Parameter Estimation The Objective Function

According to Tassios (1993) a suitable objective function to be minimized in such cases is the following 

This is equivalent to assuming that the standard error in the measurement of Yj is proportional to its value. 

Experimental values for the activity coefficients for components 1 and 2 are obtained from the vapor-liquid equilibrium data. During an experiment, the following information is obtained Pressure (P), temperature (T), liquid phase mole fraction (x, and x2=l-X ) and vapor phase mole fraction (yi and y2=l—yi). 

The activity coefficients are evaluated from the above phase equilibrium data by procedures widely available in the thermodynamics literature (Tassios, 1993 Prausnitz et al. 1986). Since the objective in this book is parameter estimation we will provide evaluated values of the activity coefficients based on 

Alternatively, one may use implicit LS estimation, e.g., minimize Equation 14.23 where liquid phase fugacities are computed by Equation 15.5 whereas vapor phase fugacities are computed by an EoS or any other available method (Prausnitz et al., 1986). 

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