Abstract of the paper ``Effective stress for transport properties of inhomogeneous porous rock''
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 p_f is least
effective at counteracting the changes caused by confining pressure for the
solid (grain) volume; p_f is more effective for the total (solid plus pore)
volume; p_f is still more effective for the pore volume;
and p_f 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.
Return to preceding page and click on title if you want
a postscript copy of this paper downloaded to your machine.