Vapor-liquid equilibria calculation

A vapor-liquid equilibrium calculation shows that a good separation is obtained, but the required product purity of butadiene <0.5 wt% and sulphur... 

These are general equations that do not depend on the particular mixing rules adopted for the composition dependence of a and b. The mixing rules given by Eqs. (4-221) and (4-222) can certainly be employed with these equations. However, for purposes of vapor/liquid equilibrium calculations, a special pair of mixing rules is far more appropriate, and will be introduced when these calculations are treated. Solution of Eq. (4-232) for fugacity coefficient at given T and P reqmres prior solution of Eq. (4-231) for V, from which is found Z = PV/RT. 

Haman, S. E. M. et al, Generalized Temperature-Dependent Parameters of the Redlich-Kwong of State for Vapor-Liquid Equilibrium Calculations, Ind. Eng. Chem. Process Des. Dev. 16, 1, (1977) p. 51. 

Several authors, notably Leland and co-workers (L2), have discussed vapor-liquid equilibrium calculations based on corresponding-states correlations. As mentioned in Section II, such calculations rest not only on the general assumptions of corresponding-states theory, but also on the additional assumption that the characterizing parameters for a mixture do not depend on temperature or density but are functions of composition only. Further, it is necessary clearly to specify these functions (commonly known as mixing rules), and experience has shown that if good results are to be obtained, these... 

Equation 4.26 defines the relationship between the vapor and liquid mole fractions and provides the basis for vapor-liquid equilibrium calculations on the basis of equations of state. Thermodynamic models are required for (/) and [ from an equation of state. Alternatively, Equations 4.21, 4.22 and 4.25 can be combined to give... 

These expressions form the basis for two alternative approaches to vapor-liquid equilibrium calculations ... 

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. 

Equation 12.22 relates the compositions of vapor and liquid streams passing each other in the stripping section of a column. Equation 12.22 can be used together with vapor-liquid equilibrium calculations to calculate a composition profile in the stripping section of the column, similar to that of the rectifying section of the column as described above. The calculation is started with an assumed bottoms composition and Equation 12.22 applied repeatedly with vapor-liquid equilibrium calculations working up the column. 

Either Equation 12.28 or Equation 12.32 can be used in conjunction with vapor-liquid equilibrium calculations to calculate the section profile for the middle section of the two-feed column. 

A vapor-liquid equilibrium calculation shows that a good separation is obtained but the required product purity of butadiene <0.5 wt% and sulfur dioxide <0.3 wt% is not obtained. Further separation of the liquid is needed. Distillation of the liquid is difficult because of the narrow temperature limits between which the distillation must operate. However, the liquid can be stripped using nitrogen (Figure 14.21c). 

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

The solution requires the concentration of the heptane and toluene in the vapor phase. Assuming that the composition of the liquid does not change as it evaporates (the quantity is large), the vapor composition is computed using standard vapor-liquid equilibrium calculations. Assuming that Raoult s and Dalton s laws apply to this system under these conditions, the vapor composition is determined directly from the saturation vapor pressures of the pure components. Himmelblau6 provided the following data at the specified temperature ... 

If a fluid composed of more than one component (e.g., a solution of ethanol and water, or a crude oil) partially or totally changes phase, the required heat is a combination of sensible and latent heat and must be calculated using more complex thermodynamic relationships, including vapor-liquid equilibrium calculations that reflect the changing compositions as well as mass fractions of the two phases. 

Flash Calculations. The ability to carry out vapor-liquid equilibrium calculations under various specifications (constant temperature, pressure constant enthalpy, pressure etc.) has long been recognized as one of the most important capabilities of a simulation system. Boston and Britt ( 6) reformulated the independent variables in the basic flash equations to make them weakly coupled. The authors claim their method works well for both wide and narrow boiling mixtures, and this has a distinct advantage over traditional algorithms ( 7). 

Many modifications of the original Redlich/Kwohg equation that appear in the literature are intended for special-purpose applications. The SRJt equation, developed for vapor/liquid equilibrium calculations, is designed specifically to yield reasonable vapor pressures for pure fluids. Thus, there is no assurance that molar volumes calculated by the SRK equation are more accurate than values given by the original Redlich/Kwong equation. 

Mauri, C. Unified procedure for solving multiphase-multicomponent vapor-liquid equilibrium calculation, bid. Eng. Chem. Process. Des. Dev., 19,482-489(1980). 

There are at least 20 physical property databases commercially available as on-line data services. Five of the databases listed include vapor-liquid-equilibrium calculations for mixtures. 

Moore, P. K., and Anthony, R. G., The continuous-lumping method for vapor-liquid equilibrium calculations. AIChEJ. 35, 1115 (1989). 

We conclude this discussion with one final reminder. The vapor-liquid equilibrium calculations we have shown in Section 6.4c are based on the ideal-solution assumption and the corresponding use of Raoult s law. Many commercially important systems involve nonideal solutions, or systems of immiscible or partially miscible liquids, for which Raoult s law is inapplicable and the Txy diagram looks nothing like the one shown for benzene and toluene. 

State whether you would use Raoull s law or Henry s law to perform vapor-liquid equilibrium calculations for each component in the following liquid mixtures (a) water and dissolved nitrogen (b) hexane, octane, and decane and (c) club soda or any other carbonated beverage. 

Vapor-liquid equilibrium calculations can sometimes be simplified through the use of a quantity called the relative volatility, which may be defined m terms of the tollowing depiction of vapor and liquid phases in equilibrium ... 

A spreadsheet that performs the required material and energy balances and vapor-liquid equilibrium calculations on this process unit is shown on the next page. In the test case, a 40 mole benzene-60 mole% toluene mixture is fed to the evaporator at 120°C and a pressure high enough to assure that the feed stream remains in the liquid state. The unit operates at 7 = lOO C and P = 800 mm Hg. 

The Soave/Redlich/Kwong and the Peng/Robinson equations were developed specifically for vapor/liquid equilibrium calculations (Sec. 14.2). 

The gas phase of the system will mainly consist of H20(g), NHj(g), and C02(g). In order to perform vapor-liquid equilibrium calculations with an activity coefficient model at pressures higher than ambient pressure, the activity coefficient model can be combined with an equation of state for the gases. Usually, there is no need for binary interaction parameters in the equation of state as gas phase fiigacities are only slightly dependent on these binary interaction parameters. For the equilibrium between ammonia in the liquid phase and ammonia in the vapor phase. Equation (13) gives ... 

For the vapor-liquid equilibrium calculations, at the equilibrium state the fugacities for all species i must be the same in all phases, namely... 

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