Negative Unjacketed Pore Modulus in Limestones? Critical Examination of a Peculiar Laboratory Observation

Abstract

Since the groundbreaking works of Biot (1941, 1962) the description of porous, fluid-saturated rocks as poroelastic composites has been of great interest in geomechanics and related disciplines in the Earth sciences. One particular and controversial aspect of the macroscopic theory of poroelasticity is its applicability to so-called micro-inhomogeneous rocks. The latter are rocks that can be conceptualized as macroscopically homogeneous, even though they are heterogeneous at pore-scale, for example, due to the presence of different minerals constituting the rock frame. Biot and Willis (1957) provided generic recipes how to measure the poroelastic constants appearing in the Biot theory. Early attempts to measure poroelastic constants from static deformation experiments in the laboratory have been reported by Geertsma (1957). In these works, in agreement with the theory of Gassmann (1951), the number of independent poroelastic constants could be reduced by one based on the assumption that the deformation proceeds at macro-and micro-scale in a homogeneous manner. Later, Brown and Korringa (1975) showed that in micro-inhomogeneous rocks one additional poroelastic constant is needed. In fact, Brown and Korringa argued that the unjacketed pore modulus is different from the unjacketed bulk modulus in micro-inhomogeneous rocks. This difference has been examined in a modeling study by Berge and Berryman (1995). Interestingly, they found that certain micro-geometries would even give rise to a negative unjacketed pore modulus. For a single elastic continuum, bulk compressibilities are strictly positive and only so-called linear compressibility's can become negative in relatively rare materials (Cairns & Goodwin, 2015). Since, poroelasticity can be conceived as a theory of two interwoven continua (Müller & Sahay, 2019), such a restriction does not apply. This means that, in principle, a negative bulk modulus is possible.