Conductive heat flow and thermally induced fluid flow around a well bore in a poroelastic medium

Abstract

Transient analytical solutions for temperature and pore pressure changes near a circular borehole under instantaneous temperature and fluid pressure changes inside the borehole are presented. The solutions couple conductive heat transfer with Darcy fluid flow, and a borehole under a nonhydrostatic far‐field stress state is simulated. The heat conduction equation is decoupled from the coupled system of isothermal governing equations, and the complete solution is obtained by superimposing this decoupled solution on the isothermal one. The solution is therefore applicable to low‐permeability media, where heat transfer is dominated by conduction only. Both cold and warm injection processes are studied, and the applications to hydraulic fracture initiation and thermally induced fluid flow are discussed. Taking Westerly granite as an example, it is concluded that the maximum thermally induced pore pressure inside the rock formation can be 30% higher than the isothermal pore pressure, with a borehole temperature and fluid pressure change ratio (Δ T /Δ p ) = 1°C/MPa. It is emphasized that the thermally induced pore pressure change can be significant inside a low‐permeability porous medium, and a coupled solution must be obtained to address the mechanical, hydraulic, and thermal responses appropriately.