Numerical simulation of a steam-water-oil mixture during thermal-steam treatment of reservoir

The article presents a mathematical model and algorithm of numerical modeling of threephase mixture of steam-water-oil in porous media under thermal-steam treatment. Twodimension problem and convection-diffusion mechanism of heat and mass transfer of mixture are considered. Physical properties of porous media are assumed homogeneous and isotropic. Explicit accounting of fracture structure is absent. Properties of steam and water are considered independent of thermodynamic parameters of the system. Physical properties of oil are also independent of thermodynamic parameters of system except for dynamic viscosity, which is depends on temperature. Description of variable steam saturation, water saturation and oil saturation is made using transient mass balance relations for each phase. From these relations and Darcy’s law an equation to calculate unsteady pressure distribution is received. Temperature calculations is implemented by heat conductivity equation with hypotheses of a quasi-equilibrium thermal state of all phases and a single temperature. The presented model also considers phase transitions between steam and water by W.H. Lee model. Finite volume method is used for spatial discretization of received equations and the direct Euler scheme is used for temporal discretization. Since the mass balance equations is highly nonlinear, the Newton’s method applied to solve them. Simulation of three-phase steam-water-oil mixture seepage through porous media under conditions of steam-gravity drainage was carried out using the constructed numerical scheme. During the analysis of the simulation results, the pecularities of proposed numerical method are shown.