Conservation equations for ground-water velocity in general conditions

Journal of Hydrologic Engineering

Volumn 5, Issue 2, 2000, Pages 206-216

  Karakas, A ^a   Kavvas, M L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; GROUNDWATER FLOW; HYDRAULIC CONDUCTIVITY; MATHEMATICAL OPERATORS; POROSITY; RANDOM PROCESSES;

CONSERVATION EQUATIONS; LIE ALGEBRA;

HYDROLOGY;

CONSERVATION; FLOW VELOCITY; GROUNDWATER; MATHEMATICAL METHOD; SEEPAGE;

FLOW VELOCITY; GROUNDWATER FLOW; NUMERICAL METHOD; SEEPAGE;

EID: 0034174398     PISSN: 10840699     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)1084-0699(2000)5:2(206)     Document Type: Article

References (43)

1. Bear, J. (1972). Dynamics of Fluids in Porous Media. American Elsevier, New York.
2. Bear, J. (1979). Hydraulics of Groundwater. McGraw-Hill, New York.
3. Bear, J., and Bachmat, Y. (1984). "Transport phenomena in porous media - Basic equations." Fundamentals of transport phenomena in porous media, J. Bear and M. Y. Corapcioglu, eds., Martinus Nijhoff, Dordrecht, The Netherlands, 3-61.
4. Bear, J., and Verruijt, A. (1987). Modeling groundwater flow and pollution. Reidel, Dordrecht, The Netherlands.
5. Bellin, A., Dagan, G., and Rubin, Y. (1996). "The impact of head gradient transient on transport in heterogeneous formations: Application to the Borden Site." Water Resour. Res., 32, 2705-2713.
6. Cushman, J. H. (1991). "On diffusion of fractal porous media." Water Resour. Res., 21, 643-644.
7. Cushman, J. H., and Ginn, T. R. (1993). "On dispersion in fractal porous media." Water Resour. Res., 29, 4513-3515.
8. Dagan, G. (1982). "Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2. The solute transport." Water Resour. Res., 18, 835-848.
9. Dagan, G. (1984). "Solute transport in heterogeneous porous formations." J. Fluid Mech., Cambridge, U.K., 145, 151-177.
10. Dagan, G. (1987). "Theory of solute transport by groundwater." Ann. Rev. Fluid Mech., 19, 183-215.
11. Dagan, G., Bellin, A., and Rubin, Y. (1996). "Lagrangian analysis of transport in heterogeneous formations under transient flow conditions." Water Resour. Res., 32, 891-899.
12. Freeze, R. A. (1975). "A stochastic-conceptual analysis of one-dimensional groundwater flow in non-uniform homogeneous media." Water Resour. Res., 11, 725-741.
13. Gelhar, L. W., and Axness, C. L. (1983). "Three-dimensional stochastic analysis of macrodispersion in aquifers." Water Resour. Res., 19, 161-180.
14. Graham, W., and McLaughlin, D. (1989a). "Stochastic analysis of nonstationary subsurface solute transport, 1. Unconditional moments." Water Resour. Res., 25, 215-232.
15. Graham, W., and McLaughlin, D. (1989b). "Stochastic analysis of nonstationary subsurface solute transport, 2. Conditional moments." Water Resour. Res., 25, 2331-2355.
16. Hassanizadeh, M., and Gray, W. G. (1979). "General conservation equations for multiphase-systems, 1. Mass, momentum and energy equations." Adv. Water Resour., 2(4), 191-203.
17. Hsu, K.-L., and Neuman, S. P. (1997). "Second-order expressions for velocity moments in two and three dimensional statistically anisotropic media." Water Resour. Res., 33, 625-637.
18. Kapoor, V., and Gelhar, L. W. (1994). "Transport in three-dimensionally heterogeneous aquifers, 1. Dynamics of concentration fluctuations." Water Resour. Res., 30, 1775-1788.
19. Kavvas, M. L., and Karakas, A. (1996). "On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers." J. Hydro., Amsterdam, 179, 321-351.
20. Kitanidis, P. K. (1988). "Prediction by the method of moments of transport in a heterogeneous formation." J. Hydro., Amsterdam, 102, 453-473.
21. Kubo, R. (1962). "Generalized cumulant expansion method." J. Phys. Soc. Japan, 117, 1100-1120.
22. Neuman, S. P. (1993). "Eulerian-Langrangian theory of transport in space-time non-stationary velocity fields: Exact non-local formalism by conditional moments and weak approximation." Water Resour. Res., 29, 633-645.
23. Neuman, S. P., Winter, C. L., and Newman, C. M. (1987). "Stochastic theory of field-scale Fickian dispersion in anisotropic porous media." Water Resour. Res., 23, 453-466.
24. 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, 887-902.
25. Oelker, E. H. (1996). "Physical and chemical properties of rocks and fluids for chemical mass transport calculations." Chapter 3, Reactive transport in porous media, P. C. Lichtner, C. I. Steefel, and E. H. Oelkers, eds., Reviews in Mineralogy, Vol. 34, 131-182.
26. Rajaram, H., and Gelhar, J. W. (1993). "Plume scale-dependent dispersion in heterogeneous aquifers, 1. Lagrangian analysis in a stratified aquifer." Water Resour. Res., 29, 3249-3260.
27. Rehlfeldt, K. R., and Gelhar, L. W. (1992). "Stochastic analysis of dispersion in unsteady flow in heterogeneous aquifers." Water Resour. Res., 28, 2085-2100.
28. Rubin, Y. (1990). "Stochastic modeling of macrodispersion in heterogeneous porous media." Water Resour. Res., 26, 133-141.
29. Rubin, Y., and Dagan, G. (1988). "Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, 1. Constant head boundary." Water Resour. Res., 24, 1689-1710.
30. Serrano, S. (1988). "General solution to random advective-dispersive transport equation in porous media, 1. Stochasticity in the sources and in the boundaries." Stochastic Hydro. Hydr., 2, 79-98.
31. Serrano, S. (1992). "The form of the dispersion equation under recharge and variable velocity, and its analytical solution." Water Resour. Res., 28, 1801-1808.
32. Serrano, S. (1993). "Groundwater flow and contaminant transport in aquifers subject to large parameter uncertainty." Computational stochastic mechanics, A. H. D. Cheng and C. Y. Yang, eds., Elsevier Science, New York, 475-491.
33. Serrano, S. (1995a). "Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity." Water Resour. Res., 31, 2733-2742.
34. Serrano, S. (1995b). "Forecasting scale-dependent dispersion from spills in heterogeneous aquifers." J. Hydro., Amsterdam, 169, 151-169.
35. Serrano, S., and Unny, T. E. (1987). "Semigroup solutions to stochastic unsteady groundwater flow subject to random parameters." Stochastic Hydro. Hydr., 1, 281-296.
36. Simmons, S. (1982). "A stochastic-convective transport representation of dispersion in one-dimensional porous media systems." Water Resour. Res., 18, 1193-1214.
37. Sposito, G., and Barry, D. A. (1987). "On the Dagan model of solute transport in groundwater: Foundational aspects." Water Resour. Res., 23, 1867-1875.
38. Van Kampen, N. G. (1974). "A cumulant expansion for stochastic linear differential equations, II." Physica, 74, 239-247.
39. Van Kampen, N. G. (1976). "Stochastic differential equations." Phys. Rep., 24. 171-228.
40. Van Kampen, N. G. (1993). Stochastic processes in physics and chemistry. North-Holland, New York.
41. Winter, C. L., Newman, C. M., and Neuman, S. P. (1984). "A perturbation expansion for diffusion in a random velocity field." SIAM J. Appl. Math., 44, 411-424.
42. Woodbury, A. D., and Sudicky, E. A. (1991). "The geostatistical characteristics of the Borden Aquifer." Water Resour. Res., 27, 533-546.
43. Zhu, J. (1998). "Specific discharge covariance in a heterogeneous semi-confined aquifer." Water Resour. Res., 34, 1951-1957.