Brown and Korringa extended Gassmann’s equations for fluid substitution in rocks to allow for arbitrarily mixed mineralogy. This extension was accomplished by adding just one additional constant—replacing the mineral bulk modulus with two less intuitive constants. Even though virtually all rocks have mixed mineralogy, the Brown and Korringa equations are seldom used because values for the constants are unknown. We estimate plausible values for the Brown-Korringa constants, based on effective medium models. The self-consistent formulation is used to describe a rock whose mineral and pore phases are randomly distributed ellipsoids—a plausible representation of randomly mixed mineral grains, as with dispersed clay in sandstone. Using the self-consistent model, the two constants are predicted to be nearly identical, justifying the use of an average mineral modulus in Gassmann’s equations. For small contrasts in mineral stiffness, the Brown-Korringa constants are approximately equal to the Voigt-Reuss-Hill average of the individual mineral bulk moduli. In a second approach, a multilayered spherical shell model is used to describe a rock where a particular solid phase preferentially coats grains or lines pores. In this case, the constants can differ substantially from each other, demonstrating the need for the Brown-Korringa equation. A third model represents weak pore-lining or pore-filling clay within an arbitrary pore geometry. The clay-fluid mix can be replaced exactly with an average fluid or “mud.” When the nonclay minerals have similar moduli, then the replacement of the clay-fluid mix causes the Brown-Korringa equation to revert to Gassmann’s equation.
A Self-Consistent Formulation of Local Field Theory. I
