Solid substitution: theory versus experiment

Abstract

Gassmann fluid substitution is widely used in geophysical practice. In the last few years, the topic of fluid/solid substitution has emerged, where the substances filling the pore space can be solids, fluids, or visco-elastic materials, such as heavy oils. Solid substitution cannot be accomplished with the Gassmann theory because the finite rigidity of the pore fill (either solid or viscoelastic) prevents pressure communication throughout the pore space, which is a key assumption of the Gassmann theory. In this paper we explore applicability of solid substitution techniques by using a sandstone saturated with a solid substance, octodecane. This substance is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid form. Our approach is to measure a dry sandstone sample under different confining pressure, then saturate it with liquid Octodecane at 35°C and measure again. After that, we cool it to 20-25°C and carry out the measurement once more. The dry properties can be used to obtain parameters necessary for fluid and solid substitution. The results show that moduli of the dry sandstone exhibit significant pressure dependency, which is reduced for the solid filled rock. Also the prediction of the Gassmann theory and Ciz and Shapiro theory underestimate the velocities. This suggests that stiffening occurs due to substantial reduction of compliance of grain contacts by the solid infill. This effect is accounted for by the solid squirt theory. The results give direct evidence of the solid squirt effect and can be used to verify and calibrate theoretical solutions for rocks saturated with solid or viscoelastic substances.