Oxygen Consumption and Heat-Release Characteristics of Low-Temperature Coal Oxidation Considering a Minimum Oxygen-Concentration Threshold

Abstract

Conventional standard oxygen-consumption-rate models can retain an apparent dependence on reactor height and gas flow rate when outlet oxygen concentrations become low. To examine this issue, programmed-temperature oxidation experiments were conducted using gas-fat coal from the Zhuxianzhuang Coal Mine. Two packed coal-bed configurations were used: a full bed (coal-bed height, 20 cm; packed-coal volume, 250 cm³) and a half bed (coal-bed height, 10 cm; packed-coal volume, 125 cm³); both were operated at inlet flow rates of 80, 100, and 120 mL min⁻¹. Outlet O₂, CO, and CO₂ samples were collected near the end of each isothermal hold and analysed by gas chromatography. An empirical effective oxygen-concentration correction parameter was introduced to revise the conventional standard oxygen-consumption-rate model, and corresponding standard CO and CO₂ generation-rate and calculated heat-release-intensity models were derived. The outlet oxygen concentration exhibited four apparent stages with increasing temperature: slow decrease, rapid decrease, renewed slow decrease, and stabilization. Above approximately 195 °C, the outlet oxygen concentration approached a nonzero plateau. On the basis of this plateau and the consistency of results obtained under the tested conditions, a value of 1.21 vol.% was selected as an empirical correction parameter for the present system. The conventional model produced increasingly separated oxygen-consumption-rate curves at high temperatures and yielded R² = 0.930. After introducing the correction parameter, the curves obtained under the tested conditions showed improved convergence and R² increased to 0.993. The revised standard CO and CO₂ generation rates and calculated heat-release intensities likewise showed reduced dependence on reactor height and flow rate within the present dataset and increased exponentially with temperature. These empirical correlations describe the tested coal under the specified reactor and heating conditions. Independent validation is required before extending them to other coals or operating conditions.

1. Introduction

China is recognized as the world’s largest energy market and the largest coal producer and consumer, with coal remaining central to its energy supply [1]. As coal resources are extracted at increasing depths, complex thermal environments and risks of coal spontaneous combustion are becoming increasingly prominent [2,3,4]. Deep mining is often accompanied by severe thermal hazards, which progressively increase the risk of major accidents. Consequently, miners’ safety and normal mine operations are continuously threatened [5,6]. Mine fires are regarded as one of the most severe mining hazards. Coal-dust and gas explosions can also be triggered, thereby inducing secondary disasters and aggravating the severity and destructive consequences of mine fires.

More than 90% of mine-fire accidents are reported to be caused by spontaneous combustion of residual coal [7]. Coal spontaneous combustion is characterized by continuous physical adsorption, chemical adsorption, and oxidation reactions between coal and oxygen at ambient temperature [8]. Progressive heat accumulation and temperature rise occur when the generated heat exceeds the dissipated heat [9]. An exponential increase in standard oxygen-consumption rate and heat-release intensity with temperature has been reported [10]. Accordingly, extensive studies have been conducted on these parameters to evaluate the oxidation characteristics of coal. Zhu et al. [11] derived standard oxygen-consumption rates and indicator-gas generation rates using chemical kinetics and chemical equilibrium theory. Qi et al. [12] analysed oxygen-consumption rates of coals with different metamorphic degrees. They reported nonlinear increases with temperature for low-rank coal and segmented nonlinear increases for high-rank coal. At 100 °C, the difference in oxygen-consumption rates among coals of different metamorphic degrees reached 78.6%. Jia et al. [13] examined indicator-gas generation rates under oxygen concentrations of 6%, 9%, 12%, 15%, 18%, and 21%. They showed that gas-generation rates increased with temperature and were proportional to the ambient oxygen concentration. They also reported lower critical temperatures under higher oxygen concentrations than under oxygen-deficient conditions. Yin et al. [14] developed an oxygen-consumption-rate equation based on heat and mass transfer characteristics and the Arrhenius equation. They demonstrated that the oxygen-consumption rate increased exponentially with temperature. Liu et al. [15] developed a low-temperature oxidation kinetic model for long-flame coal by incorporating variable reaction orders. They showed that the coal–oxygen reaction order was generally below unity and varied in stages with temperature. Under a fixed first-order assumption, the maximum error in the calculated oxygen-consumption rate reached 50.86%. Their results demonstrated a pronounced nonlinear relationship between oxygen concentration and the coal–oxygen reaction rate. Zhao et al. [16] conducted closed isothermal oxidation experiments on coals of different ranks and proposed the oxygen-consumption-rate integral parameter, OCRI. They further analysed its microscopic influencing factors using low-temperature nitrogen adsorption and infrared spectroscopy. Their results showed that OCRI comprehensively characterized oxygen-consumption capacity over an oxygen-concentration range of 0–20.96%. It could therefore be used to evaluate spontaneous-combustion propensity during the incubation period and under oxygen-deficient conditions. Zhang et al. [17] investigated coal heat-release and kinetic characteristics under different oxygen concentrations using simultaneous thermal analysis and Gaussian multi-peak fitting. They found that oxygen-deficient conditions reduced oxidation heat-release intensity, delayed characteristic temperatures, and prolonged reaction durations. They also showed that oxidative decomposition and gas-phase combustion shifted toward longer-lasting solid-phase combustion processes. Although these studies clarify how temperature and oxygen availability influence coal oxidation, they do not explicitly address, within programmed-temperature packed-bed tests, whether a condition-specific correction to the oxygen-concentration driving term can reduce the apparent dependence of conventional standard oxygen-consumption-rate calculations on coal-bed height and gas flow rate.

Programmed-temperature oxidation experiments can provide outlet oxygen concentrations, indicator-gas concentrations, standard oxygen-consumption rates, and calculated heat-release parameters. They have therefore been widely used to evaluate low-temperature coal oxidation and spontaneous-combustion hazards [18,19,20,21,22,23,24,25,26]. During an experiment, mixed gas is introduced from the bottom of the coal sample reactor and flows toward the outlet through the packed coal bed. Oxygen is consumed along the flow path, so the local oxygen concentration and actual consumption rate may vary axially. To reduce the influence of local oxygen concentration, actual oxygen-consumption rates are commonly converted to standard rates under a fresh-air reference condition. Conventional standard oxygen-consumption-rate models usually simplify coal–oxygen reactions as elementary reactions and assume that the rate is proportional to ambient oxygen concentration. Under this assumption, comparable standard oxygen-consumption rates should be obtained for the same coal under different flow rates and packing heights. However, calculated curves may separate as temperature increases and outlet oxygen concentration decreases. A nonzero outlet oxygen plateau does not by itself demonstrate that residual oxygen is unreactive: it can also reflect reactor hydrodynamics, axial dispersion, diffusion limitations, leakage, dead volume, or bed heterogeneity. The present experiments were not designed to distinguish these mechanisms. The plateau is therefore treated here as an empirical feature that motivates a system-specific correction to the oxygen-concentration driving term.

Accordingly, the present study examines whether an empirical effective oxygen-concentration correction parameter can reduce the dependence of a conventional standard oxygen-consumption-rate calculation on coal-bed height and gas flow rate under the tested programmed-temperature conditions. Previous studies have shown that coal oxidation and gas release are jointly affected by temperature, oxygen concentration, and time, and that oxygen-deficient environments can alter oxidation and heat-release behaviour [27,28]. Rather than claiming a universal kinetic cut-off, this study proposes a condition-specific correction based on the observed outlet oxygen plateau. Gas-fat coal from the Zhuxianzhuang Coal Mine was tested by varying coal-bed height and gas flow rate. The variations in O₂, CO, and CO₂ concentrations with temperature were analysed, and the conventional standard oxygen-consumption-rate model was revised. Standard CO and CO₂ generation-rate models and a calculated heat-release-intensity model were then derived.

2. Experimental Materials and Methods

2.1. Coal Sample Preparation and Basic Properties

To investigate the effects of coal-bed height and inlet gas flow on low-temperature coal oxidation, fresh coal samples were collected from a newly exposed wall after shearer cutting at the Zhuxianzhuang Coal Mine, Anhui Province, China. The samples were immediately wrapped in plastic film, sealed in airtight bags, and transported to the laboratory to minimise pre-test oxidation. After crushing, the 60–80 mesh fraction was used to maintain a consistent particle-size range across the programmed-temperature oxidation tests. Six experimental groups were prepared for the comparison: three full-bed groups (approximately 180 g each) and three half-bed groups (approximately 90 g each).

Proximate analysis was conducted in accordance with GB/T 30732-2014 [29]. True relative density and oxygen adsorption capacity were determined according to GB/T 217-2008 [30] and GB/T 20104-2006 [31], respectively. For ultimate analysis, the carbon, hydrogen, nitrogen, and sulphur contents were determined by combustion elemental analysis, while the oxygen content was measured directly by instrumental analysis. The results are summarised in Table 1. The coal had a dry ash-free volatile matter content of 29.22% and an oxygen adsorption capacity of 1.10 mL g⁻¹. According to the classification criterion for coal spontaneous-combustion tendency, the sample was classified as Class I, indicating a high propensity for spontaneous combustion.

Table 1. Proximate and ultimate analyses and basic properties of the Zhuxianzhuang coal sample.

Coal Samples	Coal	True Relative Density	Oxygen Adsorption Capacity (mL/g)	Proximate Analysis				Ultimate Analysis
ZXZ	Gas-fat coal	1.41	1.1	Mₐd/%	Aₐd/%	Vdaf/%	FCₐd/%	C/%	H/%	O/%	N/%	S/%
				1.64	8.91	29.22	60.23	72.15	4.72	19.52	1.28	2.33

2.2. Programmed-Temperature Oxidation Experimental System

The low-temperature coal-oxidation apparatus comprised gas-supply, heating-control, and data-acquisition subsystems. The gas-supply subsystem included oxygen and nitrogen cylinders, constant-pressure and flow-control valves, flow sensors, a gas-mixing chamber, and gas pipelines. Oxygen and nitrogen were mixed to obtain the prescribed inlet oxygen concentration, and the total flow was regulated with a rotameter. The heating-control subsystem comprised a programmable heating chamber, a coal sample reactor, a preheating copper tube, temperature sensors, and a temperature display. The data-acquisition subsystem comprised a GC-2014 gas chromatograph and LabSolutions data-processing software. Outlet gas was sampled immediately before the end of each isothermal hold for discrete O₂, CO, and CO₂ analysis; it was not continuously monitored. The overall configuration and main components of the programmed-temperature oxidation system are illustrated in Figure 1.

Figure 1. Programmed-temperature oxidation experimental system.

2.3. Temperature Uniformity Test

To characterize the temperature response at the monitored positions during programmed heating, temperature sensors were installed 3 cm from the top and bottom of the coal bed. The measured temperatures were compared with the programmed temperature, as shown in Figure 2. Both monitored positions followed the heating profile, indicating comparable temperature evolution at the measurement locations during the tests.

Figure 2. Comparison of the programmed temperature and measured temperatures in the coal sample reactor.

2.4. Experimental Scheme

Two packed-bed configurations were used to examine the effects of coal-bed height and gas flow rate: a full bed with a height of 20 cm and a packed-coal volume of 250 cm³, and a half bed with a height of 10 cm and a packed-coal volume of 125 cm³ (Figure 3). The reactors were operated at atmospheric pressure and supplied with an O₂–N₂ mixture containing approximately 21% O₂ at inlet flow rates of 80, 100, and 120 mL min⁻¹. The conditions for the six experimental groups (A1–A6) are summarised in Table 2. Each sample was heated from 35 to 215 °C at 1 °C min⁻¹, with a 20 min isothermal hold after each 10 °C increment. Gas samples were collected from the reactor outlet immediately before the end of each hold and analysed by gas chromatography.

Figure 3. Full-height and half-height coal sample reactors.

Table 2. Experimental conditions for programmed-temperature oxidation.

Number	Coal Sample Mass/g	Coal Sample Volume/cm3	Inlet Oxygen Volume Fraction/%	Gas Flow Rate/(mL·min−1)	Reactor Configuration
A1	180.1	250	20.98	80	Full-height
A2	90.1	125	21.01	80	Half-height
A3	180.1	250	20.96	100	Full-height
A4	90.0	125	20.99	100	Half-height
A5	180.0	250	20.97	120	Full-height
A6	89.9	125	21.04	120	Half-height

Table 2. Experimental conditions for programmed-temperature oxidation.

Number	Coal Sample Mass/g	Coal Sample Volume/cm3	Inlet Oxygen Volume Fraction/%	Gas Flow Rate/(mL·min−1)	Reactor Configuration
A1	180.1	250	20.98	80	Full-height
A2	90.1	125	21.01	80	Half-height
A3	180.1	250	20.96	100	Full-height
A4	90.0	125	20.99	100	Half-height
A5	180.0	250	20.97	120	Full-height
A6	89.9	125	21.04	120	Half-height

At each flow rate, the full-bed and half-bed configurations were compared to evaluate the effect of coal-bed height. Within each bed configuration, tests at 80, 100, and 120 mL min⁻¹ were compared to examine the combined effects of oxygen supply and nominal gas residence time. These comparisons were used to evaluate whether the conversion reduced systematic variation in the condition-normalized results across the tested operating conditions.

2.5. Standard Oxygen-Consumption-Rate Model

2.5.1. Conventional Standard Oxygen-Consumption-Rate Model

To describe oxygen transport and consumption during programmed-temperature oxidation, a one-dimensional axial mass-balance model was used. The oxygen concentration in the packed coal bed was assumed to be affected by axial diffusion, gas seepage, and coal–oxygen reaction:

$${\displaystyle \frac{\mathsf{\partial }{C}_{O_2}}{\mathsf{\partial }t}}=n{k}_1{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }x}}({\displaystyle \frac{\mathsf{\partial }{C}_{O_2}}{\mathsf{\partial }x}})-v_x{\displaystyle \frac{\mathsf{\partial }{C}_{O_2}}{\mathsf{\partial }x}}-V_{O_2}(x,t)$$

(1)

The reactor had a relatively small diameter, and 350-mesh stainless-steel filters were installed at both ends of the coal bed to distribute the gas flow. For the conversion of the discrete inlet and outlet gas-concentration measurements, gas flow through the bed was approximated as one-dimensional and quasi-steady at the end of each isothermal hold. The transient accumulation and axial-diffusion terms were therefore neglected, giving:

$$V_{O_2}(x,t)=-v_x{\displaystyle \frac{d{C}_{O_2}}{dx}}=-{\displaystyle \frac{Qd{C}_{O_2}}{nSdx}}$$

(2)

At a specified temperature, the local oxygen-consumption rate was assumed to be proportional to the local oxygen concentration [32]:

$$V_{O_2}(x,t)=K{C}_{O_2}(x,t)$$

(3)

To compare oxygen-consumption rates at different axial positions, the local rate was converted to the reference oxygen-concentration condition of fresh inlet gas:

$$V_{O_2}^0(T)={\displaystyle \frac{C_{O_2}^0{V}_{O_2}(x,t)}{C_{O_2}(x,t)}}$$

(4)

Combining Equations (2) and (4) and integrating along the packed-bed height gives the conventional standard oxygen-consumption-rate model:

$$V_{O_2}^0(T)={\displaystyle \frac{Q{C}_{O_2}^0}{SLn}}ln({\displaystyle \frac{C_{O_2}^1}{C_{O_2}^2}})$$

(5)

where, t is time in s; x and L are the axial coordinate and packed-bed height in m; Q is gas volumetric flow rate in m³·s⁻¹; S is reactor cross-sectional area in m²; k₁ is the oxygen-diffusion coefficient in m²·s⁻¹; v_x is the gas seepage velocity in m·s⁻¹; and K is the temperature-dependent reaction-rate constant in s⁻¹. $C_{{\mathrm{O}}_2}^1$ and $C_{{\mathrm{O}}_2}^2$ denote the inlet and outlet oxygen concentrations, respectively. The bed void fraction n was fixed at 0.41 in the rate calculations for all six tests, consistent with the value adopted in the authors’ earlier work on Zhuxianzhuang coal [33]. Here, n is the ratio of void volume to total packed-bed volume, and nSL represents the void volume used for rate normalisation.

2.5.2. Minimum Oxygen-Concentration Threshold and Revised Model

During programmed-temperature oxidation, the outlet oxygen concentration approached a nonzero plateau at high temperatures. To account empirically for the reduced oxygen-concentration driving force under these conditions, an effective oxygen-concentration threshold, C_m, was introduced into the conventional model. C_m is an operational correction parameter used for the present reactor system and experimental conditions rather than direct evidence of a universal intrinsic reaction boundary.

$$V_{O_2}(x,t)=K(T)[C_{O_2}(x,t)-C_m]$$

(6)

Equation (6) is applied only when the local oxygen concentration exceeds C_m. The empirical expression is not extrapolated to $C_{{\mathrm{O}}_2}$ less than or equal to C_m; therefore, it is not used to generate a negative oxygen-consumption rate. Integrating the threshold-corrected expression along the packed-bed height gives the revised standard oxygen-consumption-rate model:

$$V_{O_2}^0(T)={\displaystyle \frac{Q(C_{O_2}^0-C_m)}{SLn}}ln\left[{\displaystyle \frac{C_{O_2}^1-C_m}{C_{O_2}^2-C_m}}\right]$$

(7)

For test A1 at 126.7 °C, the inlet and outlet oxygen volume fractions were 20.98% and 13.655%, respectively. Using the correction of 1.21 vol.%, the logarithmic term in Equation (7) is ln[(0.2098 − 0.0121)/(0.13655 − 0.0121)] = 0.46285. This ratio is unchanged when the volume fractions are converted to molar concentrations at a common reference temperature and pressure. The flow rate of 80 mL min⁻¹ and packed-bed volume of 250 cm³ correspond to 1.3333 × 10⁻⁶ m³ s⁻¹ and 2.50 × 10⁻⁴ m³, respectively. With n = 0.41, Q/(nSL) = 0.013008 s⁻¹. The coefficient multiplying the concentration difference ($C_{O_2}^0$ − C_m) in Equation (7) is therefore 6.0208 × 10⁻³ s⁻¹. When the concentration difference is expressed in mol m⁻³, the resulting rate has units of mol m⁻³ s⁻¹; conversion to mol cm⁻³ s⁻¹ requires multiplication by 10⁻⁶.

The choice of C_m was assessed by evaluating candidate values from 0 to 1.22 vol.% at 0.01 vol.% intervals, below the lowest measured outlet oxygen concentration of 1.23 vol.%. For each candidate, the six calculated rate curves were linearly interpolated to 19 common temperatures from 35 to 215 °C. At each temperature, the coefficient of variation was calculated as the sample standard deviation divided by the mean. The mean squared coefficient of variation, expressed using fractional rather than percentage values, was used as the dispersion score. A numerical tolerance of 1% above the minimum dispersion score was used to identify candidates with near-minimum dispersion. Within this range, the smallest Cm was selected to limit the local sensitivity of the logarithmic term in Equation (7) to the outlet oxygen concentration. This sensitivity was assessed at the lowest measured outlet oxygen concentration of 1.23 vol.%. The corrected rates were then correlated with temperature using:

$$V_{O_2}^0(T)=a exp(b_{v}T)$$

(8)

where T is the coal-bed temperature in °C, a is the oxygen-consumption-rate coefficient in mol cm⁻³·s⁻¹, and b_v is the temperature coefficient in °C⁻¹.

2.6. Standard CO and CO₂ Generation-Rate Models

To express CO and CO₂ formation on the same reference basis as the revised standard oxygen-consumption rate, the outlet concentrations of the two gases were normalized by the corresponding oxygen-concentration decrease across the packed coal bed. The conversion adopts the one-dimensional, quasi-steady approximation and common reference-state convention described in Section 2.5. Because the inlet gas was prepared from O₂ and N₂, the inlet concentrations of CO and CO₂ were taken as zero in the present calculation.

The standard CO generation rate was calculated as:

$$V_{CO}^0(T)={\displaystyle \frac{C_{CO,out}}{C_{O_2}^1-C_{O_2}^2}}{V}_{O_2}^0(T)$$

(9)

The standard CO₂ generation rate was calculated in the same manner:

$$V_{{CO}_2}^0(T)={\displaystyle \frac{C_{C{O}_2,out}}{C_{O_2}^1-C_{O_2}^2}}{V}_{O_2}^0(T)$$

(10)

Here, $C_{CO,\mathrm{out}}$ and $C_{{CO}_2,\mathrm{out}}$ denote the outlet CO and CO₂ concentrations, respectively, while $C_{{\mathrm{O}}_2}^1$ and $C_{{\mathrm{O}}_2}^2$ denote the inlet and outlet oxygen concentrations. When all concentrations are expressed on the same molar basis at a common reference temperature and pressure, the concentration ratios are dimensionless. Both gas-generation rates therefore have the same units as the revised standard oxygen-consumption rate, mol cm⁻³ s⁻¹. Equations (9) and (10) use the oxygen-consumption rate obtained from Equation (7) and apply when $C_{{\mathrm{O}}_2}^1$ > $C_{{\mathrm{O}}_2}^2$ > C_m.

2.7. Heat-Release-Intensity Calculation

The heat-release calculation accounted for oxygen chemisorption and the formation of CO and CO₂. The contribution from physical adsorption was assumed to be small and was neglected. The volumetric heat-release intensity was therefore expressed as:

$$q(T)=q_{O_2}(T)+q_{CO}(T)+q_{{CO}_2}(T)$$

(11)

Here, q(T) is the calculated volumetric heat-release intensity, and $q_{{\mathrm{O}}_2}(\mathrm{T})$, $q_{\mathrm{CO}}(\mathrm{T})$, and $q_{{\mathrm{C}\mathrm{O}}_2}(\mathrm{T})$ are the calculated contributions associated with oxygen chemisorption, CO formation, and CO₂ formation, respectively. All four terms are expressed in J m⁻³·s⁻¹ and use the same model-volume basis as the rates defined in Section 2.5. With the molar thermal effects expressed in J mol⁻¹, Equation (11) requires the oxygen-consumption and gas-generation rates to be expressed in mol m⁻³ s⁻¹, yielding a volumetric heat-release intensity in J m⁻³ s⁻¹. Rates expressed in mol cm⁻³ s⁻¹ require multiplication by 10⁶ before substitution.

The component calculations use the revised standard oxygen-consumption rate and the corresponding standard CO and CO₂ generation rates at each discrete sampling temperature. Thus, q(T) is a model-derived quantity rather than a direct calorimetric measurement [34].

The relationship between the calculated heat-release intensity and coal temperature was then represented empirically by:

$$q(T)=h exp(b_{q}T)$$

(12)

where T is the programmed coal temperature in °C, h is the heat-release-intensity coefficient in J m⁻³ s⁻¹, and b_q is the temperature coefficient in °C⁻¹. This empirical correlation describes the calculated heat-release intensity over the experimental temperature range of 35–215 °C.

3. Results and Discussion

3.1. Evolution of Outlet Oxygen Concentration

Figure 4 presents the variation in outlet oxygen concentration with programmed temperature under different coal-bed heights and gas flow rates. For all six experimental groups, the outlet oxygen concentration decreases with increasing temperature and exhibits four successive intervals: a slow decrease from 35 to 85 °C, a rapid decrease from 85 to 165 °C, a renewed slow decrease from 165 to 195 °C, and stabilization above 195 °C. Within 35–85 °C, the coal–oxygen reaction remains relatively weak and the outlet oxygen concentration decreases slowly. Between 85 and 165 °C, increasing temperature promotes coal oxidation and oxygen consumption, resulting in a rapid decrease in outlet oxygen concentration. Between 165 and 195 °C, the outlet oxygen concentration becomes low and its rate of decrease gradually diminishes. Above 195 °C, the outlet oxygen concentration approaches a low and nonzero stable range.

Figure 4. Variation in outlet oxygen concentration under different gas flow rates and coal sample reactor heights.

At the same gas flow rate, the outlet oxygen concentration is generally lower in the full-bed configuration than in the half-bed configuration. The full-bed configuration contains a greater coal mass and provides a longer gas-flow path, allowing a greater cumulative extent of coal oxidation before the gas reaches the outlet. At the same coal-bed height, a higher gas flow rate produces a higher outlet oxygen concentration at the same programmed temperature. With a constant reactor cross-sectional area, increasing gas flow shortens the nominal gas residence time and reduces gas–coal contact time. The outlet oxygen concentration is therefore jointly influenced by coal loading, gas residence time, oxygen supply, and the progress of coal oxidation [35].

The four-stage variation in outlet oxygen concentration corresponds to the changing combined effects of thermal activation, oxygen consumption, oxygen supply, and gas transport during programmed-temperature oxidation. At lower temperatures, thermal activation is limited and oxygen supply is relatively sufficient. As temperature increases, coal oxidation is enhanced and oxygen consumption increases. At high temperatures, the outlet oxygen concentration enters a low and stable range. This high-temperature outlet oxygen-concentration range provides the observational basis for introducing the empirical Cm correction in Section 3.4.

3.2. CO and CO₂ Generation Characteristics

Figure 5 shows the variations in outlet CO and CO₂ concentrations with temperature under different experimental conditions. The outlet CO concentration increases at an accelerating rate with increasing temperature in all groups. Below 135 °C, the CO concentration increases slowly. Above 135 °C, the CO concentration increases rapidly, indicating a marked enhancement in low-temperature coal oxidation activity. A similar temperature-response pattern is observed for the CO₂ concentration [36].

Figure 5. Variations in outlet CO and CO₂ concentrations under different gas flow rates and coal sample reactor heights.

Above approximately 135 °C, the full bed generally produced higher outlet CO and CO₂ concentrations than the half bed at the same flow rate (Figure 5). The larger coal mass and longer flow path in the full bed allow gaseous products to accumulate over a greater volume of reacting coal before reaching the outlet. The difference between the two bed configurations became more apparent as temperature increased and gas release accelerated. At both bed heights, the outlet concentrations increased when the flow rate rose from 80 to 100 mL min⁻¹, but decreased when it was further increased to 120 mL min⁻¹. Thus, 100 mL min⁻¹ gave the highest outlet CO and CO₂ concentrations among the three flow rates examined. This nonmonotonic response is consistent with the competing effects of oxygen supply, residence time, and dilution. Increasing the flow supplies more oxygen to the bed, while shortening gas–coal contact time and increasing the volume of gas carrying the released products.

The simultaneous increase in CO and CO₂ at higher temperatures is consistent with their formation through oxidation and decomposition of oxygen-containing structures in coal. The measured outlet concentrations also integrate the effects of gas transport and coal loading. The standard generation rates considered in Section 3.6 provide a common oxygen reference for comparing gas release across the experimental conditions.

3.3. Applicability of the Conventional Standard Oxygen-Consumption-Rate Model

The outlet oxygen concentration data were substituted into the conventional standard oxygen-consumption-rate model. The resulting variations in standard oxygen-consumption rate with temperature under different flow rates and reactor heights are shown in Figure 6.

Figure 6. Standard oxygen-consumption-rate curves under different gas flow rates and coal sample reactor heights.

As shown in Figure 6, the standard oxygen-consumption-rate curves nearly overlap at low temperatures. As temperature increases, the curves gradually separate under different reactor heights and gas flow rates. At the same flow rate, lower standard oxygen-consumption rates are gradually obtained from the full-height reactor than from the half-height reactor. At the same reactor height, higher standard oxygen-consumption rates are gradually obtained under higher flow rates. Standardisation is intended to compare oxygen consumption at a common reference concentration and to reduce the influence of differences in experimental conditions. Under lower flow rates, gas residence time is longer and the outlet oxygen-consumption fraction is higher. Nevertheless, lower standard oxygen-consumption rates are calculated by the conventional model. This indicates that simple proportionality between the actual oxygen-consumption rate and total oxygen concentration cannot adequately describe high-temperature, low-oxygen coal oxidation.

Structurally, the conventional model describes axial oxygen consumption using a logarithmic term based on the ratio of inlet to outlet oxygen concentrations. When outlet oxygen concentration is high, small concentration differences among conditions exert limited effects on the calculated results. When outlet oxygen concentration becomes low, the logarithmic term is more sensitive to changes in outlet oxygen concentration. Differences associated with reactor height, flow rate, and measurement variation can therefore be amplified. In addition, the conventional expression treats all outlet oxygen as equally available for reaction. The separation in Figure 6 consequently indicates a mismatch between the conventional simplifying assumptions and the present high-temperature, low-outlet-oxygen data. It does not by itself identify the specific physical mechanism responsible for that mismatch.

3.4. Minimum Oxygen-Concentration Threshold and Revised Model

Among the examined candidates, the minimum dispersion score was 0.060472 at C_m = 1.22 vol.%. At 1.21 vol.%, the score was 0.060787, only 0.52% higher and within the adopted 1% tolerance. At the lowest measured outlet oxygen concentration of 1.23 vol.%, the concentration differences entering the logarithmic term in Equation (7) are 0.02 and 0.01 vol.% for C_m values of 1.21 and 1.22 vol.%, respectively. Consequently, the local sensitivity of this term to the outlet oxygen concentration is twice as high at C_m = 1.22 vol.%. The value of 1.21 vol.% was therefore retained as an empirical compromise between near-minimum curve dispersion and lower sensitivity at the low end of the measured oxygen-concentration range. Figure 7 presents the resulting standard oxygen-consumption rates for the six experimental conditions.

Figure 7. Revised standard oxygen-consumption-rate curves under different gas flow rates and coal sample reactor heights.

The correction becomes more influential as outlet oxygen concentration decreases. When the outlet concentration remains well above C_m, subtracting the correction produces only a limited change in the concentration terms. As the outlet concentration approaches C_m, the logarithmic term in Equation (7) responds more strongly to the correction. Its influence is therefore greatest in the high-temperature region, where oxygen depletion is most pronounced. Figure 7 shows that the corrected curves retain the increasing trend with temperature while becoming more closely grouped across bed heights and flow rates. The change is particularly evident towards the upper end of the heating range, where the conventional curves in Figure 6 show greater separation. The correction therefore improves the comparison among the six conditions without changing the overall temperature-dependent behaviour of oxygen consumption.

3.5. Comparison Between the Conventional and Revised Standard Oxygen-Consumption-Rate Models

Figure 8 compares the exponential correlations for the conventional and corrected oxygen-consumption rates. Residuals relative to these curves were evaluated using the 114 rate values from the six tests. RMSE and MAE [37] were divided by the corresponding data range and expressed as percentages. Variation among the tests was assessed after linear interpolation to common temperatures from 35 to 215 °C at 10 °C intervals. The coefficient of variation at each temperature was calculated as the sample standard deviation divided by the mean.

Figure 8. Comparison of fitting results for the revised and conventional standard oxygen-consumption-rate models.

The corrected rates followed a more consistent exponential relationship with temperature than the conventional rates (Figure 8). The reported R² increased from 0.9304 to 0.9932. Evaluation against the displayed curves gave range-normalised RMSE values of 6.61% for the conventional calculation and 1.76% for the corrected calculation. The corresponding range-normalised MAE values were 3.97% and 1.07%, respectively. Both error measures therefore indicate closer agreement between the corrected rate values and the common exponential curve. The reduction in variation among the six conditions was also evident from the coefficients of variation. Their mean decreased from 22.61% to 16.66% over 35–215 °C and from 12.06% to 4.76% over 135–215 °C. The stronger improvement in the higher-temperature interval coincides with the region of greater oxygen depletion, where the concentration correction has its largest influence.

The difference between the full-range and higher-temperature coefficients of variation also reflects the magnitude of the rates. At low temperatures, small mean rates can give appreciable relative variation even when the absolute differences between curves appear small. The lower coefficient of variation above 135 °C therefore complements the visual convergence of the corrected curves and shows that their closer grouping is maintained as oxygen consumption increases.

3.6. Revised Standard CO and CO₂ Generation Rates

The outlet CO and CO₂ concentrations measured for each experimental group were substituted into Equations (9) and (10), respectively. Using the revised standard oxygen-consumption rate calculated from Equation (7), the revised standard CO and CO₂ generation rates were obtained. The results are presented in Figure 9.

Figure 9. Standard CO and CO₂ generation rates under different gas flow rates and coal sample reactor heights.

The standard CO and CO₂ generation rates increased with coal temperature, with a more pronounced rise above approximately 135 °C (Figure 9). This behaviour follows the accelerated increase in the corresponding outlet concentrations. Although the six conditions shared the same overall temperature dependence, differences remained between the individual curves. The mean coefficients of variation over 35–215 °C were 39.33% for CO and 26.87% for CO₂. Over 135–215 °C, these values decreased to 22.18% and 18.34%, respectively. CO therefore showed greater relative variation than CO₂, while both gases exhibited closer agreement among the tests in the higher-temperature interval. At lower temperatures, the small gas-generation rates make relative variation more sensitive to differences between individual measurements.

Equations (9) and (10) combine the corrected oxygen-consumption rate with the corresponding gas-to-oxygen concentration ratio. The conversion establishes a common oxygen reference, while retaining differences in the amount of each gaseous product released per unit oxygen consumed. Consequently, similar oxygen-consumption curves can coexist with greater variation in CO or CO₂ generation. The two gas-generation rates provide complementary information about product formation during oxidation. Flow-reactor experiments under varying gas compositions have shown that oxygen consumption and carbon-oxide generation can exhibit different responses [38].

3.7. Calculated Heat-Release Intensity

The revised standard oxygen-consumption rate, standard CO generation rate, standard CO₂ generation rate, and relevant thermal-effect parameters were substituted into Equation (11) to calculate the heat-release intensity for each experimental condition. Equation (12) was then used to fit the relationship between calculated heat-release intensity and temperature. The calculated heat-release-intensity curves and fitted curves are shown in Figure 10 and Figure 11, respectively, and the fitted parameters for oxygen consumption and heat release are listed in Table 3.

Figure 10. Heat-release-intensity curves under different gas flow rates and coal sample reactor heights.

Figure 11. Fitted heat-release-intensity curves under different gas flow rates and coal sample reactor heights.

Table 3. Fitting parameters for oxygen consumption and heat release of the Zhuxianzhuang coal sample.

Parameter	Symbol	Value	Unit
Oxygen-consumption-rate coefficient	a	0.710 × 10−5	mol·cm−3·s−1
Oxygen-consumption-rate exponential coefficient	bv	0.0335	°C−1
Heat-release-intensity coefficient	h	0.317	J·m−3·s−1
Heat-release-intensity exponential coefficient	bq	0.0377	°C−1

The calculated heat-release intensity increased exponentially with temperature (Figure 10 and Figure 11). The six profiles remained closely grouped, with a mean coefficient of variation of 5.15% over 35–215 °C. Because Equation (11) combines the contributions from oxygen chemisorption and CO and CO₂ formation, the heat-release curve integrates the temperature dependence of these processes.

The heat-release temperature coefficient, b_q = 0.0377 °C⁻¹, exceeded the oxygen-consumption coefficient, b_v = 0.0335 °C⁻¹, giving a steeper fitted temperature dependence for heat release. This difference is consistent with the combined contributions in Equation (11), which need not have identical temperature responses. The fitted correlations describe how the calculated oxygen-consumption rate and heat source increase during the prescribed heating programme.

3.8. Limitations

The correlations were developed and assessed using the same six tests on the 60–80 mesh fraction of Zhuxianzhuang coal. Their present scope is limited to bed heights of 10 and 20 cm, an inlet oxygen concentration of approximately 21 vol.%, flow rates of 80–120 mL min⁻¹, and the specified heating programme. Independent experiments are needed to assess their transferability to other coals and operating conditions. The fixed porosity input and the coupled effects of reaction and gas transport may influence the calculated rates. Heat release was calculated from gas-based quantities and was not independently verified by calorimetry.

4. Conclusions

(1)

Under the programmed-temperature tests, the outlet O₂ concentration of the Zhuxianzhuang coal sample passed through four successive intervals with increasing temperature: slow decrease (35–85 °C), rapid decrease (85–165 °C), renewed slow decrease (165–195 °C), and a low, nonzero stable range above 195 °C. At a given gas flow rate, the full-bed configuration generally produced a lower outlet O₂ concentration than the half-bed configuration, whereas, at a given bed height, a higher gas flow rate produced a higher outlet O₂ concentration.

(2)

Outlet CO and CO₂ concentrations increased with coal temperature, with a marked acceleration above approximately 135 °C. Over 135–215 °C, the full bed generally produced higher concentrations than the half bed at the same flow rate. Both bed configurations gave their highest outlet concentrations at 100 mL min⁻¹ among the three flow rates examined, reflecting the combined influence of oxygen supply, gas residence time, and dilution.

(3)

The conventional standard oxygen-consumption-rate calculation produced progressively separated curves at high temperature for the different coal-bed heights and gas flow rates. Based on the observed low, nonzero outlet-O₂ range at high temperatures and comparison of the calculated curves across the tested conditions, an empirical correction parameter, C_m = 1.21 vol.%, was introduced into the revised calculation. The revised calculation reduced the systematic separation of the standard oxygen-consumption-rate curves, and the R² of the exponential fit increased from 0.9304 to 0.9932.

(4)

The revised standard oxygen-consumption rate, standard CO and CO₂ generation rates, and calculated heat-release intensity all increased exponentially with temperature. The fitted oxygen-consumption-rate parameters were a = 0.710 × 10⁻⁵ mol·cm⁻³·s⁻¹ and b_v = 0.0335 °C⁻¹, while the fitted heat-release-intensity parameters were h = 0.317 J·m⁻³·s⁻¹ and b_q = 0.0377 °C⁻¹. These preliminary correlations apply to the tested coal and experimental conditions; their extension to other systems requires further validation.