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Variations in filtration velocity due to random large-scale fluctuations of porosity

Published online by Cambridge University Press:  29 March 2006

Yu. A. Buyevich ,
A. I. Leonov  and
V. M. Safrai
Yu. A. Buyevich
Affiliation:
Institute of Mechanical Problems, USSR Academy of Sciences, Moscow
A. I. Leonov
Affiliation:
Institute of Mechanical Problems, USSR Academy of Sciences, Moscow
V. M. Safrai
Affiliation:
Institute of Mechanical Problems, USSR Academy of Sciences, Moscow
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Abstract

The local porosity of a real porous material (obtained by averaging over volumes containing a sufficiently large number of pores) is different from the mean porosity of the material as a whole. This difference is caused by large-scale defects of the porous structure and can be treated as a random function of position in the porous material. Such a random deviation of the local porosity from the average value causes random local flows superimposed upon the mean filtration flow. The characteristic scale of such motion is much larger than that of the flow of a fluid through individual pores. The phenomenon appears to play an important role in transport processes in filtration.

In this paper the statistical characteristics of the random fields under consideration are determined on the basis of the assumption that the local porosity is a random function of position with independent increments. Expressions for correlations of various quantities are obtained in terms of the characteristics of porosity fluctuations and the effective coefficients of diffusion caused by the random motions under study are estimated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 2 , 23 June 1969 , pp. 371 - 381
Copyright
© 1969 Cambridge University Press

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