Research on Minimum Ignition Energy Testing of Normal-Alkane Vapors

Abstract

Minimum Ignition Energy (MIE) is a critical parameter for assessing the combustion and explosion risks of liquid fuels under specific conditions. However, systematic testing methods for long-chain alkanes remain underdeveloped. In this study, an experimental apparatus was developed based on American Society for Testing and Materials Standard ASTM E582-21 to measure the MIE of liquid fuel vapors. Through systematic measurements of the minimum ignition energy (MIE) of alkane vapors, this study examines the influence of vapor concentration on MIE and elucidates the dependence of ignition energy on carbon chain length. System sensitivity parameters were calibrated using propane/air mixtures, establishing optimal testing conditions as a 2.0 mm electrode gap and a 14.0 pF capacitance. The measured minimum ignition energy (MIE) values for C₅–C₈ alkane vapors at their respective sensitive volume fractions were 0.197 mJ (at 3.4 vol%), 0.253 mJ (at 3.3 vol%), 0.303 mJ (at 3.0 vol%), and 0.323 mJ (at 2.8 vol%). The experimentally determined MIE values for C₅–C₈ alkane vapors demonstrate close agreement with literature data, confirming the reliability of the experimental system and methodology for MIE determination of liquid fuel vapors. Furthermore, the study reveals a characteristic V-shaped correlation between MIE and vapor concentration, along with a consistent shift in the sensitive concentration toward fuel-rich conditions relative to stoichiometric proportions. Extended measurements of C₉–C₁₁ alkanes revealed MIE values of 0.523 mJ (at 2.8 vol%) for n-nonane, 0.857 mJ (at 2.5 vol%) for n-decane, and 1.127 mJ (at 2.0 vol%) for n-undecane. Notably, the results demonstrate a substantial increase in MIE with carbon chain length, showing a 471% rise from C₅ to C₁₁. A nonlinear regression analysis confirmed a strong correlation between MIE and carbon chain length (R² = 0.98).

1. Introduction

Minimum Ignition Energy (MIE) is defined as the minimum electrical spark energy required to initiate combustion or explosion in a mixture of flammable gas, volatile liquid vapor, or combustible dust cloud with air under specific test conditions. It is also referred to as the critical ignition energy or minimum spark ignition energy [1]. When liquid fuels leak and form highly volatile vapors, their MIE can reach values as low as millijoule levels; for instance, the MIE of ethanol vapor is approximately 0.72 mJ [2]. Such vapors are particularly susceptible to ignition from weak energy sources such as electrostatic sparks, resulting in frequent combustion and explosion accidents in industries including petrochemical processing and aviation fuel storage and transportation [3,4]. Investigation of the MIE of liquid fuels supports the assessment of fire and explosion risks associated with specific ignition scenarios (e.g., arc discharge or friction). This research also contributes to the identification of causes underlying fuel-related fire and explosion incidents. Moreover, in environments where flammable liquid fuels are present, studies on MIE provide essential data and theoretical foundations for establishing safety standards and preventive measures, which are crucial for ensuring the safety of human life and property.

Current research on the MIE of combustible materials spans influencing factors, measurement techniques, and theoretical modeling, yet it reveals distinct focal points and limitations relevant to this study. A significant body of work has concentrated on gaseous mixtures. For instance, Fernández-Tarrazo E et al. [5] theoretically evaluated the MIE of H₂/NH₃/air mixtures, elucidating the effects of composition and pressure. Similarly, Movileanu C et al. [6] and Ghosh A et al. [7] investigated propane/air and methane/hydrogen mixtures, respectively, exploring the impacts of inert gas dilution and low temperatures on MIE. Zhang W et al. [8] further analyzed the effect of water vapor dilution on various fuel/air mixtures. Collectively, these studies provide valuable insights into gas-phase ignition but highlight a predominant focus on common, shorter-chain gaseous fuels or hydrogen, with limited data on vapors from high-boiling-point liquids.

Concurrently, advancements and challenges in experimental methodologies have been documented. Various apparatuses have been employed, from cylindrical explosion vessels with capacitive spark discharge [9] to methods based on wire melting [10] and systems designed to simulate electrostatic discharges [11]. While these efforts refine MIE measurement, conventional capacitive discharge methods are often associated with significant energy fluctuations and limited adjustment precision [12]. Standard test methods (e.g., GB/T, IEC, EN) are widely applicable to gases, dusts, and mists [13,14,15] but are not designed for, and fail to account for condensation issues with, long-chain alkane liquid fuels with flash points exceeding 60 °C.

In parallel, predictive modeling approaches have been developed to estimate MIE. These range from fundamental models based on flame kernel dynamics for hydrogen-air mixtures [16] to empirical Multivariate Linear Regression (MLR) models derived from Quantitative Structure-Property Relationship (QSPR) principles for broader chemical compounds [17]. While powerful, the accuracy of such models often depends on the availability of reliable experimental data for validation, which is scarce for certain fuel classes. Therefore, despite comprehensive research on gaseous and dust systems [18], a notable scarcity of reliable MIE data persists for long-chain alkane liquid fuels beyond C₉ [19].

Addressing the research gaps and methodological limitations identified above, this study developed an experimental apparatus and testing methodology based on ASTM E582-21 [20] for determining the MIE of alkane-based liquid fuels. A propane/air mixture was employed to calibrate the sensitive parameters of the experimental system. The reliability of the system was validated through MIE measurements of C₅–C₈ alkanes (n-pentane, n-hexane, n-heptane, and n-octane), while the influence of volume fraction on the MIE of alkane vapors was systematically investigated. Furthermore, the MIE values of C₉–C₁₁ alkanes (n-nonane, n-decane, and n-undecane) were determined to elucidate the dependence of MIE on carbon chain length, thereby providing theoretical and experimental support for establishing safety standards for long-chain alkane fuels.

2. Apparatus and Testing Methodology

2.1. Experimental Materials

In this experiment, propane was employed to calibrate the sensitive parameters of the experimental system. The minimum ignition energy (MIE) of n-pentane, n-hexane, n-heptane, and n-octane was measured and compared with published literature values to assess the reliability and accuracy of the apparatus. Furthermore, n-nonane, n-decane, and n-undecane were selected to determine the MIE of these higher-carbon-number alkanes. The specific results are summarized in

Table 1. Experimental materials.

Test Sample	Purity	Manufacturer
Propane	99.9%	Guanghan Mingyuan Gas Co., Ltd., Guanghan, China.
Dry Air	99.9%	Chengdu Jinkexing Gas Co., Ltd., Chengdu, China.
n-Pentane, n-Hexane, n-Heptane, n-Octane	99.5%	Chengdu Jinshudu Scientific Supply Co., Ltd., Chengdu, China.
n-Nonane, n-Decane, n-Undecane	99.2%	Chengdu Kelong Chemical Co., Ltd., Chengdu, China.

.

2.2. Apparatus

The MIE test system used in this study comprises several key components, including a reaction vessel, buffer tank, vacuum pump, ignition control system, and gas supply system(Provided by Shenyang Ensafe Environmental Safety Technology Co., Ltd., Liaoning, China). The apparatus was designed and built in compliance with the American Society for Testing and Materials standard ASTM E582-07. A schematic diagram of the experimental setup is presented in Figure 1.

Conventional spark discharge methods for determining the MIE of combustible materials suffer from limitations such as unstable energy release and insufficient energy adjustment accuracy [21]. The energy delivered via capacitive discharge is susceptible to voltage fluctuations, capacitance drift, and variations in circuit impedance, resulting in poor reproducibility of spark energy and compromised measurement precision. Moreover, energy adjustment—typically achieved by varying capacitance or voltage—is constrained by the finite resolution of component specifications (e.g., capacitance tolerance of ±5%), thus hindering continuous fine-tuning and further diminishing measurement accuracy.

To overcome these limitations, the present experimental system utilizes a DC constant-current source (adjustable within the range of 0–30 mA) to extend the discharge duration to 6 s, thereby minimizing the influence of voltage fluctuations and circuit impedance variations on the ignition energy and better simulating actual electrostatic discharge processes. By calibrating capacitance values—pre-selected at four levels: 5, 20, 80, and 320 pF—along with discharge voltage (1–20 kV) according to energy requirements, the system enables continuous fine-tuning of ignition energy with a precision of 0.001 mJ, significantly improving experimental accuracy. Furthermore, a two-stage temperature control system is incorporated, comprising a buffer tank heater capable of reaching 200 °C and a pipeline heating zone rated up to 500 °C, effectively eliminating measurement deviations caused by vapor condensation.

The experimental system can be configured to deliver output voltages ranging from 1 to 20 kV. Capacitors are provided at four preset levels: 5, 20, 80, and 320 pF, enabling ignition energy outputs from 0.01 to 20.00 mJ. The electrodes were fabricated from 304 stainless steel with passivated surfaces and shielded by alumina ceramic insulating flanges to ensure operational reliability and measurement precision. A high-precision electric needle valve is incorporated to accurately regulate the inflow and outflow of flammable gases, allowing control over fuel concentration with an accuracy of 0.01%. The entire setup is constructed from 304 stainless steel and includes spherical reaction vessels with volumes of 1.0 L or 5.0 L, along with a 20.0 L buffer tank, ensuring experimental stability and reproducibility. The core components of the system consist of the vapor distribution unit—connected to the buffer tank—and the combustible gas ignition control system, linked to the reaction vessel, as illustrated in Figure 2.

2.3. Testing Methodology

For all experimental stages—system calibration with propane and MIE determination for C₅–C₈ and C₉–C₁₁ alkanes—the same vessel configuration was used: the 1.0 L spherical reaction vessel for ignition tests, coupled with the 20.0 L buffer tank for fuel vapor generation and pre-mixing.

During measurement of the MIE of liquid fuel vapors, the liquid fuel is first injected into the buffer tank through a feed port and evacuated to vacuum using a vacuum pump. The system is then heated above the fuel’s boiling point (up to 200 °C) via a buffer tank heater to facilitate complete vaporization. To prevent condensation of the generated flammable vapors as they transit through the metal tubing into the reaction vessel—which could introduce errors in MIE measurements—a constant-temperature heating tape (capable of reaching 500 °C) is applied to the surfaces of both the metal transfer line and the reaction vessel. This ensures that the temperature remains above the boiling point of the fuel throughout the experimental setup.

During the gas mixing process, the reaction vessel is first evacuated to vacuum using a vacuum pump. The vapor of the liquid fuel under test and dry air from a gas cylinder are then introduced through inlet ports 1 and 2, respectively. The target concentration is set, and the inflow is precisely regulated via a high-precision electric needle valve. The system employs an automated partial-pressure-based gas mixing method. The criterion for judging mixture uniformity and stability was the stabilization of the absolute pressure inside the 1.0 L reaction vessel. The pressure was monitored using a precision pressure transducer, and the mixture was deemed ready for testing once the pressure reading remained constant (variation of <0.1 KPa) for a period of at least 60 s within this 5 min window. This protocol ensures that the mixture is quiescent and homogeneous, thereby guaranteeing the reproducibility of the initial conditions for each ignition test.

After mixing, the desired ignition energy (0.01–20.00 mJ) and voltage (approximately 8000 V) are set. The control program selects the appropriate capacitor bank according to the voltage and energy requirements and adjusts the discharge voltage to achieve the target ignition energy, E₀. An energy step size, ΔE (5–10% of the preset energy), is defined. Ignition is subsequently initiated, and the delivered energy is measured. Ignition success is determined by visual observation through the glass viewport on the reaction vessel.

To minimize random variability in measurement outcomes, the Bruceton staircase method was employed to determine the ignition energy corresponding to a 50% probability of ignition. The energy level for each subsequent test was dynamically adjusted based on the result of the previous ignition trial, with an adaptive step size used to iteratively converge toward the threshold value. This approach significantly reduces the number of tests required while improving the accuracy of the estimated MIE [22]. While Christensen notes certain limitations of the Bruceton staircase method—specifically its tendency to exclude portions of valid datasets and its dependence on confidence intervals for uncertainty estimation—this methodology remains internationally established for determining the MIE of combustible materials. This enduring acceptance stems from its primary design objective: to establish stable, reproducible engineering safety parameters rather than to pursue theoretically ideal “minimum” values. Specifically, after each trial, the energy was decreased by a step size ΔE following a successful ignition and increased by ΔE following a failure. This procedure was repeated over 20–30 trials to determine the MIE with statistical significance.

The minimum ignition energy was calculated using the Bruceton up-and-down method as follows [23]:

$$E=E_{min}+\mathsf{\Delta }E\left({\displaystyle \frac{\sum _{i=0}^{m}i\text{⋅}{n}_i}{N}}-{\displaystyle \frac{1}{2}}\right)$$

(1)

where E is the MIE (mJ); E_min denotes the lowest energy level (mJ); ΔE represents the energy step size (mJ); m is the number of energy levels; i is the energy level index; n_i is the number of tests at that energy level; and N is the total number of valid tests.

To ensure the reproducibility and comparability of all results, a consistent set of critical parameters was maintained across all experimental stages, from system calibration to the testing of C₅–C₁₁ alkanes. The key control variables were as follows:

(1)

Initial Conditions: Temperature = 25 ± 1 °C, Absolute Pressure = 0.1 MPa, Relative Humidity = 45 ± 5%.

(2)

Electrode Specifications: Material: Tungsten; Tip Geometry: 30° conical tip; Gap Distance: 2.0 mm.

(3)

Surface Condition: Electrodes were polished with fine-grit sandpaper and cleaned with ethanol prior to each test series.

(4)

Discharge Circuit Parameters: Capacitance range: 5, 20, 80, and 320 pF; Corresponding discharge duration (as measured at half-peak current): 50–200 ns.

3. Results and Discussion

3.1. Determination of Critical Thresholds

In addition to the intrinsic properties of the combustible material and external environmental conditions, system-specific parameters—such as capacitance and electrode gap distance—also significantly influence the minimum ignition energy (MIE) of combustible substances [24].

In this study, the MIE of combustible materials was measured using an electric spark ignition method. The value of the energy storage capacitor was found to influence the MIE outcome, while the electrode gap also contributed to measurement variability. Furthermore, as explosive limits differ across combustible materials, a sensitive volume fraction exists at which the most accurate MIE values can be obtained. Therefore, before conducting MIE measurements for liquid fuels, it is essential to identify the optimal system configuration—including the critical capacitance and electrode gap—under which measurements exhibit highest precision.

3.1.1. Determination of Critical Capacitance Value

The flammability limit range of propane is 2.0% to 9.5%, and the stoichiometric concentration is 4.0%. Using a fixed electrode gap of 2.0 mm, a propane/air mixture at this concentration (4.0%) was utilized in the experiments. The MIE of propane was subsequently determined using the Bruceton staircase method with a capacitance value of 14.0 pF, as described below.

(1)

An initial energy value E₀ = 0.30 mJ was set, with an energy step size of ΔE = 0.02 mJ (corresponding to 7% of E₀). A total of 24 tests were conducted under these conditions. The results are summarized in

Table 2. Measurement of propane MIE via Bruceton staircase method.

Test Number	Ignition Energy (mJ)	Results	Adjustment
1	0.30	S	reduce ΔE
2	0.28	F	increase ΔE
3	0.30	S	reduce ΔE
4	0.28	S	reduce ΔE
5	0.26	F	increase ΔE
6	0.28	S	reduce ΔE
7	0.26	S	reduce ΔE
8	0.24	F	increase ΔE
9	0.26	S	reduce ΔE
10	0.24	F	increase ΔE
…	…	…	…
23	0.28	S	reduce ΔE
24	0.26	F	over

S: success; F: fail. “…”: increase ΔE if failed, reduce ΔE if successful.

.

A total of 24 ignition tests were performed, resulting in 13 successful ignitions and 11 failed attempts. Measurements were conducted at four energy levels: 0.24 mJ (0 successes, 6 failures), 0.26 mJ (6 successes, 4 failures), 0.28 mJ (4 successes, 1 failure), and 0.30 mJ (3 successes, 0 failures).

(2)

The experimental data were organized in ascending order of energy level, with the lowest level set at 0.24 mJ. The sorted results are presented in

Table 3. Energy Level Distribution.

Energy Level (mJ)	Level Number i	Total Number of Times ni	Number of Successful Attempts	Number of Failed Attempts	i·ni
0.24	0	6	0	6	0
0.26	1	10	6	4	10
0.28	2	5	4	1	10
0.30	3	3	3	0	9
Total	/	24	13	11	29

.

As summarized in Table 3, the minimum energy level E_min was 0.24 mJ, the energy step size ΔE was 0.02 mJ, the number of energy levels m = 4, and the total number of experiments N = 24. Using the Bruceton up-and-down method, the minimum ignition energy E of propane was calculated via Equation (1) to be 0.254 mJ.

Figure 3 presents the MIE values of propane, as determined by the Bruceton staircase method, across varying capacitance values.

As shown in Figure 3, the MIE of propane exhibits an approximately U-shaped dependence on capacitance. With increasing capacitance, the MIE decreases progressively, reaching a minimum value of 0.254 mJ at 14.0 pF. Upon further increase in capacitance, the MIE rises markedly.

The observed U-shaped trend in measured ignition energy versus capacitance, culminating in a minimum at 14.0 pF (the sensitive capacitance, Figure 3), is a direct consequence of the interplay between circuit discharge characteristics and fundamental spark ignition criteria [25]. Successful ignition requires the spark to deposit enough energy to form a flame kernel that surpasses a critical radius, thereby overcoming heat losses to the electrodes and the unburned mixture, as defined by the mixture’s quenching distance. The sensitive capacitance represents the optimal value that satisfies this energy requirement while minimizing losses. With capacitances significantly smaller than 14.0 pF, the total stored energy is insufficient to create a self-sustaining, super-critical flame kernel. Conversely, with larger capacitances, while the total stored energy increases, the prolonged discharge duration leads to increased thermal diffusion losses to the electrodes during the spark event. This results in a less efficient transfer of electrical energy into the thermal energy required for kernel growth, thus necessitating a higher total ignition energy. Therefore, the identified sensitive capacitance of 14.0 pF is the point at which the energy deposition is most efficiently coupled to the combustion chemistry, minimizing the measured MIE for this specific mixture and electrode configuration.

3.1.2. Determination of Critical Optimal Electrode Gap

Experiments were conducted using a propane/air mixture at this concentration (4.0%) under standard conditions. A fixed capacitance of 14.0 pF was selected, and the minimum ignition energy (MIE) of propane was measured at varying electrode gap distances to investigate the influence of gap size on ignition energy. The results are presented in Figure 4.

As shown in Figure 4, the MIE of propane decreases progressively with increasing electrode gap distance. The ignition energy reaches a minimum value of 0.247 mJ at a gap of 2.0 mm. Upon further increase in the gap, the MIE is observed to rise gradually.

The electrode gap is a critical parameter influencing the MIE of combustible substances, as it directly affects the breakdown voltage, flame kernel development, and energy transfer efficiency [26]. An excessively small gap promotes dominant heat loss to the electrodes, dissipating thermal energy generated by the gas reaction and leaving only limited spark energy available for flame initiation. This restricts flame kernel growth and may lead to ignition failure or necessitate higher ignition energy. Conversely, an overly large gap weakens the electric field intensity, reducing electron and ion acceleration and thereby increasing the breakdown voltage required to initiate spark discharge. The elevated breakdown voltage in turn demands higher energy input to achieve ignition, resulting in an increased measured MIE [27]. Therefore, an optimal electrode gap exists that minimizes the ignition energy—denoted as the sensitive electrode gap. As shown in Figure 4, the smallest MIE was observed at a gap of 2.0 mm, indicating that the sensitive electrode gap under these experimental conditions is 2.0 mm.

Based on the analysis of the results presented in Figure 3 and Figure 4, the sensitive conditions for this test system were identified as a capacitance of 14.0 pF and an electrode gap of 2.0 mm. Under these optimized parameters, the MIE of other liquid fuels can be accurately and reliably determined.

3.2. Integrated System Validation

The minimum ignition energy (MIE) of four alkane fuel vapors was determined using the Bruceton staircase method within this experimental system. The results were compared with existing literature data to validate the reliability and accuracy of both the apparatus and the methodology. A comparative summary of the experimentally obtained MIE values and those reported in the literature is provided in

Table 4. Comparative analysis of MIE for alkane vapors (C₅-C₈).

Alkane Vapors	Experimentally Determined MIE (mJ)	Literature-Reported MIE (mJ)	Absolute Deviation (mJ)	Relative Error (%)
C5H12	0.197	0.220 [28]	0.023	10.45
C6H14	0.253	0.248 [29]	0.005	2.02
C7H16	0.303	0.240 [28]	0.063	26.25
C8H18	0.323	/	/	/

[28,29].

As summarized in Table 4, the MIE values obtained in this study for the vapors of n-pentane, n-hexane, n-heptane, and n-octane are 0.197 mJ, 0.253 mJ, 0.303 mJ, and 0.323 mJ, respectively.

The experimentally determined MIE values for C₅–C₈ alkane vapors demonstrate close agreement with literature data, with absolute deviations ranging from 0.005 to 0.063 mJ and relative errors between 2.02% and 26.25%. A strong linear correlation was observed between measured and reference values (r = 0.978), with a mean absolute error of 0.030 mJ—significantly below the accepted MIE measurement tolerance of 0.050 mJ—confirming the method’s high accuracy and reproducibility.

The elevated relative error for n-heptane (C₇H₁₆) primarily stems from limitations inherent to conventional capacitive discharge methods, which fail to account for micro-droplet quenching effects during liquid evaporation. In this study, optimized evaporation temperatures (>20 °C above boiling point) and extended heating durations (>8 h) effectively mitigated droplet-induced quenching, yielding a measured value (0.303 mJ) that more accurately reflects true vapor-phase ignition behavior. These results validate both the accuracy and reliability of the developed experimental system for determining MIE of alkane fuel vapors, establishing its suitability for investigating MIE dependence on key influencing factors.

3.3. Influence of Volume Fraction on MIE of Alkane Vapors

Within the flammability limits of liquid fuel vapors, the maximum energy release occurs during complete combustion with oxygen, i.e., when the volume fraction ratio matches the equivalence ratio in the chemical reaction equation.

However, in measurements of the minimum ignition energy (MIE) for alkane liquid vapors, the experimentally determined sensitive volume fraction consistently exceeds the chemically stoichiometric concentration. This phenomenon originates from the shift in the peak adiabatic flame temperature toward fuel-rich conditions, given the strong dependence of MIE on adiabatic flame temperature. As established by C. K. Law et al., this shift is governed primarily by the effect of product dissociation at elevated temperature [30]. Consequently, a slightly fuel-rich volume fraction—termed the sensitive volume fraction—exists at which the MIE is achieved.

Take $CxHy$ fuel as an example. The chemical equation for complete reaction with oxygen is

$$CxHy+\left(x+{\displaystyle \frac{y}{4}}\right)O_2\to xC{O}_2+{\displaystyle \frac{y}{2}}{H}_{2}O$$

(2)

The amount of O₂ required to burn 1 mol $CxHy$ is $x+{\displaystyle \frac{y}{4}}$ mol. The oxygen content in standard air is 20.95%. Therefore, the chemical stoichiometric concentration n (%) of the reaction in air is calculated as follows:

$$n={\displaystyle \frac{20.95}{0.2095+x+\frac{y}{4}}}\text{×}100\%$$

(3)

An electrode gap of 2.0 mm and a capacitance of 14.0 pF were employed. The MIE of four alkane fuel vapors—n-pentane, n-hexane, n-heptane, and n-octane—was measured across a range of volume fractions. The results are presented in Figure 5.

Table 5. Comparative analysis of alkane vapors (C₅–C₈) volume fraction.

Alkane Vapors	Flammability Limit Range (%)	Stoichiometric Volume Fractions (%)	Critical Volume Fraction (%)
C5H12	1.4~7.8	2.6	3.4
C6H14	1.1~7.5	2.2	3.3
C7H16	1.1~6.7	1.9	3.0
C8H18	1.8~6.5	1.7	2.8

compares the stoichiometric volume fractions of these alkane fuel vapors, calculated using Equations (2) and (3), with the experimentally determined sensitive volume fractions.

Figure 5 illustrates a characteristic V-shaped relationship between MIE and vapor concentration for the alkane fuels studied. Within the flammability limits, MIE decreases with increasing volume fraction, attaining relatively low values near the stoichiometric concentration. Beyond this point, further increases in fuel concentration lead to rising MIE values. Consistent with the data summarized in Table 5, the minimum ignition energy for all four alkane vapors occurs at volume fractions slightly higher than their respective stoichiometric ratios. Consequently, the critical volume fractions—corresponding to minimum MIE—are determined to be 3.4% for n-pentane, 3.3% for n-hexane, 3.0% for n-heptane, and 2.8% for n-octane.

The experimental determination of minimum ignition energy near the limiting values exhibits inherent statistical variability. As shown in Figure 5c, the primary uncertainty sources include:

(1)

Minor fluctuations in mixture homogeneity, particularly for high-boiling-point fuels where vapor condensation may occur;

(2)

The intrinsic stochastic nature of spark kernel development at energy levels approaching the minimum;

(3)

The measurement precision of the capacitive discharge circuit.

Error bars in all figures represent ±1 standard deviation derived from ≥10 repeated tests at each condition.

The experimentally observed sensitive volume fraction for alkane liquid vapors consistently exceeds the chemically stoichiometric concentration in MIE measurements. This deviation stems fundamentally from the shift in the peak adiabatic flame temperature toward fuel-rich conditions—a critical factor given the strong correlation between MIE and adiabatic flame temperature. As established by C. K. Law et al. [30], this shift is predominantly governed by product dissociation effects. In alkane/air mixtures under lean conditions, excess oxygen promotes dissociation of triatomic product molecules such as H₂O and CO₂. This endothermic process consumes substantial reaction heat, significantly reducing net heat release. In contrast, under rich conditions, unburned fuel suppresses dissociation, minimizing heat loss and maximizing net heat release slightly above the stoichiometric point. Although the specific heat of the product mixture increases monotonically with fuel concentration—a trend that would otherwise shift the temperature peak toward lean conditions—the heat reduction due to dissociation remains the dominant factor. Consequently, the adiabatic flame temperature peak occurs under slightly fuel-rich conditions. Since MIE minimization coincides with maximum adiabatic flame temperature, the measured sensitive volume fraction necessarily lies slightly above the theoretical equivalence ratio.

The foundational work of Lewis and von Elbe established that MIE for hydrocarbon-air mixtures typically follows a V-shaped dependence on equivalence ratio, well-characterized by second-order polynomial trends [31]. This characteristic pattern has been consistently observed across C₁–C₇ hydrocarbons [32]. The waveform patterns initially observed in concentration-dependent MIE plots (e.g., Figure 5c) are understood to reflect experimental scatter amplified near the minimum energy limit, rather than representing novel physical phenomena. This interpretation aligns with Eckhoff et al.’s observations for propane/air systems, where similar scatter patterns emerged near the flammability limits [33].

The characteristic V-shaped dependence of MIE on vapor concentration (φ) originates from the fundamental interplay between the critical radius of the flame kernel and the thermokinetic balance governing ignition [34]. This systematic analysis examines the underlying mechanism through integrated perspectives: flame kernel development, chemical kinetics, and thermodynamic constraints, while aligning theoretical frameworks with experimental observations.

(1)

Theory of critical size for flame kernel:

The critical radius (r_c) of a flame kernel represents the minimum spatial scale required to sustain self-propagating combustion. This parameter can be expressed as:

$$r_c\propto \sqrt{{\displaystyle \frac{E_{min}}{\rho c_p\Delta T}}}$$

(4)

where ρ denotes the mixture density, c_p the constant-pressure specific heat capacity, and ΔT = T_flame−T₀ the temperature differential between the flame and ambient environment.

Under fuel-lean conditions (low φ), the reduced reaction rate necessitates a larger r_c to accumulate sufficient thermal energy, thereby elevating the MIE. Conversely, under fuel-rich conditions (high φ), incomplete combustion diminishes the effective ΔT, which similarly demands an increased r_c to compensate for heat losses, resulting in MIE rebound. The optimal condition occurs near stoichiometric proportions, where the maximum reaction rate corresponds to the minimal r_c and consequently the lowest MIE value.

(2)

Coupling of chemical kinetics and thermodynamics:

On the fuel-lean branch of the V-shaped curve (low φ region), combustion becomes fuel-limited. Although oxygen molecules are present in excess, the scarcity of fuel molecules reduces the enthalpy of combustion per unit volume. Under these conditions, heat dissipation predominates over chemical energy release at the flame kernel boundary due to thermal conduction, necessitating higher ignition energy and thus increasing the MIE. Conversely, on the fuel-rich branch (high φ region), the reaction becomes oxygen-limited. While fuel molecules are abundant, the oxygen deficiency prevents complete oxidation—manifested as increased CO formation instead of CO₂—which substantially diminishes the effective heat release. Furthermore, the dilution effect caused by unburned fuel vapor lowers the flame temperature and further degrades combustion efficiency. These combined effects similarly elevate the MIE due to the greater energy input required to sustain the reaction.

The characteristic V-shaped relationship between volume fraction and MIE emerges from the collective effects of flame kernel critical size, chemical kinetics, and thermodynamic losses. The systematic deviation observed in the sensitive volume fraction reflects substantive differences between actual combustion conditions and idealized theoretical models, providing a theoretical basis for assessing ignition safety in liquid fuel systems. Future research could employ multiscale simulations—such as direct numerical simulation coupled with detailed chemical mechanisms—to quantitatively evaluate the relative contributions of these governing factors.

3.4. Correlation Between Alkane Carbon Chain Length and MIE

Following validation of the system and methodology, the minimum ignition energy (MIE) of long-chain alkanes (C₉–C₁₁) was measured to investigate the dependence of MIE on carbon chain length. The findings provide theoretical and experimental support for establishing safety standards for high-boiling-point long-chain alkane fuels.

Under the optimized experimental conditions, the electrode gap was set to 2.0 mm, capacitance to 14.0 pF, initial temperature to 25 °C, relative humidity to 45%, and initial pressure to 0.1 MPa. The minimum ignition energy (MIE) of n-nonane, n-decane, and n-undecane was measured across various volume fractions within their flammability limits. The results are presented in Figure 6 and summarized in

Table 6. Experimental results for alkane vapors (C₉–C₁₁).

Alkane Vapors	Flammability Limit Range (%)	MIE (mJ)	Critical Volume Fraction (%)
C9H20	0.7~5.6	0.523	2.8
C10H22	0.8~5.4	0.857	2.5
C11H24	0.6~6.5	1.127	2.0

.

As indicated in Figure 6 and Table 6, the experimentally determined MIE values for n-nonane, n-decane, and n-undecane were 0.523 mJ, 0.857 mJ, and 1.127 mJ, respectively, with corresponding sensitive volume fractions of 2.8%, 2.5%, and 2.0%.

The relationship between the MIE of alkane vapors and the carbon chain length was further investigated; the corresponding results are presented in Figure 7.

As shown in Figure 7, the MIE of long-chain alkane vapors exhibits a gradual increase with carbon chain length. The growth trend is relatively moderate from C₅ to C₈ but becomes markedly steeper beyond C₈. Owing to the measurement range limitation of the experimental system (<20 mJ), the MIE of alkanes with longer carbon chains (e.g., n-dodecane and n-tridecane) could not be accurately determined; it is inferred that their values would be substantially higher. Overall, the MIE increased by 471% from C₅ to C₁₁, with a particularly sharp rise of 115% observed from C₉ to C₁₁. The strong dependence of MIE on carbon chain length is further supported by nonlinear fitting, yielding a coefficient of determination (R²) of 0.98, which indicates a highly significant correlation.

The observed increase in MIE with carbon chain length in alkanes can be attributed to systematic changes in their physicochemical properties. At the molecular level, the reactivity of combustible substances serves as a fundamental determinant of their MIE. Highly reactive molecules demonstrate enhanced bond dissociation tendencies and greater chain-reaction propagation capability, leading to kinetically facilitated radical generation upon spark exposure. This accelerated reaction initiation significantly reduces the energy threshold required for sustained ignition [35]. Moreover, enhanced van der Waals interactions in longer-chain alkanes result in a sharp decline in the gas-phase diffusion coefficient, which considerably delays fuel–oxidizer mixing and reduces mixing efficiency within the ignition kernel [36]. Furthermore, cracking of long-chain alkanes generates more stable free radicals, diminishing the reactivity of chain-branching reactions and necessitating higher energy input to sustain combustion [37].

To our knowledge, this study presents the first systematic determination of the MIE for C₉–C₁₁ n-alkanes, thereby addressing a significant gap in the foundational safety parameters of high-boiling-point long-chain alkane fuels. Experimental results demonstrate an exponential increase in MIE with carbon chain length, evidencing a 471% rise from C₅ to C₁₁. Although long-chain alkanes are frequently perceived as lower fire risks owing to their high flash points, their vapor MIE values at critical concentrations—such as 1.127 mJ for n-undecane at 2.0 vol%—remain well below the typical human electrostatic discharge threshold (10 mJ), underscoring a persistent ignition hazard in industrial environments.

These findings offer critical insights for enhancing safety protocols in the storage and transportation of aviation kerosene and diesel components. A carbon-number-dependent model enables the precise determination of inerting concentrations—for example, through the introduction of nitrogen to suppress ignition—and supports the selection of appropriate explosion-proof electrical equipment. Furthermore, the strong correlation between MIE and carbon chain length (R² = 0.98) advances the mechanistic understanding of how molecular structure influences combustion chain reactions, providing a foundation for predictive models of ignition behavior in multi-component fuels.

4. Conclusions

This study developed a systematic experimental apparatus and measurement methodology for determining the minimum ignition energy (MIE) of n-alkane fuel vapors. The system’s sensitivity parameters were established through comprehensive MIE measurements of propane/air mixtures under varied experimental conditions. The reliability of the apparatus was validated by systematically evaluating the MIE of C₅–C₈ n-alkane vapors under standardized conditions. Furthermore, the influence of vapor concentration on MIE was thoroughly investigated. Subsequent measurements extended to C₉–C₁₁ n-alkanes revealed a pronounced dependence of MIE on carbon chain length, providing critical experimental support for the development of fuel safety standards and improved fire risk assessment.

Employing a propane/air mixture as the calibration gas, the sensitive capacitance and electrode gap of the system were determined to be 14.0 pF and 2.0 mm, respectively. Under these optimized conditions, the MIE values of four alkane vapors—n-pentane, n-hexane, n-heptane, and n-octane—were measured. The experimentally determined MIE values for C₅–C₈ alkane vapors demonstrate close agreement with literature data, with absolute deviations ranging from 0.005 to 0.063 mJ and relative errors between 2.02% and 26.25%. confirming the high reliability and precision of both the experimental apparatus and methodology for MIE determination of liquid fuel vapors.

MIE measurements for the four alkane vapors across varying volume fractions yielded values of 0.197 mJ, 0.253 mJ, 0.303 mJ, and 0.323 mJ, respectively, showing a characteristic V-shaped distribution of MIE versus concentration. The corresponding sensitive volume fractions were determined to be 3.4%, 3.3%, 3.0%, and 2.8%—systematically higher than their respective stoichiometric values. This consistent offset indicates a statistically significant shift in the optimal ignition concentration toward fuel-rich conditions.

The measured MIE values for the long-chain alkanes n-nonane, n-decane, and n-undecane were 0.523 mJ (at 2.8 vol%), 0.857 mJ (at 2.5 vol%), and 1.127 mJ (at 2.0 vol%), respectively. A significant increase in MIE with carbon chain length was observed, showing a 471% rise from C₅ to C₁₁ alkanes. The strong correlation between MIE and carbon number is further supported by a nonlinear fit yielding R² = 0.98.