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  
f(x) = (1/63)*ln(x)+(64/63)*ln(1/(1x))+ln(0.95x)ln(0.9) #  
x(min)=.01, x(max)=.7  
Variable/function values  Variable  Value  f(x) 
x  0.475 


Root 1  Variable  Value  f(x) 
x 



Root 2  Variable  Value  f(x) 
x 



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 