Diffusion of fluids in porous media with memory

Geothermics

Volumn 28, Issue 1, 1999, Pages 113-130

  Caputo, Michele ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Darcy's law; Diffusion; Memory; Porous media

Indexed keywords

DIFFUSION IN SOLIDS; MECHANICAL PERMEABILITY; NUMERICAL METHODS; POROUS MATERIALS; PRESSURE DISTRIBUTION;

DARCY'S LAW;

GEOTHERMAL FIELDS;

DIFFUSION; GEOTHERMAL SYSTEM; POROUS MEDIUM;

EID: 0033083753     PISSN: 03756505     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-6505(98)00047-9     Document Type: Article

References (31)

1. Bell, M.L., Nur, A., 1978. Strength changes due to reservoir-induced pore pressure and stressesandapplication to Lake Oroville. Journal of Geophysical Research 83, 4469-4483.
2. Biot, M.A., 1941. General theory of three dimensional consolidation. Journal of Applied Physics12,155-164.
3. Biot, M.A., 1956. General solutions of the equations of elasticity and consolidation for aporousmaterial. Journal of Applied Mechanics 78, 91-96.
4. Biot, M.A., 1956. Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics27,240-253.
5. Biot, M.A., 1973. Non linear and semilinear rheology of porous solids. Journal ofGeophysicalResearch 78, 4924-4937.
6. Biot, M.A., Willis, D.G., 1957. The elastic coefficients of the theory of consolidation. JournalofApplied Mechanics 24, 594-601.
7. Boley, B.A., Tolins, I.S., 1962. Transient coupled thermoelastic boundary value problem in thehalfspace. Journal of Applied Mechanics 29, 637-646.
8. Bolt, G.H., Groenevelt, P.H., 1969. Coupling phenomena as a possible cause of non-Darcybehaviorof water in soil. In: Bulletin of the International Association Scientific Hydrology 2, Vol.14, pp.17-26.
9. Boltzman, L., 1894. Zur Integration der Diffusiongleichung bei variabeln Diffusion Koeffizienten.InAnnalen der Physik, Vol. 53, pp. 959-964. Leipzig.
10. Booker, J.R., 1974. Time dependent strain following faulting of a porous medium. JournalofGeophysical Research 79, 2037-2044.
11. Caputo, M., 1969. Elasticità e dissipazione (Elasticity andanelasticdissipation), pp. 150. Zanichelli Publisher, Bologna.
12. Caputo, M., 1976. Vibrations of an infinite plate with frequency independent Q. Journal oftheAcoustical Society of America 60, 634-639.
13. Caputo, M., 1995. Mean fractional-order-derivatives, differential equations and filters. In:AnnaliUniversità di Ferrara, Mathematical Sciences, Vol. 41, pp.73-84.
14. Hu, X., Cushman, H., 1994. Non equilibrium statistical mechanical derivation of a nonlocalDarcyslaw for unsaturated/saturated flow. Stochastic Hydrology and Hydraulics 8, 109-116.
15. Kutilek, H.M., 1969. Non-Darcian flow of water in soils (laminar region). In: 1stInternationalAssociation Hydrological Research Symposium, Fundamentals of Transport Phenomenain PorousMedia, pp. 79-88. Haifa, Israel.
16. Mainardi, F., 1993. Fractional diffusive waves in viscoelastic solids. Applied Mechanics Review46(549), 93-97.
17. Mainardi, F., 1996. Fractional relaxation-oscillation and fractional diffusion-wavephenomena.Chaos, Solitons and Fractals 7, 1-17.
18. McNamee, J., Gibson, R.E., 1960. Displacement functions and linear transforms applied todiffusionthrough porous elastic media. Quarterly Journal of Mechanics Applied to Mathematics 13,99-111.
19. Mulargia, F., Bonafede, M., Boschi, E., 1980. Experimental study of fracture at geologicalscale.Geophysical Journal of the Royal Astronomical Society 60, 321-325.
20. Nowacki, W., 1964. Green function for a thermoelastic medium 2. In: Bulletin of the AcademyofPolish Science, Series Science Mathematics, Astronomy, Physics, Vol. 12, pp. 465-472.
21. Palciauskas, V.V., Domenico, P.A., 1982. Characterisation of drained and undrained responseofthermally loaded repository rocks. Water Resources Research 18, 281-290.
22. Rice, J.R., Cleary, M.P., 1976. Some basic stress-diffusion solutions for fluid-saturatedelasticporous media with compressible constituents. Review of Geophysics and Space Physics14,227-241.
23. Robinson, W.T., 1939. Earth tide shown by fluctuations of water-levels in wells in New MexicoandIowa. Transactions American Geophysical Union 20, 656-666.
24. Roeloffs, E.A., 1988. Fault stability changes induced beneath a reservoir with cyclic variationsinwater level. Journal of Geophysical Research 93, 2107-2124.
25. Schneider, W.R., Wyss, W., 1989. Fractional diffusion and wave equations. Journal ofMathematicalPhysics 30, 134-144.
26. Swartzendruber, D., 1962. Non-Darcy flow behaviour in liquid saturated porous media. JournalofGeophysical Research 13, 5205-5213.
27. Talwani, P., Acree, S., 1985. Pore pressure diffusion and the mechanism ofreservoir-inducedseismicity. Pure and Applied Geophysics 122, 953-965.
28. Terzaghi, K., 1923. Die Berechnung der DurchlässigkeitszifferdesTones aus dem Verlauf der Hydrodynamischen Spannungserscheinungen. SitzungsberichtAkademieWissentschafliche, Mathematik-Naturwissenschaft, Wien, Kl., Abt. 2A, pp. 132, 105.
29. Terzaghi, K., 1936. The shearing resistance of saturated soils. In: ProceedingsInternationalConference on Soil Mechanics Foundation Engineering, Vol. 1, pp. 54-55.
30. Thomas, L.K., Katz, D.L., Tek, M.R., 1968. Threshold pressure phenomena in porous media.Journalof the Society of Petroleum Engineers 2, 174-184.
31. Wyss, W., 1986. Fractional diffusion equation. Journal of Mathematical Physics 27, 2782-2785.