| Name: |
Twoeq2 - Steady state material
and energy balance on a reactor |
| 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. |
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| Reference/s |
Shacham, M., Computers
Chem. Engng. 9(2), 103 (1985). |
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Bullard, L. G. and Biegler,
L. T., Computers Chem. Engng. 15(4), 239 (1985). |
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| Model: |
2 implicit equations, indep.
variables x and T |
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Higher difficulty level |
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Constraints: 0<=x=<1 |
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Discontinuities: Undefined
for T=0 |
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Initial estimates: 1. x=1,
T= 400; 2. x=0, T= 300; 3. x=0.5, T= 320; 4. x=0, T= 350; |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19,April 2, 2001 |
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| Model Eqs. |
Steady state material and
energy balance on a reactor |POLVER05_1 |
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EXCEL
FILE |
f(x) = 120*x-75*k*(1-x) # |
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TEXT
FILE |
f(T) = -x*(873-T)+11.0*(T-300)
# |
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POLYMATH
FILE |
k = 0.12*exp(12581*(T-298)/(298*T))
# |
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x(0)=1 |
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T(0)=400 |
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| Variable/function values |
Variable |
Value |
f(x) |
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x |
1 |
120 |
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T |
400 |
627 |
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k |
5683.70 |
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| Solution |
Variable |
Value |
f(x) |
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x |
0.9638680512795 |
-1.5632E-13 |
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T |
346.16369814640 |
2.2737E-13 |
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k |
42.68213968 |
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| Additional Information |
Most methods won't converge
from initial guesses 2 and 3 |
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because of singular points |