Reactive transport and immiscible flow in geological media. I. General theory

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1945, 1996, Pages 285-301

  Dagan, G ^a,b   Cvetkovic, V ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

GEOLOGY; IMMISCIBLE FLUIDS; REACTIVE; TRANSPORT;

EID: 0029676573     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0016     Document Type: Article

References (30)

1. Bellin, A., Rinaldo, A., Bosma, W. J. P., Van der Zee, S. E. A. T. M. &: Rubin, Y. 1993 Linear equilibrium adsorbing solute transport in chemically and physically heterogeneous porous formations 1. Analytical solutions. Wat. Resour. Res. 29, 4019-4030.
2. Chrysikopoulos, V. D., Kitanidis, P. K. & Roberts, P. V. 1992 Macrodispersion of sorbing solutes in heterogeneous porous formations with spatially periodic retardation factor and velocity field. Wat. Resour. Res. 28, 1517-1530.
3. Cvetkovic, V. & Shapiro, A. M. 1990 Mass arrival of sorptive solute in heterogeneous porous media. Wat. Resour. Res. 26, 2057-2067.
4. Cvetkovic, V., Shapiro A. M. & Dagan, G. 1992 A solute-flux approach to transport in heterogeneous formations 2. Uncertainty analysis. Wat. Resour. Res. 28, 1377-1388.
5. Cvetkovic, V. & Dagan, G. 1994 Transport of kinetically sorbing solute by steady random velocity in heterogeneous porous formations. J. Fluid Mech. 265, 189-215.
6. Cvetkovic, V. & Dagan, G. 1996 Reactive transport and immiscible flow in geological media. II. Applications. Proc. R. Soc. Lond. A 452, 303-328. (Following paper.)
7. Dagan, G. 1984 Solute transport in heterogeneous porous formations. J. Fluid Mech. 145, 151-177.
8. Dagan, G. 1987 Theory of solute transport by groundwater. A. Rev. Fluid Mech. 19, 183-215.
9. Dagan, G. 1989 Flow and transport in porous formations. Berlin: Springer.
10. 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.
11. Dagan, G., Cvetkovic, V. & Shapiro, A. 1992 A solute-flux approach to transport in heterogeneous formations 1. The general framework. Wat. Resour. Res. 28, 1369-1376.
12. Dagan, G. & Cvetkovic, V. 1993 Spatial moments of a kinetically sorbing solute plume in a heterogeneous aquifer. Wat. Resour. Res. 29, 4053-4061.
13. Dake, L. P. 1986 Fundamentals of reservoir engineering. New York: Elsevier.
14. Destouni, G. & Cvetkovic, V. 1991 Field scale mass arrival of sorptive solute into the ground-water. Wat. Resour. Res. 27, 1315-1325.
15. van Duijn, C. J. & Knabner, P. 1991 Solute transport in porous media with equilibrium and non-equilibrium multiple-site adsorption: travelling waves. J. Reine Angewandte Math. 415, 1-49.
16. Freeze, R. A. 1975 A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media. Wat. Resour. Res. 11, 725-741.
17. Goldstein, S. 1953 On the mathematics of exchange processes in fixed columns. Proc. R. Soc. Land. A 219, 151-185.
18. Grundy, R. E., Van Duijn, C. J. & Dawson, C. N. 1994 Asymptotic profiles with finite mass in one-dimensional contaminant transport through porous media: the fast reaction case. Mech. Appl. Math. 47, 69-106.
19. Kabala, Z. J. & Sposito, G. 1991 A stochastic model of reactive solute transport with timevarying velocity in a heterogeneous aquifer. Wat. Resour. Res. 27, 341-350.
20. Kreft, A. & Zuber, A. 1978 On the physical meaning of the dispersion equation and its solution for different initial and boundary conditions. Chem. Engng Sci. 33, 1471-1480.
21. Le Fur, B. 1962 Influence de la capilarité et de la gravité sur le déplacement non miscible unidimensionnel dans un milieu poreux. J. Mec. J, 213-232.
22. Lichtner, P. C. 1985 Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems. Geochim. Cosmochim. Acta 49, 779-800.
23. Lichtner, P. C. 1988 The quasi-stationary state approximation to coupled mass transport and fluid-rock interaction in a porous medium. Geochim. Cosmochim. Acta 52, 143-165.
24. Quinodoz, H. A. M. & Valocchi, A. J. 1993 Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity. Wat. Resour. Res. 29, 3227-3290.
25. Rubin, J. 1983 Transport of reacting solutes in porous media: relation between mathematical nature of problem formulation and chemical nature of reactions. Wat. Resour. Res. 19, 1231-1252.
26. Rubin, Y. 1990 Stochastic modeling of macrodispersion in heterogeneous porous media. Wat. Resour. Res. 26, 133-141.
27. Rubin, Y. 1991 Prediction of tracer plume migration in disordered porous media by the method of conditional probabilities. Wat. Resour. Res. 27, 1291-1308.
28. Selroos, J. O. & Cvetkovic, V. 1994 Mass flux statistics of kinetically sorbing solute in heterogeneous aquifers: analytical solution and comparison with simulations. Wat. Resour. Res. 30, 63-69.
29. Shapiro, A. M. & Cvetkovic, V. 1988 Stochastic analysis of solute arrival time in heterogeneous porous media. Wat. Resour. Res. 24, 1711-1718.
30. Weber, W. J., McGinley, P. M. & Katz, L. E. 1991 Sorption phenomena in subsurface systems: concepts, models and effects on contaminant fate and transport. Wat. Resour. Res. 25, 499-528.