Binary data, interaction parameters

UNFI2.DTA CONTAINS UNIFAC BINARY GROUP INTERACTION PARAMETER INFORMATION. IF YOU ALREADY HAVE THESE DATA FILES IN THE CURRENT DIRECTORY ... 

For the UNIQUAC equation, there are two adjustable equation parameters for each binary. For the binary that is partially miscible, the best way to determine the two binary parameters is to fit the mutual solubility data. For the completely miscible binaries, useful interaction parameters can be obtained from vie data. However, fitting vie data to within experimental accuracy does not uniquely determine the binary parameters. The choice of a particular set of parameters can have a significant effect on the representation of the ternary lie. For the ternary system of chloroform, water, and acetone at 333°K, for example, the two binary parameters are first determined from mutual solubility data for chloroform and water and then the other binary parameters for the two miscible binaries. Somewhat improved predictions occur by fitting binary parameters to the miscible binaries. Similar predictions have also been found for ternary systems of ethyl acetate, ethanol, and water. 

The data base contains provisions for a simple augmentation by up to eight additional compounds or substitution of other compounds for those included. Binary interaction parameters necessary for calculation of fugacities in liquid mixtures are presently available for 180 pairs. 

Appendix C-7 gives interaction parameters for noncondensable components with condensable components. (These are also included in Appendix C-5). Binary data sources are given. 

PARIN first loads all pure component data by reading two records per component. The total number of components, M, in the library or data deck must be known beforehand. Next the associ-ation/solvation parameters are input for M components. Finally all the established UNIQUAC binary interaction parameters (or noncondensable-condensable interaction parameters) are read. 

In addition to these faciUties for supply of data in an expHcit form for direct use by the system, there also are options designed for the calculation of the parameters used by the system s point generation routines. Two obvious categories of this type can be identified and are included at the top left of Figure 5. The first of these appHes to the correlation of raw data and is most commonly appHed to the estimation of binary interaction parameters. 

Binary interaction parameters are determined for each pq pair p q) from experimental data. Note that = k and k = k = 0. Since the quantity on the left-hand side of Eq. (4-305) represents the second virial coefficient as predicted by Eq. (4-231), the basis for Eq. (4-305) lies in Eq. (4-183), which expresses the quadratic dependence of the mixture second virial coefficient on mole fraction. 

Detailed procedures, including computer programs for evaluating binary-interaction parameters from experimental data and then utihz-... 

For gas-liquid solutions which are only moderately dilute, the equation of Krichevsky and Ilinskaya provides a significant improvement over the equation of Krichevsky and Kasarnovsky. It has been used for the reduction of high-pressure equilibrium data by various investigators, notably by Orentlicher (03), and in slightly modified form by Conolly (C6). For any binary system, its three parameters depend only on temperature. The parameter H (Henry s constant) is by far the most important, and in data reduction, care must be taken to obtain H as accurately as possible, even at the expense of lower accuracy for the remaining parameters. While H must be positive, A and vf may be positive or negative A is called the self-interaction parameter because it takes into account the deviations from infinite-dilution behavior that are caused by the interaction between solute molecules in the solvent matrix. 

The term pt is a binary interaction parameter which must be determined from phase equilibrium data. We will discuss determination of p 9 values in more detail later. 

Traditionally, the binary interaction parameters such as the ka, kb, k, ki in the Trebble-Bishnoi EoS have been estimated from the regression of binary vapor-liquid equilibrium (VLE) data. It is assumed that a set of N experiments have been performed and that at each of these experiments, four state variables were measured. These variables are the temperature (T), pressure (P), liquid (x) and vapor (y) phase mole fractions of one of the components. The measurements of these variables are related to the "true" but unknown values of the state variables by the equations given next... 

It is well known that cubic equations of state have inherent limitations in describing accurately the fluid phase behavior. Thus our objective is often restricted to the determination of a set of interaction parameters that will yield an "acceptable fit" of the binary VLE data. The following implicit least squares objective function is suitable for this purpose... 

It is well known that cubic equations of state may predict erroneous binary vapor liquid equilibria when using interaction parameter estimates from an unconstrained regression of binary VLE data (Schwartzentruber et al.. 1987 Englezos et al. 1989). In other words, the liquid phase stability criterion is violated. Modell and Reid (1983) discuss extensively the phase stability criteria. A general method to alleviate the problem is to perform the least squares estimation subject to satisfying the liquid phase stability criterion. In other... 

Given a set of N binary VLE (T-P-x-y) data and an EoS, an efficient method to estimate the EoS interaction parameters subject to the liquid phase stability criterion is accomplished by solving the following problem... 

The implicit LS, ML and Constrained LS (CLS) estimation methods are now used to synthesize a systematic approach for the parameter estimation problem when no prior knowledge regarding the adequacy of the thermodynamic model is available. Given the availability of methods to estimate the interaction parameters in equations of state there is a need to follow a systematic and computationally efficient approach to deal with all possible cases that could be encountered during the regression of binary VLE data. The following step by step systematic approach is proposed (Englezos et al. 1993)... 

In this section we consider typical examples. They cover all possible cases that could be encountered during the regression of binary VLE data. Illustration of the methods is done with the Trebble-Bishnoi (Trebble and Bishnoi, 1988) EoS with quadratic mixing rules and temperature-independent interaction parameters. It is noted, however, that the methods are not restricted to any particular EoS/mixing rule. 

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. 

The methane-methanol binary is another system where the EoS is also capable of matching the experimental data very well and hence, use of ML estimation to obtain the statistically best estimates of the parameters is justified. Data for this system are available from Hong et al. (1987). Using these data, the binary interaction parameters were estimated and together with their standard deviations are shown in Table 14.1. The values of the parameters not shown in the table (i.e., ka, kb, kc) are zero. 

Prior work on the use of critical point data to estimate binary interaction parameters employed the minimization of a summation of squared differences between experimental and calculated critical temperature and/or pressure (Equation 14.39). During that minimization the EoS uses the current parameter estimates in order to compute the critical pressure and/or the critical temperature. However, the initial estimates are often away from the optimum and as a consequence, such iterative computations are difficult to converge and the overall computational requirements are significant. 

It is assumed that there are available NCP experimental binary critical point data. These data include values of the pressure, Pc, the temperature, Tc, and the mole fraction, xc, of one of the components at each of the critical points for the binary mixture. The vector k of interaction parameters is determined by fitting the EoS to the critical data. In explicit formulations the interaction parameters are obtained by the minimization of the following least squares objective function ... 

Table 14.8 Interaction Parameter Values from Binary Critical Point Data...

Englezos, P., G. Bygrave, and N. Kalogerakis, "Interaction Parameter Estimation in Cubic Equations of State Using Binary Phase Equilibrium Critical Point Data", Ind. Eng Chem. Res.31(5), 1613-1618 (1998). 

Englezos, P., N. Kalogerakis and P.R. Bishnoi, "A Systematic Approach for the Efficient Estimation of Interaction Parameters in Equations of State Using Binary VLE Data", Can. J. Chem. Eng., 71,322-326 (1993). 

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. 

Thus, if the saturated vapor pressure is known at the azeotropic composition, the activity coefficient can be calculated. If the composition of the azeotrope is known, then the compositions and activity of the coefficients at the azeotrope can be substituted into the Wilson equation to determine the interaction parameters. For the 2-propanol-water system, the azeotropic composition of 2-propanol can be assumed to be at a mole fraction of 0.69 and temperature of 353.4 K at 1 atm. By combining Equation 4.93 with the Wilson equation for a binary system, set up two simultaneous equations and solve Au and A21. Vapor pressure data can be taken from Table 4.11 and the universal gas constant can be taken to be 8.3145 kJ-kmol 1-K 1. Then, using the values of molar volume in Table 4.12, calculate the interaction parameters for the Wilson equation and compare with the values in Table 4.12. 

The optimum UNIQUAC interaction parameters u, between methylcyclohexane, methanol, and ethylbenzene were determined using the observed liquid-liquid data, where the interaction parameters describe the interaction energy between molecules i and j or between each pair of compounds. Table 4 show the calculated value of the UNIQUAC binary interaction parameters for the mixture methanol + ethylbenzene using universal values for the UNIQUAC structural parameters. The equilibrium model was optimized using an objective function, which was developed by Sorensen [15],... 

The Aspen NRTL-SAC solvent database was identified from the list of solvents presented in the pharmaceutical based International Committee on Harmonization s guidelines for residual solvents in API [28], Hexane, Acetonitrile and Water were selected as the basis for the X, Y and Z segments respectively, the binary interaction parameters for the segments together with molecular descriptors in terms of X,Y and Z segments were then regressed from experimental vapour-liquid and liquid-liquid equilibrium data from the Dechema database. The list of solvent parameters that were used in the case study are given in Table 13. 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

The solubilities of ammonia, carbon dioxide, and hydrogen sulfide were obtained from binary data and expressed in terms of a Henry s constant for infinite dilution and an interaction parameter ... 

Binary interaction parameters Aaa are assumed to be constants and were determined from solubility data for gaseous species a in water. 

This introduces two "interaction parameters" per binary pair. The pure component coefficients, a and b i, are evaluated from critical data and the acentricity, as proposed by Soave in his original paper (1). The pure component aii varies with reduced temperature so as to match vapor pressure. (Soave s recently revised expression for a (17) has not been used.)... 

The calculated critical points of the binary pairs, particularly the critical pressures, are quite sensitive to the values used for the interaction parameters in the mixing rules for a and b in the equation of state. One problem in undertaking this study is that no data are available on the critical lines of any of the binary pairs except for CO2 - H2O. Even for C02 - H2O, two sets of critical data available (18, 19) are in poor quantitative agreement, though they present the same qualitative picture of the critical phenomena. 

Carbon Dioxide - Water System, The data of Wiebe and Gaddy (4, 5, 6) were used exclusively in this study to determine the interaction parameters for the carbon dioxide - water binary system. These data cover the temperature and pressure range from 12°C to 100°C and from 25 atm to 700 atm respectively. As with the HzS - H2O system, a constant interaction parameter has been obtained for the gaseous phase and the carbon dioxide - rich... 

The interaction parameters for binary systems containing water with methane, ethane, propane, n-butane, n-pentane, n-hexane, n-octane, and benzene have been determined using data from the literature. The phase behavior of the paraffin - water systems can be represented very well using the modified procedure. However, the aromatic - water system can not be correlated satisfactorily. Possibly a differetn type of mixing rule will be required for the aromatic - water systems, although this has not as yet been explored. 

Ethane - Hater System. The data used for the determination of the interaction parameters for the ethane - water binary are those of Culberson and McKetta (21), Culberson et al. (22)... 

A constant interaction parameter was capable of representing the mole fraction of water in the vapor phase within experimental uncertainty over the temperature range from 100°F to 460°F. As with the methane - water system, the temperature - dependent interaction parameter is also a monotonically increasing function of temperature. However, at each specified temperature, the interaction parameter for this system is numerically greater than that for the methane - water system. Although it is possible for this binary to form a three-phase equilibrium locus, no experimental data on this effect have been reported. 

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