Select thermodynamic models for process simulation
A Practical Guide to a Three Steps Methodology

Example 3.10: Find the parameters to fit the vapour pressure of ethyl oleate

Experimental data on the vapour pressure of ethyl oleate have been obtained experimentally for IFPEN using saturation and synthetic method techniques. The results are given in the table3-16.

Table 1: Experimental data for vapour pressure of ethyl oleate
Temperature (°C) 80.902 100.89 120.78 139.53 161.26 181.4 202.31
Vapour pressure (Pa) 0.35 2.06 9.15 31.58 131.59 416.46 1112.08
Temperature (°C) 118.93 129.04 139.10 149.14 150.08 179.06
Vapour pressure (Pa) 8.68 18.16 36.85 63.16 118.17 348.16

What are the best parameters to fit these data with theDIPPR equation:

image

Analysis:

Solution:

See complete results in file (xls):

Some help on nomenclature and tips to use this file can be found here.

The objective function must first be selected. Different residues can be constructed.

The selected equation is not linear, so a numerical solver is required to minimise the root mean square error. In the solution, the Excel solver is used. Some initial values have to be determined at first. Error minimisation must be carried out with various initial values so as not to remain trapped in a local minimum. Obviously, in this specific case, many local solutions may exist.

The reader is invited to try out several combinations of initial values and objective functions in the excel sheet that is provided. Many solutions are equivalent.

When looking closer at the DIPPR equation, it appears that, except for the parameter E, all other are linear combination parameters. Hence, using a fixed value for E, the others can be found using the linear regression solution, using

image
where the matrix image is defined as:

image

and the vector image represents, in our case, the vapour pressures at different temperatures (temperatures are Ci). When this set of values is used as initial guess for the minimisation procedure, the solution offers excellent stability. This option is proposed in the "Use Regression" sheet of the example excel file.