Three-Dimensional Multiphase Flow Simulation in Petroleum Reservoirs using the Mass Fractions as Dependent Variables

Abstract

Abstract This paper describes a numerical methodology for solving three-dimensional multiphase flow in petroleum reservoirs. The mathematical model encompasses the Darcy's equations and the mass conservation equation for the oil, gas and water components. To account for the gas phase appearance/disappearance, without employing special strategies, the method uses the mass fractions as dependent variables. The mathematical model uses boundary-fitted coordinates which permits to deal with complex reservoir boundaries and offers the opportunity of better representing curvilinear geological structures. The solution is fully implicit and includes the proposition of a well model for non-orthogonal discretization. Introduction The simulation of the multiphase flow of oil, gas and water in porous media are usually carried out using the saturation and pressure as dependent variables. However, there are thermodynamic conditions in petroleum reservoirs in which the gas is dissolved in the oil, but the gas phase is absent. Since the saturation is related to the existence of the phase, when the gas phase disappears, but the gas component is still present. in the oil phase, the numerical scheme must take into account the phase appearance/disappearance. To deal with this problem it is necessary to change the variables during the simulation, or to avoid the phase disappearance, keeping a residual value for the saturation. These strategies poses numerical difficults and may cause instabilities during the solution procedure. One alternative for by-passing this problem is to use the mass fractions of the components as dependent variables, as done in Prais and Campagnolo and Britto. This guarantees that, in the case of the gas phase disappearance, the mass fraction of the gas component, representing the total mass of gas dissolved in the other phases, will be non-zero. This paper presents a numerical method for solving 3D multiphase flow of oil, water and gas in complex reservoirs using the mass fractions as dependent variables and a fully implicit formulation. For handling the complex geometries of the reservoirs, a non-orthogonal boundary-fitted coordinate system is used. This type of structured discretization has been previously used by Maliska et al for modeling two and three phase flows with IMPES formulation. Curvilinear orthogonal grids have been used in the past by Hirasaki and O'Dell, Sharp and Anderson and Robertson and Woo among others. The model is applied to solve three-dimensional two-phase and three-phase flows in petroleum reservoirs.