Liquid phase activity coefficient UNIQUAC equation

Here y/ and are the corresponding activity coefficients of component i in phase 1 and phase 2, x, and x3 are the mole fractions of component i in the system and in phases 1 and 2, respectively. The interaction parameters between water, ethanol, cyclohexane are used to estimate the activity coefficients from the UNIQUAC. Equations 1 and 2 are solved for the mole fraction (x) of component i in the two liquid phases. This method of calculation gives a single tie line. 

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

The only quantities that are different in these equations for the two liquid phases are the activity coefficients, y/ and y" Equations suitable for calculating activity coefficients for liquid-liquid systems include the NRTL and UNIQUAC equations (Chapter 1). By combining Equations 2.31a and 2.31b with Equation 2.30, the following is obtained for the mixed A -value ... 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

Given a prediction of the liquid-phase activity coefficients, from say the NRTL or UNIQUAC equations, then Equations 4.69 and 4.70 can be solved simultaneously for x and x . There are a number of solutions to these equations, including a trivial solution corresponding with x[ = x[. For a solution to be meaningful ... 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Equilibrium compositions of liquid phases at equilibrium are calculated by equating the component fugacities, similar to vapor-liquid equilibrium calculations, described in more detail in Chapter 2. The activity coefficients may be calculated by equations presented in Section 1.3.3, in particular the UNIQUAC and NRTL equations. The composition dependence of these equations is developed to the point where the same equation with the same constants can predict activity coefficients over wide ranges of composition, thus allowing it to predict two immiscible liquid phases at equilibrium. 

Another point that should be observed in extraction calculations is the non-ideal nature of the system, which is responsible for the occurrence of two liquid phases in equilibrium. The liquid-liquid equilibrium distribution coefficients, or A -values, are highly composition-dependent and must be calculated by appropriate methods, namely those based on liquid activity coefficients. The NRTL and UNIQUAC liquid activity equations (Chapter 1) are among the more accurate ones for predicting liquid-liquid equilibria. The A -Value is defined as the ratio of the mole fraction of a component in one liquid phase to its mole fraction in the other, and is calculated as... 

Activity coefficients are generally predicted by one of the Wilson, UNIQUAC, NRTL, or van Laar methods. The Wilson and UNIQUAC methods are presented briefly here. Most chemical engineering thermodynamics textbooks have a section on phase equilibria that can provide more detailed descriptions. The Wilson equation [1] is only used with miscible fluids. For highly non-ideal fluids and for systems in which liquid-liquid splitting occurs, the NRTL method is applicable [2], When no experimental data are available, the UNIQUAC method can be used [3,4]. 

Laar Margules Wilson nonrandom, two liquid phases (NRTL), or Renon-Prausnitz and Universal Quasi-Chemical Activity Coefficients (UNIQUAC). All of these equations have two constants except for the NRTL, which has three. 

Using one of these activity coefficient equations it is possible to calculate liquid-liquid equihbrium (LLE) behavior of multicomponent hquid systems. Consider, for example, the ternary system of Figure 1. A system of overall composition A splits into two liquid phases B and C. The calculation of compositions of B and C is analogous to the flash ciculation of vapor-liquid equilibrium problems. By using the UNIQUAC equations to obtain the partition coefficients, Kj, this problem can be solved for any composition A of the overall system. The calculations are lengthy but computer programs for this purpose (2) have been published. In this paper simpler approximate methods for phase equilibrium problems of environmental interest is sought. For the moment it is sufficient to note that the activity coefficients provide the means of complete liquid-liquid equihbrium computations. 

In an attempt to place calculations of liquid-phase activity coefficients on a simpler, yet more theoretical basis, Abrams and Prausnitz used statistical mechanics to derive a new expression for excess free energy. Their model, called UNIQUAC (universal qua si-chemical), generalizes a previous analysis by Guggenheim and extends it to mixtures of molecules that differ appreciably in size and shape. As in the Wilson and NRTL equations, local concentrations are used. However, rather than local volume fractions or local mole fractions, UNIQUAC uses the local area fraction 0,j as the primary concentration variable. 

The UNIFAC method for predicting liquid-phase activity coefficients is based on the UNIQUAC equation (5-72), wherein the molecular volume and area parameters in the combinatorial terms are replaced by... 

Most of the empirical and semitheoretical equations for liquid-phase activity coefficient listed in Table 5.3 apply to liquid-liquid systems. The Wilson equation is a notable exception. As examples, the van Laar equation will be discussed next, followed briefly by the NRTL, UNIQUAC, and UNIFAC equations. 

Vapor-Liquid Equilibrium Data Collection (Gmehling et al., 1980). In this DECHEMA data bank, which is available both in more than 20 volumes and electronically, the data from a large fraction of the articles can be found easily. In addition, each set of data has been regressed to determine interaction coefficients for the binary pairs to be used to estimate liquid-phase activity coefficients for the NRTL, UNIQUAC, Wilson, etc., equations. This database is also accessible by process simulators. For example, with an appropriate license agreement, data for use in ASPEN PLUS can be retrieved from the DECHEMA database over the Internet. For nonideal mixtures, the extensive compilation of Gmehling (1994) of azeotropic data is very useful. 

Calculate the solubility of benzene(2) in ethanol(l) at 260 K. The activity coefficients in the liquid phase should be taken into account by the UNIQUAC equation. The UNIQUAC parameters and melting data are ... 

Here and are the corresponding activity coefficients of component i in extracted phase and raffinate phase. The UNIQUAC equation for the liquid-phase activity coefficient is represented as follows ... 

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