Figure 8.31 (page 472):

RTD for the optimal reactor configuration.

Code for Figure 8.31

Text of the GNU GPL.

main.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

global a b fixrate theta1 theta2 theta3 c0
a=5; b=0.05;
c0=5;
conv=0.95;
d  = sqrt((1-2*b)*(1-2*b) - 4*b*(b+1));
w1 = (1-2*b + d)/(2*b);
w2 = (1-2*b - d)/(2*b);
x1  = sqrt(w1/a);
x2  = sqrt(w2/a);
c=linspace(0.01,10,300)';
y = 1./rxrate(c);
%%
%% find the outlet of the first PFR, c1, which satisfies r(c1)=1/x2
%%
fixrate=rxrate(x2);
x0=c0;
[x, fval, info] = fsolve('solverate',x0);
info;
c1=x;
%%
%% size the first PFR, theta1 is size such that c(theta1)=c1
%%
t0=0;
ncs=10;
cout = linspace(c0,c1,ncs);
opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, tout] = ode15s(@pfr,cout,t0,opts);
theta1 = tout(ncs);
%%
%% size the cstr, theta2= (c1-c2)/r(c2), c2=x2
%%
c2=x2;
theta2 = (c1-c2)/rxrate(c2);
%%
%% size the second PFR, c3, which satisfies c3=(1-conv)*c0
%%
c3 = (1-conv)*c0;
t0=0;
ncs=10;
cout = linspace(c2,c3,ncs);
opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, tout] = ode15s(@pfr,cout,t0,opts);
theta3 = tout(ncs);
c0; c1; c2; c3;
theta1; theta2; theta3;
%%
%% optimal reactor is PFR --->    CSTR --->  PFR
%%                    theta1      theta2     theta3

%%compute the rtd
npts=100;
thetamin=theta1+theta3;
thetamax= thetamin + 5*theta2;
theta = linspace(thetamin,thetamax,npts)';
p = 1/theta2*exp(-(theta-(theta1+theta3))/theta2);
table = [0 0; thetamin 0; [theta p]];
plot (table(:,1), table(:,2));
title ('Figure 8.31')

rxrate.m

function rate = rxrate(c)
  global a b fixrate
  rate = c./(1+a*c.*c) + b*c;

solverate.m

function retval = solverate(c)
  global a b fixrate
  retval = fixrate - rxrate(c);

pfr.m

function dtdc = pfr(c,t)
  dtdc = - 1/rxrate(c);