Oneeq10

Name: Oneeq10 - Batch Distillation at Infinite Reflux
Source: Paterson, W. R., 1986, Chem. Engng. Sci., 41, 1935
Reference/s Shacham, M. 1989, Chem. Engng. Sci., 44(7), 1495
       
Model: 1 implicit equation, indep. variable name: x
  Higher difficulty level
  Constraints: 0<=x<=1
  Discontinuities: function undefined for x<0 and x>0.95
  Initial range: xmin=0.01, xmax=0.7
       
Solved by Shacham, M., POLYMATH 5.1, build 19 , Nov. 20, 2000
       
Model Eqs. Batch Distillation at Infinite Reflux |POLVER05_1

EXCEL FILE  

f(x) = (1/63)*ln(x)+(64/63)*ln(1/(1-x))+ln(0.95-x)-ln(0.9) #

TEXT FILE  

x(min)=.01, x(max)=.7

POLYMATH FILE 

     
Variable/function values Variable Value f(x)
  x 0.475

3.6884E-03
       
Root 1 Variable Value f(x)
  x

0.036210083704

2.7756E-17
       
Root 2 Variable Value f(x)
  x

0.500000000001

-5.5511E-17
       
Additional information f'(x)=0 at x=0.229. The radius of convergence of derivative based
  methods is very small if started in the region in between the two
  roots
       
Function plot