k = 0.5   ;
vDot = 0.0005;  
cNaOH0 = 0.05;  
cEtAc0 = 0.05;   
length = 
      100;   
diam = 
      0.05;   
vol = 
      Pi*diam^2/4*length;
recycle1 = 0;
recycle2 = 1;
recycle3 = 5;
rate1 = 
        k*cEtAc0^2*(1 - x)^2/(1 + 
                recycle1*(1 - x)^2);
rate2 = 
        k*cEtAc0^2*(1 - x)^2/(1 + 
                recycle2*(1 - x)^2);
rate3 = 
        k*cEtAc0^2*(1 - x)^2/(1 + 
                recycle3*(1 - x)^2);
x01 = recycle1*xF/(1 + recycle1);
x02 = recycle2*xF/(1 + recycle2);
x03 = recycle3*xF/(1 + recycle3);

soln1 = 
      FindRoot[vol/vDot/cEtAc0 == (recycle1 + 1)*
            Integrate[1/rate1, {x, x01, xF}], {xF, 
          0.1}]
soln2 = 
      FindRoot[vol/vDot/cEtAc0 == (recycle2 + 1)*
            Integrate[1/rate2, {x, x02, xF}], {xF, 
          0.7}]
soln3 = 
      FindRoot[vol/vDot/cEtAc0 == (recycle3 + 1)*
            Integrate[1/rate3, {x, x03, xF}], {xF, 0.5}]

Why are these numbers so different from the ones provided by Peters et al. (2003), 0.831, 0.596, 0.131? (They do show the expected trend: conversion decreases as recycle increases. Does the solution depend on the choice of the initial guess?)

lrr3@psu.edu (02/04/2008, 5 pm)