On the ergodicity hypothesis in heterogeneous formations

Mathematical Geology

Volumn 31, Issue 1, 1999, Pages 113-134

  Zhan, Hongbin ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Ensemble average; Hydraulic conductivity; Spatial average; Stochastic

Indexed keywords

GROUNDWATER; HYDRAULIC CONDUCTIVITY; MATHEMATICAL METHOD;

EID: 0033008834     PISSN: 08828121     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007549532023     Document Type: Article

References (21)

1. Arfken, G. B., and Weber, H. J., 1995, Mathematical methods for physicists, 4th Ed.: Academic Press, San Diego, 1029 p.
2. Christakos, G., Hristopulos, D. T., and Miller, C. T., 1995, Stochastic diagrammatic analysis of groundwater flow in heterogeneous porous media: Water Resources Res., v. 31, no. 7, p. 1687-1703.
3. Cressie, N., 1993, Statistics for spatial data, revised Ed.: Wiley, New York, 900 p.
4. Dagan, G., 1982, Stochastic modeling of groundwater flow by unconditional and conditional probabilities 1. conditional simulation and the direct problem: Water Resources Res., v. 18, no. 4, p. 813-833.
5. Dagan, G., 1989, Flow and transport in porous formations: Springer-Verlag, Berlin, 465 p.
6. Dagan, G., 1990, Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion: Water Resources Res., v. 26, no. 6, p. 1281-1290.
7. Dagan, G., 1991, Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations: Jour. Fluid Mech., v. 233, p. 197-210.
8. Follin, S., and Thunvik, R., 1994, On the use of continuum approximations for regional modeling of groundwater flow through crystalline rocks: Advances in Water Resources, v. 17, p. 133-145.
9. Gelhar, L. W., 1993, Stochastic subsurface hydrology: Prentice Hall, Englewood Cliffs, 390 p.
10. Grimmett, G. R., and Stirzaker, D. R., 1992, Probability and random processes, 2nd Ed.: Clarendon Press, Oxford, 541 p.
11. 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 Resources Res., v. 14, no. 5, p. 953-959.
12. Neuman, S. P., Winter, C. L., and Newman, C. M., 1987, Stochastic theory of field scale dispersion in anisotropic porous media: Water Resources Res., v. 23, no. 3, p. 453-466.
13. Rajaram, H., and Gelhar, L. W., 1993, Plume scale-dependent dispersion in heterogeneous aquifers, 2. Eulerian analysis and three-dimensional aquifers: Water Resources Res., v. 29, no. 9, p. 3261-3276.
14. Ross, S. M., 1993, Introduction to probability models, 5th Ed.: Academic Press, San Diego, 556 p.
15. Salandin, P., Rinaldo, A., and Dagan, G., 1991, A note on transport in stratified formations by flow tilted with respect to the bedding: Water Resources Res., v. 27, no. 11, p. 3009-3017.
16. Serrano, S. E., 1990, Stochastic differential equation models of erratic infiltration: Water Resources Res., v. 26, no. 4, p. 703-711.
17. Serrano, S. E., 1995, Forecasting scale-dependent dispersion from spills in heterogeneous aquifers: Jour. Hydrology, v. 169, p. 151-169.
18. Serrano, S. E., 1998, Analytical decomposition of the nonlinear unsaturated flow equation: Water Resources Res, v. 34, no. 3, p. 397-407.
19. Stark, H., and Wood, J. W., 1986, Probability, random processes, and estimation theory for engineers: Prentice-Hall, Englewood Cliffs, NJ, 430 p.
20. Tompkins, J. A., Gan, K. C., Wheater, H. S., and Hirano, F., 1994, Prediction of solute dispersion in heterogeneous porous media: effects of ergodicity and hydraulic condcutivity discretisation: Jour. Hydrology, v. 159, p. 105-123.
21. Tompson, A. F. B., and Gelhar, L. W., 1990, Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media: Water Resources Res., v. 26, no. 10, p. 2541-2562.