Upscaling sorption/desorption processes in reactive transport models to describe metal/radionuclide transport: A critical review

Environmental Science and Technology

Volumn 44, Issue 21, 2010, Pages 7996-8007

  Miller, Andrew W ^a,b   Rodriguez, Derrick R ^a   Honeyman, Bruce D ^a  

^a Department of Geology and Geological Engineering   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX MODEL; COMPLEX SYSTEMS; CONCEPTUAL MODEL; CRITICAL REVIEW; DISCRETIZATIONS; ENVIRONMENTAL SCIENCE; EXPERIMENTAL EVIDENCE; FIELD SCALE; GAIN INSIGHT; MATHEMATICAL CODES; NUMERICAL SOLVERS; PREDICTIVE CAPABILITIES; PROCESS KNOWLEDGE; REACTIVE TRANSPORT MODELING; REACTIVE TRANSPORT MODELS; SCALING BEHAVIOR; UPSCALING;

MATHEMATICAL TECHNIQUES;

MODELS;

METAL; RADIOISOTOPE;

DESORPTION; ERROR ANALYSIS; EXPERIMENTAL STUDY; HETEROGENEITY; LITERATURE REVIEW; MATHEMATICAL ANALYSIS; METAL; NUMERICAL MODEL; PHYSICOCHEMICAL PROPERTY; RADIONUCLIDE; REACTIVE TRANSPORT; SORPTION; UPSCALING;

DESORPTION; GEOCHEMICAL ANALYSIS; MODEL; PHYSICAL CHEMISTRY; POLLUTION TRANSPORT; PROCESS CONTROL; QUALITY CONTROL; REVIEW; SCALE UP; SIMULATION;

ABSORPTION; ADSORPTION; ENVIRONMENT; ENVIRONMENTAL POLLUTANTS; KINETICS; METALS; MODELS, CHEMICAL; PHYSICAL PROCESSES; RADIOISOTOPES;

EID: 78549252479     PISSN: 0013936X     EISSN: 15205851     Source Type: Journal    
DOI: 10.1021/es101822v     Document Type: Review

References (131)

1. Scheibe, T. D.; Yabusaki, S. Scaling of flow and transport behavior in heterogeneous groundwater systems. Adv. Water Resour. 1998, 22, 223-238.
2. Mills, R. T.; Hammond, G. E.; Lichtner, P. C.; Sripathi, V.; Mahinthakumar, G.; Smith, B. F. Modeling subsurface reactive flows using leadership-class computing. J. Phys.: Conf. Ser. 2009, 180, 10.1088/1742-6595/ 180/1/012062.
3. Wersin, P.; Hochella, M. F., Jr.; Perrson, P.; Redden, G.; Leckie, J. O.; Harris, D. W. Interaction between aqueous uranium (VI) and sulfide minerals: Spectroscopic evidence for sorption and reduction. Geochim. Cosmochim. Acta 1994, 58, 2829-2843.
4. Waychunas, G. A.; Fuller, C. C.; Davis, J. A. Surface complexation and precipitate geometry for aqueous Zn (II) sorption on ferrihydrite I. X-ray absorption extended fine structure spectroscopy analysis. Geochim. Cosmochim. Acta 2002, 66, 1119-1137.
5. 3. J. Colloid Interface Sci. 1997, 187, 62-82.
6. 2- complex formation at different ionic strengths. Radiochim. Acta 2000, 88, 603-606.
7. 3 (aq) species. Radiochim. Acta 2001, 89, 511-518.
8. Zheng, Z.; Tokunaga, T. K.; Wan, J. Influence of calcium carbonate on U (VI) sorption to soils. Environ. Sci. Technol. 2003, 37, 5603-5608.
9. Dong, W.; Ball, W. P.; Liu, C.; Wang, Z.; Stone, A. T.; Bai, J.; Zachara, J. M. Influence of calcite and dissolved calcium on uranium (VI) sorption to a Hanford subsurface sediment. Environ. Sci. Technol. 2005, 39, 7949-7955.
10. Fox, P.; Davis, J. A.; Zachara, J. M. The effect of calcium on aqueous uranium (VI) speciation and adsorption to ferrihydrite and quartz. Geochim. Cosmochim. Acta 2006, 70, 1379-1387.
11. Kohler, M.; Curtis, G. P.; Kent, D. B.; Davis, J. A. Experimental investigation and modeling of uranium (VI) transport under variable chemical conditions. WaterResour. Res. 1996, 32, 3539-3551.
12. Morrison, S. J.; Spangler, R. R.; Tripathi, V. S. Adsorption of uranium (VI) on amorphous ferric oxyhydroxide at high concentrations of dissolved carbon (VI) and sulfur (VI). J. Contam. Hydrol. 1995a, 17, 333-346.
13. Morrison, S. J.; Tripathi, V. S.; Spangler, R. R. Coupled reaction/transport modeling of a chemical barrier for controlling uranium (VI) contamination in groundwater. J. Contam. Hydrol. 1995b, 17, 347-363.
14. 2. Radiochim. Acta 1999, 85, 33-48.
15. Zachara, J. M.; Girvin, D. C.; Schmidt, R. L.; Resch, C. T. Chromateadsorption on amorphousironoxyhydroxideinthe presence of major groundwater ions. Environ. Sci. Technol. 1987, 21, 589-594.
16. Swedlund, P. J.; Webster, J. G.; Miskelly, G. M. Goethite adsorption of Cu (II), Pb (II), Cd (II), and Zn (II) in the presence of sulfate: Properties of the ternary complex. Geochim. Cosmochim. Acta 2009, 73, 1548-1562.
17. Zhang, G. Y.; Peak, D. Studies of Cd (II)-sulfate interactions at the goethite-water interface by ATR-FTIR spectroscopy. Geochim. Cosmochim. Acta 2007, 71, 2158-2169.
18. Van Geen, A.; Robertson, A. P.; Leckie, J. O. Complexation of carbonate species at the goethite surface: Implications for adsorption of metal ions in natural waters. Geochim. Cosmochim. Acta 1994, 58, 2073-2086.
19. Lenhart, J. J.; Honeyman, B. D. Uranium (VI) sorption to hematite in the presence of humic acid. Geochim. Cosmochim. Acta 1999, 63, 2891-2901.
20. Schmeide, K.; Pompe, S.; Bubner, M.; Heise, K. H.; Bernhard, G.; Nitsche, H. Uranium (VI) sorption onto phyllite and selected minerals in the presence of humic acid. Radiochim. Acta 2000, 88, 723-728.
21. 2+ adsorption to goethite in the presence of fulvic acids. Geochim. Cosmochim. Acta 2008, 72, 5857-5870.
22. Honeyman, B. D.; Ranville, J. F. Colloid properties and their effects on radionuclide transport through soils and groundwater. In Geochemistry of Soil Radionuclides; Zhang, P.-C., Brady, M. V., Eds.; SSSA Special Publication 59; Soil Science Society of America: Madison, 2002; pp 131-163.
23. 3. J. Colloid Interface Sci. 1976, 55, 281-288.
24. Farley, K. J.; Dzombak, D. A.; Morel, F. M. M. A surface precipitation model for the sorption of cations on metal oxides. J. Colloid Interface Sci. 1985, 106, 226-242.
25. 3 (s). Geochim. Cosmochim. Acta 1989, 53, 2787-2796.
26. Davis, J. A.; James, R. O.; Leckie, J. O. Surface ionization and complexation at the oxide/water interface I. Computation of electrical double layer properties in simple electrolytes. J. Colloid Interface Sci. 1978a, 63, 480-499.
27. Davis, J. A.; Leckie, J. O. Surface ionization and complexation atthe oxide/waterinterface II. Surface properties ofamorphous iron oxyhydroxide and adsorption of metal ions. J. Colloid Interface Sci. 1978b, 67, 90-107.
28. Davis, J. A.; Leckie, J. O. Surface ionization and complexation at the oxide/water interface III. Adsorption of anions. J. Colloid Interface Sci. 1980, 74, 32-43.
29. Hiemstra, T.; van Riemsdijk, W. H. A surfacestructural approach to ion adsorption: The charge distribution (CD) model. J. Colloid Interface Sci. 1996, 179, 488-508.
30. Arai, Y.; McBeath, M.; Bargar, J. R.; Joye, J.; Davis, J. A. Uranyl adsorption and surface speciation at the imogolite-water interface: Self-consistent spectroscopic and surface complexation models. Geochim. Cosmochim. Acta 2006, 70, 2492-2509.
31. Ponthieu, M.; Juillot, F.; Hiemstra, T.; van Riemsdijk, W. H.; Benedetti, M. F. Metal ion binding to iron oxides. Geochim. Cosmochim. Acta 2006, 70, 2679-2698.
32. Weber, W. J., Jr.; McGinley, P. M.; Katz, L. E. A distributed reactivity model for sorption by soils and sediments 1. Conceptual basis and equilibrium assessments. Environ. Sci. Technol. 1992, 26, 1955-1962.
33. Chen, W.; Wagenet, R. J. Solute transport in porous media with sorption-site heterogeneity. Environ. Sci. Technol. 1995, 29, 2725-2734.
34. Qafoku, N. P.; Zachara, J. M.; Liu, C.; Gassman, P. L.; Qafoku, O. S.; Smith, S. C. Kinetic desorption and sorption of U (VI) during reactive transport in a contaminated hanford sediment. Environ. Sci. Technol. 2005, 39, 3157-3165.
35. Haggerty, R.; Gorelick, S. M. Multiple-rate mass transfer for modeling diffusion and surface reactions in media with porescale heterogeneity. Water Resour. Res. 1995, 31, 2383-2400.
36. Liu, C.; Zachara, J. M.; Qafoku, N. P.; Wang, Z. Scale-dependent desorption of uranium from contaminated subsurface environments. Water Resour. Res. 2008, 44, 10.1029/2007WR006478.
37. Davis, J. A.; Coston, J. A.; Kent, D. B.; Fuller, C. C. Application of the surface complexation concept to complex mineral assemblages. Environ. Sci. Technol. 1998, 32, 2820-2828.
38. Honeyman, B. D. Cation and Anion Adsorption in Binary Mixtures of Adsorbents: An Investigation of the Concept of Adsorptive Additivity. Ph. D. Dissertation, Stanford University, Stanford, CA, 1984.
39. Davis, J. A.; Meece, D. E.; Kohler, M.; Curtis, G. P. Approaches to surface complexation modeling of uranium (VI) adsorption on aquifer sediments. Geochim. Cosmochim. Acta 2004, 68, 3621-3641.
40. Payne, T. E.; Davis, J. A.; Ochs, M.; Olin, M.; Tweed, C. J.; Altmann, S.; Askarieh, M. M. Comparative evaluation of surface complexation models for radionuclide sorption by diverse geologic material. In Surface Complexation Modeling; Lutzenkirchen, J., Ed.; Elsevier Ltd.: Amsterdam, 2006; Vol. 11, pp 605-633.
41. Waite, T. D.; Davis, J. A.; Fenton, B. R.; Payne, T. E. Approaches to modeling uranium (VI) adsorption on natural mineral assemblages. Radiochim. Acta 2000, 88, 687-693.
42. Turner, D. R.; Bertetti, F. P.; Pabalan, R. T. Applying surface complexation modeling to radionuclide sorption. In Surface Complexation Modeling; Lutzenkirchen, J., Ed.; Elsevier Ltd.: Amsterdam, 2006; Vol. 11, pp 553-604.
43. Curtis, G. P.; Davis, J. A.; Naftz, D. L. Simulation of reactive transport of uranium (VI) in groundwater with variable chemicalconditions. Water Resour. Res. 2006, 42, W04404, 04410.01029/02005WR003979.
44. Stollenwerk, K. G. Modeling the effects of variable groundwater chemistry in adsorption of molybdate. Water Resour. Res. 1995, 31, 347-357.
45. Stollenwerk, K. G. Molybdate transport in a chemically complex aquifer: Field measurements compared with solute-transport model predictions. Water Resour. Res. 1998, 34, 2727-2740.
46. Kent, D. B.; Abrams, R. H.; Davis, J. A.; Coston, J. A.; Le Blanc, D. R. Modeling the influence of variable pH on the transport of zinc in a contaminated aquifer using semiempirical surface complexation models. Water Resour. Res. 2000, 36, 3411-3425.
47. Kent, D. B.; Davis, J. A.; Anderson, C. D.; Rea, B. A. Transport of chromium and selenium in apristine sandand gravel aquifer: Role of adsorption processes. Water Resour. Res. 1995, 31, 1041-1050.
48. Davis, J. A.; Kent, D. B.; Coston, J. A.; Hess, K. M.; Joye, J. L. Multispecies reactive tracer test in an aquifer with spatially variable chemical conditions. Water Resour. Res. 2000, 36, 119-134.
49. Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Modeling solute transport influenced by multiprocess nonequillibrium and transformation reactions. Water Resour. Res. 1992, 28, 175-182.
50. Neville, C. J.; Ibaraki, M.; Sudicky, E. A. Solute transport with mutiprocess nonequilibrium: a semi-analytial soution approach. J. Contam. Hydrol. 2000, 44, 141-159.
51. Li, L.; Barry, D. A.; Culligan-Hensley, P. J.; Bajracharya, K. Mass transfer in soils with local stratification of hydraulic conductivity. Water Resour. Res. 1994, 30, 2891-2900.
52. Griffioen, J. W.; Barry, D. A.; Parlange, J.-Y. Interpretation of two-region model parameters. Water Resour. Res. 1998, 34, 373-384.
53. Brusseau, M. L. Transport of rate-limited sorbing solutes in heterogeneous porous media: Application of a one-dimensional multifactor nonidealitymodelto field data. Water Resour. Res. 1992, 28, 2485-2497.
54. Gelhar, L. W.; Welty, C.; Rehfeldt, K. R. A critical review of data on field-scale dispersion in aquifers. Water Resour. Res. 1992, 28, 1955-1974.
55. Beckie, R. Analysis of scale effects in large-scale solute-transport models In Scale Dependence and Scale Invariance in Hydrology; Sposito, G., Ed.; Cambridge University Press: Cambridge, UK, 1998; pp 314-334.
56. Brusseau, M. L.; Zachara, J. M. Transport of Co2+ in a physically and chemically heterogeneous porous medium. Environ. Sci. Technol. 1993, 27, 1937-1939.
57. Liu, C.; Zachara, J. M.; Yantasee, W.; Majors, P. D.; McKinley, J. P. Microscopic reactive diffusion of uranium in the contaminated sediments at Hanford, United States. Water Resour. Res. 2006, 42.
58. Liu, C.; Zachara, J. M.; Qafoku, O. S.; McKinley, J. P.; Heald, S. M.; Wang, Z. Dissolution of uranyl microprecipitates in subsurface sediments at Hanford Site, USA. Geochim. Cosmochim. Acta 2004, 68, 4519-4537.
59. White, A. F.; Brantley, S. L. The effect of time weathering of silicate minerals: why do weathering rates differ in the laboratory and the field. Chem. Geol. 2003, 202, 479-506.
60. Maher, K.; Steefel, C. I.; De Paolo, D. J.; Viani, B. E. The mineral dissolution rate conundrum: Insights from reactive transport modeling of U isotopes and pore fluid chemistry in marine sediments. Geochim. Cosmochim. Acta 2006, 70, 337-363.
61. Li, L.; Peters, C. A.; Celia, M. A. Upscaling geochemical reaction rates using pore-scale network modeling. Adv. Water Resour. 2006, 29, 1351-1370.
62. Li, L.; Peters, C. A.; Celia, M. A. Effects of mineral spatial distribution on reaction rates in porous media. Water Resour. Res. 2007, 43, W01419, 01410.01029/02005WR004848.
63. Pang, L.; Close, M.; Schneider, D.; Stanton, G. Effect of porewater velocity on chemical nonequilibrium transport of Cd, Zn, and Pb. J. Contam. Hydrol. 2002, 57, 241-258.
64. Zhang, X.; Crawford, J. W.; Young, I. M. Does pore watervelocity affect the reaction rates of adsorptive solute transportinsoils? Demonstration with pore-scale modeling. Adv. Water Resour. 2008, 31, 425-437.
65. Acharya, R. C.; Valocchi, A. J.; Werth, C. J.; Willingham, T. W. Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional porous media. Water Resour. Res. 2007, 43, 10.1029/2007WR005969. (Pubitemid 350210182)
66. Cirpka, O. A.; Kitanidis, P. K. Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments. Water Resour. Res. 2000, 36(5), 1221-1236.
67. Li, L.; Steefel, C. I.; Yang, L. Scale dependence of mineral dissolution rates within single pores and fractures. Geochim. Cosmochim. Acta 2008, 72, 360-377.
68. Werth, C. J.; Cirpka, O. A.; Grathwohl, P. Enhanced mixing and reaction through flowfocusing in heterogeneous porous media. Water Resour. Res. 2006, 42, 10.1029/2005WR004511. (Pubitemid 46184054)
69. Tartakovsky, D. M.; Redden, G.; Lichtner, P. C.; Scheibe, T. D.; Meakin, P. Mixing-induced precipitation: Experimental study and multiscale numerical analysis. Water Resour. Res. 2008, 44, 10.1029/2006WR005725.
70. Li, L.; Steefel, C. I.; Kowalsky, M. B.; Englert, A.; Hubbard, S. S. Effects of physical and geochemical heterogeneities in mineral transformation and biomass accumulation during biostimulation experiments at Rifle, Colorado. J. Contam. Hydrol. 2010, 112, 45-63.
71. Burr, D. T.; Sudicky, E. A.; Naff, R. L. Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: Mean displacement, plume spreading, and uncertainty. Water Resour. Res. 1994, 30, 791-815.
72. Espinoza, C.; Valocchi, A. J. Stochastic analysis of onedimensional transport of kinetically adsobing solutes in chemically heterogeneous aquifers. Water Resour. Res. 1997, 33, 2429-2445.
73. Harvey, C.; Gorelick, S. M. Rate-limited mass transfer or macrodispersion: Which dominates plume evolution at the Macrodispersion Experiment (MADE) site. Water Resour. Res. 2000, 36, 637-650.
74. Wood, B. The role of scaling laws in upscaling. Adv. Water Resour. 2009, 32, 723-736.
75. Barnett, M. O.; Jardine, P. M.; Brooks, S. C.; Selim, H. M. Adsorption and transport of uranium (VI) in subsurface media. Soil Sci. Soc. Am. J. 2000, 64, 908-917.
76. Gabriel, U.; Gaudet, J.-P.; Spadini, L.; Charlet, L. Reactive transport of uranyl in a goethite column: an experimental and modeling study. Chem. Geol. 1998, 151, 107-128.
77. Szecsody, J. E.; Zachara, J. M.; Chilakapati, A.; Jardine, P. M.; Ferrency, A. S. Importance of flow and particle-scale heterogeneity on Co (II/III) EDTA reactive transport. J. Hydrol. 1998, 209, 112-136.
78. Appelo, C. A. J.; Van Loon, L. R.; Wersin, P. Multicomponent diffusion of a suite of tracers (HTO, Cl, Br, I, Na, Sr, Cs) in a single smaple of Oplinus Clay. Geochim. Consmochim. Acta 2010, 74, 1201-1219.
79. + to micaceous subsurface sediments from the Hanford site, USA. Geochim. Cosmochim. Acta 2002, 66, 193-211.
80. Steefel, C. I.; Carroll, S.; Zhao, P.; Roberts, S. Cesium migration in Hanford sediment: a multisite cation exchange model based on laboratory experiments. J. Contam. Hydrol. 2003, 67, 219-246.
81. Davis, J. A.; Curtis, G. P. Application of Surface Complexation Modeling to Describe Uranium (VI) Adsorption and Retardation at the Uranium Mill Tailings Site at Naturita, Colorado; NUREG/CR-6820; U. S. Nuclear Regulatory Commission: Washington, DC, 2003.
82. Fuller, C. C.; Davis, J. A.; Coston, J. A.; Dixon, E. Characterization of metal adsorption variability in a sand and gravel aquifer, Cape Cod, Massachusetts, U. S. A. J. Contam. Hydrol. 1996, 22, 165-187.
83. Loganathan, V. A.; Barnett, M. O.; Clement, T. P.; Kanel, S. R. Scaling of adsorption reactions: U (VI) experiments and modeling. Appl. Geochem. 2009, 24, 2051-2060.
84. Arnold, T.; Zorn, T.; Bernhard, G.; Nitsche, H. Sorption of uranium (VI) onto phyllite. Chem. Geol. 1998, 151, 129-141.
85. Arnold, T.; Zorn, T.; Zanker, H.; Bernhard, G.; Nitsche, H. Sorption behavior of U (VI) of phyllite: experiments and modeling. J. Contam. Hydrol. 2001, 47, 219-231.
86. Lutzenkirchen, J.; Boily, J.-F.; Lovgren, L.; Sjoberg, S. Limitations of the potentiometric titration technique in determining the proton active site density of goethite surfaces. Geochim. Cosmochim. Acta 2002, 66, 3389-3396.
87. Payne, T. E.; Edis, R.; Fenton, B. R.; Waite, T. D. Comparison of laboratory uranium sorption data with 'in situ distribution coefficients' at the Koongarra uranium deposit, Northern Australia. J. Environ. Radioact. 2001, 57, 35-55.
88. Curtis, G. P.; Fox, P.; Kohler, M.; Davis, J. A. Comparison of in situ KD values with a laboratory determined surface complexation model. Appl. Geochem. 2004, 19, 1643-1653.
89. VI sorption behavior on silicate mineral mixtures. J. Contam. Hydrol. 2001, 47, 241-253.
90. Bertetti, F. P.; Pabalan, R. T.; Almendarez, M. G. Studies of neptunium (V) sorption on quartz, clinoptilolite, montmorillonite, and alpha-alumina. In Adsorption of Metals by Geomedia; Jenne, E. A., Ed.; Academic Press: San Diego, 1998; pp 131-148.
91. Oreskes, N. Why Believe a Computer? Models, Measures, and Meaning in the Natural World. In The Earth Around Us: Maintaining a Livable Planet; Schneiderman, J. S., Ed.; W. H. Freeman and Co.: San Francisco, 2000; pp 70-82.
92. Kantar, C.; Honeyman, B. D. Citric acid enhanced remediation of solids contaminated with uranium by soil flushing and soil washing. J. Environ. Eng. 2006, 132, 247-255.
93. Neiss, J.; Stewart, B. D.; Nico, P. S.; Fendorf, S. Speciationdependant microbial reduction of uranium within iron-coated sands. Environ. Sci. Technol. 2007, 41, 7343-7348.
94. Senko, J. M.; Istok, J. D.; Suflita, J. M.; Krumholz, L. R. In-Situ evidence for uranium immobilization and remobilization. Environ. Sci. Technol. 2002, 36, 1491-1496.
95. Boggs, J. M.; Young, S. C.; Beard, L. M.; Gelhar, L. W.; Rehfeldt, K. R.; Adams, E. E. Field study of dispersion in a heterogeneous aquifer 1. Overview and site description. Water Resour. Res. 1992, 28, 3281-3291.
96. Beven, K. How far can we go in distributed hydrological modelling. Hydrol. Earth Syst. Sci. 2001a, 5, 1-12.
97. Bryant, S. L.; Thompson, K. E. Theory, modelingandexperiment and reactive transport in porous media. Curr. Opin. Colloid Interface Sci. 2001, 6, 217-222.
98. Beven, K. Onexplanatory depth and predictive power. Hydrol. Processes 2001b, 15, 3069-3071.
99. Fernandez-Garcia, D.; Sanchez-Vila, X.; Illangasekare, T. H. Convergent-flow tracer tests in heterogeneous media: combined experimental-numerical analysis for determination of equivalent transport parameters. J. Contam. Hydrol. 2002, 57, 129-145.
100. Chao, H.-C.; Rajaram, H.; Illangasekare, T. H. Intermediatescale experiments and numerical simulations of transport under radial flow in a two-dimensional heterogeneous porous media. Water Resour. Res. 2000, 36, 2869-2884.
101. Barth, G. R.; Hill, M. C.; Illangasekare, T. H.; Rajaram, H. Predictive modeling of flow and transport in a two-dimensional intermediate-scale, heterogeneous porous medium. Water Resour. Res. 2001a, 37, 2503-2512.
102. Barth, G. R.; Illangasekare, T. H.; Hill, M. C.; Rajaram, H. Anew tracer-density criterion for heterogeneous porous media. Water Resour. Res. 2001b, 37, 21-31.
103. Levy, M.; Berkowitz, B. Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J. Contam. Hydrol. 2003, 64, 203-226.
104. Illangasekare, T. H.; Ramsey, J. L., Jr.; Jensen, K. H.; Butts, M. B. Experimental study of movement and distribution of dense organic contaminants in heterogeneous aquifers. J. Contam. Hydrol. 1995, 20, 1-25.
105. Heiderscheidt, J. L.; Siegrist, R. L.; Illangasekare, T. H. Intermediate-scale 2D experimental investigation of in-situ chemical oxidation using potassium permanganate for remediationof complex DNAPL sources. J. Contam. Hydrol. 2008, 102, 3-16.
106. Zhu, C.; Hu, F. Q.; Burden, D. S. Multi-component reactive transport modeling of natural attenuation of an acid groundwater plume at a uranium mill tailings site. J. Contam. Hydrol. 2001, 52, 85-108.
107. Van Cappellen, P. Reactive surface area control of the dissolution kinetics of biogenic silica in deep-sea sediments. Chem. Geol. 1996, 132, 125-130.
108. Lichtner, P. C.; Tartakovsky, D. M. Stochastic analysis of effective rate constant for heterogeneous reactions. Stochastic Environ. Res. Risk Assess. 2003, 17, 419-429.
109. Meile, C.; Tuncay, K. Scale dependence of reaction rates in porous media. Adv. Water Resour. 2006, 29, 62-71.
110. Rajaram, H. Time and scale dependent effective retardation factors in heterogeneous systems. Adv. Water Resour. 1997, 20, 217-230. (Pubitemid 27384004)
111. Haggerty, R.; Harvey, C.; von Schwerin, C. F.; Meigs, L. C. What controls the apparent time-scale of solute mass transfer in aquifers and soils? A comparison of experimental results. Water Resour. Res. 2004, 40, 10.1029/2002WR001716.
112. Renard, P.; de Marsily, G. Calculating equivalent permeability: a review. Adv. Water Resour. 1997, 20, 253-278.
113. Gasda, S. E.; Celia, M. A. Upscaling relative permeabilities in a structured porous medium. Adv. Water Resour. 2005, 28, 493-506.
114. Wood, B. D.; Cherblanc, F.; Quintard, M.; Whitaker, S. Volume averaging for determining the effective dispersion tensor: Closure using periodic unit cells and comparison with ensemble averaging. Water Resour. Res. 2003, 39, 1210.
115. Cushman, J. H. On Measurement, Scale, and Scaling. Water Resour. Res. 1986, 22, 129-134.
116. Dagan, G. Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation, formation to regional scale. Water Resour. Res. 1986, 22, 120S-134S.
117. Neuman, S. P.; di Federico, V. Correlation, Flow, and Transport in Multiscale Permeability Fields. In Scale Dependence and Scale Invariance in Hydrology; Sposito, G., Ed.; Cambridge University Press: Cambridge, 1998; pp 354-397.
118. Selroos, J.-O.; Cvetkovic, V. Modeling solute advection coupled with sorption kinetics in heterogeneous formations. Water Resour. Res. 1992, 28, 1271-1278.
119. Baveye, P.; Rogasik, H.; Wendroth, O.; Onasch, I.; Crawford, J. W. Effect of sampling volume on the measurement of soil physical properties: simulation with x-ray tomography data. Meas. Sci. Technol. 2002, 13, 775-784.
120. Brown, G. O.; Hsieh, H. T.; Lucero, D. A. Evaluation of laboratory dolomite core sample size using representative elementary volume concepts. Water Resour. Res. 2000, 36, 1199-1207.
121. Zhang, D.; Zhang, R.; Chen, S.; Soll, W. E. Pore scale study of flow in porous media: Scale dependency, REV, and statistical REV. Geophys. Res. Lett. 2000, 27, 1195-1198.
122. Tidwell, V. C.; Wilson, J. L. Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution. Water Resour. Res. 1999, 35, 3375-3387.
123. Rubin, J. Transport of reacting solutes inporous media: Relation between mathematical nature of problem formulation and chemical nature of reactions. Water Resour. Res. 1983, 19, 1231-1252.
124. Quintard, M.; Whitaker, S. Transport in chemically and mechanically heterogeneous porous mediaIV: large-scale mass equilibrium for solute transport with adsorption. Adv. Water Resour 1998, 22, 33-57. (Pubitemid 29007178)
125. Konikow, L. F.; Bredehoeft, J. D. Ground-water models cannot be validated. Adv. Water Resour. 1992, 15, 75-83.
126. Bredehoeft, J. D. From models to performance assessment: The conceptualization problem. Ground Water 2003, 41, 571-577.
127. Oreskes, N.; Belitz, K. Philosophical Issues in Model Assessment. In Model Validation: Perspectives in Hydrological Science; John Wiley and Sons, Ltd.: 2001; pp 23-41.
128. Oreskes, N.; Shrader-Frechette, K.; Belitz, K. Verification, validation, and confirmation of numerical modelsinthe earth sciences. Science 1994, 263, 641-646.
129. Steefel, C. I.; De Paolo, D. J.; Lichtner, P. C. Reactive transport modeling: An essential tool and a new research approach for the Earth sciences. Earth Planet. Sci. Lett. 2005, 240, 539-558.
130. Murray, A. B. Reducing model complexity for explanation and prediction. Geomorphology 2007, 90, 178-191.
131. U. S. DOE 2010. Complex Systems Science for Subsurface Flow and Transport: Report from the August2009 Workshop; DOE/SC-0123; U. S. Department of Energy Office of Science. www.science.doe.gov/ober/BER-workshops.html (accessed March 30th, 2010).