| Name: | Threeq7 - Steady state operation of an adiabatic CSTR | ||
| Source: | Seadet, J. D. et al., Computers chem. Engng.,14 71(1990). | ||
| Reference/s | Gupta, Y.P. (1995). Ind. Eng. Chem. Res. 34, 536-544 | ||
| Model: | 3 implicit equations, indep. variables CA, CB and T | ||
| Lower difficulty level | |||
| Constraints: 0<=CA<=1, 0<=CB<=1, 0<=CC<=1, T>0 | |||
| Discontinuities: Undefined for T=0 and when 1+KA*CB=0 | |||
| Initial estimates: 1.T=300, CA=3, CB=0; 2. T=350, CA=3, CB=0; | |||
| 3.T=400, CA=3, CB=0; 4.T=600, CA=3, CB=0; | |||
| 5. T=700, CA=3, CB=0; | |||
| Solved by | Shacham, M., POLYMATH 5.1, build 19, April 5, 2001 | ||
| Model Eqs. | Steady state operation of an adiabatic CSTR |POLVER05_3 | ||
| f(CA) = CA0-CA-theta*k1*CA/(1+KA*CB) # | |||
| f(CB) = CB-CB0-(theta*k1*CA/(1+KA*CB)-theta*k2*CB+theta*k2p*CC) # | |||
|
f(T) = 85*(T-T0)+0.02*(T^2-T0^2)-((16000+3*T-0.002*T^2)*((CA0-CA)/CA0) +(30000+4*T-0.003*T^2)*CC/CA0) # |
|||
| CC = (CC0+theta*k2*CB)/(1+theta*k2p) # | |||
| k1 = 4e6*exp(-60000/(8.314*T)) # | |||
| KA = 17*exp(-7000/(8.314*T)) # | |||
| k2 = 3e4*exp(-80000/(8.314*T)) # | |||
| k2p = 3e4*exp(-90000/(8.314*T)) # | |||
| T0 = 298 # | |||
| CA0 = 3 # | |||
| CB0 = 0 # | |||
| CC0 = 0 # | |||
| theta = 300 # | |||
| CA(0)=3 | |||
| CB(0)=0 | |||
| T(0)=300 | |||
| Variable/function values | Variable | Value | f(x) |
| CA | 3 | -1.2853E-01 | |
| CB | 0 | -1.2853E-01 | |
| T | 300 | 1.9392E+02 | |
| CC | 0.00 | ||
| theta | 300 | ||
| k1 | 1.428E-04 | ||
| KA | 1.027E+00 | ||
| k2 | 3.527E-10 | ||
| k2p | 6.400E-12 | ||
| T0 | 2.980E+02 | ||
| CA0 | 3.00 | ||
| CB0 | 0.00 | ||
| CC0 | 0.00 | ||
| Solution 1 | Variable | Value | f(x) |
| CA | 2.7873203092940 | -3.0531E-16 | |
| CB | 0.2126796260201 | -3.0531E-16 | |
| T | 310.212556340 | -2.2737E-13 | |
| CC | 6.4686127E-08 | ||
| k1 | 3.152768321E-04 | ||
| KA | 1.1264778653520 | ||
| k2 | 1.013827367E-09 | ||
| k2p | 2.099275102E-11 | ||
| Solution 2 | Variable | Value | f(x) |
| CA | 2.3804209271400 | 9.9920E-16 | |
| CB | 0.6195774301750 | 1.1102E-15 | |
| T | 333.492475848 | -9.0949E-13 | |
| CC | 1.6426848E-06 | ||
| k1 | 1.599455327E-03 | ||
| KA | 1.3614614093880 | ||
| k2 | 8.837662641E-09 | ||
| k2p | 2.398774591E-10 | ||
| Solution 3 | Variable | Value | f(x) |
| CA | 0.1263969394304 | 8.8818E-16 | |
| CB | 2.8499084983470 | 1.3323E-15 | |
| T | 462.569151959 | -3.6380E-12 | |
| CC | 2.369456222E-02 | ||
| k1 | 6.705676413E-01 | ||
| KA | 2.7539764669600 | ||
| k2 | 2.773094840E-05 | ||
| k2p | 2.059184000E-06 | ||
| Solution 4 | Variable | Value | f(x) |
| CA | 3.801064064E-03 | -8.8818E-16 | |
| CB | 1.7136336431310 | 2.4425E-15 | |
| T | 594.027432439 | -3.6380E-11 | |
| CC | 1.2825652928060 | ||
| k1 | 2.117809213E+01 | ||
| KA | 4.1199826416980 | ||
| k2 | 2.768367299E-03 | ||
| k2p | 3.654782339E-04 | ||
| Solution 5 | Variable | Value | f(x) |
| CA | 3.797570282E-04 | 5.3291E-15 | |
| CB | 0.6888918938783 | 2.6645E-15 | |
| T | 691.624151130 | 2.9104E-11 | |
| CC | 2.3107283490930 | ||
| k1 | 1.176034598E+02 | ||
| KA | 5.0321966065050 | ||
| k2 | 2.722292150E-02 | ||
| k2p | 4.782570881E-03 | ||