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