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 kappa F , the compressibility kappa of the closed container is given byEquationHere kappa A 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 kappa A . phi is the porosity, i.e., the volume fraction corresponding to the pore system or cavity in question. The equation contains two distinct effective compressibilities, kappa M and kappa (sub phi ) , of the material exclusive of the pore fluid. When this material is homogeneous, one has kappa M = kappa (sub phi ) , 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 kappa (sub phi ) instead of kappa M in one term. Our result is intimately related to the reciprocity theorem of elasticity. Special cases are discussed.