This paper presents a discussion on the development of a coupled geomechanics-thermal reservoir simulator using finite element method (FEM). The Galerkin's least square (GLS) technique is employed to discretize the saturation equation in order to stabilize the solutions. Unlike the conventional thermal reservoir simulators which are usually developed using finite deference method (FDM), the proposed FEM models have the advantage of easily incorporating the full permeability tensor. A numerical example is presented to evaluate the suitability and the validity of the developed coupled simulator.
The coupling between the processes of heat transfer, multiphase fluid flow and stress/deformation has become an increasingly important subject in the area of the oil industry(1). Particularly, the coupling is crucial in such problems as borehole stability, hydraulic fracturing and injection orproduction induced deformation on the ground surface during the thermal recovery processes in the heavy oil or oil sand reservoirs.
Numerical modeling of the coupled processes is complex, and has been historically carried out in the areas of geomechanics modeling and the reservoir simulation. Theformer is to compute the stress-strain behavior, therefore the deformation; the latter is to essentially model the multiphase flow and heat transfer in porous media. Each of these disciplines simplifies the part of the problem that is not of primary interest. These approaches are unacceptable in situations where the coupling is strong and the changes of porosity and permeability cannot be accounted by rock compressibility alone.
Gutierrez and Lewis(2) extend Biot's theory to multiphase fluid flow in deformable porous media. Based on their formulation, they conclude that the coupling between the geomechanics and the multiphase flow occurs simultaneously. Thus, fully coupled system equations of deformations, multiphase flow and heat transfer should be solved simultaneously. Development of such kinds of fully coupled geomechanics-multiphase flow-heat transfer simulators needstremendous effort, since the existing FEM geomechanics codes and the FDM reservoir simulators cannot be used.
Settari and Mourits(3) present an approach to couple the stress-strain behavior to multiphase flow, heat transfer usingporosity as a coupling parameter. The geomechanics module and the thermal reservoir simulator are used in a staggered manner. Pore pressure and temperature changes are calculated from the thermal reservoir simulator and transferred to the geomechanics module. The stress changes and the displacements are then calculated in the geomechanics simulation. An iterative algorithm is used to ensure that theporosity calculated from the geomechanics module is the same as that from the thermal reservoir simulator. The staggered technique employed to solve the coupled system equations allows for the use of the existing geomechanics codes in conjunction with a standard reservoir simulator. Currently, most of the commercial coupled geomechanics-multiphase flow-heat transfer simulators are developed in this way. The disadvantage of these kinds of coupled simulators is that the thermal reservoir module, usually developed using finite difference method (FDM), cannot accommodate the full permeability tensor, since they adopt the standard discretization scheme such as 5-spot for 2-D problems and 7-spot for 3-D problems.