## Code for Figure 8.31

### main.m

```
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78% 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]];
save -ascii leven_rtd.dat table;
if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot (table(:,1), table(:,2));
% TITLE
end % PLOTTING

```

### rxrate.m

```
1
2
3function rate = rxrate(c)
global a b fixrate
rate = c./(1+a*c.*c) + b*c;

```

### solverate.m

```
1
2
3function retval = solverate(c)
global a b fixrate
retval = fixrate - rxrate(c);

```

### pfr.m

```
1
2function dtdc = pfr(c,t)
dtdc = - 1/rxrate(c);

```