Activity coefficients, liquid phase NRTL equation

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 ... 

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. 

A distillation column is separating 100 mol/s of a 30 mol% acetone, 70 mol% methanol mixture at atmospheric pressure. The feed enters as a saturated liquid. The column has a total condenser and a partial reboiler. We desire a distillate with an acetone content of 72 mol%, and a bottoms product with 99.9 mol% methanol. A reflux ratio of 1.25 the minimum will be used. Calculate the number of ideal stages required and the optimum feed location. VLE for this system is described by the modified Raoult s law, with the NRTL equation for calculation of liquid-phase activity coefficients, and the Antoine equation for estimation of the vapor pressures. 

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. 

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 most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

Physical property data for many of the key components used in the simulation for the ethanol-from-lignocellulose process are not available in the standard ASPEN-Plus property databases (11). Indeed, many of the properties necessary to successfully simulate this process are not available in the standard biomass literature. The physical properties required by ASPEN-Plus are calculated from fundamental properties such as liquid, vapor, and solid enthalpies and density. In general, because of the need to distill ethanol and to handle dissolved gases, the standard nonrandom two-liquid (NRTL) or renon route is used. This route, which includes the NRTL liquid activity coefficient model, Henry s law for the dissolved gases, and Redlich-Kwong-Soave equation of state for the vapor phase, is used to calculate properties for components in the liquid and vapor phases. It also uses the ideal gas at 25°C as the standard reference state, thus requiring the heat of formation at these conditions. 

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... 

The fugacity coefficient is usually obtained by solving an equation of state (e.g., Peng-Robinson Redlich-Kwong). The activity coefficient is obtained from a liquid phase activity model such as Wilson or NRTL (see Walas, 1985). 

The development of equations that successfully predict multicomponent phase equilibrium data from binary data with remarkable accuracy for engineering purposes not only improves the accuracy of tray-to-tray calculations but also lessens the amount of experimentation required to establish the phase equilibrium data. Such equations are the Wilson equation (13), the non-random two-liquid (NRTL) equation (14), and the local effective mole fractions (LEMF) equation (15, 16), a two-parameter version of the basically three-parameter NRTL equation. Larson and Tassios (17) showed that the Wilson and NRTL equations predict accurately ternary activity coefficients from binary data Hankin-son et al. (18) demonstrated that the Wilson equation predicts accurately... 

The compositions of the vapor and liquid phases in equihbrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single hquid is in equihbrium with its vapor, tlie general nature of Fig. 14.18 is not different in any essential way from that of Fig. 10.8(d). Since limited miscibility imphes highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, vahd for a species at hifinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates actual behavior for only a very small composition range. Thus is large, and its composition dependence is often not adequately represented by simple equations. Nevertheless, the NRTL and UNI-QUAC equations and the UNIFAC method (App. H) provide suitable correlations for activity coefficients. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

Compilations of infinite-dilution activity coefficients, when available for the solute of interest, may be used to rank candidate solvents. Partition ratios at finite concentrations can be estimated from these data by extrapolation from infinite dilution using a suitable correlation equation such as NRTL [Eq. (15-25)]. Examples of these lands of calculations are given by Walas [Phase EquU ria in Chemical Engineering (Butterworth-Heinemann, 1985)]. Most activity coefficients available in the literature are for small organic molecules and are derived from vapor-liquid equilibrium measurements or azeotropic composition data. 

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. 

Typical non-ideal binaries forming two liquid phases is the n-butanol-water system at 1 atmospheric pressure. A solution with approximately 2 mole% n-butanol in water exists at equilibrium with another liquid phase with approximately 38 mole% n-butanol in water. The fugacity of n-butanol in both phases is about 0.48. A phase diagram of this binary is illustrated in Figure 1.16. The curves, which closely match the experimental data, are based on calculations using the NRTL equation for activity coefficients. 

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]. 

If the equilibrium data are given in analytical form, a McCabe-Thiele computer program can be used. Appendix F is an example of a Mathcad programs to implement the McCabe-Thiele method (Hwalek, 2001). It generates the required VLE data from the Antoine equation for vapor pressure and the NRTL equation for liquid-phase activity coefficients. Appendix F-l is for column feed as saturated liquid Appendix F-2 is for column feed as saturated vapor. 

Predict and plot liquid-phase activity coefficients over the entire range of solubility using the NRTL equation with 012 = 0.30. 

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. 

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. 

Consider mixtures of benzene(l), acetonitrile(2), and water(3) at 1.0133 bar, 333 K. Binary liquid mixtures of benzene and water are almost completely immiscible, so we expect the ternary to have a water-rich phase and an organic-rich phase with acetonitrile distributed between them. To model the activity coefficients, we choose the NRTL equation (see Appendix J) and use parameter values from Table J.l [12]. 

The introductory discussion of models for liquid-phase activity coefficients, presented in Chapter 5, included a description of the Wilson equation, which is appropriate for many nonelectrolyte mixtures that exhibit large deviations from ideality. However, the Wilson model cannot correlate liquid-liquid equilibrium data, and therefore it cannot be used in LLE and VLLE calculations. To overcome this deficiency, Renon and Prausnitz [1] devised the NRTL model for (NonRandom, Two-Liquid). 

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