Figure 8.30:

Inverse of reaction rate versus concentration; optimal sequence to achieve 95% conversion is PFR--CSTR--PFR.

Code for Figure 8.30

Text of the GNU GPL.

main.m


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% 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));
[dummy,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));
[dummy,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

% now compute segregated reactor conversion
npts = 50;
zseg = linspace(0,1,npts);
cseg0 = [c0;0];
[dummy,cseg] = ode15s(@seg,zseg,cseg0);
csegfin = cseg(npts,2);

% solve for cinf, which seems to be the same as what would come out of
% a cstr of theta2 with feed conc c0
x0=c0;
[x, fval, info] = fsolve('climit',x0);
info;
cinf=x;

% now compute maximally mixed conversion
npts=50;
z=linspace(0,1,npts);
[dummy,cmm] = ode15s(@mm,z,cinf);
cmmfin = cmm(npts);
table = [c y];
extras = [c0 1/rxrate(c0) c1 1/rxrate(c1) c2 1/rxrate(c2) c3 1/rxrate(c3) ...
          c1 1/rxrate(c1) ;
          c0 0          c1 0          c2 0          c3 0          ...
          c2 1/rxrate(c2)];

save leven.dat table extras;
if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot (table(:,1), table(:,2), ...
       extras(:,1), extras(:,2), ...
       extras(:,3), extras(:,4), ...
       extras(:,5), extras(:,6), ...
       extras(:,7), extras(:,8), ...
       extras(:,9), extras(:,10));
axis ([0,6,0,10])
% TITLE
end % PLOTTING

rxrate.m


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

solverate.m


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

pfr.m


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

seg.m


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function xdot = seg(z,x)
  global theta1 theta2 theta3
  c    = x(1);
  ctot = x(2);
  if (z < 1)
    t = z/(1-z);
    if (t <= theta1+theta3)
      p=0;
    else
      p=exp(-(t-(theta1+theta3) )/theta2)/theta2;
    end
    xdot = [-rxrate(c)/(1-z)^2; p*c/(1-z)^2];
    else
      xdot = [0; 0];
    end

climit.m


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function retval = climit(c)
  global theta2 c0
  retval = c-c0+rxrate(c)*theta2;

mm.m


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function dcdz = mm(z,c)
  global theta1 theta2 theta3 c0
  if (z == 0.)
    dcdz = 0;
  else
    t = (1-z)/z;
    if (t <= theta1+theta3)
      f = 0;
    else
      f = 1/theta2;
    end
    dcdz = - (f*(c-c0) + rxrate(c) )/(z*z);
  end