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Thermal Stability

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

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.

Keywords

Batch Reactor Thermal Explosion Formaldehyde Reaction Batch Cycle Maximum Allowable Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Principal Symbols

B

dimensionless number defined in (4.36)

c

mass heat capacity [J kg−1 K−1]

\(\mathcal{C}\)

dimensionless concentration

CA

concentration of reactant A [mol m−3]

Ea

activation energy [J mol−1]

h

incremental step

ΔHR

molar enthalpy change of reaction [J  mol−1]

k0

preexponential factor [s−1]

qE

dimensionless rate of heat exchange

qR

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]

tE

characteristic time of heat exchange [s]

tR

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]

Greek Symbols

θ

generic model parameter

Λ

dimensionless group defined in (4.7)

ρ

density [kg m−3]

τ

dimensionless time

τb

dimensionless batch time

τI

dimensionless induction time

τM

dimensionless time to maximum reaction rate

Φ

dimensionless group defined in (4.8)

Ω

dimensionless group defined in (4.6)

Subscripts and Superscripts

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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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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