Coal spontaneous combustion tendency evaluation method based on nonlinear dynamic mutation theory

Abstract

The invention discloses a coal spontaneous combustion tendency evaluation method based on a nonlinear dynamic mutation theory, and the method comprises the steps: modeling a coal spontaneous combustion process as a cuspidal point mutation system, taking CO concentration as a state variable, taking volatile components and oxidation temperature of coal as control variables, and building and solving a cuspidal point mutation equation; acquiring data through a temperature programming experiment, and solving an uplink sudden change temperature and a downlink sudden change temperature; the upward sudden change temperature is used as a core index for evaluating the coal spontaneous combustion tendency, and the lower the value is, the higher the tendency is; the descending sudden change temperature is used as a critical criterion for judging whether the fire area is thoroughly extinguished or not. Therefore, asymmetry of heating and cooling paths is explained theoretically, clear theoretical guidance and an accurate temperature scale are provided for fire prevention and extinguishing of a coal mine, and the experimental method is simple, convenient and easy to popularize and apply to rapid screening of coal samples.

Description

Technical Field

[0001] This application relates to the field of coal mine safety technology, and in particular to a method for assessing the tendency of coal spontaneous combustion based on nonlinear dynamic catastrophe theory. Background Technology

[0002] In recent years, when evaluating the spontaneous combustion tendency of coal, single parameters such as crosspoint temperature (CPT), adiabatic oxidation rate, programmed oxidation, or activation energy are commonly used. However, these parameters have significant limitations. They can only focus on and characterize the single feature of coal's "ease of ignition," failing to accurately depict the asymmetry of the "heating-cooling" path during spontaneous combustion, nor effectively reflect the prevalent "hysteresis" phenomenon in this process. This directly leads to a lack of reliable evidence on-site when determining whether spontaneous combustion has been extinguished.

[0003] The development of spontaneous combustion of coal is a nonlinear dynamic process, and its evolutionary characteristics exhibit stage-specific differences depending on the degree of oxidation. In the initial stage of spontaneous combustion, the chemical reaction rate of coal oxidation is low, and the related parameters such as temperature, weight loss rate, and indicator gases (e.g., CO, CO2, CH4, C2H4) change relatively slowly. However, as the oxidation reaction progresses to a certain extent, the chemical reaction rate accelerates significantly, and the changes in the aforementioned indicator gases also accelerate accordingly, ultimately leading to spontaneous combustion. Not only do the parameters exhibit significant nonlinear characteristics during the heating process of spontaneous combustion, but the cooling process also exhibits significant nonlinear characteristics. However, the cooling process is asymmetrical with the heating process, a phenomenon known as the "hysteresis" effect. This "hysteresis" effect is specifically manifested in two aspects in the nonlinear dynamics of spontaneous combustion of coal: 1) When the system begins to cool down, the parameters of spontaneous combustion of coal cannot immediately recover to the state at the time of heating, and a relaxation time is required; 2) There is a time lag between the response of macroscopic parameters to changes in microscopic parameters, that is, the changes in macroscopic parameters lag behind those in microscopic parameters. This lag effect occurs because the oxidation reaction of coal requires a process, and temperature changes cannot immediately affect the coal oxidation reaction; there is a certain time delay, which leads to the aforementioned lag phenomenon.

[0004] The cross-point temperature method assesses spontaneous combustion tendency by tracking the intersection temperature of the coal oxidation heating curve and the environmental heat dissipation curve. However, this method has significant limitations in practical applications: mechanistically, it relies solely on a single temperature intersection point, neglecting the differences in the "hysteresis zone" and "overlap zone" of coal spontaneous combustion, failing to reveal the dynamic nature of discontinuous mutations, and unable to explain the nonlinear characteristics of asynchronous temperature and CO concentration in the "hysteresis phenomenon." Furthermore, experimental test results are sensitive to conditions such as the heating rate, with large fluctuations in CPT values, requiring repeated calibration. The equipment is complex and time-consuming, making it difficult to adapt to rapid screening of large-scale coal samples.

[0005] The adiabatic oxidation temperature rise rate method focuses solely on the intensity of exothermic coal oxidation, neglecting the coupled process of "oxidation exothermics - environmental heat dissipation" in on-site coal spontaneous combustion. This makes it impossible to distinguish the root cause of temperature rise rate changes or reveal lag phenomena and the nature of spontaneous combustion mutations. Furthermore, this method requires a strictly adiabatic environment, with a single-sample testing cycle of 3-7 days and energy consumption 5-8 times that of conventional experiments, resulting in high costs and making it unsuitable for the rapid screening needs of multiple batches in coal mines. Secondly, this method produces weak signals in the initial oxidation stage, making it difficult to capture early characteristics and lacking early warning capabilities, thus limiting its guidance for initial fire suppression.

[0006] The programmed temperature-increase oxidation method heats coal samples at a fixed rate and detects gas or thermal effects. However, this method is disconnected from its theoretical application. The constant-rate heating does not align with the actual phenomenon of slow temperature rise and uneven heat dissipation in spontaneous combustion of coal, making it unable to simulate unsteady-state oxidation. It struggles to reveal the abrupt changes in spontaneous combustion and cannot explain the phenomenon of high CO concentration despite temperature drops in the lag zone. While this method has a short experimental cycle, it requires gas detection and temperature control equipment, is complex to operate, and yields significant differences at different heating rates, necessitating multiple verifications. The cost is 3-4 times that of traditional testing. Furthermore, the acquired parameters are discrete, unable to dynamically track spontaneous combustion, lack critical values ​​for extinguishing it, and offer weak support for on-site decision-making.

[0007] The activation energy single-parameter method assesses the spontaneous combustion tendency of coal by calculating the activation energy, but it has the limitations of a single parameter. Activation energy only statically characterizes the ease of oxidation, failing to reflect the reaction path changes from "low-temperature oxidation to high-temperature combustion," and cannot explain the kinetic nonlinearity in hysteresis phenomena, let alone reveal the discontinuous and abrupt characteristics of spontaneous combustion. Secondly, activation energy requires at least three types of heating experiments, which are complex and require specialized personnel, making it difficult to promote in coal mines. Furthermore, as a static parameter, it cannot dynamically track the entire spontaneous combustion process, lacks adaptability to "hysteresis zones" and "overlapping zones," and lacks quantitative indicators for extinguishing fires, thus failing to influence practical decision-making.

[0008] Currently used traditional methods for assessing coal spontaneous combustion mostly rely on apparent macroscopic thermal characteristic parameters (such as temperature rise rate, critical temperature, and gaseous products) as the core basis, employing empirical or semi-empirical judgments. The variation pattern of CO concentration during coal spontaneous combustion exhibits significant stage-specific characteristics: when the temperature drops to a certain level, the CO concentrations produced during the heating and cooling processes essentially overlap. This indicates that the CO concentration changes during the heating and cooling stages of coal spontaneous combustion can be divided into two regions: a "lag zone" and an "overlap zone." This pattern aligns with actual field observations; during the extinguishing of coal spontaneous combustion in goaf areas, even after the fire source temperature has dropped to a low level, the detected CO concentration remains at a relatively high value. However, the mechanism and influencing factors of this "lag" effect are not yet clearly understood, and thus have the following limitations: (1) Failure to reveal the underlying mechanism: Traditional methods have theoretical limitations. They are unable to reveal the discontinuous and abrupt dynamic nature of coal spontaneous combustion from slow oxidation to violent combustion, nor can they provide a sufficient and reasonable theoretical explanation for the complex nonlinear phenomena that occur in the process.

[0009] (2) Relying on a large number of experiments and high cost: Traditional methods rely on a large amount of experimental data. Taking adiabatic oxidation as an example, the experiment has a long cycle, complex equipment, and high energy consumption, which makes it difficult to meet the actual needs of rapid screening of large-scale coal samples.

[0010] (3) Single judgment dimension: It is impossible to dynamically track and describe the entire process of coal spontaneous combustion from initial oxidation to final combustion, and it also lacks clear and quantitative critical parameters that can guide on-site firefighting work, making it difficult to provide accurate support for on-site decision-making. Summary of the Invention

[0011] To address the aforementioned problems, this application provides a method for assessing the tendency of coal spontaneous combustion based on nonlinear dynamic catastrophe theory. The method includes: establishing a dynamic model to describe the coal spontaneous combustion process based on cusp catastrophe theory; wherein the dynamic model includes one state variable and two independent control variables; the state variable is a parameter characterizing the evolution stages of coal spontaneous combustion, and the two control variables are a first control variable reflecting the intrinsic properties of coal spontaneous combustion and a second control variable reflecting the external environmental conditions of coal spontaneous combustion; deriving a cusp catastrophe equation describing the dynamic interaction of variables during the coal spontaneous combustion process based on the equilibrium surface equation of cusp catastrophe theory and the correlation between the first control variable, the second control variable, and the state variable; and then, by covering the coal spontaneous combustion process... Experiments were conducted to study the entire cycle of coal spontaneous combustion, from low-temperature oxidation to accelerated oxidation and cooling. Data on the first control variable, the second control variable, and state variables were collected at different stages. The collected data were substituted into the cusp catastrophe equation to solve for the upward and downward catastrophe temperatures of coal spontaneous combustion. The upward catastrophe temperature is the critical temperature at which coal spontaneous combustion transitions from the slow oxidation stage to the rapid oxidation stage, and the downward catastrophe temperature is the critical temperature at which the state variables undergo significant changes during the cooling process of coal spontaneous combustion. The upward catastrophe temperature is used as an evaluation index for the tendency of coal spontaneous combustion, and the strength of the tendency is determined based on the numerical characteristics of the upward catastrophe temperature. The downward catastrophe temperature is used as the basis for determining the extinguishing state of the fire zone, and the relationship between the coal body temperature and the downward catastrophe temperature is used to determine whether the fire zone is completely extinguished.

[0012] In some possible implementations, the state variable is selected from at least one of the characteristic gas concentrations generated during coal spontaneous combustion, the coal sample weight loss rate, and the coal sample heat release rate; wherein the characteristic gas concentrations include at least one of CO concentration, CO2 concentration, and C2H4 concentration; the first control variable is selected from industrial analysis parameters or coal quality characteristic parameters of the coal; wherein the industrial analysis parameters include at least one of volatile matter content, moisture content, and ash content, and the coal quality characteristic parameters include at least one of fixed carbon content, specific surface area of ​​coal, and porosity of coal; the second control variable is selected from at least one of the temperature, oxygen concentration, ventilation rate, and ambient pressure of the environment in which the coal spontaneously combusts.

[0013] In some possible implementations, based on the equilibrium surface equation of cusp catastrophe theory, and combined with the correlation between the first control variable, the second control variable, and the state variable, a cusp catastrophe equation describing the dynamic interaction of variables during coal spontaneous combustion is derived. This includes: using the original equilibrium surface equation of cusp catastrophe as a basis, transforming the original equilibrium surface equation into a standard cusp catastrophe equation passing through the origin of the initial state of coal spontaneous combustion through coordinate transformation; the initial state is when the coal has not been oxidized, and the state variable, the first control variable, and the second control variable are all at their initial baseline values; establishing a first correlation between the first control variable and the state variable, and a second correlation between the second control variable and the state variable; the first correlation is a linear or nonlinear relationship, and the second correlation is a functional relationship based on the laws of reaction kinetics; substituting the first and second correlations into the standard cusp catastrophe equation, and replacing the control variable parameters in the equation, to obtain the cusp catastrophe equation.

[0014] In some possible implementations, the cusp catastrophe equation is expressed as: ; in, For state variables, The value of the first control variable. , , , , , It is a constant, obtained through experiments. This is the value of the second control variable.

[0015] In some possible implementations, an experiment covering the entire cycle of low-temperature oxidation, accelerated oxidation, and cooling of coal spontaneous combustion is called a programmed temperature-increase oxidation experiment. The specific process of solving the upward and downward mutation temperatures includes: constructing the discriminant of the coal spontaneous combustion cusp mutation equation, which is used to determine the number and distribution of real roots of the equation; when the discriminant equals 0, the equation has repeated roots, and the values ​​of the second control variables corresponding to the repeated roots are the upward and downward mutation temperatures, respectively; where the upward mutation temperature corresponds to the temperature at which the discriminant first equals 0 during the coal spontaneous combustion heating process, and the downward mutation temperature corresponds to the temperature at which the discriminant first equals 0 during the coal spontaneous combustion cooling process.

[0016] In some possible implementations, the upward abrupt change temperature is the critical temperature point at which coal spontaneous combustion transitions from the low-temperature oxidation stage to the accelerated oxidation stage, used to warn of the occurrence of coal spontaneous combustion; the downward abrupt change temperature is the critical temperature point at which coal spontaneous combustion falls back from the accelerated oxidation stage to the low-temperature oxidation stage after fire extinguishing measures are taken, used to determine whether the fire zone has been completely extinguished.

[0017] One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages: In this invention, a coal spontaneous combustion tendency assessment method based on nonlinear dynamic catastrophe theory is presented. This method utilizes catastrophe theory to reveal the inherent nonlinear dynamic mechanism of the entire coal spontaneous combustion process, clarifies the mathematical explanation of hysteresis phenomena, and enhances the theoretical depth of the field. Using the upward catastrophe temperature as a tendency indicator provides clear physical meaning, and the results are consistent with classical methods but more objective, reducing human experience errors. Furthermore, this invention innovatively proposes the downward catastrophe temperature as a critical criterion for successful fire extinguishing, providing a precise "temperature scale" and solving the problem of determining coal spontaneous combustion tendency. Attached Figure Description

[0018] To more clearly illustrate the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A schematic flowchart of an embodiment of a coal spontaneous combustion tendency assessment method based on nonlinear dynamic catastrophe theory provided by an embodiment of the present invention; Figure 2 This is a schematic diagram of the cusp catastrophe theory model in an embodiment of the present invention; Figure 3 This is a schematic diagram of the cusp abrupt change in temperature equilibrium surface and control plane during the spontaneous combustion of coal in an embodiment of the present invention. Figure 4 This is a schematic diagram of the set of cusp mutation temperatures in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0021] In the relevant descriptions of this embodiment, the terms "including," "containing," and "possessing" are all open terms and are generally understood to include but not be limited to; the term "at least one" is generally understood to mean one or more, where "multiple" refers to two or more; the term "at least one of the following" or similar expressions refer to any combination of these items, including any combination of single or multiple items, for example, "at least one of a, b, or c", or "at least one of a, b, and c", which can all mean: a, b, c, ab (i.e., a and b), ac, bc, or abc, where a, b, and c can be single or multiple; the symbol "A / B" is used to describe the selection relationship of associated objects, generally indicating an "or" relationship.

[0022] In the following description of the embodiments, the terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms "a" and "the" as used in the embodiments of this application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise.

[0023] Those skilled in the art should understand that, in the following description of the embodiments of this application, the sequence of numbers does not imply the order of execution. Some or all steps may be executed in parallel or sequentially. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0024] Those skilled in the art will understand that the numerical ranges in the embodiments of this application should be understood to specifically disclose each intermediate value between the upper and lower limits of the range. Any stated value or intermediate value within a stated range, as well as any other stated value or each smaller range between intermediate values ​​within a range, are also included within this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0025] Unless otherwise stated, the technical / scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. While this application describes only preferred methods and materials, any methods and materials similar or equivalent to those described herein may be used in the implementation or testing of this application. All references to this specification are incorporated by way of citation to disclose and describe the methods and / or materials associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0026] To illustrate the technical solution of the present invention, specific embodiments are described below.

[0027] Figure 1 A schematic flowchart illustrating an embodiment of a coal spontaneous combustion tendency assessment method based on nonlinear dynamic catastrophe theory provided by this invention is shown below. Figure 1 As shown, the above method may include: S101 establishes a dynamic model to describe the spontaneous combustion process of coal based on the cusp catastrophe theory. The dynamic model includes one state variable and two independent control variables. The state variable is a parameter that can characterize the evolution stage of spontaneous combustion of coal. The two control variables are the first control variable reflecting the intrinsic properties of spontaneous combustion of coal and the second control variable reflecting the external environmental conditions of spontaneous combustion of coal. It should be noted that current technologies, based on thermodynamic equilibrium theory or empirical observation, treat the spontaneous combustion of coal as a continuous, linear heating process, failing to fully reflect its complex kinetic nature. This invention will overcome this limitation by introducing catastrophe theory from the nonlinear kinetics branch into the study of spontaneous combustion, treating the process as a discontinuous energy state transition. Further analysis from a kinetic perspective reveals a clear system of variables in the spontaneous combustion process: one is the state variable, namely the degree of development of spontaneous combustion, used to characterize the evolutionary stage of the process; the other consists of two independent control variables, which, based on the above analysis, can be identified as the internal and external causes of spontaneous combustion, jointly driving the dynamic changes of the process. Therefore, the most suitable catastrophe form for describing the development process of spontaneous combustion is the cusp catastrophe.

[0028] In some embodiments, the catastrophe equation of the dynamic model can be expressed as: ; in, For state variables; and These are two parameters related to the control variables.

[0029] In some embodiments, the state variable may be at least one selected from the concentration of characteristic gas generated during coal spontaneous combustion, the coal sample weight loss rate, and the coal sample heat release rate; wherein, the concentration of characteristic gas may include at least one selected from the concentration of CO, the concentration of CO2, and the concentration of C2H4. In some embodiments, the first control variable may be selected from industrial analysis parameters or coal quality characteristic parameters of coal; wherein, the industrial analysis parameters may include at least one of volatile matter content, moisture content, and ash content, and the coal quality characteristic parameters may include at least one of fixed carbon content, specific surface area of ​​coal, and porosity of coal. In some embodiments, the second control variable may be at least one selected from the temperature, oxygen concentration, ventilation rate, and ambient pressure of the environment in which the coal spontaneously combusts; for example, the second control variable may be the oxidation temperature, which is the temperature of the coal itself or the ambient temperature of the environment in which the coal is located.

[0030] S102, based on the equilibrium surface equation of cusp catastrophe theory, combined with the correlation between the first control variable, the second control variable and the state variable, the cusp catastrophe equation describing the dynamic relationship of variables in the process of spontaneous combustion of coal is derived. In some embodiments, step S102 may specifically include: S1021, based on the original equilibrium surface equation of cusp catastrophe, transforms the original equilibrium surface equation into a standard cusp catastrophe equation passing through the origin of the initial state of coal spontaneous combustion through coordinate transformation; the initial state is when the coal has not been oxidized, and the state variables, the first control variable, and the second control variable are all in the state of the initial reference value. S1022, Establish the first correlation between the first control variable and the state variable, and the second correlation between the second control variable and the state variable; the first correlation is a linear or nonlinear relationship, and the second correlation is a functional relationship based on the laws of reaction kinetics; S1023, Substitute the first correlation and the second correlation into the standard cusp catastrophe equation, and replace the control variable parameters in the equation to obtain the cusp catastrophe equation.

[0031] Specifically, according to the catastrophe equation of the dynamic model, the potential equation for cusp catastrophe is three-dimensional, and the standard equation of its equilibrium surface can be expressed by the following formula: ; in, and There are two control variables.

[0032] In some embodiments, the control variable refers to the influencing factors of the degree of spontaneous combustion of coal. Since the two control variables are required to be independent of each other, as mentioned above, the most appropriate selection method is to classify and screen them: one is selected from the internal factors affecting spontaneous combustion of coal, and the other is selected from the external factors.

[0033] Among them, the intrinsic factors can be mathematically described as: ; in, This represents the combined effect of all intrinsic factors influencing spontaneous combustion of coal. (1≤i≤m) represent the various intrinsic sub-factors affecting coal spontaneous combustion. It is understandable that the essence of coal combustion is the production of combustible volatiles through pyrolysis, and these volatiles play a crucial role throughout the entire combustion process. Therefore, to simplify the relevant model of coal spontaneous combustion, we can select the volatile matter content of coal as a single variable and define it as the intrinsic control variable affecting coal spontaneous combustion.

[0034] The mathematical expression for the external factors affecting spontaneous combustion of coal can be represented as: ; In the formula, This represents the combined effect of all external factors influencing spontaneous combustion of coal. (1≤i≤n) represent the various external sub-factors affecting coal spontaneous combustion. Understandably, considering the difficulty of quantification, the importance of their impact on coal spontaneous combustion, and the ease of operation, in this embodiment of the invention, oxidation temperature can be selected as a single external control variable affecting coal spontaneous combustion.

[0035] In some embodiments, the model of mutation theory is as follows: Figure 2 As shown, where, Figure 2 The control surface is a projection of the equilibrium surface, wherein the control surface uses the O(X, p, q) coordinate system and the equilibrium surface uses the Q (x, u, v) coordinate system.

[0036] See Figure 2 As shown, since the original equilibrium surface equation does not pass through the origin, to correctly apply the catastrophe theory, we must first transform the Q (x, u, v) coordinate system into the O (x, p, q) coordinate system, which can be expressed as: ; in, This is the value in the Q coordinate system; Let be the direction cosine from the Q coordinate system to the O coordinate system. After the coordinate transformation, the standard equation of the equilibrium surface in the O coordinate system becomes: ; because Xand x The directions are the same, therefore .in addition: ; ; According to the right-hand rule, we can conclude that: ; Because the equilibrium surface passes through the origin in the new coordinate system, therefore: ; Based on the above description, all the unknown parameters in the above formula can be calculated: ; Substituting the above equation into the standard equation of the equilibrium surface in the O coordinate system after coordinate transformation, we get: ; make , , We can obtain the catastrophe theory equation in the new coordinate system, namely: ; in, X For state variables, M and N These are functions of two independent control variables. As mentioned earlier, the state variables... X CO concentration, M A function of volatile matter, N It is a function of temperature.

[0037] Assuming a linear relationship between volatile matter content and CO concentration during coal spontaneous combustion, i.e.: ; in, V The volatile matter content of coal. , This is a constant, determined experimentally. According to the Arrhenius equation, the relationship between CO concentration and oxidation temperature in the coal oxidation reaction can be expressed by the following equation: ; in, Oxidation temperature; , , , Since is a constant, determined experimentally, the cusp catastrophe equation for the spontaneous combustion development process of coal can be expressed as: .

[0038] In some embodiments, the above constants , as well as , , , The methods for determining this may include: At least three coal samples with different values ​​of the first control variable were selected, and the above full-cycle experiment was carried out respectively. For each coal sample, multiple sets of data of the first control variable, the second control variable, and the state variable were collected. The data were fitted by the least squares method or the nonlinear regression method to obtain the specific values ​​of the corresponding constants.

[0039] S103, through experiments covering the entire cycle of coal spontaneous combustion from low-temperature oxidation to accelerated oxidation to cooling, collected data on the first control variable, the second control variable, and the state variable at different stages. The collected data were substituted into the cusp catastrophe equation to solve for the upward catastrophe temperature and the downward catastrophe temperature of coal spontaneous combustion. The upward catastrophe temperature is the critical temperature at which coal spontaneous combustion transitions from the slow oxidation stage to the rapid oxidation stage, and the downward catastrophe temperature is the critical temperature at which the state variable changes significantly during the cooling process of coal spontaneous combustion. In some embodiments, the above experimental process can be a programmed temperature oxidation experiment, through which CO concentration data at different temperatures are obtained.

[0040] For example, the operating parameters of the programmed temperature rise oxidation experiment may include: a heating rate of 0.1~10℃ / min, an experimental atmosphere of gaseous atmosphere with an oxygen content of 15%~25%, an experimental temperature range of 25℃ (ambient temperature) to 700℃ (intense coal oxidation temperature), a cooling phase in which the temperature is reduced from the highest experimental temperature to the ambient temperature through natural cooling or forced temperature control, and a data acquisition interval of 1~60s during the experiment.

[0041] In some embodiments, the specific process of determining the upward and downward mutation temperatures may include: Construct a discriminant for the cusp mutation equation of coal spontaneous combustion. The discriminant is used to determine the number and distribution of real roots of the equation. When the discriminant is equal to 0, the equation has repeated roots. The values ​​of the second control variables corresponding to the repeated roots are the upward change temperature and the downward change temperature, respectively. The upward change temperature corresponds to the temperature at which the discriminant is equal to 0 for the first time during the coal spontaneous combustion heating process, and the downward change temperature corresponds to the temperature at which the discriminant is equal to 0 for the first time during the coal spontaneous combustion cooling process.

[0042] For example, the standard equation of the above equilibrium surface is a cubic equation in one variable, and its discriminant is: ; It should be noted that the discriminant... The discriminant is not only a key criterion for determining the number of real roots of an equation, but also the bifurcation set of cusp mutations. This bifurcation set contains both stable and unstable states; a slight disturbance to the system can cause it to transition from an unstable state to a stable one. Specifically, the discriminant... The correspondence between the sign of the symbol and the number of real roots of the standard equation of the equilibrium surface is as follows: When When, the equation has 3 distinct real roots; when When, the equation has 3 real roots, when When two of the three real roots are the same, When the three real roots are identical; when When the equation has only one real root, the equation has only one real root.

[0043] S104 uses the upward sudden temperature as an evaluation index for the spontaneous combustion tendency of coal, and determines the strength of the spontaneous combustion tendency of coal based on the numerical characteristics of the upward sudden temperature; uses the downward sudden temperature as a basis for determining the extinguishing state of the fire zone, and determines whether the fire zone is completely extinguished based on the relationship between the coal body temperature and the downward sudden temperature.

[0044] In some embodiments, the upward abrupt change temperature is the critical temperature point at which coal spontaneous combustion transitions from the low-temperature oxidation stage to the accelerated oxidation stage, used to warn of the occurrence of coal spontaneous combustion; the downward abrupt change temperature is the critical temperature point at which coal spontaneous combustion falls back from the accelerated oxidation stage to the low-temperature oxidation stage after fire extinguishing measures are taken, used to determine whether the fire zone has been completely extinguished.

[0045] For example, the set of cusp abrupt temperature changes during the development of spontaneous combustion in coal can be as follows: Figure 3 As shown. See also Figure 3 As shown, the entire process can be divided into three parts: the rising temperature (T) 上行 ), temperature of sudden change (T) 突变 ) and downward temperature (T) 下行 In fact, all state points can only exist in T. 上行 Or T 上行 In terms of trends, T 突变 In reality, this doesn't exist; it represents the set of process temperatures in the equilibrium surface of a cusp abrupt change. The system's state point changes from T with variations in parameters. 下行 Jump directly to T 上行 Or vice versa, without going through T 突变 Current status.

[0046] from Figure 3 As can be seen, the equilibrium surface related to coal spontaneous combustion can be divided into three parts: the lower leaf, the middle leaf, and the upper leaf. The lower and upper leaves represent the low-temperature oxidation stage and the accelerated oxidation stage, respectively, while the middle leaf represents the abrupt change stage. For a given coal sample with a relatively constant volatile matter content, its coal oxidation heating process will follow the following... Figure 3The fixed path shown is abcdf. Here, abc is located in the lower leaf and represents the low-temperature oxidation process. In this process, the oxidation of coal is very slow, with most of the heat generated dissipating into the surrounding environment and only a small amount feeding back to the coal sample surface, leading to a slow accumulation of heat. When the reaction reaches the upward abrupt change temperature point c, the heat generated cannot diffuse to the environment in time, resulting in rapid heat accumulation and a significantly accelerated oxidation rate. The CO concentration increases dramatically in a short period. Therefore, cd represents the abrupt change in coal spontaneous combustion, transitioning from the low-temperature oxidation stage to the accelerated oxidation stage. df is located in the upper leaf and represents the accelerated oxidation process. It is generally believed that spontaneous combustion has already occurred at this point. If appropriate fire extinguishing measures are not taken, the spontaneous combustion will become uncontrollable and continue to escalate.

[0047] In some implementations, after spontaneous combustion of coal occurs, if targeted control measures such as nitrogen injection and grouting are taken, the temperature of the spontaneous combustion will gradually decrease, and the system will undergo a cooling process of fdeba. In the early stages of fire extinguishing, the CO concentration decreases very slowly; even if the coal temperature has dropped to a low level, the CO concentration detected on-site remains high. However, when the coal temperature further drops to a specific critical value, namely the downward abrupt temperature point e, the CO concentration will decrease rapidly in a short period of time, exhibiting a completely different change characteristic from the initial stage.

[0048] It is evident that the heating and cooling processes of spontaneous coal combustion do not overlap, but rather exhibit a certain lag. This lag explains why extinguishing spontaneous coal combustion requires more energy than the energy generated during its development. The closed curve enclosed by bcde represents the energy difference between the two.

[0049] The ascending abrupt change temperature is the critical point for the transition from the slow oxidation stage to the accelerated oxidation stage, and can be used to evaluate the spontaneous combustion status of coal. Furthermore, the lower the ascending abrupt change temperature, the greater the risk of spontaneous combustion. The ascending and descending abrupt change temperatures can be obtained from the bifurcation set on the control plane, which is the projection of all abrupt change points on the equilibrium surface onto the control plane. The set of cusp abrupt change temperatures in the coal spontaneous combustion development process can be obtained by the following formula: ; Based on the above formula, the cusp mutation temperature set curve of the coal spontaneous combustion mutation equation is plotted as follows: Figure 4 As shown. From Figure 4 As can be seen, there are two abrupt change points for coal with a certain amount of volatile matter. The difference between the upward and downward abrupt change temperature points decreases as the volatile matter increases. However, when the volatile matter is 100%, the abrupt change critical point still exists, meaning that there is no such thing as absolutely non-spontaneous coal in nature.

[0050] For example, in step S104 above, determining the strength of the coal's spontaneous combustion tendency based on the numerical characteristics of the upward sudden change temperature can be as follows: the lower the upward sudden change temperature, the stronger the coal's spontaneous combustion tendency; for example, if the upward sudden change temperature is ≤350K, the coal is determined to have a strong spontaneous combustion tendency; if 350K < upward sudden change temperature ≤400K, the coal is determined to have a moderate spontaneous combustion tendency; if the upward sudden change temperature is >400K, the coal is determined to have a weak spontaneous combustion tendency. Determining whether the fire zone is completely extinguished based on the relationship between the coal body temperature and the downward sudden change temperature can be as follows: when the coal body temperature is consistently lower than the downward sudden change temperature for 24~168 hours, and the value of the synchronously monitored state variable falls back to within 10% of the initial value of the unoxidized state, the fire zone is determined to be completely extinguished, with no risk of reignition.

[0051] In this embodiment of the invention, cusp mutations possess several key characteristics. At the critical point, even a slight increment in the control variable can lead to a significant change in the state variable. Furthermore, the state change process of a temperature-catastrophic system is irreversible; the paths from a downward temperature to an upward temperature are not identical to those from an upward temperature to a downward temperature, and the upward mutation point is generally not the same as the downward mutation point. Once the system enters an upward temperature state, greater energy is required to return it to a downward temperature state. In catastrophe theory, a finite change in the control variable will cause a change in the value of the state variable at the equilibrium position. In a general system, a small perturbation of the control variable may only cause small changes in the initial and final values ​​of the state variable, but near the critical point, a small perturbation of the control variable may lead to a huge change in the state variable; this perturbation instability of the control variable is called bifurcation.

[0052] Furthermore, existing technologies cannot clearly explain the common field phenomenon of "coal temperature decreasing but CO continuing to be released," nor can they provide clear and differentiated temperature control targets during firefighting. This invention, through simulation calculations, clearly reveals the asymmetry (i.e., lag) between the heating and cooling processes of coal spontaneous combustion. Based on this, it innovatively defines two key critical temperatures: an upward abrupt change temperature point for early warning of spontaneous combustion, and a downward abrupt change temperature point for determining whether the fire zone is under control. The downward abrupt change temperature point is typically significantly lower than the upward abrupt change temperature point. Theoretically, this thoroughly explains the problem of low temperature and high CO levels in areas such as goafs after firefighting, clarifying that the root cause of this phenomenon lies in the system still being in the lag zone of the cooling path, not having fallen below the downward abrupt change point. Based on this, this invention can guide underground coal mine workers to cool the coal body below the downward abrupt change temperature point to ensure the fire is completely extinguished, effectively avoiding the risk of reignition due to misjudgment of the fire zone's state, and greatly improving the efficiency and safety of coal mine fire prevention and extinguishing work.

[0053] Furthermore, existing technologies often use apparent parameters or comprehensive indices as criteria for determining the tendency. However, the embodiments of this invention can obtain data through a relatively simple programmed temperature rise test, and then substitute this data into the catastrophe equation derived in these embodiments to calculate the upward catastrophe temperature point. The upward catastrophe temperature point is proposed as the core indicator for evaluating the relative magnitude of coal spontaneous combustion tendency; the lower the value, the more easily the coal sample spontaneously combusts. This indicator is not empirically set, but directly derived from a theoretical model characterizing system stability, with a clear physical meaning. Therefore, the order of coal spontaneous combustion tendency evaluated based on the upward catastrophe temperature point is completely consistent with the conclusions drawn from traditional adiabatic oxidation tests, proving the reliability of this theoretical indicator. Moreover, compared to the complex adiabatic oxidation method, the method proposed in this patent has a shorter experimental cycle, lower cost, and is easier to standardize and promote in engineering, providing a practical and feasible technical path for rapid, batch screening of coal samples.

[0054] The various embodiments in this specification are described in a progressive manner. For the same or similar parts between the various embodiments, please refer to each other. Each embodiment focuses on describing the differences from other embodiments.

[0055] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A method for assessing the spontaneous combustion tendency of coal based on the theory of nonlinear dynamics catastrophe, characterized in that, The application relates to a method for evaluating coal spontaneous combustion tendency and judging fire extinguishing state. The application comprises the following steps: a dynamic model for describing the coal spontaneous combustion process is established based on a cusp catastrophe theory; the dynamic model comprises one state variable and two independent control variables; the state variable is a parameter capable of representing the evolution stage of the coal spontaneous combustion; the two control variables are a first control variable reflecting the internal property of the coal spontaneous combustion and a second control variable reflecting the external environmental condition of the coal spontaneous combustion; a cusp catastrophe equation for describing the dynamic action relationship among the variables in the coal spontaneous combustion process is derived based on the balance surface equation of the cusp catastrophe theory and the correlation among the first control variable, the second control variable and the state variable; the first control variable, the second control variable and the state variable data at different stages are collected through experiments covering the whole cycle of the low-temperature oxidation, accelerated oxidation and temperature reduction of the coal spontaneous combustion; the collected data are substituted into the cusp catastrophe equation, and the uplink mutation temperature and downlink mutation temperature of the coal spontaneous combustion are obtained by solving; the uplink mutation temperature is a critical temperature for the coal spontaneous combustion to transit from the slow oxidation stage to the rapid oxidation stage; the downlink mutation temperature is a critical temperature for the state variable to change significantly in the temperature reduction process of the coal spontaneous combustion; 2. The method of claim 1, wherein, the uplink mutation temperature is taken as an evaluation index of the coal spontaneous combustion tendency, and the uplink mutation temperature is used to judge the strength of the coal spontaneous combustion tendency; the downlink mutation temperature is taken as a judgment basis of the fire extinguishing state, and the relationship between the coal body temperature and the downlink mutation temperature is used to judge whether the fire is completely extinguished.

3. The method of claim 2, wherein, The state variable is selected from at least one of the characteristic gas concentration, the coal sample weight loss rate and the coal sample heat release rate generated in the coal spontaneous combustion process; the characteristic gas concentration comprises at least one of the CO concentration, the CO2 concentration and the C2H4 concentration; the first control variable is selected from the industrial analysis parameters or the coal quality characteristic parameters of the coal; the industrial analysis parameters comprise at least one of the volatile matter content, the moisture content and the ash content; the coal quality characteristic parameters comprise at least one of the fixed carbon content, the specific surface area of the coal and the porosity of the coal; the second control variable is selected from at least one of the temperature, the oxygen concentration, the ventilation rate and the environmental pressure of the environment where the coal spontaneous combustion is located. The balance surface equation of the cusp catastrophe theory is combined with the correlation among the first control variable, the second control variable and the state variable to derive the cusp catastrophe equation for describing the dynamic action relationship among the variables in the coal spontaneous combustion process, which comprises the following steps: a standard cusp catastrophe equation passing through the original point of the initial state of the coal spontaneous combustion is obtained by converting the original balance surface equation of the cusp catastrophe through coordinate transformation; the initial state is that the coal has not been oxidized, and the state variable, the first control variable and the second control variable are all in the initial reference value state; a first correlation between the first control variable and the state variable and a second correlation between the second control variable and the state variable are established; the first correlation is a linear or nonlinear relationship, and the second correlation is a functional relationship based on the reaction kinetics law. The first correlation relationship and the second correlation relationship are substituted into the standard cusp catastrophe equation, and a control variable parameter in the equation is replaced, to obtain the cusp catastrophe equation.

4. The method of claim 3, wherein, The cusp catastrophe equation is expressed as: ； wherein, is a state variable, is a first control variable value, , , , , , is a constant, obtained by experiment, is a second control variable value.

5. The method of claim 4, wherein, The experiment through covering the whole cycle of low-temperature oxidation and accelerated oxidation to temperature reduction of coal spontaneous combustion is a programmed temperature rising oxidation experiment; and the specific process of solving the upgoing catastrophe temperature and the downgoing catastrophe temperature comprises: A discriminant of the cusp catastrophe equation of coal spontaneous combustion is constructed, and the discriminant is used to determine the number and distribution of real roots of the equation; When the discriminant is equal to 0, the equation has a multiple root, and the second control variable values corresponding to the multiple root are the upgoing catastrophe temperature and the downgoing catastrophe temperature respectively; wherein the upgoing catastrophe temperature corresponds to a temperature at which the discriminant is equal to 0 for the first time in the temperature rising process of coal spontaneous combustion, and the downgoing catastrophe temperature corresponds to a temperature at which the discriminant is equal to 0 for the first time in the temperature reduction process of coal spontaneous combustion.

6. The method of claim 5, wherein, The upgoing catastrophe temperature is a critical temperature point at which coal spontaneous combustion jumps from the low-temperature oxidation stage to the accelerated oxidation stage, and is used to warn the occurrence of coal spontaneous combustion; and the downgoing catastrophe temperature is a critical temperature point at which coal spontaneous combustion falls back from the accelerated oxidation stage to the low-temperature oxidation stage after taking fire extinguishing measures, and is used to determine whether a fire area has been completely extinguished.

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