Investigation into maximum temperature of synthesis reaction for single kinetically controlled liquid–liquid semibatch reactions with arbitrary reaction order


Maximum temperature of synthesis reaction (MTSR) is an essential concept to assess the thermal runaway risk and design safe operating conditions for semibatch reactors (SBRs). According to the definition, the values of MTSR will change with the reaction temperature (T). So far, the behavior of MTSR for liquid–liquid semibatch reactions with arbitrary reaction order has not been thoroughly researched. In this work, it is theoretically and experimentally verified that MTSR versus T profiles are prone to present an ‘S’ shape for strongly exothermic kinetically controlled liquid–liquid reactions. That means that the dependence of MTSR on T is complex. A theoretical criterion to determine whether MTSR will increase with T increasing is developed in this work. This criterion states that if the criterion is negative, MTSR will increase as T increases. To validate this criterion, the nitration of 4-chloro benzotrifluorid by mixed acid was conducted. The theoretical criterion can contribute to design safe operating conditions for SBRs.

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Fig. 3
Fig. 4
Scheme 1
Fig. 5
Fig. 6


A :

Pre-exponential factor (s−1)

C :

Molar concentration (mol m−3)

C p :

Heat capacity (J kg−1 K−1)

d a :

Stirrer diameter (m)

D :

Diffusion coefficient (cm2 s−1)


Damköhler number

E :

Activation energy (kJ kmol−1)


Enhancement factor

f :

Function of the dimensionless time and conversion of B

H :

Equilibrium distribution coefficient


Hatter number

ΔH :

Heat production per mole (kJ mol)

k n,m :

Reaction rate constant (mol−n−m+1 s−1)

kL2 :

Mass transfer coefficient (L mol−1s−1)


The maximum temperature of synthesis reaction under adiabatic condition (°C)


Dimensionless form of MTSR

M :

Molecular mass (gmol−1)

N :

Mole number (mol)

n a :

Stirrer speed (s−1)

P :

Power dissipated by the stirrer (W)

q :

Heat release rate (W)

Q :

Heat release rate (kJ)

r :

Reaction rate (mol m−3 s−1)

R :

Ideal gas constant, equal to 8.314 kJ kmol−1 K−1


Reynolds number

t :

Time or characteristic time (s)

T :

Temperature (K)

T R :

Reference temperature, equal to 300 K

ΔTad :

Adiabatic temperature rise (K)

V :

Liquid volume (m3)

X :

The fractional conversion

x :

Sulfuric acid strength or molar fraction

A, B, C, D:

Components A, B, C and D






Continuous phase


Correction value


Dispersed phase












Kinetics order toward component B


Kinetics order toward component A








Stoichiometric point








Start of the dosing period


Before addition


After addition


Dimensionless activation energy, equal to E/(RTR)

τ :

Dimensionless temperature, equal to T/TR

Δτad,0 :

Dimensionless adiabatic temperature rise

ε :

Relative volume increase at the end of the semi-batch period

θ :

Dimensionless time, equal to t/tD,

ν :

Stoichiometric coefficient

κ :

Dimensionless reaction rate constant, equal to exp[γ(1–1/τ)]

ρ :

Molar density (kmol m−3)

μ :

Viscosity (kg m−1s−1)


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This work has been financially supported by National Key R&D Program of China (2017YFC0804701-4) and the Fundamental Research Funds for the Central Universities (30917011312).

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Correspondence to Zichao Guo.

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Jiang, X., Feng, W., Guo, Z. et al. Investigation into maximum temperature of synthesis reaction for single kinetically controlled liquid–liquid semibatch reactions with arbitrary reaction order. J Therm Anal Calorim (2020).

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  • MTSR
  • Kinetic regime
  • Heterogeneous
  • Semibatch
  • Isothermal