Comparison of the low-frequency predicitons of Biot’s and de Boer’s poroelasticity theories with Gassmann’s equation

Abstract

Predictions of Biot’s theory (BT) of poroelasticity [J. Acoust. Soc. Am. 28, 168 (1956)] and de Boer’s theory of porous media (TPM) [Theory of Porous Media (Springer, Berlin, 2000)] for the low-frequency bulk modulus of a fluid-saturated porous medium are compared with the Gassmann equation [Vierteljahrsschr. Naturforsch. Ges. Zur. 96, 1 (1951)]. It is shown that BT is consistent with the Gassmann equation, whereas TPM is not. It is further shown that the bulk modulus of a suspension of solid particles in a fluid as predicted by TPM is only correct if the particles are incompressible.