Vapor-liquid equilibrium multicomponent solutions

To calculate the multicomponent vapor-liquid equilibrium, equilibrium constants for chemical reactions 1-9 are taken from literature in comparison to the original publication, in the present work different numerical values for the second dissociations of hydrogen sulfide and sulfur dioxide were chosen (cf. Appendix III). Henry s constants are evaluated from single solute solubility data without neglecting Poynting corrections ... 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

The vapor pressure curve forms the basis for the description of vapor-liquid equilibrium for a pure fluid. As the temperature increases, the vapor pressure curve for the vapor-liquid situation ends at the critical pressure. In the case of a binary or multicomponent solution, the critical point is not necessarily a maximum with respect to either temperature or pressure. It is then possible for a vapor or liquid to exist at temperature or pressures higher than the critical pressure of the mixture. At constant temperature, it is then possible for condensation to take place as the pressure is decreased. At constant pressure, condensation may take place as the temperature is increased. Vaporization can take place at constant temperature as the pressure is increased and decreased. This unusual behavior can be useful in some process situations, for example, in the recovery of natural gas from deep wells. If the conditions are right, liquefaction of the product stream is possible. At the same time, the heavier components of the mixture may be separated from the lighter components. 

Now we will use the ideal solution model to develop a mathematical description of vapor-liquid equilibrium in a multicomponent solution. We will make the assumption that we have a system that is separated into a coexisting vapor and liquid phase. The vapor phase will be assumed to behave like an ideal gas, while the liquid phase will be assumed to behave as an ideal solution. 

The activity coefficient of a component in a mixture is a function of the temperature and the concentration of that component in the mixture. When the concentration of the component proaches zero, its activity coefficient approaches the limiting activity coefficient of th component in the mixture, or the activity coefficient at infinite dilution, y . The limiting activity coefficient is useful for several reasons. It is a strictly dilute solution property and can be used dir tly in nation 1 to determine the equilibrium compositions of dilute mixtures. Thus, there is no reason to extrapolate uilibrium data at mid-range concentrations to infinite dilution, a process which may introduce enormous errors. Limiting activity coefficients can also be used to obtain parameters for excess Gibbs energy expressions and thus be used to predict phase behavior over the entire composition range. This technique has been shown to be quite accurate in prediction of vapor-liquid equilibrium of both binary and multicomponent mixtures (5). 

The Wilson equation is widely used for many nonpolar, polar, and associated solutions in vapor-liquid equilibrium systems. It is often best for hydrogen-bonded substances. For multicomponent solutions, it makes effective use of binary-solution parameters to give good results, but it cannot predict the liquid immiscibihty phenomena. 

Table 2.4-4 Adsorbed solution theories for the description or prediction of multicomponent adsorption equilibria. In the light gray area new theoretical models are listed. The theories in the double-framed area require experimental data of binary adsorptives. VLE denotes vapor liquid equilibrium. The meaning of VAE is vapor adsorbate equilibrium...

The general principles of design of multicomponent fractionators are the same in many respects as those for binary systems, but the dearth of adequate vapor-liquid equilibrium data imposes severe restrictions on their application. These are especially needed for liquids which are not ideal, and the danger of attempting new designs without adequate equilibrium data or pilot-plant study for such solutions cannot be overemphasized. Inadequate methods of dealing with tray efficiencies for multicomponents represent another serious problem still to be solved. 

In a multicomponent system of n components (i = 1,..., k,. .ri], to obtain the compositions of the vapor phase and the liquid phase leaving the separator under equilibrium, along with the total molar flow rates of the liquid product and the vapor product from the flash drum for a given feed condition, will require the solution of the appropriate governing equations. For a system of n components, there are n equations (6.3.53) describing vapor-liquid equilibrium, n equations (6.3.54) or (6.3.55), describing Xu in terms of Xif or in terms of Xif and one equation. 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

We take up the topic of multicomponent equilibria by drawing a distinction between systems in which several or all components are present in the two equilibrated phases, and those in which only one component plays a key role by distributing itself in significant amounts between the phases in question. Vapor-liquid equilibria of mixtures and other similar multicomponent systems involving the appearance of several solutes in each phase are the prime example of the former, while distributions of a single component occur in a number of different contexts, which we take up in turn below. They include the equilibrium of a single gas with a liquid solvent, or a solid (gas... 

The general VLE problem involves a multicomponent system of N constituent species for which the independent variables are T,P,N -I liquid-phase mole fractions, and N - I vapor-phase mole fractions. (Note that = 1 and yi = 1, where Xi and yi represent liquid and vapor mole fractions respectively.) Thus there are 2N independent variables, and application of the phase rule shows that exactly N of these variables must be fixed to establish the intensive state of the system. This means that once N variables have been specified, the remaining N variables can be determined by simultaneous solution of the N equilibrium relations ... 

Calculation of Bubble-Point Pressure and Dew-Point Pressure Using Equilibrium Constants. Since the total pressure P

bubble-point and dew-point pressure as was done in the case of ideal solutions. A method will now be presented for calculating the bubble-point pressure and the dew-point pressure, which is applicable to both binary and multicomponent systems which are non-ideal. At the bubble point the system is entirely in the liquid state except for an infinitesimal amount of vapor. Consequently, since ti, = 0 and n — n% equation 19 becomes... 

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