Effect of non-Fourier heat transfer on the thermoporoelastic response of a borehole

Abstract

In the framework of classical thermoporoelasticity, heat conduction is generally assumed to follow Fourier’s law, resulting in an infinite speed of heat propagation. Recent laboratory experiments on porous rocks revealed a significant time delay between the heat flux and the temperature gradient. To address this observation, I have formulated a modified thermoporoelasticity model by integrating hyperbolic heat conduction theory and accounting for the time of thermal relaxation. This non-Fourier thermoporoelasticity model is then applied to analyze a wellbore exposed to cooling fluid and non-hydrostatic in situ stresses. I utilize the Laplace transform and load decomposition approaches concurrently to derive solutions in the Laplace domain. The Stehfest inversion algorithm is employed to convert these solutions into the time domain. Our numerical findings demonstrate that during early stages, non-Fourier heat conduction notably impacts temperature, pore pressure, and stresses, particularly in the immediate vicinity of the borehole.