Dynamic Moduli and Mechanical Responses of a Fluid-Saturated Cylindrical Rock Specimen Under Harmonic Vibration with Thermal Effect

Abstract The undersurface fluid saturated rock formations usually exhibit elastic moduli dispersion under field operations such as seismic survey, wellbore drilling, hydraulic fracturing, etc. Although the elastic moduli dispersion of fluid saturated rocks is regularly measured in laboratory, the mechanisms causing the dispersion are still unclear. In this work, we use the theory of porothermoelastodynamics to analytically simulate the poromechanical responses and investigate the mechanisms for the elastic moduli dispersion of a fluid-saturated cylindrical rock specimen subject to harmonic vibration with thermal effect. The theory of porothermoelastodynamics is used to derive the analytical solutions of pore pressure, displacement, and stress of a fluid-saturated cylindrical rock sample subject to harmonic vibration with thermal effect. These solutions are then used to calculate the frequency-dependent elastic moduli of the rock sample. A Ruhr sandstone is selected as an example to illustrate the solutions and the mechanisms of the dispersion due to the coupled motions of the rock matrix and fluids in pore spaces. The analytical solution is then used to match and explain laboratory measurements with thermal effect.