Vapor compositions, interpolation

FIG. 2-10 Enthalpy-concentration diagram for aqueous ethyl alcohol. Reference states Enthalpies of hquid water and ethyl alcohol at 0 C are zero. NOTE In order to interpolate equilihrium compositions, a vertical may he erected from any liquid composition on the hoihug hue and its intersection with the auxihary hue determined. A horizontal from this intersection will estahhsh the equihhrium vapor composition on the dew hue. (Bosnjakovic, Techuische Thermo-dynamik, T. Steinkopff, Leipzig, 1935. )... 

A method for interpolation of calculated vapor compositions obtained from U-T-x data is described. Barkers method and the Wilson equation, which requires a fit of raw T-x data, are used. This fit is achieved by dividing the T-x data into three groups by means of the miscibility gap. After the mean of the middle group has been determined, the other two groups are subjected to a modified cubic spline procedure. Input is the estimated errors in temperature and a smoothing parameter. The procedure is tested on two ethanol- and five 1-propanol-water systems saturated with salt and found to be satisfactory for six systems. A comparison of the use of raw and smoothed data revealed no significant difference in calculated vapor composition. 

The present author (4) has previously preferred to use raw isobaric data coupled with Barker s method (2) and the Wilson equation (5), but interpolation of the calculated discrete vapor composition values requires smoothing of boiling point-liquid composition data at some stage. 

Step 4. The smoothed temperatures were used to interpolate vapor compositions. 

By interpolation, the bubble point is 97 C, close enough to 96°C so that the vapor compositions can be calculated using Eq. (19.9). The vapor b equilibrium with the liquid is 60.4 mole percent n-hexane, 29.2 mole percent n-heptane, and 10.4 mole percent n-octane. 

FIGURE 8.17 Temperature-composition diagram for ethanol-water at 1 atm, using data points from [1]. The curves are simple smooth interpolations. The arrows show the graphical solution for the bubble point (temperature-specified) and vapor composition. 

In both cases the empirical constants are given for the three temperatures of 1000,1500, and 2000 K. Table 5-5 also includes some six values for the partial pressure ratios pw/pc of water vapor to carbon dioxide, namely 0, 0.5, 1.0, 2.0,3.0, and . These ratios correspond to composition values of pc / (pc + pw) =1/(1+ pw tyc) of 0, 1/3, 1/2, 2/3, 3/4, and unity. For emissivity calculations at other temperatures and mixture compositions, linear interpolation of the constants is recommended. 

To begin the calculations the column variables must be first initialized to some estimated values. Simple methods can be used for this purpose, based on the column specifications and possibly supplemented by shortcut methods. The column temperature profile may be assumed linear, interpolated between estimated condenser and reboiler temperatures. The values for Lj and Vj may be based on estimated reflux ratio and product rates, assisted by the assumption of constant internal flows within each column section. The compositions Xj- and T, may be assumed uniform throughout the column, set equal to the compositions of the liquid and vapor obtained by flashing the combined feeds at average column temperature and pressure. The other variables to be initialized are Rf,Rj, and Sj, which are calculated from their defining equations. The values for Qj may either be fixed at given values (zero on most stages) or estimated. 

Figure 12.2 Vapor pressure pH20.g of the H2O-P2O5 system as a function of composition and temperature. Evaluated data from [11-14], isotherms with interpolated compositions. Isotherms for 100 and 110°C partially extrapolated for low concentrations. The solid lines connecting the data points are guides for the eye.

The data from the given references fit fairly well together without discontinuities. Intermediate compositions were interpolated by polynomial fitting. Intermediate temperatures were linearly interpolated by using a In PH20,g versus 1/T plot according to the Clausius-Clapeyron equation. The isotherms for 100 and 110 °C at low concentrations are extrapolated. The extrapolated data points fit sufficiently well to the vapor pressure data of pure water [7]. 

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