CN112233729A - General form and solving method of polymer insulation pyrolysis reaction mechanism function - Google Patents

Abstract

The invention relates to a general characterization form and a solution method of a polymer insulation pyrolysis reaction mechanism function. It includes the following steps: on the basis of the differential expression of the reaction mechanism function, a 4-parameter integral expression model of the reaction mechanism function is constructed; based on the kinetic equation of the polymer insulating material under non-isothermal conditions, the construction of the experimental function is given Form; based on the experimental function to solve the integral expression of the polymer insulation pyrolysis reaction mechanism function. The invention can characterize various existing reaction mechanism functions, has better universality and application range, can effectively reflect the aging and deterioration process of polymer insulation, and provides research on the aging mechanism of polymer insulation materials and remaining life prediction. basic method.

Description

A general form and solution method of a polymer insulation pyrolysis reaction mechanism function

technical field

The invention relates to the field of insulation material aging assessment, in particular to a general characterization form and a solution method of a polymer insulation pyrolysis reaction mechanism function.

Background technique

Polymer insulating materials are widely used in electrical equipment insulation systems due to their excellent insulating properties, heat resistance and easy processing. However, due to the effects of electrical, magnetic, thermal and other stresses, the polymer insulating material will experience aging and deterioration, which may lead to safety accidents in severe cases. Many power equipment has been put into operation for more than ten years or even decades, and it is urgent to formulate a scientific condition maintenance strategy. Therefore, the research on the aging mechanism and life prediction method of polymer insulating materials has important engineering application value.

In the process of aging and deterioration, materials must be accompanied by chemical changes, and there will be the output or overflow of substances, resulting in different deformations and internal stresses inside the substances. These changes are manifested in solid-phase reactions, and an active region or active site is formed at the reactant interface, which is the nuclei. Under the action of various stresses, the crystal nucleus continuously grows, grows, and diffuses, eventually leading to material failure. As a mathematical description of the growth behavior of crystal nuclei, the reaction mechanism function is used to characterize many evolutionary processes such as high-temperature cracking of petroleum and coal, polymerization and solidification of polymers, and dehydration and decomposition of inorganic substances, revealing the occurrence path and decomposition of chemical reactions. properties to determine material stability and longevity.

The study of reaction mechanism function has been developed rapidly after the concept of crystal nucleus was proposed. In the past century, many thermodynamic researchers have proposed and perfected different types of solid-state kinetic models. Although these kinetic mode functions give a basic description of the reaction process of many solid-state substances, due to the complexity of the heterogeneous reaction itself, coupled with the irregularity of the particle geometry and packing of the actual sample, and the reaction Due to the variability of physical and chemical properties of substances, the actual thermal decomposition curve often does not conform to the predicted mechanism, and the solved reaction mechanism function must be distorted. For a long time, the lack of a more general functional form of reaction mechanism has resulted in the difference and complexity of material thermodynamic analysis. In principle, this limitation can be overcome by increasing the number of kinetic model functions. Although these models can explain the deviation of some material reaction mechanisms from the ideal model, they lack practical physical meaning, and the number of models cannot be increased indefinitely. Another solution is to seek a more general mathematical model that covers as many reaction mechanisms as possible and has better generalizability.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the prior art, the present invention provides a general characterization form and a solution method of a polymer insulation pyrolysis reaction mechanism function, including the following steps.

1. A general characterization form and solution method of a polymer insulation pyrolysis reaction mechanism function, comprising the following steps:

(1) On the basis of the differential expression of the reaction mechanism function, a 4-parameter integral expression model of the reaction mechanism function is constructed. The specific expression is:

(1-1)

(1-1)

For a specific material pyrolysis reaction, q , m , n , and p are constants in the formula;

(2) Based on the kinetic equation of the polymer insulating material under non-isothermal conditions, the structural form of the experimental function is given;

(3) Based on the experimental function, the integral expression of the polymer insulation pyrolysis reaction mechanism function is solved.

2. Optionally, the differential expression of the reaction mechanism function is:

(1-2)

(1-2)

Among them, m , n , p represent exponential factors of different values, and one of the exponential factors is always 0 when applied.

3. Optionally, the construction of the experimental function specifically includes the following steps:

(1) The kinetic equation of the polymer insulating material under non-isothermal conditions is:

(1-3)

(1-3)

(2) Shift the term of equation (1-3) and integrate both ends simultaneously to obtain:

(1-4)

(1-4)

Where u=E/RT , P(u) is called the temperature integral, as shown in the following formula (1-5):

(1-5)

(1-5)

(3) The temperature integral P(u) is approximately expressed by the Senum-Yang temperature integral, as shown in the following formula (1-6):

(1-6)

(1-6)

(4) Taking α = 0.5 as the reference point, it can be obtained from formula (1-4):

(1-7)

(1-7)

where u _0.5 is the corresponding u value when α = 0.5;

(5) Equation (1-4) divided by Equation (1-7) can be obtained:

(1-8)

(1-8)

(6) Substitute equations (1-1) and (1-6) into (1-8) to obtain:

(1-9)

(1-9)

(7) Order:

(1-10)

(1-10)

(8) The thermal weight loss analysis of the polymer insulating material is carried out, and the activation energy of the material at different conversion rates α is obtained according to the thermal weight loss curve;

(9) Substitute the activation energy E and temperature T obtained in the range of the conversion rate α of the polymer insulating material into the formula (1-10) to form the experimental function curve. If the pyrolysis reaction can be described by a single reaction mechanism function, regardless of the temperature rise What is the rate, and each experimental curve should coincide with each other.

4. Optionally, the solution of the integral expression of the polymer insulation pyrolysis reaction mechanism function specifically includes the following steps:

(1) Order:

(1-11)

(1-11)

(2) Substitute different conversion rates α into formula (1-11), and the corresponding parameters m , n , and p can be obtained from the experimental curve obtained by fitting formula (1-10) by the least square method;

(3) Substitute equations (1-1) and (1-6) into equations (1-4) to obtain:

(1-12)

(1-12)

(4) In formula (1-12), the parameters m , n , p , u, E, β , and R are known, and the unknowns are only the values of q and A , and the parameters corresponding to the two conversion rates α are arbitrarily selected and substituted into formula (1) -12), the q value can be obtained by solving the equation system;

(5) Substitute the obtained parameters q , m , n , and p into formula (1-1) to obtain the reaction mechanism function followed by the pyrolysis reaction process of the obtained material.

The present invention provides a general characterization form and a solution method of a polymer insulation pyrolysis reaction mechanism function, the model can characterize various existing reaction mechanism functions, has better universality and application range, and can better describe Some multivariate reactions can effectively characterize the aging and deterioration process of insulating materials, and provide a basic method for studying the aging mechanism of insulating materials and predicting the remaining life.

Description of drawings

FIG. 1 is a schematic diagram of the experimental flow of the present invention.

Figure 2 is the thermogravimetric curve of cross-linked polyethylene.

Figure 3 is a straight line fitted by the improved Flynn-Wall-Ozawa method.

Figure 4 shows the experimental curves of cross-linked polyethylene at different heating rates.

Detailed ways

The present invention will be further described below with reference to specific embodiments and accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

As shown in Figure 1, a general characterization form and solution method of a polymer insulation pyrolysis reaction mechanism function, taking cross-linked polyethylene as an example, mainly includes the following steps.

(1) The differential expression of the reaction mechanism function is:

(1-1)

(1-1)

Among them, m , n , p represent exponential factors of different values, and one of the exponential factors is always 0 when applied;

In general, the calculation of the residual life of a material is closely related to the integral expression form G ( α ) of the reaction mechanism function, so it is of great significance to study the integral expression model followed by the pyrolysis reaction of the material. On the basis of the differential expression of the reaction mechanism function, a 4-parameter integral expression model of the reaction mechanism function is constructed. The specific expression is:

(1-2)

(1-2)

For a specific material pyrolysis reaction, q , m , n , and p are constants in the formula.

(2) Based on the kinetic equation under non-isothermal conditions, the structural form of the experimental function is given:

1) The kinetic equation under non-isothermal conditions is:

(1-3)

(1-3)

2) Shift the term of Equation (1-3) and integrate both ends at the same time to obtain:

(1-4)

(1-4)

Where u=E/RT , P(u) is called the temperature integral, as shown in the following formula (1-5):

(1-5)

(1-5)

3) The temperature integral P(u) is approximately expressed by the Senum-Yang temperature integral, as shown in the following formula (1-6):

(1-6)

(1-6)

4) Taking α = 0.5 as the reference point, it can be obtained from formula (1-4):

(1-7)

(1-7)

where u _0.5 is the corresponding u value when α = 0.5;

5) Equation (1-4) divided by Equation (1-7) can be obtained:

(1-8)

(1-8)

6) Substitute equations (1-2) and (1-6) into (1-8) to get:

(1-9)

(1-9)

7) Order:

(1-10)

(1-10)

8) Using the TGA-DSC3+ synchronous thermal analysis analyzer from Mettler, Switzerland, the cable cross-linked polyethylene sample was tested by thermogravimetry, 10 mg per sample, the upper temperature limit was 600 °C, and under the condition of 50 ml/min nitrogen Carry out the experiment, select the alumina crucible for use, and the heating rate is set to 5, 10, 15, 20 and 25 ℃/min respectively. The thermogravimetric curve (TG) of the measured cross-linked polyethylene is shown in Figure 2;

The Flynn-Wall-Ozawa method can solve the activation energy without setting the reaction mechanism function. The traditional Flynn-Wall-Ozawa method selects the Doyle approximation method for characterization, which has a large calculation error. The present invention selects the improved Flynn-Wall-Ozawa method, and its concrete expression form is

(1-11)

(1-11)

The same conversion rate α is selected for β under different heating rates, and G ( α ) is a constant value for the same pyrolysis reaction, then ln( β / T ^1.89466100 ) and 1 / T satisfy a linear relationship, which can be obtained by fitting the slope. get activation energy E ;

The corresponding temperature values at different conversion rates α are shown in Table 1, and the fitting curves for different conversion rates α are shown in Figure 3. The activation of cross-linked polyethylene at different conversion rates α is calculated from the slope of the fitting curve. can, as shown in Table 2;

Table 1 Temperature values corresponding to different conversion ratios

<i>α</i> 5°C/min 10°C/min 15°C/min 20°C/min 25°C/min 0.2 451.381 461.798 469.017 474.94 480.326 0.3 457.378 467.909 475.196 480.912 486.474 0.4 461.761 472.349 479.644 485.553 490.879 0.5 465.219 475.977 483.347 489.393 494.685 0.6 468.373 479.288 486.811 493.183 497.583 0.7 471.267 482.273 489.836 496.112 501.012 0.8 474.353 485.591 493.275 499.345 504.619

Table 2 Activation energies at different conversion rates

Conversion rate <i>α</i>(%) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Activation energy (kJ/mol) 241.43 244.84 246.9 246.05 247.68 246.47 245.33

9) Substitute the activation energy E and temperature T obtained in the range of the cross-linked polyethylene conversion rate α into formula (1-10) to form the experimental function curve. Figure 4 shows the experimental function curve obtained by fitting under different heating rates, which can be It can be seen that the experimental curves under the five heating rates almost all overlap, indicating that the cross-linked polyethylene pyrolysis reaction follows a single reaction mechanism function.

(3) Based on the experimental function of cross-linked polyethylene, the integral expression of the pyrolysis reaction mechanism function is solved:

1) Order:

(1-12)

(1-12)

2) Substitute different conversion rates α into formula (1-12), and from the fitted experimental curve, m = 0.6689, n = -0.1420, p = 0.0902;

3) Substitute formula (1-2) and formula (1-6) into formula (1-4) to obtain:

(1-13)

(1-13)

4) In formula (1-13), the parameters m , n , p , u, E, β , and R are known, and the unknowns are only the values of q and A , and any two conversion rates corresponding to α = 0.2 and α = 0.3 are taken. Substitute the parameters into equation (1-13), and solve the equation system to get q = 2.1150;

5) Substituting the obtained parameters q , m , n , and p into formula (1-2), the reaction mechanism function of the cross-linked polyethylene pyrolysis reaction process can be obtained as follows:

(1-14)

(1-14)

To sum up, the present invention provides a general characterization form and solution method for the reaction mechanism function of polymer insulation pyrolysis, the model can characterize various existing reaction mechanism functions, and has better universality and application range, It provides a basic method for studying the aging mechanism of insulating materials and predicting the remaining life.

The above-mentioned embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above-mentioned embodiments, and any other changes, modifications, substitutions, combinations, The simplification should be equivalent replacement manners, which are all included in the protection scope of the present invention.

Claims (4)

1. A general representation form and solving method of a polymer insulation pyrolysis reaction mechanism function is characterized by comprising the following steps:

(1) on the basis of a differential expression of a reaction mechanism function, a 4-parameter reaction mechanism function integral expression model is constructed, and the specific expression is as follows:

(1-1)

for a particular material pyrolysis reaction, in the formulaq、m、n、pIs a constant;

(2) based on a kinetic equation of the polymer insulating material under a non-isothermal condition, giving a construction form of an experimental function;

(3) and solving a function integral expression of the polymer insulation pyrolysis reaction mechanism based on the experimental function.

2. The general characterization form and solution method for polymer insulation pyrolysis reaction mechanism function according to claim 1, wherein the differential expression of the reaction mechanism function is:

(1-2)

wherein,m、n、pindex factors representing different values, one of which is always 0 when applied.

3. The general characterization form and solution method for polymer insulation pyrolysis reaction mechanism function according to claim 1, wherein the configuration of the experimental function specifically comprises the following steps:

(1) the kinetic equation of the polymer insulation material under non-isothermal conditions is as follows:

(1-3)

(2) shifting the term of equation (1-3) and integrating both ends simultaneously can yield:

(1-4)

whereinu=E/RT，P(u)Referred to as temperature integral, as shown in the following formulas (1-5):

(1-5)

(3) integral of temperatureP(u)Expressed approximately by Senum-Yang temperature integration, as shown in the following formulas (1-6):

(1-6)

(4) to be provided withα=0.5 as a reference point, which can be obtained from the formula (1-4):

(1-7)

in the formulau _0.5Is composed ofαWhen =0.5, the correspondinguA value;

(5) the formula (1-4) is divided by the formula (1-7):

(1-8)

(6) substituting formulae (1-1) and (1-6) into (1-8) can give:

(1-9)

(7) order:

(1-10)

(8) carrying out thermal weight loss analysis on the polymer insulating material, and obtaining different conversion rates according to a thermal weight loss curveαThe activation energy of the lower material;

(9) will be in the conversion of polymer insulation materialαActivation energy obtained within the rangeEAnd temperatureTThe equations (1-10) are substituted to form experimental function curves, and if the pyrolysis reaction can be described by a single reaction mechanism function, the experimental curves should coincide with each other regardless of the temperature rise rate.

4. The general characterization form and solution method for polymer insulation pyrolysis reaction mechanism function according to claim 1, wherein the solution of the integral expression of the polymer insulation pyrolysis reaction mechanism function specifically comprises the following steps:

(1) order:

(1-11)

(2) will vary in conversion rateαSubstituting the formula (1-11), and obtaining the corresponding parameters by fitting the formula (1-10) with the least square methodm、n、p；

(3) The compound represented by the formula (1-1) or (1-6) may be substituted with the compound represented by the formula (1-4):

(1-12)

(4) parameters of the formulae (1-12)m、n、p、u、E、β、RThe unknown quantity is known onlyqAndAvalue, arbitrarily two conversion ratesαThe corresponding parameters are substituted into the formula (1-12), and the equation set is solved to obtainqA value;

(5) the parameters to be obtainedq、m、n、pSubstituting the formula (1-1) to obtain a reaction mechanism function followed by the pyrolysis reaction process of the required material.

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