Reservoir Simulation With a Control-Volume Finite-Element Method

Summary This paper describes a control-volume finite-element (CVFE) method incorporating linear triangular elements for the simulation of thermal multiphase flow in porous media. The technique adopts the usual finite-element shape functions to evaluate flow potentials at the control-volume boundaries and uses the conservation equations for each control volume. The main advantage of the CVFE method over the finite-difference method is in the representation of complex reservoir geometries. In addition, desirable features, such as local grid refinement for near-well resolution, can be achieved simply and consistently. The control-volume approach enforces local mass conservation and permits a direct physical interpretation of the resulting discrete equations. These are significant advantages over the classical Petrov-Galerkin or variational finite-element methods. The method was implemented in a general-purpose thermal simulator. Numerical examples compare the proposed method with five-point and nine-point finite-difference schemes in terms of grid-orientation effects and run time. The CVFE method was found to reduce grid-orientation effects significantly. At the same time, computational cost was much lower than for the nine-point scheme. The geometric flexibility of the method also is demonstrated.