%% 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')

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;

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;