Dew-point calculation for

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. 

Bubble Point-Dew Point Calculations for Composition-Independent K- Values... 

Low tray efficiency High tray AP Reboiler tube leaks Corrosion to tower shell Dew-point calculation for overhead... 

The second example deals with a dew-point calculation for a typical natural gas mixture based on the BWR-11 equation of state. 

Section 4.1 via Section 4.1.2 formally illustrates vapor-Uquid equilibria vis-a-vis distillation in a closed vessel along with bubble-point and dew-point calculations for multicomponent systems. How vapor-liquid equilibrium is influenced by chemical reactions in the liquid phase is treated in Section 5.2.1.2, where two subsections, 5.2.1.2.1 and 5.2.1.2.2, deal with reactions influencing vapor-Uquid equilibria in isotopic systems. We next encounter open systems in Chapter 6. The equations of change for any two-phase system (e.g. a vapor-Uquid system) are provided in Section 6.2.1.1 based on the pseudo-continuum approach for the dependences of species concentrations... 

We proceed, therefore, with a qualitative and quantitative consideration of activity coefficients and later. Section 13.16, we will see how they are used in carrying out bubble and dew point calculations for real solutions. 

We discussed bubble and dew point calculations for ideal solutions in Examples 13.2 through 13.7. And in Examples 13.9 and 13.11 we carried out B.P. pressure calculations for nonideal solutions assuming, however, vapor phase ideality. 

Example 8.6 illustrates how you solve a dew-point calculation for a binary mixture of a non-ideal liquid and a nonideal gas with T known. This problem corresponds to quadrant I in Figure 8.2. Develop an analogous solution for the bubble point with the liquid-phase mole fractions and T known (quadrant II). As in Example 8.6, use the van der Waals equation for vapor nonideality and the three-suffix Margules equation for liquids. Assume that critical properties, liquid volumes, and Antoine coefficients for each species are readily available and that the three-suffix Margules parameters have been determined. 

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... 

BUDET calculates the bubble-point temperature or dew-point temperature for a mixture of N components (N < 20) at specified pressure and liquid or vapor composition. The subroutine also furnishes the composition of the incipient vapor or liquid and the vaporization equilibrium ratios. 

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) ... 

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]. 

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). 

In Sec. 10.5 we treated dew- and bubble-point calculations for multicomponent systems that obey Raoult s law [Eq. (10.16)], an equation valid for low-pressure VLE when an ideal-liquid solution is in equilibrium with an ideal gas. Calculations for the general case are carried out in exactly the same way as for Raoult s law,... 

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... 

Calculate dew-point equilibrium for the feed. A vapor is at its dew-point temperature when the first drop of liquid forms upon cooling the vapor at constant pressure and the composition of the vapor remaining is the same as that of the initial vapor mixture. At dew-point conditions, K, = A = Ki Xt, or Xj = Nj /Kj, and Nj /Kj = 1.0, where Yj is the mole fraction of component i in the vapor phase, Xi is the mole fraction of component i in the liquid phase, A is the mole fraction of component i in the original mixture, and Kj is the vapor-liquid equilibrium K value. 

Calculation of the Dew-Point Pressure for a Two-Component System. At the dew point the system is essentially all vapor except for an infinitesimal amount of liquid- Under these conditions the composition of the vapor is equal to the overall composition. According to equation 7... 

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. 

---