Difference between revisions of "Diels-Alder Reaction Experimental Design"
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(→Model Formulation) |
(→Optimum Experimental Design Problem) |
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\displaystyle \min_{x, G, F, u} && trace(F^{-1} (t_{t_f})) \\[1.5ex] | \displaystyle \min_{x, G, F, u} && trace(F^{-1} (t_{t_f})) \\[1.5ex] | ||
\mbox{s.t.} \\ | \mbox{s.t.} \\ | ||
− | + | \dot{x}(t) & = & f(x(t), u(t),p), \\ | |
+ | \\ | ||
+ | \dot{h}(t) & = & \frac{n_3(t) \ \cdot \ M_3}{m_{tot}} \ \cdot \ 100 \\ | ||
\\ | \\ | ||
− | \dot{ | + | \dot{G}(t) & = & f_x(x(t),u(t),p)G(t) \ + \ f_p(x(t),u(t),p) \\ |
\\ | \\ | ||
− | \dot{ | + | \dot{F}(t) & = & w(t) (h_x(x(t),u(t),p)G(t))^T (h_x(x(t),u(t),p)G(t)) \\ |
− | + | ||
− | + | ||
\\ | \\ | ||
0 & = & g(x(t_o),x(t_f),p) \\ | 0 & = & g(x(t_o),x(t_f),p) \\ |
Revision as of 14:08, 4 December 2015
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Model Formulation
Differential equation system:
Solvent:
Reaction velocity constant:
Total mass:
Temperature in Kelvin:
The ODE system is summarized to:
Optimum Experimental Design Problem
Name | Symbol | Initial value (![]() |
Molar number 1 | ![]() |
![]() |
Molar number 2 | ![]() |
![]() |
Molar number 3 | ![]() |
![]() |
Name | Symbol | Value |
Molar Mass | ![]() |
0.1362 |
Molar Mass | ![]() |
0.09806 |
Molar Mass | ![]() |
0.23426 |
Molar Mass | ![]() |
0.236 |
Universal gas constant | ![]() |
8.314 |
Reference temperature | ![]() |
293 |
Name | Symbol | Value |
Steric factor | ![]() |
![]() |
Steric factor | ![]() |
![]() |
Activation energie | ![]() |
![]() |
Activation energie | ![]() |
![]() |
Catalyst deactivation coefficient | ![]() |
![]() |
with
Name | Symbol | Interval |
Initial molar number 1 | ![]() |
[0.4,9.0] |
Initial molar number 2 | ![]() |
[0.4,9.0] |
Initial molar number 3 | ![]() |
[0.4,9.0] |
Concentration of the catalyst | ![]() |
[0.0,6.0] |
Initial molar number 1 | ![]() |
[20.0,100.0] |