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Porous Media Primer for Physicists

  • Chapter
Percolation Theory for Flow in Porous Media

Part of the book series: Lecture Notes in Physics ((LNP,volume 880))

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Abstract

This chapter provides an introduction to concepts and fundamental relationships of pore-scale phenomena in such a way that is hoped to reduce uncertainty in understanding of porous media for a typically trained physicist without a background in the particular subject. The first topic is how and why percolation theory should be considered. Then, certain pitfalls of conventional interpretations are described. In particular we examine in detail the (casually) presumed mapping between pressure-saturation curves and the pore-size distribution, and find that complications due to finite column size, flow rates (equilibrium), and the phase connectivity described in terms of the accessibility function from percolation theory make such assumptions unjustifiable. Finally various treatments of porous media are discussed, such as capillary bundle, network, and fractal models. The serious problems associated with reliance on capillary bundle models are listed and corrections are referred to later chapters.

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Authors and Affiliations

  1. Department of Earth and Environmental Sciences, Wright State University, Dayton, OH, USA

    Allen Hunt

  2. Department of Agronomy, Iowa State University, Ames, IA, USA

    Robert Ewing

  3. Department of Earth and Environmental Sciences, Wright State University, Dayton, OH, USA

    Behzad Ghanbarian

Authors
  1. Allen Hunt
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  2. Robert Ewing
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Problems

Problems

  1. 3.1

    Remember that pumice (specific gravity of the solid portion typically ca. 2.65) may float on water. Does this mean that the holes in pumice cannot be connected? Use the Scher and Zallen results (Chap. 1) to set an upper limit on the porosity of a regular pumice, for which all the “holes” are the same size. Assume that the holes are spherical. What lattice would you choose for this calculation?

  2. 3.2

    Assuming a solid material density of 2.65, calculate the minimum porosity required for the condition that pumice float. Is the Scher and Zallen result useful as a predictor? In a fractal model the porosity of a medium may approach 1. Do you expect that the holes in pumice (due to gas bubbles) are of uniform size, or highly variable?

  3. 3.3

    If the holes in pumice are due to gas bubbles, did the gas escape? How? Can the relevant porosities for these questions be the porosity not accessible to an infinite cluster instead of the bulk porosity?

  4. 3.4

    Suppose that the pumice was formed in a violent explosion that resulted when the gas bubbles “percolated.” What sort of size distribution of pieces of pumice would you expect to find?

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Hunt, A., Ewing, R., Ghanbarian, B. (2014). Porous Media Primer for Physicists. In: Percolation Theory for Flow in Porous Media. Lecture Notes in Physics, vol 880. Springer, Cham. https://doi.org/10.1007/978-3-319-03771-4_3

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