Scotti, and, L. Tamellini, (2013), Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model, Comput. Geosci., 17 (1), 25-42.
30. Gaganis, P., and, L. Smith, (2001), A Bayesian approach to the quantification of the effect of model error on the predictions of groundwater models, Water Resour. Res., 37 (9), 2309-2322.
31. Ghanem, R. G., and, P. D. Spanos, (1991), Stochastic Finite Elements-A Spectral Approach, Springer, Berlin.
32. Gillespie, D., (1977), Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 25, 2340-2361.
33. Gramling, C. M., C. F. Harvey, and, L. C. Meigs, (2002), Reactive transport in porous media: A comparison of model prediction with laboratory visualization, Environ. Sci. Technol., 36, 2508-2514.
34. Haggerty, R., S. A. McKenna, and, L. C. Meigs, (2000), On the late-time behavior of tracer test breakthrough curves, Water Resour. Res., 36 (12), 3467-3479.
35. Hering, J. G., and, F. M. M. Morel, (1988), Kinetics of trace-metal complexation: Role of alkaline-earth metals, Environ. Sci. Technol., 22 (12), 1469-1478.
36. Huang, S., M. Sankaran, and, R. Ramesh, (2007), Collocation-based stochastic finite element analysis for random field problems, Probab. Eng. Mech., 22, 194-205.
37. Hurvich, C. M., and, C. L. Tsai, (1989), Regression and time series model selection in small sample, Biometrika, 76 (2), 297-307.
38. James, A. L., and, C. M. Oldenburg, (1997), Linear and Monte Carlo uncertainty analysis for subsurface contaminant transport simulation, Water Resour. Res., 33 (11), 2495-2508.
39. Jose, S. C., and, O. A. Cirpka, (2004), Measurement of mixing-controlled reactive transport in homogeneous porous media and its prediction from conservative tracer test data, Environ. Sci. Technol., 38, 2089-2096.
40. Kashyap, R. L., (1982), Optimal choice of AR and MA parts in autoregressive moving average models, IEEE Trans. Pattern Anal., 4 (2), 99-104.
41. Kuntz, B. W., S. Rubin, B. Berkowitz, and, K. Singha, (2011), Quantifying solute transport at the Shale Hills Critical Zone Observatory, Vadose Zone J., 10, 843-857.
42. Laloy, E., B. Rogiers, J. A. Vrugt, D. Mallants, and, D. Jacques, (2013), Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov Chain Monte Carlo simulation and polynomial chaos expansion, Water Resour. Res., 49, 2664-2682, doi: 10.1002/wrcr.20226.
43. Levy, M., and, B. Berkowitz, (2003), Measurement and analysis of non-Fickian dispersion in heterogeneous porous media, J. Contam. Hydrol., 64 (3-4), 203-226.
44. Li, W., Z. Lu, and, D. Zhang, (2009), Stochastic analysis of unsaturated flow with probabilistic collocation method, Water Resour. Res., 45, W08425, doi: 10.1029/2008WR007530.
45. Liao, Q., and, D. Zhang, (2013), Probabilistic collocation method for strongly nonlinear problems: 1. Transform by location, Water Resour. Res., 49, 7911-7928, doi: 10.1002/2013WR014055.
46. Liao, Q., and, D. Zhang, (2014), Probabilistic collocation method for strongly nonlinear problems: 2. Transform by displacement, Water Resour. Res., 50, 8736-8759, doi: 10.1002/2014WR016238.
47. Lin, G., A. M. Tartakovsky, and, D. M. Tartakovsky, (2010), Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids, J. Comput. Phys., 229, 6995-7012.
48. Lindenberg, K., and, A. H. Romero, (2007), Numerical study of A + A → 0 and A + B → 0 reactions with inertia, J. Chem. Phys., 127, paper no. 174506, doi: 10.1063/1.2779327.
49. Lu, D., M. Ye, S. P. Neuman, and, L. Xue, (2012), Multimodel Bayesian analysis of data-worth applied to unsaturated fractured tuffs, Adv. Water Resour., 35, 69-82.
50. Matthies, H. G., (2008), Stochastic finite elements: Computational approaches to stochastic partial differential equations, ZAMM, 88 (11), 849-873.
51. National Research Council (2001), Conceptual Models of Flow and Transport in the Fractured Vadose Zone, Natl. Acad. Press, Washington, D. C.
52. Neuman, S. P., (2002), Accounting for conceptual model uncertainty via maximum likelihood Bayesian model averaging, Acta Univ. Carolinae Geol., 46 (2-3), 529-534.
53. Neuman, S. P., (2003), Maximum likelihood Bayesian averaging of alternative conceptual-mathematical models, Stochastic Environ. Res. Risk Assess., 17 (5), 291-305, doi: 10.1007/s00477-003-0151-7.
54. Neuman, S. P., L. Xue, M. Ye, and, D. Lu, (2012), Bayesian analysis of data-worth considering model and parameter uncertainties, Adv. Water Resour., 36, 75-85.
55. Oladyshkin, S., and, W. Nowak, (2012), Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion, Reliab. Eng. Syst. Safety, 106, 179-190.
56. Oladyshkin, S., F. P. J. de Barros, and, W. Nowak, (2012), Global sensitivity analysis: A flexible and efficient framework with an example from stochastic hydrogeology, Adv. Water Resour., 37, 10-22.
57. Oladyshkin, S., H. Class, and, W. Nowak, (2013), Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: Methodology and application to history matching for carbon dioxide storage in geological formations, Comput. Geosci., 17 (4), 671-687.
58. Palanichamy, J., T. Becker, M. Spiller, J. Kangeter, and, S. Mohan, (2007), Multicomponent reaction modelling using a stochastic algorithm, Comput. Visualization Sci., 12, 51-61.
59. Porta, G., L. Tamellini, V. Lever, and, M. Riva, (2014), Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion, Water Resour. Res., 50, 9414-9431, doi: 10.1002/2014WR015838.
60. Rahman, Md. A., C. J. Surabhin, W. Nowak, and, O. A. Cirpka, (2005), Experiments on vertical transverse mixing in a large-scale heterogeneous model aquifer, J. Contam. Hydrol., 80 (3-4), 130-148.
61. Rajabi, M. M., B. Ataie-Ashtiani, and, C. T. Simmons, (2015), Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations, J. Hydrol., 520, 101-122.
62. Raje, D. S., and, V. Kapoor, (2000), Experimental study of bimolecular reaction kinetics in porous media, Environ. Sci. Technol., 34, 1234-1239.
63. Rashidi, M., L. Peurrung, A. F. B. Tompson, and, T. J. Kulp, (1996), Experimental analysis of pore-scale flow and transport in porous media, Adv. Water Resour., 3, 163-180.
64. Riva, M., A. Guadagnini, and, A. Dell'Oca, (2015), Probabilistic assessment of seawater intrusion under multiple sources of uncertainty, Adv. Water Resour., 75, 93-104.
65. Rubin, S., I. Dror, and, B. Berkowitz, (2012), Experimental and modeling analysis of coupled non-Fickian transport and sorption in natural soils, J. Contam. Hydrol., 132, 28-36.
66. Saltelli, A., S. Tarantola, and, F. Campolongo, (2000), Sensitivity analysis as an ingredient of modeling, Stat. Sci., 15 (4), 377-395.
67. Samper, F. J., and, S. P. Neuman, (1989a), Estimation of spatial covariance structures by adjoint state maximum likelihood cross validation: 1. Theory, Water Resour. Res., 25 (3), 351-362.
68. Samper, F. J., and, S. P. Neuman, (1989b), Estimation of spatial covariance structures by adjoint state maximum likelihood cross validation: 2. Synthetic experiments, Water Resour. Res., 25 (3), 363-371.
69. Samper, J., and, J. Molinero, (2000), Predictive uncertainty of numerical models of groundwater flow and solute transport, Eos Trans. AGU, 81 (48), Fall Meet. Suppl., Abstract H11G-04.
70. Sánchez-Vila, X., and, J. Carrera, (2004), On the striking similarity between the moments of breakthrough curves for a heterogeneous medium and a homogeneous medium with a matrix diffusion term, J. Hydrol., 294 (1-3), 164-175.
71. Sanchez-Vila, X., D. Fernàndez-Garcia, and, A. Guadagnini, (2010), Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation, Water Resour. Res., 46, W12510, doi: 10.1029/2010WR009539.
72. Schwarz, G., (1978), Estimating the dimension of a model, Ann. Stat., 6 (2), 461-464.
73. Silliman, S. E., and, E. S. Simpson, (1987), Laboratory evidence of the scale effect in dispersion of solutes in porous media, Water Resour. Res., 23 (8), 1667-1673.
74. Silliman, S. E., L. F. Konikow, and, C. I. Voss, (1987), Laboratory investigation of longitudinal dispersion in anisotropic porous media, Water Resour. Res., 23 (11), 2145-2151.
75. Sobol, I. M., (1993), Sensitivity estimates for nonlinear mathematical models, Math. Model. Comput. 1, 407-414.
76. Srinivasan, G., D. M. Tartakovsky, B. A. Robinson, and, A. B. Aceves, (2007), Quantification of uncertainty in geochemical reactions, Water Resour. Res., 43, W12415, doi: 10.1029/2007WR006003.
77. Sudret, B., (2008), Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Syst. Safety, 93, 964-979.
78. Sun, A. Y., M. Zeidouni, J. P. Nicot, Z. Lu, and, D. Zhang, (2013), Assessing leakage detectability at geologic CO2 sequestration sites using the probabilistic collocation method, Adv. Water Resour., 56, 49-60.
79. Tartakovsky, A. M., G. Redden, P. C. Lichtner, T. D. Scheibe, and, P. Meakin, (2008), Mixing-induced precipitation: Experimental study and multiscale numerical analysis, Water Resour. Res., 44, W06S04, doi: 10.1029/2006WR005725.
80. Tartakovsky, A. M., G. D. Tartakovsky, and, T. D. Scheibe, (2009), Effects of incomplete mixing on multicomponent reactive transport, Adv. Water Resour., 32 (11), 1674-1679.
81. Tartakovsky, D. M., (2007), Probabilistic risk analysis in subsurface hydrology, Geophys. Res. Lett., 34, L05404, doi: 10.1029/2007GL029245.
82. Tiedeman, C. R., M. C. Hill, F. A. D'Agnese, and, C. C. Faunt, (2003), Methods for using groundwater model predictions to guide hydrogeologic data collection, with application to the Death Valley regional ground-water flow system, Water Resour. Res., 39 (1), 1010, doi: 10.1029/2001WR001255.
83. Tiedeman, C. R., D. M. Ely, M. C. Hill, and, G. M. O'Brien, (2004), A method for evaluating the importance of system state observations to model predictions, with application to the Death Valley regional groundwater flow system, Water Resour. Res., 40, W12411, doi: 10.1029/2004WR003313.
84. Webster, M., M. A. Tatang, and, G. J. McRae, (1996), Application of the probabilistic collocation method for an uncertainty analysis of a simple ocean model, Tech. Rep. 4, MIT Joint Program on the Sci. and Policy of Global Change. [Available at http://web.mit.edu/globalchange/www/MITJPSPGC-Rpt4.pdf.]
85. Wiener, N., (1938), The homogeneous chaos, Am. J. Math., 60, 897-936.
86. Xiu, D., and, G. E. Karniadakis, (2002), The Wiener-Askey polynomial chaos for stochastic differential equations, J. Sci. Comput., 24 (2), 619-644.
87. Xue, L., D. Zhang, A. Guadagnini, and, S. P. Neuman, (2014), Multimodel Bayesian analysis of groundwater data worth, Water Resour. Res., 50, 8481-8496, doi: 10.1002/2014WR015503.
88. Ye, M., S. P. Neuman, and, P. D. Meyer, (2004), Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff, Water Resour. Res., 40, W05113, doi: 10.1029/2003WR002557.
89. Ye, M., P. D. Meyer, and, S. P. Neuman, (2008), On model selection criteria in multimodel analysis, Water Resour. Res., 44, W03428, doi: 10.1029/2008WR006803.
90. Yuste, S. B., J. J. Ruiz-Lorenzo, and, K. Lindenberg, (2008), Coagulation reactions in low dimensions: Revisiting subdiffusive A+A reactions in one dimension, Phys. Rev. E, 80, 051114.
91. Zinn, B., L. C. Meigs, C. F. Harvey, R. Haggerty, W. J. Peplinski, and, C. F. Von Schwerin, (2004), Experimental visualization of solute transport and mass transfer processes in two-dimensional conductivity fields with connected regions of high conductivity, Environ. Sci. Technol., 38 (14), 3916-3926.