Difference between revisions of "Diels-Alder Reaction Experimental Design"
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− | k = k_1 \ \cdot \ exp(- \frac{E_1}{R} \ \cdot \ (\frac{1}{T} \ - \ \frac{1}{T_{ref}}) ) \ + \ k_{cat} \ \cdot \ c_{cat} \ \cdot \ exp(-\lambda \ \cdot \ t) \ \cdot \ exp( - \frac{E_{cat}}{R} \ \cdot \ (\ \frac{1}{T} \ - \ \frac{1}{T_{ref}}) ) | + | k = k_1 \ \cdot \ exp(- \frac{E_1}{R} \ \cdot \ (\frac{1}{T(t)} \ - \ \frac{1}{T_{ref}}) ) \ + \ k_{cat} \ \cdot \ c_{cat} \ \cdot \ exp(-\lambda \ \cdot \ t) \ \cdot \ exp( - \frac{E_{cat}}{R} \ \cdot \ (\ \frac{1}{T(t)} \ - \ \frac{1}{T_{ref}}) ) |
</math> | </math> | ||
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<math> | <math> | ||
− | T = \vartheta + 273 | + | T(t) = \vartheta (t) + 273 |
</math> | </math> | ||
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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.} & \dot{x} = f(x,u,p,t), \forall \, t \in I\\ | \mbox{s.t.} & \dot{x} = f(x,u,p,t), \forall \, t \in I\\ | ||
+ | & \dot{n_1}(t) = -k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}}, \\ | ||
+ | & \\ | ||
+ | & \dot{n_2}(t) = -k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}}, \\ | ||
+ | & \\ | ||
+ | & \dot{n_2}(t) = \ \ k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}} | ||
& 0 = g(x(t_o),x(t_f),p) \\ | & 0 = g(x(t_o),x(t_f),p) \\ | ||
& 0 \ge c(x,u,p), \forall \, t \in I\\ | & 0 \ge c(x,u,p), \forall \, t \in I\\ |
Revision as of 12:26, 4 December 2015
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Model Formulation
Differential equation system:
Reaction velocity constant:
Total mass:
Temperature in Kelvin:
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): {\begin{array}{cl}\displaystyle \min _{{x,G,F,u}}&trace(F^{{-1}}(t_{{t_{f}}}))\\[1.5ex]{\mbox{s.t.}}&{\dot {x}}=f(x,u,p,t),\forall \,t\in I\\&{\dot {n_{1}}}(t)=-k\cdot {\frac {n_{1}(t)\ \cdot \ n_{2}(t)}{m_{{tot}}}},\\&\\&{\dot {n_{2}}}(t)=-k\cdot {\frac {n_{1}(t)\ \cdot \ n_{2}(t)}{m_{{tot}}}},\\&\\&{\dot {n_{2}}}(t)=\ \ k\cdot {\frac {n_{1}(t)\ \cdot \ n_{2}(t)}{m_{{tot}}}}&0=g(x(t_{o}),x(t_{f}),p)\\&0\geq c(x,u,p),\forall \,t\in I\\&0=h(x,u,p),\forall \,t\in I\\&x\in {\mathcal {X}},\,u\in {\mathcal {U}},\,p\in P.\end{array}}
Name | Symbol | Initial value (![]() |
Molar number 1 | ![]() |
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Molar number 2 | ![]() |
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Molar number 3 | ![]() |
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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 | ![]() |
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Steric factor | ![]() |
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Activation energie | ![]() |
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Activation energie | ![]() |
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Catalyst deactivation coefficient | ![]() |
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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] |