A simplified solution to predict surface uplift induced by a point non-isothermal well leakage

In many geological, geothermal, and hydrocarbon engineering operations, fluids are typically injected at a temperature different from that of the surrounding subsurface formation. The pressurization resulting from injection induces mechanical expansion of the porous medium. Moreover, injected fluids may be colder or hotter than the surrounding formation, thereby generating thermal contraction or expansion of the geological medium, respectively. Although numerical simulations are essential to predict and analyse the coupled thermo-hydro-mechanical (THM) behaviour, rapid evaluation tools are often required to explore multiple scenarios and perform inverse assessments efficiently. Here, we analytically estimate ground surface displacements due to point non-isothermal injections by combining an existing solution for the deformation due to steady state hydraulic head variations with a novel solution for the deformation due to temperature variations. This solution has been verified satisfactorily against results from a coupled THM numerical model and field measurements (levelling and PS-INSAR) from a leakage case at the geothermal power plant in Landau, Germany. In terms of computational cost, the analytical solution is significantly less demanding than fully coupled THM numerical simulations, allowing systematic sensitivity analyses. The results provide insight into the contribution of hydraulic head and temperature to the ground surface displacements, and allow a better understanding of the effect of the natural geothermal gradient. The solution can be used not only to predict ground displacement under different injection scenarios, but also to perform inverse analyses and infer subsurface parameters from uplift observations.