| Name: |
Sixeq2a - Steady state solution
for reaction rate equations - 1st parameter set |
| Source: |
Shacham, M., pp. 891-923 in
A. W. Westerberg and H. H. Chien (Eds), |
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Proc. of FOCAPD 2, CACHE Publications,
Ann Arbor, Michigan, 1984. |
| Reference/s |
Bullard, L. G. and Biegler,
L. T., Computers Chem. Engng. 15(4), 239 (1991). |
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| Model: |
6 implicit equations, indep.
variables x1 to x6 |
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Average difficulty level |
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Constraints: xi are nonnegative
for I=1,2,…6 |
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Discontinuities: none |
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Initial estimates: 1. (0.99,
0.05, 0.05, 0.99, 0.05, 0); 2.(0.05, 0.99, 0.05, 0.05, 0.99,
0); |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19, April 9, 2001 |
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| Model Eqs. |
Steady state solution for
reaction rate equations - 1st parameter set |POLVER05_1 |
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EXCEL
FILE |
f(x1) = 1-x1-k1*x1*x6+kr1*x4
# |
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TEXT
FILE |
f(x2) = 1-x2-k2*x2*x6+kr2*x5
# |
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POLYMATH
FILE |
f(x3) = -x3+2*k3*x4*x5 # |
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f(x4) = k1*x1*x6-kr1*x4-k3*x4*x5
# |
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f(x5) = 1.5*(k2*x2*x6-kr2*x5)-k3*x4*x5
# |
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f(x6) = 1-x4-x5-x6 # |
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k1 = 31.24 # |
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k2 = 2.062 # |
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kr1 = 0.272 # |
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kr2 = 0.02 # |
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k3 = 303.03 # |
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x1(0)=.99 |
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x2(0)=.05 |
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x3(0)=.05 |
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x4(0)=.99 |
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x5(0)=.05 |
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x6(0)=0 |
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| Variable/function values |
Variable |
Value |
f(x) |
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x1 |
0.99 |
0.279 |
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x2 |
0.05 |
0.951 |
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x3 |
0.05 |
29.950 |
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x4 |
0.99 |
-15.269 |
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x5 |
0.05 |
-15.001 |
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x6 |
0 |
-0.04 |
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k1 |
31.24 |
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k2 |
2.062 |
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kr1 |
0.272 |
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kr2 |
0.02 |
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k3 |
303.03 |
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| Solution |
Variable |
Value |
f(x) |
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x1 |
0.9700739407529 |
0 |
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x2 |
0.9800492938353 |
-3.686E-17 |
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x3 |
0.0598521184942 |
-1.388E-17 |
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x4 |
0.9900268865935 |
0 |
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x5 |
0.0000997509107 |
0 |
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x6 |
0.0098733624958 |
4.337E-17 |
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| Infeasible solution |
Variable |
Value |
f(x) |
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x1 |
1.0332985964390 |
3.88E-17 |
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x2 |
1.0221990642970 |
6.94E-17 |
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x3 |
-0.0665971928906 |
-8.83E-13 |
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x4 |
-0.0001097977609 |
4.45E-13 |
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x5 |
1.0011422708840 |
4.42E-13 |
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x6 |
-0.0010324725201 |
-3.9262E-13 |
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| Additional information |
Most algorithms converge to
the infeasible solution from |
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the second initial estimate |