A control-volume finite-element model for simulating oil-water reservoirs

Gottardi, G. and Dall'Olio, D., 1992. A control-volume finite-element model for simulating oil water reservoirs. J. Pet. Sci. Eng., 8:29-41. A two-phase two-dimensional immiscible flow model is presented. The model is based on the well known control-volume finite-element (CVFE) technique which uses linear triangular finite-element shape functions to estimate the value of the variables at the boundaries of the control volume associated with each node. The use of linear interpolation functions allows the elemental matrices of the model to be expressed in a closed form. Integration in time is obtained by using a full implicit finite-difference (FD) scheme. With respect to grid construction, the CVFE method offers the same flexibility as the finite-element (FE) method and a better physical interpretation of the discretized mass balance equations. Moreover, the method can be easily implemented in exisitng FE simulators which use linear triangular elements without requiring relevant changes. Numerical examples are presented to compare the performances of the CVFE and the Galerk in upstream-weighting FE methods with regard to grid orientation effects, mass-balance errors and run time.