On multiphase negative flash for ideal solutions

There is a recent interest to solve multiphase negative flash problems where the phase amounts can be negative for normal positive feed composition. Solving such a negative flash problem using successive substitution needs an inner loop for phase distribution calculation at constant fugacity coefficients. It is shown that this inner loop, named here as multiphase negative flash for ideal solutions, can be solved either by Michelsen's algorithm for multiphase normal flash, or by its variation which uses F − 1 phase amounts as independent variables. In either case, the resulting algorithm is actually simpler than the corresponding normal flash algorithm. Unlike normal flash, multiphase negative flash for ideal solutions can diverge if the feasible domain for phase amounts is not closed. This can be judged readily during the iteration process. The algorithm can also be extended to the partial negative flash situation where several phase amounts must be non-negative and at least one phase amount can be negative.

► It is shown that multiphase negative flash for ideal solutions can be solved easily as unconstrained minimization.
► The algorithm is actually simpler than the counterpart for normal flash, no matter F or F − 1 independent phase amounts are used.
► Negative flash can have a diverging solution and the condition for divergence is proved.
► Criteria for divergence judgment during iteration are given.
► The algorithm is also extended to multiphase partial negative flash for ideal solutions.