Calling

The purpose of the asterisk is to call attention to the difference in normalization. 

The sum of the squared differences between calculated and measures pressures is minimized as a function of model parameters. This method, often called Barker s method (Barker, 1953), ignores information contained in vapor-phase mole fraction measurements such information is normally only used for consistency tests, as discussed by Van Ness et al. (1973). Nevertheless, when high-quality experimental data are available. Barker s method often gives excellent results (Abbott and Van Ness, 1975). 

In the maximum-likelihood method used here, the "true" value of each measured variable is also found in the course of parameter estimation. The differences between these "true" values and the corresponding experimentally measured values are the residuals (also called deviations). When there are many data points, the residuals can be analyzed by standard statistical methods (Draper and Smith, 1966). If, however, there are only a few data points, examination of the residuals for trends, when plotted versus other system variables, may provide valuable information. Often these plots can indicate at a glance excessive experimental error, systematic error, or "lack of fit." Data points which are obviously bad can also be readily detected. If the model is suitable and if there are no systematic errors, such a plot shows the residuals randomly distributed with zero means. This behavior is shown in Figure 3 for the ethyl-acetate-n-propanol data of Murti and Van Winkle (1958), fitted with the van Laar equation. 

The most frequent application of phase-equilibrium calculations in chemical process design and analysis is probably in treatment of equilibrium separations. In these operations, often called flash processes, a feed stream (or several feed streams) enters a separation stage where it is split into two streams of different composition that are in equilibrium with each other. 

Again, Equations (7-8) and (7-9) are then used to calculate new compositions. These compositions, normalized, and the new value for T are utilized in thermodynamic subroutine calls to find equilibrium ratios and enthalpies for use in the next iteration. 

Each iteration requires only one call of the thermodynamic liquid-liquid subroutine LILIK. The inner iteration loop requires no thermodynamic subroutine calls thus is uses extremely little computation effort. 

CALL SUMSCJ TO OBTAIN NEW VALUES CF DEPENDENT VARIABLES DERIVATIVES, AND SSQ. 

INITIAL CALL TO THIS SUBROUTINE MUST BE MADE WITH KEY.EQ.O... 

B1JS2 CALLED AND ONLY TEMP DEPENDENT PARAMETERS... 

TEMP UNCHANGED. 8IJS2 NOT CALLED. SECOND VIRIAL... 

SUBSEQUENT CALLS WHEN ALL VARIABLES ARE CHANGED, 3 IF ONLY COMPOSITION... 

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