## Apps.VandeVusse History

September 11, 2012, at 09:10 AM by 69.169.131.76 -
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September 11, 2012, at 09:06 AM by 69.169.131.76 -
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(:title Van de Vusse Reactor:) (:keywords nonlinear, reactor, reaction, Van de Vusse, chemical, kinetics, model, library, examples, APMonitor:) (:description Simulate the Van de Vusse reactor with APMonitor Online:)

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 2A->D.

(:html:) <a href='/online/view_pass.php?f=van_de_vusse.apm'>Solve Van de Vusse Reactor Dynamics</a> <br>

<font size=2><pre>

# Publication Date: November 1973

Model

```  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 = 1.287e10    ! A->B Pre-exponential factor (1/hr)
k20 = 1.287e10    ! B->C Pre-exponential factor (1/hr)
k30 = 9.043e9     ! 2A->D Pre-exponential factor (1/hr)
E1 = 9758.3       ! A->B Activation Energy (K)
E2 = 9758.3       ! B->C Activation Energy (K)
E3 = 8560         ! 2A->D Activation Energy (K)
dHr1 = 4.2        ! A->B Heat of Reaction (kJ/mol A)
dHr2 = -11        ! B->C Heat of Reaction (kJ/mol B)
dHr3 = -41.85     ! 2A->D Heat of Reaction (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))

r1 = k1*VR*Ca
r2 = k2*VR*Cb
r3 = k3*VR*Ca^2
End Intermediates

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

! species balances
VR * \$Ca = -r1 - 2*r3 + F*(Ca0-Ca)
VR * \$Cb =  r1   - r2 - F*Cb
VR * \$Cc =  r2        - F*Cc
VR * \$Cd =  r3        - F*Cd

! energy balance on reactor
rho*Cp*VR*\$T = F*rho*Cp*(T0 - T) &
- r1*dHr1         &
- r2*dHr2         &
- r3*dHr3         &
+ kw*AR*(Tk - T)

! energy balance on cooling
mK * CpK * \$Tk = Qk + kw*AR*(T - Tk)
End Equations
```

End Model

File *.info

``` F, T0
F, F
F, Ca0
F, T0
F, Qk
S, Tk
S, Ca
S, Cb
S, Cc
S, Cd
C, T
```

End File

File overrides.dbs

``` nlc.web = 2
nlc.ctrl_units = 3
nlc.hist_units = 2
nlc.cv_type = 1
nlc.ev_type = 1
nlc.reqctrlmode = 1
nlc.csv_read = 1
nlc.hist_hor = 100
nlc.web_plot_freq = 10
nlc.nodes = 2
nlc.imode = 7
```

End File

File *.csv time 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 End File </pre></font> (:htmlend:)