Transport processes in porous media. 2. Numerical modeling

Abstract

The  paper proposes a numerical model for transport in heterogeneous porous media, built on the background of the continuous modeling from the first part of this work. The macroscopic behaviour of a microscopic particles ensamble is obtained by numerical simulation of their microscopic motion, in the molecular dynamics manner [Kiplik and Banavar, 1995].
The particles motion is governed by a random walk on a grid, similarly to the cellular automaton presented by Nishidate and Baba [1996]. The macroscopic description is given by space-time coarse-grained averages which provide a continuous description of the system [Vamos et al., 1996, our first paper, in this issue]. A first test was achieved by an accurate numerical soluiton of the one-dimensional diffusion equation. The number of particles and the averaging space-time scale needed  for a macroscopical description of the diffusion process with a given precision and the behaviour of systems with small concentrations are discussed in [Vamos et al., 1997b]. The model for diffusion in random environments was obtained by embededing the particles system into a random advection field. Numerical results are in good agreement with analytical ones obtained by Matheron and de Marsily [1980], using their model for statified aquifers.

Authors

C. Vamos
Tiberiu Popoviciu Institute of Numerical Analysis

N. Suciu
Tiberiu Popoviciu Institute of Numerical Analysis

U. Jaeckel
Forschungszentrum Julich GmbH, Institut fur Chemie und Dynamik der Geosphare, Deutschland

H. Vereecken
Forschungszentrum Julich GmbH, Institut fur Chemie und Dynamik der Geosphare, Deutschland

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C. Vamoş, N. Suciu, U. Jaeckel, H. Vereecken (1998), Transport processes in porous media. 2. Numerical modeling, Rom J. of Hydr. & Water Resour., 5(1-2), 85-97

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Rom. J. Hydr. & Water Resour.

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References

[1] C. W Gardiner,  1983, Handbook of Stochastic Methods (for  Physics), Chemistry and Natural Science),  Springer-Verlag, New York.
[2] J. Koplik and J. R. Banavarm, 1995,  Continuum deductions form molecular hydrodynamics,  Annu. Rev. Fluid Mech. 27, 257-292.
[3] L D. Landau and E. M. Lifchitz, 1988,  Statistical Physics (in romanian), Ed. Tehnică, București.
[4] G. Matheron and G. de Marsily, 1980,  Is Transport in porous media always diffusive?  Water Resour. Res. 16, 901-917.
[5] K. M. Nishidate and R. J. Gaylord, 1996, Cellular automaton model for random walkers,  Phys. Rev. Lett., 77 (9), 1675-78.
[6] L. Z. Rumshinski, 1974,  Mathematical Processing of Experimental Data (in romanian), Ed. Tehnică, București.
[7] H.  Schwarze, U. Jaekel and H. Vereecken, 1998,  Estimation of macrodispersion by different approximation methods for flow and transport in randomly hetergeneous media (to be published).
[8] N. Suciu, C. Vamoș, A. Georgescu, U. Jaekel and H. Vereecken, 1998, Transport processes in porous media. 1. Continuous modeling (this issue).
[9] B. F. A Tompson and L. W. Gelhar, 1990, Numerical simulation in three-dimensional randomly hetergeneous media,  Water Resour. Res. 26 (10), 2541-2562.
[10] C. Vamoș, A. Georgescu, N. Suciu and I. Turcu, 1996a, Balance equations for physical with corpuscular structure, Physica A, 227, 81-92.
[11] C. Vamoș, A. Georgescu and N. Suciu, 1996b, Balance equations for a finite number of particles,  St. Cerc. Mat., 48, 115-127.
[12] C. Vamoș, N. Suciu and A. Georgescu, 1997a, Hydrodynamic equations for one-dimensional systems of inelastic particles, Phys. Rev. E. 55, 6277-6280.
[13] C. Vamoș, N. Suciu and M. Peculea, 1997b,  Numerical modelling of the one-dimensional diffusion by random walkers, Rev. Anal. Numer. Theorie Approximation, 26 (1-2), 237-247.
[14] N. G.. van Kampen, 1981,  Stochastic Processes in Physics and Chemistry,  North-Holland, Amsterdam.

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