Reactor


The continuously stirred tank reactor is a popular model for benchmarking. It is a simple A to B reaction and has exothermic reaction instability with a prolonged cooling jacket temperature above 305 K.

See also Van de Vusse Reactor


CSTR Simulation with Python


! APMonitor Modeling Language
! http://www.apmonitor.com

! CSTR model from
! Michael A. Henson and Dale E. Seborg.  Nonlinear
!   Process Control. Prentice Hall PTR, Upper 
!   Saddle River, New Jersey, 1997.
! Description:
! Continuously Stirred Tank Reactor with energy
!   balance and reaction A->B.
!   The temperature of the cooling
!     jacket is the control.
Model cstr
  Parameters
    ! Manipulated Variables
    Tc = 270    ! Temperature of cooling jacket (K)

    ! Parameters
    q = 100     ! Volumetric Flowrate (m^3/sec)
    V = 100     ! Volume of CSTR (m^3)
    rho = 1000  ! Density of A-B Mixture (kg/m^3)
    Cp = .239   ! Heat capacity of A-B Mixture (J/kg-K)
    mdelH = 5e4 ! Heat of reaction for A->B (J/mol)
                ! E - Activation energy in the 
                !  Arrhenius Equation (J/mol)
                ! R - Universal Gas Constant 
                !  = 8.31451 J/mol-K
                ! EoverR = E/R
    EoverR = 8750
    k0 = 7.2e10 ! Pre-exponential factor (1/sec)
                ! U - Overall Heat Transfer 
                !  Coefficient (W/m^2-K)
                ! A - Area - this value is specific
                !  for the U calculation (m^2)
                ! UA = U * A
    UA = 5e4
    Caf = 1     ! Feed Concentration (mol/m^3)
    Tf = 350    ! Feed Temperature (K)
  End Parameters

  Variables
    ! Differential States
    Ca = 0.9    ! Concentration of A in CSTR (mol/m^3)
    T  = 305    ! Temperature in CSTR (K)
  End Variables

  Equations
    ! note: the $ denotes time differential
    !  (e.g. $x is dx/dt)

    ! mole balance for species A
    V * $Ca = q*(Caf-Ca) - k0*V*exp(-EoverR/T)*Ca

    ! energy balance
    rho*Cp*V * $T = q*rho*Cp*(Tf - T) + V*mdelH*k0*exp(-EoverR/T)*Ca + UA*(Tc-T)
  End Equations
End Model