Liquid activity models

The simulation is performed with the Radfrac module in ASPEN Plus and the NRTL liquid-activity model [20]. Tracing the RCM (Figure 3.15) shows that acetone and chloroform are unstable nodes, toluene is a stable node and the maximum-boiling azeotrope acetone-chloroform is a saddle. The distillation boundary shows a strong curvature. 

To get an idea about the relative volatilities of components we proceed with a simple flash of the outlet reactor mixture at 33 °C and 9 bar. The selection of the thermodynamic method is important since the mixture contains both supercritical and condensable components, some highly polar. From the gas-separation viewpoint an equation of state with capabilities for polar species should be the first choice, as SR-Polar in Aspen Plus [16]. From the liquid-separation viewpoint liquid-activity models are recommended, such as Wilson, NRTL or Uniquac, with the Hayden O Connell option for handling the vapor-phase dimerization of the acetic acid [3]. Note that SR-Polar makes use of interaction parameters for C2H4, C2H6 and C02, but neglects the others, while the liquid-activity models account only for the interactions among vinyl acetate, acetic acid and water. To overcome this problem a mixed manner is selected, in which the condensable components are treated by a liquid-activity model and the gaseous species by the Henry law. 

Liquid activity models must be used in vapor-liquid equilibria calculations, with the appropriate model tested against available data. Models often used include Margules, Van Laar, Wilson, nonrandom two-liquid (NRTL), and universal quasi-chemical (UNIQUAC). For mixtures, mixing rules are used to combine pure component parameters. Table 16.28 suggests regions of applicability for different models. 

The next stage of the input consists of selecting thermodynamic models. Here the process has two distinct parts (1) high-pressure reaction section (2) low-pressure distillation section. Consequently, two thermodynamic models should be considered equation of state and liquid activity model, respectively. 

The selection of appropriate thermodynamic models and the accuracy of parameters are crucial for the reliability of design studies aided by simulation. Chapters 5 and 6 are devoted to these issues. Table 3.1 presents a global view of the methods for separation processes. They are classified as matrix with mixture-type in rows against pressure range in columns. Low-pressure domain may be covered by traditional methods, as ideal vapour combined with liquid activity models. Vapour non-ideality must be considered already at medium pressures. The equations of state models have no alternatives at higher pressures. 

EOS = equation of state model LACT = liquid activity model... 

Table 3.2 presents a selection of the most used thermodynamic options for phase equilibrium with suitable enthalpy and entropy methods. The accuracy of both phase equilibrium and enthalpy/entropy computation must be examined when using EOS models. For example, often a cubic EOS underestimates the enthalpy of vaporisation. In this case other methods are more accurate, as those based on three-parameters corresponding states law (Lee-Kesler, Curl-Pitzer, etc.). Mixtures rich in components with particular behaviour, as or CH, need special methods for accurate simulation. When binary interaction parameters for liquid activity models are absent, the UNI FAC predictive method may be employed. It is worth to note that UNIFAC is suitable only for exploratory purposes, but not for final design. When high non-ideal mixtures are involved at higher pressure then the combination of EOS with liquid activity models is recommended (see Chapter 6). 

Binary interaction coefficients for liquid activity models. Note that there are distinct values for VLE and LEE. Several sets of values may be available, depending on pressure and temperature range. The non-ideality of the vapour phase should be considered at higher pressure or vacuum applications. The possibility of molecular associations in vapour or liquid phase should be examined. 

Electrolyte systems ionic parameters for different species, equilibrium constants for different reactions, as well as interaction parameters in liquid activity models. 

The most critical aspect in simulation is the selection of appropriate thermodynamic models. Different models can be used on different parts of the flowsheet, or for some units. For example, equation of state model can be used for the whole flowsheet, but liquid activity models are more suitable for separations. The accuracy of model parameters should be checked systematically. Thermodynamic analysis tools should be used systematically to evaluate the accuracy of phase equilibria before detailed simulation of separations. 

It is important to note that in the equation (6.19) G is excess Gibbs free energy. This function can be calculated accurately by means of liquid activity models. C is a constant depending on the particular type of EOS. Note also that in the mixing rules of Huron Vidal the parameters in the liquid activity model are not equal with those found at other pressures, and must be regressed again from experimental data. 

This time the mixing rules proposed by Wong Sandler can make use of the interaction parameters already identified for liquid activity models, such as no supplementary regression is needed. In this way, a huge existing experimental... 

The equation (6.36) combines the fligacity description for the vapour phase with liquid activity modelling, but needs the pure liquid fugacity as function of more accessible properties. In Chapter 5 the following relation was demonstrated ... 

At this point is worthy to mention DECHEMA database (Nagata, Gmehling and Onken, 1977), as a thesaurus of interaction parameters with various liquid activity models. This database has been updated several times, and may be accessed from some software systems, as Aspen Plus. 

Wilson (1964) brought the first major contribution in the field of modem liquid activity models by developing the local composition concept. This is related to the segregation caused by different interaction energies between pairs of molecules. Thus, the probability of finding a species 1 surrounded by molecules of species 2, relative to the probability of being surrounded by the same species 1, is given by the expression ... 

UNIFAC is recommended only for exploratory purposes. A true liquid activity model should replace it when experimental data becomes available. Sometimes the predictions by UNIFAC are surprisingly good, when sufficient experimental data was available. 

Azeotropic points are available for a great number of binary mixtures. The information can be extrapolated via a liquid activity model over the whole concentration range, but the accuracy is not guaranteed. 

As discussed, some liquid activity models can be put in a linear form by means of the function Q-x In/, +%2 ln/2, in fact the excess Gibbs free energy. The linearisation of the van Laar model may be formulated as follows ... 

Table 6.5 summarises the recommendations regarding liquid activity models. UNIQUAC gives good results in most cases. For mixtures of strong polar molecules all LACT models should be checked. Wilson is a good choice for homogeneous organic mixtures. NRTL and UNIQUAC are recommended for immiscible systems. 

Table 6.7 Parameters of liquid activity models issued from regression...

The important fact is that we may use a standard liquid activity model, as van Laar or NRTL, to describe the non-ideality of the interaction solute-solvent. Example 6.6 will illustrate this topic. 

The next step is the regression of experimental data with a liquid activity model. As illustration we select van Laar, with temperature dependency, ay = Oy + by / T. 

The binary mixture water (1) / butanone (2) exhibits an interesting phase behaviour the azeotrope lies outside the immiscibility region. Study the ability of a liquid activity model to describe accurately both VLE and LLE. 

Term of simple liquid activity model in inside-out methods, defined by Eq. (4.88). 

For determination of fluid phase partition coefficients, K, one may take a symmetric approach that uses Equation of States (EOS) for all fluid phases or an unsymmetrical approach that makes use of liquid activity models for the liquid phase retaining the equation of state models for the gas phase. 

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