Thermal Stability

  • Fabrizio Caccavale
  • Mario Iamarino
  • Francesco Pierri
  • Vincenzo Tufano
Part of the Advances in Industrial Control book series (AIC)


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.


Batch Reactor Thermal Explosion Formaldehyde Reaction Batch Cycle Maximum Allowable Temperature 
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List of Principal Symbols


dimensionless number defined in (4.36)


mass heat capacity [J kg−1 K−1]


dimensionless concentration


concentration of reactant A [mol m−3]


activation energy [J mol−1]


incremental step


molar enthalpy change of reaction [J  mol−1]


preexponential factor [s−1]


dimensionless rate of heat exchange


dimensionless rate of heat production by reaction


universal gas constant [J mol−1 K−1]


normalized objective sensitivity


heat transfer area [m2]


dimensionless Semenov number


time [s]


characteristic time of heat exchange [s]


characteristic reaction time [s]


temperature [K]


dimensionless temperature


overall heat transfer coefficient [J m−2 K−1 s−1]


volume [m3]

Greek Symbols


generic model parameter


dimensionless group defined in (4.7)


density [kg m−3]


dimensionless time


dimensionless batch time


dimensionless induction time


dimensionless time to maximum reaction rate


dimensionless group defined in (4.8)


dimensionless group defined in (4.6)

Subscripts and Superscripts


adiabatic conditions


critical value




maximum allowable value


maximum value




initial value


reference value


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Fabrizio Caccavale
    • 1
  • Mario Iamarino
    • 2
  • Francesco Pierri
    • 3
  • Vincenzo Tufano
    • 4
  1. 1.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  2. 2.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  3. 3.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  4. 4.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly

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