| Name: |
Sixeq4a - Modeling of a CSTR
for a complex sequence of reactions - original formulation |
| 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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Higher 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) |
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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 - original formulation |POLVER05_3 |
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EXCEL
FILE |
f(CA) = V- vo*(CAO-CA)/(-rA)
# |
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TEXT
FILE |
f(CB) = V - vo*(CBO-CB)/(-rB)
# |
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POLYMATH
FILE |
f(CC) = V- vo*CC/rC # |
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f(CD) = V - vo*CD/rD # |
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f(CE) = V - vo*CE/rE # |
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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 |
499.77 |
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CB |
0.01 |
498.29 |
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CC |
1 |
499.74 |
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CD |
0.01 |
500.05 |
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CE |
1 |
494.63 |
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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 |
0.002666326911275 |
-7.4465E-12 |
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CB |
0.033464055791484 |
-1.2506E-12 |
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CC |
0.837065955801026 |
-2.5466E-11 |
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CD |
0.000396698449818 |
-2.4964E-05 |
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CE |
0.808537855402075 |
-5.5707E-12 |
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T |
372.764586231268 |
3.9290E-09 |
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R |
1.987 |
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k1B |
279.507881241430 |
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k2C |
39.225986593370 |
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r1B |
-0.024939401661107 |
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r2C |
-0.036769752446913 |
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k3E |
92.643973569630200 |
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rA |
-0.049878803322214 |
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rB |
-0.098478906554932 |
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r3E |
0.036751720700094 |
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rC |
0.038048452536408 |
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rD |
0.000018031746819 |
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rE |
0.036751720700094 |
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SRH |
445.939621006497 |
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| Additional information |
None of the algorithms converges
when starting form the initial |
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estimates shown. The solution
with five digits accuracy should |
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be entered as initial guess
to reach the solution. |