## Stirred Reactor

## Apps.StirredReactor History

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## Van de Vusse Reactor

The Van de Vusse reaction kinetics are employed in many benchmarking problems. This model is a simple stirred tank reactor model with reactions A->B->C and A->2D. Note that in the original reference, the reactor volume was listed as 0.01 L. This model has been modified for the original intent of 10 L reactor volume.

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# Continuously Stirred Tank Reactor with energy

# balance and reactions A->B->C and A->2D

Model cstr

Parameters F = 14.19 ! Feed rate (l/hr) Qk = -1579.5 ! Jacket cooling rate (kJ/hr) Ca0 = 5.1 ! Inlet feed concentration (mol/m^3) T0 = 104.9 ! Inlet feed temperature (degC) k10 = 1.287e12 ! A->B Pre-exponential factor (1/hr) k20 = 1.287e12 ! B->C Pre-exponential factor (1/hr) k30 = 9.043e9 ! A->2D Pre-exponential factor (1/hr) E1 = 9758.3 ! A->B Activation Energy (K) E2 = 9758.3 ! B->C Activation Energy (K) E3 = 8560 ! A->2D Activation Energy (K) dHrAB = 4.2 ! A->B Heat of Reaction (kJ/mol A) dHrBC = -11 ! B->C Activation Energy (kJ/mol B) dHrAD = -41.85 ! A->2D Activation Energy (kJ/mol A) rho = 0.9342 ! density (kg/l) Cp = 3.01 ! Heat capacity of reactants (kJ/kg-K) kw = 4032 ! Heat transfer coefficient (kJ/h-K-m^2) AR = .215 ! Area of jacket cooling (m^2) VR = 10.0 ! Reactor volume (l) mK = 5 ! Mass of cooling (kg) CpK = 2 ! Heat capacity of cooling (kJ/kg-K) End Parameters Variables ! Differential States Ca = 2.2291 ! Concentration of A in CSTR (mol/l) Cb = 1.0417 ! Concentration of B in CSTR (mol/l) Cc = 0.91397 ! Concentration of C in CSTR (mol/l) Cd = 0.91520 ! Concentration of D in CSTR (mol/l) T = 79.591 ! Temperature in CSTR (degC) Tk = 77.69 ! Cooling jacket temperature (degC) End Variables Intermediates k1 = k10*exp(-E1/(T+273.15)) k2 = k20*exp(-E2/(T+273.15)) k3 = k30*exp(-E3/(T+273.15)) End Intermediates Equations ! note: the $ denotes time differential ! (e.g. $x is dx/dt) ! species balances VR * $Ca = -k1*VR*Ca - k3*VR*Ca^2 + F*(Ca0-Ca) VR * $Cb = k1*VR*Ca - k2*VR*Cb - F*Cb VR * $Cc = k2*VR*Cb - F*Cc VR * $Cd = k3*VR*Ca^2 - F*Cd ! energy balance on reactor rho*Cp*VR*$T = F*rho*Cp*(T0 - T) & - VR*(k1*Ca*dHrAB + k2*Cb*dHrBC + k3*Ca^2*dHrAD) & + kw*AR*(Tk - T) ! energy balance on cooling mK * CpK * $Tk = Qk + kw*AR*(T - Tk) End Equations

End Model

The Van de Veer reaction kinetics are employed in many benchmarking problems. This model is a simple stirred tank reactor model with reactions A->B->C and A->2D. Note that in the original reference, the reactor volume was listed as 0.01 L. This model has been modified for the original intent of 10 L reactor volume.

The Van de Vusse reaction kinetics are employed in many benchmarking problems. This model is a simple stirred tank reactor model with reactions A->B->C and A->2D. Note that in the original reference, the reactor volume was listed as 0.01 L. This model has been modified for the original intent of 10 L reactor volume.

## Van de Veer Reactor

The Van de Veer reaction kinetics are employed in many benchmarking problems. This model is a simple stirred tank reactor model with reactions A->B->C and A->2D. Note that in the original reference, the reactor volume was listed as 0.01 L. This model has been modified for the original intent of 10 L reactor volume.

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The Van de Veer reaction kinetics are employed in many benchmarking problems. This model is a simple stirred tank reactor model with reactions A->B->C and A->2D. Note that in the original reference, the reactor volume was listed as 0.01 L. This model has been modified for the original intent of 10 L reactor volume.

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# Continuously Stirred Tank Reactor with energy

# balance and reactions A->B->C and A->2D

Model cstr

Parameters F = 14.19 ! Feed rate (l/hr) Qk = -1579.5 ! Jacket cooling rate (kJ/hr) Ca0 = 5.1 ! Inlet feed concentration (mol/m^3) T0 = 104.9 ! Inlet feed temperature (degC) k10 = 1.287e12 ! A->B Pre-exponential factor (1/hr) k20 = 1.287e12 ! B->C Pre-exponential factor (1/hr) k30 = 9.043e9 ! A->2D Pre-exponential factor (1/hr) E1 = 9758.3 ! A->B Activation Energy (K) E2 = 9758.3 ! B->C Activation Energy (K) E3 = 8560 ! A->2D Activation Energy (K) dHrAB = 4.2 ! A->B Heat of Reaction (kJ/mol A) dHrBC = -11 ! B->C Activation Energy (kJ/mol B) dHrAD = -41.85 ! A->2D Activation Energy (kJ/mol A) rho = 0.9342 ! density (kg/l) Cp = 3.01 ! Heat capacity of reactants (kJ/kg-K) kw = 4032 ! Heat transfer coefficient (kJ/h-K-m^2) AR = .215 ! Area of jacket cooling (m^2) VR = 10.0 ! Reactor volume (l) mK = 5 ! Mass of cooling (kg) CpK = 2 ! Heat capacity of cooling (kJ/kg-K) End Parameters Variables ! Differential States Ca = 2.2291 ! Concentration of A in CSTR (mol/l) Cb = 1.0417 ! Concentration of B in CSTR (mol/l) Cc = 0.91397 ! Concentration of C in CSTR (mol/l) Cd = 0.91520 ! Concentration of D in CSTR (mol/l) T = 79.591 ! Temperature in CSTR (degC) Tk = 77.69 ! Cooling jacket temperature (degC) End Variables Intermediates k1 = k10*exp(-E1/(T+273.15)) k2 = k20*exp(-E2/(T+273.15)) k3 = k30*exp(-E3/(T+273.15)) End Intermediates Equations ! note: the $ denotes time differential ! (e.g. $x is dx/dt) ! species balances VR * $Ca = -k1*VR*Ca - k3*VR*Ca^2 + F*(Ca0-Ca) VR * $Cb = k1*VR*Ca - k2*VR*Cb - F*Cb VR * $Cc = k2*VR*Cb - F*Cc VR * $Cd = k3*VR*Ca^2 - F*Cd ! energy balance on reactor rho*Cp*VR*$T = F*rho*Cp*(T0 - T) & - VR*(k1*Ca*dHrAB + k2*Cb*dHrBC + k3*Ca^2*dHrAD) & + kw*AR*(Tk - T) ! energy balance on cooling mK * CpK * $Tk = Qk + kw*AR*(T - Tk) End Equations

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# APMonitor Modeling Language

# https://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

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## Reactor

Continuously Stirred Tank 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.