Chemical Engineering: Fit the Antoine Parameters from Vapor Pressure data
2011.4.20
Lecture note of Dr. Hiroshi Yamamoto
There are 2 type of programs that fit Antoine Parameter.
HTML5 version, for iPad/Mac/PC, with Safari (Mobile Safari)/Chrome/FireFox4 Browser. IE9 is out of support.
JAVA version, Mac/PC, with JRE(Java Runtime Environment)
At first, prepair vapor pressure.
| No | P（mmHg） | T(℃） |
| 1 | 15.1 | 17.4 |
| 2 | 32.8 | 30 |
| 3 | 59.0 | 40 |
| 4 | 59.0 | 40 |
| 5 | 95.5 | 50 |
| 6 | 152.8 | 60.1 |
| 7 | 277.2 | 74.9 |
| 8 | 404.3 | 75.2 |
| 9 | 670.6 | 100 |
Pressure Unit is mmHg or KPa, Temperature unit is °C or K. Please make table with spread sheet.
Then run the program. (HTML5 version)
Please paste Vapor Pressure data without title. The delimiter is tab. And set several radio button. This program need boiling point data to get initial guess of Antoine B and C parameter. If you want append boiling point data to fitting, check th Append to T-VP data box. And push RUN button. You will get the result immediately. Red circles are Experimental data. And blue data are Calculated by antoine equation.
Copy Antoine parameters to spread sheet. And calculate vapor pressure.
There is very large error at experimental value #8. In chemical area data, it may have ecxperimental error.
Pirika method is very good method for such dirty, including experimental errors data.
Almost all commercial Process Simulator, they use Marquart Method to solve these problem. If you select Least Square option, you can easily find out why Marquart Method is not adequate for these problem. (Picture is JAVA version)
(Sometime, you can not copy & paste to text area with JAVA, in that case you need edit java.policy file.)
Copy Antoine Parameters and paste it spread sheet.
P（mmHg） |
T(℃） |
AntA(LS) |
AntB(LS) |
AntC(LS) |
P_Calc(LS) |
Δ |
Δ*Δ |
15.1 |
17.4 |
6.7028832 |
1243.946 |
219.557 |
28.4 |
13.3 |
176.7408655 |
32.8 |
30 |
6.7028832 |
1243.946 |
219.557 |
52.3 |
19.5 |
379.1380981 |
59.0 |
40 |
6.7028832 |
1243.946 |
219.557 |
81.3 |
22.3 |
499.1273913 |
59.0 |
40 |
6.7028832 |
1243.946 |
219.557 |
81.3 |
22.3 |
499.1273913 |
95.5 |
50 |
6.7028832 |
1243.946 |
219.557 |
122.5 |
27.0 |
728.6271162 |
152.8 |
60.1 |
6.7028832 |
1243.946 |
219.557 |
179.8 |
27.0 |
728.4173895 |
277.2 |
74.9 |
6.7028832 |
1243.946 |
219.557 |
300.8 |
23.6 |
559.010094 |
404.3 |
75.2 |
6.7028832 |
1243.946 |
219.557 |
303.8 |
-100.5 |
10092.48218 |
670.6 |
100 |
6.7028832 |
1243.946 |
219.557 |
645.9 |
-24.7 |
610.2817263 |
SUM= |
14272.95225 |
In his case, #8 error improve -123.9 to -100.5. But other data point, result become very worse. This is defect of Least Square Method. You can use this method only for clean data set.
Pirika Method is very srong to error input. There is amother merit to use Pirika Method. I've already determined 1900 molecule's Antoine parameter with this method. I show n-alkane result as example. The determined Antoine B parameter by Pririka Method, that are very consistent to Carbon number for both Hydrocarbon molecule and Alcohol compounds. With Marquart Method, determinded Antoine Parameters have no tendency. Please refer to theoretical approach for this problem.
I made new program that estimate antoine parameters from it chemical structure. If you have only one experimental data (Boiling point), the accuracy is very high.
