# Effective conductivity in steady well-type flows through porous formations

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## Abstract

A steady flow generated by a well of given strength takes place in a two-dimensional heterogeneous porous formation where the conductivity *K* is modeled as a random space function (RSF). As a consequence, the flow-variables become RSF s, and we wish to compute the effective conductivity (EC) by means of the self-consistent approximation. Toward this aim, the porous formation is sought as a collection of circular, non overlapping, inclusions with different (and statistically independent) conductivities. We compute the EC by adapting a procedure which was originally developed for mean uniform flows. Overall, the EC is found to be position-dependent, and therefore it can not be regarded as a medium’s property (unless one is dealing with large distances from the well). Then, it is shown how results of the present study can be used for practical applications.

## Keywords

Porous media Sink-flow Heterogeneity Stochastic modelling Self-consistent approximation Effective conductivity## Notes

### Acknowledgements

The constructive comments from three anonymous Referees were deeply appreciated, and they have significantly improved the early version of the manuscript. The author thanks Giovanna Ameno (Department of Agricultural Sciences, University of Naples - Federico II, Italy) for the valuable assistance during the literature review.

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