A GENERAL APPROACH TO THE TESTING OF BINARY 'SOLUBILITY' SYSTEMS FOR THERMODYNAMIC CONSISTENCY

A comparison of implicit Runge-Kutta and orthogonal collocation methods is made for the numerical solution to the ordinary differential equation which describes the high-pressure vapor-liquid equilibria of a binary system. The systems of interest are limited to binary 'solubility' systems where one of the components is supercritical and exists as a noncondensable gas in the pure state. Of the two methods--implicit Runge-Kutta and orthogonal collocation--this paper attempts to present some preliminary but not necessarily conclusive results that the implicit Runge-Kutta method is superior for the solution to the ordinary differential equation utilized in the thermodynamic consistency testing of binary 'solubility' systems.; Due to the extreme nonlinearity of thermodynamic properties in the region near the critical locus, an extended cubic spline fitting technique is devised for correlating the P-x data. The least-squares criterion is employed in smoothing the experimental data. Even though the derivation is presented specifically for the correlation of P-x data, the technique could easily be applied to any thermodynamic data by changing the endpoint requirements.; The volumetric behavior of the systems must be given or predicted in order to perform thermodynamic consistency tests. A general procedure is developed for predicting the volumetric behavior required and some indication as to the expected limit of accuracy is given. Utilizing the procedures mentioned above, a general approach to the testing of binary 'solubility' systems for thermodynamic consistency is developed. Tests are presented for several systems retrieved from the literature where the cgs system of units was employed throughout.; An evaluation is made for a current solubility apparatus. Results shown indicate that the apparatus is inappropriate for determining consistent solubility data. However, the apparatus should yield accurate VLE data for normal systems.