Dynamics of a Catalytic Fluidized Bed Reactor
Author's Data: Housam Binous
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Acknowledgement :

This problem was presented in the excellent book by W. F. Ramirez, Computational Methods for Process Simulation, Second Edition, 1997, Butterworth Heinemann, Oxford.

Off[General::"spell1"]

Governing Equations

K = 6 10^-4 Exp[20.7 - 15000/T[t]]

eq1 = 
      D[p[t], {t, 1}] ==  
        0.1 + 320 pp[t] - 321 p[t]
eq2 = 
      D[T[t], {t, 1}] ==  
        1752 + 266.667 Tp[t] - 269.267 T[t]
eq3 = 
      D[pp[t], {t, 1}] ==  
        1866.8 (p[t] - (1 + K) pp[t])
eq4 = 
      D[Tp[t], {t, 1}] ==  
        10369 K pp[t] + 1.2964*(T[t] - Tp[t])

sol = 
      NDSolve[{eq1, eq2, eq3, eq4, p[0] ==  0.1, pp[0] == 0, 
          T[0] ==  600, Tp[0] == 690}, {p[t], pp[t], T[t], 
          Tp[t]}, {t, 0, 1000}]

<< Graphics`Graphics`

Partial pressure of the reactant in the gas phase and particles

plt1 = 
      LogLinearPlot[Evaluate[p[t] /. sol], {t, 10^-6, 5 10^-1}, 
        PlotStyle ->  RGBColor[1, 0, 0], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {0, 0.1}}, 
        PlotPoints ->  5000]

plt2 = 
      LogLinearPlot[Evaluate[pp[t] /. sol], {t, 10^-6, 5 10^-1}, 
        PlotStyle ->  RGBColor[0, 0, 1], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {0, 0.1}}, 
        PlotPoints ->  5000]

plt1b = 
      LogLinearPlot[Evaluate[p[t] /. sol], {t, 5 10^-1, 5 10^2}, 
        PlotStyle ->  RGBColor[1, 0, 0], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {0, 0.1}}, 
        PlotPoints ->  5000]

plt2b = 
      LogLinearPlot[Evaluate[pp[t] /. sol], {t, 5 10^-1, 5 10^2}, 
        PlotStyle ->  RGBColor[0, 0, 1], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {0, 0.1}}, 
        PlotPoints ->  5000]

Show[plt1, plt2, plt1b, plt2b, 
      DisplayFunction ->  $DisplayFunction]

Temperatures of the gas phase and particles

plt3 = 
      LogLinearPlot[Evaluate[T[t] /. sol], {t, 10^-6, 5 10^-1}, 
        PlotStyle ->  RGBColor[1, 0, 0], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {600, 700}}, 
        PlotPoints ->  5000]

plt4 = 
      LogLinearPlot[Evaluate[Tp[t] /. sol], {t, 10^-6, 5 10^-1}, 
        PlotStyle ->  RGBColor[0, 0, 1], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {600, 700}}, 
        PlotPoints ->  5000]

plt3b = 
      LogLinearPlot[Evaluate[T[t] /. sol], {t, 5 10^-1, 5 10^2}, 
        PlotStyle ->  RGBColor[1, 0, 0], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {600, 700}}, 
        PlotPoints ->  5000]

plt4b = 
      LogLinearPlot[Evaluate[Tp[t] /. sol], {t, 5 10^-1, 5 10^2}, 
        PlotStyle ->  RGBColor[0, 0, 1], 
        DisplayFunction ->  Identity, 
        PlotRange ->  {{10^-6, 5 10^2}, {600, 700}}, 
        PlotPoints ->  5000]

Show[plt3, plt4, plt3b, plt4b, 
      DisplayFunction ->  $DisplayFunction]