| Name: |
Teneq3 - Small flow sheeting
system with recycle |
| Source: |
Swaney, R. E. and Wilhelm,
C. E., Proceedings of FOCAPD III, 391 (1990) |
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| Reference/s |
Bullard, L. G. and Biegler,
L. T., Computers Chem. Engng. 15(4), 239 (1991). |
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| Model: |
10 implicit equations, indep.
variables x1 to x10 |
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Lower difficulty level |
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Constraints: xi are nonnegative
for I=1,2,…10 |
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Discontinuities: Undefined
for some infeasible values of the variables (x3=-x4, etc) |
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Initial estimates: 1.(0.9,
0.1, 1, 0.2, 0.5, 0.8, 0.2, 0.7, 0.2, 0.1) ; |
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2.(0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.5, 0.5, 0.5); |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19, April 17, 2001 |
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| Model Eqs. |
Small flow sheeting system
with recycle |POLVER05_3 |
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EXCEL
FILE |
f(x1) = x3-x1-x9 # |
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TEXT
FILE |
f(x2) = x4-x2-x10 # |
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POLYMATH
FILE |
f(x3) = (x3/(x3+x4)-xAinf)*exp(-(kA+kB)*tau)+xAinf-x5/(x5+x6)
# |
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f(x4) = x3+x4-x5-x6 # |
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f(x5) = x7/(x7+x8)-KA*x9/(x9+x10)
# |
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f(x6) = x8/(x7+x8)-KB*x10/(x9+x10)
# |
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f(x7) = x5-x7-x9 # |
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f(x8) = x6-x8-x10 # |
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f(x9) = x1-0.9 # |
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f(x10) = x2-0.1 # |
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tau=22.5/(x3+x4) # |
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xAinf=kB/(kA+kB) # |
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KA=0.4409 # |
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KB=1.8299 # |
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kA=0.08 # |
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kB=0.03 # |
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x1(0)=0.9 |
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x2(0)=0.1 |
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x3(0)=1 |
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x4(0)=0.2 |
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x5(0)=0.5 |
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x6(0)=0.8 |
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x7(0)=0.2 |
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x8(0)=0.7 |
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x9(0)=0.2 |
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x10(0)=0.1 |
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| Variable/function values |
Variable |
Value |
f(x) |
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x1 |
0.9 |
-0.1 |
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x2 |
0.1 |
0 |
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x3 |
1 |
-0.0406 |
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x4 |
0.2 |
-0.1 |
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x5 |
0.5 |
-0.0717 |
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x6 |
0.8 |
0.1678 |
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x7 |
0.2 |
0.1 |
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x8 |
0.7 |
8.327E-17 |
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x9 |
0.2 |
0 |
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x10 |
0.1 |
0 |
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tau |
18.75 |
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kB |
0.03 |
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KA |
0.4409 |
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KB |
1.8299 |
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kA |
0.08 |
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xAinf |
0.2727 |
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| Solution |
Variable |
Value |
f(x) |
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x1 |
0.9 |
-5.55E-17 |
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x2 |
0.1 |
0 |
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x3 |
1.1898916711704 |
-5.55E-17 |
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x4 |
0.2952987508752 |
0 |
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x5 |
0.5533206920487 |
-5.55E-17 |
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x6 |
0.9318697299969 |
-1.110E-16 |
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x7 |
0.2634290208783 |
0 |
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x8 |
0.7365709791217 |
-8.327E-17 |
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x9 |
0.2898916711704 |
0 |
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x10 |
0.1952987508752 |
0 |
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tau |
15.1495725167753 |
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