Activity Coefficients liquids

Four model forms will be discussed in this section for the calculation of the liquid activity coefficient as functions of mole fractions and system temperamre. They are van Laar, Wilson, nonrandom two-liquid (NRTL), and UNIQUAC. In these four model forms, van Laar and Wilson cannot describe LLE. On the other hand, NRTL and UNIQUAC can be used for the equilibrium of all phases. 

For a two-component system, there are six parameters that need to be determined from phase equilibrium data. They are ay, ap, by, bji, cy = cp, and dy = dp. These binary parameters are available in the Aspen Physical Property System for a large number of component pairs. 

Wilson Model. This model can also be used for highly nonideal systems, especially alcohol-water systems. The equation for the calculation of Uquid activity coefficient is  

The above model parameters in Eq. (2.21) are unsymmetrical. The Aspen Physical Property System has a large number of built-in binary parameters for the Wilson model. The binary parameters have been regressed using the vapor-liquid equilibrium data from the Dortmund 

Nonrandom Two-Uquid (NRTL) Model. This model is recommended for highly nonideal chemical systems and can be used for both VLB and LLE applications. The equation for the NRTL model is  

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It must be emphasised that extreme caution needs to be exercised when using predicted values for liquid activity coefficients in design calculations. 

In order to model liquid-phase nonideality at moderate pressures, the liquid activity coefficient y, must be known ... 

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. 

Mixture property Define the model to be used for liquid activity coefficient calculation, specify the binary mixture (composition, temperature, pressure), select the solute to be extracted, the type of phase equilibrium calculation (VLE or LLE) and finally, specify desired solvent performance related properties (solvent power, selectivity, etc.)... 

Vasiltsova, T.V. et al.. Thermodynamic properties of mixtures containing ionic liquids. Activity coefficients of ethers and alcohols in l-methyl-3-ethyl-imid-azolium bis(trifluoromethyl-sulfonyl)imide using the transpiration method, /. Chem. Eng. Data, 50,142,2005. 

For systems of the type under consideration, that is, consisting of two volatile components and a salt, there has been controversy over whether binary or ternary forms of correlating equations should be used, and over whether the presence of the salt should be included in the liquid mole fraction data used to calculate liquid activity coefficient values for the two volatile components. One point, however, is absolutely clear. It would be thermodynamically incorrect not to acknowledge the presence of the salt in calculating liquid-phase activity coefficients. 

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. 

Equation (4.5) is probably the form that first comes to mind when Henry s law is mentioned. It is applicable up to two atmospheres of pressure (P) and liquid mole fractions (x,) of up to 1%. Higher values of pressure or liquid mole fractions require corrections using vapor phase fugacity coefficients and liquid activity coefficients or fugacity coefficients. 

The Lee-Erbar-Edmister method is of the same type, but uses different expressions for the fugacity and activity coefficients. The vapor phase equation of state is a three-parameter expression, and binary interaction corrections are included. The liquid phase activity and fugacity coefficient expressions were derived to extend the method to lower temperatures and to improve accuracy. Binary interaction terms were included in the liquid activity coefficient equation. 

Note the use of activities, as well as of an equilibrium constant based on activities. The kinetic constants for autocatalyzed and catalyzed reactions, k and k, were determined from initial reaction rates with liquid activity coefficients calculated by UNIQUAC. Near chemical equilibrium the fCT is about 6, while Kx is about 5. Table 8.7 gives activation energies and pre-exponential factors obtained by nonlinear regression. The simulation shows tbat the autocatalysis effect is neghgible below 150 °C, but it might increase to 20% at 180 °C. 

Effect of composition. The main effect of composition on K-values and relative volatilities is a result of the effect of composition on the liquid activity coefficient. Composition also has an effect on the fugacify coefficient. The latter effect is generally small at low pressorea. 

Flgurs 1J Effect of composition an liquid activity coefficients, fa) For the positive-deviation system n-propanol water at 1 atm (6) for toe negative-deviation system acetone-chloroform at 1 atm. (From R. H. Ferry, Chemical Engineer Handbook, 5th ed.. 1973, Copyright by McGraw-Hill. Inc. Reprinted by permission.)... 

ELBRO-FV cannot model water as a solvent, otherwise it was often better than UNIFAC-FV in accuracy. For water-containing systems UNIFAC liquid activity coefficient estimations should be used with ELBRO-FV polymer activity coefficients. 

The Scatchard-Hildebrand regular-solution model expresses the liquid activity coefficients y in a binary mixture as... 

Equilibrium Data Collection in the Chemistry Data Series published by DECHEMA. VLE calculations are performed assuming an ideal vapor phase and a standard Wilson liquid activity coefficient model. This takes the form... 

Mixtures may also form two or more liquid phases at equilibrium. For example, a 50/50 mol% liquid mixture of toluene in water will partition into a water-rich liquid phase and a toluene-rich liquid phase. We just used infinite-dilution /f-values as a means to predict azeotropic behavior. We can argue that we should use infinite-dilution liquid activity coefficients to alert us to the potential for liquid/liquid behavior. We do so as follows. 

We start by computing the infinite-dilution binary data shown in Table IX. The upper values are X-values at the boiling point of the more plentiful species. We will also need liquid activity coefficients if we wish to consider extraction processes the lower values in each entry are infinite-dilution binary liquid activity coefficients at ambient conditions. 

We see that we have both an upper bound and a lower bound on the column reflux ratio. Does having an upper bound make intuitive sense We have set the. solvent flow proportional to the distillate product flow i.e., S = RsD. As we increase the reflux ratio R, the ratio of solvent feed flow. RsD, to reflux flow, RD, decreases. This decreases the solvent concentration throughout the column, thus reducing its impact on the liquid activity coefficients that we are using to separate A from B. With an infinite reflux ratio, the. solvent flow reduces to zero, and we have a normal column operating at total reflux which we know cannot separate A from B. 

As in Example 4, the EXTRACT block in the Aspen Plus process simulation program (version 12.1) is used to model this problem, but any of a number of process simulation programs such as mentioned earlier may be used for this purpose. The first task is to obtain an accurate fit of the liquid-liquid equilibrium (LLE) data with an appropriate model, realizing that liquid-liquid extraction simulations are very sensitive to the quality of the LLE data fit. The NRTL liquid activity-coefficient model [Eq. (15-27)] is utilized for this purpose since it can represent a wide range of LLE systems accurately. The regression of the NRTL binary interaction parameters is performed with the Aspen Plus Data Regression System (DRS) to ensure that the resulting parameters are consistent with the form of the NRTL model equations used within Aspen Plus. 

Therefore, if we can devise an equation for as a function of the liquid mole fraction x we can create an expression for the liquid activity coefficient, y, as a function of the liquid mole fraction. 

T,-,- binai-y interaction parameter in liquid activity coefficient models... 

The binary constants Ay and A are determined from binary VLE data. For a three-component system (Wohl, 1946), the liquid activity coefficients are calculated by Equation 1.35a ... 

The UNIQUAC equation is the basis for the development of the group contribution method, the UNIFAC equation, which predicts liquid activity coefficients from component structures on the basis of interactions between chemical functional groups. 

A liquid solution of ethanol (1) and benzene (2) at 35°C contains 30% mole ethanol. Infinite dilution activity coefficients are given yr = 8.9, Y2°° = 4.1. The vapor pressures of ethanol and benzene at 35°C are 16.625 and 49.875 kPa, respectively. Calculate the A -valucs of ethanol and benzene, the vapor phase composition, and the total pressure. The Margules liquid activity coefficient equation may be used, and the vapor phase may be assumed an ideal gas. 

The calculations for this example are based on the Margules liquid activity coefficient equation with the following parameters ... 

The liquid phase is a non-ideal solution, for which liquid activity coefficients can be predicted with good accuracy by the Wilson equation (Equation 1.36). The vapor phase is assumed to behave as an ideal gas at the relatively low pressure of 35 kPa. Under these conditions, the K-values may be calculated by Equation 1.29a. 

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