Deviation optimum binary

Figure 1. Optimum binary deviation parameters (k and ji j) and confidence ellipses for the fit of the LHW equation of state to the Nz + Ar VE data of Ref. 11, pp. 166-168...

As expected, Equation 10 worked well for the 14 paraffin binaries the average deviation of the predicted from the optimum values was only 0.02. However, when all 26 hydrocarbon binaries were included, the average deviation increased to 0.05. 

Equation 11 was much less satisfactory, even when the coefficient was adjusted to minimize the deviation. The optimum value of the coefficient was 0.18, in agreement with Lin s conclusion for rare-gas mixtures, but the root-mean-square deviation of k j was 0.08. Any relationship involving I, the first ionization potential, is doomed to failure when applied to heavy hydrocarbon mixtures because I, for a given homologous series, is very weakly dependent on carbon number. For example, the I of n-decane is 10.19 eV, only 0.24 eV less than that of n-hexane, while that of n-eicosane should be about 10.04 eV. Thus, a correlation of kijs for methane-paraffin binaries based solely on ionization potentials would give the same result for all Ci0+ paraffins. 

In this work, the binary interaction parameter (k,j) was fitted to experimental vapor-hquid equilibrium data. The objective fimction used to optimize the kij parameter for any binary mixture was the minimization of the deviation between the model s prediction of the bubble pressure and the experimental value. The optimized ky values are suimnarized in Table 1. For comparison, optimum ky values are also shown for the PR EoS. A semi-predictive approach was used to determine the sensitivity of the results to the interaction parameter using the CO2 coupled binary interaction parameters. 

To determine which model is best, one finds data on the various binary pairs in the mixture. These data consist of measurements of tenperature, pressure, and conposition of a liquid in equilibrium with its vapor. Sometimes, the concentration of the vapor is also measured. From the ten erature and the liquid-phase conposition, the pressure and vapor-phase compositions are calculated with the thermodynamic model. The sum of the squared deviations between the experimental and the calculated pressure and between the experimental and the calculated vapor conpositions is the objective function. The decision variables are the adjustable parameters in the thermodynamic model. Through the procedures of Chapter 14. the objective function is minimized and the optimum set of parameters is found. The standard process simulators incorporate a tool to do these regressions. 

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