Parameter Estimation difficulties with starting estimates

The solubility parameter model has difficulty with temperature effects and also fails to predict solubilities in several instances, such as with silicones. However it is a good starting point for estimating the solubility characteristics of a SCF as a function of temperature and pressure. The most likely temperatures and pressures under which a material is soluble in a supercritical fluid are where the solubility parameters are within a value of unity of each other. See Fig. 1, taken from Fig. 2 of Ref 5 by Allada, for a graph of 6 versus T and P for CO2. This effect allows one to selectively remove a particular component from a material by tuning the 5 of the SCF using T and P. 

Less-experienced researchers may start with trying to estimate the pre-exponentials feo and the activation energies Ea using the standard Arrhenius expression. Our tests showed that three out of five software packages had severe difficulties to obtain a converged solution for the parameter estimation run, which is easily explained by the strong correlation between both parameters. 

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