A Generalized Polynomial Form of the Objective Function in Flash Calculations

This work centers on the recasting of the Rachford-Rice objective function into a polynomial function of the vapor fraction. The degree of this polynomial is one less than the number of components in the system and its coefficients can be calculated from the feed composition and the equilibrium ratios. A recursive expression is developed that involves symmetric functions and can be easily programmed on a computer, or scientific calculator. The principal advantage of this new form of the objective function is that the theory of polynomials is well-developed. The location of their zeroes can be predicted with confidence by techniques based on sound mathematical principles, such as the Fourier-Budan theorem. The polynomial in the vapor fraction is well- behaved over the two-phase region and its root can be quickly located by a hybrid method of interval-halving technique and Newton-Raphson procedure. The validity of the new objective function and its automatic coefficient-generating algorithm are tested using several multicomponent systems for which experimental data are available. The new objective function is not prone to the erratic behavior of the Rachford-Rice function and is not sensitive to initial guess of the root.