An One-Step Algorithm For Multiphase Equilibrium Calculation Using Equations Of State

Procedures for the multiphase equilibrium calculation are generally based on Gibbs free energy minimization or equation-solving methods. Equation-solving methods often involve sequential procedures for a priori the phase identification and then the phase equilibrium calculation. An one-step equation-solving algorithm (?-method), based on modifying the mole fraction summation of each phase, was adopted for the calculation of multiphase equilibria using equations of state. It requires only one-step solution of minimization problem and provides phase number present at phase equilibrium, their quantities and compositions simultaneously. And phase identification in advance is not required.Han and Rangaiah (1997) reported an algorithm based on the penalty function method and the minimization problem was solved by a version of successive linear programming methods. Their algorithm included an outer iteration and an inner one. The artificial variables were introduced in the inner iteration for solving search direction of variables. The radius vector including artificial variables introduced should be initialized, converted and operated. The method was relatively complicated.In this study, the Marquardt method is used for the minimization of the object function: f(w)= ()+∑hj 2(w)Where is a weighting parameter, τV,τI and τII are the phase characteristic variables for vapor, liquid I and liquid II respectively. Equality constraints are devoted by h(w) = 0 while any one of them is written as hj(w).By properly selecting the damping factor-λ, the object function can be minimized with a satisfied convergence rate. And the determination for the search direction of variables becomes very convenient.The method was verified with several typical multiphase systems, including n-C16H34-H2O-H2, C7H8-H2O-H2, CO2-DME (dimethyl ether) and DME-H2O usingdifferent equations of state and mixing rules: the fugacity coefficients for the former two systems were calculated using the Peng-Robinson equation of state and those for the latter two were calculated using the Soave-Redlich-Kwong equation of state, and the van der Waals mixing rule was used for the former three systems and the GE model mixing rule was used for the last one. The multi-components phase diagrams were drawn and the results show that the modified ?-method is successful and reliable for multiphase equilibrium calculation.Graduate student: Xu Huilin (Chemical Engineering) Directed by: Associate Professor Chen Jian...