Ensemble solute transport in two-dimensional operator-scaling random fields

Water Resources Research

Volumn 44, Issue 2, 2008, Pages

  Monnig, Nathan D ^a   Benson, David A ^a   Meerschaert, Mark M ^b  

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

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; BROWNIAN MOVEMENT; HYDRAULIC CONDUCTIVITY; PARAMETER ESTIMATION;

PLUME GROWTH RATES; SELF-SIMILARITY PARAMETER;

SOLUTE TRANSPORT;

ANISOTROPY; BROWNIAN MOVEMENT; HYDRAULIC CONDUCTIVITY; PARAMETER ESTIMATION; SOLUTE TRANSPORT;

ANISOTROPY; BROWNIAN MOTION; HYDRAULIC CONDUCTIVITY; MEASUREMENT METHOD; PLUME; SOLUTE TRANSPORT; STOCHASTICITY; STRATIFICATION; THEORETICAL STUDY;

EID: 41149093872     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2007WR005998     Document Type: Article

References (41)

1. Ababou, R., and L. W. Gelhar (1990), Self-similar randomness and spectral conditioning: Analysis of scale effects in subsurface hydrology, in Dynamics of Fluids in Hierarchical Porous Media, edited by J. H. Cushman, chap. XIV, pp. 393-428, Academic, San Diego, Calif.
2. 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, W01415, doi:10.1029/2004WR003755.
3. 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.
4. Biermé, H., M. M. Meerscheart, and H. P. Scheffler (2007), Operator scaling random fields, Stochastic Processes Their Appl., 117, 312-332.
5. Bruining, J., D. van Batenburg, L. W. Lake, and A. P. Yang (1997), Flexible spectral methods for the generation of random fields with power-law semivariograms, Math. Geol., 29, 823-848.
6. Caccia, D. C., D. 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.
7. Castle, J. W., F. J. Molz, S. Lu, and C. L. Dinwiddie (2004), Sedimentology and fractal-based analysis of permeability data, John Henry member, Straight Cliffs formation (upper Cretaceous), Utah, U.S.A., J. Sediment. Res., 74, 270-284.
8. Dagan, G. (1994), The significance of heterogeneity of evolving scales to transport in porous formations, Water Resour. Res., 30, 3327-3336.
9. Deshpande, A., P. B. Flemings, and J. Huang (1997), Quantifying lateral heterogeneities in fluvio-deltaic sediments using three-dimensional reflection seismic data: Offshore Gulf of Mexico, J. Geophys. Res., 102, 15,385-15,402.
10. Di Federico, V., and S. P. Neuman ( 1997), Scaling of random fields by means of truncated power variograms and associated spectra, Water Resour. Res., 33, 1075-1086.
11. Di Federico, V., and S. P. Neuman (1998), Transport in multiscale log conductivity fields with truncated power variograms, Water Resour. Res., 34, 963-974.
12. Di Federico, V., S. P. Neuman, and D. M. Tartakovsky (1999), Anisotropy, lacunarity, and upscaled conductivity and its autocovariance in multiscale random fields with truncated power variograms, Water Resour. Res., 35, 2891-2908.
13. Gelhar, L. W., and C. L. Axness (1983), Three dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19, 161-180.
14. Gelhar, L. W., C. Welty, and K. R. Rehfeldt (1992), A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28, 1955-1974.
15. Hassan, A. E., J. H. Cushman, and J. W. Delleur (1997), Monte Carlo studies of flow and transport in fractal conductivity fields: Comparison with stochastic perturbation theory, Water Resour. Res., 33, 2519-2534.
16. Herrick, M. G., D. A. Benson, M. M. Meerschaert, and K. R. 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.
17. Hewett, T. A. (1986), Fractal distributions of reservoir heterogeneity and their influence on fluid transport, presented at the 61st Annual Technical Conference, Soc. of Pet. Eng., New Orleans, La.
18. Kapoor, V., and L. W. Gelhar (1994a), Transport in three-dimensionally heterogeneous aquifers: 1. Dynamics of concentration fluctuations, Water Resour. Res., 30, 1775-1788.
19. Kapoor, V., and L. W. Gelhar (1994b), Transport in three-dimensionally heterogeneous aquifers: 2. Predictions and observations of concentration fluctuations, Water Resour. Res., 30, 1789-1802.
20. Kapoor, V., and P. K. Kitanidis (1998), Concentration fluctuations and dilution in aquifers, Water Resour. Res., 34, 1181-1194.
21. Kemblowski, M. W., and J.-C. Wen (1993), Contaminant spreading in stratified soils with fractal permeability distributions, Water Resour. Res., 29, 419-425.
22. 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, 583-594.
23. Liu, H. H., and F. J. Molz (1997a), Multifractal analyses of hydraulic conductivity distributions, Water Resour. Res., 33, 2483-2488.
24. Liu, H.H., and F. J. Molz (1997b), Block scale dispersivity for heterogeneous porous media characterized by stochastic fractals, Geophys. Res. Lett., 24, 2239-2242.
25. Lu, S., F. Molz, and H. H. Liu (2003), An efficient, three-dimensional, anisotropic, fractional Brownian motion and truncated fractional Levy motion simulation algorithm based on successive random additions, Comput. Geosci., 29, 15-25.
26. Mandelbrot, B. B., and J. R. Wallis (1969), Robustness of the rescaled ranges R/S in the measurement of noncyclic long run statistical dependence, Water Resour. Res., 5, 967-988.
27. Matheron, M., and G. de Marsily (1980), Is transport in porous media always diffusive?, Water Resour. Res., 16, 901-917.
28. Mercado, A. (1967), The spreading pattern of injected water in a permeability-stratified aquifer, Int. Assoc. Sci. Hydrol. Publ., 72, 23-36.
29. Molz, F. J., and G. K. Boman (1993), A stochastic interpolation scheme in subsurface hydrology, Water Resour. Res., 29, 3769-3774.
30. Molz, F. J., and G. K. Boman (1995), Further evidence of fractal structure in hydraulic conductivity distributions, Geophys. Res. Lett., 22, 2545-2548.
31. Molz, F. J., O. Güven, J. G. Melville, and C. Cardone (1990), Hydraulic conductivity measurement at different scales and contaminant transport modeling, in Dynamics of Fluids in Hierarchical Porous Formations, edited by J. H. Cushman, pp. 37-59, Academic, San Diego, Calif.
32. Molz, F. J., H. H. Liu, and J. Szulga (1997), Fractional Brownian motion and fractional Gaussian noise in subsurface hydrology: A review, presentation of fundamental properties, and extensions, Water Resour. Res., 33, 2273-2286.
33. Molz, F. J., H. Rajaram, and S. Lu (2004), Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions, Rev. Geophys., 42, RG1002, doi:10.1029/2003RG000126.
34. Neuman, S. P. (1990), Universal scaling of hydraulic conductivities and dispersivities in geologic media, Water Resour. Res., 26, 1749-1758.
35. Neuman, S. P. (1995), On advective transport in fractal permeability and velocity fields, Water Resour. Res., 31, 1455-1460.
36. Painter, S., and G. Mahinthakumar (1999), Prediction uncertainty for tracer migration in random heterogeneities with multifractal character, Adv. Water Resour., 23, 49-57.
37. Rajaram, H., and L. Gelhar (1995), Plume-scale dependent dispersion in aquifers with a wide range of scales of heterogeneity, Water Resour. Res., 31, 2469-2482.
38. Sapozhnikov, V., and E. Foufoula-Georgiou (1996), Self-affinity in braided rivers, Water Resour. Res., 32, 1429-1440.
39. Tennekoon, L., M. C. Boufadel, D. Lavallee, and J. Weaver (2003), Multi-fractal anisotropic scaling of the hydraulic conductivity, Water Resour. Res., 39(7), 1193, doi:10.1029/2002WR001645.
40. Welty, C., and L. W. Gelhar (1989), Evaluation of longitudinal dispersivity from tracer test data, Rep. 320, Ralph M. Parsons Lab. for Water Resour. and Hydrodyn., Mass. Inst. of Technol., Cambridge.
41. Zhan, H., and S. W. Wheatcraft (1996), Macrodispersivity tensor for non-reactive solute transport in isotropic and anisotropic fractal porous media: Analytical solutions, Water Resour. Res., 32, 3461-3474.