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A symmetric dual-channel accelerating rate calorimeter with the varying thermal inertia consideration
Thermochimica Acta 678 (2019) 178304
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A symmetric dual-channel accelerating rate calorimeter with the varying thermal inertia consideration
T
Jiong Dinga,b, Liming Yua, Jichen Wanga, Qiyue Xua,b, Suijun Yanga,b, Shuliang Yea,b,
⁎
a b
Institute of Industry and Trade Measurement Technology, College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou, PR China Zhejiang Engineering Laboratory of Chemicals Safety Testing Technology and Instruments, Hangzhou, PR China
ARTICLE INFO
ABSTRACT
Keywords: Thermal inertia Accelerating rate calorimetry Instrumentation Thermal kinetics
The thermal inertia determination and correction are the significant steps in accelerating rate calorimetric based kinetics calculation and thermal hazard evaluation. However, the existing kinetics approaches based on the constant thermal inertia ignore the fact that the sample’s heat dissipation is varying during the pseudo-adiabatic reaction. To overcome this shortcoming, an amended thermal inertia expression is proposed and a symmetric dual-channel accelerating rate calorimeter is developed in this article. A novel kinetics approach is presented with the varying thermal inertia consideration based on the measured electrical power data. With the different mass percent DTBP/toluene solutions experiments, the validities and advantages of the proposed calorimetry and the corresponding thermal analysis method are verified. Meanwhile, the challenges in the engineering implementation of this proposed method are analyzed and discussed at the end of the article.
1. Introduction The kinetics evaluation from adiabatic calorimetric data is a fundamental task in chemical process safety study based on accelerating rate calorimetry. To obtain the accurate kinetic results, the thermal inertia should be determined validly in the experiment and corrected in the numerical simulation. However, the exact determination and correction are not easily to carry out. When the accelerating rate calorimeter (ARC) was first developed by Townsend and Tou, the definition of thermal inertia, which is based on the ratio of the heat capacity between the whole reactive system (sample and sample container) and the sample, was presented to describe the heat dissipation of sample quantitatively [1]. This definition ignores the fact that the heat dissipation and heat capacity of the sample is varying during the reaction. This makes the errors in thermal behavior recording and kinetics computation. In order to obtain the accurate kinetics results and pure adiabatic thermal behavior, the history of ARC development and its kinetics approach can be considered as a history of a struggle for sample’s heat dissipation avoiding and correcting. For sample’s thermal dissipation reduction, some improvements in calorimeter instrumentation were carried out in the past several decades. The representative technologies are the pressure and power compensations. With the pressure compensation, the ratio between the volume and heat capacity of the container increases and the thermal
inertia decreases. The typical instruments of this kind are Phi-TEC II from HEL Group, APTAC from Netzsch Group and VSP2 from Fauske & Associates. LLC. The other technology is power compensation with the principle that the container’s enthalpy change comes from the electrical heating, not the sample’s reaction exotherm. The commercial calorimeters based on this principle are the VariPhi module from Netzsch Group [2], the DARC from the Omnical Inc [3] and the TAC-CP 500A from the Young Instruments Company [4]. Theoretically, the adiabatic temperature rise obtained from the power compensated calorimeter is considered as ideal and doesn’t need any correction [5]. While considering the instantaneity of the temperature tracking and the furnace’s dynamic response, the assumption that the adiabaticity of the reactive system is unreachable in engineering, especially when the sample’s selfheat rate is large. The reason is that the furnace’s temperature is always lagged due to the dynamic response of the temperature sensing and controlling [6]. This means that there still has limitation in studying the safety aspects and characterization of chemicals by using power compensated adiabatic calorimeters. In addition, the constructional and operational complexities make the pressure or power compensated adiabatic calorimeters are not wider used than the classic ARCs in actual thermal hazard studying and evaluation. This means that the thermal inertia correction in mathematics is inevitable in kinetics studying by means of ARCs. According to the thermal inertia definition, almost all the adiabatic correction
⁎ Corresponding author at: Institute of Industry and Trade Measurement Technology, College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou, PR China. E-mail address: [email protected] (S. Ye).
https://doi.org/10.1016/j.tca.2019.178304 Received 26 March 2019; Received in revised form 23 May 2019; Accepted 31 May 2019 Available online 03 June 2019 0040-6031/ © 2019 Elsevier B.V. All rights reserved.
Thermochimica Acta 678 (2019) 178304
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(4) The heat dissipation of the reactive system is simplified as a first order model. It depends on the temperature difference between the reactive system and furnace.
Table 1 The parameters used in the simulations. Parameter A E N R QDTBP cDTBP cToluene cBomb MBomb τ1 τ2 τ3 Rmax
Value
Unit 15
5.5 × 10 1.57 × 105 1 8.314 1350 2 2 0.5 7 0.3 20 60 0.67
s−1 J/mol / J/(mol•K) J/g J/(g•K) J/(g•K) J/(g•K) g s s s K/s
2.2. Modelling Selecting the DTBP/toluene solution as an example, with dynamic characteristics and reactive system’s heat dissipation consideration, the first approximation model of the classical ARC is shown in expression (1).
E d = A (1 ) nexp ( ) dt RTs dTs d QDTBPMDTBP = × dt dt CDTBPMDTBP + CTolueneMToluene + CBombMBomb Ts Tf 3 dTTC Ts TTC = dt 1 dTf TTC Tf dTf dTf = (if > RmaxK s 1, then = RmaxK s 1) dt 2 dt dt
methods are based on the assumption that the thermal inertia is constant during the whole reaction process in the past forty years, such as the correction method proposed by Townsend and Tou themselves [1], Fisher method [7], Enhanced-Fisher method [8] and so on. These correction methods are widely used and plausible in thermal hazard evaluation [9–11]. With thermal inertia determination larger than realistic in the actual assessment, the simulated thermal hazard indicators (TMRad, SADT) are usually conservative. Nonetheless, for accurate thermal decomposition kinetics studying, this may makes error and distortion. The reason is that all these methods neglect the fact that the thermal inertia is varying during the reaction because of the sample’s thermal dissipation, specific heat capacity changing and so on [12–14]. To overcome the lack of consideration that the sample’s thermal dissipation is varying in ARC based kinetics studying, a symmetric dualchannel accelerating rate calorimeter is developed to quantify the heat loss during the reaction. The corresponding data treatment algorithm is proposed with varying thermal inertia consideration in this article. In order to verify the validity of this calorimeter and kinetics approach, the experiments are performed by means of different mass percent ditert-butyl peroxide (DTBP)/toluene solutions. All the details are described in the following sections.
(1) Where, α is the extent of conversion. A is the activation energy. Ts is the temperature of sample in Kelvin. Tf is the temperature of furnace. TTC is the temperature of sample thermocouple. R is the gas constant. n is the reaction order. t is the time. QDTBP is the heat release of DTBP per unit mass. MDTBP, MToluene, MBomb is the mass of DTBP, toluene and bomb (sample container), respectively. cDTBP, cToluene, cBomb is the specific heat capacity of DTBP, toluene and bomb, respectively. τ1, τ2 and τ3 is the time constant of thermocouple, furnace, reactive system heat dissipation, respectively. The Rmax is the maximum heating rate of the furnace. It depends on the power of the furnace’s heaters. The values of the thermal kinetics parameters come from reference [18]. All the parameters used in the simulations are as shown in Table1, including thermophysical properties of the sample and container, the time constants, kinetics parameters of DTBP decomposition. Assuming the DTBP starts to decompose at 385.2 K, the time constant of thermocouple comes from the OMEGA’s tutorial [19]. The value of furnace’s time constant derives from the furnace’s heat capacity consideration. The value of time constant of heat dissipation is estimated with the low thermal conductivity of air consideration.
2. Numerical simulation of the heat loss during the pseudoadiabatic reaction The simulations study on the relationship between the dynamic response of the calorimeter and the sample’s thermal dissipation quantitatively. Also, its influence on kinetics computation is investigated.
2.3. Simulations In the simulations, a set of different mass percent DTBP/toluene solutions are selected as samples. The sum of the mass of DTBP and toluene is fixed at 5 g. The mass percent of the samples are set as 20%, 30%, 40% and 50%. The time-temperature curves of the samples with different mass percent are shown in Fig. 1. With the mass percent increasing, the self-heat rate is increasing rapidly. When the mass percent is 40% or 50%, the sample’s temperature decreases suddenly near the end of the reaction. The reason is that limiting to the maximum rate of furnace’s temperature rising and the temperature tracking lag, the temperature gradient between reactive system and furnace becomes larger as shown in Fig. 2. This makes the heat loss of the sample becomes larger promptly as shown in Fig. 3. Based on the regular kinetics based approach that the constant thermal inertia is adopted, the kinetics results are shown in Table 2 with nonlinear fitting [20,21]. Selecting the residual between the simulated and the predicted self-heat rate as the objective function, the vector of the kinetic parameters is calculated by the followed expression.
2.1. Hypotheses In order to analyze the variation of the thermal dissipation in ARC, a lumped parameter model concerning the heat transfer between the reaction system and environment is chosen to simulate the thermal behaviors of the calorimeter. To simplify the model, the assumptions used are made as followings: (1) The reactive system is considered to be at a uniform temperature. The heat capacities of the reactive system are considered as constant. (2) The dynamic responses of the sample thermocouple and furnace are simplified as a first order model [15–17]. The time constants of thermocouple and furnace are considered as temperature independent. (3) The furnace is considered as temperature uniform. The heat capacity of the air between the furnace and the reactive system is not considered. The temperature of the air is equal to the temperature of furnace.
N
=
[( i=1
dTm (t , E , A, n) )i dt
(
Where N is the data number, 2
dT ( t ) ) i ]2 dt dTm (t , E , A, n) dt
(2) is the predicted self-heat rate
Thermochimica Acta 678 (2019) 178304
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3. Instrumentation and kinetics approach 3.1. The amended varying thermal inertia expression Considering the dynamic heat transfer during the furnace’s temperature tracking, the temperature gradient between the sample and the furnace is non-negligible, especially when the sample’s self-heat rate is high. This makes the thermal dissipation of the reactive system and the thermal inertia varying. Due to describe this situation accurately, an amended expression of thermal inertia is used in this article.
(T,t)= Fig. 1. The time-temperature curves of the DTBP/toluene solutions with different mass percent.
Pex (T , t ) Pex (T , t ) = Pex (T , t ) Ploss (T , t ) Ms d(T (t ) Cs (T , t ))/dt
(3)
Where, the Φ(T,t) is the amended thermal inertia. Pex is the heat generation rate by the sample reaction. Ploss is the heat loss rate of the sample, including the heat absorbed by the sample container, the heat loss of the whole reaction system. Cs(T,t) is the heat capacity of the sample. Ms is the mass of the sample. The preconditions of the amended expression are: (1) the mass of the sample is constant during the reaction. And all the samples (reactants and products) are in the furnace’s temperature field. (2) The temperature of the sample is considered as uniform. 3.2. Instrumentation of the symmetric dual-channel accelerating rate calorimeter Structure in principle of the symmetric dual-channel accelerating rate calorimeter is shown in Fig. 4. The Thermocouple-R is a sheathed thermocouple to measure the reference’s temperature. The Thermocouple-S is a sheathed thermocouple to measure the sample’s temperature. The Heater-R is an electrical heater which is inserting in the reference. The Heater-S is inserting in the sample. The heating areas of the Heater-S and Heater-R are at the top of the sheaths. And the other place of the sheath generates almost no heat due to the electrical impedance control. This makes the generated electrical heat is absorbed by the reference mostly. The operating mode of the dual-channel ARC is Heat-Wait-Search sequence. The temperature control strategies of the symmetric dual-channel accelerating rate calorimeter are shown in Fig. 5. During the adiabatic reaction, the furnace traces the exothermic sample’s temperature by using the furnace heaters. The furnace’s temperature control strategy is same to the classic ARC. The reference is an inactive chemical with the heat capacity similar to the sample. The reference’s temperature traces the sample’s temperature by using Heater-R. During the reaction, the temperature difference between the reference and the sample keeps zero with the power controlled HeaterR. The heater-S is just for symmetric and heat capacity match. It is powered off during the reaction. In order to reduce the measuring errors, the sample rates of the Thermocouple-R and Thermocouple-S are set as 10 Hz. The Heater-R is connecting as a four-wire resistor for high precision power measurement. In order to satisfy the precondition of the amended thermal inertia expression, the sample container is sealed by a stopper at the neck of the bomb. The photo of the symmetric dual-channel accelerating rate calorimeter is shown in Fig. 6.
Fig. 2. The temperature gradient curves between reactive system and furnace of the different mass percent DTBP/toluene solutions.
Fig. 3. The heat loss curves of the different mass percent DTBP/toluene solutions. Table 2 The kinetics results of DTBP/toluene solutions. DTBP mass percent
ΔTad(K) (corrected)
Heat Release per unit mass (J/g)
E (kJ/ mol)
A (s−1)
n
20% 30% 40% 50%
101.577 155.274 230.516 299.196
1015.8 1035.2 1152.6 1196.8
155 157 158 179
4.23 × 1015 6.48 × 1015 5.96 × 1016 3.45 × 1017
0.9 0.9 1.7 2.0
3.3. The kinetics approach based on the novel accelerating rate calorimeter The assumptions of the followed kinetics approach are the indiscrimination of heat capacity and heat dissipation rate between the sample and reference during the reaction. According to the heat balance equation, the thermal inertia expression of the reference side is as following.
under the constant thermal inertia, preset kinetic model and parameters. The distortions of the calculated kinetic parameters are remarkable when the DTBP mass percent is high. The reason is that the heat loss is large and rapid changing in the great self-heat rate range. While in the kinetic computation, the thermal inertia is still considered as constant.
ref (T,t)=
PH (T , t ) PH (T , t ) = PH (T , t ) Ploss _r (T , t ) Mr d(Tr (t ) Cr (T , t ))/dt
(4)
The Φref(T,t) is the equivalent thermal inertia. PH is the power of 3
Thermochimica Acta 678 (2019) 178304
J. Ding, et al.
Fig. 4. Structure in principle of the symmetric dual-channel accelerating rate calorimeter.
Mr d(Tr (t ) Cr (T , t )) Ms d(T (t ) Cs (T , t )) = dt dt
(6)
Then,
PH (T , t ) = Pex (T , t ) = Ms ×
ref (T , t ) =
(T , t )
d(T × Cs (T , t )) dt
(7) (8)
(T , t )
The heat of reaction is calculated through the integrating of the electric heater power.
Qs =
Fig. 5. The temperature control strategies of the symmetric dual-channel accelerating rate calorimeter during the temperature tracking. Ts is the sample’s temperature, Tf is the furnace’s temperature, Tr is the reference’s temperature. Pr is the power of the electrical heater inserting in the reference. The data acquisition system records the value of Ts and Tf timely for further kinetics calculation.
t (Tfinal) t (Tonset )
Pex (T , t )dt =
t (Tfinal) t (Tonset )
PH (T , t )dt
(9)
Selecting the n-order reaction as an example, the expression of the self-heat rate is as followed.
dT ( t ) = dt
A × Qs E exp( )(1 (T , t ) Cs (T , t ) Ms RT (t )
T Tonset
PH (T , t ) dT (t )) n Qs (10)
(T , t ) × Cs (T , t ) =
PH (T , t ) Ms ×
dT dt
(T , t ) × T (t ) ×
dCs (T , t ) dT (t ) / dt dt
PH (T , t ) Ms ×
dT (t ) dt
(11)
Where, α is the extent of conversion. It is obtained by integrating and normalizing the heat release. Because the specific heat capacity is weak correlation with time, in a very small time intervals, the Cs(T,t) is proposed as constant, and the dCs(T,t)/dt is zero. According to the nonlinear fitting, the kinetic parameters is calculated from expression (10). If the reaction is autocatalytic or multi-stage, this method is still suitable by using the autocatalytic or multi-stage model. 4. Experimental verification Di-t-butyl peroxide (DTBP) with purity 97% is provided by Aladdin biochemical technology Co., LTD. DTBP is a colorless liquid with a molecular formula of C8H18O2. Toluene with purity higher than 99%, is provided by Huadong medicine Co., LTD. The mass percent of the DTBP/toluene solutions are set as 15%, 20%, 25% and 30%. The masses of the solutions are fixed as 8 g. The mass of the steel bomb is 13.5 g. For each experiment, the test is conducted in the Heat-Wait-Search (HWS) mode, applying an initial furnace temperature of 365.15 K (92 O C), a wait time of 15 min, a search time of 15 min and a temperature increment of 5 K. The threshold of the self-heating rate for exotherm detection is set as 0.02 K/min. The exothermic results of different mass percent DTBP/toluene solutions are shown in Table 3. Where, the
Fig. 6. The photo of the symmetric dual-channel accelerating rate calorimeter.
Heater-R. Ploss_r is the heat loss rate of the reference, including the heat absorbed by the container, the heat loss of the whole reaction system. Cr(T,t) is the heat capacity of the sample. Mr is the mass of the sample. Assuming the heat capacities of the sample and reference are equal, the two containers are symmetrical, then the heat losses of the sample and reference are always same due to their temperatures are identical and they are in the same temperature environment. Based on this, the followed equations can be obtained.
Ploss _r = Ploss
(5) 4
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Table 3 The measured results of DTBP/toluene solutions with different mass percent. DTBP mass percent
Const_Φ
TONSET (OC)
TFINAL (OC)
Measured_ΔTad (OC)
Corrected_ΔTad (OC)
15% 20% 25% 30%
1.42 1.42 1.42 1.42
121.8 116.8 112.8 116.9
184.1 194.4 215.4 231.4
62.3 77.6 102.6 114.5
88.5 110.2 145.7 162.6
Const_Φ is the thermal inertia from the classical definition. TONSET is the detected initial self-heat temperature. TFINAL is the final decomposition temperature. Measured_ΔTad is the measured adiabatic temperature rise. Corrected_ΔTad is the adiabatic temperature rise after classical thermal inertia correction. Generally, the adiabatic temperature rises are increasing with the DTBP mass percent, but not linearly. The reason is that the heat dissipations of sample in different DTBP mass percent are different. Meanwhile, the onset temperatures are decreasing with the DTBP mass percent generally. This is because the self-heating detection thresholds are equal in all the experiments. While due to the difference of DTBP mass percent, the exothermic rate at the corresponding temperature is different in each experiment. Nevertheless, the 30% mass percent DTBP/toluene is an exception. This is because of the measurement uncertainty of the self-designed symmetric dual-channel ARC. While, all the measured onset temperatures are similar to the acknowledged values in reference [18]. The measured temperature-time curves of different mass percent DTBP/toluene solutions are shown in Fig. 7. The pseudo-adiabatic reaction times are onset temperature dependent. For high concentration DTBP/toluene solution, the furnace’s tracking heat rate is lagged, especially in the violent reaction stage. This makes a large temperature gradient between the reaction system and the furnace, then causes the heat loss and amended thermal inertia increasing. According to the recorded electrical heater power by the acquisition system, the curves of time-power are shown in Fig. 8. In the experiment of 30% mass percent of DTBP/toluene solutions, in the areas near the time at the maximum reaction rate, the recorded power is saturated. The reason is that the sample’s heat release rate is larger than the maximum power of the electrical heater. This makes the reference’ temperature tracking lag and power integrating errors. According to the expression (11), the products of heat capacity and thermal inertia are obtained in Fig. 9. In the reaction process, the CS(T,t)Φ(T,t) increases rapidly in the end. The reason is that at the end of the reaction, the furnace temperature tracking is lagged and incapable because of the high self-heat rate of the sample. This makes the thermal inertia increasing rapidly and observably.
By integrating the recorded electrical power data, the heat release of the sample is obtained in Table 4. The heat release per gram value is similar to the experiential results of DTBP from differential scanning calorimetry experiments. In the 30% mass percent experiment, the value is smaller than the experiential. The reason is the saturation of the heater power during the rapid reaction stage and the integrating errors. Based on the calculated products of heat capacity and thermal inertia, the total heat release integrating from electronic power, the n-order kinetic parameters are calculated. Compared with the kinetic results calculated from the constant thermal inertia and classical ARC, the simulated temperature-time curves fitting results based on the kinetic parameters obtained from this proposed calorimetry and its kinetics approach is much closer to the experimental curves, as shown in Fig. 10. In Fig. 10(c), the deviation between calculated based on varying thermal inertia and experimental curves is much larger than other experiments. The reason is that the error ratio of the electric power measurement in the low power range is larger due to the shortcoming of the electric power measurement circuit. In the 25% mass percent DTBP/toluene solution experiment, the onset temperature is lower. This makes the reference heater working at the low power condition for a long time. According to the expressions (9) and (10), the error of the electric power measurement effects the veracities of total heat release and CS(T,t)Φ(T,t). Then it lead to the error in temperaturetime curve simulation based on calculated kinetic parameters and the varying thermal inertia. The results of the kinetic parameters are shown in Table 4. Because the toluene is not participating in the reaction, the values of activation energy and pre-exponential factor should be independent of the mass percent [22,23]. Compared with the results from the constant thermal inertia, the standard deviations of activation energy and pre-exponential factor from varying thermal inertia consideration are much smaller. In the classical ARC based kinetics approaches, the temperature-time data with large self-heat rate seems unmanageable, because of the ignoring of the huge and varying heat dissipation in kinetics computation. However, with the novel calorimetry and kinetics approach, the impact from this issue can be decline remarkably. This means that Fig. 7. The time-temperature curves of the DTBP/toluene solutions with different mass percent. The black dot curves are the sample’s temperatures. The red curves are the furnace’s temperatures. The blue curves are the reference’s temperatures. The temperature difference between the sample and reference is smaller remarkable than the difference between sample and furnace. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
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Thermochimica Acta 678 (2019) 178304
J. Ding, et al.
Fig. 8. The time-power curves of the DTBP/toluene solutions with different mass percent. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent.
Fig. 9. The products of varying thermal inertia and heat capacity of the DTBP/toluene solutions with different mass percent. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent.
the hazard indicators simulation based on the kinetic parameters based on the proposed method are more reliable. In order to investigate the reliability of the proposed calorimeter and the corresponding kinetic approach, the repetitive experiments are carried out and the kinetic results are calculated as shown in Table 5. The average values and standard deviations of TONSET, TFINAL, heat release per gram DTBP, activation energy, pre-exponential factor and reaction order for each mass percent DTBP/toluene solution are calculated from five times repetitive experiments. For five times 20% mass percent DTBP/toluene experiments, all of the onset temperatures are 117 OC, approximately. This makes the deviations of TONSET and TFINAL are much smaller. While for other mass percent solutions, the onset temperatures vacillate between two adjacent HWS steps. This makes the deviations larger. In a word, compared with the experiential results in references [18] and [23], all the measured and calculated results are in a reasonable range. This implies the reliabilities of the proposed calorimetry and its kinetics approach.
Table 4 The kinetics results from constant and varying thermal inertia consideration.
The proposed method
The classic ARC and its kinetics approach
DTBP mass percent
Heat release per unit mass (J/g)
E (kJ/ mol)
lnA (s−1)
n
15% 20% 25% 30% Average Deviation 15% 20% 25% 30% Average Deviation
1420 1319 1427 1259 1356.3 81.5 / / / / / /
147 155 156 163 155.3 6.6 139 152 175 179 161.3 19.0
34.4 36.2 36.2 37.0 36.0 1.1 33.4 36.0 37.1 38.6 36.3 2.2
0.9 1.0 1.0 1.1 1.0 0.1 0.8 0.9 1.2 1.4 1.1 0.3
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Fig. 10. The results of the temperature-time fitting of different mass percent DTBP/toluene solutions. The black curves are the experimental data. The red dot curves are the fitted results with varying thermal inertia consideration. The blue dot curves are the fitted results with constant thermal inertia. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
Table 5 The results of repetitive experiments with different mass percent DTBP/toluene solutions. DTBP mass percent
TONSET (OC)
15% 20% 25% 30%
121.1 117.7 116.1 115.6
TFINAL (OC) ± ± ± ±
3.8 0.3 3.5 3.1
188.5 193.2 215.1 229.6
± ± ± ±
5.1 0.9 4.2 3.1
Heat Release per unit mass (J/g)
E (kJ/mol)
ln A (s−1)
n
1317.5 1310.8 1369.2 1243.1
150.4 155.2 158.2 160.6
34.7 36.1 36.2 36.3
0.9 0.9 1.0 1.1
± ± ± ±
43.8 12.6 35.6 42.2
± ± ± ±
2.8 1.6 2.7 3.5
± ± ± ±
0.2 0.2 0.1 0.1
± ± ± ±
0.1 0.1 0.1 0.1
kinetics approaches, the heat capacity of the sample is considered as constant or the heat capacity should be measured for kinetics precision improvement. Incontestably, there are several challenges of this method should be further studied.
5. Conclusions Other than the traditional definition of thermal inertia, the varying thermal inertia expression is proposed based on the thermal dissipation of the sample in this article. Then, a symmetric dual-channel accelerating rate calorimeter is realized with the architectural designing and temperature control strategies developing. Based on the measured sample’s temperature, time and equivalent heat release rate, a novel kinetics approach with varying thermal inertia consideration is presented and verified by different mass percent DTBP/toluene solutions experiments. The experimental results show that the novel calorimetry and its data treatment methods can inhibit the influence of varying and large heat dissipation in kinetics computation. The beneficial effects of this study as following. Firstly, compared with the classical ARC, the total heat release of the sample can be measured directly by power data integrating in the symmetric dual-channel accelerating rate calorimeter. And the more reasonable thermal inertia correction and more accurate kinetics results can be obtained with the varying sample’s heat dissipation consideration. Secondly, it reduces the requirement of the experimental data of the ARC in kinetics computation. In the previous ARC based kinetics approach, in order to decrease the heat dissipation of the reactive system, the effective action is decreasing the mass of the sample. This makes the large thermal inertia and abnormal correction, especially in energetic material testing. While in the proposed calorimeter and kinetics approach, this precondition is less demanding. Based on this benefit, the calorimeter and its kinetics approach studied in this article may be a feasible method for more precise thermal hazard evaluation of energetic material [24,25]. Thirdly, the measurement of the heat capacity during the quasiadiabatic reaction can be avoid. In the proposed kinetics approach, based on the precondition that the heat capacities of sample and reference are same, the product of the thermal inertia and heat capacity can be obtained through expression (10). However, in the previous
(1) The energy density of the electronic heater should be increased. In this study, the nominal power of the electrical heater is 60 W. However, when the mass percent of DTBP/toluene is larger than 30%, the temperature of the reference is lagged than sample’s temperature. The reason is the power of the heater is not large enough. For specification improving, the higher energy density heater should be adopted in this calorimeter. Also, the precision of the electrical power measurement should be improved. (2) The instantaneity of the furnace’s and reference’s temperature tracking should be optimized. To reduce the heat dissipation of the reactive system essentially, some sensor and actuator dynamic forecasting and compensation should be adopted in this calorimeter [26,27]. Acknowledgments This work was supported by Zhejiang provincial public welfare research program (Grant No. LGF18B030001), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY17F010011, No. LQ15F030003). References [1] D.I. Townsend, J.C. Tou, Thermal hazard evaluation by an accelerating rate calorimeter, Thermochim. Acta 37 (1980) 1–30. [2] S. Chippett, Low thermal inertia scanning adiabatic calorimeter, US Patent US7021820, 2006. [3] F.L. Wu, Differential adiabatic compensation calorimeter and methods of operation, US Patent 2015/0124851A1, 2015. [4] Q.Y. Xu, J. Ding, S.J. Yang, S.L. Ye, Modeling of a power compensated adiabatic reaction system for temperature control design and simulation analyses,
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[16] S. Augustin, T. Fröhlich, C. Ament, T. Güther, K. Irrgang, L. Lippmann, Dynamic properties of contact thermometers for high temperatures, Measurement 51 (2014) 387–392. [17] L. Michalski, K. Eckersdrof, J. Kucharski, J. McGhee, Temperature Measurement, second edition, John Wiley & Sons Ltd., 2001. [18] R.J.A. Kersten, M.N. Boers, M.M. Stork, C. Visser, Results of a round-robin with ditertiary-butyl peroxide in various adiabatic equipment for assessment of runaway reaction hazards, J. Loss Prev. Process Ind. 18 (2005) 145–151. [19] OMEGA company. https://www.omega.com/temperature/Z/pdf/z052.pdf. [20] A. Kossoy, Y. Akhmetshin, Identification of kinetic models for the assessment of reaction hazards, Process. Saf. Prog. 26 (3) (2007) 209–220. [21] J. Ding, Q. Chen, Q.Y. Xu, S.J. Yang, S.L. Ye, ARC thermal inertia correction method based on C80 data merging, CIESC Journal 70 (1) (2019) 417–424 (In Chinese). [22] A. Kimura, T. Otsuka, Performance evaluation of differential accelerating rate calorimeter for the thermal runaway reaction of di-tert-butyl peroxide, J. Therm, Anal. Cal. 113 (2013) 1585–1591. [23] Y.S. Duh, C.S. Kao, W.L.W. Lee, Chemical kinetics on thermal decompositions of ditert-butyl peroxide studied by calorimetry, J. Therm. Anal. Cal. 127 (2017) 1071–1087. [24] E.F. Rothgery, D.E. Audette, R.C. Wedlich, D.A. Csejka, The study of the thermal decomposition of 3-nitro-1,2,4-triazol-5-one (NTO) by DSC, TGA-MS, and ARC, Thermochim. Acta 185 (2) (1991) 235–243. [25] C.Y. Zhang, S.H. Jin, J.W. Ji, B.C. Jing, F. Bao, G.Y. Zhang, Q.H. Shu, Thermal hazard assessment of TNT and DNAN under adiabatic condition by using accelerating rate calorimeter (ARC), J. Therm. Anal. Cal. 131 (2018) 89–93. [26] S. Augustin, T. Frohlich, H. Mammen, K. Irrgang, U. Meiselbach, Determination of the dynamic behavious of high-speed temperature sensors, Meas. Sci. Technol. 23 (2012) 074024(9pp). [27] A.A. Minakov, C. Schick, Dynamics of the temperature distribution in ultra-fast thin-film calorimeter sensors, Thermochim. Acta 603 (2015) 205–217.
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A symmetric dual-channel accelerating rate calorimeter with the varying thermal inertia consideration
T
Jiong Dinga,b, Liming Yua, Jichen Wanga, Qiyue Xua,b, Suijun Yanga,b, Shuliang Yea,b,
⁎
a b
Institute of Industry and Trade Measurement Technology, College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou, PR China Zhejiang Engineering Laboratory of Chemicals Safety Testing Technology and Instruments, Hangzhou, PR China
ARTICLE INFO
ABSTRACT
Keywords: Thermal inertia Accelerating rate calorimetry Instrumentation Thermal kinetics
The thermal inertia determination and correction are the significant steps in accelerating rate calorimetric based kinetics calculation and thermal hazard evaluation. However, the existing kinetics approaches based on the constant thermal inertia ignore the fact that the sample’s heat dissipation is varying during the pseudo-adiabatic reaction. To overcome this shortcoming, an amended thermal inertia expression is proposed and a symmetric dual-channel accelerating rate calorimeter is developed in this article. A novel kinetics approach is presented with the varying thermal inertia consideration based on the measured electrical power data. With the different mass percent DTBP/toluene solutions experiments, the validities and advantages of the proposed calorimetry and the corresponding thermal analysis method are verified. Meanwhile, the challenges in the engineering implementation of this proposed method are analyzed and discussed at the end of the article.
1. Introduction The kinetics evaluation from adiabatic calorimetric data is a fundamental task in chemical process safety study based on accelerating rate calorimetry. To obtain the accurate kinetic results, the thermal inertia should be determined validly in the experiment and corrected in the numerical simulation. However, the exact determination and correction are not easily to carry out. When the accelerating rate calorimeter (ARC) was first developed by Townsend and Tou, the definition of thermal inertia, which is based on the ratio of the heat capacity between the whole reactive system (sample and sample container) and the sample, was presented to describe the heat dissipation of sample quantitatively [1]. This definition ignores the fact that the heat dissipation and heat capacity of the sample is varying during the reaction. This makes the errors in thermal behavior recording and kinetics computation. In order to obtain the accurate kinetics results and pure adiabatic thermal behavior, the history of ARC development and its kinetics approach can be considered as a history of a struggle for sample’s heat dissipation avoiding and correcting. For sample’s thermal dissipation reduction, some improvements in calorimeter instrumentation were carried out in the past several decades. The representative technologies are the pressure and power compensations. With the pressure compensation, the ratio between the volume and heat capacity of the container increases and the thermal
inertia decreases. The typical instruments of this kind are Phi-TEC II from HEL Group, APTAC from Netzsch Group and VSP2 from Fauske & Associates. LLC. The other technology is power compensation with the principle that the container’s enthalpy change comes from the electrical heating, not the sample’s reaction exotherm. The commercial calorimeters based on this principle are the VariPhi module from Netzsch Group [2], the DARC from the Omnical Inc [3] and the TAC-CP 500A from the Young Instruments Company [4]. Theoretically, the adiabatic temperature rise obtained from the power compensated calorimeter is considered as ideal and doesn’t need any correction [5]. While considering the instantaneity of the temperature tracking and the furnace’s dynamic response, the assumption that the adiabaticity of the reactive system is unreachable in engineering, especially when the sample’s selfheat rate is large. The reason is that the furnace’s temperature is always lagged due to the dynamic response of the temperature sensing and controlling [6]. This means that there still has limitation in studying the safety aspects and characterization of chemicals by using power compensated adiabatic calorimeters. In addition, the constructional and operational complexities make the pressure or power compensated adiabatic calorimeters are not wider used than the classic ARCs in actual thermal hazard studying and evaluation. This means that the thermal inertia correction in mathematics is inevitable in kinetics studying by means of ARCs. According to the thermal inertia definition, almost all the adiabatic correction
⁎ Corresponding author at: Institute of Industry and Trade Measurement Technology, College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou, PR China. E-mail address: [email protected] (S. Ye).
https://doi.org/10.1016/j.tca.2019.178304 Received 26 March 2019; Received in revised form 23 May 2019; Accepted 31 May 2019 Available online 03 June 2019 0040-6031/ © 2019 Elsevier B.V. All rights reserved.
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(4) The heat dissipation of the reactive system is simplified as a first order model. It depends on the temperature difference between the reactive system and furnace.
Table 1 The parameters used in the simulations. Parameter A E N R QDTBP cDTBP cToluene cBomb MBomb τ1 τ2 τ3 Rmax
Value
Unit 15
5.5 × 10 1.57 × 105 1 8.314 1350 2 2 0.5 7 0.3 20 60 0.67
s−1 J/mol / J/(mol•K) J/g J/(g•K) J/(g•K) J/(g•K) g s s s K/s
2.2. Modelling Selecting the DTBP/toluene solution as an example, with dynamic characteristics and reactive system’s heat dissipation consideration, the first approximation model of the classical ARC is shown in expression (1).
E d = A (1 ) nexp ( ) dt RTs dTs d QDTBPMDTBP = × dt dt CDTBPMDTBP + CTolueneMToluene + CBombMBomb Ts Tf 3 dTTC Ts TTC = dt 1 dTf TTC Tf dTf dTf = (if > RmaxK s 1, then = RmaxK s 1) dt 2 dt dt
methods are based on the assumption that the thermal inertia is constant during the whole reaction process in the past forty years, such as the correction method proposed by Townsend and Tou themselves [1], Fisher method [7], Enhanced-Fisher method [8] and so on. These correction methods are widely used and plausible in thermal hazard evaluation [9–11]. With thermal inertia determination larger than realistic in the actual assessment, the simulated thermal hazard indicators (TMRad, SADT) are usually conservative. Nonetheless, for accurate thermal decomposition kinetics studying, this may makes error and distortion. The reason is that all these methods neglect the fact that the thermal inertia is varying during the reaction because of the sample’s thermal dissipation, specific heat capacity changing and so on [12–14]. To overcome the lack of consideration that the sample’s thermal dissipation is varying in ARC based kinetics studying, a symmetric dualchannel accelerating rate calorimeter is developed to quantify the heat loss during the reaction. The corresponding data treatment algorithm is proposed with varying thermal inertia consideration in this article. In order to verify the validity of this calorimeter and kinetics approach, the experiments are performed by means of different mass percent ditert-butyl peroxide (DTBP)/toluene solutions. All the details are described in the following sections.
(1) Where, α is the extent of conversion. A is the activation energy. Ts is the temperature of sample in Kelvin. Tf is the temperature of furnace. TTC is the temperature of sample thermocouple. R is the gas constant. n is the reaction order. t is the time. QDTBP is the heat release of DTBP per unit mass. MDTBP, MToluene, MBomb is the mass of DTBP, toluene and bomb (sample container), respectively. cDTBP, cToluene, cBomb is the specific heat capacity of DTBP, toluene and bomb, respectively. τ1, τ2 and τ3 is the time constant of thermocouple, furnace, reactive system heat dissipation, respectively. The Rmax is the maximum heating rate of the furnace. It depends on the power of the furnace’s heaters. The values of the thermal kinetics parameters come from reference [18]. All the parameters used in the simulations are as shown in Table1, including thermophysical properties of the sample and container, the time constants, kinetics parameters of DTBP decomposition. Assuming the DTBP starts to decompose at 385.2 K, the time constant of thermocouple comes from the OMEGA’s tutorial [19]. The value of furnace’s time constant derives from the furnace’s heat capacity consideration. The value of time constant of heat dissipation is estimated with the low thermal conductivity of air consideration.
2. Numerical simulation of the heat loss during the pseudoadiabatic reaction The simulations study on the relationship between the dynamic response of the calorimeter and the sample’s thermal dissipation quantitatively. Also, its influence on kinetics computation is investigated.
2.3. Simulations In the simulations, a set of different mass percent DTBP/toluene solutions are selected as samples. The sum of the mass of DTBP and toluene is fixed at 5 g. The mass percent of the samples are set as 20%, 30%, 40% and 50%. The time-temperature curves of the samples with different mass percent are shown in Fig. 1. With the mass percent increasing, the self-heat rate is increasing rapidly. When the mass percent is 40% or 50%, the sample’s temperature decreases suddenly near the end of the reaction. The reason is that limiting to the maximum rate of furnace’s temperature rising and the temperature tracking lag, the temperature gradient between reactive system and furnace becomes larger as shown in Fig. 2. This makes the heat loss of the sample becomes larger promptly as shown in Fig. 3. Based on the regular kinetics based approach that the constant thermal inertia is adopted, the kinetics results are shown in Table 2 with nonlinear fitting [20,21]. Selecting the residual between the simulated and the predicted self-heat rate as the objective function, the vector of the kinetic parameters is calculated by the followed expression.
2.1. Hypotheses In order to analyze the variation of the thermal dissipation in ARC, a lumped parameter model concerning the heat transfer between the reaction system and environment is chosen to simulate the thermal behaviors of the calorimeter. To simplify the model, the assumptions used are made as followings: (1) The reactive system is considered to be at a uniform temperature. The heat capacities of the reactive system are considered as constant. (2) The dynamic responses of the sample thermocouple and furnace are simplified as a first order model [15–17]. The time constants of thermocouple and furnace are considered as temperature independent. (3) The furnace is considered as temperature uniform. The heat capacity of the air between the furnace and the reactive system is not considered. The temperature of the air is equal to the temperature of furnace.
N
=
[( i=1
dTm (t , E , A, n) )i dt
(
Where N is the data number, 2
dT ( t ) ) i ]2 dt dTm (t , E , A, n) dt
(2) is the predicted self-heat rate
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3. Instrumentation and kinetics approach 3.1. The amended varying thermal inertia expression Considering the dynamic heat transfer during the furnace’s temperature tracking, the temperature gradient between the sample and the furnace is non-negligible, especially when the sample’s self-heat rate is high. This makes the thermal dissipation of the reactive system and the thermal inertia varying. Due to describe this situation accurately, an amended expression of thermal inertia is used in this article.
(T,t)= Fig. 1. The time-temperature curves of the DTBP/toluene solutions with different mass percent.
Pex (T , t ) Pex (T , t ) = Pex (T , t ) Ploss (T , t ) Ms d(T (t ) Cs (T , t ))/dt
(3)
Where, the Φ(T,t) is the amended thermal inertia. Pex is the heat generation rate by the sample reaction. Ploss is the heat loss rate of the sample, including the heat absorbed by the sample container, the heat loss of the whole reaction system. Cs(T,t) is the heat capacity of the sample. Ms is the mass of the sample. The preconditions of the amended expression are: (1) the mass of the sample is constant during the reaction. And all the samples (reactants and products) are in the furnace’s temperature field. (2) The temperature of the sample is considered as uniform. 3.2. Instrumentation of the symmetric dual-channel accelerating rate calorimeter Structure in principle of the symmetric dual-channel accelerating rate calorimeter is shown in Fig. 4. The Thermocouple-R is a sheathed thermocouple to measure the reference’s temperature. The Thermocouple-S is a sheathed thermocouple to measure the sample’s temperature. The Heater-R is an electrical heater which is inserting in the reference. The Heater-S is inserting in the sample. The heating areas of the Heater-S and Heater-R are at the top of the sheaths. And the other place of the sheath generates almost no heat due to the electrical impedance control. This makes the generated electrical heat is absorbed by the reference mostly. The operating mode of the dual-channel ARC is Heat-Wait-Search sequence. The temperature control strategies of the symmetric dual-channel accelerating rate calorimeter are shown in Fig. 5. During the adiabatic reaction, the furnace traces the exothermic sample’s temperature by using the furnace heaters. The furnace’s temperature control strategy is same to the classic ARC. The reference is an inactive chemical with the heat capacity similar to the sample. The reference’s temperature traces the sample’s temperature by using Heater-R. During the reaction, the temperature difference between the reference and the sample keeps zero with the power controlled HeaterR. The heater-S is just for symmetric and heat capacity match. It is powered off during the reaction. In order to reduce the measuring errors, the sample rates of the Thermocouple-R and Thermocouple-S are set as 10 Hz. The Heater-R is connecting as a four-wire resistor for high precision power measurement. In order to satisfy the precondition of the amended thermal inertia expression, the sample container is sealed by a stopper at the neck of the bomb. The photo of the symmetric dual-channel accelerating rate calorimeter is shown in Fig. 6.
Fig. 2. The temperature gradient curves between reactive system and furnace of the different mass percent DTBP/toluene solutions.
Fig. 3. The heat loss curves of the different mass percent DTBP/toluene solutions. Table 2 The kinetics results of DTBP/toluene solutions. DTBP mass percent
ΔTad(K) (corrected)
Heat Release per unit mass (J/g)
E (kJ/ mol)
A (s−1)
n
20% 30% 40% 50%
101.577 155.274 230.516 299.196
1015.8 1035.2 1152.6 1196.8
155 157 158 179
4.23 × 1015 6.48 × 1015 5.96 × 1016 3.45 × 1017
0.9 0.9 1.7 2.0
3.3. The kinetics approach based on the novel accelerating rate calorimeter The assumptions of the followed kinetics approach are the indiscrimination of heat capacity and heat dissipation rate between the sample and reference during the reaction. According to the heat balance equation, the thermal inertia expression of the reference side is as following.
under the constant thermal inertia, preset kinetic model and parameters. The distortions of the calculated kinetic parameters are remarkable when the DTBP mass percent is high. The reason is that the heat loss is large and rapid changing in the great self-heat rate range. While in the kinetic computation, the thermal inertia is still considered as constant.
ref (T,t)=
PH (T , t ) PH (T , t ) = PH (T , t ) Ploss _r (T , t ) Mr d(Tr (t ) Cr (T , t ))/dt
(4)
The Φref(T,t) is the equivalent thermal inertia. PH is the power of 3
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Fig. 4. Structure in principle of the symmetric dual-channel accelerating rate calorimeter.
Mr d(Tr (t ) Cr (T , t )) Ms d(T (t ) Cs (T , t )) = dt dt
(6)
Then,
PH (T , t ) = Pex (T , t ) = Ms ×
ref (T , t ) =
(T , t )
d(T × Cs (T , t )) dt
(7) (8)
(T , t )
The heat of reaction is calculated through the integrating of the electric heater power.
Qs =
Fig. 5. The temperature control strategies of the symmetric dual-channel accelerating rate calorimeter during the temperature tracking. Ts is the sample’s temperature, Tf is the furnace’s temperature, Tr is the reference’s temperature. Pr is the power of the electrical heater inserting in the reference. The data acquisition system records the value of Ts and Tf timely for further kinetics calculation.
t (Tfinal) t (Tonset )
Pex (T , t )dt =
t (Tfinal) t (Tonset )
PH (T , t )dt
(9)
Selecting the n-order reaction as an example, the expression of the self-heat rate is as followed.
dT ( t ) = dt
A × Qs E exp( )(1 (T , t ) Cs (T , t ) Ms RT (t )
T Tonset
PH (T , t ) dT (t )) n Qs (10)
(T , t ) × Cs (T , t ) =
PH (T , t ) Ms ×
dT dt
(T , t ) × T (t ) ×
dCs (T , t ) dT (t ) / dt dt
PH (T , t ) Ms ×
dT (t ) dt
(11)
Where, α is the extent of conversion. It is obtained by integrating and normalizing the heat release. Because the specific heat capacity is weak correlation with time, in a very small time intervals, the Cs(T,t) is proposed as constant, and the dCs(T,t)/dt is zero. According to the nonlinear fitting, the kinetic parameters is calculated from expression (10). If the reaction is autocatalytic or multi-stage, this method is still suitable by using the autocatalytic or multi-stage model. 4. Experimental verification Di-t-butyl peroxide (DTBP) with purity 97% is provided by Aladdin biochemical technology Co., LTD. DTBP is a colorless liquid with a molecular formula of C8H18O2. Toluene with purity higher than 99%, is provided by Huadong medicine Co., LTD. The mass percent of the DTBP/toluene solutions are set as 15%, 20%, 25% and 30%. The masses of the solutions are fixed as 8 g. The mass of the steel bomb is 13.5 g. For each experiment, the test is conducted in the Heat-Wait-Search (HWS) mode, applying an initial furnace temperature of 365.15 K (92 O C), a wait time of 15 min, a search time of 15 min and a temperature increment of 5 K. The threshold of the self-heating rate for exotherm detection is set as 0.02 K/min. The exothermic results of different mass percent DTBP/toluene solutions are shown in Table 3. Where, the
Fig. 6. The photo of the symmetric dual-channel accelerating rate calorimeter.
Heater-R. Ploss_r is the heat loss rate of the reference, including the heat absorbed by the container, the heat loss of the whole reaction system. Cr(T,t) is the heat capacity of the sample. Mr is the mass of the sample. Assuming the heat capacities of the sample and reference are equal, the two containers are symmetrical, then the heat losses of the sample and reference are always same due to their temperatures are identical and they are in the same temperature environment. Based on this, the followed equations can be obtained.
Ploss _r = Ploss
(5) 4
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Table 3 The measured results of DTBP/toluene solutions with different mass percent. DTBP mass percent
Const_Φ
TONSET (OC)
TFINAL (OC)
Measured_ΔTad (OC)
Corrected_ΔTad (OC)
15% 20% 25% 30%
1.42 1.42 1.42 1.42
121.8 116.8 112.8 116.9
184.1 194.4 215.4 231.4
62.3 77.6 102.6 114.5
88.5 110.2 145.7 162.6
Const_Φ is the thermal inertia from the classical definition. TONSET is the detected initial self-heat temperature. TFINAL is the final decomposition temperature. Measured_ΔTad is the measured adiabatic temperature rise. Corrected_ΔTad is the adiabatic temperature rise after classical thermal inertia correction. Generally, the adiabatic temperature rises are increasing with the DTBP mass percent, but not linearly. The reason is that the heat dissipations of sample in different DTBP mass percent are different. Meanwhile, the onset temperatures are decreasing with the DTBP mass percent generally. This is because the self-heating detection thresholds are equal in all the experiments. While due to the difference of DTBP mass percent, the exothermic rate at the corresponding temperature is different in each experiment. Nevertheless, the 30% mass percent DTBP/toluene is an exception. This is because of the measurement uncertainty of the self-designed symmetric dual-channel ARC. While, all the measured onset temperatures are similar to the acknowledged values in reference [18]. The measured temperature-time curves of different mass percent DTBP/toluene solutions are shown in Fig. 7. The pseudo-adiabatic reaction times are onset temperature dependent. For high concentration DTBP/toluene solution, the furnace’s tracking heat rate is lagged, especially in the violent reaction stage. This makes a large temperature gradient between the reaction system and the furnace, then causes the heat loss and amended thermal inertia increasing. According to the recorded electrical heater power by the acquisition system, the curves of time-power are shown in Fig. 8. In the experiment of 30% mass percent of DTBP/toluene solutions, in the areas near the time at the maximum reaction rate, the recorded power is saturated. The reason is that the sample’s heat release rate is larger than the maximum power of the electrical heater. This makes the reference’ temperature tracking lag and power integrating errors. According to the expression (11), the products of heat capacity and thermal inertia are obtained in Fig. 9. In the reaction process, the CS(T,t)Φ(T,t) increases rapidly in the end. The reason is that at the end of the reaction, the furnace temperature tracking is lagged and incapable because of the high self-heat rate of the sample. This makes the thermal inertia increasing rapidly and observably.
By integrating the recorded electrical power data, the heat release of the sample is obtained in Table 4. The heat release per gram value is similar to the experiential results of DTBP from differential scanning calorimetry experiments. In the 30% mass percent experiment, the value is smaller than the experiential. The reason is the saturation of the heater power during the rapid reaction stage and the integrating errors. Based on the calculated products of heat capacity and thermal inertia, the total heat release integrating from electronic power, the n-order kinetic parameters are calculated. Compared with the kinetic results calculated from the constant thermal inertia and classical ARC, the simulated temperature-time curves fitting results based on the kinetic parameters obtained from this proposed calorimetry and its kinetics approach is much closer to the experimental curves, as shown in Fig. 10. In Fig. 10(c), the deviation between calculated based on varying thermal inertia and experimental curves is much larger than other experiments. The reason is that the error ratio of the electric power measurement in the low power range is larger due to the shortcoming of the electric power measurement circuit. In the 25% mass percent DTBP/toluene solution experiment, the onset temperature is lower. This makes the reference heater working at the low power condition for a long time. According to the expressions (9) and (10), the error of the electric power measurement effects the veracities of total heat release and CS(T,t)Φ(T,t). Then it lead to the error in temperaturetime curve simulation based on calculated kinetic parameters and the varying thermal inertia. The results of the kinetic parameters are shown in Table 4. Because the toluene is not participating in the reaction, the values of activation energy and pre-exponential factor should be independent of the mass percent [22,23]. Compared with the results from the constant thermal inertia, the standard deviations of activation energy and pre-exponential factor from varying thermal inertia consideration are much smaller. In the classical ARC based kinetics approaches, the temperature-time data with large self-heat rate seems unmanageable, because of the ignoring of the huge and varying heat dissipation in kinetics computation. However, with the novel calorimetry and kinetics approach, the impact from this issue can be decline remarkably. This means that Fig. 7. The time-temperature curves of the DTBP/toluene solutions with different mass percent. The black dot curves are the sample’s temperatures. The red curves are the furnace’s temperatures. The blue curves are the reference’s temperatures. The temperature difference between the sample and reference is smaller remarkable than the difference between sample and furnace. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
5
Thermochimica Acta 678 (2019) 178304
J. Ding, et al.
Fig. 8. The time-power curves of the DTBP/toluene solutions with different mass percent. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent.
Fig. 9. The products of varying thermal inertia and heat capacity of the DTBP/toluene solutions with different mass percent. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent.
the hazard indicators simulation based on the kinetic parameters based on the proposed method are more reliable. In order to investigate the reliability of the proposed calorimeter and the corresponding kinetic approach, the repetitive experiments are carried out and the kinetic results are calculated as shown in Table 5. The average values and standard deviations of TONSET, TFINAL, heat release per gram DTBP, activation energy, pre-exponential factor and reaction order for each mass percent DTBP/toluene solution are calculated from five times repetitive experiments. For five times 20% mass percent DTBP/toluene experiments, all of the onset temperatures are 117 OC, approximately. This makes the deviations of TONSET and TFINAL are much smaller. While for other mass percent solutions, the onset temperatures vacillate between two adjacent HWS steps. This makes the deviations larger. In a word, compared with the experiential results in references [18] and [23], all the measured and calculated results are in a reasonable range. This implies the reliabilities of the proposed calorimetry and its kinetics approach.
Table 4 The kinetics results from constant and varying thermal inertia consideration.
The proposed method
The classic ARC and its kinetics approach
DTBP mass percent
Heat release per unit mass (J/g)
E (kJ/ mol)
lnA (s−1)
n
15% 20% 25% 30% Average Deviation 15% 20% 25% 30% Average Deviation
1420 1319 1427 1259 1356.3 81.5 / / / / / /
147 155 156 163 155.3 6.6 139 152 175 179 161.3 19.0
34.4 36.2 36.2 37.0 36.0 1.1 33.4 36.0 37.1 38.6 36.3 2.2
0.9 1.0 1.0 1.1 1.0 0.1 0.8 0.9 1.2 1.4 1.1 0.3
6
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Fig. 10. The results of the temperature-time fitting of different mass percent DTBP/toluene solutions. The black curves are the experimental data. The red dot curves are the fitted results with varying thermal inertia consideration. The blue dot curves are the fitted results with constant thermal inertia. (a) 15% mass percent. (b) 20% mass percent. (c) 25% mass percent. (d) 30% mass percent (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
Table 5 The results of repetitive experiments with different mass percent DTBP/toluene solutions. DTBP mass percent
TONSET (OC)
15% 20% 25% 30%
121.1 117.7 116.1 115.6
TFINAL (OC) ± ± ± ±
3.8 0.3 3.5 3.1
188.5 193.2 215.1 229.6
± ± ± ±
5.1 0.9 4.2 3.1
Heat Release per unit mass (J/g)
E (kJ/mol)
ln A (s−1)
n
1317.5 1310.8 1369.2 1243.1
150.4 155.2 158.2 160.6
34.7 36.1 36.2 36.3
0.9 0.9 1.0 1.1
± ± ± ±
43.8 12.6 35.6 42.2
± ± ± ±
2.8 1.6 2.7 3.5
± ± ± ±
0.2 0.2 0.1 0.1
± ± ± ±
0.1 0.1 0.1 0.1
kinetics approaches, the heat capacity of the sample is considered as constant or the heat capacity should be measured for kinetics precision improvement. Incontestably, there are several challenges of this method should be further studied.
5. Conclusions Other than the traditional definition of thermal inertia, the varying thermal inertia expression is proposed based on the thermal dissipation of the sample in this article. Then, a symmetric dual-channel accelerating rate calorimeter is realized with the architectural designing and temperature control strategies developing. Based on the measured sample’s temperature, time and equivalent heat release rate, a novel kinetics approach with varying thermal inertia consideration is presented and verified by different mass percent DTBP/toluene solutions experiments. The experimental results show that the novel calorimetry and its data treatment methods can inhibit the influence of varying and large heat dissipation in kinetics computation. The beneficial effects of this study as following. Firstly, compared with the classical ARC, the total heat release of the sample can be measured directly by power data integrating in the symmetric dual-channel accelerating rate calorimeter. And the more reasonable thermal inertia correction and more accurate kinetics results can be obtained with the varying sample’s heat dissipation consideration. Secondly, it reduces the requirement of the experimental data of the ARC in kinetics computation. In the previous ARC based kinetics approach, in order to decrease the heat dissipation of the reactive system, the effective action is decreasing the mass of the sample. This makes the large thermal inertia and abnormal correction, especially in energetic material testing. While in the proposed calorimeter and kinetics approach, this precondition is less demanding. Based on this benefit, the calorimeter and its kinetics approach studied in this article may be a feasible method for more precise thermal hazard evaluation of energetic material [24,25]. Thirdly, the measurement of the heat capacity during the quasiadiabatic reaction can be avoid. In the proposed kinetics approach, based on the precondition that the heat capacities of sample and reference are same, the product of the thermal inertia and heat capacity can be obtained through expression (10). However, in the previous
(1) The energy density of the electronic heater should be increased. In this study, the nominal power of the electrical heater is 60 W. However, when the mass percent of DTBP/toluene is larger than 30%, the temperature of the reference is lagged than sample’s temperature. The reason is the power of the heater is not large enough. For specification improving, the higher energy density heater should be adopted in this calorimeter. Also, the precision of the electrical power measurement should be improved. (2) The instantaneity of the furnace’s and reference’s temperature tracking should be optimized. To reduce the heat dissipation of the reactive system essentially, some sensor and actuator dynamic forecasting and compensation should be adopted in this calorimeter [26,27]. Acknowledgments This work was supported by Zhejiang provincial public welfare research program (Grant No. LGF18B030001), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY17F010011, No. LQ15F030003). References [1] D.I. Townsend, J.C. Tou, Thermal hazard evaluation by an accelerating rate calorimeter, Thermochim. Acta 37 (1980) 1–30. [2] S. Chippett, Low thermal inertia scanning adiabatic calorimeter, US Patent US7021820, 2006. [3] F.L. Wu, Differential adiabatic compensation calorimeter and methods of operation, US Patent 2015/0124851A1, 2015. [4] Q.Y. Xu, J. Ding, S.J. Yang, S.L. Ye, Modeling of a power compensated adiabatic reaction system for temperature control design and simulation analyses,
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