Characteristic scales in the exponent of a power law, for the permeability as a function of porosity, in a two dimensional disordered porous system

Abstract:

We report numerical calculations of the permeability as a function of porosity for a two dimensional disordered porous medium. This medium is represented using the well known" Swiss Cheese" model. The fluid is modeled using a Cellular Automata algorithm. We find that the permeability, far away from the percolation threshold, decays exponentially with the number of obstacles. As a consequence of this exponential behavior, a power law dependence of the permeability as a function of the porosity is obtained, for this model system. We find that the exponent is given by the ratio between two characteristic scales. One scale is the ratio of the area of one obstacle divided by the total area of the sample, and the other scale is equal to the average number of additional obstacles necessary for the permeability to be reduced to about 0.37 of its original value. We discuss the importance of this result and compare it to other …

Año de publicación:

1997

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Fuente:

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