Figure 6.13:

Eigenvalues of Jacobian matrix vs. reactor temperature.

Code for Figure 6.13

Text of the GNU GPL.

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
% 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 k_m T_m E c_Af c_A C_ps T_f DeltaH_R U T_a
%
% multiplicity parameters
%
% units are kmol, min, kJ, K, m^3
%
%
k_m      = 0.001;
T_m      = 298;
E        = 8000;
c_Af     = 2;
C_p      = 4;
rho      = 1000;
C_ps     = rho*C_p;
T_f      = 298;
T_a      = T_f;
DeltaH_R = -3e5;
U        = 0;


x0=[1; T_f];
nc_As = 250;
clear tmp_table;
c_Avect = linspace(0.999*c_Af, .003*c_Af, nc_As);
for i = 1: nc_As
  c_A = c_Avect(i);
  opts = optimset ('MaxFunEvals', 2000*numel (x0), ...
                   'MaxIter', 500*numel (x0));
  [x, fval, info] = fsolve('st_st_cA', x0, opts);
  theta = x(1);
  T     = x(2);
  conv     = (c_Af - c_A) / c_Af;
  %
  % compute the eigenvalues of the Jacobian
  %
  k = k_m*exp(-E*(1/T - 1/T_m));
  Jac = [-1/theta - k,     -k*c_A*E/(T*T);
        -k*DeltaH_R/C_ps, -U/C_ps - 1/theta - k*c_A*DeltaH_R/C_ps*E/(T*T)];
  lambda = eig(Jac);
  a=real(lambda(1)); b=imag(lambda(1)); c=real(lambda(2)); d=imag(lambda(2));
  if (a >= c)
    lamrow = [a b c d];
  else
    lamrow = [c d a b];
  end
  tmp_table(i,:) = [theta, T, conv, lamrow, info];
  x0=x;
end
table = [tmp_table];
save -ascii st_st_eig.dat table;

if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot(table(:,2),[table(:,4),table(:,6)]);
axis([280,460,-1,1]);

figure()
plot(table(:,3),[table(:,4),table(:,6)]);
axis([0,1,-1,1]);
% TITLE
end % PLOTTING

st_st_cA.m


1
2
3
4
5
6
7
function retval = st_st_cA(x)
global k_m T_m E c_Af c_A C_ps T_f DeltaH_R U T_a
theta = x(1);
T     = x(2);
k         = k_m*exp(-E*(1/T - 1/T_m));
retval(1) = c_Af - (1+k*theta)*c_A;
retval(2) = U*theta*(T_a - T) + C_ps*(T_f - T) - k*theta*c_A*DeltaH_R;