Flow to a heated borehole in porous, thermoelastic rock: Analysis

Exact solutions are obtained for fluid flow induced by the heating of a borehole. The rock is modeled as a fluid‐saturated, porous, thermoelastic medium. The temperature and pore pressure fields are governed by a pair of diffusion equations, which are coupled through a source term in the pressure equation proportional to the temperature rate. The pressure profile exhibits a maximum that grows in magnitude and propagates away from the borehole. For a constant heat flux applied as an instantaneous step, the fluid flux to the borehole takes a finite initial value, and decays monotonically. When the heat flux exhibits a finite rise time, the fluid flux is initially zero, rises to a maximum, and then decays. At late time, the inverse of the fluid flux is linear in ln t; this observation can be exploited to estimate the permeability and fluid diffusivity of low‐permeability rock. Sample calculations are shown for Westerly granite.