Binary VLE

UNIQUAC equation with binary parameters estimated by supplementing binary VLE data with ternary tie-line data. 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

Three parameters are estimated from binary VLE data and correspond to ... 

A. The first four data cards contain control parameters which are read only once for a series of binary VLE data sets. 

Multiple sets of binary VLE data may be correlated by continuing with another set of cards starting at part B. The last set of cards must be followed with a blank card to end the program. 

Banerjee, T., Singh, M. K., Khanna, A. Prediction of binary VLE for imidazolium based ionic liquid systems using COSMO-RS. Ind. Eng. Chem. Res. 2006, 45, 3207-3219. 

PARAM ETER ESTIMATION USING BINARY VLE DATA... 

Only two of the four state variables measured in a binary VLE experiment are independent. Hence, one can arbitrarily select two as the independent variables and use the EoS and the phase equilibrium criteria to calculate values for the other two (dependent variables). Let Q, (i=l,2,...,N and j=l,2) be the independent variables. Then the dependent ones, g-, can be obtained from the phase equilibrium relationships (Modell and Reid, 1983) using the EoS. The relationship between the independent and dependent variables is nonlinear and is written as follows... 

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... 

Constrained Gauss-Newton Method for Regression of Binary VLE Data... 

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. 

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). 

Broul et al. (13) and Hala (14) developed a correlation scheme for systems containing two solvents and one salt, which they applied to several salt concentrations, not just to the saturation level as in the studies mentioned above. They utilized the binary VLE data for the three binaries (solvent 1-salt solvent 2-salt and solvent 1-solvent 2) along with the ternary data to correlate successfully the ternary results. They employed the Margules equation (15) with the addition of a term to account for the coulombic interactions. 

Figure 3A.1 requires explanation. At 4.137 MPa, the two-phase region is a trapezoid. The trapezoid extends from binary VLE between COz and HjS to binary VLE between H2S and CH4. To the left of this trapezoid, the fluid is a vapor. These fluids would be rich in methane. To the right of the trapezoid the mixture is a liquid. 

The measured variables of binary VLE are Xi, yi, T, and P. Experimental values of the activity coefficient of species i in the liquid are related to these variables by Eq. (4-282), written ... 

Again subscript i identifies species, and j and I are dummy indices. All summations are over all species, and Tjy = 1 fori = j. Values for tlie parameters ( ,7 —nyy) are found by regression of binary VLE data, and are given by Gmeliling et al. ... 

Until now, an anempt at explaining the observed modifications of VLEs induced by the presence of the solute has been made. Some compounds do not interfere with the binary VLEs therefore, the one-phase region is the same as in the binary system (at temperatures and pressures higher than MCP). But, we have seen that, in general, the... 

D.3. Program VDW Binary VLE vyith the van der Waals One-Fluid Mixing Rules (IPVDW and 2PVDW)... 

Example D,3,B Fitting Binary VLE Data with the Two-parameter van der Waals One-fluid Mixing Rule... 

---