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).
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