Dew point calculation

Similarly, for a dew-point calculation (incipient condensation) a is 1 (again Q = 0) and Equation (7-13) leads to... 

For bubble and dew-point calculations we have, respectively, the objective functions... 

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

The vapor-liquid x-y diagram in Figures 4.6c and d can be calculated by setting a liquid composition and calculating the corresponding vapor composition in a bubble point calculation. Alternatively, vapor composition can be set and the liquid composition determined by a dew point calculation. If the mixture forms two-liquid phases, the vapor-liquid equilibrium calculation predicts a maximum in the x-y diagram, as shown in Figures 4.6c and d. Note that such a maximum cannot appear with the Wilson equation. 

While the main driving force in [43, 44] was to avoid direct particle transfers, Escobedo and de Pablo [38] designed a pseudo-NPT method to avoid direct volume fluctuations which may be inefficient for polymeric systems, especially on lattices. Escobedo [45] extended the concept for bubble-point and dew-point calculations in a pseudo-Gibbs method and proposed extensions of the Gibbs-Duhem integration techniques for tracing coexistence lines in multicomponent systems [46]. 

Combined physical and chemical equilibrium. Vapour-liquid equilibria were determined in this work by performing dew-point calculations. The procedure is ... 

The critical data and values used for inert components were those given by Ambrose (24). The interaction parameters between the water and the inert component were found by performing a dew-point calculation as described above but with the interaction parameter k.. rather than P taken as the iteration variable. 

With some slight modifications the same scheme can be adopted for dew point calculations. 

Again, this seems to be a rather nice application for computer technology. Even a good-quality programmable calculator can store a number of vapor-pressure curves. At least for hydrocarbons, equations for these curves can be extracted from the API (American Petroleum Institute) data book. Also, a programmable calculator can perform bubble-point and dew-point calculations, with over 10 components, without difficulty. 

Estimating the unknown but required starting values of conditions and compositions is an important and sensitive part of these calculations. The composition of the feed is always known, as is the composition of one of the two phases in bubble and dew point calculations. With the Chao-Seader, Grayson-Streed, and Lee-Erbar-Edmister methods, it is possible to assume that both phases have the composition of the feed for the first trial. This assumption leads to trouble with the Soave-Redlich-Kwong, the Peng-Robinson and the Lee-Kesler-Ploecker... 

Alternatively, obtain the lefthand side of Eq, (1.16) for dew-point calculation, If smaller than unity, decrease temperature. If greater than unity, increase temperatuie. Repeat steps 2 and 3 until converged,... 

This modified Raoult s law was used for data reduction in Sec. 11.6. Bubble- and dew-point calculations made with Eq. (11.74) are, of course, somewhat simpler than those shown by Figs. 12.12 through 12.15. Indeed, the BUBL P calculation yields final results in a single step, without iteration. The additional assumption of liquid-phase ideality (yk - 1), on the other hand, is justified only infrequently. We note that yk for ethanol in Table 12.1 is greater than 8. 

Thus for dew-point calculations, where the y-, are known, the problem is to find the set of K-values that satisfies Eq. (14.35). 

DEW T. The scheme for this dew-point calculation is shown in Fig. 12.15. Since we know neither the xk values nor the temperature, all values of both 4>fc and yk are set equal to unity. Iteration is again controlled by T, and here we find an initial value by... 

There are three basic phase equilibrium calculations (1) a flash calculation - phase split at specified conditions, (2) bubble point calculation, and (3) dew point calculation. For bubble and dew points, there are two types of calculations. First, the temperature is specified and the pressure is calculated. The alternative occurs when the pressure is specified and the temperature is calculated. 

The gas oil used was a typical hydrotreated fraction with a high content of aromatics. The detailed properties of the feedstock can be examined in Table I (5). Gas oil condensation in the sampling lines was found negligible from experimental observation. In addition, dew point calculations at temperatures and pressures prevalent, after sample evacuation, in the vacuum box confirmed the negligible condensation of hydrocarbons in the sampling system. 

The composition of the vapor was given and that of the liquid was calculated therefore, this was a [dew-point( calculation. 

Once you have a Txy diagram like that of Figure 6.4-1, bubble- and dew-point calculations become trivial. To determine a bubble-point temperature for a given liquid composition, go to the liquid curve on the Txy diagram for the system pressure and read the desired temperature from the ordinate scale. (If you are not sure why this works, go back and consider again how the curve was generated.) You can then move horizontally to the vapor curve to determine the composition of the vapor in equilibrium with the given liquid at that temperature. 

This would correspond to the dew-point calculation as performed for a vapor-liquid equilibrium condition. That is, it would correspond to a point or locus of points on the saturated vapor curve, as distinguished from the saturated liquid curve. (For a single or pure component, they are one and the same.)... 

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