# Example 30 - Nonlinear Regression
# Catalytic Reforming Reac.
# Verified Final Values: ks = 0.002784, KCH4 = 101.999
# Ref: Prob 3.10 in Problem Solving in Chemical...
[
PCH4 PH2O PCO2 PH2 r
0.06298 0.23818 0.0042 0.01669 0.00013717
0.03748 0.26315 0.00467 0.01686 0.00015584
0.05178 0.29557 0.00542 0.02079 0.00020028
0.04978 0.23239 0.00177 0.07865 5.7E-05
0.04809 0.29491 0.00655 0.02464 0.0002015
0.03849 0.24171 0.00184 0.06873 7.887E-05
0.03886 0.26048 0.00381 0.0148 0.00014983
0.0523 0.26286 0.05719 0.01635 0.00015988
0.05185 0.33529 0.00718 0.0282 0.00026194
0.06432 0.24787 0.00509 0.02055 0.00014426
0.09609 0.28457 0.00652 0.02627 0.00020195
]
nlinfit r = ks*KCH4*(PCH4*PH2O^2-PCO2*PH2^4/5.051e-5)/(1+KCH4*PCH4)
m(ks)=1
m(KCH4)=1
r = ks*KCH4*(PCH4*PH2O^2-PCO2*PH2^4/5.051e-5)/(1+KCH4*PCH4)
| Variable |
Initial guess |
Value |
95% confidence |
| ks |
1 |
0.00278427 |
0.00003132 |
| KCH4 |
1 |
101.93935 |
7.2015189 |
NOTE: Calculations exceeded the maximum number of iterations.
| R^2 |
R^2adj |
Rmsd |
Variance |
| 0.9968601 |
0.9965113 |
9.333E-07 |
1.171E-11 |
Nonlinear Regression Plot

Nonlinear Regression Residuals Plot

Source data points and calculated data points
| |
PCH4 |
PH2O |
PCO2 |
PH2 |
r |
r calc |
Delta r |
| 1 |
0.06298 |
0.23818 |
0.0042 |
0.01669 |
0.00013717 |
0.00013642 |
7.5266E-07 |
| 2 |
0.03748 |
0.26315 |
0.00467 |
0.01686 |
0.00015584 |
0.00015237 |
3.4702E-06 |
| 3 |
0.05178 |
0.29557 |
0.00542 |
0.02079 |
0.00020028 |
0.00020359 |
-3.3103E-06 |
| 4 |
0.04978 |
0.23239 |
0.00177 |
0.07865 |
0.000057 |
0.00006296 |
-5.9602E-06 |
| 5 |
0.04809 |
0.29491 |
0.00655 |
0.02464 |
0.0002015 |
0.00019883 |
2.6724E-06 |
| 6 |
0.03849 |
0.24171 |
0.00184 |
0.06873 |
0.00007887 |
0.00008277 |
-3.9005E-06 |
| 7 |
0.03886 |
0.26048 |
0.00381 |
0.0148 |
0.00014983 |
0.00015063 |
-7.9861E-07 |
| 8 |
0.0523 |
0.26286 |
0.05719 |
0.01635 |
0.00015988 |
0.00015837 |
1.5118E-06 |
| 9 |
0.05185 |
0.33529 |
0.00718 |
0.0282 |
0.00026194 |
0.00025915 |
2.7909E-06 |
| 10 |
0.06432 |
0.24787 |
0.00509 |
0.02055 |
0.00014426 |
0.00014775 |
-3.492E-06 |
| 11 |
0.09609 |
0.28457 |
0.00652 |
0.02627 |
0.00020195 |
0.00020297 |
-1.0183E-06 |
General
| Algorithm |
LM |
| Sample size |
11 |
| Model vars |
2 |
| Indep vars |
4 |
| Iterations |
64 |
| Max iterations |
64 |