12. Steady-State Non-Isothermal Reactor Design : The Steady State Energy Balance and Adiabatic PFR Applications *



1. Applications of the PFR/PBR User Friendly Energy Balance Equations top

NOTE: The PFR and PBR formulas are very similar.

Heat exchange for a PFR:
a = heat exchange area per unit volume of reactor; for a tubular reactor, a = 4/D
Catalyst weight is related to reactor volume by:
Heat exchange for a PBR:
Steady State Energy Balance (with no work):
Final Form of the Differential Equations in Terms of Conversion:

A.        

Final Form in terms of Molar Flow Rates

 

B.        

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If we include pressure drop:

C.       

Note: the pressure drop will be greater for exothermic adiabatic reactions than it will be for isothermal reactions

Balance on Heat Exchanger Coolant

Solve simultaneously using an ODE solver (Polymath/MatLab). If Ta is not constant, then we must add an additional energy balance on the coolant fluid:

Co-Current Flow
Counter-Current Flow

with Ta = Tao at W = 0

For an exothermic reaction: with counter current heat exchange

A Trial and Error procedure for counter current flow problems is required to find exit conversion and temperature.

  1. Consider an exothermic reaction where the coolant stream enters at the end of the reactor at a temperature Ta0, say 300 K.
  2. Assume a coolant temperature at the entrance (X = 0, V = 0) to the reactor Ta2 =340 K.
  3. Calculate X, T, and Ta as a function of V. We can see that our guess of 340 K for Ta2 at the feed entrance (X = 0) gives a coolant temperature of 310 K, which does not match the actual entering coolant temperature of 300 K.
  4. Now guess a coolant temperature at V = 0 and X = 0 of 330 K. We see that the exit coolant temperature of Ta2 = 330 K will give a coolant temperature at V = V1 of 300 K.
12.1A ↔ B Liquid Phase Adiabatic
12.2A ↔ B Liquid Phase Constant Ta
12.3A ↔ B Liquid Phase Variable Ta, Co-Current
12.4A ↔ B Liquid Phase Variable Ta, Counter Current
12.1 Sketch the Ambient Temperature as a function of V.
12.2 Elementary Liquid Phase Reaction
12.5 Exothermic, Reversible Reaction
12.6 Adiabatic Reaction in a PBR.
12.7 PBR with heat exchange.
12.8 PBR with heat exchange and variable coolant flow rate.
12.3 Nonisothermal Reactions.
Variable Coolant Temperature.

 

* All chapter references are for the 1st Edition of the text Essentials of Chemical Reaction Engineering .

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