A Thermo–Hydro–Mechanical (T–H–M) coupled analytical solution for an open-hole under 3D asymmetric loads

The integrity of open-hole wellbores in deep, high-pressure high-temperature (HPHT), and unconventional reservoirs is critically affected by the coupled interactions of mechanical loads, temperature variations, and pore fluid seepage. This Thermo–Hydro–Mechanical (T–H–M) coupling governs the evolution of the near-wellbore stress field and plays a decisive role in maintaining wellbore stability under complex geological conditions However, existing studies often rely on two-dimensional simplifications or slow numerical models, and lack a generalized analytical framework to characterize three-dimensional (3D) asymmetric T–H–M coupling. To address this limitation, this study develops a 3D steady-state analytical solution for the T–H–M coupled near-wellbore stress field in open-hole formations. Using the linear superposition principle, we decompose the coupled system into three independent subproblems… and superimpose their analytical solutions to obtain the total stress field under linearly depth-dependent loads. The results reveal a pronounced non-axisymmetric stress distribution governed by horizontal stress anisotropy, with the maximum circumferential compression occurring in the direction of the minimum horizontal principal stress. Temperature differentials between the drilling fluid and the formation exert a dominant influence on wellbore stability: fluid cooling—occurring when the drilling-fluid temperature is lower than the formation temperature—induces thermal tensile stresses that mitigate compressive stress concentrations and thereby suppress shear failure; in contrast, fluid heating exacerbates compressive stresses and promotes wellbore instability. Seepage-induced tensile stresses near the wellbore wall counteract mechanical and thermal compression, resulting in radial stress reversal in the near-wellbore zone. The proposed analytical solution provides an accurate, computationally efficient, and physically interpretable framework for predicting near-wellbore stress distributions under complex three-dimensional thermal–mechanical–hydraulic coupling conditions; it delivers both theoretical insight and actionable guidance for temperature management, drilling-fluid system optimization, and wellbore integrity design in deep, high-pressure high-temperature, and geothermal drilling applications.