| Name: |
Twoeq4b - Wilson coeff. from
azeotropic data (ethyl alcohol - n hexane)- 2nd form. |
| Source: |
Cutlip, M. B. and Shacham,
M, Problem Solving in Chemical |
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Engineering with Numerical
Methods (2nd Ed.), Prentice Hall
Inc., |
| Reference/s |
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| Model: |
2 implicit equations, indep.
variables G12 and G21 |
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Average difficulty level |
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Constraints: G12>=0, G21>=0 |
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Discontinuities: Undefined
for G12<0 or G21<0 |
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Initial estimates: 1. G12=0.1,
G21=0.1; 2.G12=0.5, G21=0.5; 3. G12=0.8, G21=0.8 |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19, April 2, 2001 |
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| Model Eqs. |
Wilson coeff. from azeotropic
data (ethyl alcohol - n hexane)- 2nd form. |POLVER05_1 |
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EXCEL
FILE |
f(G21) = t1*t2*(ln(gamma2)+ln(t2))+x1*(G12*t2-G21*t1)
# |
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TEXT
FILE |
f(G12) = t1*t2*(ln(gamma1)+ln(t1))-x2*(G12*t2-G21*t1)
# |
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POLYMATH
FILE |
t=58.7 # |
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pw1=21 # |
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x1=(pw1/46.07)/(pw1/46.07+(100-pw1)/86.18)
# |
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P2 = 10^(6.87776-1171.53/(224.366+t))
# |
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P1 = 10^(8.04494-1554.3/(222.65+t))
# |
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gamma2=760/P2 # |
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gamma1=760/P1 # |
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x2=1-x1 # |
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t1=x1+x2*G12 # |
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t2=x2+x1*G21 # |
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g2calc=exp(-ln(t2)-x1*(G12*t2-G21*t1)/(t1*t2))
# |
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g1calc=exp(-ln(t1)+x2*(G12*t2-G21*t1)
/(t1*t2)) # |
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G21(0)=0.8 |
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G12(0)=0.8 |
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| Variable/function values |
Variable |
Value |
f(x) |
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G21 |
0.8 |
2.2629E-01 |
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G12 |
0.8 |
5.1922E-01 |
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t |
58.7 |
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pw1 |
21 |
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x1 |
0.3321 |
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P2 |
548.3315 |
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P1 |
331.5158 |
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gamma2 |
1.3860 |
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gamma1 |
2.2925 |
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x2 |
0.6679 |
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t1 |
0.8664 |
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t2 |
0.9336 |
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g2calc |
1.0478 |
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g1calc |
1.2065 |
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| Solution |
Variable |
Value |
f(x) |
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G21 |
0.3017535528355 |
1.7347E-17 |
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G12 |
0.0785888934885 |
-2.0817E-17 |
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t |
58.7 |
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pw1 |
21 |
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x1 |
0.3321117719491 |
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P2 |
548.3315489669 |
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P1 |
331.5158092912 |
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gamma2 |
1.3860227474270 |
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gamma1 |
2.2925000217180 |
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x2 |
0.6678882280509 |
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t1 |
0.3846003687656 |
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t2 |
0.7681041351750 |
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g2calc |
1.3860227474270 |
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g1calc |
2.2925000217180 |
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| Additional Information |
In this form the radius of
convergence of most methods increases |
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to include also the 3rd initial
guess. |