A Porothermoelastic Model Considering the Dynamic Temperature-Perturbation Boundary Effect for Borehole Stability in Fractured Porous Rocks

Conventional drilling design tends to inappropriately predict the mud density required for borehole stability of deep fractured porous rocks, such as shale, tight sandstone, and hot dry rock because it is treated as a single porosity case and even introduces the influence of weak plane to cover the effect the fracture system. Fractured porous rocks naturally display two different poromechanical responses because the matrix system and the fracture system have respective hydraulic and mechanical properties when the external loadings are applied. Moreover, the inaccurate temperature variations of fractured rock further lead to the incorrect prediction of the pore-pressure and stress fields considering the thermo-hydro-mechanical coupling, since the constant temperature difference between the drilling mud and formation rock is often chosen as a boundary condition to solve the temperature balance equation. The dynamic temperature-perturbation boundary condition is related to the temperature at the borehole wall. Therefore, this paper firstly uses the API RP 13D model in combination with the circulating temperature-fields model of Raymond (Raymond, 1969) to obtain a set of fully transient analytical solutions to circulating temperature fields including the four types of temperature inside the drilling pipe, borehole annulus, at the borehole wall, and formation. Furthermore, Under LTE (local thermal equilibrium) condition, this paper considers the dynamic temperature-perturbation boundary condition and provides semi-analytical porothermoelastic solutions to the field variables around a vertical borehole subjected to non-hydrostatic stresses in fractured porous rock with dual porosity and dual permeability. The solutions for field variables are obtained in line with the plane strain assumption. The variables include the related to displacements, stresses, and two pore-pressures in the matrix system and fracture system, The model is verified by the analytical solutions in the case of a porous medium with a single porosity one under LTE condition. This work conducts a quantitative study of the relation between the fracture spacing, fracture width, and the safe mud-pressure window that is most commonly comprised of the upper limit fracture pressure and the lower limit collapse pressure. The main results show that the dual-porosity medium displays a higher borehole instability potential than the single porosity one. The temperature difference related to the cooling effect increases with increasing drilling-mud circulating time. This increasingly cooling effect increases the higher risk of the tensile transverse fracturing when the constant temperature-perturbation boundary condition chooses a smaller temperature difference than that of the dynamic case at a later time. The drilling mud-pressure window narrows with increasing time when the coupled thermo-hydro-mechanical model is considered. It suggests that the drilling engineer takes into consideration of the dynamic temperature-perturbation boundary effect, fracture spacing, and fracture width into the predrilling design of the time-dependent safe mud-pressure window.