Calculation of critical points of multicomponent mixtures using the BWRS equation

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A computational procedure has been developed for solving two nonlinear equations that characterize the critical state for multi­component mixtures described by the Benedict-Webb-Rubin-Starling (BWRS) equation of state. The two equations are obtained by setting to zero the quadratic and the cubic forms in the Taylor series expansion of the Helmholtz free energy as a function of the mole numbers. The procedure treats finding a zero of the quadratic form (which defines the stability limit) as an eigenvalue problem where temperature is the eigenvalue at a given volume. The cubic form is treated then as a function of volume alone and its zeros are found by the secant method. A computer program has been developed and used for calculating vapour-liquid and liquid-liquid critical points for multicomponent systems. A proposal was developed for providing initial guesses for volume and temperature which permitted convergence to a vapour-liquid critical point in all cases. The proposed algorithm has been used to perform critical point computations on mixtures with up to 20 components. It is capable of converging to a vapour-liquid critical point (if one exists) for all the systems studied in three to six iterations. High density, liquid­liquid critical points have also been calculated by making an appropri­ate initial volume guess. It was found that the BWRS equation can have many stable and unstable points satisfying the critical criteria for a given mixture. Even for pure components, a second unstable critical point can be calculated.
Bibliography: p. 76-82.
Dahouk, M. A. (1982). Calculation of critical points of multicomponent mixtures using the BWRS equation (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from doi:10.11575/PRISM/17781