Eeective Stress for Transport Properties of Inhomogeneous Porous Rock

General e ective-stress rules are derived for various physical properties of inhomogeneous porous rocks. Some rigorous relations arising in the analysis show that the uid (pore) pressure pf is least e ective at counteracting the changes caused by con ning pressure for the solid (grain) volume; pf is more e ective for the total (solid plus pore) volume; pf is still more e ective for the pore volume; and pf is most e ective at maintaining the uid content of the pores. Although these results are expected intuitively, this analysis provides the rst rigorous demonstration. During analysis of coe cients, 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 con ning pressure is always at least as e ective as the uid pressure at changing the uid 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 in uenced by uid pressure than con ning 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.