A practical solution to the mechanical perturbations induced by non-isothermal injection into a permeable medium

- Non-isothermal injection into cylindrical reservoir is considered.
- We propose an easy-to-use analytical solution to the heat transport in radial flow.
- The solution is applied to analytical expressions for thermoelasticity.
- The validity is corroborated by comparison with numerical simulations.
- Poroelastic and thermoelastic response are compared.

Non-isothermal fluid injection into a geological formation causes alterations of the pressure and temperature fields, which affect the mechanical stability of the reservoir. This coupled thermo-hydro-mechanical behavior has become a matter of special interest because of public concern about induced seismicity. The response is complex and its evaluation often requires numerical modeling. Nevertheless, analytical solutions are useful in improving our understanding of interactions, identifying the controlling parameters, testing codes and in providing a rapid assessment of the system response to an alteration. We present analytical expressions for hydraulic and thermal driven displacements and stresses for unidirectional and radial geometries. To obtain them, an easy-to-use solution to the transient advection-conduction heat transfer problem is developed, whereas the fluid flow is assumed at steady-state. The validity is verified by comparison with numerical simulations and yields fairly accurate results. The solution is then used to illustrate some features of the poroelastic and thermoelastic response and, in particular, the sensitivity of stresses to the outer mechanical boundary conditions.