Low Pressure Vapor-Liquid Equilibrium

Separations using, Distillation, Extraction, Gas Absorption, etc., represent the main unit operations in the Chemical and Petroleum Industries, often reaching 50% of the total plant cost. 

Essential for the successful design and operation of such units is the relationship among the compositions of the phases present  

Consider, for example, the separation of a mixture of methanol and water to recover methanol of 99% purity using the packed tower discussed in Example 1.7. The relationship between the composition of the vapor bubbles and that of the liquid surrounding them at the operating conditions of pressure and temperature - from the bottom of the tower to the top - will determine the height and reflux ratio necessary to achieve the desired separation. 

This relationship represents one case of the general subject of Phase Equilibrium which becomes, thus, one of the most important areas of Chemical Engineering Thermodynamics applications. 

We will concentrate on Vapor-Liquid Equilibrium (VLE) because of its wide applicability. In addition, the methodology involved and discussed here is typical to all types of phase equilibria. Finally, for convenience reasons that will become apparent in Section 13.4, we consider in this Chapter Low Pressure VLE and High Pressure VLE, in the next one. 

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These results are representative of values obtained for vapor phases at typical conditions of low-pressure vapor/liquid equilibrium. 

Once the interaction energies were obtained, they were used to calculate the parameters in the UNIQUAC and Wilson models given by Eq. (24). To test the validity of the method, low-pressure vapor-liquid equilibrium (VLE) predictions were made for several binary aqueous systems. The calculations were done using the usual method assuming an ideal vapor phase (Sandler, 1999). Figures 7 and 8 show the low-pressure VLE diagrams for the binary aqueous mixtures of ethanol and acetone [see Sum and Sandler (1999a,b) for results for additional systems and values of the... 

The g sni solution models fit low-pressure vapor-liquid equilibrium data for many liquid solutions. These models with fitted parameters are the prime interest to be incorporated into equations of state. To set Equation (4.433) to be equal to these g sm s, the v s in the equation are set to the standard-state pure-liquid volumes of a low-pressure vapor-liquid equilibrium mixture. Novenario et al. [19] calculated the saturated liquid volume for a large number of substances at low pressures with the PR eos and expressed the volume as a multiple of b. 

The pressure of a saturated Peng-Robinson liquid with k= 1.15 is between 0 and 2 atm for all the substances tested. Since Gibbs energy of a liquid is insensitive to pressure at low pressures, vT = 1.15 fc is adopted as the standard state in PR eos for pure liquids at low-pressure vapor-liquid equilibrium. Similarly, the volume of the liquid mixture is set to be v = 1.15 b. Substitution of Equation (4.434) into Equation (4.433) leads to... 

Be able to correlate the low-pressure vapor-liquid equilibrium data for a nonideal liquid mixture (that is. to be able to compute the conditions of vapor-liquid equilibrium and develop. r-v, T-x y, and P-x-y diagrams for nonideal mixtures using activity coefficient models (the y -cj) method) (Sec. 10.2)... 

Low-Pressure Vapor-Liquid Equilibrium in Nonideal Mixtures 519... 

LOW-PRESSURE VAPOR-LIQUID EQUILIBRIUM IN NONIDEAL MIXTURES... 

As another example of low-pressure vapor-liquid equilibrium, we consider the n-pentane-propionaldehyde mixture at 40.0 C. Eng and Sandler took data on this system using the dynamic still of Fig. 10.2-5. The x-y-P-T data in Table 10.2-1 and Fig. 10.2-8fl and b were obtained by them. (Such data can be tested for thermodynamic consistency see Problem 10.2-12.) As is evident, this system is nonideal and has an azeotrope at about 0.656 mole fraction pentane and 1.3640 bar. We will use these data to test the UNIFAC prediction method. 

Finally, because of its rigorous mixing rules, and the success of the empiric correlations for the estimation of Bjf and By, the virial equation finds extensive use in the estimation of vapor fugacities for low pressure vapor-liquid equilibrium calculations, especially in systems containing polar components. The liquid phase fugacities, in such cases, are calculated using the standard state fugacity approach that will be discussed in Section 11.10. 

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