Effective stress for transport properties of inhomogeneous porous rock

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Abstract
General effective‐stress rules are derived for various physical properties of inhomogeneous porous rocks. Some rigorous relations arising in the analysis show that the fluid (pore) pressure pf is least effective at counteracting the changes caused by confining pressure for the solid (grain) volume; pf is more effective for the total (solid plus pore) volume; pf is still more effective for the pore volume; and pf is most effective at maintaining the fluid content of the pores. Although these results are expected intuitively, this analysis provides the first rigorous demonstration. During analysis of coefficients, care is taken to distinguish between rigorous inequalities (following from thermodynamics) and empirical inequalities (commonly observed, but not required by thermodynamics). For microscopically homogeneous rocks (the Gassmann limit), it is shown that the confining pressure is always at least as effective as the fluid pressure at changing the fluid permeability; therefore it is impossible to use any “equivalent homogeneous rock” to explain experimental results of Zoback and Byerlee (1975) and others (wherein it has been shown experimentally that the permeability sometimes is more strongly influenced by fluid pressure than confining pressure). We show that the equivalent homogeneous rock paradigm may be successfully replaced by the “two‐constituent porous medium” paradigm. In principle, the new paradigm can explain the data, but new measurements of pore compressibilities are required before quantitative comparisons can be made.