Uncertainty of one-dimensional ground-water flow in strongly heterogeneous formations

Journal of Hydrologic Engineering

Volumn 4, Issue 2, 1999, Pages 152-159

  Zhan, Hongbin ^a   Wheatcraft, Stephen W ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF NEVADA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; FUNCTIONS; HYDRAULIC CONDUCTIVITY; MONTE CARLO METHODS; ONE DIMENSIONAL; POROUS MATERIALS; STATISTICAL METHODS;

HETEROGENEOUS FORMATIONS; QUASIANALYTICAL METHOD; STANDARD DEVIATION;

GROUNDWATER FLOW;

AQUIFER; BOUNDARY CONDITIONS; GROUNDWATER FLOW; HETEROGENEOUS MEDIUM;

EID: 0033117610     PISSN: 10840699     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)1084-0699(1999)4:2(152)     Document Type: Article

References (39)

1. Adomian, G. (1983). Stochastic systems. Academic, New York.
2. Adomian, G. (1986). Nonlinear stochastic operator equations. Academic, New York.
3. Adomian, G. (1994). Solving frontier problems of physics: The decomposition method. Kluwer, Dordrecht, The Netherlands.
4. Bellin, A., Salandin, P., and Rinaldo, A. (1992). "Simulation of dispersion in heterogeneous porous formations: Statistics, first-order theories, convergence of computations." Water Resour. Res., 28(9), 2211-2227.
5. Chin, D., and Wang, T. (1992). "An investigation of the validity of first-order stochastic dispersion theories in isotropic porous media." Water Resour. Res., 28(6), 1531-1542.
6. Dagan, G. (1982). "Stochastic modeling of groundwater flow by unconditional and conditional probabilities. 1. Conditional simulation and the direct problem." Water Resour. Res., 18(4), 813-833.
7. Dagan, G. (1984). "Solute transport in heterogeneous porous formations." J. Fluid Mech., Cambridge, U.K., 145, 151-177.
8. Dagan, G. (1994). "An exact nonlinear correction to transverse macrodispersivity for transport in heterogeneous formations." Water Resour. Res., 30(10), 2699-2705.
9. Deng, F.-W., and Cushman, J. H. (1995). "On higher-order corrections to the flow velocity covariance tensor." Water Resour. Res., 31(7), 1659-1672.
10. Dikow, E. (1988). "Stochastic analysis of groundwater flow in a bounded domain by spectral methods." Transp. Porous Media, 3, 173-184.
11. Gelhar, L. W., and Axness, A. C. (1983). "Three-dimensional stochastic analysis of macrodispersion in aquifers." Water Resour. Res., 19(1), 161-180.
12. Gelhar, L. W. (1986). "Stochastic subsurface hydrology from theory to applications." Water Resour. Res., 22(9), 135S-145S.
13. Goltz, M. N., and Roberts, P. V. (1988). "Simulations of physical non-equilibrium solute transport models: Application to a large-scale field experiment." J. Contaminant Hydro., 3, 37-63.
14. Gutjahr, A. L., and Gelhar, L. W. (1981). "Stochastic models of subsurface flow: Infinite versus finite domains and stationarity." Water Resour. Res., 17(2), 337-350.
15. Gutjahr, A. L., Gelhar, L. W., Bakr, A. A., and MacMillan, J. R. (1978). "Stochastic analysis of spatial variability in subsurface flows. 2. Evaluation and application." Water Resour. Res., 14(5), 953-959.
16. Hsu, K.-C., Zhang, D., and Neuman, S. P. (1996). "High-order effects on flow and transport in randomly heterogeneous porous media." Water Resour. Res., 32(3), 571-582.
17. Killey, R. W. D., and Moltayner, G. L. (1988). "Twin lake tracer tests: Setting, methodology, and hydraulic conductivity distribution." Water Resour. Res., 24(10), 1585-1612.
18. Mol, F. J., Güven, O., Melville, J. G., and Cardone, C. (1990). "Chapter III: Hydraulic conductivity measurement at different scales and contaminant transport modeling." Dynamics of fluids in hierarchical porous media, J. H. Cushman, ed., Academic, San Diego.
19. Montoglou, A., and Wilson, J. L. (1982). "The turning bands method for simulation of random fields using line generation by a spectral method." Water Resour. Res., 18(5), 1379-1394.
20. Naff, R. L., and Vecchia, V. (1986). "Stochastic analysis of three-dimensional flow in a bounded domain." Water Resour. Res., 22(5), 695-704.
21. Neuman, S. P., and Zhang, Y-K. (1990). "A quasi-linear theory of non-Fickian and Fickian subsurface dispersion. 1. Theoretical analysis with application to isotropic media." Water Resour. Res., 26(5), 887-902.
22. Paleologos, E. K., Neuman, S. P., and Tartakovsky, D. (1996). "Effective hydraulic conductivity of bounded, strongly heterogeneous porous media." Water Resour. Res., 32(5), 1333-1341.
23. Pfleiderer, S., and Moltyaner, G. L. (1993). "Use of velocity and conductivity data for the quantification of heterogeneity: A comparison." Water Resour. Res., 29(12), 4151-4156.
24. Rehfeldt, K. R., Gelhar, L. W, Southard, J. B., and Dasinger, A. M. (1989). "Estimates of macrodispersivity based on analyses of hydraulic conductivity variability at the MADE site." Electric Power Res. Inst. Rep. EPRI EN-6405, Project 2485-5, Palo Alto, Calif.
25. Ross, S. M. (1993). Introduction to probability models, 5th Ed., Academic, San Diego.
26. Rubin, Y., and Dagan, G. (1988). "Stochastic analysis of boundaries etfects on head spatial variability in heterogeneous aquifers. 1. Constant head boundary." Water Resour. Res., 24(10), 1689-1697.
27. Rubin, Y., and Dagan, G. (1989). "Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers. 2. Impervious boundary." Water Resour. Res., 25(4), 707-712.
28. Rubin, Y., and Gomez-Hernandez, J. J. (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.
29. Serrano, S. E. (1990a). "Modeling infiltration in hysteretic soils." Adv. Water Resour., 13(1), 12-23.
30. Serrano, S. E. (1990b). "Stochastic differential equation models of erratic infiltration." Water Resour. Res., 26(4), 703-711.
31. Serrano, S. E. (1995a), "Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity." Water Resour. Res., 31(11), 2733-2742.
32. Serrano, S. E. (1995b). "Forecasting scale-dependent-dispersion from spills in heterogeneous aquifers." J. Hydro., Amsterdam, 169, 151-169.
33. Stark, H., and Wood, J. W. (1986). Probability, random processes, and estimation theory for engineers. Prentice-Hall, Englewood Cliffs, N.J.
34. Sudicky, E. A. (1986). "A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process." Water Resour. Res., 22(13), 2069-2082.
35. Tompson, A. F. B. (1993). "Numerical simulation of chemical migration in physically and chemically heterogeneous porous media." Water Resour. Res., 29(11), 3709-3726.
36. Tompson, A. F. B., and Gelhar, L. W. (1990). "Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media." Water Resour. Res., 26(10), 2541-2562.
37. Van Lent, T., and Kitanidis, P. K. (1996). "Effects of first-order approximations on head and specific discharge covariances in high-contrast log conductivity." Water Resour. Res., 32(5), 1197-1207.
38. Woodbury, A. D., and Sudicky, E. A. (1991). "Geostatistical characteristics of the Borden aquifer." Water Resour. Res., 27(4), 533-546.
39. Zhang, Y.-K., and Neuman, S. P. (1990). "A quasi-linear theory of non-Fickian and Fickian subsurface dispersion. 2. Application to anistropic media and the Borden site." Water Resour. Res., 26(5), 903-914.