Erratum: Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab (Water Resources Research (2011) 47 (W10519) DOI: 10.1029/2011WR010857);Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab

Water Resources Research

Volumn 47, Issue 10, 2011, Pages

  Major, Elizabeth ^a   Benson, David A ^a   Revielle, Jordan ^a   Ibrahim, Hamed ^a   Dean, Arianne ^a   Maxwell, Reed M ^a   Poeter, Eileen ^a   Dogan, Mine ^b  

^a Department of Metallurgical and Materials Engineering   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AIR; POTASSIUM IODIDE; SANDSTONE; STATISTICAL MECHANICS; VELOCITY;

ADVECTION-DISPERSION EQUATION; BREAKTHROUGH CURVE; HETEROGENEOUS MATERIALS; LOGICAL INFERENCE; LONGITUDINAL DISPERSIVITY; NONLOCAL TRANSPORT; OPTIMIZED PARAMETER; PREDICTIVE ABILITIES;

ADVECTION;

ADVECTION; COMPARATIVE STUDY; DATA SET; EXPERIMENTAL STUDY; HOMOGENEITY; HYDRAULIC CONDUCTIVITY; IMMOBILIZATION; LONGITUDINAL GRADIENT; MEASUREMENT METHOD; NUMERICAL MODEL; POTASSIUM; SANDSTONE; SLAB; TEMPORAL VARIATION; UPSCALING; VELOCITY; X-RAY;

EID: 80055051700     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011WR011577     Document Type: Erratum

References (73)

1. Ashby, S., and R. D. Falgout (1996), A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations., Nuclear Sci. Engin., 124, 145-159. (Pubitemid 126564896)
2. Becker, M., and A. Shapiro (2003), Interpreting tracer breakthrough tailing from different forced-gradient tracer experiment configurations in fractured bedrock, Water Resour. Res., 39(1), 1024, doi:10.1029/2001WR 001190.
3. Bel, G., and E. Barkai (2005), Weak ergodicity breaking in the continuoustime random walk, Phys. Rev. Lett., 94(24), 240602, doi:10.1103/PhysRevLett.94.240602. (Pubitemid 41636460)
4. Benson, D. A., and M. M. Meerschaert (2009), A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations, Adv. Water Resour., 32, 532-539, doi:10.1016/j.advwatres.2009. 01.002.
5. Benson, D. A., C. Tadjeran, M. M. Meerschaert, I. Farnham, and G. Pohll (2004), Radial fractional-order dispersion through fractured rock, Water Resour. Res., 40(12), W12416, doi:10.1029/2004WR003314.
6. Benson, D. A., M. M. Meerschaert, B. Baeumer, and H.-P. Scheffler (2006), Aquifer operator scaling and the effect on solute mixing and dispersion, Water Resour. Res., 42(1), W01415, doi:10.1029/2004WR 003755.
7. Berkowitz, B., H. Scher, and S. Silliman (2000), Anomalous transport in laboratory-scale, heterogeneous porous media, Water Resour. Res., 36(1), 149-158, doi:10.1029/1999WR900295. (Pubitemid 30042117)
8. 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(2), RG2003, doi:10.1029/2005RG000178. (Pubitemid 46044201)
9. Caccia, D., D. B. Percival, M. J. Cannon, G. M. Raymond, and J. B. Bassingthwaighte (1997), Analyzing exact fractal time series: Evaluating dispersional analysis and rescaled range methods, Physica A, 246, 609-632(24), doi:10.1016/S0378-4371 (97) 00363-4. (Pubitemid 127379081)
10. Carrera, J., X. Sánchez-Vila, I. Benet, A. Medina, G. Galarza, and J. Guimerà (1998), On matrix diffusion: Formulations, solution methods and qualitative effects, Hydrogeol. J., 6, 178-190, doi:10.1007/s100400050143. (Pubitemid 128546161)
11. Chakraborty, P., M. M. Meerschaert, and C. Y. Lim (2009), Parameter estimation for fractional transport: A particle-tracking approach, Water Resour. Res., 45(10), W10415, doi:10.1029/2008WR007577.
12. Cushman, J. H., and T. R. Ginn (1993), Nonlocal dispersion in media with continuously evolving scales of heterogeneity, Transp. Por. Media, 13(1), 123-138.
13. Dentz, M., and B. Berkowitz (2003), Transport behavior of a passive solute in continuous time random walks and multirate mass transfer, Water Resour. Res., 39(5), 1111, doi:10.1029/2001WR001163.
14. Dentz, M., and D. Bolster (2010), Distribution-versus correlation-induced anomalous transport in quenched random velocity fields, Phys. Rev. Lett., 105(24), 244-301.
15. Dogan, M., R. L. Van Dam, G. C. Bohling, J. J. Butler, and D. W. Hyndman (2011), Hydrostratigraphic analysis of the MADE site with full-resolution GPR and direct-push hydraulic profiling, Geophys. Res. Lett., 38(6), L06405, doi:10.1029/2010GL046439.
16. Fernàndez-Garcia, D., and J. J. Gómez-Hernández (2007), Impact of upscaling on solute transport: Traveltimes, scale dependence of dispersivity, and propagation of uncertainty, Water Resour. Res., 43(2), W02423, doi:10.1029/2005WR004727. (Pubitemid 46502890)
17. Fernàndez-Garcia, D., G. Llerar-Meza, and J. J. Gómez-Hernández (2009), Upscaling transport with mass transfer models: Mean behavior and propagation of uncertainty, Water Resour. Res., 45(10), W10411, doi:10. 1029/2009WR007764.
18. Fiori, A., I. Janković, and G. Dagan (2006), Modeling flow and transport in highly heterogeneous three-dimensional aquifers: Ergodicity, Gaussianity, and anomalous behavior-2. Approximate semianalytical solution, Water Resour. Res., 42(6), W06D13, doi:10.1029/2005WR004752. (Pubitemid 44156594)
19. Fulger, D., E. Scalas, and G. Germano (2008), Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation, Phys. Rev. E, 77(2), 021122, doi:10.1103/PhysRevE.77.021122. (Pubitemid 351366235)
20. Gelhar, L., A. Gutjahr, and R. Naff (1979), Stochastic analysis of macrodispersion in a stratified aquifer, Water Resour. Res., 15(6), 1387-1397, doi:10.1029/WR015i006p01387.
21. Gouze, P., Y. Melean, T. Le Borgne, M. Dentz, and J. Carrera (2008), Non-Fickian dispersion in porous media explained by heterogeneous microscale matrix diffusion, Water Resour. Res., 44(11), W11416, doi:10.1029/2007WR006690.
22. Haggerty, R., and S. M. Gorelick (1995), Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity, Water Resour. Res., 31(10), 2383-2400, doi:10.1029/95WR01583. (Pubitemid 26475182)
23. 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, doi:10.1029/2000WR900214. (Pubitemid 32039902)
24. Haggerty, R., S. W. Fleming, L. C. Meigs, and S. A. McKenna (2001), Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in singlewell injection-withdrawal tests, Water Resour. Res., 37(5), 1129-1142, doi:10.1029/2000WR900334. (Pubitemid 32532639)
25. Herrick, M., D. Benson, M. Meerschaert, and K. McCall (2002), Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous system, Water Resour. Res., 38(11), 1227, doi:10.1029/2001WR000914.
26. Hosking, J. R. M. (1981), Fractional differencing, Biometrika, 68, 165-176.
27. Isaacs, G. L. (1963), An iteration formula for fractional differences, Proc. London Math. Soc., s3-13(1), 430-460.
28. Janković, I., A. Fiori, and G. Dagan (2006), Modeling flow and transport in highly heterogeneous three-dimensional aquifers: Ergodicity, Gaussianity, and anomalous behavior. Part 1: Conceptual issues and numerical simulations, Water Resour. Res., 42(6), W06D12, doi:10.1029/2005WR 004734.
29. Jones, J., and C. S. Woodward (2001), Newton-Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems, Adv. Water Resour., 24, 763-774. (Pubitemid 32593051)
30. Kitanidis, P. K. (1990), Effective hydraulic conductivity for gradually varying flow, Water Resour. Res., 26, 1197-1208, doi:10.1029/WR026i 006p01197.
31. Klise, K. A. (2005), Analysis of non-Fickian dispersion for laboratory-scale tracer experiments in cross-bedded sandstone, Master's thesis, University of New Mexico, Albuquerque, NM.
32. Klise, K. A., V. C. Tidwell, and S. A. McKenna (2008), Comparison of laboratory-scale solute transport visualization experiments with numerical simulation using cross-bedded sandstone, Adv. Water Resour., 31(12), 1731-1741, doi:10.1016/j.advwatres.2008.08.013.
33. Kollet, S. J., and R. M. Maxwell (2006), Integrated surface-groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model, Adv. Water Resour., 29, 945-958. (Pubitemid 43832572)
34. Kollet, S. J., and R. Maxwell (2008), Demonstrating fractal scaling of baseflow residence time distributions using a fully coupled groundwater and land surface model, Geophys. Res. Lett., 35, L07402, doi:10.1029/2008GL033215. (Pubitemid 351858631)
35. Labolle, E. M., G. E. Fogg, and A. F. B. Tompson (1996), Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods, Water Resour. Res., 32(3), 583-593, doi:10.1029/95WR03528. (Pubitemid 26351894)
36. Le Borgne, T., and P. Gouze (2008), Non-Fickian dispersion in porous media: 2. model validation from measurements at different scales, Water Resour. Res., 44(6), W06427, doi:10.1029/2007WR006279.
37. Major, E. R. (2011), Comparison of classical and non-local transport theories in a "perfectly" sampled sandstone slab, Master's thesis, Colorado School of Mines, Golden, CO.
38. Mandelbrot, B. B., and J. R. Wallis (1969), Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence, Water Resour. Res., 5, 967-988, doi:10.1029/WR005i005p00967.
39. Maxwell, R. (2010), SLIM FAST-A User's Manual, V.4, GWMI, 49 pp., available at http://igwmc.mines.edu/about/GWMI2010-01.pdf.
40. Maxwell, R., C. Welty, and A. Tompson (2003), Streamline-based simulation of virus transport resulting from long term artificial recharge in a heterogeneous aquifer, Adv. Water Resour., 22(3), 203-221.
41. Maxwell, R., C. Welty, and R. Harvey (2007), Revisiting the Cape Cod bacteria injection experiment using a stochastic modeling approach, Environ. Sci. Technol., 41(15), 5548-5558. (Pubitemid 47224838)
42. Maxwell, R., S. Carle, and A. Tompson (2008), Contamination, risk, and heterogeneity: On the effectiveness of aquifer remediation, Environ. Geol., 54, 1771-1786. (Pubitemid 351743677)
43. Maxwell, R., A. Tompson, and S. Kollet (2009), A serendipitous, long-term infiltration experiment: Water and tritium circulation beneath the CAM-BRIC trench at the Nevada test site, J. Contam. Hydrol., 108(1-2), 12-28, doi:10.1016/j.jconhyd.2009.05.002.
44. McDonald, M., and A. Harbaugh (1983), A modular three-dimensional finite-difference ground-water flow model, Open-File Rept. 83-875, U. S. Geological Survey.
45. Meerschaert, M. M., and H.-P. Scheffler (2001), Limit Distributions for Sums of Independent Random Vectors, 512 pp., Wiley, Hoboken, N. J.
46. Meerschaert, M. M., T. J. Kozubowski, F. J. Molz, and S. Lu (2004), Fractional Laplace model for hydraulic conductivity, Geophys. Res. Lett., 31(8), L08501, doi:10.1029/2003GL019320. (Pubitemid 38893041)
47. Mercado, A. (1967), The spreading pattern of injected water in a permeabilitystratified aquifer, Proc. Int. Assoc. Sci. Hydrology Symp. Haifa, 72, 23-36.
48. Monnig, N. D., D. A. Benson, and M. M. Meerschaert (2008), Ensemble solute transport in two-dimensional operator-scaling random fields, Water Resour. Res., 44(2), W02434, doi:10.1029/2007WR005998. (Pubitemid 351442510)
49. Montroll, E. W., and G. H. Weiss (1965), Random walks on lattices, J. Math. Phys., 6(2), 167-181.
50. Morales-Casique, E., S. P. Neuman, and A. Guadagnini (2006), Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: Theoretical framework, Adv. Water Resour., 29(8), 1238-1255. (Pubitemid 44109098)
51. Moreno, L., Y. W. Tsang, C. F. Tsang, F. V. Hale, and I. Neretnieks (1988), Flow and tracer transport in a single fracture-A stochastic-model and its relation to some field observations, Water Resour. Res., 24(12), 2033-2048, doi:10.1029/WR024i012p02033. (Pubitemid 19301586)
52. Neuman, S. P. (1993), Eulerian-Lagrangian theory of transport in spacetime nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximation, Water Resour. Res., 29(3), 633-645, doi:10.1029/92WR02306. (Pubitemid 23382797)
53. Neuman, S. P., and S. Orr (1993), Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation, Water Resour. Res., 29(2), 341-364, doi:10.1029/92WR02062. (Pubitemid 23381681)
54. Neuman, S. P., and D. M. Tartakovsky (2009), Perspective on theories of non-Fickian transport in heterogeneous media, Adv. Water Resour., 32(5), 670-680, doi:10.1016/j.advwatres.2008.08.005.
55. Poeter, E., M. Hill, E. Banta, S. Mehl, and S. Christensen (2005), UCODE-2005 and six other computer codes for universal sensitivity analysis, calibration, and uncertainty evaluation, U. S. Geological Survey Techniques and Methods 6-A11, p. 283.
56. Revielle, J. (2009), Incorporating hydraulic conductivity measurements into fractal aquifer realizations and its effect on solute transport, Master's thesis, Colorado School of Mines, Golden, CO.
57. Riva, M., A. Guadagnini, D. Fernandez-Garcia, X. Sánchez-Vila, and T. Ptak (2008), Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site, J. Contam. Hydrol., 101(1-4), 1-13.
58. Rubin, Y., and J. Gómez-Hernández (1990), A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations, Water Resour. Res., 26(4), 691-701, doi:10.1029/WR026i004p00691.
59. Rubin, Y., A. Bellin, and A. E. Lawrence (2003), On the use of block-effective macrodispersion for numerical simulations of transport in heterogeneous formations, Water Resour. Res., 39(9), 1242, doi:10.1029/ 2002WR001727.
60. Salamon, P., D. Fernàndez-Garcia, and J. J. Gómez- Hernández (2007), Modeling tracer transport at the MADE site: The importance of heterogeneity, Water Resour. Res., 43(8), W08404, doi:10.1029/2006WR 005522.
61. Schumer, R., D. A. Benson, M. M. Meerschaert, and B. Baeumer (2003), Fractal mobile/immobile solute transport, Water Resour. Res., 39(10), 1296, doi:10.1029/2003WR002141.
62. Siirila, E., A. Navarre-Sitchler, R. Maxwell, and J. McCray (2011), A quantitative methodology to assess the risks to human health from CO2 leakage into groundwater, Adv. Water Resour., doi:10.1016/j.adv watres.2010.11.005 (in press).
63. 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, doi:10.1029/WR023i008p01667. (Pubitemid 17634263)
64. Tartakovsky, D. M., and S. P. Neuman (1998), Transient flow in bounded randomly heterogeneous domains: 1. Exact conditional moment equations and recursive approximations, Water Resour. Res., 34(1), 1-12, doi:10.1029/ 97WR02118. (Pubitemid 28031183)
65. Tennekoon, L., M. C. Boufadel, D. Lavalee, and J. Weaver (2003), Multifractal anisotropic scaling of the hydraulic conductivity, Water Resour. Res., 39(7), 1193, doi:10.1029/2002WR001645.
66. Tidwell, V. C., and J. L. Wilson (1997), Laboratory method for investigating permeability upscaling, Water Resour. Res., 33(7), 1607-1616, doi:10.1029/97WR00804. (Pubitemid 27295402)
67. Tidwell, V. C., and J. L. Wilson (2000), Heterogeneity, permeability patterns, and permeability upscaling: Physical characterization of a block of Massillon sandstone exhibiting nested scales of hetergeneity, SPE Reservoir Eval. Eng., 3(4), 283-291.
68. Tompson, A., S. Carle, N. Rosenberg, and R. Maxwell (1999), Analysis of groundwater migration from artificial recharge in a large urban aquifer: A simulation perspective, Water Resour. Res., 35(10), 2981-2998, doi:10.1029/1999WR900175. (Pubitemid 29461965)
69. Tsang, Y. W. (1995), Study of alternative tracer tests in characterizing transport in fractured rocks, Geophys. Res. Lett., 22(11), 1421-1424, doi:10.1029/95GL01093. (Pubitemid 26465252)
70. Tsang, Y. W., C. F. Tsang, I. Neretnieks, and L. Moreno (1988), Flow and tracer transport in fractured media: A variable aperture channel model and its properties, Water Resour. Res., 24(12), 2049-2060, doi:10.1029/WR024i012p02049. (Pubitemid 19301587)
71. Zhang, Y., and D. A. Benson (2008), Lagrangian simulation of multidimensional anomalous transport at the MADE site, Geophys. Res. Lett., 35, L07403, doi:10.1029/2008GL033222. (Pubitemid 351858632)
72. Zhang, Y., D. A. Benson, and D. M. Reeves (2009), Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications, Adv. Water Resour., 32(4), 561-581.
73. 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. (Pubitemid 38955638).