Analytical Solution for Transient Temperature Field Around a Cased and Cemented Wellbore

摘要

Thermal recovery techniques have been widely used to enhance production in heavy oil reservoirs. The high temperatures increase the fluid mobility. The thermal stresses generated by high temperature changes may cause material damage, such as collapse, buckling or shear failure of the casing and hydraulic sealing loss of the cement sheath due to its cracking. High temperatures in open-hole completions may lead to grain shearing or cracking, increasing effective borehole radius. The evaluation of the stress state induced by temperature changes is of major interest in oil wellbore drilling and exploitation.rnThe temperature field around the well is usually evaluated by numerical techniques such as the finite difference method or analytically through Laplace transform, assuming a constant temperature at the borehole wall. The method proposed herein considers the radial heat conduction through the bore-face. Multilayer cylindrical of heterogeneous materials in perfect thermal contact and with constant physical properties composes the geometry of the problem. The heat conduction equation is evaluated through the separation-of-variables method, using Bessel functions. The problem domain is defined at the finite interval bounded by the radius of thermal influence, evaluated as the heat front advances. At the borehole wall, the boundary condition is given by a constant heat transfer rate.rnThis solution was implemented in a computer program. The results were compared with numerical solutions. They presented a better computational performance in terms of time and model simplicity.