Parameter Estimation Using the Entire Binary Phase Equilibrium Data

3 PARAMETER ESTIMATION USING THE ENTIRE BINARY PHASE EQUILIBRIUM DATA 

It is known that in five of the six principal types of binary fluid phase equilibrium diagrams, data other than VLE may also be available for a particular binary (van Konynenburg and Scott, 1980). Thus, the entire database may also contain VL2E, VL E, VL]L2E, and L,L2E data. In this section, a systematic approach to utilize the entire phase equilibrium database is presented. The material is based on the work of Englezos et al. (1990b 1998) 

Let us assume that for a binary system there are available N, VL E, N2 VL2E, N3 L]L2E and N4 VL)L2E data points. The light liquid phase is L, and L2 is the heavy one. Thus, the total number of available data is N=N +N2+N3+N4. Gas-gas equilibrium type of data are not included in the analysis because they 

The residuals are functions of temperature, pressure, composition and the interaction parameters. These functions can easily be derived analytically for any equation of state. At equilibrium the value of these residuals should be equal to zero. However, when the measurements of the temperature, pressure and mole fractions are introduced into these expressions the resulting values are not zero even if the EoS were perfect. The reason is the random experimental error associated with each measurement of the state variables. 

The values of the elements of the weighting matrices R, depend on the type of estimation method being used. When the residuals in the above equations can be assumed to be independent, normally distributed with zero mean and the same constant variance, Least Squares (LS) estimation should be performed. In this case, the weighting matrices in Equation 14.35 are replaced by the identity matrix I. Maximum likelihood (ML) estimation should be applied when the EoS is capable of calculating the correct phase behavior of the system within the experimental error. Its application requires the knowledge of the measurement 

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Parameter Estimation Using the Entire Binary Phase Equilibrium Data... 

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