| Name: |
Teneq1b - Chemical Equilibrium
Problem - R = 40 |
| Source: |
Hiebrt, K. L., ACM Trans.
Math. Software 8, 1(1982) |
| Reference/s |
Bullard, L. G. and Biegler,
L. T., Computers Chem. Engng. 15(4), 239 (1991). |
| |
Shacham, M., pp. 891-923 in
A. W. Westerberg and H. H. Chien (Eds), |
| |
Proc. of FOCAPD 2, CACHE Publications,
Ann Arbor, Michigan, 1984. |
| |
|
|
|
| Model: |
10 implicit equations, indep.
variables x1 to x10 |
| |
Higher difficulty level |
| |
Constraints: xi are nonnegative
for I=1,2,…10 |
| |
Discontinuities: Undefined
for negative values of x1,x2,x3,x4 |
| |
Initial estimates: 1. (2,
5, 80, 1, 0, 0, 0, 0,20, 5); 2.(1, 1, 20, 1,0, 0, 0, 0, 0, 1); |
| |
3. (2, 5, 40, 1, 0, 0, 0,
0, 0, 5); |
| |
|
|
|
| Solved by |
Shacham, M., POLYMATH 5.1,
build 19, April 9, 2001 |
| |
|
|
|
| Model Eqs. |
Chemical Equilibrium Problem
|POLVER05_1 |
|
EXCEL
FILE |
f(x1) = x1+x4-3 # |
|
TEXT
FILE |
f(x2) = 2*x1+x2+x4+x7+x8+x9+2*x10-R
# |
|
POLYMATH
FILE |
f(x3) = 2*x2+2*x5+x6+x7-8
# |
| |
f(x4) = 2*x3+x5-4*R # |
| |
f(x5) = x1*x5-0.193*x2*x4
# |
| |
f(x6) = x6*sqrt(x2)-0.002597*sqrt(x2*x4*xs)
# |
| |
f(x7) = x7*sqrt(x4)-0.003448*sqrt(x1*x4*xs)
# |
| |
f(x8) = x8*x4-1.799e-5*x2*xs
# |
| |
f(x9) = x9*x4-0.0002155*x1*sqrt(x3*xs)
# |
| |
f(x10) = x10*x4^2-3.846e-5*x4^2*xs
# |
| |
R = 40 # |
| |
xs = x1+x2+x3+x4+x5+x6+x7+x8+x9+x10
# |
| |
x1(0)=2 |
| |
x2(0)=5 |
| |
x3(0)=80 |
| |
x4(0)=1 |
| |
x5(0)=0 |
| |
x6(0)=0 |
| |
x7(0)=0 |
| |
x8(0)=0 |
| |
x9(0)=20 |
| |
x10(0)=5 |
| |
|
|
|
| Variable/function values |
Variable |
Value |
f(x) |
| |
x1 |
2 |
0 |
| |
x2 |
5 |
0 |
| |
x3 |
80 |
2 |
| |
x4 |
1 |
0 |
| |
x5 |
0 |
-0.965 |
| |
x6 |
0 |
-0.062 |
| |
x7 |
0 |
-0.052 |
| |
x8 |
0 |
-0.010 |
| |
x9 |
20 |
19.959 |
| |
x10 |
5 |
4.996 |
| |
R |
40 |
|
| |
xs |
113 |
|
| |
|
|
|
| Solution |
Variable |
Value |
f(x) |
| |
x1 |
2.99763549788728 |
-4.441E-16 |
| |
x2 |
3.96642685827836 |
-1.421E-14 |
| |
x3 |
79.9996980829447 |
-8.882E-16 |
| |
x4 |
0.00236450211272 |
0 |
| |
x5 |
0.00060383411050 |
-2.168E-19 |
| |
x6 |
0.00136594705508 |
-2.168E-18 |
| |
x7 |
0.06457266816721 |
0 |
| |
x8 |
3.53081557628766 |
-6.939E-18 |
| |
x9 |
26.43154979533460 |
-3.469E-17 |
| |
x10 |
0.00449980202242 |
-1.323E-23 |
| |
R |
40 |
|
| |
xs |
116.9995325642010 |
|
| |
|
|
|
| Additional information |
Only constrained algorithm
that keeps the values of x1,x2,x3 and x4 |
| |
positive throughout the iterations
converges from initial guesses 2 and 3. |