Module 9 - Diabatic CSTR

cstr_ss.m Solves for the steady-state of the diabatic CSTR by using fsolve.

Note: The fsolve function must be available. This is standard with MATLAB 4.x, but requires the optimization toolbox for MATLAB 5.x. To run this file, the user must first enter the global parameter vector CSTR_PAR which has 11 elements.

Case 2 values are shown in the function code. The book illustrates that the Case 2 parameter values have three possible solutions, depending on the initial guesses for the states. See pages 564-565 and Table M9.2 for the following

  x0 = [9;300];   % initial guess for concentration and temperature
  x = fsolve('cstr_ss',x0);

The solution obtained for case 2 and this initial guess is

  x = 
        8.5636
      311.1710

which is a low temperature steady-state.

For guess 2

  x0 = [5;350];   % initial guess for concentration and temperature
  x = fsolve('cstr_ss',x0);

The solution obtained for this initial guess is

  x = 
        5.518
      339.1

which is an intermediate temperature steady-state.

The following is for a third initial guess

  x0 = [1;450];   % initial guess for concentration and temperature
  x = fsolve('cstr_ss',x0);

The solution obtained for case 2 and this initial guess is

  x = 
        2.359
      368.1

which is a high temperature steady-state.

cstr_dyn.m Solves for the dynamics of the diabatic reactor by using ode45.

To reproduce Figure M9.2, use:

   x0 = [9;300];
   [t,x] = ode45('cstr_dyn',[0 30],x0); % MATLAB 5.x
   [t,x] = ode45('cstr_dyn',0,30,x0);   % MATLAB 4.x

To reproduce Figure M9.3, use:

   x0 = [5;325];
   [t,x] = ode45('cstr_dyn',[0 30],x0); % MATLAB 5.x
   [t,x] = ode45('cstr_dyn',0,30,x0);   % MATLAB 4.x

To reproduce Figure M9.4, use:

   x0 = [1;400];
   [t,x] = ode45('cstr_dyn',[0 30],x0); % MATLAB 5.x
   [t,x] = ode45('cstr_dyn',0,30,x0);   % MATLAB 4.x

cstr_amat.m Finds the Jacobian and eigenvalues for the cstr model, given the steady-state concentration and temperature.

See pages 569-570 for examples.

cstr_run.m Generates the phase-plane plot shown in Figure M9.5.

Do not forget to put values for all 11 elements of the CSTR_PAR vector. To use this file for MATLAB 5.x, you need to modify the calls to ode45 within the file.

cstr_io.m Generates the steady-state input-output curve.

See Figure M9.9 and page 578 for an example. Do not forget to enter the 11 elements of the CSTR_PAR vector.

cstr_cusp.m Generates the cusp "catastrophe" shown in Figure M9.11.

Do not forget to enter the 11 elements of the CSTR_PAR vector.