Macroscopic mechanical properties of fluid-saturated sandstone at variable temperatures

Abstract

Rocks can be viewed as composites of solid minerals with pores or cracks filled with softer material such as pore fluids, kerogen, bitumen, and other organic matter. The mechanical properties of highly viscous soft phases are highly sensitive to ambient temperatures and lead to temperature-dependent static and dynamic observations with the composite rock. However, the constituents operate by forming some effective (averaged) mechanical properties of the composite rock, and yet these averaged properties are still little known. To reveal such macroscopic temperature-dependent mechanical properties and measure their values in rock samples, a double-porosity model of porous rock with nonlinear viscosity is developed. The model is based on rigorous continuum mechanics with physically meaningful, real-valued, and time- and frequency-independent material properties and elegantly unifies the existing frequency-dependent microscopic squirt flow and mesoscopic wave-induced fluid flow models. The approach is used to accurately model the broad attenuation peaks and Young’s modulus dispersion observed in previously published laboratory experiments with glycerol-saturated Berea sandstone and invert for its mechanical properties. The observations are explained as mainly due to the temperature-dependent elastic coupling caused by non-Newtonian fluid within microcracks. Several hitherto unknown mechanical properties of the rock are constrained quantitatively: the average porosity of the microcracks, the effective high-pressure bulk modulus of the drained frame, the internal stiffness defect within the rock frame, the solid viscosities associated with bulk and shear deformations, and an exponent of nonlinearity for viscosity. These parameters constitute a Biot-consistent mechanical model of the rock, which can be used to simulate its behavior in arbitrary experimental environments. The rigorous first-principle model can be used in many applications: detailed and physically accurate interpretations of laboratory experiments, numerical wavefield simulations and seismic data inversion, reservoir characterization, geothermal exploration, thermal-enhanced oil recovery, and exploration for deep oil and gas resources in high-temperature environments.