Chapter 3:
From Components
to Models
Abstract
Read the abstractTable of contents
See the table of contentsList of examples
- 3-1: Vapour pressure predictions of methane using different formulas
- 3-2: Quality evaluation of molar volume correlations
- 3-3: Evaluation of the ideal gas heat capacity equations for n-pentane
- 3-4: Quality evaluation of vapourisation enthalpy correlations
- 3-5: Comparison of second virial coefficient calculation methods
- 3-6: Comparison of critical points and acentric factor from different databases
- 3-7: Use of the group contribution methods of Joback and Gani
- 3.8: Diesel fuel characterization
- 3.9: Vapour pressures of di-alcohols
- 3.10: Find the parameters to fit the vapour pressure of ethyl oleate
- 3.11: Fitting of BIP coefficients for the mixture water + MEA with the NRTL model
- 3.12: Separation of n-butane from 1,3 butadiene at 333.15K using vapour-liquid equilibrium
- 3.13: Draw the heteroazeotropic isothermal phase diagram of the binary mixture of water and butanol at 373.15 K
- 3.14: Isothermal phase diagram using the Flory Huggins activity coefficient model
- 3.15: Use of an equation of state for pure component vapour pressure calculations
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.
| 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:
Analysis:
- The given properties are vapour pressure as a function of temperature all along saturation curve.
- Component is a hydrocarbon with very few data published.
- Phases are vapour and liquid in the range 350 K to 475 K.
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.
- Absolute pressure difference
- Relative pressure difference
- Absolute log(pressure) difference
- Relative log(pressure) difference
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
where the matrix
is defined as :
and the vector 
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.