Theory and application of a fully coupled thermo-hydro-mechanical finite element model

Abstract

This paper describes the theory, finite element formulations and application of a multiphase fluid flow and heat transfer within a deforming porous medium. Tthe coupled governing equations are derived in terms of displacements, pore pressures and temperatures. Application of the model to a one-dimensional problem involving heating of a saturated soil layer indicates that the interdependence between fluid flow, heat flow and deformation processes are qualitatively well captured. The agreement between the computed results and analytical solutions for the problem of a cylindrical heat source within a saturated elastic medium has been close; this verifies that the coupled consolidation and heat conductance formulations have been encoded correctly. For validation, a centrifuge experiment that was performed at Cambridge University involving application of heat through a cylindrical heating element that was placed within a fully-saturated (with water) normally-consolidated clay deposit under well-defined initial and boundary conditions, was analyzed. Since the mechanical characteristics of the medium play a major role on the resulting pore pressure and stress response, a critical-state based constitutive model that is highly suited to characterizing the behavior of soft clay deposits, as was used in the centrifuge experiment, was implemented into the numerical model. Application of the code to this problem has indicated that temperature and pore pressure response can be well captured both in terms of trend and magnitude. To test the influence of the adopted stress-strain model, the analyses were repeated using a nonlinear elastic model. The results indicated that temperature distribution was not affected, but the generated excess pore pressure was significantly influenced (underpredicted by about 50%) by using a model that did not properly account for local yielding of the soil as occurred in the vicinity of the heater. The numerical model described in this paper is considered suitable for analysis of petroleum recovery projects that involve enhanced operations such as thermal injection and hydro-fracturing.