Fitted binary interaction parameters

Figure 1 shows a comparison of calculated and experimental phase compositions at 40 , 50 , and 60 C. The fit of phase compositions for the L1L2G equilibrium at 60 C and 12.2 MPa is very good, while the fit of the L1L2L3 phase ecjuilibrium at 40 C and 8.4 MPa is semi-quantitative, at best. Since the three phases at 40 C correspond to a different three-phase equilibrium than the L1L2G equilibrium at 50 C, which was used to fit binary interaction parameters, the poorer fit at 40 C is not unexpected. Indeed, these results show that L1L2L3 ecjuilibrium can be predicted with parameters obtained from an entirely different three-phase region. 

However, hydrogen bonding can influence the thermodynamic properties of systems with macromolecules as well. Figures 2.9 and 2.10 present the VLB of polymer-solvent systems, in which both self- and cross-association interactions occur between the solvent molecules and between the solvent molecnles and the polymer functional groups, respectively. All parameters were adopted by Tsivintzelis and Kontogeorgis [68] who showed that the NRHB model is able to satisfactorily predict (without the use of any binary adjustable parameter) the VLB of such binary mixtures, while using one fitted binary interaction parameter, the model very accurately... 

The mixing rules for evaluating mixture constants should not contain more than one fitted binary Interaction parameter, and if possible this parameter should be temperature, pressure, and composition independent. 

Water-Hydrocarbon Systems. The application of the PR equation to two and three-phase equilibrium calculations for systems containing water has recently been Illustrated by Peng and Robinson ( ). As in the case of other hydrocarbon-non-hydrocarbon mixtures, one fitted binary interaction parameter for water with each of the hydrocarbons is required. These parameters were obtained from experimental data available in the literature on each of the water-hydrocarbon binaries. 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

The key to obtaining good representation of experimental data is fitting a single binary interaction parameter, ky, to each set of binary data. In most of the modeling described here, our main concern lies with the binary interaction parameters between each of the components and C02, since C02 introduces the most asymmetry (i.e., difference in size and energy parameters) into the system. In a few cases, we include nonzero binary interaction parameters for some of the other components. 

The applicability of the lattice EOS in the modelling of the VLE of mixtures of molecules of different sizes was examined next. The results for the I S-n-heptane system at 310K and 352K are shown in Figure 3 (23). For the temperatures modelled, it is seen that there is a good agreement between the fitted and the experimental data, again with the use of one temperature independent binary interaction parameter. 

It is often necessary to add user components to complete a simulation model. The design engineer should always be cautious when interpreting simulation results for models that include user components. Phase equilibrium predictions for flashes, decanters, extraction, distillation, and crystallization operations should be carefully checked against laboratory data to ensure that the model is correctly predicting the component distribution between the phases. If the fit is poor, the binary interaction parameters in the phase equilibrium model can be tuned to improve the prediction. 

The combinatorial part In yp is calculated from pure-component properties. The residual part In yf is calculated by using binary interaction parameters for solute-solvent group pairs determined by fitting phase equilibrium data. Both parts are based on the UNIQUAC set... 

In using simulation software, it is important to keep in mind that the quality of the results is highly dependent upon the quahty of the liquid-liquid equilibrium (LLE) model programmed into the simulation. In most cases, an experimentally vmidated model will be needed because UNIFAC and other estimation methods are not sufficiently accurate. It also is important to recognize, as mentioned in earlier discussions, that binary interaction parameters determined by regression of vapor-liquid equilibrium (VLE) data cannot be rehed upon to accurately model the LLE behavior for the same system. On the other hand, a set of binary interaction parameters that model LLE behavior properly often will provide a reasonable VLE fit for the same system—because pure-component vapor pressures often dominate the calculation of VLE. 

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. 

When fitting VLE data with the IPVDW model, it is found that the binary interaction parameter kij is approximately zero for relatively simple mixtures, such as alkane mixtures, whereas for some other mixtures such as hydrocarbons with industrial gases like carbon dioxide and organic solvents, it is not only nonzero but will also change in value with temperature. For highly nonideal mixtures, which are our main concern here, accurate correlation of VLE is not possible by this method. 

When using binary interaction parameters, it is best to use parameters fitted to binary data at or near the temperature of interest. If data are available at multiple temperatures, it is possible to include limited temperature dependence. It is also possible to fit parameters for a binary pair to ternary data, but only if parameters for the other two binary pairs in the ternary system are already known. Binary interaction parameters are not interchangeable between methods, so it is important to use exactly the same EOS or activity-coefficient model in both data regression and phase-equilibrium calculations. 

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. 

In Great Britain, the National Engineering Laboratory (NEL, formerly a government agency but now privatized) has prodnced a database for thermodynamic and transport properties. PPDS contains correlations for properties of a large number of pure components these are based on evaluated experimental data where possible but also include some estimated properties. For mixtures, the database contains binary interaction parameters fitted to data for use with common equation-of-state and liqnid-activity methods for calculating phase eqnilibria. Information is available at their Web site [14]. 

Simplification of the equation and reduction of data requirement have been achieved in newer equations by addressing binary molecular interactions only. Interactions of clusters of greater than two molecules are not explicitly addressed, but their constituent molecular pairs are included as binary interactions. In this way only binary interaction parameters appear in all activity coefficient equations—for binary solutions as well as for multi-component solutions. By fitting binary solution data all solution parameters can be obtained, for multi-component solutions as well. The need for experimental data on multi-component solutions is eliminated, as all required parameters can be determined by fitting binary solution data. 

Equations (4.345) and (4.346) are the van Laar activity-coefQcient equations that are used for fitting data by adjusting the parameters A21 and A 2- Although these parameters are derived from pure-component parameters, as shown in Equations (4.347) and (4.348), they are, nevertheless, considered mixture-specific binary interaction parameters and are thus indicated with subscripts because they are determined by fitting binary mixture data. Equations (4.347) and (4.348), while showing the source of derivation of the parameters, are not used for their determination. 

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