Theoretical solution for 3D transient thermal–hydraulic–mechanical coupled axisymmetric problem and its application to casing–cement–formation system

Abstract

In geomechanics and geoscience, the study of coupled processes is of paramount importance. This paper presents a theoretical solution, grounded in Biot’s theory, for the 3D transient thermal–hydraulic–mechanical (THM) coupled axisymmetric problem. Mathematical techniques such as the Laplace transform, Fourier expansion and the stress function method are employed to derive the THM solution. The Laplace transform is employed to manage time-dependent terms in transient equations, Fourier expansion is used to meet boundary conditions and stress functions establish connections between the stress field, seepage field, and temperature field. The validity of the THM solution is subsequently confirmed, demonstrating its accuracy. The theoretical solution is then applied to a casing–cement–formation system, a crucial structure frequently encountered in the oil industry. Given that the casing is generally considered impermeable, particular focus is placed on the boundary conditions at the casing–cement interface. A modeling of casing–cement–formation system is then conducted to show the THM coupling effect due to the temperature–pressure load. Furthermore, contour plots are employed to analyze the response of the system to linear loads.