| Name: | Oneeq20a - Equilibrium conversion in a tubular reactor - original form | ||
| Source: | N. Brauner, M. Shacham and M. Cutlip, Chem. Eng. Educ., 30 (1), 20-25 (1996). | ||
| Reference/s | |||
| Model: | 1 implicit equation, indep. variable name: xa | ||
| High difficulty level | |||
| Constraints: 0<=xa<=1 | |||
| Discontinuities: function undefined for xa=1.029 | |||
| Initial range: xamin=0.75, xamax=1.2 | |||
| Solved by | Shacham, M., POLYMATH 5.1, build 19, April 1, 2001 | ||
| Model Eqs. | Equilibrium conversion in a tubular reactor - original form |POLVER05_1 | ||
| f(xa)=-ra/FA0 # | |||
| T=313 # | |||
| P0=10 # | |||
| FA0=20*P0/(0.082*450) # | |||
| k1=1.277*1.e9*exp(-90000/(8.31*T)) # | |||
| k2=1.29*1.e11*exp(-135000/(8.31*T)) # | |||
| den=1+7*P0*(1-xa)/(1+xa) # | |||
| xa1=1+xa # | |||
| ra = (-k1*P0*(1-xa)/xa1+k2*P0*P0*xa*xa/(xa1^2))/den # | |||
| xa(min)=.75, xa(max)=1.2 | |||
| Variable/function values | Variable | Value | f(x) |
| xa | 0.85 | 2.69E-08 | |
| T | 313 | ||
| P0 | 10 | ||
| FA0 | 5.420054201 | ||
| k1 | 1.19915E-06 | ||
| k2 | 3.71E-12 | ||
| den | 6.675675676 | ||
| xa1 | 1.85 | ||
| ra | -1.45634E-07 | ||
| Root | Variable | Value | f(x) |
| xa | 0.999251497006000 | 7.9049E-10 | |
| T | 313 | ||
| P0 | 10 | ||
| FA0 | 5.42005420054200 | ||
| k1 | 1.1991500E-06 | ||
| k2 | 3.7120483E-12 | ||
| den | 1.02620741295400 | ||
| xa1 | 1.99925149700600 | ||
| ra | -4.2844995E-09 | ||
| Additional information | There is a scaling problem. Function value is very small | ||
| throughout the entire range of interest (order of E-8). | |||
| A point discontinuity very close to the root. | |||
| Function plot | |||