function xdot = vdv_ode(t,x);
% 
% Solves the two differential equations modeling the van de vusse reaction
% scheme in an isothermal CSTR. The states are the concentration of A and
% B in the reactor.
%
% [t,x] = ode45(vdv_ode,[0 5],x0)
% integrates from t = 0 to t = 5 min, with initial conditions
% ca0 = x0(1) and cb0 = x0(2), and x0 is a column vector
% 16 Jan 99
% b.w. bequette
%

% since the states are passed to this routine in the x vector, 
% convert to natural notation

  ca = x(1);
  cb = x(2);

% the parameters are:

  k1 = 5/6;    % rate constant for A-->B (min^-1)
  k2 = 5/3;    % rate constant for B-->C (min^-1)
  k3 = 1/6;    % rate constant for 2A-->D (mol/(l min))

% the input values are:

  fov = 4/7;   % dilution rate (min^-1)
  caf = 10;    % mol/l

% the modeling equations are:

  dcadt = fov*(caf-ca) - k1*ca -k3*ca*ca;
  dcbdt = -fov*cb + k1*ca - k2*cb;

% now, create the column vector of state derivatives

  xdot = [dcadt;dcbdt];