WO2022241866A1 - 一种基于补偿功率调制的绝热反应动态比热容测定方法 - Google Patents

一种基于补偿功率调制的绝热反应动态比热容测定方法 Download PDF

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WO2022241866A1
WO2022241866A1 PCT/CN2021/098589 CN2021098589W WO2022241866A1 WO 2022241866 A1 WO2022241866 A1 WO 2022241866A1 CN 2021098589 W CN2021098589 W CN 2021098589W WO 2022241866 A1 WO2022241866 A1 WO 2022241866A1
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reaction
sample
heat capacity
specific heat
adiabatic
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PCT/CN2021/098589
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French (fr)
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丁炯
陈金宇
叶树亮
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中国计量大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00—Investigating or analyzing materials by the use of thermal means
    • G01N25/20—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity

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  • the invention relates to the field of calorimetric technology and instruments for chemical process safety, and more specifically relates to a method and a device for measuring the dynamic specific heat capacity of an adiabatic reaction based on compensation power modulation.
  • the adiabatic acceleration calorimeter is an instrument invented based on the adiabatic acceleration calorimetry method. It records the time-temperature-pressure data during the exothermic process of the reaction by simulating the adiabatic environment of the chemical reaction, so that researchers can use numerical methods to calculate the reaction heat analysis. Kinetic parameters, so it has a wide range of applications in the fields of chemical process safety evaluation, chemical thermal risk evaluation, energetic material performance and thermal stability evaluation, etc.
  • the determination of the dynamic specific heat capacity of the reaction process is very important in the assessment of the thermal hazard of chemicals.
  • the present invention combines the actual situation to invent a method for measuring the dynamic specific heat capacity of an adiabatic reaction based on compensation power modulation, and Based on this method, a realization device is designed, which improves the research level of thermal analysis kinetics and the accuracy of thermal hazard assessment of chemicals.
  • the specific heat capacity of the sample in the reaction process is regarded as a constant, which leads to problems such as deviations in thermal analysis kinetics research and thermal risk safety assessment.
  • the invention designs a method for measuring dynamic specific heat capacity of adiabatic reaction based on compensation power modulation.
  • the design idea of the present invention is expressed as follows: firstly, the idea of heat loss power compensation is proposed, the heat loss power of the sample is the enthalpy change per unit time of the reaction tank, the temperature rise rate of the reaction tank and the heat capacity of the reaction tank measured in advance are measured in real time by the temperature measuring sensor, It can realize the accurate calculation of the heat loss power of the sample; and use the algorithm to control the compensation heater to realize the complete heat insulation of the sample. Second, by superimposing high-frequency cosine modulation power in the compensation heater, the temperature rise rate oscillation during the reaction process is realized. Finally, the differential calculation and discrete Fourier transform are performed on the adiabatic reaction temperature of the sample in the modulated state, and the modulation temperature rise and self-accelerating reaction temperature rise signals are separated to realize the dynamic specific heat capacity calculation.
  • the inventive method is specifically:
  • the full power of the compensation heater is P Max , and the reaction system is heated from time 1.
  • the electric power for heating consists of two parts, one is the compensation power for the heat loss of the sample, and the other is the modulation power.
  • the compensation power P EH at time n can be calculated by using the formula (1).
  • the modulation power P w at time n is calculated by formula (2);
  • the duty ratio of the PWM signals at each moment is the ratio of the required electric power to the total power of the compensation heater, that is (P EH +P w )/P Max ;
  • the obtained temperature rise rate-time signal is divided every x seconds, and for any x second signal obtained, the real part, imaginary part and modulus of the signal are obtained by decomposing on the complex plane;
  • a, ⁇ , C b (T), m b , ⁇ t, and m s are all known quantities, and at the same time use the arctangent function to process the real part and imaginary part of any x-second signal, which can be obtained In the formula (3) and A.
  • the present invention obtains the dynamic change of the specific heat capacity of the sample in the reaction process which cannot be obtained by the traditional adiabatic calorimetry method by means of modulation, differentiation and spectrum analysis. Compared with the traditional constant specific heat capacity, the dynamic specific heat capacity can more accurately reflect the thermal decomposition process of the sample, thereby solving more accurate kinetic parameters of the thermal decomposition reaction of the sample.
  • Fig. 1 has the furnace body part of the adiabatic accelerated calorimetry device with the dynamic measurement function of specific heat capacity
  • Fig. 2 has the reaction cell part of the adiabatic acceleration calorimetry device of specific heat capacity dynamic measurement function
  • Fig. 3 is a block diagram of the hardware design of the adiabatic acceleration calorimetry device with the dynamic measurement function of the specific heat capacity;
  • Fig. 4 has the flow chart of the temperature control algorithm of the adiabatic accelerated calorimetry device with the dynamic measurement function of specific heat capacity
  • Figure 6 shows adiabatic reaction temperature rise rate graph of toluene solution with 20% mass fraction DTBP under the linear change heat capacity
  • Figure 9 is a diagram of the temperature rise rate of the adiabatic reaction of toluene solution with 20% mass fraction DTBP under the nonlinear change of specific heat capacity
  • Fig. 10 is a schematic diagram of the calculated non-linear variation specific heat capacity.
  • reaction cell + sample the total energy released by the reaction system (reaction cell + sample) and the temperature change of the reaction system is as follows:
  • P EH is the compensation power required to keep the system completely adiabatic
  • P sample is the exothermic power of the sample
  • t onset is the start time of the reaction
  • t final is the end time of the reaction
  • C s (T) is the dynamic specific heat capacity of the sample
  • C b (T) is the specific heat capacity of the reaction cell (can be determined in advance)
  • m s is the mass of the sample
  • m b is the mass of the reaction cell
  • T onset is the start temperature of the adiabatic reaction
  • T final is the end temperature of the adiabatic reaction.
  • the formula (1) can be decomposed into the following two formulas:
  • Equation (2) indicates that the exothermic power of the sample only acts on itself, so that the temperature of the sample rises from T onset to T final
  • Equation (3) indicates that the heat required for the temperature of the reaction cell to rise from T onset to T final is heated by compensation Provided by the electrical power input by the device.
  • Equation (4) shows the relationship between the self-generated heat power of the sample, the specific heat of the sample and the temperature rise rate of the sample
  • Equation (5) shows the compensation power value required when the sample is completely adiabatic, that is, when the compensation heater feeds the reaction system
  • the value of P EH can be calculated and obtained according to the actually measured dT/dt.
  • a is the modulation power amplitude, which is usually much smaller than the compensation power
  • ⁇ is the angular frequency of the modulation power, and its value is much larger than the spectral range of the sample self-reaction exothermic temperature rise rate.
  • Equation (13) is the final solution equation for the dynamic specific heat capacity of the sample.
  • the unknowns A and It can be obtained by measuring the temperature of the sample, calculating the temperature rise rate and solving the Fourier transform; although the specific heat capacity C b (T) of the reaction cell is a known quantity that changes with the temperature, the degree of change is slow, so by C b (T ) is negligible for the calculation error introduced by T derivation.
  • the model can be used to finally solve the dynamic specific heat capacity of the reaction process.
  • Equation (5) is the calculation formula of the compensation power in the model, in which the specific heat capacity and mass of the reaction cell are known in advance, and the temperature rise rate of the sample is calculated from the temperature-time curve obtained in real time .
  • the temperature change from the n-2th time to the n-1th time is ⁇ T(n-1)
  • the temperature from the n-1th time to the nth time Change to ⁇ T(n) then the differential expressions of formula (4) and formula (5) are:
  • Formula (7) can be expressed as:
  • the present invention uses the dynamic specific heat capacity obtained through actual calculation in combination with the nonlinear fitting method to modify the existing dynamic solution method, specifically as follows:
  • ⁇ onset is the conversion rate of the sample at the beginning of the reaction (generally, the value is 0)
  • ⁇ final is the conversion rate of the sample at the end of the reaction (generally, the value is 1).
  • n the reaction order.
  • the nonlinear fitting based on the reaction model is carried out to realize the three-factor calculation of thermal analysis kinetics.
  • the core idea of the nonlinear fitting method is to use the solved kinetic parameters (activation energy E, pre-exponential factor A, reaction order n) as undetermined coefficients.
  • the self-accelerating temperature rise rate is measured through experiments, and the two are fitted, and the fitting degree SS is used as the evaluation index to obtain the unknown vector ⁇ (E,A,n) of the kinetic equation, and the expression of SS
  • the formula is:
  • an adiabatic acceleration calorimetry device capable of measuring dynamic specific heat capacity is designed, including a calorimetric furnace, a compensation heater, a cylindrical reaction pool, a reaction pool and a sample temperature sensor.
  • the specific structure diagram is shown in Figure 1 and Figure 2:
  • Fig. 1 is the basic structure of the calorimetric furnace, comprising a furnace cover shell 1, a furnace cover 3 is fixed in the described furnace cover shell, a reaction pool and a wire through hole 2 of a sample temperature measuring sensor are arranged on the described furnace cover, compensation heating The device wire through hole 5 and the cylindrical reaction pool assembly structure 4. It also includes a furnace shell 9, which is equipped with a support column 12, and the support column is used to support the ceramic fiber piece 11, and the furnace bottom 10 and the furnace wall 7 are fixed on the ceramic fiber piece. There are holes 6 for assembling furnace wall heating rods on the wall, and furnace wall heating rod wire through holes 8 are also arranged on the furnace shell.
  • Figure 2 shows the reaction cell, the compensation heater, and the sample and reaction cell temperature sensor (used to measure the temperature of the sample and reaction cell, and the default temperature field of the sample and reaction cell is uniform).
  • the compensation heater 13 adopts a heating rod.
  • the temperature measuring sensor 14 of the sample and the reaction cell adopts an N-type thermocouple.
  • the shape of the reaction pool 15 is cylindrical, and its specific structure is a hollow cylinder with a certain wall thickness.
  • the material of the reaction pool is titanium alloy with high temperature resistance, high strength, good mechanical properties and excellent corrosion resistance.
  • a temperature measurement and power control circuit including a main control circuit, a power supply module, a temperature measurement module, a temperature control module and a communication module.
  • the specific hardware design block diagram is shown in Figure 3:
  • the main control circuit is the core part of the system to realize the control of the whole machine, and the normal and orderly realization of the functions of each unit depends on the control of the main control circuit.
  • the power supply module is used for the power supply of the whole main control circuit and the compensation heater.
  • the temperature measurement module is responsible for measuring the temperature of the furnace cover, furnace wall, furnace bottom, reaction pool and samples.
  • the temperature control circuit includes a furnace body heating rod control circuit and a compensation heater control circuit.
  • the communication module sends the temperature data of the sample.
  • the compensation power and the modulation power are provided by the electric power output by the heating rod in Fig. 2.
  • the compensation heater uses the DC power supply of the switching power supply, and then uses the temperature control module to realize the on-off control of the power supply. Specifically, the temperature control module outputs a PWM signal to control the compensation heating
  • the power supply of the device is turned on and off, so as to realize the output of the required electric power.
  • the temperature control frequency of the instrument in this embodiment is 5 Hz, and the temperature measurement frequency is 100 Hz, that is, the duty cycle of the PWM signal is changed 5 times every 1 second, and the temperature of the reaction system is measured every 0.01 second.
  • the calculation of compensation power requires the mass and specific heat capacity of the reaction cell, as well as the temperature rise rate of the sample during the reaction process.
  • the first two are known quantities, the mass can be obtained directly by weighing, and the specific heat capacity is a certain value after the reaction cell material is known, and only the final sample temperature rise rate needs to be calculated.
  • the calculation and delivery of the compensation power starts from the 0.4th second of the experiment, and the derivative calculation of the temperature-time signal at the 0.2 second can be calculated to obtain the temperature rise rate of the sample at the 0.2 second, and the temperature rise rate approximately represents the first 0.4 second temperature rise rate.
  • the compensation power required by the reaction system at the 0.4 second is the product of the mass of the reaction cell, the specific heat capacity of the reaction cell and the temperature rise rate of the sample calculated at the 0.2 second. In this way, the compensation power for the 0.6th second, 0.8th second or even the nth second can be obtained.
  • the actual modulation power value required for every 0.2 second is obtained by discretizing the signal, then the actual modulation power value of the 0.4th second is a cos( 0.4 ⁇ ), the actual modulation power at the 0.6th second is a cos(0.6 ⁇ ), and the actual modulation power at the nth second is a cos(n ⁇ ).
  • the final output electric power every 0.2 seconds can be obtained by summing the compensation power every 0.2 seconds obtained from the above calculation and the modulation power.
  • the ratio of this electric power to the total power of the heating rod is the duty cycle of the PWM output signal.
  • the temperature-time signal of the sample can be finally obtained.
  • the dynamic specific heat capacity of the sample can be obtained.
  • the obtained temperature rise rate-time signal is divided every 20s, and the specific heat capacity can be calculated every 20s.
  • the theoretical temperature rise rate dT m (t, ⁇ )/dt can be obtained through formula (22), and at this time a Actual temperature rise rate dT/dt.
  • all dT m (t, ⁇ )/dt and dT/dt are obtained at a certain time interval, and the calculation of formula (23) is performed on them to obtain a selection of three factors for evaluating the kinetics of this group Good or bad fit, the smaller the value, the higher the fit, and the closer the selected dynamic three factors are to the actual situation.
  • the search algorithm is used to search the kinetic three factors, and a group with the best fitting degree is obtained, that is, the optimal kinetic parameter value of the sample reaction is obtained.
  • the reaction process with a certain amplitude modulation power was simulated by using Matlab software.
  • the simulated reactants used 20% mass fraction DTBP toluene solution, and the parameters of the reaction kinetics were all derived from ASTM E2781, where the reaction order was set to 1, and the pre-exponential factor of the reaction was set to 5.5 ⁇ 10 15 s -1 ,
  • the activation energy of the reaction is set to 157000J/mol
  • the initial reaction temperature is set to 398.2K
  • the ideal gas constant is set to 8.314J/(mol*K)
  • the heat of reaction per unit mass of the solution is set to 225J/g
  • the mass of the heat transfer medium and the reaction cell Set it to 50g, set the specific heat capacity of the heat transfer medium and sample cell to 0.5J/(K*g), set the sample mass to 6.0g, set the reaction step to 0.05s, set the simulation time to 240min, and set the modulation power to cos(2 ⁇ t ).
  • the specific heat capacity of the sample is set to a change value that increases linearly from 2J/(K*g) to 3J/(K*g) within the simulation time, and the simulation results are shown in Figure 5, Figure 6, and Figure 7 .
  • Figure 5 the reaction starts at 398.2K and stops at 490.9K, and the reaction is most violent at 110min to 115min.
  • Fig. 6 before 110 min, the fluctuation is basically sinusoidal, and the temperature rise rate of the reaction fluctuates sharply between 110 min and 115 min.
  • Figure 7 shows the dynamic specific heat capacity every 20 s calculated by the model. It can be seen that except for the time period from 110 to 115 min, the calculated specific heat capacity increases linearly, which is in line with expectations. From 110 to 115min, due to the overlap of the spectrum of the reaction exothermic power and the modulation power, there is a deviation in the calculated dynamic specific heat capacity. This deviation can be eliminated by changing the modulation frequency during this time period.
  • the simulation results are shown in Figure 8, Figure 9, and Figure 10. It can be seen from Figure 8 that the reaction starts at 398.2K and stops at 503.7K, and the reaction is most violent at 100min to 105min. It can be seen from Figure 9 that the temperature rise rate of the reaction fluctuates sharply between 100 min and 105 min.
  • Figure 10 shows the dynamic specific heat capacity every 20 s calculated by the model. It can be seen that except for the time period from 100 to 105 min, the calculated specific heat capacity is consistent with the expected change.

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Abstract

一种基于补偿功率调制的绝热反应动态比热容测定方法。通过补偿绝热量热反应过程中的样品热散失功率，实现反应过程的完全绝热；并对补偿功率进行调制，实现反应过程中的温升速率振荡；最后对调制状态下的样品绝热反应温度进行微分计算、离散傅里叶变换，开展调制温升信号与自加速反应温升信号的分离，实现动态比热容计算。利用调制、微分、频谱分析等手段，求出了传统绝热量热方法无法求得的反应过程中样品比热容的动态变化。动态比热容相较于传统的恒定比热容能更准确反映样品的热分解过程，从而求解出更加准确的样品热分解反应动力学参数。

Description

一种基于补偿功率调制的绝热反应动态比热容测定方法 技术领域
本发明涉及面向化工过程安全的量热技术及仪器领域，更具体的涉及一种基于补偿功率调制的绝热反应动态比热容测定方法与实现装置。
背景技术
自绝热加速量热方法被发明以来，它都是用于分析化学反应的理想方法之一。绝热加速量热仪是基于绝热加速量热方法发明的仪器，其通过模拟化学反应绝热环境，记录反应放热过程中的时间-温度-压力数据，使得研究人员能够运用数值的方法计算反应热分析动力学参数，因此在化工工艺安全评价、化学品热危险性评估、含能材料性能与热稳定性评价等领域中具有广泛的应用。
上世纪七十年代，陶氏化学公司(DOW)提出绝热加速量热方法，之后Columbia Scientific成功将其商业化。研究人员利用这项技术在求取热分析动力学参数(指前因子、反应级数、反应活化能等)及开发热危险性表征方法 [1-2]时一直遵循着两个前提，一是默认样品处于完全的绝热状态，即样品在反应放热过程中与周围环境不发生热量的交换，二是默认样品在反应过程中的比热容是恒定不变的，其值在反应前或反应后测定得到 [3]。然而，对于经典型绝热加速量热仪而言，这两个前提都是无法实现的。对于前者，由于反应池的存在，当样品发生反应放热时，势必会将部分热量传导给反应池使其升温，这导致了绝热加速量热仪所模拟的仅为准绝热环境，而非完全绝热环境。在过去的几十年中，通过引入压力和功率补偿技术，这个问题已经逐渐得到解决，例如英国HEL公司的Phi-TEC II [4]、德国Netzsch公司的APTAC [5]、美国Omnical technology公司的DARC [6]和国内杭州仰仪科技有限公司的TAC-CP 500A [7]，这些仪器基本可以创造一个完全绝热的环境。
对于后者，在考虑实际化学反应的情况下也无法成立。在反应过程中，反应物不断消耗，产物不断生成，反应物与产物又具有不同的比热容，因此该化学反应的物质比热容是不断变化的。即使是纯净物，其比热容通常也与物态、温度、压力相关。变化的比热容使得基于经典绝热加速量热方法的热分析动力学研究及热危险性评估与真实情况存在较大的偏差，也使得通过绝热温升ΔT计算的放热 量这一评价热危险性的关键指标缺乏说服力。但由于缺乏工具，当前研究人员仍使用恒定比热容进行数值分析。这在热危险性评价中将产生不良后果，当比热容设置过大，则容易导致评估过于保守，使化学品储运成本升高或化工生产效率降低；反之，则容易出现评估不足，引发安全事故。
综上所述，测定反应过程的动态比热容在化学品热危险性评估等方面十分重要。为准确获得反应过程中的比热容，进而获得更加真实的反应过程动力学参数，开展准确的化工过程安全评估，本发明结合实际情况，发明一种基于补偿功率调制的绝热反应动态比热容测定方法，并基于此方法设计了实现装置，提高了热分析动力学研究水平和化学品热危险性评估的准确性。
参考文献
[1]Townsend D.I.,Tou J.C.Thermal hazard evaluation by an accelerating rate calorimeter[J].Thermochimica Acta,1980,37(1):1-30.
[2]Tou J.C.,Whiting L.F.The thermokinetic performance of an accelerating rate calorimeter[J].Thermochimica Acta,1981,48(1):21-42.
[3]孙金华,丁辉.化学物质热危险性评价[M].科学出版社,北京,2005.
[4]HEL GROUP Phi-TEC II:Adiabatic Calorimeter for vent sizing and accurate thermal runaway testing[EB/OL].
http://www.helgroup.com/reactor-systems/thermal-hazards-and-calorimetry/phitec-ii/.
[5]Iwata Y,Momota M,Koseki H.Thermal risk evaluation of organic peroxide by automatic pressure tracking adiabatic calorimeter[J].Journal of Thermal Analysis and Calorimetry,2006,85(3):617-622.
[6]Charles F.Askonas,Dr.James P.Burelbach.The versatile VSP2:a tool for adiabatic thermal analysis and vent sizing application[C].North American Thermal Analysis Society,28th Annual Conference,2000.
[7]Kimura A,Otsuka T.Performance evaluation of differential accelerating rate calorimeter for the thermal runaway reaction of di-tert-butyl peroxide[J].Journal of Thermal Analysis and Calorimetry,2013,113(3):1858-1591.
发明内容
针对背景技术中提到的现有经典绝热加速量热理论中将反应过程的样品比热容视作常数，导致热分析动力学研究和热危险性安全评估存在偏差等问题。本发明设计了一种基于补偿功率调制的绝热反应动态比热容测定方法。
本发明的设计思想表述如下：首先提出热散失功率补偿的思想，样品热散失功率即反应池单位时间的焓变，通过测温传感器实时测定反应池温升速率以及事 先测定的反应池热容，可实现样品热散失功率的精确计算；并利用算法控制补偿加热器实现样品完全绝热。其次，通过在补偿加热器中叠加高频余弦调制功率，实现反应过程中的温升速率振荡。最后，对调制状态下的样品绝热反应温度进行微分计算、离散傅里叶变换，开展调制温升与自加速反应温升信号的分离，实现动态比热容计算。
本发明方法具体是：
a).在样品绝热反应实验开始前，测定反应池的比热容C b(T)与质量m b，测定样品的质量m s；
b).实验时，首先将样品温度上升到样品发生反应的起始温度，以样品开始反应的起始时刻为0时刻，每隔Δt的时间采集一次反应体系的温度，0时刻到1时刻样品的温度变化为ΔT(1)，1时刻到2时刻样品的温度变化为ΔT(2)，第n-1时刻到第n时刻样品的温度变化为ΔT(n)；
c).补偿加热器的满功率为P Max，从1时刻开始对反应体系加热，加热的电功率由两部分组成，一个是样品热散失的补偿功率，另一个是调制功率。利用公式(1)可以计算出n时刻的补偿功率P EH。当加载的调制功率的幅值为a、频率为w时，利用公式(2)计算出n时刻的调制功率P w；
Figure PCTCN2021098589-appb-000001
P w＝a×cos(n×Δt×ω)           (2)
d).通过计算与输出不同占空比的PWM信号，来进行不同补偿功率的输出，每个时刻的PWM信号的占空比为所需电功率与补偿加热器总功率的比值，即(P EH+P w)/P Max；
e).反应结束后，得到样品反应过程的温度-时间信号，对该信号进行微分计算，得到样品的温升速率-时间信号；
f).对得到的温升速率-时间信号每隔x秒进行分割，对于得到任一个x秒信号，通过复平面上分解，求得信号的实部、虚部和模；
g).利用公式(3)求得每x秒的样品动态比热容C s(T)。
Figure PCTCN2021098589-appb-000002
对于公式(3)，a、ω、C b(T)、m b、Δt、m s均为已知量，同时利用反正切函数对任一个x秒信号的实部与虚部处理，可求得公式(3)中的
Figure PCTCN2021098589-appb-000003
和A。
本发明的有益效果：本发明利用调制、微分、频谱分析等手段，求出了传统绝热量热方法无法求得的反应过程中样品比热容的动态变化。该动态比热容相较于传统的恒定比热容能更准确反映样品的热分解过程，从而求解出更加准确的样品热分解反应动力学参数。
附图说明
图1具有比热容动态测定功能的绝热加速量热装置的炉体部分；
图2具有比热容动态测定功能的绝热加速量热装置的反应池部分；
图3具有比热容动态测定功能的绝热加速量热装置的硬件设计框图；
图4具有比热容动态测定功能的绝热加速量热装置的温控算法流程图；
图5线性变化热容下20％质量分数DTBP的甲苯溶液绝热反应温升图；
图6线性变化热容下20％质量分数DTBP的甲苯溶液绝热反应温升速率图；
图7计算得到的线性变化比热容示意图；
图8非线性变化比热容下20％质量分数DTBP的甲苯溶液绝热反应温升图；
图9非线性变化比热容下20％质量分数DTBP的甲苯溶液绝热反应温升速率图；
图10计算得到的非线性变化比热容示意图。
具体实施方式
在传统的绝热加速量热方法中，化学反应热一部分被反应池吸收。为更加真实模拟工业生产绝热状态，可通过由补偿加热器对样品的热散失进行补偿，来保证一个完全绝热的环境形成。反应体系(反应池+样品)所释放的总能量与反应体系的温度变化关系如下：
Figure PCTCN2021098589-appb-000004
其中，P EH为保持体系完全绝热所需的补偿功率，P sample为样品的放热功率，t onset为反应的开始时间，t final为反应的结束时间，C s(T)为样品动态比热容，C b(T)为反应池的比热容(可事先测定)，m s为样品的质量，m b为反应池的质量，T onset为绝热反应的开始温度，T final为绝热反应的结束温度。
若满足样品完全绝热，即样品在反应过程中既不向外界放热也不向外界吸热，其反应的放热量仅供自己提升温度所用，式(1)可分解为下列两式：
Figure PCTCN2021098589-appb-000005
Figure PCTCN2021098589-appb-000006
式(2)表示样品的放热功率仅作用于自身，使样品温度从T onset上升到T final，式(3)则表示反应池的温度从T onset上升到T final所需要的热量由补偿加热器输入的电功率所提供。
对式(2)、式(3)两边求导可得下列两式：
Figure PCTCN2021098589-appb-000007
Figure PCTCN2021098589-appb-000008
式(4)表明了样品自产热功率与样品比热以及样品温升速率的关系，式(5)则表明了在样品完全绝热时所需的补偿功率值，即当补偿加热器向反应体系输入P EH的功率时，样品处于完全绝热的环境。其中，P EH的数值可根据实际测得的dT/dt计算获取。
在样品保持完全绝热的情况下，在补偿的电加热功率上额外叠加一小幅度的余弦调制项a cos(ωt)，(t final-t onset)>>1/ω时，有式(6)接近于0：
Figure PCTCN2021098589-appb-000009
其中，a为调制功率幅度，通常其值远远小于补偿功率；ω为调制功率的角频率，其取值远大于样品自反应放热温升速率频谱范围。基于在整个绝热反应阶段，叠加的余弦调制功率积分近似为0，式(1)可描述为：
Figure PCTCN2021098589-appb-000010
对式(7)两边同时求导，可得：
Figure PCTCN2021098589-appb-000011
由于P EH的计算表达式由式(5)决定，即根据上一时刻的温升变化速率dT/dt 计算，将其代入式(8)后，可得：
Figure PCTCN2021098589-appb-000012
对式(9)中的温升速率dT/dt进行频谱分离，令dT/dt在ω频率点的表达式为
Figure PCTCN2021098589-appb-000013
其中A为幅度，
Figure PCTCN2021098589-appb-000014
为相角，均未知。则式(9)在ω频率下的功率守恒展开为：
Figure PCTCN2021098589-appb-000015
令
Figure PCTCN2021098589-appb-000016
则式(10)变换为：
Figure PCTCN2021098589-appb-000017
令
Figure PCTCN2021098589-appb-000018
则式(11)变换为：
Figure PCTCN2021098589-appb-000019
最终解得C s(T)的表达式：
Figure PCTCN2021098589-appb-000020
式(13)即为样品动态比热容的最终求解方程。其中未知量A和
Figure PCTCN2021098589-appb-000021
可通过对样品温度测量，温升速率计算及傅里叶变换求解获取；反应池比热容C b(T)虽为一随温度变化的已知量，但是其变化程度缓慢，所以由C b(T)对T求导所引入的计算误差忽略不计。
综上所述，可以通过对补偿功率的调制，与反应温升曲线的分析，最终利用模型求解反应过程动态比热容。
上述模型为理论求解的结果，若要将其用于实际的绝热仪器中，则需对上述过程进行离散化处理。首先是在补偿功率的获取上，式(5)为模型中补偿功率的计算公式，其中反应池的比热容与质量事先已知，而样品的温升速率则由实时获取的温度-时间曲线计算获得。在实际的温度采集中，假设每隔Δt的时间采集一次温度，第n-2时刻到第n-1时刻的温度变化为ΔT(n-1)，第n-1时刻到第n时刻的温度变化为ΔT(n)，则式(4)、式(5)的差分表达形式为：
Figure PCTCN2021098589-appb-000022
Figure PCTCN2021098589-appb-000023
式(7)可表示为：
Figure PCTCN2021098589-appb-000024
进而再经相同的恒等变换，式(13)可以转换为：
Figure PCTCN2021098589-appb-000025
通过式(17)，当确定了温度采集的频率，并获得样品的温度变化曲线，就可以在实际的应用中获得样品动态比热容。
上述中提到针对功率调制的反应体系，现有的基于传统绝热加速量热方法的热分析动力学参数求解方法不再适用。因此，本发明利用实际计算得到的动态比热容结合非线性拟合法进行现有动力学求解方法的修正，具体如下：
当样品实现了完全绝热的自加速分解反应后，式(4)等价于：
Figure PCTCN2021098589-appb-000026
其中H为样品反应热，α为样品反应过程的转化率。
对式(18)进行积分运算，并由实测比热容值代入，计算可得反应热：
Figure PCTCN2021098589-appb-000027
其中，α onset为反应开始时样品的转化率(一般取值为0)，α final为反应结束时样品的转化率(一般取值为1)。
反应过程中反应转化率α与H，C s(T)，T之间的对应关系为：
Figure PCTCN2021098589-appb-000028
对于基元反应，即：
Figure PCTCN2021098589-appb-000029
其中r为反应体系的化学反应速率，dα/dt为反应转化率变化速率，k(T)为反应速率常数，E为反应活化能，k 0为指前因子，R为普适气体常数，n为反应级数。
可将式(20)代入式(21)后建立自反应放热方程，得到反应模型：
Figure PCTCN2021098589-appb-000030
最后再进行基于反应模型的非线性拟合，实现热分析动力学三因子计算。非线性拟合方法的核心思想是将求解的动力学参数(活化能E、指前因子A、反应级数n)作为待定系数，一方面以最小二乘拟合方法进行模型计算得到自加速温升速率，另一方面经过实验测得自加速温升速率，将两者进行拟合，以拟合度SS作为评价指标，获取动力学方程未知向量θ(E,A,n)，SS的表达式为：
Figure PCTCN2021098589-appb-000031
通过设置不同的活化能E、指前因子A、反应级数n求取SS，当SS取最小值时，此时得到的最优向量解θ(E,A,n)即为样品反应的动力学参数值。
求解样品的动态比热容不仅可以改进求解热分析动力学参数的方法，还可以求取样品在反应过程中的放热量，公式如下：
Figure PCTCN2021098589-appb-000032
实施例：
本实施例设计了一种可测定动态比热容的绝热加速量热装置，包括量热炉、补偿加热器、圆柱形反应池、反应池与样品测温传感器。具体结构图如图1、图2所示：
图1为量热炉的基本结构，包括炉盖外壳1，所述的炉盖外壳内固定有炉盖3，所述炉盖上有反应池与样品测温传感器的导线通孔2、补偿加热器导线通孔5以及圆柱形反应池装配结构4。还包括炉体外壳9，所述炉体外壳内装配有支撑柱12，所述支撑柱用于支撑陶瓷纤维件11，所述陶瓷纤维件上固定有炉底10与炉壁7，所述炉壁上有装配炉壁加热棒的孔6，所述炉体外壳上还有炉壁加热棒导线通孔8。
图2为反应池、补偿加热器以及样品与反应池测温传感器(用以测量样品与反应池的温度，默认样品与反应池温度场均一)。所述补偿加热器13采用加热棒。所述样品与反应池测温传感器14采用N型热电偶。所述反应池15外形为圆柱形，其具体结构是具有一定壁厚的中空的圆柱体，反应池材料采用耐高温、强度高、机械性能好、抗蚀性能优异的钛合金。
基于上述绝热加速量热装置，设计了温度测量与功率控制电路，包括主控电路、电源模块、温度测量模块、温控模块与通讯模块。具体硬件设计框图如图3所示：
所述主控电路是系统实现整机控制的核心部分，各单元功能正常有序的实现均依赖主控电路调控。所述电源模块用于整个主控电路的供电与补偿加热器供电。所述温度测量模块负责测量炉盖、炉壁、炉底与反应池、样品的温度。所述温控电路包括炉体加热棒控制电路和补偿加热器控制电路。所述通讯模块发送样品的温度数据。
完成仪器的机械与硬件设计后，设计程序算法实现补偿功率和调制功率的计算与输出，具体流程图如图4所示。
补偿功率和调制功率由图2的加热棒输出的电功率提供，所述补偿加热器使用开关电源的直流供电，然后采用温控模块实现电源通断控制，具体为温控模块输出PWM信号控制补偿加热器电源通断，从而实现所需电功率的输出。
首先计算补偿功率。本实施例的仪器的控温频率为5Hz，测温频率为100Hz，即每隔1秒改变5次PWM信号的占空比，每隔0.01秒测量反应体系的温度。根据公式(15)可知，计算补偿功率需要知道反应池的质量与比热容，以及反应过程中的样品温升速率。其中，前两者均为已知量，质量可以直接通过称量获得，比热容则在已知反应池材料后为一定值，只有最后的样品温升速率需要计算获得。补偿功率的计算与下发从实验开始的第0.4秒开始，对第0.2秒的温度-时间信号进行求导计算即可求得第0.2秒的样品温升速率，以此温升速率近似代表第0.4秒的温升速率。则第0.4秒反应体系需要的补偿功率即为反应池质量与反应池比热容与第0.2秒计算的样品温升速率的乘积。以此方式可以求得第0.6秒、第0.8秒乃至第n秒的补偿功率。
然后计算调制功率。当在补偿功率上叠加一个a cos(ωt)的调制信号时，通过对该信号的离散化处理得到每0.2秒所需的实际调制功率值，则第0.4秒的实际调制功率值为a cos(0.4ω)，第0.6秒的实际调制功率为a cos(0.6ω)，第n秒的实际调制功率为a cos(nω)。
将上述计算得到的每0.2秒的补偿功率与调制功率求和，就可以得到每0.2秒最终的输出电功率。此电功率与加热棒总功率的比值，即为PWM输出信号的占空比。由此就实现了每0.2秒的功率控制，继而实现温度控制。
利用上述仪器对样品进行测试，最终可以得到的是样品的温度-时间信号。通过对该信号的进一步分析处理，才能得到样品动态比热容。具体数据处理方法为：
1.对温度-时间信号进行求导，得到样品的温升速率-时间信号。
2.对得到的温升速率-时间信号每隔20s进行分割，每20s可以计算一次比热容。
3.对于得到任一个20s信号，均可以在复平面上进行分解，可以求得信号的实部、虚部和模。
4.利用反正切函数对信号的实部与虚部处理，可以求得式(17)中的
Figure PCTCN2021098589-appb-000033
而算得的模即为式(17)中的A。
5.对于式(17)，a、ω、C b(T)、m b、Δt、m s均为已知量，再将求得的A与
Figure PCTCN2021098589-appb-000034
代入，即可以求得每20s的样品的动态比热容C s(T)。
对于上述得到的动态比热容C s(T)，将其运用到热分析动力学参数的求解中去，目的是求取反应的活化能、指前因子与反应级数，具体的求取过程基于反应模型的非线性拟合，式(22)即为自加速分解反应模型，其中，式中的k 0、E、n即为所需要求解的动力学三因子，式中的m s、R为一定值，式中的H、C s(T)、T、T onset为可以测得或求得的量。则在某一时刻t，当选取一组动力学三因子，可以通过式(22)求得理论上的温升速率dT m(t,θ)/dt，同时此时通过实际数据可求得一个实际的温升速率dT/dt。在整个反应的过程中，以一定的时间间隔求取所有的dT m(t,θ)/dt与dT/dt，对它们进行式(23)的运算，得到一个评价该组动力学三因子选取好坏的拟合度，其值越小，说明拟合程度越高，选取的动力学三因子越贴近实际情况。之后利用搜索算法对动力学三因子进行搜索，得到拟合程度最好的一组，即求得了最优的样品反应的动力学参数值。
由于缺乏标准物质(存在热分解自放热且比热与成份已知)来验证本发明方法，所以此处通过仿真验证进行相应说明。
利用Matlab软件对施加了一定幅值调制功率的反应过程进行了仿真。仿真的反应物使用了20％质量分数DTBP甲苯溶液，其反应动力学的参数均来源于ASTM E2781，其中，反应级数设置为1，反应的指前因子设置为5.5×10 15s -1，反应活化能设置为157000J/mol，反应起始温度设置为398.2K，理想气体常数设置为8.314J/(mol*K)，溶液单位质量反应热设置为225J/g，传热介质及反应池质量 设置为50g，传热介质及样品池比热容设置为0.5J/(K*g)，样品质量设置为6.0g，反应步长设置为0.05s，仿真时间设置为240min，调制功率设置为cos(2πt)。
第一次仿真时设定样品比热容为在仿真时间内从2J/(K*g)线性增加到3J/(K*g)的一个变化值，仿真结果如图5、图6、图7所示。从图5中可以看出，反应从398.2K开始，于490.9K停止，并且反应在110min到115min最为剧烈。从图6中则可以看出，110min之前基本呈正弦形波动，反应的温升速率在110min到115min之间剧烈的波动上升。图7为通过模型计算的每20s的动态比热容，可以看出除了110到115min的时间段，计算的比热容呈线性增加，符合预期。在110到115min中，由于反应放热功率与调制功率的频谱重合，导致计算的动态比热容存在偏差，这种偏差可通过改变该时间段的调制频率的方法消除。
第二次仿真时设定样品比热容＝1+当前温度/起始温度J/(K*g)，即一个起始值是2J/(K*g)，且增加趋势与温升趋势一致，呈非线性的变化值，仿真结果如图8、图9、图10所示。从图8中可以看出，反应从398.2K开始，于503.7K停止，并且反应在100min到105min最为剧烈。从图9中则可以看出，反应的温升速率在100min到105min之间剧烈的波动上升。图10为通过模型计算的每20s的动态比热容，可以看出除了100到105min的时间段，计算的比热容均与预期变化一致。
上述两次仿真分别模拟了样品比热容是一线性变化的值以及一非线性变化的值的时候的情况，仿真结果均表明了本发明的方法可以准确计算样品反应过程中变化的比热容，从而验证了本方法的可行性。

Claims (7)

  1. 一种基于补偿功率调制的绝热反应动态比热容测定方法，其特征在于：
    对绝热反应过程中的样品动态热散失通过补偿加热实时补偿，使得样品在反应过程中处于一个完全绝热的环境；
    对补偿功率进行调制，即在补偿加热的同时加载一余弦调制项以实现反应过程中的温升速率振荡；
    对调制状态下的样品绝热反应温度进行微分计算、离散傅里叶变换，开展调制温升信号与自加速反应温升信号的分离，实现动态比热容测定，具体包括以下步骤：
    a).测量反应池比热容与质量、样品质量；
    b).计算补偿加热器输出实时功率；
    c).由温控模块输出不同占空比的PWM信号；
    d).测量样品反应过程的温度变化；
    e).对样品温度变化进行微分处理；
    f).求解得到动态比热容。
  2. 根据权利要求1所述的一种基于补偿功率调制的绝热反应动态比热容测定方法，其特征在于：在步骤b)之前还包括将样品温度上升到样品发生反应的起始温度，以样品开始反应的起始时刻为0时刻，每隔Δt的时间采集一次反应体系的温度。
  3. 根据权利要求2所述的一种基于补偿功率调制的绝热反应动态比 热容测定方法，其特征在于：步骤b)中所述的实时功率包括实时补偿功率和实时调制功率。
  4. 根据权利要求1所述的一种基于补偿功率调制的绝热反应动态比热容测定方法，其特征在于：每个时刻的PWM信号的占空比为所需实时功率与补偿加热器总功率的比值。
  5. 根据权利要求1所述的一种基于补偿功率调制的绝热反应动态比热容测定方法，其特征在于：经过步骤d)后得到样品反应过程的温度-时间信号。
  6. 根据权利要求1所述的一种基于补偿功率调制的绝热反应动态比热容测定方法，其特征在于：经过步骤e)后得到样品的温升速率-时间信号。
  7. 根据权利要求6所述的一种基于补偿功率调制的绝热反应动态比热容测定方法，其特征在于：步骤f)具体是：
    1).对得到的温升速率-时间信号每隔x秒进行分割，对于得到任一个x秒信号，通过复平面上分解，求得信号的实部、虚部和模；
    2).计算每x秒的样品动态比热容C s(T)：
    Figure PCTCN2021098589-appb-100001
    其中a为调制功率的幅度，ω为调制功率的角频率，C b(T)为反应池的比热容，m b为反应池的质量，m s为测定样品的质量，Δt为温度采集间隔，
    Figure PCTCN2021098589-appb-100002
    为相位角，由x秒信号的实部与虚部确定，A为x秒信号在复平面上分解得到的模。
PCT/CN2021/098589 2021-05-21 2021-06-07 一种基于补偿功率调制的绝热反应动态比热容测定方法 WO2022241866A1 (zh)

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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5335993A (en) * 1992-03-02 1994-08-09 Ta Instruments, Inc. Method and apparatus for thermal conductivity measurements
JPH09222404A (ja) * 1996-02-19 1997-08-26 Agency Of Ind Science & Technol 比熱容量測定方法及びその装置
CN106018474A (zh) * 2016-07-15 2016-10-12 广东省特种设备检测研究院顺德检测院 一种液体比热容测量系统
CN106645274A (zh) * 2016-09-19 2017-05-10 中国计量大学 一种应用于绝热反应量热的样品动态热容测算方法
WO2020151780A1 (de) * 2019-01-24 2020-07-30 Friedrich-Schiller-Universität Jena Vorrichtung und verfahren zur simultanen bestimmung der temperaturabhängigen thermischen leitfähigkeit, thermischen diffusivität und spezifischen wärmekapazität
CN111812149A (zh) * 2020-07-20 2020-10-23 南京工业大学 一种基于机器学习的绝热加速量热方法

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6561692B2 (en) * 2000-03-23 2003-05-13 Ta Instruments-Waters Llc Differential scanning calorimeter
GB201119036D0 (en) * 2011-11-03 2011-12-14 Univ Oxford Brookes A method of controlling a dynamic physical system
AU2018200711B2 (en) * 2017-02-01 2023-11-09 Julius Industrial & Scientific Pty Ltd Method for measurement of subterranean soil characteristics for water management purposes
CN109974902B (zh) * 2019-03-29 2020-09-11 中国计量大学 一种具有动态热惯量修正特征的绝热加速量热仪
CN109945994B (zh) * 2019-04-15 2021-03-02 中国计量大学 一种基于焦耳热效应的加速量热仪绝热性能评价方法

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5335993A (en) * 1992-03-02 1994-08-09 Ta Instruments, Inc. Method and apparatus for thermal conductivity measurements
JPH09222404A (ja) * 1996-02-19 1997-08-26 Agency Of Ind Science & Technol 比熱容量測定方法及びその装置
CN106018474A (zh) * 2016-07-15 2016-10-12 广东省特种设备检测研究院顺德检测院 一种液体比热容测量系统
CN106645274A (zh) * 2016-09-19 2017-05-10 中国计量大学 一种应用于绝热反应量热的样品动态热容测算方法
WO2020151780A1 (de) * 2019-01-24 2020-07-30 Friedrich-Schiller-Universität Jena Vorrichtung und verfahren zur simultanen bestimmung der temperaturabhängigen thermischen leitfähigkeit, thermischen diffusivität und spezifischen wärmekapazität
CN111812149A (zh) * 2020-07-20 2020-10-23 南京工业大学 一种基于机器学习的绝热加速量热方法

Non-Patent Citations (10)

* Cited by examiner, † Cited by third party
Title
CHARLES F. ASKONAS, DR. JAMES P. BURELBACH: "The versatile VSP2: a tool foradiabatic thermal analysis and vent sizing application[C] ", ANALYSIS SOCIETY, 2000
HEL GROUP PHI-TEC II: ADIABATIC CALORIMETER FOR VENT SIZING AND ACCURATE THERMAL RUNAWAY TESTING[EB/OL, Retrieved from the Internet <URL:http://www.helgroup.com/reactor-systems/thermal-hazards-and-calorimetry/phitec-i>
IWATA YMOMOTA MKOSEKI H: "Thermal risk evaluation of organic peroxide by automatic pressure tracking adiabatic calorimeter[J", JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY, vol. 85, no. 3, 2006, pages 617 - 622, XP019402643, DOI: 10.1007/s10973-006-7651-x
JIONG DING, JICHEN WANG, LU GUO, QIYUE XU, SHUIJUN YANG, SHULIANG YE: "Optimization of Temperature Tracking Control in Adiabatic Accelerating Ｒate Calorimeter Based on the Dynamic Characteristics Compensation", JOURNAL OF TRANSDUCTION TECHNOLOGY, DONGNAN DAXUE CHUBANSHE, NANJING, CN, vol. 31, no. 12, 31 December 2018 (2018-12-31), CN , pages 1805 - 1810, XP055950553, ISSN: 1004-1699 *
KIMURA AOTSUKA T: "Performance evaluation of differential accelerating rate calorimeter for the thermal runaway reaction of di-tert-butyl peroxide[J", JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY, vol. 113, no. 3, 2013, pages 1858 - 1591, XP055945545, DOI: 10.1007/s10973-013-3282-1
KIMURA ARATA, OTSUKA TERUHITO: "Performance evaluation of differential accelerating rate calorimeter for the thermal runaway reaction of di-tert-butyl peroxide", JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY, KLUWER, DORDRECHT,, NL, vol. 113, no. 3, 1 September 2013 (2013-09-01), NL , pages 1585 - 1591, XP055945545, ISSN: 1388-6150, DOI: 10.1007/s10973-013-3282-1 *
See also references of EP4113110A4
SUN JINHUADING HUI: "Thermal hazard evaluation of chemical substances [M", SCIENCE PRESS, 2005
TOU J.CWHITING L.F: "The thermokinetic performance of an accelerating rate calorimeter[J].", THERMOCHIMICA ACTA, vol. 48, no. 1, 1981, pages 21 - 42
TOWNSEND D.ITOU J.C: "Thermal hazard evaluation by an accelerating rate calorimeter[J", THERMOCHIMICA ACTA, vol. 37, no. 1, 1980, pages 1 - 30, XP026580809, DOI: 10.1016/0040-6031(80)85001-5

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