We propose a novel approach to ash calculation, with particular application to negative ash. The ability to compute a negative ash for any composition state is important in practice, as the construction of analytical solutions for multicomponent systems by the method of characteristics (MOC) relies heavily on the identi cation of tie lines and tie-line extensions. MOC solutions are at the heart of some techniques for the calculation of the minimum miscibility pressure, and are the key building blocks for fast simulation of multidimensional reservoir ows by the front-tracking / streamline method. The basis of the proposed negative-ash method is a parameterization of the tie-line eld. Rather than solving the Rachford-^sRice equation (or any of its variants) we solve directly for the parameters defning the tie line. For an N-component system, our approach leads to a system of N - 2 quadratic equations, which we solve effciently using a Newton method. The iterative method is very robust: unlike other negative ash 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 ash calculation is explicit.
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