| Name: |
Sixeq4b - Modeling of a CSTR
for a complex sequence of reactions- revised form. |
| Source: |
Fogler, S. H., Personal communications
(2000) |
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| Reference/s |
Shacham, M.and Brauner N.,
Computers chem. Engng. (submitted, 2001) |
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| Model: |
6 implicit equations, indep.
variables CA, CB, CC, CD, CE and T |
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Average difficulty level |
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Constraints: CA, CB, CC, CD
and CE are nonnegative |
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Discontinuities: Undefined
for T=0 |
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Initial estimates: 1.(0.5,
0.01, 1, 0.01, 1, 420) 2.(0.05, 0.001, 1, 0.05, 1, 400); |
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3.(0.1, 0.2, 0.5, 0.1, 0.7,
350) 2.(0.1, 0.2, 0.5, 0.1, 0.7, 380); |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19, April 16, 2001 |
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| Model Eqs. |
Modeling of a CSTR for a complex
sequence of reactions- revised form. |POLVER05_3 |
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EXCEL
FILE |
f(CA) = V*(-rA)- vo*(CAO-CA)
# |
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TEXT
FILE |
f(CB) = V*(-rB) - vo*(CBO-CB)
# |
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POLYMATH
FILE |
f(CC) = V*rC- vo*CC # |
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f(CD) = V*rD - vo*CD # |
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f(CE) = V*rE - vo*CE # |
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f(T) = 5000*(350-T) - 25*(20+40)*(T-300)
+ V*SRH # |
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rA = 2*r1B # |
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rB = r1B+2*r2C # |
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rC = -3*r1B + r2C # |
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rD = -r3E - r2C # |
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rE = r3E # |
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r1B = -k1B*CA*CB # |
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r2C = -k2C*CC*CB^2 # |
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r3E = k3E*CD # |
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k1B = 0.4*exp((20000/R)*(1/300-1/T))
# |
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k2C = 10*exp((5000/R)*(1/310-1/T))
# |
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k3E = 10*exp((10000/R)*(1/320-1/T))
# |
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SRH = -rA*20000 + 2*r2C*10000
+ 5000*r3E # |
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R = 1.987 # |
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V = 500 # |
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vo = 75/3.3 # |
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CAO = 25/vo # |
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CBO = 50/vo # |
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CA(0)=.5 |
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CB(0)=.01 |
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CC(0)=1 |
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CD(0)=.01 |
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CE(0)=1 |
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T(0)=420 |
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| Variable/function values |
Variable |
Value |
f(x) |
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CA |
0.5 |
2.9109E+04 |
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CB |
0.01 |
1.4520E+04 |
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CC |
1 |
4.3657E+04 |
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CD |
0.01 |
-2.1106E+03 |
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CE |
1 |
2.0918E+03 |
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T |
420 |
5.92E+08 |
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R |
1.987 |
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k1B |
5824.501 |
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k2C |
83.809 |
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r1B |
-29.123 |
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r2C |
-0.008 |
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k3E |
422.912 |
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rA |
-58.245 |
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rB |
-29.139 |
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r3E |
4.229 |
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rC |
87.359 |
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rD |
-4.221 |
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rE |
4.229 |
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SRH |
1.186E+06 |
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V |
500.000 |
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vo |
22.727 |
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CAO |
1.100 |
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CBO |
2.200 |
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| Solution |
Variable |
Value |
f(x) |
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CA |
0.002666326911334 |
2.4869E-14 |
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CB |
0.033464055791589 |
3.5527E-14 |
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CC |
0.837065955800961 |
2.8422E-14 |
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CD |
0.000396698449814 |
4.8225E-16 |
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CE |
0.808537855382225 |
1.4211E-14 |
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T |
372.764586230922 |
1.7462E-10 |
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R |
1.987 |
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k1B |
279.507881234417 |
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k2C |
39.225986593124 |
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r1B |
-0.024939401661106 |
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r2C |
-0.036769752446911 |
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k3E |
92.643973568468000 |
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rA |
-0.049878803322212 |
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rB |
-0.098478906554928 |
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r3E |
0.036751720699192 |
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rC |
0.038048452536407 |
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rD |
0.000018031747719 |
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rE |
0.036751720699192 |
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SRH |
445.939621001986 |
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| Infeasible solution |
Variable |
Value |
f(x) |
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CA |
-0.002818489527374 |
-9.2371E-14 |
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CB |
-0.035077648835548 |
-8.5265E-14 |
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CC |
0.812393532255130 |
-1.2434E-13 |
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CD |
0.000433468786528 |
1.3312E-14 |
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CE |
0.841400733249403 |
-3.9080E-14 |
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T |
371.421990965300 |
-1.5716E-09 |
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R |
1.987 |
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k1B |
253.515466973549 |
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k2C |
38.280400798793 |
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r1B |
-0.025064056580168 |
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r2C |
-0.038265191001633 |
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k3E |
88.231238473553200 |
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rA |
-0.050128113160335 |
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rB |
-0.101594438583434 |
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r3E |
0.038245487874973 |
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rC |
0.036926978738869 |
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rD |
0.000019703126660 |
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rE |
0.038245487874973 |
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SRH |
428.485882548900 |
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| Additional information |
Some algorithms converge to
an infeasible solution |
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from initial guesses 3 and
4. |