Solution of the Rachford Rice equation using perturbation analysis
Numerical simulation of two-phase fluid flow requires the Rachford Rice equation to be solved repeatedly at each grid block and at each time step to estimate the distribution of mass between the gas and the liquid phase. Despite its simplicity and monotonicity, the non-linearity of the Rachford Rice function imposes the need to utilize iterative methods which may take a considerable amount of time depending on the shape of the specific function. Therefore, due to the extensive number of solutions needed during a simulation run, any attempt to increase the speed or the robustness of the solution method is welcome.
In this work, a new solution method is proposed that is based on perturbation theory. The idea lies in the fact that the shape and the root location of the Rachford Rice equation is usually dominated by only few of the mixture components and a closed form solution is directly available for their subset. The effect of the ignored components on the exact solution can be taken into account by considering their contribution as a perturbation of the subset solution. This way very accurate approximations of the solution are obtained at a very low computation cost. Unlike most available methods based on the Newton-Raphson technique, the method in this work does not need an initial estimate of the solution. The value of the proposed method is demonstrated through its application to three example fluids.