| Name: | Foureq1 - Steady state operation of an adiabatic CSTR | ||
| Source: | Seader, J. D. et al., Computers chem. Engng.,14 71(1990). | ||
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| Reference/s | Gupta, Y.P. (1995). Ind. Eng. Chem. Res. 34, 536-544 | ||
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| Model: | 4 implicit equations, indep. variables CA, CB, CC 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. (3, 0, 0, 300); 2. (3, 0, 0, 350); | |||
| 3.(3, 0, 0, 400); 4. (0, 2, 1, 600); 5. (3, 0, 0,700) | |||
| Solved by | Shacham, M., POLYMATH 5.1, build 19, April 15, 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(CC) = CC-CC0-theta*k2*CB+theta*k2p*CC # | |||
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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) # |
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| 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)=0 | |||
| CB(0)=0.6 | |||
| CC(0)=3 | |||
| T(0)=691 | |||
| Variable/function values | Variable | Value | f(x) |
| CA | 3 | -1.2853E-01 | |
| CB | 0 | -1.2853E-01 | |
| CC | 0 | 0.0000E+00 | |
| T | 300.00 | 1.9392E+02 | |
| 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 | ||
| theta | 300.00 | ||
| Solution 1 | Variable | Value | f(x) |
| CA | 2.7873203092938 | -3.0531E-16 | |
| CB | 0.2126796260201 | -2.2204E-16 | |
| CC | 6.468613E-08 | -3.8039E-22 | |
| T | 310.2125563399750 | -2.2737E-13 | |
| k1 | 3.15276832125E-04 | ||
| KA | 1.12647786535E+00 | ||
| k2 | 1.01382736739E-09 | ||
| k2p | 2.09927510185E-11 | ||
| Solution 2 | Variable | Value | f(x) |
| CA | 2.3804209271402 | -1.7208E-14 | |
| CB | 0.6195774301750 | -1.7319E-14 | |
| CC | 1.6426847740E-06 | -1.7298E-19 | |
| T | 333.4924758483970 | 1.3642E-12 | |
| k1 | 1.59945532722E-03 | ||
| KA | 1.36146140939E+00 | ||
| k2 | 8.83766264109E-09 | ||
| k2p | 2.39877459055E-10 | ||
| Solution 3 | Variable | Value | f(x) |
| CA | 0.1263969394304 | -3.1086E-15 | |
| CB | 2.8499084983472 | -3.1086E-15 | |
| CC | 0.0236945622224 | 1.6558E-17 | |
| T | 462.5691519589690 | 0.00 | |
| k1 | 0.6705676413292 | ||
| KA | 2.7539764669601 | ||
| k2 | 2.77309484090E-05 | ||
| k2p | 2.05918400600E-06 | ||
| Solution 4 | Variable | Value | f(x) |
| CA | 3.80106406388E-03 | -2.6645E-15 | |
| CB | 1.7136336431305 | 2.6645E-15 | |
| CC | 1.2825652928056 | -5.2180E-15 | |
| T | 594.0274324392960 | 1.46E-11 | |
| k1 | 21.1780921290670 | ||
| KA | 4.1199826416982 | ||
| k2 | 2.76836729937E-03 | ||
| k2p | 3.65478233891E-04 | ||
| Solution 5 | Variable | Value | f(x) |
| CA | 3.79757028182E-04 | 1.3323E-15 | |
| CB | 0.6888918938783 | -5.7732E-15 | |
| CC | 2.3107283490935 | 7.5495E-15 | |
| T | 691.6241511300760 | -7.28E-12 | |
| k1 | 117.6034597549030 | ||
| KA | 5.0321966065053 | ||
| k2 | 2.72229214955E-02 | ||
| k2p | 4.78257088073E-03 | ||