Activity Coefficient Methods

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Other important equations of state which can be related to fugacity and activity have been developed by Redlich-Kwong [56] with Chueh [10], which is an improvement over the original Redlich-Kwong, and Palmer s summary of activity coefficient methods [51]. 

Unless liquid phase activity coefficients have been used, it is best to use the same equation of state for excess enthalpy that was selected for the vapour-liquid equilibria. If liquid-phase activity coefficients have been specified, then a correlation appropriate for the activity coefficient method should be used. 

Solubility modelling with activity coefficient methods is an under-utilized tool in the pharmaceutical sector. Within the last few years there have been several new developments that have increased the capabilities of these techniques. The NRTL-SAC model is a flexible new addition to the predictive armory and new software that facilitates local fitting of UNIFAC groups for Pharmaceutical molecules offers an interesting alternative. Quantum chemistry approaches like COSMO-RS [25] and COSMO-SAC [26] may allow realistic ab-initio calculations to be performed, although computational requirements are still restrictive in many corporate environments. Solubility modelling has an important role to play in the efficient development and fundamental understanding of pharmaceutical crystallization processes. The application of these methods to industrially relevant problems, and the development of new... 

Activity coefficient methods work fairly well at temperatures well below the critical, at which the liquid phase is largely incompressible, and up to moderate pressures. 

The term (a, /xi) is called the activity coefficient. Methods of measuring the activity and activity coefficient are given in Chapter 5. Tabulations of Gibbs energies of mixing of numerous systems defined in various ways are available in standard reference books, such as Hultgren et al. (1973) and Kubaschewski et al. (1993). 

The UNIFAC (UNIQUAC functional group activity coefficient) method is an extension of the UNIQUAC (Universal quasi chemical) method, which has been used widely in chemical process engineering to describe partitioning in organic systems as occur in petroleum and chemical processing (Fredenslund et al., 1975,1977). It has been applied less frequently to aqueous systems. It expresses the activity coefficient as the sum of a "combinational" component, which quantifies the nature of the area "seen" by the solute molecule, and a "residual" component, which is deduced from group contributions. Arbuckle (1983,1986), Banerjee (1985), Banerjee and Howard (1988), and Campbell and Luthy (1985) have tested the applicability of the method to water solubility. 

For the analytical equations, there are two methods to compute the vapour-liquid equilibrium for systems. The equation of state method (also known as the direct or phi-phi method) uses an equation of state to describe both the liquid and vapour phase properties, whereas the activity coefficient method (also known as the gamma-phi approach) describes the liquid phase via an activity coefficient model and the vapour phase via an equation of state. Recently, there have also been modified equation of state methods that have an activity coefficient model built into the mixing mles. These methods can be both correlative and predictive. The predictive methods rely on the use of group contribution methods for the activity coefficient models such as UNIFAC and ASOG. Recently, there have also been attempts to develop group contribution methods for the equation of state method, e.g. PRSK. " For a detailed history on the development of equations of state and their applications, as well as activity coefficient models, refer to Wei and Sadus, Sandler and Walas. ... 

In which yi is the activity coefficient of component i in the solution, yf is the combinatorial part and ytR is the residual part. Up to this point, all of the group contribution and activity coefficient methods (i.e. NRTL-SAC) have been the same, but the methods in which the activities have been calculated are different. In the UNIFAC model, the combinatorial part for component i is found from the following equation [8] ... 

The goal of predictive phase equilibrium models is to provide reliable and accurate predictions of the phase behavior of mixtures in the absence of experimental data. For low and moderate pressures, this has been accomplished to a considerable extent by using the group contribution activity coefficient methods, such as the UNIFAC or ASOG models, for the activity coefficient term in eqn. (2.3.8). The combination of such group contribution methods with equations of state is very attractive because it makes the EOS approach completely predictive and the group contribution method... 

Furthermore, for most vapor mixtures allow pressure, 0,- is very close to unity (there are exceptions to this assumption for example, associating gases such as hydrogen fluoride or acetic acid), and that leads to the equilibrium relation we used in this monograph to calculate the vapor-liquid phase equilibrium by the direct use of activity coefficient methods ... 

Click and then the box on the left (in the Data Browser option). The part of the process represented by that box is then described. You can also click on the box and then the FI key to obtain the same information. The Help menu provides detailed help in all areas. For example, the Help/Physical Property Methods/Choosing a Property Method gives advice about which thermodynamic model is recommended for different applications. The Guidelines for Choosing a Property Method and Guidelines for Choosing an Activity Coefficient Method are sub-menus that outline decision trees to guide your choice. 

Bofh EOS and activity-coefficient methods require binary interaction parameters. In process simulation software, the necessary parameters may already be built into a data bank. Sometimes, parameters for the system of interest may be found in the literature. If not, however, the parameters must be fitted to mixture data. 

The UNIFAC (universal functional activity coefficient) method [16] is similar to the ASOG method and is based on the four postulates of Wilson and Deal [13] regarding solution of groups. In UNIFAC, the activity coefficient is made of two parts. 

Equation (1.6-8) has been applied by Snave to correlate solubilitses of solid carbon dioxide in liquid hydrocarbons at low temperatures. Alternatively, My res and Prausnitz. Preston and Prausnitz,3 and more tacantly Teller and Knapp6 also coreslated such solubilities but they ured the conventional activity-coefficient method Eqs, (1,6-3) and (1.6-6). 

It uses activity coefficient methods to calculate vapor-liquid equilibrium. It will estimate a minimum reflux ratio (Rmin) assuming no pinch point in the rectifying section. The actual reflux ratio (RR) is set as a multiple of Rmin (R = C Rmin). 

It has been customary to apply an activity coefficient method to aid in the prediction of vapor-liquid equilibria of polar mixtures. At high pressures approaching the critical state of the fluid mixture, the activity coefficient method requires such thermodynamic properties as partial molar volumes or partial molar heats of solution that are very difficult,... 

Equation 19 shows that the activity coefficient method for high-pressure fluid-phase equilibria requires information for the partial molar volume, Vi1-, which is very difficult to obtain. 

As an alternative, group contribution methods can be applied to predict the required activity coefficients. Methods like UNIFAC or modified UNIFAC are based on the functional groups of the components and group interaction parameters, which are fitted to a large number of experimental data. The calculated activity coefficients therefore have a high accuracy (Gmehling et ah, 2002) and can be used for reactive systems. Especially for very fast reactions, group contribution methods are often recommended. 

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