A robust negative flash based on a parameterization of the tie-line field

We propose a novel approach to flash calculation, with particular application to negative flash. The basis of the method is a parameterization of the tie-line field. Rather than solving the Rachford–Rice equation (or any of its variants) we solve directly for the parameters defining the tie line. For an N  -component system, our approach leads to a system of N−2$N-2$quadratic equations, which we solve efficiently using a Newton method. The iterative method is very robust: unlike other negative flash procedures, the solution displays continuous dependence on the overall composition, even in the transition to negative concentrations. We illustrate the properties and behavior of the proposed approach on three-component and four-component systems, and we then generalize the method to systems of N components. From the global triangular structure of the system with constant K-values, it follows that the system of N⁻² quadratic equations can only have two roots. For the important case of three components, the flash calculation is explicit.