Statistical Approach to Flow through Porous Media

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Abstract
Some of the problems are discussed which arise in the application to flow in porous media of the Bearman‐Kirkwood theory of transport in fluids. The outstanding feature of porous media is their lack of isotropy on the microscale. The Bearman‐Kirkwood analysis is reconsidered for anisotropic systems. The effect of the anisotropic pair‐correlation function on the momentum balance equation is considered. Modifications to the nonequilibrium perturbation of the pair‐correlation function are considered which lead to tensorial transport coefficients. The averages for the statistically isotropic porous medium which lead to Darcy's law are developed. Some additional problems are considered such as appropriate macroaverages for thermodynamic quantities. The theory rests on an assumed form for the nonequilibrium distribution function. This form awaits theoretical justification.

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