Values, convergence pressure

The widespread availabihty and utihzation of digital computers for distillation calculations have given impetus to the development of analytical expressions for iregression equation and accompanying regression coefficients that represent the DePriester charts of Fig. 13-14. Regression equations and coefficients for various versions of the GPA convergence-pressure charts are available from the GPA. 

Step 6. Using the convergence pressure determined in Step 5, together with the system temperature and system pressure, obtain K-values for the components from the appropriate convergence-pressure K-charts. 

For a temperature of 100°F, the convergence pressure is approximately 2,500 psia (dotted line) for the pseudo system methane-n-pentane (see Figure 8-3C). For n-pentane at convergence pressure of 3,000 psia (nearest chart) the K-value reads 0.19. The DePriester charts [80] check this quite well (see Figures 8-4A and B, and Figure 8-3D). 

Interpolation between charts of convergence pressure can be calculated, depending on how close the operating pressure is to the convergence pressure. The K-factor (or K-values) do not change rapidly with convergence pressure, (psia) [79]. 

Brown, see Cajander et al. (1960), developed a method which relates the equilibrium constant K to four parameters component, pressure, temperature, and the convergence pressure. The convergence pressure is the pressure at which all K values tend to 1. The Brown Kw equation is limited to low pressure and its use is generally restricted to vacuum... 

Notice that the K-factor charts in Appendix A apply to petroleum mixtures which have convergence pressure of 5000 psia. The other charts of this correlation (not reproduced in Appendix A) are for use with mixtures with other convergence pressures. A value of convergence pressure applicable to the fluid of interest must be estimated in order to select the correct set of graphs. 

The value of pressure for which the K-factors appear to converge to unity is known as the convergence pressure. If a mixture is at its true critical temperature, the curves in reality will converge to a value of 1.0... 

This method of estimating convergence pressure involves a trial-and-error procedure in which a first trial value of convergence pressure is used to obtain K-factors. A reasonable estimate of convergence pressure for a first trial value may be obtained from5... 

The estimate of convergence pressure is taken from the point this locus crosses the temperature at which calculations are desired. If this convergence pressure is not reasonably close to the first trial value of convergence pressure, the procedure should be repeated. The estimated value of convergence pressure can be used as die new trial value. 

EXAMPLE 14-1 The compositions of the gas and liquid from a black oil at 1300 psia and 160°F calculated with Equation 12—17 are given in the table below. A convergence pressure of 5000 psia was used to obtain the Refactors. What value of convergence pressure should have been used for this mixture at 160°F ... 

When the operating pressure is considerably less than the convergence pressure, an error in the estimate of convergence pressure has little effect on the resulting calculations. As operating pressure approaches convergence pressure, however, equilibrium ratios become very sensitive to the convergence pressure used and care must be taken in the selection of the correct value. 

The correlations from which the equilibrium ratio data in Appendix A were taken include charts for convergence pressures of 800, 1000, 1500, 2000, 3000, 5000, and 10,000 psia. When the convergence pressure for the mixture is between the values for which charts are provided, interpolate between charts. Interpolation is necessary when the operating pressure is near the convergence pressure. At low pressure, simply use the chart with convergence pressure nearest the value for the mixture. 

The book can be covered in one semester with the following schedule Chapter 1 4, class days Chapter 2 4 days Chapter 3 (omit kinetic theory) 3 days Chapter 5 2 days Chapter 6 (omit heating value and Joule-Thomson effect) 2 days Chapter 8 2 days Chapter 9 2 days Chapter 10 3 days Chapter 11 6 days Chapter 12 (omit differential vaporization) 3 days Chapter 13 3 days Chapter 14 (convergence pressure only) 1 day Chapter 16 2 days Chapter 17 2 days. This schedule leaves several class meetings for examinations or other topics desired by the instructor. 

CONVERGENCE-PRESSURE VAPOR-LIQUID EQUILIBRIUM K VALUES 1.49... 

Use convergence-pressure vapor-liquid equilibrium K-value charts (Figs. 1.15 through 1.26). 

Calculate the dew-point temperature of the mixture at a pressure of 310 psia and an assumed convergence pressure of 800 psia. At various assumed temperatures and at a pressure of 310 psia, the K values for methane, nitrogen, and ethane, as obtained from Figs. 1.15,1.18, and 1.21, are fisted in Table 1.12, as are the corresponding values of A, /Ki. At the dew-point temperature, the latter will add up to 1.0. It can be seen from the table that the dew point lies between —60 and —50°F (222 and 227 K). Therefore, the condensation will take place in the last heat exchanger in the train, because that one lowers the stream temperature from —20°F (244 K) to —100°F (200 K). 

FIGURE 1.15 K values for nitrogen convergence pressure = 800 psia. (Note 1 psi = 6.895 kPa.) (Courtesy ofNGPA.)... 

Strictly speaking, the convergence pressure of a binary mixture equals the critical pressure of the mixture only if the system temperature coincides with the mixture critical temperature. For multi-component mixtures, furthermore, the convergence pressure depends on both the temperature and the liquid composition of mixture. For convenience, a multicomponent mixture is treated as a pseudobinary mixture in this K-value approach. The pseudobinary mixture consists of a light component, which is the lightest component present in not less than 0.001 mol fraction in the liquid, and a pseudoheavy... 

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