CIESC Journal ›› 2019, Vol. 70 ›› Issue (1): 379-387.doi: 10.11949/j.issn.0438-1157.20180678

• Process safety • Previous Articles     Next Articles

Calculate time to maximum rate under adiabatic condition by numerical calculation method

Yi ZHU(),Hao WANG,Liping CHEN(),Zichao GUO,Zhongqi HE,Wanghua CHEN   

  1. Department of Safety Engineering, School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
  • Received:2018-06-21 Revised:2018-10-05 Online:2019-01-05 Published:2018-10-29
  • Contact: Liping CHEN;


The maximum reaction rate arrival time (TMRad) is a very important parameter in chemical process thermal risk assessment. The general method for calculation of TMRad is based on N-order model kinetic analysis. However, the chemical reaction process is so complicated that only do kinetic analysis based on N-order without consider the type of reaction may cause large deviation or even incorrect assessments. Therefore, this paper proposes to calculate TMRad and TD24 by numerical calculation methods based on reaction model. 20% DTBP toluene solution and CHP represent N-order reaction and autocatalytic reaction, respectively. The analysis of ARC test data of two substances shows this method can be used to calculate TMRad and TD24 of N-order reaction reliably, but the comparison of autocatalytic reaction with two methods shows that although the fitting effect is very good, the general method calculated result has a large deviation, because the kinetic parameters are different under two models, this paper also perform the deviation size analysis. Therefore, it can be seen that the numerical calculation method has wide-range applicability, and to an exothermal curve, it is necessary to use the method to evaluate the TMRad and TD24 based on the understanding of the reaction type, so that the evaluation result is more reliable and accurate.

Key words: thermodynamics, thermal decomposition reaction, stability, safety, time to maximum rate under adiabatic condition, N-order, autocatalysis

CLC Number: 

  • O 642.1


Calculation flowchart based on fourth-order Runge-Kutta method"

Table 1

ARC test information for 20% DTBP toluene solution of this work and other related works"

Workms /gCp,s/(J·g-1·K-1)mb /gCp,b/(J·g-1·K-1)φTon /℃Tf /℃
this work4.95215.320.421.65115.3181.71
Kossoy et al[11]NANANANA1.665125.8NA


Experimental data of 20% DTBP toluene solution exothermal curve and fitting result"

Table 2

Kinetic parameters of this work and other related works (N-order)"

WorkA/s-1E/(kJ·mol-1nΔTAD /K
this work9.12×1016165.371.0566.41
Kossoy et al[11]3.67×1015155.380.98NA


Temperature rise rate curve of 20% DTBP toluene solution under different T0"


TMRad results calculated by numerical methods and general methods (20% DTBP toluene solution)"

Table 3

ARC test information for CHP of this work"

ms /gCp,s/(J·g-1·K-1)mb/gCp,b/(J·g-1·K-1)φTon /℃Tf /℃


Experimental data of CHP exothermal curve and fitting result"

Table 4

Kinetic parameters of this work (N-order and BP model)"

calculate modelA /s-1E /(kJ·mol-1)nΔTAD /K
BP model2.66×1012(A1) 6.84×1011(A2)128.60(E1) 116.38(E2)0.40(n1) 1.42(n2) 1.06(n3)46.11
N-order model6.29×1023213.941.3346.11


Temperature rise rate curves of CHP under different T0"


TMRad results calculated by numerical methods and general methods (CHP)"


Fitting curves of experimental data and extrapolated simulation curves"


Deviations of TMRad calculated by N-order model with real value (BP model)"

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