| Name: |
Sixeq3 - Bubble point of a
nonideal binary mixture (isobutanol-water) |
| Source: |
Henley, E. J. and Rosen, E.
M., Material and Energy Balance |
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Computations, Wiley: New York, 1969 |
| Reference/s |
Shacham, M., N. Brauner and
M. Pozin, Computers chem. Engng. 22, 321-323(1998) |
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| Model: |
6 implicit equations, indep.
variables x11, x12, x21, x22, t and beta1 |
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Higher difficulty level |
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Constraints: x11, x12, x21,
x22 and beta1 are bounded between zero and one |
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Discontinuities: Undefined
for t=-191.15 and t= -235, |
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additional discontinuities
outside of the feasible region |
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Initial estimates: 1.(0, 1,
1, 0, 100, 0.8) 2.(0.05, 0.95, 1, 0, 100, 0.8); |
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3.(0.1, 0.9, 1, 0, 100, 0.8)
2.(0, 1.0, 0.3, 0.7, 100, 0.8); |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19, April 4, 2001 |
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| Model Eqs. |
Bubble point of a nonideal
binary mixture (isobutanol-water) |POLVER05_3 |
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EXCEL
FILE |
f(x11)=x11-0.2/(beta1+(1-beta1)*k11/k12)
# |
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TEXT
FILE |
f(x12)=x12-x11*k11/k12 # |
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POLYMATH
FILE |
f(x21)=x21-0.8/(beta1+(1-beta1)*k21/k22)
# |
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f(x22)=x22-x21*k21/k22 # |
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f(t)=x11*(1-k11)+x21*(1-k21)
# |
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f(beta1)=(x11-x12)+(x21-x22)
# |
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p1=10^(7.62231-1417.9/(191.15+t))
# |
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p2=10^(8.10765-1750.29/(235+t))
# |
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A=1.7 # |
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B=0.7 # |
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gamma11=10^(A*x21*x21/((A*x11/B+x21)^2))
# |
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gamma21=10^(B*x11*x11/((x11+B*x21/A)^2))
# |
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gamma12=10^(A*x22*x22/((A*x12/B+x22)^2))
# |
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gamma22=10^(B*x12*x12/((x12+B*x22/A)^2))
# |
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k11=gamma11*p1/760 # |
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k21=gamma21*p2/760 # |
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k12=gamma12*p1/760 # |
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k22=gamma22*p2/760 # |
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x11(0)=0 |
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x12(0)=1 |
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x21(0)=1 |
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x22(0)=0 |
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t(0)=100 |
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beta1(0)=0.8 |
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| Variable/function values |
Variable |
Value |
f(x) |
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x11 |
0 |
-1.8478E-02 |
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x12 |
1 |
1.0000E+00 |
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x21 |
1 |
4.7512E-02 |
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x22 |
0 |
-1.9953E-01 |
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t |
100 |
-4.8243E-03 |
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beta1 |
0.8 |
0 |
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p1 |
565.343 |
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p2 |
763.666 |
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A |
1.7 |
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B |
0.7 |
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gamma11 |
50.119 |
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gamma21 |
1 |
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gamma12 |
1 |
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gamma22 |
5.012 |
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k11 |
37.282 |
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k21 |
1.005 |
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k12 |
0.744 |
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k22 |
5.036 |
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| Solution |
Variable |
Value |
f(x) |
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x11 |
0.0226982050031 |
2.0817E-17 |
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x12 |
0.6867475652564 |
-8.8818E-16 |
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x21 |
0.9773017949969 |
1.11E-16 |
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x22 |
0.3132524347436 |
-1.11E-16 |
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t |
88.5378298767092 |
-8.88E-16 |
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beta1 |
0.7329990726454 |
1.11E-16 |
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p1 |
357.050287513596 |
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p2 |
498.658802103785 |
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A |
1.7 |
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B |
0.7 |
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gamma11 |
33.3664899761041 |
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gamma21 |
1.0046055214574 |
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gamma12 |
1.1028206986512 |
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gamma22 |
3.1342223411214 |
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k11 |
15.6756774201151 |
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k21 |
0.6591518235747 |
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k12 |
0.5181084835912 |
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k22 |
2.0564573133559 |
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| False solution |
Variable |
Value |
f(x) |
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x11 |
-3.60705966344E-12 |
-3.1634E-12 |
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x12 |
2.21070994628E-10 |
4.7069E-10 |
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x21 |
2.25589821898E-10 |
7.41E-11 |
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x22 |
9.11767606707E-13 |
-4.45E-11 |
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t |
8.08592408374E+01 |
1.97E-10 |
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beta1 |
6.61021756207E+09 |
-1.05E-23 |
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p1 |
256.814444632665 |
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p2 |
368.374236773243 |
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A |
1.7 |
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B |
0.7 |
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gamma11 |
69.2047546606069 |
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gamma21 |
1.0026342410709 |
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gamma12 |
1.0000112511327 |
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gamma22 |
4.9845791143404 |
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k11 |
23.3852376764521 |
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k21 |
0.4859797675227 |
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k12 |
0.3379175448501 |
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k22 |
2.4160401669487 |
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| Additional information |
An initial guesses with x11>0.8
cause no convergence or convergence |
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to a false solution |