Access by Xinjiang University

Hydrodynamic dispersion in a hierarchical network with a power-law distribution of conductances

Oil and Gas Program, PUC-Rio, Rua Marquês de São Vicente, 225 - Gávea 22453-900, Rio de Janeiro - RJ - Brazil

Phys. Rev. E 71, 036304 – Published 17 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036304

Abstract

Dispersion is studied on a two-dimensional hierarchical pore network with a power-law distribution of conductances, i.e., $P (g) \sim g^{μ - 1}$ , with $g ∊ (0, 1)$ , and $μ$ is the disorderliness parameter $(μ > 0)$ . A procedure for computing tracer dispersion transport on hierarchical networks was developed. The results show that the effective diffusion coefficient of the network scales similarly as conduction on the same lattice. This means that the disorder length scales for conduction and diffusion processes are the same, and can be predicted from percolation theory. The dispersivity, $ξ \equiv D_{‖} ∕ U$ , was found to diverge rapidly as $μ \to 0$ . The result is in agreement with the model developed by Bouchaud and Georges (C.R. Acad. Sci. (Paris) 307 1431, 1988). A limiting value of $μ \approx 0.45$ was found, below which the convection-dispersion equation is no longer valid.

Article Text

References (23)

B. Zemel, Tracers in the Oil Field (Elsevier, Amsterdam, 1995).
G. Dagan, Flow and Transport in Porous Formations (Springer-Verlag, New York, 1989).
J. H. Cushman, Dynamics of Fluids in Hierarchical Porous Media (Academic, New York, 1992).
J. Bear, Dynamics of Fluids in Porous Media (Elsevier, New York, 1972).
D. Zhan, Stochastic Methods for Flow in Porous Media: Coping with Uncertainty (Academic, San Diego, 2002).
J. Honerkamp, Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis (VCH, New York, 1994).
D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1991).
S. P. Neuman, Water Resour. Res.31, 1455 (1995).
M. Giona, W. A. Schwalm, M. K. Schwalm, and A. Adrover, Chem. Eng. Sci. 51, 4717 (1996).
R. Angulo and E. Medina, J. Stat. Phys. 75, 735 (1994).
Ricardo Paredes and V. Alvarado, Phys. Rev. E 58, 771 (1998).
M. Giona, W. A. Schwalm, M. K. Schwalm, and A. Adrover, Chem. Eng. Sci. 51, 4731 (1996).
S. Roux, C. Mitescu, E. Charlaix, and C. Baudet, J. Phys. II 19, L687 (1992).
M. O. Cáceres, Phys. Rev. E 69, 036302 (2004).
J. Adler, A. Aharony, R. Blumenfeld, A. B. Harris, and Y. Meir, Phys. Rev. B 47, 5770 (1993).
E. Villermaux and D. Schweich, J. Phys. II 2, 1023 (1992).
J. Koplik, S. Redner, and D. Wilkinson, Phys. Rev. A 37, 2619 (1988).
S. Redner, J. Koplik, and D. Wilkinson, J. Phys. A 20, 1543 (1987).
L. de Arcangelis, J. Koplik, S. Redner, and D. Wilkinson, Phys. Rev. Lett. 57, 996 (1986).
J. C. Bacri, J. P. Bouchaud, A. Georges, E. Guyon, J. P. Hulin, N. Rakotomalala, and D. Salin, in Hydrodynamics of Dispersed Media, edited by J. P. Hulin, A. M. Cazabat, F. Carmona, and E. Guyon (North-Holland, Amsterdam, 1990).
J. P. Bouchaud and A. Georges, C. R. Acad. Sci., Ser. II, 307, 1431 (1988).
J. P. Bouchaud and A. Georges, Phys. Rep. 4–5, 127 (1990).
E. Duering and D. J. B. R. Blumenfeld, J. Stat. Phys. 67, 133 (1992).

Physical Review E

Export citation

Export citation

Hydrodynamic dispersion in a hierarchical network with a power-law distribution of conductances

Abstract

Article Text

References (23)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation