ABSTRACT:

The mechanical behavior of a borehole in a thermo-poro-elastic medium under non-isotropic far-field tectonic stresses is studied with a focus on the non-isothermal condition. The theory proposed by Coussy (1989) is adopted to account for thermal effects in low-permeability but fractured rocks. By decomposing the problem into axisymmetric and deviatoric loading cases, the analytical solutions in the Laplace space are obtained for each case. Through the numerical Stehfest method, the pore pressure, temperature and stress distributions around the borehole in time and space are obtained. Some conclusions are drawn: first, the pore pressure diffusion has little influence on the temperature, but the thermal effect can change the pore pressure; second, the thermal effect has a strong impact on the distribution of the hoop stresses and strong cooling, around the borehole for example, leads to an more tensile tangential stress; third, the deviatoric loading has little effect on the temperature distribution. Based on these results, a new criterion is developed to predict the breakdown pressure in the presence of temperature variations.

1. INTRODUCTION

The mechanical behavior of a wellbore in a fluidsaturated porous media has attracted a great deal of attention in the oil and gas industry during the past several decades, because of the importance of wellbore stability during drilling, production and stimulation. The theory of linear poroelasticity first proposed by Biot [1] and re-formulated by Rice and Cleary [2], is commonly used to characterize the elastic response arising from pore pressure and fluid flow around the wellbore. Based on this theory, the stress analysis near a borehole can be described by a coupled deformation-diffusion process [3-5]. Detournay and Cheng [3] first provided the poroelastic transient and plane-strain analytical solution. However, for the extraction of heavy oil and geothermal energy and the disposal of nuclear waste, neglecting heat transfer in the analysis will lead to unrealistic results. Heat conduction and associated temperature change has a strong effect on rock volumetric deformation. Here we consider the effect of a temperature gradient on the fluid flow and stress distribution near a wellbore in a porous medium. Many theories have been developed to include the thermal effects [6-11], even though the theory of isothermal porous media has many other engineering applications. In particular, Coussy [11] developed a general theory without any decoupling for saturated porous materials based on thermodynamics principles. In his model, thermal effects caused by the saturating fluid are taken into account through a latent heat associated with the increase of fluid mass content at a different temperature from the rock matrix. The fluid mass plays a role as the heat sink or source in the porous media. For the purpose of simplicity, only heat conduction in the porous rocks is considered in his model, while heat advection carried out by the saturating fluid is neglected since the fluid velocity is small during the heat transfer process. For geothermal drilling, stimulation and production operations, minimizing wellbore instability is an important issue in reducing costs.

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