Figure 5.14 (page 236):

Fractional error in the QSSA molar flowrate of C_2H_4 versus reactor volume.

Code for Figure 5.14

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.

% This program solves part of ethane pyrolysis example that is in the
% text.  It generates the error plot for the ethane example
% It is titled ethane_error.m
% 
% It was last edited 2/5/97

global k kp P R1 T

%E in Joules, mass in grams, T in Kelvin, time in sec, volume in cm3


Components_1 = [' C2H6 = 1,',' CH3 = 2,',' CH4 = 3,',' C2H5 = 4'];
Components_2 = [' H = 5,',' C2H4 = 6,', ' H2 = 7,',' H2O = 8'];
Ao = [1e17,2e11,3e14,3.4e12,1.6e13]';
Ea = [356000,44000,165000,28000,0]';
nu = [-1,2,0,0,0,0,0,0
      -1,-1,1,1,0,0,0,0
      0,0,0,-1,1,1,0,0
      -1,0,0,1,-1,0,1,0
      1,0,0,-1,-1,0,0,0];

R = 8.3144;  %(J/gmole-K)
R1 = 82.057;	%cc-atm/gmole-K
T = 925;
EXP = exp(-Ea/(R*T));
k = Ao.*EXP;
kp = (k(1)/(2*k(3)) + ((k(1)/(2*k(3)))^2 + ...
     ((k(1)*k(4))/(k(3)*k(5))))^0.5);
C1o = (50/760)/(82.057*T);  %gmole/cm3
C8o = (710/760)/(82.057*T);
Qf = 35.0;	%cc/sec
N1o = C1o*Qf;	%gmole/sec
N8o = C8o*Qf;
P = 1.0;	%atm
Initial = [N1o,0,0,0,0,0,0,N8o]';


v = [0:1:100]';

opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, solution] = ode15s(@rxrate,v,Initial,opts);
answer = [v solution];

Initial_q = [N1o,0,0,0,N8o]';
% The total mole balance neglects H, CH3 and C2H5 because at 925K they
% are of order 10^-6 the concentration(molar flowrate) of ethane and
% ethane will only change by one order of magnitude.


opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, solution_q] = ode15s(@rate_q,v,Initial_q,opts);
answer_q = [v solution_q];

%% Delete first row to avoid floating point exception.

Ethylene_exact = solution(2:end,6);
Ethylene_qss = solution_q(2:end,3);
err = abs((Ethylene_exact - Ethylene_qss)./Ethylene_exact);
erro = err*100;
%error = [v(2:length(v)), erro];
% JBR, 2/22/98
error = [v(2:length(v)), err];

semilogy (error(:,1),error(:,2))
title ('Figure 5.14')

rxrate.m

function dNdv = rxrate(v,x)
  global k P R1 T
  
  N1 = x(1);
  N2 = x(2);
  N3 = x(3);
  N4 = x(4);
  N5 = x(5);
  N6 = x(6);
  N7 = x(7);
  N8 = x(8);

  Ntot = N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8;
  Ctot = P/(R1*T);
  C1 = (N1/Ntot)*Ctot;
  C2 = (N2/Ntot)*Ctot;
  C4 = (N4/Ntot)*Ctot;
  C5 = (N5/Ntot)*Ctot;

  r1 = k(1)*C1;
  r2 = k(2)*C1*C2;
  r3 = k(3)*C4;
  r4 = k(4)*C1*C5;
  r5 = k(5)*C4*C5;

  dNdv = zeros (8, 1);

  dNdv(1) = -r1 - r2 - r4 + r5;
  dNdv(2) = 2*r1 - r2;
  dNdv(3) = r2;
  dNdv(4) = r2 - r3 + r4 - r5;
  dNdv(5) = r3  - r4 - r5;
  dNdv(6) = r3;
  dNdv(7) = r4;
  dNdv(8) = 0;

rate_q.m

function dNdv = rate_q(v,x)
  global  k kp P R1 T
  
  N1 = x(1);
  N3 = x(2);
  N6 = x(3);
  N7 = x(4);
  N8 = x(5);

  Ntot = N1 + N3 + N6 + N7 + N8;
  Ctot = P/(R1*T);
  C1 = (N1/Ntot)*Ctot;
  C2 = (2*k(1))/k(2);
  C4 = kp*C1;
  C5 = k(1)/(k(5)*kp);

  r1 = k(1)*C1;
  r2 = 2*k(1)*C1;
  r3 = k(3)*kp*C1;
  r4 = k(4)*k(1)/(k(5)*kp)*C1;
  r5 = k(1)*C1;

  dNdv = zeros (5, 1);

%  dNdv(1) = -r1 - r2 - r4 + r5;
  dNdv(1) = - r2 - r4;
  dNdv(2) = r2;
  dNdv(3) = r3;
  dNdv(4) = r4;
  dNdV(5) = 0;