Abstract
In this chapter, the problem of the thermal stability of batch reactors in the presence of highly exothermic reactions is addressed. The reactor dynamics is investigated under adiabatic and isoperibolic conditions, and runaway boundaries are determined in terms of the dimensionless groups appearing in the mathematical model. Classical runaway criteria based on the geometry of the temperature profile and on the parametric sensitivity of the system are presented and discussed. Moreover, the operational limits arising from the maximum allowable temperature in the reactor are also highlighted. The chapter is then closed by a case study aiming at the determination of runaway boundaries for the phenol–formaldehyde reaction introduced in the previous chapters.
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Abbreviations
- B :
-
dimensionless number defined in (4.36)
- c :
-
mass heat capacity [J kg−1 K−1]
- \(\mathcal{C}\) :
-
dimensionless concentration
- C A :
-
concentration of reactant A [mol m−3]
- E a :
-
activation energy [J mol−1]
- h :
-
incremental step
- ΔH R :
-
molar enthalpy change of reaction [J mol−1]
- k 0 :
-
preexponential factor [s−1]
- q E :
-
dimensionless rate of heat exchange
- q R :
-
dimensionless rate of heat production by reaction
- \(\mathcal{R}\) :
-
universal gas constant [J mol−1 K−1]
- s :
-
normalized objective sensitivity
- S :
-
heat transfer area [m2]
- Se :
-
dimensionless Semenov number
- t :
-
time [s]
- t E :
-
characteristic time of heat exchange [s]
- t R :
-
characteristic reaction time [s]
- T :
-
temperature [K]
- \(\mathcal{T}\) :
-
dimensionless temperature
- U :
-
overall heat transfer coefficient [J m−2 K−1 s−1]
- V :
-
volume [m3]
- θ :
-
generic model parameter
- Λ :
-
dimensionless group defined in (4.7)
- ρ :
-
density [kg m−3]
- τ :
-
dimensionless time
- τ b :
-
dimensionless batch time
- τ I :
-
dimensionless induction time
- τ M :
-
dimensionless time to maximum reaction rate
- Φ :
-
dimensionless group defined in (4.8)
- Ω :
-
dimensionless group defined in (4.6)
- ad:
-
adiabatic conditions
- c:
-
critical value
- j:
-
jacket
- ma:
-
maximum allowable value
- max :
-
maximum value
- r:
-
reactor
- 0:
-
initial value
- o :
-
reference value
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Caccavale, F., Iamarino, M., Pierri, F., Tufano, V. (2011). Thermal Stability. In: Control and Monitoring of Chemical Batch Reactors. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-0-85729-195-0_4
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