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

doi:10.11949/j.issn.0438-1157.20180678

Abstract

Abstract:

The maximum reaction rate arrival time (TMR_ad) is a very important parameter in chemical process thermal risk assessment. The general method for calculation of TMR_ad 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 TMR_ad and T_D24 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 TMR_ad and T_D24 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 TMR_ad and T_D24 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

摘要：

最大反应速率到达时间(TMR_ad)是化工工艺热风险评估中一个十分重要的参数。一般计算TMR_ad的方法是基于N级模型的分析。但对于复杂的反应过程统一采用N级模型分析计算可能会引起较大偏差甚至得到错误的评估。因此，提出运用基于反应类型的数值计算方法进行TMR_ad和T_D24的评估，通过分别代表N级反应和自催化反应的20% DTBP甲苯溶液和CHP的ARC测试分析表明：对于N级反应，该方法能可靠地用于TMR_ad和T_D24的求取；而对于自催化反应，尽管拟合效果很好，原有方法计算偏差很大，原因是不同模型下动力学参数不同，还进行偏差大小分析。由此可知该数值计算方法有广泛的适用性，对于放热曲线，需在了解其反应类型的基础上利用该方法进行TMR_ad和T_D24的评估，由此评估的结果更为可靠准确。

关键词: 热力学, 热分解反应, 稳定性, 安全, 最大反应速率到达时间, N级, 自催化

CLC Number:

O 642.1

Yi ZHU, Hao WANG, Liping CHEN, Zichao GUO, Zhongqi HE, Wanghua CHEN. Calculate time to maximum rate under adiabatic condition by numerical calculation method[J]. CIESC Journal, 2019, 70(1): 379-387.

朱益, 王浩, 陈利平, 郭子超, 何中其, 陈网桦. 基于数值计算方法计算最大反应速率到达时间[J]. 化工学报, 2019, 70(1): 379-387.

Figures/Tables 13

Fig.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

Work	m_s /g	C_p_,s/(J·g^-1·K^-1)	m_b /g	C_p_,b/(J·g^-1·K^-1)	φ	T_on /℃	T_f /℃
this work	4.95	2	15.32	0.42	1.65	115.3	181.71
Kossoy et al^[11]	NA^①	NA^①	NA^①	NA^①	1.665	125.8	NA^①

Fig.2 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)

Work	A/s^-1	E/（kJ·mol^-1）	n	ΔT_AD /K
this work	9.12×10¹⁶	165.37	1.05	66.41
Kossoy et al^[11]	3.67×10¹⁵	155.38	0.98	NA^①

Fig.3 Temperature rise rate curve of 20% DTBP toluene solution under different T0

Fig.4 TMRad results calculated by numerical methods and general methods (20% DTBP toluene solution)

Table 3 ARC test information for CHP of this work

m_s /g	C_p_,s/(J·g^-1·K^-1)	m_b/g	C_p_,b/(J·g^-1·K^-1)	φ	T_on /℃	T_f /℃
0.22	2	14.67	0.42	14.75	120.64	166.80

Fig.5 Experimental data of CHP exothermal curve and fitting result

Table 4 Kinetic parameters of this work (N-order and BP model)

calculate model	A /s^-1	E /(kJ·mol^-1)	n	ΔT_AD /K
BP model	2.66×10¹²(A₁) 6.84×10¹¹(A₂)	128.60(E₁) 116.38(E₂)	0.40(n₁) 1.42(n₂) 1.06(n₃)	46.11
N-order model	6.29×10²³	213.94	1.33	46.11

Fig.6 Temperature rise rate curves of CHP under different T0

Fig.7 TMRad results calculated by numerical methods and general methods (CHP)

Fig.8 Fitting curves of experimental data and extrapolated simulation curves

Fig.9 Deviations of TMRad calculated by N-order model with real value (BP model)

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