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

Abstract

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 on the fracture system. When the external loadings are applied, fractured porous rocks naturally display two different poromechanical responses of the matrix system and the fracture system considering respective hydraulic and mechanical properties. Besides, the constant temperature difference between the drilling mud and formation rock is often chosen as a boundary condition to solve the temperature balance equation, and thus the incorrect prediction of temperature variations of fractured rock further leads to inappropriate evaluation of the pore pressure and stress fields considering the thermo-hydromechanical (THM) coupling (porothermoelastic model), since a dynamic temperature-perturbation boundary condition related to the temperature at the borehole wall actually accounts for the circulating effect of the drilling mud. Therefore, this paper first uses the Surname et al. (1995) 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 local thermal equilibrium (LTE) condition, one considers the dynamic temperature-perturbation boundary condition and provides semianalytical porothermoelastic solutions to the field variables around a vertical borehole subjected to nonhydrostatic 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 displacements, stresses, and two pore pressures of 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. The main results show that the dual-porosity medium displays a higher borehole instability potential than the single-porosity one. 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 porothermoelastic model is considered. It suggests that the drilling engineer takes into consideration the dynamic temperature-perturbation boundary effect, fracture spacing, and fracture width into the predrilling design of the time-dependent safe mud-pressure window (SMPW).