DePriester charts

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

A trial-and-error procedure is required with any K-value correlation that takes into account the effect of composition. One cannot calculate K values until phase compositions are known, and those cannot be known until the K values are available to calculate them. For K as a function of T and P only, the DePriester charts provide good starting values for the iteration. These nomographs are shown in Fig. 13-14/7 andZ . SI versions of these charts have been developed by Dadyburjor [Chem. Eng. Prog., 74(4), 85 (1978)]. 

The Kellogg and DePriester charts and their subsequent extensions and generahzations use the molar average boiling points of the liquid and vapor phases to represent the composition effect. An alternative measure of composition is the convergence pressure of the system, which is defined as that pressure at which the Kvalues for aU the components in an isothermal mixture converge to unity. It is analogous to the critical point for a pure component in the sense that the two... 

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. 

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). 

A feed to a column has the composition given in the table below, and is at a pressure of 14 bar and a temperature of 60°C. Calculate the flow and composition of the liquid and vapour phases. Take the equilibrium data from the Depriester charts given in Chapter 8. 

Equilibrium constants were taken from the Depriester charts (Chapter 8). ... 

To obtain the composition of the top and bottom products, first calculate the relative volatility of each component using the conditions of the feed as a first guess. The relative volatility depends on temperature and pressure. The bubble point of the feed at 400 psia (27.6 bar) and at the feed composition, calculated using ASPEN [57], is 86.5 °F (130 °C). The K-values of the feed are listed in Table 6.7.1. Bubble and dew points could also be calculated using K-values from the DePriester charts [31] and by using the calculation procedures given in Chapter 3. Next, calculate the relative volatility of the feed stream, defined by Equation 6.27.18, for each component relative to the heavy key component. 

Figure 8 4A. DePriester Charts K-Values of light hydrocarbon systems, generalized oorreiations, low-temperature range. Used by permission DePnester, C.L., The American Institute of Chemical Engineers, Chemical Eng. Prog. Ser. 49 No. 7 (1953), ail rights reserved.

Originally there were charts prepared to make use of these definitions. The DePriester Charts for the homologous series of light hydrocarbons can serve as a basis with approximate validity for simple calculations of VLE situations. 

Because of the complex concentration functionality of the m-values, VLE calculations in general require iterative procedures suited only to computer solutions. However, in the case of mixtures of light hydrocarbons, we may assume as a reasonable approximation that both the liquid and the vapor phases are ideal. This allows m-values for light hydrocarbons to be calculated and correlated as functions of T and P. Approximate values can be determined from the monographs prepared by DePriester (1953). The DePriester charts have been fit to the following equation (McWilliams, 1973) ... 

Figure 2-11. Modified DePriester chart (in S.I. units) at low tenperatures...

Figure 2-12. Modified DePriester chart at high tenqjeratures...

Table 2-3. The last line gives the mean errors in the K values conpared to the values from the DePriester charts. This equation is valid from-70°C (365.7°R) to 200°C (851.7°R) and for pressures from 101.3 kPa (14.69 psia) to 6000 kPa (870.1 psia). If K and p are known, then Eq. 12-301 can be solved for T.

Since T,jj and Pdmm known, the 10 K can be determined easily [say, from the DePriester charts or Eq. f 2-3011. Now there are only 22 linear equations to solve simultaneously. This can be done, but trial-and-error procedures are sirtpler. 

C. Plan. Calculate K from DePriester charts or from Eq. (2-301. Use Newtonian convergence with the Rachford-Rice equation, Eq. (2=46), to converge on the correct V/F value. Once the correct V/F has been found, calculate X from Eq. (2=38) and y from Eq. (2=39). Calculate V from V/F and L from overall mass balance, Eq. (2=5). 

These are close enough. They aren t perfect, because V/F wasn t exact. Essentially the same answer is obtained if Eq. (2=30) is used for the K values. Note Equation (2=30) may seem more accurate since one can produce a lot of digits however, since it is a fit to the DePriester chart it can t be more accurate. 

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