On the Dependence of the Elastic Properties of a Porous Rock on the Compressibility of the Pore Fluid

Abstract

An equation is derived for the dependence of the elastic properties of a porous material on the compressibility of the pore fluid. More generally, the elastic properties of a container of arbitrary shape are related to the compressibility of the fluid filling a cavity in the container. If the pore system or cavity under consideration is filled with a fluid of compressibility [Formula: see text], the compressibility κ* of the closed container is given by [Formula: see text] Here [Formula: see text] is the compressibility of the container with the fluid pressure held constant in the interconnected pore system or cavity. Fluids in other pores or cavities not connected with the one in question contribute to the value of [Formula: see text]. ϕ is the porosity, i.e., the volume fraction corresponding to the pore system or cavity in question. The equation contains two distinct effective compressibilities, [Formula: see text] and [Formula: see text], of the material exclusive of the pore fluid. When this material is homogeneous, one has [Formula: see text], and the equation reduces to a well‐known relation by Gassmann. For the other elastic properties, we also obtain expressions which generalize Gassmann’s work and which also differ from it only in the appearance of [Formula: see text] instead of [Formula: see text] in one term. Our result is intimately related to the reciprocity theorem of elasticity. Special cases are discussed.

Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material

“…A short list of papers pertinent to the present study includes Biot(1941Biot( , 1956, Gassmann (1951), Biot and Willis (1957), Biot (1962), Deresiewicz and Skalak (1963), Mandl (1964), Nur and Byerlee (1971), Brown and Korringa (1975), Rice and Cleary (1976), Burridge and Keller (1981), Zimmerman et al (1986Zimmerman et al ( ,1994, Berryman and Milton (1991), Thompson and Willis (1991)], Pride et al (1992), Berryman and Wang (1995), Tuncay and Corapcioglu (1995), Alexander and Cheng (1991), Charlez, P. A., and Heugas, O. (1992), Abousleiman et al (1998), Ghassemi and Diek (2002), Tod (2003).…”

Reservoir stress path and induced seismic anisotropy: results from linking coupled fluid-flow/geomechanical simulation with seismic modelling

“…(6). Fluid substitution can also be included into this rock physics model, using either the Brown and Korringa (1975) anisotropic extension to Gassmann's equation, which is appropriate as a low-frequency end member, or incorporating the dispersive effects of squirt flow between pores (e.g., Chapman 2003). In this paper, we focus on the development of stress-induced anisotropy, assuming that the rock has no intrinsic anisotropy, and that large-scale fracture sets are not present.…”

Aligned vertical fractures, HTI reservoir symmetry and Thomsen seismic anisotropy parameters for polar media

“…See Gassmann (1951), Skempton (1954), Biot and Willis (1957), Brown andKorringa (1975), andBerryman (1999) for background. For present purposes, the main point is that B typically lies in the range 0 ≤ B ≤ 1, where B = 0 corresponds to fractures containing air but no liquids, while B = 1 corresponds to a fluid saturant with a very large bulk moduluscomparable to that of the surrounding matrix material (i.e., K f K 0 ).…”