A simulation method for leakage characteristics of high-pressure hydrogen-doped natural gas pipeline based on CFD

Abstract

The application discloses a high-pressure hydrogen-doped natural gas pipeline leakage characteristic simulation method based on CFD and belongs to the technical field of oil and gas safety, which comprises the following steps: step 1, determining a leakage working condition and calculating a jet flow condition of a leakage hole; step 2, establishing a jet flow area geometric model and dividing a grid; step 3, establishing and solving a jet flow model; step 4, analyzing jet flow characteristics and determining diffusion source intensity; step 5, establishing a diffusion area geometric model and dividing a grid; step 6, establishing and solving a diffusion model; and step 7, analyzing hydrogen-doped natural gas diffusion characteristics and determining an explosion danger distance. The diffusion source intensity calculated in the jet flow model is used as an inlet boundary of a subsequent diffusion model, so that the whole leakage field can be accurately described, the problem that an under-expanded jet flow structure of a leakage hole cannot be captured due to the limitation of calculation resources in the prior art is overcome, and the subsequent diffusion concentration field cannot be accurately described, and the method can provide guidance for the safety management of the hydrogen-doped natural gas pipeline.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil and gas safety, and particularly relates to a high-pressure hydrogen-doped natural gas pipeline leakage characteristic simulation method based on CFD. BACKGROUND

[0002] Hydrogen energy is a recognized clean energy with broad application prospects. It has the advantages of convenient storage and transportation, diverse utilization methods, high utilization rate, and wide sources, and can help solve energy crisis, global warming, and environmental pollution. The low heat value of hydrogen is more than twice that of traditional fuels such as natural gas and gasoline, and the combustion product is only water, which means zero carbon emissions. Unlike traditional fossil fuels, hydrogen energy can become an important way to promote energy reform and achieve carbon neutrality. Hydrogen transportation is an important link in the hydrogen energy industry chain. For long-distance transportation of hydrogen, pipeline is undoubtedly an economical and efficient choice. In order to shorten the transition period and take into account economic and safety factors, adding a certain proportion of hydrogen to natural gas and using existing natural gas pipelines or networks for transportation may be the best way to achieve large-scale hydrogen transportation.

[0003] At present, natural gas pipeline transportation technology has basically matured, but after adding hydrogen, new technical and safety problems will be brought. Methane and hydrogen are both flammable and explosive gases, with explosion limit ranges of 5-15 vol% and 4-75.6 vol%, respectively. Due to the more easily leaking nature of hydrogen, its wider explosion limit range in air, and its much lower minimum ignition energy than methane, the addition of hydrogen will exacerbate the risk of combustion and explosion accidents after pipeline leakage.

[0004] Gas leakage expansion has two flow states: critical and subcritical. Critical flow refers to the expansion of gas through the leakage port, with the flow rate reaching the local sound speed at the outlet and the flow reaching the maximum value, but the pressure is not expanded to atmospheric pressure. After the gas flows out of the leakage port, it continues to expand and depressurize, forming an under-expanded jet pattern. Subcritical flow refers to the complete expansion of gas to atmospheric pressure at the leakage port, forming a free jet outside the leakage port. When the operating pressure of a hydrogen-doped natural gas pipeline is greater than the critical pressure (0.19 MPa), an under-expanded jet will be formed. The operating pressure range of high-pressure long-distance pipelines is 1.5-12 MPa, which is much higher than the critical pressure, so the leakage of high-pressure hydrogen-doped natural gas pipelines is critical flow. Critical flow gas forms a complex under-expanded jet structure outside the leakage port, which has a significant impact on the diffusion of gas in the far field.

[0005] In order to capture the detailed features of the under-expanded jet, very dense grids are required. In addition, the time step required for transient CFD simulation of under-expanded jets is 10 -7 -10 -5On the other hand, diffusion modeling is very space-consuming. The leaking gas needs to diffuse in a large enough area to avoid the adverse effects of boundary conditions. For the overall CFD model including the leakage and diffusion domains, the required calculation time is unacceptable. Therefore, the present application proposes a CFD-based simulation method for the leakage characteristics of high-pressure hydrogen-doped natural gas pipelines, which divides the leakage process of high-pressure hydrogen-doped natural gas pipelines into a near-field jet stage and a far-field diffusion stage, and uses the diffusion source strength calculated in the jet model as the subsequent diffusion model entrance boundary to achieve an accurate description of the entire leakage field. SUMMARY

[0006] The present application divides the leakage process of high-pressure hydrogen-doped natural gas pipelines into a near-field jet stage and a far-field diffusion stage, uses the diffusion source strength calculated in the jet model as the subsequent diffusion model entrance boundary, proposes a CFD-based simulation method for the leakage characteristics of high-pressure hydrogen-doped natural gas pipelines, and overcomes the problem that the existing method cannot capture the under-expanded jet structure of the leakage port due to the limitation of computing resources, and thus cannot accurately describe the subsequent diffusion concentration field.

[0007] The present application is implemented by the following technical solutions:

[0008] The CFD-based simulation method for the leakage characteristics of high-pressure hydrogen-doped natural gas pipelines described above includes the following steps:

[0009] Step 1: Select a typical high-pressure hydrogen-doped natural gas pipeline leakage process as the research object, divide the high-pressure hydrogen-doped natural gas pipeline leakage process into a near-field jet stage and a far-field diffusion stage, determine the high-pressure hydrogen-doped natural gas pipeline leakage conditions, mainly including pipeline operating pressure, leakage hole diameter, and hydrogen doping ratio, and calculate the jet conditions of the leakage hole.

[0010] The calculation formula of the pressure, temperature, density, and flow rate of hydrogen-doped natural gas at the leakage hole is as follows:

[0011]

[0012]

[0013] In the formula, P0 is the pipeline operating pressure, Pa; T0 is the pipeline operating temperature, K; γ is the adiabatic index; R is the universal gas constant; P is the pressure at the leakage hole, Pa; T is the temperature at the leakage hole, K; ρ is the density of hydrogen-doped natural gas at the leakage hole, kg / m3; u is the flow rate of hydrogen-doped natural gas at the leakage hole, m / s. e e e 3 e

[0014] The calculation formula of the leakage rate of critical flow is as follows: ​​​​​

[0015]

[0016] where: Q is the gas leakage rate, kg / s; A e is the leakage hole area, m 2 ;

[0017] Step 2, establish the geometry model of the jet flow area; adopt a two-dimensional axisymmetric calculation domain to reduce the cost of computing resources, the jet flow model is composed of a leakage hole and an ambient atmospheric area; adopt a non-structured mesh division method to divide the mesh of the jet flow area; the velocity and pressure gradient of the under-expanded jet flow structure are relatively large, in order to reduce the calculation time and ensure the accuracy of numerical simulation, the mesh near the leakage hole is locally encrypted; and the mesh independence of the jet flow area is verified;

[0018] Step 3, establishment and solution of the jet flow CFD model; the control equations include mass, momentum and energy conservation equations, the component transport equation calculates the molar fraction of each component of hydrogen-doped natural gas, the state equation selects the Peng-Robinson equation, and the turbulence model selects the k-ε model; the inlet boundary condition of the jet flow model is determined according to the jet flow condition of the leakage hole, and the outlet boundary adopts pressure outlet; due to the very high velocity of the near-field jet flow, the influence of gravity can be ignored; a double-precision pressure solver is selected, and the SIMPLE algorithm is used for pressure-velocity coupling; in order to ensure the calculation accuracy, the turbulent kinetic energy and turbulent dissipation rate are discretized by the second-order upwind format, and the transient equation is discretized by the second-order implicit format; the time step is set to 10 -5 s, the time step number is 5000 steps, and the maximum iteration number of the time step is 50 times;

[0019] Step 4, analyze the jet flow characteristics of high-pressure hydrogen-doped natural gas; because the jet flow velocity reaches the speed of sound, the jet flow area will reach a steady state in a short time, only the flow field characteristics after the jet flow field is stable are analyzed; the velocity, Mach number, pressure, temperature, H2 molar fraction and CH4 molar fraction of the jet flow area are determined; the diffusion source intensity (velocity, temperature, H2 molar fraction and CH4 molar fraction, etc.) at the 10x m (x m is the distance from the jet flow outlet to the Mach disk) cross section is fitted by using a nonlinear curve fitting Boltzmann model, and is used as the inlet boundary of the diffusion model, which can ensure that the supersonic and oscillation regions are avoided;

[0020] The calculation formula of the distance from the jet flow outlet to the Mach disk is:

[0021]

[0022] where: x m is the distance from the jet flow outlet to the Mach disk, m; P a is the external environment pressure, Pa; de Leak hole diameter, m; Boltzmann model equation form:

[0023]

[0024] In the formula: A1, A2, x0 and dx are fitting parameters;

[0025] Step 5, a three-dimensional diffusion region geometric model is established; the calculation domain is discretized in the form of hexahedral elements, and mesh refinement is carried out around the diffusion model inlet section and near the ground; the mesh of the diffusion model is verified for irrelevance;

[0026] Step 6, establishment and solving of the diffusion CFD model; the control equations include mass, momentum and energy conservation equations, the component transport equation calculates the molar fraction of each component of hydrogen-doped natural gas, the state equation adopts the Peng-Robinson equation, and the turbulence model selects the k-ε model; the jet flow condition at the 10x m section of the jet flow model is determined, and the outlet boundary adopts pressure outlet; the diffusion model is solved by a pressure-based solver, and the convection term is discretized by a second-order upwind scheme;

[0027] Step 7, analysis of the diffusion characteristics of high-pressure hydrogen-doped natural gas; the lower explosion limit of hydrogen-doped natural gas is calculated, and the explosion danger distance of hydrogen-doped natural gas pipeline leakage is determined;

[0028] The formula for calculating the lower explosion limit of hydrogen-doped natural gas is:

[0029]

[0030] In the formula: i and mix are gas components i and mixed gas respectively; Y i is the molar fraction of component i in the total combustible gas, %; LFL i is the lower explosion limit of component i, %; LFL mix is the lower explosion limit of the mixed gas, %; N is the number of combustible gas components.

[0031] The above technical scheme is adopted in the present application, and the following beneficial effects can be achieved:

[0032] (1) The present application proposes a high-pressure hydrogen-doped natural gas pipeline leakage characteristic simulation method based on CFD, which considers the influence of near-field under-expansion jet on far-field diffusion.

[0033] (2) The high-pressure hydrogen-doped natural gas pipeline leakage characteristic simulation method based on CFD proposed in the present application not only ensures the accuracy of numerical calculation, but also improves the calculation efficiency, and maximally reduces the cost of numerical calculation. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a step diagram of a CFD-based high-pressure hydrogen-doped natural gas pipeline leakage characteristic simulation method of the present application.

[0035] Figure 2 is a two-stage schematic diagram of a hydrogen-doped natural gas pipeline leakage process in an embodiment of the present application.

[0036] Figure 3 is a jet region geometric model diagram established in an embodiment of the present application.

[0037] Figure 4 is a near-field jet characteristic (velocity) nephogram of hydrogen-doped natural gas pipeline leakage in an embodiment of the present application.

[0038] Figure 5 is a diffusion source intensity (velocity) fitting curve diagram at 10x m cross section in an embodiment of the present application.

[0039] Figure 6 is a diffusion region geometric model diagram established in an embodiment of the present application.

[0040] Figure 7 is a far-field diffusion characteristic (hydrogen-doped natural gas molar fraction) nephogram of hydrogen-doped natural gas pipeline leakage in an embodiment of the present application. DETAILED DESCRIPTION

[0041] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is further described below in conjunction with the accompanying drawings of the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0042] As shown in Figure 1 , a CFD-based high-pressure hydrogen-doped natural gas pipeline leakage characteristic simulation method includes the following steps:

[0043] Step 1, a typical high-pressure hydrogen-doped natural gas pipeline leakage process is selected as the research object, the high-pressure hydrogen-doped natural gas pipeline leakage process is divided into a near-field jet stage and a far-field diffusion stage; the high-pressure hydrogen-doped natural gas pipeline leakage conditions are determined, mainly including pipeline operating pressure, leakage hole diameter and hydrogen-doping ratio; the jet conditions of the leakage hole are calculated;

[0044] Step 2, a jet region geometric model is established; a two-dimensional axisymmetric calculation domain is used to reduce the calculation resource cost, the jet model is composed of a leakage hole and an environmental atmosphere region; a non-structural grid division method is used to divide the grid of the jet region; the velocity and pressure gradient of the under-expanded jet structure are relatively large, in order to reduce the calculation time and ensure the accuracy of the numerical simulation, the grid of the region near the leakage hole is locally encrypted; and the grid independence of the jet region is verified;

[0045] Step 3, establishment and solving of the jet CFD model; the control equation includes mass, momentum and energy conservation equation, the component transport equation calculates the molar fraction of each component of the hydrogen-doped natural gas, the state equation selects the Peng-Robinson equation, the turbulent flow model selects the k-ε model; the jet model inlet boundary condition is determined according to the jet condition of the leakage hole, and the outlet boundary adopts the pressure outlet; since the velocity of the near-field jet is very high, the influence of gravity can be ignored; the double-precision pressure solver is selected, and the SIMPLE algorithm is used for pressure-velocity coupling; in order to ensure the calculation accuracy, the turbulent kinetic energy and the turbulent dissipation rate are discretized by the second-order upwind format, and the transient equation adopts the second-order implicit format; the time step is set to 10 -5 s, the time step is set to 10

[0046] Step 4, analysis of the jet characteristics of the high-pressure hydrogen-doped natural gas; since the jet velocity reaches the sound velocity, the jet area will reach a stable state in a short time, and only the flow field characteristics after the jet field is stable are analyzed; the velocity, Mach number, pressure, temperature, H2 molar fraction and CH4 molar fraction of the jet area are determined; the diffusion source intensity (velocity, temperature, H2 molar fraction and CH4 molar fraction, etc.) at the 10x m (x m section from the jet outlet to the Mach disc) is fitted by using the nonlinear curve fitting Boltzmann model, and is taken as the inlet boundary of the diffusion model to ensure that the supersonic and oscillation areas are avoided;

[0047] Step 5, establishment of a three-dimensional diffusion area geometric model; the calculation domain is discretized in the form of hexahedral elements, and the grid is refined around the diffusion model inlet section and near the ground; the grid independence verification of the diffusion model is performed;

[0048] Step 6, establishment and solving of the diffusion CFD model; the control equation includes mass, momentum and energy conservation equation, the component transport equation calculates the molar fraction of each component of the hydrogen-doped natural gas, the state equation adopts the Peng-Robinson equation, and the turbulent flow model selects the k-ε model; the diffusion model inlet boundary condition is determined according to the jet condition of the jet model at the 10x m section, and the outlet boundary adopts the pressure outlet; the diffusion model is solved by the pressure-based solver, and the convection term is discretized by the second-order upwind format;

[0049] Step 7, analysis of the diffusion characteristics of the high-pressure hydrogen-doped natural gas; the lower explosive limit of the hydrogen-doped natural gas is calculated, and the explosion danger distance of the hydrogen-doped natural gas pipeline leakage is determined.

[0050] The application principle of the application will be further described in combination with specific examples.

[0051] Example: The hydrogen-doped ratio of KY hydrogen-doped natural gas pipeline is 10%, the pipeline operating temperature is 293.15K, the pipeline operating pressure is 6MPa, and the existing leakage hole diameter is 12mm. According to the method of the present application, the leakage characteristics of the pipeline are analyzed, and the explosion hazard distance after leakage is determined. The implementation steps are as follows:

[0052] Step 1, the leakage process of KY high-pressure hydrogen-doped natural gas pipeline is selected as the research object, and the high-pressure hydrogen-doped natural gas pipeline leakage process is divided into near-field jet stage and far-field diffusion stage, as shown in Figure 2 ; The jet conditions of the leakage hole under the working conditions of a pipeline operating pressure of 6MPa, a leakage hole diameter of 12mm and a hydrogen-doped ratio of 10% are shown in Table 1;

[0053] Table 1 Leakage hole jet conditions

[0054] Leak hole pressure (MPa) 3.06 Leak hole temperature (K) 233.59 Density of hydrogen-doped natural gas at leak hole (kg / m 3 )]]> 24.35 Leak hole hydrogen-doped natural gas flow rate (m / s) 447.55 Leak rate (kg / s) 1.23

[0055] Step 2, the established jet area geometric model is shown in Figure 3 ; A two-dimensional axisymmetric calculation domain is used to reduce the cost of computing resources. The jet model is composed of a leakage hole and an environmental atmosphere area. The overall size of the calculation domain is 1.5m(long) x 1m(width). A non-structured grid division method is used to divide the grid of the jet area. The velocity and pressure gradient of the under-expanded jet structure are relatively large. In order to reduce the calculation time and ensure the accuracy of numerical simulation, the grid near the leakage hole is locally encrypted. The grid independence of the jet area is verified;

[0056] Step 3, establishment and solution of jet CFD model; the control equations include mass, momentum and energy conservation equations. The component transport equation calculates the molar fraction of each component of hydrogen-doped natural gas. The Peng-Robinson equation is selected as the state equation, and the k-ε model is selected as the turbulence model. The constant mass flow of 1.11kg / s is selected as the boundary condition of the inlet (ab), and the environmental pressure and temperature are selected as the boundary condition of the pressure outlet (bcde). Since the velocity of the near-field jet is very high, the influence of gravity can be ignored. The double-precision pressure solver is selected, and the SIMPLE algorithm is used for pressure-velocity coupling. In order to ensure the calculation accuracy, the turbulent kinetic energy and turbulent dissipation rate are discretized by the second-order upwind format, and the transient equation is discretized by the second-order implicit format. The time step is set to 10 -5 s, the time step is set to 10

[0057] Step 4, the jet characteristics (velocity) of high-pressure hydrogen-doped natural gas are as follows Figure 4As shown, the barrel shock structure can be clearly seen, especially the Mach disk is clearly visible; since the jet velocity reaches the speed of sound, the jet area will reach a stable state in a short time, only the flow field characteristics after the jet field is stable are analyzed; the velocity, Mach number, pressure, temperature, H2 mole fraction and CH4 mole fraction in the jet area are determined; the diffusion source intensity (velocity, temperature, H2 mole fraction and CH4 mole fraction, etc.) at the 10x m = 0.61m(x m is the distance from the jet outlet to the Mach disk) cross section is fitted by using a nonlinear curve fitting Boltzmann model, the velocity fitting curve is shown in Figure 5 , and taking it as the inlet boundary of the diffusion model can ensure to avoid supersonic and oscillation area; step 5, the established three-dimensional diffusion area geometric model is shown in Figure 6 ; the calculation domain is discretized in the form of hexahedral elements, and the grid is refined around the diffusion model inlet cross section and near the ground; the grid independence verification is performed on the diffusion model grid;

[0058] Step 6, establishment and solution of the diffusion CFD model; the control equations include mass, momentum and energy conservation equations, the component transport equation is used to calculate the mole fraction of each component of hydrogen-doped natural gas, the Peng-Robinson equation is used as the state equation, and the k-ε model is selected as the turbulence model; the inlet boundary condition of the diffusion model is determined according to the jet condition at the 10x m cross section of the jet model, and the pressure outlet is used as the outlet boundary; the diffusion model is solved by a pressure-based solver, and the second-order upwind format is used to discretize the convection term;

[0059] Step 7, the diffusion characteristics (hydrogen-doped natural gas mole fraction) of high-pressure hydrogen-doped natural gas are shown in Figure 7 , with the increase of diffusion distance, the diffusion height of hydrogen-doped natural gas increases; this is mainly due to the fact that the densities of H2 and CH4 are lower than that of air, and the hydrogen-doped natural gas is more easily diffused into the atmosphere after the velocity attenuation; when the hydrogen-doping ratio is 10%, the lower explosion limit of the calculated hydrogen-doped natural gas is 4.88 vol%, and according to the hydrogen-doped natural gas mole fraction cloud map shown in Figure 7 , the explosion danger distance under this leakage condition is 10.26 m.

Claims

1. A CFD-based method for simulating leakage characteristics of high-pressure hydrogen-blended natural gas pipelines, characterized in that, Includes the following steps: Step 1: Select a typical high-pressure hydrogen-blended natural gas pipeline leakage process as the research object, and divide the high-pressure hydrogen-blended natural gas pipeline leakage process into a near-field jet stage and a far-field diffusion stage; determine the high-pressure hydrogen-blended natural gas pipeline leakage conditions, mainly including pipeline operating pressure, leakage orifice diameter and hydrogen blending ratio; calculate the leakage orifice jet conditions; Formulas for calculating the pressure, temperature, density, and flow rate of hydrogen-blended natural gas at the leak point: Where: P0 is the pipeline operating pressure, Pa; T0 is the pipeline operating temperature, K; γ is the adiabatic index; R is the universal gas constant; P e For the leakage orifice pressure, Pa; T e For the leakage hole temperature, K; ρ e The density of hydrogen-doped natural gas at the leak point, in kg / m³ 3 ;u e The flow velocity of hydrogen-doped natural gas at the leak hole is in m / s; Formula for calculating the leakage rate of critical flow: In the formula: Q is the gas leakage rate, kg / s; A e The area of ​​the leakage hole is m. 2 ; Step 2: Establish the geometric model of the jet region; use a two-dimensional axisymmetric computational domain to reduce computational resource costs. The jet model consists of a leak hole and the ambient atmospheric region; use an unstructured mesh generation method to mesh the jet region; the velocity and pressure gradients of the underexpanded jet structure are relatively large. In order to reduce computation time and ensure the accuracy of numerical simulation, the mesh near the leak hole is locally refined; and the mesh independence of the jet region is verified. Step 3: Establishment and solution of the jet CFD model; the governing equations include mass, momentum, and energy conservation equations; the component transport equations calculate the mole fraction of each component in the hydrogen-doped natural gas; the Peng-Robinson equations are used as the equation of state; and the k-ε model is used as the turbulence model; the inlet boundary conditions of the jet model are determined based on the jet conditions of the leakage orifice, and the outlet boundary adopts a pressure outlet; since the velocity of the near-field jet is very high, the influence of gravity can be ignored; a double-precision pressure solver is selected, and the SIMPLE algorithm is used for pressure-velocity coupling; to ensure calculation accuracy, the turbulent kinetic energy and turbulent dissipation rate are discretized using a second-order upwind scheme, and the transient equations are presented using a second-order implicit scheme; the time step is set to 10. -5 s, the time step is 5000 steps, and the maximum number of iterations for the time step is 50; Step 4: Analyze the characteristics of the high-pressure hydrogen-blended natural gas jet. Since the jet velocity reaches the speed of sound, the jet region will reach a stable state in a short time; therefore, only the flow field characteristics after the jet field stabilizes are analyzed. The velocity, Mach number, pressure, temperature, H2 mole fraction, and CH4 mole fraction of the jet region are determined. A nonlinear curve fitting Boltzmann model is used to fit the 10x... m The diffusion source intensity at the cross section is fitted, and the diffusion source intensity is the velocity, temperature, H2 mole fraction, and CH4 mole fraction. Using this as the inlet boundary of the diffusion model can ensure that supersonic and oscillating regions are avoided. Formula for calculating the distance from the jet exit to the Mach disk: In the formula: x m P is the distance from the jet exit to the Mach disk, in meters (m). a External environmental pressure, Pa; d e Let be the diameter of the leaking orifice, in meters; the equations of the Boltzmann model are as follows: In the formula: A1, A2, x0 and dx are fitting parameters; Step 5: Establish a three-dimensional geometric model of the diffusion region; the computational domain is discretized in the form of hexahedral elements, and the mesh is refined around the inlet section of the diffusion model and near the ground; the mesh of the diffusion model is verified for independence. Step 6: Establishment and solution of the diffusion CFD model; the governing equations include mass, momentum, and energy conservation equations; the component transport equations calculate the mole fraction of each component in the hydrogen-doped natural gas; the Peng-Robinson equation is used as the equation of state; the k-ε model is selected as the turbulence model; the inlet boundary conditions of the diffusion model are based on the jet model at 10x m The jet conditions at the cross section are determined, and the outlet boundary adopts a pressure outlet; the diffusion model is solved by a pressure-based solver, and the convection term is discretized using a second-order upwind scheme; Step 7: Analyze the diffusion characteristics of high-pressure hydrogen-blended natural gas; calculate the lower explosive limit of hydrogen-blended natural gas and determine the explosion hazard distance of a leak in a hydrogen-blended natural gas pipeline; Formula for calculating the lower explosive limit of hydrogen-blended natural gas: In the formula: i and mix represent gas component i and the mixed gas, respectively; Y i LFL is the mole fraction of component i in the total combustible gas, in %; i The lower explosive limit (LFL) of component i, in percent; mix is the lower explosive limit of the gas mixture, %; N is the number of combustible gas components.

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