AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
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Optimum Experimental Design in Chemical Engineering<br />
Tetramethyl<br />
Cyclohexadien<br />
+<br />
k2 + C<strong>at</strong><br />
Pi−Complex +<br />
C<strong>at</strong><br />
λ<br />
Maleinacid<br />
Anhydrid<br />
Maleinacid<br />
Anhydrid<br />
Deactiv. C<strong>at</strong><br />
k1<br />
k3<br />
Diels−Alder<br />
Product<br />
− C<strong>at</strong><br />
non-c<strong>at</strong>alyzed and c<strong>at</strong>alyzed reaction p<strong>at</strong>h<br />
deactiv<strong>at</strong>ion of <strong>the</strong> c<strong>at</strong>alyst<br />
b<strong>at</strong>ch process<br />
measurements: product mass concentr<strong>at</strong>ion<br />
control of educt molar numbers, c<strong>at</strong>alyst<br />
concentr<strong>at</strong>ion, temper<strong>at</strong>ure profile<br />
five unknown model parameters<br />
ṅ 1 = −k · n1 · n 2<br />
m tot<br />
, n 1 (0) = n a1<br />
ṅ 2 = −k · n1 · n 2<br />
m tot<br />
, n 2 (0) = n a2<br />
ṅ 3 = k · n1 · n 2<br />
m tot<br />
, n 3 (0) = 0<br />
k = k 1 · exp − E 1<br />
R ·<br />
1<br />
T − 1<br />
!!<br />
T ref<br />
+ k k<strong>at</strong> · c k<strong>at</strong> · exp (−λ · t) · exp − E k<strong>at</strong><br />
R ·<br />
n 4 = n a4 T = ϑ + 273<br />
m tot = n 1 · M 1 + n 2 · M 2 + n 3 · M 3 + n 4 · M 4<br />
1<br />
T − 1<br />
!!<br />
T ref<br />
Sebastian F. Walter, HU <strong>Berlin</strong> () Not So Short <strong>Tutorial</strong> OnAlgorithmic Differenti<strong>at</strong>ion Wednesday, 04.06.2010 18 / 39
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