Streamline method for simulation of compositional nonisothermal flow of viscoplastic oils

The purpose of this work is to develop a numerical method that allows to carry out calculations of nonisothermal compositional flow faster than traditional finite-volume methods. A plane problem of oil, water and gas flow is considered. Oil phase is represented by two components — light and heavy fractions, which like water, can gasify. The work takes into account not only the nonlinearity of the oil flow law, but also the temperature dependence of parameters of this law. This statement of the problem is relevant for modeling of high-viscosity oilfields development. To reduce the computational complexity of the problem, the streamline method with splitting by physical processes is used, which consists in separating convective transport directed along the flow propagation from processes associated with heat conduction and gravity, the direction of which does not coincide with the convective flow. A distinctive feature of the proposed method is the joint solution of pressure equations, energy and components mass balance both on streamlines and on the initial grid. This feature allows to perform correct calculations for oil flow with complex temperature-dependent rheology. Numerical solution of system of flow equations on two-dimensional grid and on streamlines is performed by IMPEC method. For the presented streamline method, an algorithm for taking into account thermal conductivity, as well as transition criteria between calculations on streamlines and on a two-dimensional grid is proposed. The developed program was verified by comparison with analytical solutions, as well as with the results of calculations by finite-volume methods on five-point and nine-point difference stencils.