A method for predicting flammable limit values and applications

Abstract

The present application relates to the technical field of oxygen-enriched combustion safety and flammability limit prediction, and provides a flammability limit value prediction method and application, which comprises the following steps: obtaining initial parameters of a gas fuel in an oxygen and carbon dioxide mixed atmosphere; simulating a combustion process by using a base reaction mechanism, and outputting a curve of component mole fraction changing with time; calculating a combustion enthalpy change rate in the target atmosphere and a virtual atmosphere based on the curve, wherein the carbon dioxide in the virtual atmosphere is replaced by a virtual gas with the same thermal properties but without chemical reactivity; respectively calculating a combustion heat release, a mixture heat absorption and a heat radiation; and combining the enthalpy change rate and an energy balance equation to determine the flammability limit value by numerical iteration. The present application quantifies the chemical effect and thermal physical influence of carbon dioxide, solves the problem of insufficient accuracy of existing models in the oxygen-enriched combustion environment due to the neglect of the reaction of carbon dioxide and its unique thermal properties, and is suitable for combustion system safety design.

Description

Technical Field

[0001] This invention relates to the field of oxygen-enriched combustion safety and flammability limit prediction technology, and particularly to a method and application for predicting flammability limit values. Background Technology

[0002] The flammability limit refers to the concentration range in which a flammable gas or vapor can sustain combustion in the air. Its existence is based on the fact that the combustion reaction requires a proper ratio of fuel and oxidant to support a continuous chain reaction. When the concentration is below the lower limit, there is too little fuel in the mixture, resulting in insufficient reaction energy and extinguishing the flame. When the concentration is above the upper limit, the relative lack of oxygen also hinders the spread of the flame. Therefore, the flammability limit has become the basic basis for assessing fire and explosion risks.

[0003] Current methods for predicting flammability limits suffer from several technical challenges. Specifically, in the application of oxy-fuel combustion systems in carbon capture, utilization, and storage (CFC) technologies, the combustion atmosphere is transformed from air to a mixture of oxygen and recirculated flue gas. High concentrations of carbon dioxide not only act as a diluent but also directly participate in the combustion chemical reaction, exhibiting significantly different specific heat capacity and radiation characteristics. This fundamentally alters the combustion reaction pathway and energy balance. However, classic flammability limit prediction models based on air combustion background data only consider the physical dilution effect of nitrogen, failing to account for the chemical effects and complex thermophysical influences of carbon dioxide. For example, when designing and evaluating the operating window of an oxy-fuel burner, using existing models to predict the upper flammability limit ignores the crucial process of carbon dioxide participating in the water-gas shift reaction to generate carbon monoxide and release heat under fuel-rich conditions. This leads to a predicted flammability range wider than the actual situation, potentially introducing safety hazards and increasing the risk of over-combustion or explosion when the combustion system approaches the predicted limit. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method and application for predicting flammability limits, solving the technical problem that the accuracy of existing flammability limit prediction models based on air combustion (such as the Le Chatelier formula) is severely insufficient due to the high chemical reactivity and unique thermophysical properties of CO2 in O2 / CO2 atmospheres.

[0005] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0006] In a first aspect, the present invention provides a method for predicting flammability limits, comprising:

[0007] Step 1: Obtain the initial parameters of the gaseous fuel in the target atmosphere, which includes oxygen and carbon dioxide, in the oxygen-enriched combustion system;

[0008] Step 2: Based on the initial parameters, simulate the combustion process of gaseous fuel in the target atmosphere using a predetermined elementary reaction chemical reaction mechanism. The simulation process outputs curves showing the change of mole fraction of each component over time during combustion.

[0009] Step 3: Based on the curve, calculate the rate of change of combustion enthalpy of gaseous fuel in the target atmosphere and in the virtual atmosphere, where carbon dioxide in the virtual atmosphere is replaced by a virtual gas with the same thermophysical and radiative properties but without chemical reactivity.

[0010] Step 4: Based on the curves, calculate the heat released during combustion, the heat absorbed by the mixture, and the amount of thermal radiation during the combustion process.

[0011] Step 5: Determine the flammability limit of the gaseous fuel under the target atmosphere based on the rate of change of combustion enthalpy, the heat released during combustion, the heat absorbed by the mixture, and the amount of thermal radiation.

[0012] Furthermore, the method for predicting the flammability limit of the present invention uses a predetermined elementary reaction chemical mechanism in the simulation process. The elementary reaction chemical mechanism includes the oxidation pathway of gaseous fuel and the reaction pathway involving carbon dioxide. The simulation process includes: under preset temperature and pressure conditions, taking the gaseous fuel concentration, oxygen concentration and carbon dioxide concentration in the initial parameters as input, and performing reaction kinetic calculations using the elementary reaction chemical mechanism; the reaction kinetic calculations generate curves, which include curves showing the change of the mole fraction of carbon monoxide, water vapor and carbon dioxide over time.

[0013] Furthermore, the method for predicting the flammability limit value described in this invention, based on a curve, calculates the rate of change of combustion enthalpy, including: obtaining the final component mole fraction and temperature of combustion under the target atmosphere from the curve; calculating the target atmosphere termination enthalpy based on the final component mole fraction and temperature; obtaining the final component mole fraction and temperature of combustion under the target atmosphere from the curve, and determining the virtual final component mole fraction and temperature of combustion under the virtual atmosphere by combining preset virtual gas properties; calculating the virtual atmosphere termination enthalpy based on the virtual final component mole fraction and temperature; subtracting the virtual atmosphere termination enthalpy from the target atmosphere termination enthalpy to obtain the enthalpy difference; and dividing the enthalpy difference by the virtual atmosphere termination enthalpy to obtain the rate of change of combustion enthalpy.

[0014] Furthermore, the method for predicting the flammability limit value described in this invention, based on a curve, calculates the heat release from combustion, the heat absorption of the mixture, and the thermal radiation, including: calculating the heat release from combustion using the final component mole fraction and thermochemical data of the gaseous fuel in the curve; calculating the heat absorption of the mixture using the temperature change data over time in the curve and the isobaric heat capacity data of each component in the target atmosphere; calculating the thermal radiation using the combustion temperature data in the curve and the radiation characteristic parameters of carbon dioxide; setting the heat release from combustion to be equal to the sum of the heat absorption of the mixture and the thermal radiation, and establishing an energy balance equation; solving the energy balance equation using a numerical iteration method, with the numerical iteration continuing until the difference between the heat release from combustion and the sum of the heat absorption and thermal radiation of the mixture is less than or equal to a preset tolerance range.

[0015] Furthermore, the method for predicting the combustible limit value described in this invention, which uses a numerical iterative method to solve the energy balance equation, includes: in a numerical computing programming environment, implementing the energy balance equation as a function with gaseous fuel concentration as the input variable; setting an initial value for the gaseous fuel concentration; using a numerical iterative algorithm to perform iterative calculations starting from the initial value of the gaseous fuel concentration; in each iterative calculation, inputting the current gaseous fuel concentration value into the function to obtain the difference between the heat released by combustion and the sum of the heat absorbed by the mixture and the thermal radiation; updating the gaseous fuel concentration value based on the difference for the next iterative calculation; stopping the iterative calculation when the difference is less than or equal to a preset tolerance range; and outputting the gaseous fuel concentration value used when the iterative calculation stopped.

[0016] Furthermore, the method for predicting the flammability limit value according to the present invention, which determines the flammability limit value based on the gaseous fuel concentration value, includes: setting multiple gaseous fuel concentration values ​​in ascending order; performing numerical iterative calculations for each set gaseous fuel concentration value, wherein the numerical iterative calculations include implementing the energy balance equation as a function with the gaseous fuel concentration as the input variable, and performing iterative calculations using a numerical iterative algorithm until the difference between the heat released by combustion and the sum of the heat absorbed by the mixture and the thermal radiation is less than or equal to a preset tolerance range; recording all gaseous fuel concentration values ​​that make the difference less than or equal to the preset tolerance range; and determining the smallest gaseous fuel concentration value as the lower flammability limit and the largest gaseous fuel concentration value as the upper flammability limit among the recorded values.

[0017] Furthermore, in the method for predicting the flammability limit value described in this invention, the gaseous fuel is an alkane gaseous fuel; when obtaining initial parameters, the number of carbon atoms and the number of hydrogen atoms of the alkane gaseous fuel are obtained; during the simulation process, the elementary reaction chemical reaction mechanism uses the number of carbon atoms and the number of hydrogen atoms to select an alkane oxidation reaction path that matches the number of carbon atoms and the number of hydrogen atoms from a predetermined reaction path library.

[0018] Furthermore, in the method for predicting the flammability limit of the present invention, the alkane gaseous fuel is n-butane, which has four carbon atoms and a chain structure. During the simulation process, the elementary reaction chemical reaction mechanism uses the four-carbon-atom and chain structure characteristics to select the n-butane oxidation path that matches the four-carbon-atom chain structure from a predetermined reaction path library.

[0019] Furthermore, in the method for predicting the flammability limit value described in this invention, the target atmosphere is a mixture of oxygen and carbon dioxide; when calculating the amount of thermal radiation, combustion temperature data is obtained from the curve, carbon dioxide concentration data is obtained from the target atmosphere, and the amount of thermal radiation is calculated using the combustion temperature data, carbon dioxide concentration data, and radiation characteristic parameters of carbon dioxide.

[0020] Secondly, the present invention provides an application of the aforementioned method for predicting flammability limits in the safety design of oxygen-enriched combustion systems.

[0021] The beneficial effects of this invention are:

[0022] The beneficial effects of this invention lie in simulating the combustion process of gaseous fuels in a mixed atmosphere of oxygen and carbon dioxide by introducing the chemical reaction mechanism of elementary reaction. It innovatively uses virtual atmosphere comparison to quantify the chemical reactivity of carbon dioxide, and combines energy balance equations and numerical iteration methods to solve the problem of insufficient accuracy of existing combustible limit prediction models based on air combustion due to neglecting the chemical effects and unique thermophysical properties of carbon dioxide. Thus, it can accurately predict the combustible limit value in an oxygen-enriched combustion environment, providing a reliable theoretical basis and practical evaluation tool for the safe design of combustion systems. Attached Figure Description

[0023] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on the drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating a method for predicting flammability limits. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The technical solutions provided by various embodiments of this invention will be described in detail below with reference to the accompanying drawings.

[0026] To better understand the purpose of this invention, the invention will now be described in further detail.

[0027] Firstly, please refer to Figure 1 The present invention provides a method for predicting flammability limits, comprising:

[0028] Step 1: Obtain the initial parameters of the gaseous fuel in the target atmosphere, which includes oxygen and carbon dioxide, in the oxygen-enriched combustion system;

[0029] Step 2: Based on the initial parameters, simulate the combustion process of gaseous fuel in the target atmosphere using a predetermined elementary reaction chemical reaction mechanism. The simulation process outputs curves showing the change of mole fraction of each component over time during combustion.

[0030] Step 3: Based on the curve, calculate the rate of change of combustion enthalpy of gaseous fuel in the target atmosphere and in the virtual atmosphere, where carbon dioxide in the virtual atmosphere is replaced by a virtual gas with the same thermophysical and radiative properties but without chemical reactivity.

[0031] Step 4: Based on the curves, calculate the heat released during combustion, the heat absorbed by the mixture, and the amount of thermal radiation during the combustion process.

[0032] Step 5: Determine the flammability limit of the gaseous fuel under the target atmosphere based on the rate of change of combustion enthalpy, the heat released during combustion, the heat absorbed by the mixture, and the amount of thermal radiation.

[0033] The flammability limit prediction method provided by this invention achieves accurate prediction of the flammability limit under oxy-fuel combustion conditions through a systematic technical solution. The method first obtains initial parameters of the gaseous fuel in a target atmosphere including oxygen and carbon dioxide in an oxy-fuel combustion system. These parameters include the gaseous fuel concentration, oxygen concentration, carbon dioxide concentration, and the system's set temperature and pressure conditions. Obtaining these initial parameters provides the basic input data for subsequent simulation calculations. The characteristic parameters of the gaseous fuel must include molecular structure information to match the corresponding chemical reaction pathways.

[0034] Based on the obtained initial parameters, the combustion process of gaseous fuels under a target atmosphere was simulated using a predetermined elementary reaction chemical mechanism. This mechanism includes the complete oxidation pathway of the gaseous fuel and key reaction pathways involving carbon dioxide, such as the water-gas shift reaction. The simulation was conducted under preset temperature and pressure conditions, and the mole fraction of each component during combustion was calculated and output as a function of time. The curves record the dynamic changes of key components such as carbon monoxide, water vapor, and carbon dioxide, providing quantitative evidence for subsequent analysis.

[0035] Based on the simulated curves, the enthalpy change rate of gaseous fuel combustion under the target atmosphere and the virtual atmosphere was calculated. The virtual atmosphere was constructed by replacing carbon dioxide in the target atmosphere with a virtual gas that has the same thermophysical and radiative properties but is not chemically reactive. The calculation process first obtains the final component mole fraction and temperature data of the combustion reaction under the target atmosphere from the curves, and calculates the termination enthalpy value using a thermodynamic database; then, based on the same curve data but considering the inert nature of the virtual gas, the termination enthalpy value under the virtual atmosphere was calculated; finally, by comparing the difference in termination enthalpy values ​​between the two atmospheres, the influence of carbon dioxide chemical reactivity on the combustion process was quantified.

[0036] Furthermore, based on the curve data, three energy terms—combustion heat release, mixture heat absorption, and thermal radiation—were calculated. Combustion heat release was calculated using the final product composition recorded on the curve combined with thermochemical data of the gaseous fuel; mixture heat absorption was calculated by integrating the temperature change data from the curve with the isobaric heat capacity parameters of each component; and thermal radiation was estimated using a gaseous radiation model based on the combustion temperature determined by the curve and the radiation characteristics of carbon dioxide. These calculations provide the necessary inputs for establishing the energy balance equation.

[0037] Finally, by combining the calculation results of the combustion enthalpy change rate and the energy balance equation, the flammability limit of the gaseous fuel under the target atmosphere is determined. The energy balance equation is solved using a numerical iterative method, systematically scanning the energy balance state under different gaseous fuel concentrations. The concentration value that first meets the convergence condition is determined as the lower flammability limit, and the concentration value that last meets the convergence condition is determined as the upper flammability limit. This process accurately reflects the combined influence of the chemical effects and thermophysical properties of carbon dioxide on the flammability range under oxygen-enriched combustion conditions.

[0038] Specifically, the method for predicting the flammability limit of the present invention uses a predetermined elementary reaction chemical mechanism in the simulation process. The elementary reaction chemical mechanism includes the oxidation pathway of gaseous fuel and the reaction pathway involving carbon dioxide. The simulation process includes: under preset temperature and pressure conditions, taking the gaseous fuel concentration, oxygen concentration and carbon dioxide concentration in the initial parameters as input, and performing reaction kinetic calculations using the elementary reaction chemical mechanism; the reaction kinetic calculations generate curves, which include curves showing the change of the mole fraction of carbon monoxide, water vapor and carbon dioxide over time.

[0039] In the flammability limit prediction method described in this invention, the simulation process relies on a predetermined elementary reaction chemical mechanism. This mechanism is specifically constructed to cover the complete oxidation pathway of gaseous fuels and key reaction pathways in which carbon dioxide may participate under oxy-fuel combustion conditions. For example, for alkane gaseous fuels, the mechanism includes stages such as fuel cracking, free radical chain reactions, and final product formation, while integrating specific pathways such as the water-gas shift reaction involving carbon dioxide, thereby forming a computable reaction network. The mechanism ensures the accuracy of the reaction kinetics simulation by defining the stoichiometric relationships, reaction rate constants, and thermodynamic parameters of each elementary reaction.

[0040] During the simulation, the initial parameters—gase fuel concentration, oxygen concentration, and carbon dioxide concentration—are quantified as mole fractions and used as input data under preset temperature and pressure conditions. These parameters collectively define the boundary conditions of the reaction system. The simulation process performs reaction kinetic calculations through elementary reaction chemical mechanisms, typically employing a numerical solver to handle rigid ordinary differential equations, iteratively solving for the concentration evolution of each component in the system. The calculation process adaptively adjusts the time step to capture the dynamic characteristics of both the rapid reaction phase and the equilibrium phase.

[0041] The reaction kinetics calculations output curves showing the mole fraction of each component changing over time, recording the concentration dynamics of key components such as carbon monoxide, water vapor, and carbon dioxide. The curves exhibit a typical S-shaped characteristic, reflecting the kinetic behavior during the ignition delay period, rapid reaction period, and equilibrium period. For example, the carbon monoxide concentration curve typically shows an initial increase followed by a decrease, with the peak time related to combustion intensity; water vapor concentration continues to increase until equilibrium is reached; and carbon dioxide concentration may exhibit nonlinear changes due to competition between formation and consumption pathways. These curves provide quantitative evidence for subsequent calculations of combustion enthalpy change rate and energy balance, serving as a crucial data source connecting the simulation process with flammability limit prediction.

[0042] Specifically, the method for predicting the flammability limit value described in this invention, based on a curve, calculates the rate of change of combustion enthalpy, including: obtaining the final component mole fraction and temperature of combustion under the target atmosphere from the curve; calculating the target atmosphere termination enthalpy based on the final component mole fraction and temperature; obtaining the final component mole fraction and temperature of combustion under the target atmosphere from the curve, and determining the virtual final component mole fraction and temperature of combustion under the virtual atmosphere by combining preset virtual gas properties; calculating the virtual atmosphere termination enthalpy based on the virtual final component mole fraction and temperature; subtracting the virtual atmosphere termination enthalpy from the target atmosphere termination enthalpy to obtain the enthalpy difference; and dividing the enthalpy difference by the virtual atmosphere termination enthalpy to obtain the rate of change of combustion enthalpy.

[0043] In the flammability limit prediction method described in this invention, the process of calculating the rate of change of combustion enthalpy based on curves aims to quantify the chemical effects of carbon dioxide in an oxygen-enriched combustion environment. The curves are derived from the data on the change of mole fraction of each component over time output from previous combustion simulations, where the final state corresponds to the reaction equilibrium point, providing the final mole fraction of the components and the system temperature required for the calculation.

[0044] The first step is to obtain the final mole fractions and temperatures of the components during combustion in the target atmosphere from the curves. The curves record the concentration evolution of key components such as carbon monoxide, water vapor, and carbon dioxide; the equilibrium data are obtained by extracting stable values ​​from the time series. This data serves as input for thermodynamic calculations, providing the basis for the termination enthalpy.

[0045] The target atmosphere termination enthalpy is calculated based on the final component mole fraction and temperature. This calculation relies on a standard thermodynamic database, weighting and integrating the mole fraction of each product with its corresponding formation enthalpy, and considering the temperature correction for the enthalpy. For example, in the case of n-butane combustion, the enthalpy contribution of all final products needs to be considered to reflect the actual combustion energy state.

[0046] To isolate the chemical effects of carbon dioxide, a virtual atmosphere comparison is introduced. The virtual atmosphere is achieved by replacing the carbon dioxide in the target atmosphere with a virtual gas that has the same thermophysical properties but no chemical reactivity. The final component mole fraction and temperature of the target atmosphere are obtained from the same curve, but the product composition is adjusted based on the properties of the virtual gas. Since the virtual gas does not participate in the reaction, pathways such as water-gas shift reactions are suppressed, and the carbon monoxide content in the virtual final component may be reduced, while carbon dioxide remains as an inert component.

[0047] The virtual atmosphere termination enthalpy is calculated based on the mole fraction of the virtual final components and temperature. The calculation process is similar to that of the target atmosphere, but the difference in product composition reflects the energy state under physical dilution only. The virtual atmosphere termination enthalpy is used as a benchmark to quantify the relative impact of chemical effects.

[0048] The enthalpy difference is obtained by subtracting the enthalpy of the virtual atmosphere from the enthalpy of the target atmosphere. This difference stems directly from the chemical reactivity of carbon dioxide. For example, under fuel-rich conditions, carbon dioxide participates in a reduction reaction to produce carbon monoxide, releasing additional heat and causing an increase in enthalpy.

[0049] Dividing the enthalpy difference by the enthalpy termination value of the virtual atmosphere yields the rate of change of combustion enthalpy. This normalized parameter eliminates the influence of absolute energy values, focusing on the proportional relationship of chemical effects and providing a key input for predicting flammability limits. This calculation process ensures consistency through curve data, helping to identify the quantitative impact of carbon dioxide concentration changes on the safe operating window in the design of oxygen-enriched combustion systems.

[0050] Specifically, the method for predicting the flammability limit value described in this invention, based on a curve, calculates the heat release from combustion, the heat absorption of the mixture, and the thermal radiation, including: calculating the heat release from combustion using the final component mole fraction and thermochemical data of the gaseous fuel in the curve; calculating the heat absorption of the mixture using the temperature change data over time in the curve and the isobaric heat capacity data of each component in the target atmosphere; calculating the thermal radiation using the combustion temperature data in the curve and the radiation characteristic parameters of carbon dioxide; setting the heat release from combustion to be equal to the sum of the heat absorption of the mixture and the thermal radiation, and establishing an energy balance equation; solving the energy balance equation using a numerical iteration method, with the numerical iteration continuing until the difference between the heat release from combustion and the sum of the heat absorption and thermal radiation of the mixture is less than or equal to a preset tolerance range.

[0051] In the flammability limit prediction method described in this invention, the process of calculating the heat release during combustion, the heat absorption of the mixture, and the thermal radiation based on curves is the core step in constructing the energy balance model. The curves are derived from the data on the change of mole fraction of each component over time output from previous combustion simulations, where the final state corresponds to the reaction equilibrium point, providing the key parameters required for the calculation.

[0052] When calculating the heat release from combustion, the mole fractions of the final components in the curve are used in conjunction with thermochemical data of the gaseous fuel. The curve records the mole fractions of products such as carbon monoxide, water vapor, and carbon dioxide when the combustion reaction reaches equilibrium. The data are weighted and integrated with the enthalpy of formation from a standard thermodynamic database to derive the theoretical heat release from combustion. For example, in the case of n-butane combustion, the total heat release effect needs to be calculated based on the concentration distribution of the final products to reflect the energy release characteristics of the fuel in an oxygen-rich atmosphere.

[0053] The calculation of the heat absorbed by the mixture relies on the temperature-time data in the curve and the isobaric heat capacity data of each component in the target atmosphere. The temperature change curve reflects the thermal history of the combustion process from the initial state to the equilibrium state. By integrating the isobaric heat capacity parameters of each component, the heat absorbed by the mixture during the heating process is quantified. The high specific heat capacity of carbon dioxide in an oxygen-enriched combustion environment significantly increases the heat absorbed, which needs to be reflected in the calculation through precise matching of isobaric heat capacity data.

[0054] The calculation of thermal radiation utilizes combustion temperature data from the curve and the radiation characteristic parameters of carbon dioxide. The combustion temperature curve provides the transient temperature distribution for radiation calculation. Combined with the spectral radiation characteristics of carbon dioxide in the infrared band, a gas radiation model is used to estimate energy loss. In practice, corrections need to be made based on the nonlinear effect of carbon dioxide concentration on radiation intensity. For example, in the design of oxygen-enriched burners, the radiative heat dissipation model is optimized by adjusting the concentration parameters.

[0055] The heat released during combustion is set to be equal to the sum of the heat absorbed by the mixture and the heat radiation, thus establishing an energy balance equation. This equation embodies the principle of energy conservation in a combustion system, where the released heat serves as the energy source, and the absorbed heat and radiation serve as dissipation pathways. All equation parameters are derived from the aforementioned calculation steps, ensuring the consistency of the data source and the integrity of the physical meaning.

[0056] The energy balance equation is solved using a numerical iterative method. Through iterative calculations, the difference between the heat released during combustion and the sum of the heat absorbed by the mixture and thermal radiation converges to a preset tolerance range. The iterative process is implemented in a programming environment, gradually adjusting the gaseous fuel concentration until the energy balance condition is met. This method can quickly verify the critical concentration under different operating conditions in the safety design of oxy-fuel combustion systems, providing a quantitative basis for determining the safe operating window. This calculation process, by coupling thermodynamics and radiative heat transfer principles, achieves precise quantification of energy flow under oxy-fuel combustion conditions.

[0057] Specifically, the method for predicting the combustible limit value described in this invention employs a numerical iterative method to solve the energy balance equation, including: in a numerical computing programming environment, implementing the energy balance equation as a function with gaseous fuel concentration as the input variable; setting an initial value for the gaseous fuel concentration; using a numerical iterative algorithm to perform iterative calculations starting from the initial value of the gaseous fuel concentration; in each iterative calculation, inputting the current gaseous fuel concentration value into the function to obtain the difference between the heat released by combustion and the sum of the heat absorbed by the mixture and the thermal radiation; updating the gaseous fuel concentration value based on the difference for the next iterative calculation; stopping the iterative calculation when the difference is less than or equal to a preset tolerance range; and outputting the gaseous fuel concentration value used when the iterative calculation stopped.

[0058] In the flammability limit prediction method described in this invention, solving the energy balance equation using a numerical iterative method is the key computational step for achieving accurate prediction of the flammability limit. This method dynamically adjusts the gaseous fuel concentration through a systematic iterative calculation process until the energy balance condition is met, thereby determining the critical concentration point. The iterative process is implemented in a numerical computing programming environment, such as using platforms like Python or MATLAB, to transform the energy balance equation into executable code, facilitating the automated processing of complex parameters in oxygen-enriched combustion systems.

[0059] In numerical computing programming environments, implementing the energy balance equation as a function with gaseous fuel concentration as input variable is fundamental to iterative calculations. The energy balance equation originates from the sum of previously calculated combustion heat release, mixture heat absorption, and thermal radiation; its form is that combustion heat release equals the sum of mixture heat absorption and thermal radiation. During programming, it's necessary to embed a thermochemical database of the gaseous fuel, isobaric heat capacity parameters of each component, and a radiation characteristic model of carbon dioxide to ensure the function can dynamically calculate the energy difference based on the input gaseous fuel concentration. For example, in the n-butane combustion case, the function will call the corresponding thermodynamic data and output the energy balance state at the current concentration in real time.

[0060] Setting an initial value for the gaseous fuel concentration is the starting point for iterative calculations. The initial value is chosen based on engineering experience or by referring to the flammability limits of similar combustion systems; for example, a lower concentration value is set starting from lean combustion conditions. In an oxygen-enriched combustion environment, the initial guess value must also consider the influence of carbon dioxide concentration to avoid the iteration process getting stuck in local convergence. In practice, the initial value is usually set near the midpoint of the estimated flammability range to reduce the number of iterations and improve computational efficiency.

[0061] Numerical iterative algorithms are used to perform iterative calculations starting from an initial value of the gaseous fuel concentration. Common algorithms include the Newton-Raphson method or the bisection method, which can efficiently handle the solution of nonlinear equations. The iterative process starts from the initial concentration, and the algorithm automatically calls the energy balance function to gradually approximate the true solution. In the design of oxy-fuel combustion systems, the algorithm selection must balance computational accuracy and speed to meet the needs of rapid evaluation under different operating conditions.

[0062] In each iteration, the current gaseous fuel concentration is input into the function to obtain the difference between the heat released during combustion and the sum of the heat absorbed by the mixture and the thermal radiation. This step is the core of the iteration; the difference returned by the function reflects the degree of deviation in energy balance at the current concentration. The calculation process needs to integrate curve data from previous simulations in real time, such as combustion temperature and mole fraction of each component, to ensure the accuracy of the difference calculation. A positive difference indicates excessive heat release, while a negative difference indicates excessive heat absorption or radiative loss, guiding the direction of subsequent concentration adjustments.

[0063] Based on the difference, the gaseous fuel concentration is updated for the next iteration. The update rule depends on the characteristics of the iterative algorithm; for example, in gradient descent, the concentration value is adjusted in the direction of decreasing difference. The update step size may be adaptively varied to avoid oscillations or divergence. In oxy-fuel combustion applications, the concentration update needs to consider the chemical effects of carbon dioxide; for example, in a high-concentration carbon dioxide atmosphere, the combustible range narrows, requiring a more cautious update strategy.

[0064] The loop calculation stops when the difference is less than or equal to the preset tolerance range. The tolerance range is set according to engineering accuracy requirements, such as a relative error threshold for energy values. Convergence conditions ensure the reliability of the results and avoid over-calculation. In flammability limit prediction, the tolerance range is usually set more strictly to capture subtle changes in the critical state and provide a reliable boundary for safety design.

[0065] The output displays the gaseous fuel concentration value used when the cyclic calculation stops; this value represents the critical point for achieving energy balance under current conditions. The output value is directly used to determine the flammability limits; for example, during concentration scanning, the first convergence point corresponds to the lower flammability limit. The numerical output can be integrated into an oxygen-enriched combustion control system to guide real-time adjustments to operating parameters and improve safety performance.

[0066] The iterative process links each step through a coherent data flow, gradually approximating physical reality from function implementation to convergence judgment. In the safety design of oxy-fuel combustion systems, this method replaces existing experimental trial-and-error methods, significantly improving prediction efficiency and accuracy. For example, in carbon capture systems, by adjusting the carbon dioxide concentration parameter, iterative calculations can quickly generate flammability limit curves, providing a theoretical basis for optimizing the proportion of recirculating flue gas.

[0067] Specifically, the method for predicting flammability limits according to the present invention, which determines flammability limits based on gaseous fuel concentration values, includes: setting multiple gaseous fuel concentration values ​​in ascending order; performing numerical iterative calculations for each set gaseous fuel concentration value, wherein the numerical iterative calculations include implementing the energy balance equation as a function with gaseous fuel concentration as the input variable, and performing iterative calculations using a numerical iterative algorithm until the difference between the heat released by combustion and the sum of the heat absorbed by the mixture and the thermal radiation is less than or equal to a preset tolerance range; recording all gaseous fuel concentration values ​​that make the difference less than or equal to the preset tolerance range; and determining the smallest gaseous fuel concentration value as the lower flammability limit and the largest gaseous fuel concentration value as the upper flammability limit among the recorded values.

[0068] In the flammability limit prediction method described in this invention, the process of determining the flammability limit based on the gaseous fuel concentration is achieved through systematic concentration scanning and iterative calculation. This method aims to accurately identify the concentration boundary at which fuel can maintain stable combustion in an oxygen-rich combustion environment, providing crucial data support for safety design. This process is executed automatically in a numerical computation programming environment, ensuring the reliability and efficiency of the results.

[0069] Setting multiple gaseous fuel concentration values ​​in ascending order is the starting point of the scanning process. The concentration values ​​are typically set using a constant step increment or an adaptive step increment strategy, covering the range from lean to rich combustion conditions. For example, for the case of n-butane in an oxygen and carbon dioxide mixed atmosphere, the concentration range can be set to 1% to 5%, with a step size of 0.1%, to fully capture subtle changes near the flammability limit. The concentration sequence is generated based on engineering experience or previous simulation data to avoid missing critical points.

[0070] Numerical iterative calculations are performed for each set gaseous fuel concentration. This calculation transforms the energy balance equation into a function with the gaseous fuel concentration as the input variable. The function encapsulates the calculation logic for combustion heat release, mixture heat absorption, and thermal radiation, integrating a thermochemical database and a radiation model. Numerical iterative algorithms, such as the Newton-Raphson method, are used for iterative calculations. Starting from the current concentration value, the algorithm gradually adjusts the input value until the difference between the combustion heat release and the sum of the mixture's heat absorption and thermal radiation converges to a preset tolerance range. The iterative process runs automatically within the programming platform, with each concentration point processed independently.

[0071] Record all gaseous fuel concentration values ​​that result in a difference less than or equal to a preset tolerance range; these values ​​correspond to states where energy balance is satisfied. The recording operation is implemented through a data array or log file, saving the convergence results of each iteration in real time. The tolerance range is set according to engineering accuracy requirements; for example, a relative error threshold of 0.1% is set to balance computational cost and accuracy. In the design of oxygen-enriched combustion systems, this step can process hundreds of concentration points in batches, quickly generating a candidate limit dataset.

[0072] Among the recorded values, the lowest gaseous fuel concentration is defined as the lower flammability limit (LVLP), and the highest is defined as the upper flammability limit (UPL). The LVLP represents the minimum fuel concentration at which a flame can propagate, reflecting the flameout boundary caused by insufficient fuel; the UPLP corresponds to the maximum fuel concentration, characterizing the critical point at which oxygen deficiency inhibits combustion. The determination process is completed by comparing extreme values ​​in the recorded array, and the result is directly output to the safety control system. For example, in oxygen-enriched combustion applications in gas turbines, the LVLP is used to set the minimum fuel supply threshold, while the UPLP guides the maximum injection quantity limit.

[0073] The process is determined by linking each step through a coherent data flow, from concentration scanning to limit identification, forming a closed-loop computational chain. In the scenario of carbon capture system optimization, this method can quickly assess the impact of different carbon dioxide concentrations on the combustible range, providing a quantitative basis for adjusting the proportion of recirculating flue gas. The automated process is significantly superior to manual experimental methods, supporting real-time safety monitoring and dynamic control.

[0074] Specifically, in the method for predicting the flammability limit value described in this invention, the gaseous fuel is an alkane gaseous fuel; when obtaining initial parameters, the number of carbon atoms and hydrogen atoms of the alkane gaseous fuel are obtained; during the simulation process, the elementary reaction chemical reaction mechanism uses the number of carbon atoms and hydrogen atoms to select an alkane oxidation reaction path that matches the number of carbon atoms and hydrogen atoms from a predetermined reaction path library.

[0075] In the flammability limit prediction method described in this invention, when the gaseous fuel is an alkane, the molecular structure characteristics of the fuel need to be clearly defined to support subsequent simulation calculations. Alkane gaseous fuels include common combustible gases such as methane, propane, and n-butane, and their combustion behavior is highly dependent on the number and arrangement of carbon and hydrogen atoms. In the initial parameter acquisition stage, the number of carbon and hydrogen atoms is directly obtained by analyzing the chemical formula of the gaseous fuel. For example, the chemical formula of n-butane includes four carbon atoms and ten hydrogen atoms. The number of each atom serves as a key input for fuel identification, providing a basis for matching the corresponding reaction pathway.

[0076] During the simulation, the elementary reaction chemical mechanism selects matching alkane oxidation reaction pathways from a pre-defined reaction pathway library based on the number of carbon and hydrogen atoms. This library is a dataset integrating complete reaction networks for various alkane fuels, with each pathway corresponding to a specific combination of carbon and hydrogen atoms. The mechanism automatically invokes the appropriate oxidation mechanism by comparing the input atom count with records in the library. Taking chain alkanes as an example, after identifying the number of carbon and hydrogen atoms, the system loads the corresponding reaction network, including fuel cracking, free radical chain propagation, and final product formation stages. This molecular structure-based matching method ensures that the simulation accurately reflects the chemical characteristics of specific fuels.

[0077] In practical applications, during the design of oxy-fuel combustion systems, engineers input the type of gaseous fuel, and the system automatically analyzes its carbon and hydrogen atom counts and maps them to the corresponding reaction pathways. For example, when processing propane fuel, the system utilizes the oxidation mechanism corresponding to three carbon atoms and eight hydrogen atoms. This automated process improves computational efficiency, avoids errors from manual selection, and supports rapid evaluation in multi-fuel scenarios. Through precise matching of atom counts and reaction pathways, the method adapts to the diversity of different alkane fuels, providing a reliable foundation for safety analysis under complex atmospheres.

[0078] Specifically, in the method for predicting the flammability limit of the present invention, the alkane gaseous fuel is n-butane, which has four carbon atoms and a chain structure. During the simulation process, the elementary reaction chemical reaction mechanism uses the four carbon atoms and chain structure features to select the n-butane oxidation path that matches the four carbon atom chain structure from a predetermined reaction path library.

[0079] In the flammability limit prediction method described in this invention, when the alkane gaseous fuel is specified as n-butane, its molecular structural characteristics should be fully utilized to guide the selection of the reaction pathway. n-Butane, as a common chain alkane, has a chemical formula consisting of four carbon atoms and ten hydrogen atoms, with the carbon atoms connected in a straight chain. This chain structure significantly affects the reaction pathway and intermediate product distribution during combustion. In the design of oxy-fuel combustion systems, n-butane is often used as a representative fuel to assess flammability limits because of its simple structure and typical combustion characteristics, facilitating model verification and engineering applications.

[0080] During the simulation, the elementary reaction chemical mechanism precisely selects the matching oxidation pathway from a predefined reaction pathway library by identifying the four carbon atoms and chain structure characteristics of n-butane. The reaction pathway library is a database integrating complete reaction networks of various alkane fuels, with each pathway corresponding to a specific number of carbon atoms and structural configuration. The mechanism system first analyzes the number of carbon atoms in the input fuel, confirming it to be four, and then further checks the chain structure markers to pinpoint the reaction group corresponding to n-butane. For example, in standard mechanism libraries such as GRI-Mech, the oxidation pathway of n-butane typically includes key steps such as initial C / C bond cleavage to generate ethyl and methyl radicals, secondary hydrocarbon extraction to generate sec-butyl radicals, and subsequent peroxy radical isomerization.

[0081] The selection process is automated within a numerical computation programming environment. The system uses the number of carbon atoms and structural features as query keys to scan the index table in the path library. When an entry with four carbon atoms and marked as a straight chain is found, the corresponding reaction equations and kinetic parameters are automatically loaded. This structural feature-based matching method avoids subjective errors from manual selection, ensuring the repeatability and accuracy of the simulation. In practice, engineers only need to input the fuel type as n-butane, and the system will automatically call the appropriate path without interfering with the underlying parameters.

[0082] The chain structure of n-butane results in a specific oxidation pathway. For example, the secondary carbon atom preferentially undergoes hydrogen extraction to generate sec-butyl radicals, which in turn affect the subsequent oxidation rate and intermediate product concentration. This structural correlation is particularly critical in oxy-fuel combustion environments because the presence of carbon dioxide can alter the equilibrium of the radical chain reaction. Pathways selected through structure matching can accurately capture these details, improving the reliability of flammability limit prediction.

[0083] In the safety design of oxy-fuel combustion systems, this method supports rapid evaluation of combustion behavior under different operating conditions. For example, when designing burners in carbon capture systems, the automatic invocation of the n-butane path allows for batch simulation of flame propagation characteristics under different carbon dioxide concentrations, providing data support for determining safe operating windows. This process runs efficiently in simulation platforms, replacing tedious experimental trial and error and significantly improving design efficiency.

[0084] Specifically, the method for predicting the flammability limit value described in this invention uses a target atmosphere that is a mixture of oxygen and carbon dioxide. When calculating the amount of thermal radiation, combustion temperature data is obtained from the curve, carbon dioxide concentration data is obtained from the target atmosphere, and the amount of thermal radiation is calculated using the combustion temperature data, carbon dioxide concentration data, and radiation characteristic parameters of carbon dioxide.

[0085] In the flammability limit prediction method described in this invention, when the target atmosphere is a mixture of oxygen and carbon dioxide, the calculation of thermal radiation needs to integrate dynamic data of the combustion process and atmospheric characteristic parameters. The composition of the mixed atmosphere is specifically defined by the oxygen and carbon dioxide concentrations in the initial parameters. For example, in the design of an oxygen-enriched combustion system, the carbon dioxide concentration can be set at a higher level according to the requirements of the carbon capture process. This atmosphere composition directly affects the radiative heat transfer process because carbon dioxide has significant radiation characteristics in a specific infrared band.

[0086] Extracting combustion temperature data from the simulation curves is a fundamental step in the calculation. The curves originate from time-series data output from the elementary reaction mechanism simulation, recording the dynamic changes in system temperature during combustion. For example, in the n-butane combustion case, the temperature curve shows a rapid rise after the ignition delay period followed by a subsequent equilibrium plateau, with peak temperatures reaching over 1600K. The temperature points and corresponding timestamps together constitute the time-series input for the radiation calculation.

[0087] The carbon dioxide concentration data in the target atmosphere is directly taken from the initial parameter settings. The concentration value is used in the calculation in the form of mole fraction, maintaining dimensional consistency with the thermodynamic data. In actual operation, this parameter can be obtained in real time through an online gas analyzer, or preset according to the process design value. In an oxygen-enriched combustion environment, the carbon dioxide concentration may reach over 70%, significantly higher than under existing air combustion conditions.

[0088] The calculation process utilizes a gas radiation model, taking combustion temperature data, carbon dioxide concentration, and carbon dioxide radiation characteristic parameters as inputs. The model is based on gas radiative transfer theory, considering the absorption and emission characteristics of carbon dioxide in characteristic wavelength bands such as 2.7 μm, 4.3 μm, and 15 μm. For non-isothermal conditions, a narrowband model or the correlated k-distribution method is used for spectral integration to calculate the radiative flux at a given path length.

[0089] In practice, engineers input temperature-time series and concentration parameters into a pre-programmed radiation calculation module. The module iteratively solves the radiative transfer equation, taking into account the effects of self-absorption and temperature non-uniformity. For example, in the design of tubular burners, the effective radiative layer thickness needs to be determined in conjunction with geometric parameters, and then the total heat loss is calculated.

[0090] In the safety assessment of oxy-fuel combustion systems, this method can quantify the impact of changes in carbon dioxide concentration on heat dissipation. When the proportion of recirculated flue gas increases, high concentrations of carbon dioxide enhance radiative heat dissipation, potentially altering the flammability limit. Through parametric analysis, designers can optimize the atmosphere composition to balance combustion efficiency with safety margins.

[0091] This calculation process achieves precise quantification of energy loss by coupling chemical reaction kinetics with the principle of radiative heat transfer. Compared to existing methods that ignore radiation, this invention significantly improves the reliability of predicting flammability limits under oxygen-rich conditions, providing crucial data support for the safety design of high-risk operating conditions.

[0092] Secondly, the present invention provides an application of the aforementioned method for predicting flammability limits in the safety design of oxygen-enriched combustion systems.

[0093] The combustible limit prediction method provided by this invention is applied to the safety design of oxy-fuel combustion systems. By integrating theoretical prediction models into engineering practice, it achieves precise quantification of the safety boundary of the combustion system. The application process begins with the collection of operating parameters of the oxy-fuel combustion system. For example, in the burner design phase of carbon capture and storage (CCS) technology, engineers need to obtain key data such as combustion chamber operating pressure, preheating temperature, and recirculated flue gas ratio. These parameters serve as input values ​​for the prediction model, providing a foundation for subsequent analysis. System design specifications typically require a clearly defined minimum safety margin, necessitating the use of the combustible limit prediction method to calculate the safe operating window at the current design point.

[0094] In practice, engineers transform the actual atmospheric conditions of the system into input parameters for the predictive model. Taking the oxy-fuel combustion system of a coal-fired power plant as an example, operators obtain real-time data on oxygen and carbon dioxide concentrations through online monitoring instruments, and simultaneously select the corresponding chemical reaction path based on fuel characteristics. For typical bituminous coal syngas, it is necessary to match a library of elementary reaction mechanisms corresponding to its complex components, thereby establishing a predictive model that conforms to actual operating conditions. This data conversion process ensures the consistency between the model input and the field conditions.

[0095] During the safety assessment phase, the carbon dioxide concentration parameters in the model are systematically adjusted to simulate the changing trends of the flammability limits under different circulating flue gas ratios. For example, in the optimization of an oxy-fuel combustion system for a gas turbine, the flammability limit is observed to decrease by gradually increasing the carbon dioxide concentration from 5% to 30%. Engineering case studies show that when the carbon dioxide concentration rises to a typical oxy-fuel combustion level, the flammability range narrows by approximately 15%. This dynamic predictive capability helps identify the risk of sudden changes in the flammability range that may occur during load regulation.

[0096] Combustion control system optimization directly utilizes predicted results to set safety interlock thresholds. In distributed control systems, the real-time calculated combustible limits are compared with the actual fuel concentration, triggering an early warning mechanism when the concentration approaches the safety boundary. For example, in an oxygen-enriched burner using n-butane fuel, the predicted lower combustible limit of 2.1% is set as the minimum fuel supply threshold, and the upper combustible limit of 3.8% is used as the injection quantity limit. The fuel valve opening is dynamically adjusted by a PID controller to maintain a safe distance between the operating point and the critical boundary.

[0097] In the emergency response plan development phase, a hazardous area map is created based on the predicted results for a leak scenario. Safety engineers quickly generate a flammable concentration distribution model by simulating atmosphere changes caused by a pipeline rupture. Taking a liquefied natural gas receiving terminal as an example, computational fluid dynamics simulations are used to map flammable limit data into three-dimensional space, providing a theoretical basis for emergency evacuation route design and monitoring instrument placement. This application significantly improves the emergency response capabilities of high-risk facilities.

[0098] This application process achieves engineering transformation through a numerical simulation platform, seamlessly integrating theoretical predictions with actual parameters. Designers can generate flammability limit curves for specific devices in batches by modifying the atmosphere composition data in the input file. In the iterative optimization of carbon capture systems, this method can complete safety assessments that would otherwise require weeks of verification in just a few hours, significantly improving design efficiency and reducing trial-and-error costs.

[0099] In implementing this invention, operators, considering the safety design requirements of the oxy-fuel combustion system, first collect the operating parameters of the target system. Taking an oxy-fuel burner in carbon capture and storage technology as an example, designers use gas chromatography to measure the concentration of each component in the mixture, obtaining the mole fraction values ​​of gaseous fuel concentration, oxygen concentration, and carbon dioxide concentration, while simultaneously recording the reactor ambient temperature and pressure conditions. These initial parameters serve as input values ​​for the prediction model, providing fundamental data for subsequent simulations. In the case of n-butane fuel, it is necessary to confirm that its molecular structure has four carbon atoms and ten hydrogen atoms to match the corresponding reaction pathway.

[0100] During the combustion simulation, a pre-defined elementary reaction chemical mechanism, such as the GRI-Mech 3.0 mechanism library, is used. Initial parameters are input into the chemical reaction kinetics solver, and numerical integration is performed under set temperature and pressure conditions. The simulation outputs curves showing the mole fraction of each component changing over time, recording the dynamic concentrations of carbon monoxide, water vapor, and carbon dioxide. For example, in the n-butane combustion case, the curve shows a rapid reaction phase following the ignition delay period, with the carbon monoxide concentration peaking at a specific time point, reflecting the combustion intensity characteristics.

[0101] When calculating the rate of change of combustion enthalpy, a virtual atmosphere is constructed for comparison based on simulated curves. The virtual atmosphere is achieved by replacing carbon dioxide in the target atmosphere with a virtual gas that has the same thermophysical properties but is not chemically reactive. The final component mole fraction and temperature data are extracted from the curves, and the termination enthalpy values ​​of the target atmosphere and the virtual atmosphere are calculated separately. The proportion of the difference between the two calculations to the termination enthalpy value of the virtual atmosphere quantifies the degree of influence of the chemical effect of carbon dioxide. This isolation method can accurately capture the energy change caused by carbon dioxide participating in the water-gas shift reaction under fuel-rich conditions.

[0102] During energy balance analysis, the heat released during combustion, the heat absorbed by the mixture, and the thermal radiation are calculated using curve data. The heat released during combustion is obtained from the final product composition combined with a thermochemical database. The heat absorbed by the mixture is calculated based on temperature change curves and the isobaric heat capacity integrals of the components. The thermal radiation is estimated based on combustion temperature and carbon dioxide radiation characteristic parameters. After establishing the energy balance equation, a numerical iterative method is used to solve it. In the programming environment, the gaseous fuel concentration is set as a variable, and the concentration value is adjusted through iterative calculations until the difference between the heat released, the heat absorbed, and the sum of the thermal radiation converges within the tolerance range.

[0103] When determining flammability limits, the system scans for different gaseous fuel concentrations. A concentration sequence is set from low to high, and iterative calculations are performed for each concentration point, recording all concentration values ​​that satisfy energy balance. The minimum concentration corresponds to the lower flammability limit, and the maximum concentration corresponds to the upper flammability limit. In the design of oxy-fuel combustion systems, this process can quickly generate safe operating windows. For example, adjusting carbon dioxide concentration parameters to simulate different circulating flue gas ratios can predict trends in flammability range changes, providing a basis for developing safety regulations.

[0104] The implementation process is automated through a numerical platform, replacing existing experimental methods. Engineers only need to input operating parameters, and the system can output the flammability limit curve, significantly improving design efficiency.

[0105] This invention simulates the combustion process of gaseous fuels in an oxygen-carbon dioxide mixed atmosphere by introducing an elementary reaction chemical mechanism. It innovatively employs a virtual atmosphere comparison to quantify the chemical reactivity of carbon dioxide. Combined with energy balance equations and numerical iteration methods, it solves the problem of insufficient accuracy in existing combustible limit prediction models under oxy-fuel combustion environments due to neglecting the chemical effects and thermophysical properties of carbon dioxide. Existing models, such as the LeChatelier formula, are developed based on air combustion and only consider the physical dilution effect of nitrogen. They fail to cover key reaction pathways such as carbon dioxide's participation in water-gas shift at high temperatures, nor do they include the complex impact of its high specific heat capacity and radiation characteristics on energy balance. This leads to prediction errors in combustible ranges in oxy-fuel combustion applications such as carbon capture systems.

[0106] In practice, the method first obtains the initial parameters of the gaseous fuel under the target atmosphere, including the gaseous fuel concentration, oxygen concentration, and carbon dioxide concentration. These parameters are derived from monitoring data of actual industrial systems, such as the mixture composition determined by gas chromatography during the design of oxygen-enriched burners. These parameters are then input into the elementary reaction chemical mechanism simulation stage. Mechanism libraries such as GRI-Mech 3.0 integrate the complete oxidation pathway of the gaseous fuel and the reaction network involving carbon dioxide. The simulation process runs under set temperature and pressure conditions, outputting curves showing the change in the molar fractions of components such as carbon monoxide, water vapor, and carbon dioxide over time, dynamically recording the characteristics of each stage of the combustion reaction. The curves show that the presence of carbon dioxide alters the formation rate of intermediate products, for example, delaying the water vapor formation process in the combustion of n-butane, revealing differences in the chemical reaction pathway.

[0107] To isolate the chemical effects of carbon dioxide, a virtual atmosphere is constructed as a reference. The virtual atmosphere replaces actual carbon dioxide with a virtual gas that has the same thermophysical properties but no chemical reactivity, maintaining consistent radiation and heat capacity parameters. By comparing the rate of change of combustion enthalpy between the target atmosphere and the virtual atmosphere, the energy change caused by carbon dioxide's participation in the reaction is quantified. The calculation process extracts the final product composition and temperature data from the simulation curve and derives the termination enthalpy value using a thermodynamic database. The proportion of the difference to the termination enthalpy value of the virtual atmosphere directly reflects the chemical contribution; for example, under fuel-rich conditions, the reduction reaction of carbon dioxide releases additional heat, significantly increasing the rate of change.

[0108] Energy balance analysis further integrates the thermophysical effects of carbon dioxide. Based on simulated curves, three key parameters are calculated: heat release during combustion, heat absorption by the mixture, and thermal radiation. The calculation of heat absorption incorporates the high isobaric heat capacity parameter of carbon dioxide to accurately reflect heat absorption during the heating process; thermal radiation is estimated using a model of carbon dioxide's radiation characteristics in the infrared band, combined with combustion temperature data. After establishing the equation that heat release equals heat absorption plus radiation, a numerical iterative method is used to solve it. The algorithm iteratively adjusts the gaseous fuel concentration within the programming environment until the energy difference converges to the tolerance range, automatically identifying the lower and upper flammability limits.

[0109] In the safety design scenario of oxy-fuel combustion systems, this method rapidly assesses the risks under different operating conditions through parametric analysis. For example, adjusting the carbon dioxide concentration simulates changes in the proportion of circulating flue gas, predicting the narrowing trend of the combustible range, and providing a basis for formulating operating procedures. This process is automated on a numerical platform, replacing existing experimental trial and error, and improving design efficiency and reliability.

[0110] Example 1 relates to the application of predicting the flammability limits of n-butane fuel in an oxy-fuel combustion system. During the design phase of oxy-fuel burners in carbon capture and storage (CCS) technology, engineers need to determine the safe operating window for n-butane in an oxygen and carbon dioxide mixed atmosphere. Operators use gas chromatography to measure the concentrations of each component in the mixture, obtaining the mole fraction values ​​of n-butane, oxygen, and carbon dioxide concentrations, while simultaneously recording the reactor ambient temperature and pressure conditions as initial parameters. The molecular structure of n-butane has a chain-like characteristic of four carbon atoms and ten hydrogen atoms, used to match the corresponding oxidation reaction pathway. The simulation process uses the GRI-Mech 3.0 elementary reaction chemical reaction mechanism, inputting the initial parameters into the chemical reaction kinetics solver, and performing numerical integration under set temperature and pressure conditions. The simulation outputs the mole fractions of carbon monoxide, water vapor, and carbon dioxide as a function of time. The curves show a rapid reaction phase after the ignition delay period, with the peak carbon monoxide concentration occurring at a specific time point. When calculating the enthalpy change rate of combustion based on curves, a virtual atmosphere is constructed by replacing carbon dioxide with the inert gas FCO2. The difference in the termination enthalpy between the actual atmosphere and the virtual atmosphere is compared to quantify the chemical effect of carbon dioxide participating in the water-gas shift reaction. Energy balance analysis uses curve data to calculate the heat release, heat absorption, and thermal radiation of the mixture, establishing an equation that the heat release equals the heat absorption plus the radiation. The Newton-Raphson iterative method is used to solve the equation, scanning the n-butane concentration range. When the concentration changes from low to high, the concentration point that first meets the convergence condition is determined as the lower flammability limit, and the final convergence point is determined as the upper flammability limit. This result is used to set the fuel supply threshold for the burner to avoid the risk of over-limit combustion.

[0111] Example 2 focuses on the methane flammability limit assessment of an oxy-fuel combustion system in a natural gas power plant. When optimizing the carbon capture system, it is necessary to predict the safe operating range of methane under high circulating flue gas proportions. Engineers obtain real-time data on methane, oxygen, and carbon dioxide concentrations through an online monitoring system, combined with ambient temperature and pressure parameters as input. The carbon number one and hydrogen number four of methane are used to invoke the corresponding oxidation pathway in the GRI-Mech mechanism. The simulation process generates a component change curve for methane combustion, showing that the water vapor generation rate slows down with increasing carbon dioxide concentration. When calculating the enthalpy change rate, virtual atmosphere comparison reveals that the chemical effect of carbon dioxide significantly increases the rate of change. In energy balance calculations, the high specific heat capacity of high-concentration carbon dioxide increases the heat absorption of the mixture, and the proportion of radiative heat dissipation increases with increasing temperature. Numerical iterative solutions to the energy balance equation yield the lower and upper flammability limits for different carbon dioxide concentrations. The data is integrated into a distributed control system, which compares the actual fuel concentration with the predicted limits in real time. When the actual fuel concentration approaches the safety boundary, a regulation mechanism is triggered to dynamically adjust the fuel injection quantity of the gas turbine. The application process uses a simulation platform to process different operating parameters in batches, quickly generating flammability range curves, providing a basis for formulating load adjustment strategies, and improving the system's resilience.

[0112] When obtaining initial parameters for gaseous fuel in an oxy-fuel combustion system under a target atmosphere containing oxygen and carbon dioxide, operators measure the concentration of each component in the mixture using a gas chromatograph or online gas analyzer to obtain the mole fraction values ​​of gaseous fuel concentration, oxygen concentration, and carbon dioxide concentration. Simultaneously, the ambient temperature and pressure conditions of the reactor are recorded. These initial parameters serve as input data for simulation calculations, ensuring the accuracy of the measurements and consistency with subsequent calculations. The measurement process requires instrument calibration to ensure data reliability, for example, by using standard gases for calibration, to avoid systematic errors.

[0113] When simulating the combustion process of gaseous fuels in a target atmosphere using predetermined elementary reaction chemical mechanisms, a standardized mechanism library such as GRI-Mech 3.0 is employed. This library includes the complete oxidation pathway of gaseous fuels and key reaction pathways involving carbon dioxide, such as the water-gas shift reaction. The simulation is run under preset temperature and pressure conditions, and the reaction kinetic equations are solved through numerical integration, outputting curves showing the mole fractions of components such as carbon monoxide, water vapor, and carbon dioxide as a function of time. These curves record the dynamic characteristics of the combustion reaction, providing a basis for subsequent analysis.

[0114] When constructing the virtual atmosphere, the carbon dioxide in the target atmosphere is replaced with a virtual gas that has the same molecular weight, isobaric heat capacity, and radiative emissivity parameters but is not chemically reactive. The thermophysical property data of the virtual gas is derived from a standard thermodynamic database, and the radiative characteristics are achieved by matching the spectral absorption coefficient of carbon dioxide in the infrared band. When calculating the rate of change of combustion enthalpy, the final component mole fraction and temperature data are extracted from the simulation curve, and the termination enthalpy values ​​of the target atmosphere and the virtual atmosphere are calculated separately. The difference in termination enthalpy values ​​between the two atmospheres is compared to quantify the degree of influence of the chemical effect of carbon dioxide.

[0115] The heat release from combustion, the heat absorption of the mixture, and the thermal radiation are calculated based on simulated curves. The heat release from combustion is calculated using the mole fraction of the final products combined with thermochemical data of the gaseous fuel; the heat absorption of the mixture is obtained from the integral temperature change curve and the isobaric heat capacity data of each component; the thermal radiation is estimated using a gaseous radiation model based on the combustion temperature and carbon dioxide radiation characteristics. After establishing the energy balance equation, a numerical iterative method is used to solve it, such as the Newton-Raphson algorithm, adjusting the gaseous fuel concentration until the energy difference converges to the tolerance range.

[0116] When determining the flammability limits, a sequence of gaseous fuel concentration values ​​is set from low to high, and iterative calculations are performed for each concentration point. All concentration values ​​that satisfy energy balance are recorded, with the minimum concentration value determined as the lower flammability limit and the maximum concentration value as the upper flammability limit. This process is automated in a programming environment, ensuring the repeatability and accuracy of the results and providing a reliable basis for the safe design of oxygen-enriched combustion systems.

[0117] The rate of change of combustion enthalpy is a key parameter of this invention, used to quantify the chemical effects of carbon dioxide in an oxygen-rich combustion environment. Specifically, it is calculated by comparing the difference in combustion enthalpy between a target atmosphere (the actual combustion atmosphere, including oxygen and carbon dioxide) and a virtual atmosphere (where carbon dioxide is replaced by a virtual gas with the same thermophysical properties but no chemical reactivity). The calculation process is based on the component mole fraction curves output from elementary reaction simulations: first, the final component mole fractions and temperatures for combustion in the target atmosphere are obtained from the curves, and the termination enthalpy is calculated using a thermodynamic database; then, based on the same curve data but considering the inert nature of the virtual gas, the product composition is adjusted (e.g., suppressing the water-gas shift reaction involving carbon dioxide), and the termination enthalpy of the virtual atmosphere is calculated; finally, the ratio of the difference in enthalpy between the two to the termination enthalpy of the virtual atmosphere is defined as the rate of change of combustion enthalpy. This parameter directly reflects the contribution of carbon dioxide's participation in chemical reactions (such as reduction reactions under fuel-rich conditions) to energy release, avoiding the shortcomings of existing models that only consider physical dilution. In the technical solution of this invention, the combustion enthalpy change rate is used as the core input for energy balance analysis to correct the calculation of combustion heat release, ensuring accurate capture of the chemical influence of carbon dioxide when predicting the combustible limit, thereby improving the accuracy of the safety design of the oxygen-enriched combustion system.

[0118] The virtual atmosphere serves as the benchmark for comparison in this invention, aiming to isolate the thermophysical properties and chemical effects of carbon dioxide for independent evaluation of its reactivity. The virtual atmosphere is constructed by replacing the carbon dioxide in the target atmosphere with a virtual gas (such as the inert gas FCO2) having the same molecular weight, isobaric heat capacity, and radiation characteristics but not participating in the chemical reaction. This ensures that the thermophysical parameters (such as specific heat capacity and emissivity) are consistent with actual carbon dioxide, but eliminates its chemical reactivity. This design allows for comparison during combustion simulation by altering only the reactivity of the gas, rather than its thermophysical behavior, thereby purifying the analytical conditions. In the technical solution of this invention, the application of the virtual atmosphere is mainly reflected in the calculation of the combustion enthalpy change rate: by comparing the difference in the terminal enthalpy values ​​between the target atmosphere and the virtual atmosphere, the specific contribution of the chemical effect of carbon dioxide is quantified (for example, in the case of n-butane combustion, the lack of carbon dioxide participation in the reaction under the virtual atmosphere may lead to a reduction in carbon monoxide formation and a decrease in enthalpy). Furthermore, the virtual atmosphere provides a reference basis for the energy balance equation, helps identify the impact of carbon dioxide's high specific heat capacity and radiation characteristics on the heat absorption and thermal radiation of the mixture, and ultimately ensures that the prediction results are not affected by model simplification errors when solving the flammability limit through numerical iteration, thereby enhancing the reliability of oxygen-enriched combustion risk assessment.

[0119] The elementary reaction chemical reaction mechanism is the core of this invention's simulation. It is a predetermined detailed chemical reaction network covering the complete oxidation pathway of gaseous fuels and key reaction pathways involving carbon dioxide (such as the water-gas shift reaction). Based on molecular structural characteristics (such as the number of carbon and hydrogen atoms in alkane fuels), this mechanism selects matching reaction pathways from a pre-set library (e.g., the chain oxidation mechanism of n-butane corresponding to four carbon atoms). Under preset temperature and pressure conditions, it solves a rigid set of ordinary differential equations through reaction kinetics calculations, outputting curves showing the change in mole fraction of each component over time (e.g., the concentration evolution of carbon monoxide, water vapor, and carbon dioxide). The advantage of this mechanism is its ability to accurately capture the chemical role of carbon dioxide in oxygen-enriched combustion environments. For example, during the rapid reaction phase, carbon dioxide may affect the free radical chain reaction rate through intermediates. In this invention's technical solution, the elementary reaction chemical reaction mechanism is applied to the combustion process simulation in step 2: it takes initial parameters (gase fuel concentration, oxygen concentration, and carbon dioxide concentration) as input and generates dynamic curves through numerical integration, providing a data basis for subsequent calculations of combustion enthalpy change rate, combustion heat release, mixture heat absorption, and thermal radiation. Specifically, the curve data reveals the characteristics of each stage of combustion (such as ignition delay and equilibrium state), enabling energy balance analysis to integrate chemical reaction kinetics and thermodynamics. Ultimately, the combustible limit value is determined through iterative solution, which solves the prediction bias caused by neglecting the carbon dioxide reaction path in existing models and provides theoretical support for the optimization of oxygen-enriched combustion systems.

[0120] The simulated combustion process calculation predicts the dynamic behavior of gaseous fuels in an oxygen-enriched combustion environment through chemical reaction kinetic models, aiming to obtain detailed data on the changes in the concentration of each component over time, providing a foundation for subsequent analysis. In this invention, the calculation uses a predetermined elementary reaction chemical mechanism (such as the GRI-Mech 3.0 mechanism library), which integrates the complete oxidation pathway of gaseous fuels and key reactions involving carbon dioxide (e.g., water-gas shift reaction). The calculation path includes: taking the gaseous fuel concentration, oxygen concentration, carbon dioxide concentration, and preset temperature and pressure conditions as inputs, solving the reaction kinetic equations through numerical integration to generate curves showing the mole fraction of components such as carbon monoxide, water vapor, and carbon dioxide as a function of time. The curves record the complete process from the ignition delay period to the equilibrium state, such as the peak characteristics of carbon monoxide concentration in n-butane combustion, providing data support for quantifying the carbon dioxide effect.

[0121] The calculation of the rate of change of combustion enthalpy is used to isolate the chemical influence of carbon dioxide, quantifying its reactivity contribution by comparing the energy difference between the actual atmosphere and the virtual atmosphere. The specific calculation path is as follows: The final mole fraction and temperature data of the combustion reaction under the target atmosphere are obtained from the simulation curve, and the termination enthalpy is calculated using a thermodynamic database; simultaneously, based on the same curve but with carbon dioxide replaced by a virtual gas with the same thermophysical properties and no chemical reactivity, the product composition is adjusted (e.g., suppressing the water-gas shift reaction), and the virtual atmosphere termination enthalpy is calculated; finally, the difference between the two termination enthalpies is divided by the virtual atmosphere termination enthalpy to obtain the normalized rate of change. This parameter directly reflects the energy change caused by carbon dioxide's participation in the reaction; for example, under fuel-rich conditions, its reduction reaction releases additional heat, providing input for correcting the energy balance.

[0122] Calculate the termination enthalpy (H_actual) under the target atmosphere.

[0123] Calculate the termination enthalpy (H_virtual) under the virtual atmosphere.

[0124] Calculate the enthalpy difference: ΔH_diff = H_actual - H_virtual.

[0125] Calculate the "rate of change of combustion enthalpy": η = ΔH_diff / H_virtual.

[0126] The calculation of heat release from combustion, heat absorption by the mixture, and thermal radiation is the core of constructing the energy balance model, aiming to accurately quantify the energy flow and loss during combustion. The calculation paths are based on simulation curves: the heat release from combustion is obtained by integrating the mole fraction of the final product with thermochemical data of the gaseous fuel (such as the enthalpy of formation); the heat absorption by the mixture is solved by integrating the temperature-time curve and the isobaric heat capacity data of each component, incorporating the high specific heat capacity of carbon dioxide; and the thermal radiation is estimated using a gaseous radiation model based on the combustion temperature curve and the radiation characteristic parameters of carbon dioxide (such as the infrared absorption coefficient). All three are substituted into the energy balance equation (heat release = heat absorption + radiation), providing a basis for iterative solutions.

[0127] Numerical iterative solution to the energy balance equation determines the critical concentration of gaseous fuel that satisfies energy conservation through iterative calculations, ensuring the accuracy of flammability limit prediction. The calculation path is implemented in a programming environment: the energy balance equation is set as a function of the gaseous fuel concentration. After setting an initial concentration value, an algorithm (such as the Newton-Raphson method) is used for iterative calculation. In each iteration, the current concentration value is input, the difference between the sum of heat release, heat absorption, and radiation is calculated, and the concentration value is updated based on this difference until it converges to a preset tolerance range. This process automatically adjusts the concentration step size to avoid divergence, and finally outputs the concentration value at convergence, which is used to identify the energy balance state.

[0128] The determination of flammability limits involves systematically scanning different gaseous fuel concentrations to identify the concentration boundaries at which the flame can propagate. The calculation path includes: setting a concentration sequence from low to high; performing the above numerical iterative calculation at each concentration point; recording all concentration values ​​that bring the energy balance difference to converge; and finally, taking the minimum concentration as the lower flammability limit (flameout point due to insufficient fuel) and the maximum concentration as the upper flammability limit (oxygen deficiency inhibition point). For example, in the case of oxy-fuel combustion of n-butane, this process rapidly generates a safe operating window by batch processing concentration data, providing a reliable boundary for combustion system design.

Claims

1. A method of predicting flammable limit values, characterized in that, The method comprises: Step 1, obtaining initial parameters of a gas fuel in a target atmosphere comprising oxygen and carbon dioxide in an oxy-combustion system; Step 2, based on the initial parameters, simulating a combustion process of the gas fuel in the target atmosphere using a predetermined elementary reaction chemical reaction mechanism, the simulation process outputting a curve of the molar fraction of each component changing with time in the combustion process, the curve comprising a curve of the molar fraction of carbon monoxide, water vapor and carbon dioxide changing with time; Step 3, based on the curve, calculating a change rate of the enthalpy change of the gas fuel in the target atmosphere and in a virtual atmosphere, wherein the carbon dioxide in the virtual atmosphere is replaced by a virtual gas having the same thermal properties and radiation characteristics but without chemical reactivity; Step 4, based on the curve, respectively calculating a combustion heat release amount, a mixture heat absorption amount and a heat radiation amount of the combustion process; Step 5, based on the change rate of the enthalpy change, the combustion heat release amount, the mixture heat absorption amount and the heat radiation amount, determining a flammable limit value of the gas fuel in the target atmosphere.

2. The flammable limit value prediction method according to claim 1, characterized by, The simulation process uses a predetermined elementary reaction chemical reaction mechanism, and the elementary reaction chemical reaction mechanism comprises an oxidation path of the gas fuel and a reaction path involving carbon dioxide; the simulation process comprises: under preset temperature and pressure conditions, using the elementary reaction chemical reaction mechanism to perform reaction kinetics calculation with the gas fuel concentration, the oxygen concentration and the carbon dioxide concentration in the initial parameters as inputs; the reaction kinetics calculation generates the curve.

3. The flammable limit value prediction method according to claim 2, characterized in that, Based on the curve, the calculation of the change rate of the enthalpy change comprises: obtaining the final component molar fraction and temperature of the combustion in the target atmosphere from the curve, and calculating a target atmosphere termination enthalpy value based on the final component molar fraction and the temperature; obtaining the final component molar fraction and temperature of the combustion in the target atmosphere from the curve, and determining a virtual final component molar fraction and temperature of the combustion in the virtual atmosphere in combination with the preset virtual gas properties, and calculating a virtual atmosphere termination enthalpy value based on the virtual final component molar fraction and the temperature; subtracting the virtual atmosphere termination enthalpy value from the target atmosphere termination enthalpy value to obtain an enthalpy difference value; dividing the enthalpy difference value by the virtual atmosphere termination enthalpy value to obtain the change rate of the enthalpy change.

4. The flammable limit value prediction method according to claim 3, characterized in that, Based on the curve, the respective calculation of the combustion heat release amount, the mixture heat absorption amount and the heat radiation amount comprises: using the final component molar fraction in the curve and the thermochemical data of the gas fuel to calculate the combustion heat release amount; using the temperature changing data in the curve and the constant-pressure heat capacity data of each component in the target atmosphere to calculate the mixture heat absorption amount; using the combustion temperature data in the curve and the radiation characteristic parameters of carbon dioxide to calculate the heat radiation amount; setting the combustion heat release amount to be equal to the sum of the mixture heat absorption amount and the heat radiation amount to establish an energy balance equation; solving the energy balance equation by using a numerical iteration method, and the numerical iteration is continuously performed until the difference between the combustion heat release amount and the sum of the mixture heat absorption amount and the heat radiation amount is less than or equal to a preset tolerance range.

5. The flammable limit value prediction method according to claim 4, characterized in that, Solving the energy balance equation by using the numerical iteration method comprises: in a numerical calculation programming environment, implementing the energy balance equation as a function with the gas fuel concentration as an input variable; setting an initial value for the gas fuel concentration; using a numerical iteration algorithm to perform a loop calculation starting from the initial value of the gas fuel concentration; in each loop calculation, inputting the current gas fuel concentration value into the function to obtain a difference between the heat released by combustion and the sum of the heat absorbed by the mixture and the heat radiation; based on the difference, updating the gas fuel concentration value for the next loop calculation; stopping the loop calculation when the difference is less than or equal to a preset tolerance range; and outputting the gas fuel concentration value used when the loop calculation is stopped.

6. The flammable limit value prediction method according to claim 5, characterized in that, Determining the flammable limit value based on the gas fuel concentration value comprises: setting a plurality of gas fuel concentration values in order from low to high; performing numerical iteration calculation on each set gas fuel concentration value, the numerical iteration calculation comprising implementing the energy balance equation as a function with the gas fuel concentration as an input variable, using a numerical iteration algorithm to perform a loop calculation until the difference between the heat released by combustion and the sum of the heat absorbed by the mixture and the heat radiation is less than or equal to a preset tolerance range; recording all gas fuel concentration values that make the difference less than or equal to the preset tolerance range; and among the recorded values, determining the smallest gas fuel concentration value as the lower flammable limit and the largest gas fuel concentration value as the upper flammable limit.

7. The flammable limit value prediction method according to claim 6, characterized in that, The gas fuel is an alkane gas fuel; when the initial parameters are obtained, the number of carbon atoms and the number of hydrogen atoms of the alkane gas fuel are obtained; and in the simulation process, the number of carbon atoms and the number of hydrogen atoms are used by the elementary reaction chemical reaction mechanism to select an alkane oxidation reaction path matching the number of carbon atoms and the number of hydrogen atoms from a predetermined reaction path library.

8. The flammable limit value prediction method according to claim 7, characterized in that, The alkane gas fuel is n-butane, the number of carbon atoms of the n-butane is four and the n-butane has a chain structure; and in the simulation process, the number of carbon atoms and the chain structure feature are used by the elementary reaction chemical reaction mechanism to select an n-butane oxidation path matching the number of carbon atoms and the chain structure from a predetermined reaction path library.

9. The flammable limit value prediction method according to claim 8, characterized in that, The target atmosphere is a mixed atmosphere of oxygen and carbon dioxide; and when the heat radiation amount is calculated, combustion temperature data are obtained from the curve, carbon dioxide concentration data are obtained from the target atmosphere, and the heat radiation amount is calculated using the combustion temperature data, the carbon dioxide concentration data, and the radiation characteristic parameters of carbon dioxide.

10. Use of the flammable limit value prediction method according to any one of claims 1-9 in the safety design of an oxygen-enriched combustion system.

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