Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Stochastic Hydrology and Hydraulics

Volumn 12, Issue 2, 1998, Pages 117-140

  Zhang, You Kuan ^a   Lin, Jie ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345169498     PISSN: 09311955     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004770050013     Document Type: Article

References (46)

1. Ababou R, McLaughlin D, Gelhar LW, Tompson AFB (1989) Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media. Transp. Porous Media, 4, 549-565
2. Anderson MP, Woessner WW (1992) Applied Groundwater Modeling. Academic Press, San Diego, p. 381
3. Bellin A, Salandin P, Rinaldo A (1992) Simulation of dispersion in heterogeneous porous formations: statistics, first-order theories, convergence of computations. Water Resour. Res., 28(9), 2211-2227
4. Barry DA, Coves J, Sposito G (1988) On the Dagan model of solute transport in groundwater application to the Borden site. Water Resour. Res., 24(10), 1805-1817
5. Burr DT, Sudicky EA, Naff RL (1994L) Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: Mean displacement, plume spreading, and uncertainty. Water Resour. Res., 30(3), 791-815
6. Chin DA, 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
7. Cushman JH (Ed.) (1990) Dynamics of Fluids in Hierarchical Porous Media. Academic, San Diego, Calif.
8. Cushman JH, Hu BX, Ginn TR (1994) Nonequilibrium statistical mechanics of preasymptotic dispersion. J. Stat. Phys., 75, 859-878
9. Dagan G (1982) Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 2. The solute transport. Water Resour. Res., 18(4), 835-848
10. Dagan G (1984) Solute transport in heterogeneous porous formations. J. Fluid Mech., 145, 151-177
11. Dagan G (1987) Theory of solute transport by groundwater. Ann. Rev. Fluid Mech., 19, 183-215
12. Dagan G (1988) Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers. Water Resour. Res., 24(9), 1491-1500
13. Dagan G (1989) Flow and Transport in Porous Formations. Springer-Verlag. Berlin Heidelberg, Germany
14. Dagan G (1990) Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion. Water Resour. Res., 26(6), 1281-1290
15. Dagan G (1991) Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations. J. Fluid Mech., 233, 197-210
16. Dagan G (1994) An exact nonlinear correction to transverse macrodispersivity for transport in heterogeneous formations. Water Resour. Res., 30(10), 2699-2705
17. Dagan G (1995) Comment on "Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: Mean displacement, plume spreading, and uncertainty" by T.D. Burr, E.A. Sudicky, and R.L. Naff. Water Resour. Res., 31(5), 1439-1441
18. Garabedian SP, LeBlanc DR, Gelhar LW, Celia, MA (1991) Large-scale natural gradient tracer test in sand and gravel, Cape Code, Massachusetts, 2. Analysis of spatial moments for a nonreactive tracer. Water Resour. Res., 27(5), 911-924
19. Gelhar LW, Axness CL (1983) Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res., 19(1), 161-180
20. Gelhar LW (1993) Stochastic Subsurface Hydrology. Prentice-Hall. Englewood Cliffs, New Jersery
21. Hristopulos DT, Christakos G (1997) Variational calculation of the effective fluid permeability of heterogeneous media, Phy. Rev. E, 55(6), 7288-7298
22. Hsu K-C, Zhang D, Neuman SP (1996) Higher-order effects on flow and transport in randomly heterogeneous porous media. Water Resour. Res., 32(3), 571-582
23. Jaekel U, Vereecken H (1997) Renormalization group analysis of macrodispersion in a directed random flow. Water Resour. Res., 33(10), 2287-2299
24. Killey RWD, Moltyaner GL (1988) Twin lake tracer tests: Setting methodology, and hydraulic conductivity distribution. Water Resour. Res., 24(10), 1585-1612
25. Kitanidis PK (1988) Prediction by the method of moments of transport in a heterogeneous formation. Jour. Hydrology, 102(1-4), 453-473
26. Kitanidis PK (1994) The concept of the dilution index. Water Resour. Res., 30(7), 2011-2026
27. Mackay DM, Freyberg DL, Roberts PV, Cherry JA (1986) A natural gradient experiment in a sand aquifer, 1. Approach and overview of plume movement. Water Resour. Res., 22, 2017-2030
28. Neuman SP, Winter CL, Newman CM (1987) Stochastic theory of field-scale Fickian dispersion in anisotropic porous media. Water Resour. Res., 23, 453-466
29. Neuman SP, 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
30. Pollock DW (1994) User's guide for MODPATH/MODPATH-PLOT, Verson 3: A particle tracking post-processing package for MODFLOW. The U.S. Geological Survey finite-difference ground-water flow model, U.S. Geological Survey. Open-File Report 94-464
31. Quinodoz HAM, Valocchi J (1990) Macrodispersion in heterogeneous aquifers: Numerical experiments. In: Moltyaner, G. (ed.) International conference and workshop on transport and mass exchange processes in sand and gravel aquifers: field and modeling studies. AGU, Ottawa, Ont., Canada
32. Robin MJL, Gutjahr AL, Sudicky EA, Wilson JL (1993) Cross-correlated random field generator with direct Fourier transform method. Water Resour. Res., 29(7), 2385-2397
33. Rubin Y, Dagan G (1988) Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, 1. Constant head boundary. Water Resour. Res., 24(10), 1689-1697
34. Rubin Y, Dagan G (1989) Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, 2. Impervious boundaries. Water Resour. Res., 25(4), 707-712
35. Rubin Y (1990) Stochastic modeling of macrodispersion in heterogeneous porous media. Water Resour. Res., 26(1), 133-141
36. Salandin P, Rinaldo A, Dagan G (1991) A note on transport in stratified formations by flow tilted with respect to the bedding. Water Resour. Res., 27(11), 3009-3017
37. Salandin P, Fiorotto V (1993) Numerical simulations of non-ergodic transport in natural formations. Proc. XXV IAHR, Tokyo, 55-62
38. Selroos J-O (1995) Temporal moments for nonergodic solute transport in heterogeneous aquifers. Water Resour. Res., 31(7), 1705-1712
39. Sudicky EA, Naff RL (1995) Reply. Water Resour. Res., 31(5), 1443-1444
40. Tompson AFB, Gelhar L W (1990) Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media. Water Resour. Res., 25(10), 2541-2562
41. Zhang Y-K, Chi JA (1995) An evaluation of nonlinearity in spatial second moments of ensemble mean concentration in heterogeneous porous media. Water Resour. Res., 31(12), 2991-3005
42. Zhang D, Neuman SP (1995) Eulerian-Lagrangian analysis of transport conditioned on hydraulic data, 3. Spatial moments, travel time distribution, mass flow rate, and cumulative release across a compliance surface. Water Resour. Res., 31(1), 65-75
43. Zhang Q (1995) Transient behavior of mixing induced by a random velocity field. Water Resour. Res., 31(3), 577-591
44. Zhang Y-K, Neuman SP (1990) A quasi-linear theory of non-Fickian and Fickian subsurface dispersion, 2, Application to anisotropic media and the Borden site. Water Resour. Res., 26(5), 903-914
45. Zhang Y-K, Zhang D, Lin J (1996) Non-ergodic solute transport in three-dimensional heterogeneous isotropic aquifers. Water Resour. Res., 32(9), 2955-2963
46. Zhang Y-K, Zhang D (1997) Time-dependent dispersion of non-ergodic plumes in two-dimensional heterogeneous porous media. Journal of Hydrologie Engineering, 2(2), 91-94