|
Name: |
Threeq4b - Eq. composition in a constant volume
gas-phase batch reactor - rev. form |
|
Source: |
Shacham, M., N. Brauner, and M. B. Cutlip,
Chem. Eng. Educ, 28(1), 30(1994) |
|
Reference/s |
Cutlip, M. B. and Shacham, M, Problem Solving
in Chemical |
|
|
Engineering with Numerical Methods, Prentice Hall Inc., 1999 |
|
|
|
|
|
|
Model: |
3 implicit equations, indep. variables CD,CX,CZ |
|
|
Higher difficulty level |
|
|
Constraints: CA, CB, CC,CD,CX,CY and CZ are
nonnegative |
|
|
Discontinuities: none |
|
|
Initial estimates: 1. CD=0.7, CX=0.2, Cz=0.4;
2.CD=0, CX=0.1, Cz=0; |
|
|
3. CD=1, CX=1, Cz=1 4. CD=10, CX=10, Cz=10 |
|
|
|
|
|
|
Solved by |
Shacham, M., POLYMATH 5.1, build 19, April
4, 2001 |
|
|
|
|
|
|
Model Eqs. |
Equilibrium composition in a constant volume
gas-phase batch reactor |POLVER05_3 |
|
EXCEL
FILE |
f(CD) = CC*CD-KC1* (CA*CB) # |
|
TEXT
FILE |
f(CX) = CX*CY-KC2 *(CB*CC) # |
|
POLYMATH
FILE |
f(CZ) = CZ-KC3 *(CA*CX) # |
|
|
CY=CX+CZ # |
|
|
CC=CD-CY # |
|
|
CA=CA0-CD-CZ # |
|
|
CB=CB0-CD-CY # |
|
|
KC1=1.06 # |
|
|
KC2=2.63 # |
|
|
KC3=5 # |
|
|
CA0=1.5 # |
|
|
CB0=1.5 # |
|
|
CD(0)=0.7 |
|
|
CX(0)=0.2 |
|
|
CZ(0)=0.4 |
|
|
|
|
|
|
|
|
|
|
|
Variable/function values |
Variable |
Value |
f(x) |
|
|
CD |
0.7 |
-1.4800E-02 |
|
|
CX |
0.2 |
6.7400E-02 |
|
|
CZ |
0.4 |
-5.5511E-17 |
|
|
CY |
0.60 |
|
|
|
CC |
0.1 |
|
|
|
CA |
0.40 |
|
|
|
CB |
0.20 |
|
|
|
CA0 |
1.50 |
|
|
|
CB0 |
1.50 |
|
|
|
KC1 |
1.06 |
|
|
|
KC2 |
2.63 |
|
|
|
KC3 |
5.00 |
|
|
|
|
|
|
|
Solution 1 |
Variable |
Value |
f(x) |
|
|
CD |
0.7053344059695 |
-1.3878E-17 |
|
|
CX |
0.1777924200537 |
-8.3267E-17 |
|
|
CZ |
0.3739765850146 |
-5.5511E-17 |
|
|
CY |
0.5517690050683 |
|
|
|
CC |
0.1535654009011 |
|
|
|
CA |
0.4206890090159 |
|
|
|
CB |
0.2428965889622 |
|
|
|
|
|
|
|
Infeasible solution 1 |
Variable |
Value |
f(x) |
|
|
CD |
0.0555561340633 |
-2.7756E-17 |
|
|
CX |
0.5972196082270 |
4.4409E-16 |
|
|
CZ |
1.0820734849200 |
2.2204E-16 |
|
|
CY |
1.6792930931470 |
|
|
|
CC |
-1.6237369590830 |
|
|
|
CA |
0.3623703810169 |
|
|
|
CB |
-0.2348492272101 |
|
|
|
|
|
|
|
Infeasible solution 2 |
Variable |
Value |
f(x) |
|
|
CD |
1.0701041278950 |
2.7756E-16 |
|
|
CX |
-0.3227156095103 |
2.2204E-16 |
|
|
CZ |
1.1305335070740 |
0.0000E+00 |
|
|
CY |
0.8078178975638 |
|
|
|
CC |
0.2622862303310 |
|
|
|
CA |
-0.7006376349689 |
|
|
|
CB |
-0.3779220254586 |
|
|
|
|
|
|
|
Additional information |
Convergence to infeasible solutions from initial
guesses 3 and 4 |