State function based flash specifications

A variety of flash specifications of practical importance can be formulated as minimization of a thermodynamic state function. It is well known that the solution for the PT-flash yields the global minimum of the mixture Gibbs energy, but in addition specifications of PH, PS, TV, UV or SV all permit selections of thermodynamic state functions for which a global minimum must be located. Two important advantages are obtained with the minimization based approach. First, the desired solution is known to be unique, and second, stability analysis can be used to verify its correctness and to determine the number of equilibrium phases. For the PT-flash the solution can be determined by unconstrained minimization, whereas the remaining specifications are accompanied by one or two nonlinear constraints and thus less straightforward to attack. We present here two approaches for dealing with such specifications. The first is a nested optimization approach where T and/or P are the dependent variables in the outer loop, and where a PT-flash is solved in the inner loop. The essential advantage of this formulation is that it is very easy to implement but the drawback is the additional cost of the nested loops. The second approach is based on a modified objective function in which all constraints are removed, but where a saddle point rather than a minimum must be located. The resulting equations are solved by a global Newtonʹs method, and it is shown that a common Jacobian matrix can be used with all the specifications given above.