| Name: |
Oneeq10 - Batch Distillation
at Infinite Reflux |
| Source: |
Paterson, W. R., 1986, Chem.
Engng. Sci., 41, 1935 |
| Reference/s |
Shacham, M. 1989, Chem.
Engng. Sci., 44(7), 1495 |
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| Model: |
1 implicit equation, indep.
variable name: x |
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Higher difficulty level |
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Constraints: 0<=x<=1 |
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Discontinuities: function
undefined for x<0 and x>0.95 |
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Initial range: xmin=0.01,
xmax=0.7 |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19 , Nov. 20, 2000 |
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| Model Eqs. |
Batch Distillation at Infinite
Reflux |POLVER05_1 |
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EXCEL
FILE |
f(x) = (1/63)*ln(x)+(64/63)*ln(1/(1-x))+ln(0.95-x)-ln(0.9)
# |
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TEXT
FILE |
x(min)=.01, x(max)=.7 |
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POLYMATH
FILE |
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| Variable/function values |
Variable |
Value |
f(x) |
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x |
0.475 |
3.6884E-03 |
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| Root 1 |
Variable |
Value |
f(x) |
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x |
0.036210083704 |
2.7756E-17 |
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| Root 2 |
Variable |
Value |
f(x) |
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x |
0.500000000001 |
-5.5511E-17 |
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| Additional information |
f'(x)=0 at x=0.229. The radius
of convergence of derivative based |
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methods is very small if started
in the region in between the two |
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roots |
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| Function plot |
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