High-rank Coals Research Articles

Quantitative characterization of multiphase methane in coals using the NMR relaxation method

The gas content test for coalbed methane (CBM) reservoirs consists of measurements of lost, desorbed and residual gas, and it is a crucial parameter for evaluation of such reservoirs and optimization of favorable zones. The desorbed and residual methane contents are non-simultaneously determined by on-site desorption test, which is both time-consuming and susceptible to a volume effect – leading to a large variation in the results. Conventionally, adsorbed methane content is indirectly estimated by a volumetric method, which has the shortcoming of being unable to directly measure in-situ adsorbed gas content. Thus, it is important to develop an effective and convenient method for quantitative characterization of multiphase methane in coals using a single technique. In this study, we performed a series of nuclear magnetic resonance (NMR) adsorption measurements on 15 sub-bituminous coals and anthracites. The transverse relaxation time (T2) distributions of methane are measured for three peaks: P1 (T2 = 0.1–8 ms), P2 (T2 = 10–300 ms), and P3(T2 = 300–2000 ms), corresponding to adsorbed methane in the coal matrix, free methane within larger pores, and lastly free methane in the space between the sample and the sample cell, respectively. In this study, the NMR calibration coefficient of free methane (Kfree-methane) is set to 3.44 × 10−1 cm3/p.u., regardless of the coal rank. In contrast, the NMR adsorbed methane calibration coefficient (Kadsorbed-methane) varies substantially in coals of different ranks, but show little difference in coals with the same coal rank. We suggest the Kadsorbed-methane of 3.2 × 10−2 cm3/p.u., 2.3 × 10−2 cm3/p.u. and 3.6 × 10−2 cm3/p.u., corresponding to low-, medium- and high-rank coals, respectively, for estimating the adsorbed methane content. Using these calibration coefficients, multiphase methane can be quantitatively estimated using the NMR measurement alone. The method is applicable both in the laboratory and in the field, for desorbed and residual gas quantification.

A study on the flowability of gas displacing water in low-permeability coal reservoir based on NMR technology

Flowability of gas and water through low-permeability coal plays crucial roles in coalbed methane (CBM) recovery from coal reservoirs. To better understand this phenomenon, experiments examining the displacement of water by gas under different displacement pressures were systematically carried out based on nuclear magnetic resonance (NMR) technology using low-permeability coal samples of medium-high coal rank from Yunnan and Guizhou, China. The results reveal that both the residual water content (Wr) and residual water saturation (Sr) of coal gradually decrease as the displacement pressure (P) decreases. When P is 0–2 MPa, the decline rates of Wr and Sr are fastest, beyond which they slow down gradually. Coal samples with higher permeability exhibit higher water flowability and larger decreases in Wr and Sr. Compared with medium-rank coal, high-rank coal shows weaker fluidity and a higher proportion of irreducible water. The relationship between P and the cumulative displaced water content (Wc) can be described by a Langmuir-like equation, Wc = WLP/(PL + P), showing an increase in Wc in coal with an increase in P. In the low-pressure stage from 0 to 2 MPa, Wc increases most rapidly, while in the high-pressure stage (P > 2 MPa), Wc tends to be stable. The minimum pore diameter (d′) at which water can be displaced under different displacement pressures was also calibrated. The d′ value decreases as P increases in a power relationship; i.e., d′ the coal gradually decreases with the gradual increase in P. Furthermore, the d′ values of most of the coal samples are close to 20 nm under a P of 10 MPa.

Investigation on the surface electrical characteristics of coal and influencing factors

Electromagnetic radiation (EMR) can be used for the early warning of coal and rock underground spaces. However, the EMR generation mechanism for loaded coal or rock remains unclear, which limits the prediction accuracy of EMR technology. This study examined the electrical characteristics of the micro-surface of coals with different metamorphisms using atomic force microscopy, analyzing the generation mechanism of electric charge. The results showed that the surface potential and surface electrical charging density (SECD) of coal vary in the range of −28.5 to −87.4 μV and 58.98–312.97 μC/m2, respectively, demonstrating V-shaped trends with the rise in coal rank. At the nanoscale, both positive and negative electrical potential zones were observed, indicating the surface has weak electrical property. While at the micrometer scale, only very weak negative or neutral electrical potential zones were observed on the coal surface. Electronegativity of functional groups has significant influence on the negative electrical property of coal surface. As the dominant influencing group, the OH group has higher cumulative electronegativity than the other three groups in lower rank coals. However, the electronegativity of high-rank coals is determined by the combination of CC, OH, and CO groups. Overall, our results can not only provide a new way to exploring the mechanisms of EMR generated by the deformation and fracture of coal from the microscopic scale, but also have important theoretical and practical significance for revealing gas adsorption/desorption mechanism.

Influences of hydraulic fracturing on microfractures of high-rank coal under different in-situ stress conditions

The influence of hydraulic fracturing on coal microfractures (10–1000 μm) is an important part of the stimulation mechanism of coalbed methane (CBM) hydraulic fracturing, which is of great significance to improve the productivity of CBM. In this work, high-rank coal samples from Chengzhuang and Sihe Mine were selected for hydraulic fracturing simulation experiments, using stereoscopic microfracture scanning and binarization image processing methods, the mean aperture, surface density, connectivity, mean length and fracture porosity of microfractures were compared and analyzed under different in-situ stress conditions before and after hydraulic fracturing, and the permeability changes were calculated. It is found that hydraulic fracturing could increase the permeability of microfractures in coal seam significantly, and the permeability of microfractures after hydraulic fracturing was 0.43–14.82 times that before fracturing. Hydraulic fracturing did not induce new microfractures, but only the expansion of the original microfractures, which caused the mean aperture, mean length and fracture porosity of microfractures to increase by 39.85%, 47.70% and 115.59%, respectively. Stronger heterogeneity and larger horizontal in-situ stress difference will inhibit the expansion of microfractures. Under the same hydraulic fracturing conditions, there are larger interlayer differences for coal samples with stronger heterogeneity, and hydraulic fracturing will prioritize microfractures in the direction of parallel bedding planes. In addition, the smaller the horizontal in-situ stress difference, the microfractures expand uniformly during hydraulic fracturing, which is more conducive to the connection of microfractures.

The influence of steam drying process on combustion behavior of Indonesian low-rank coals

Steam drying process of the Low Rank Coals (LRCs) has been conducted to produce coal which is comparable with the High Rank Coal (HRC). Characterization of the raw and dried coals was carried out through proximate, ultimate, calorific value, Fourier Transform Infrared (FTIR) spectroscopy and Thermo Gravimetry-Differential Thermal Analysis (TG-DTA) to study the combustion behavior of the coals. This study used Indonesian low rank coals coming from Tabang (TKK coal) and Samurangau (SP coal), East Kalimantan. The results indicate that the calorific value of the dried coals increases significantly due to the decrease in moisture content of the coal. The FTIR spectrums show that the methylene-ethylene (RCH3/CH2) and aromaticity-aliphaticity ratios (Rar/al) of the dried coals increased while the ratio of RCO/ar decreased which reflect that the rank of the coals increased equivalent to the high rank coal (bituminous). Meanwhile, the TG-DTA indicates that the ignition temperature (Tig) and combustion rate (Rmax) of the dried coals increased. This analysis expresses that the dried coals produced by steam drying process have better combustion behavior due to the higher calorific value than those of the raw coals.

Coal Type, Temperature and Gasifiying Agent Effects on Low-Rank Coal Gasification Using CFD Method

Low-Rank Coal (LRC) gasification utilising Fluidised Bed Gasifier (FBG) is more efficient for LRC that has higher reactivity, moisture, tar, volatile, and ash content but lower calorific value compared to other types of coals. This work investigated the application of Computational Fluid Dynamics (CFD) in simulating LRC gasification under different temperatures which is lower (873K), normal (973K) and higher (1073K) temperature atmosphere. Besides that, the effect of LRC type and gasifying agents on the producer gas CO+H2 composition, Lower Heating Value (LHV) and Cold Gas Efficiency (CGE) were also studied using High-rank Coal (HRC) as comparison. The results obtained showed that LRC gasification using oxygen increased LHV and CGE. Lower temperature gasification using oxygen at 873 increased CO+H2, LHV and CGE for LRC compared to higher temperatures at 973K and 1073K. This prediction suggests that LRC gasification using oxygen at lower temperature increases the LRC gasification efficiency.

Effect of coal ranks on light aromatics production during reforming of pyrolysis volatiles over HZSM-5 under Ar and H2-assisted atmospheres

Light aromatics (LAs) can be produced from catalytic fast pyrolysis or catalytic hydropyrolysis of coals, which represents one of the most promising alternatives to liquid fossil fuels. In this work, catalytic upgrading of volatiles was performed in a drop bed reactor under an inert atmosphere (Ar) and a reducing atmosphere (H2) over HZSM-5. H2 is consumed during hydropyrolysis process. Coal samples were hydropyrolyzed to produce higher gas yield and lower content of residual char. The presence of H2 can yield more reactive H radicals which acts on C–O bond and C–C bond during pyrolysis conversion of coal. The released behavior of LAs is closely related to coal structure to a large extent. Catalytic pyrolysis of low rank coals produces more BTEXN than that of high rank coals. The H2 accelerated the formation of LAs, especially for low rank coals. A correlation was established between the aromatic-C structure of coals and LAs through the characterization and semi-quantitative analysis of coal structure and tar. The co-effect of HZSM-5 and H2 showed the highest yield of LAs during the low rank coals pyrolysis. The organic-oxygen species and C–H groups in the upgraded tar decreased gradually with the increase of coalification degree. Meanwhile, high aromaticity in coal can cause a poor pyrolysis reactivity, which may have influenced the secondary cracking reaction over HZSM-5.

Transformation of minerals at the boundary of magma-coal contact zone: case study from Wolonghu Coal Mine, Huaibei Coalfield, China

Mesozoic and Cenozoic magma activity in the Wolong Lake mining area of Huaibei is frequent, and the degree of magma intrusion into coal seams remarkable. On the one hand, magma intrusion affects the utilization of coal resources; on the other hand, the macro and trace elements in coal are redistributed to form new mineral types. This study uses the Wolong Lake magma intrusion coal seam as a research object. The mineral paragenesis for igneous rock, coke, and thermally-altered coal in an igneous intrusion zone is studied using SEM, XRD, and Raman spectroscopy. During igneous intrusion, the temperature and pressure of igneous rock metamorphose ambient low-rank coal to high-rank coal and coke. The response mechanism of minerals and trace elements to magmatic intrusion is discussed. The results are: ① SEM analysis shows that ankerite and pyrite are formed from magma intrusion. Both minerals are strongly developed in the magma-coal contact zone, and less well developed in thermally-altered coal. ② XRD analysis shows that igneous intrusion strongly influences the types and content of minerals in coke and thermally-altered coal. In addition to the increase amounts of ankerite and pyrite, chlorite, serpentine, and muscovite, and other secondary minerals, are generated following igneous intrusion. ③ Raman analysis suggests that thermally-altered coal possesses the characteristics of both pyrite and coke. Coke from the magma-coal boundary zone possesses the typical characteristics of pyrite. Igneous rock contains a mineral similar to pyrite, confirmed by both having similar Raman peaks. The scattering intensity of Ag indicates that the formation pressure of pyrite increases from thermally-altered coal via the boundary between the coke zone and the igneous rock.

Experimental Study on Temperature Response of Different Ranks of Coal to Liquid Nitrogen Soaking

Liquid nitrogen freeze–thaw has been used in oil, shale gas and coalbed methane exploitation as an efficient fracturing technology. This paper aimed to study the effect of different coal ranks and liquid nitrogen soaking times on the temperature distribution of coal samples, and to explore the temperature evolution mechanism of different coal ranks during liquid nitrogen soaking. For these objectives, the temperature change process, thermophysical parameters and infrared spectrum of different coal ranks under liquid nitrogen soaking were tested using, respectively, (a) liquid nitrogen soaking temperature measurement, (b) laser thermal instrument and (c) Fourier transform infrared spectrometer. The results showed that the temperature curves of coal samples under liquid nitrogen soaking were divided into an accelerated cooling stage I, a decelerated cooling stage II, and a maintained low-temperature stage III. As the number of liquid nitrogen soaking increased, the time required to reach low-temperature Stage III gradually shortened. During the rise in coal sample temperature, it increased with time in accordance with a logarithmic function. The order of absolute values of maximum heating/cooling speed was lignite > bituminite > anthracite. The higher coal rank is, more oxygen-containing functional groups were removed by coalification. The less content of oxygen-containing functional groups led to closer molecular structure, which resulted in smaller thermal conductivity and ultimately caused slower temperature transfer. The study results are of important guides to understand further the action process and mechanism of liquid nitrogen soaking on coal.

The Feasibility of Replacing Coal with Biomass in Iron-Ore Pelletizing Plants with Respect to Melt-Induced Slagging

Combustion-generated fly ash particles in combination with the particles arising from the disintegration of iron-ore pellets, could give rise to the build-up of deposits on the refractory linings of the induration facility. Due to climate change and other environmental issues, there is a desire to cut down on use of fossil fuels. Therefore, it is of interest to investigate the feasibility of replacing coal with less carbon-intensive alternatives such as upgraded biomass, e.g., biochar and pyrolysis bio-oil. While the combustion of biomass can be carbon-neutral, the effects of biomass ash upon slagging during the iron-ore pelletizing process in a grate-kiln setup is unknown. In the present study, the effect of the interaction between the pellet dust and biomass-ash upon melt formation and the viscosity of the resulting melt, which can collectively affect melt-induced slagging, was theoretically assessed. The slagging potential of 15 different biomass fuels, suitable for the pelletizing process, was quantified and compared with one another and a reference high-rank coal using a thermodynamically derived slagging index. The replacement of coal with biomass in the pelletizing process is a cumbersome and challenging task which requires extensive and costly field measurements. Therefore, given the wide-ranging nature of the biomasses investigated in this study, a prescreening theoretical approach, such as the one employed in the present work, could narrow down the list, facilitate the choice of fuel/s, and help reduce the costs of the subsequent experimental investigations.

On how mild oxidation affects the structure of carbons: Comparative analysis by different techniques

Understanding how the structure of carbonaceous materials changes upon oxidation at mild temperature as a function of the graphitic order is of great importance for the development of clean combustion technologies, such as carbon fuel cells. The micro- and nanostructures of a range of carbon materials at room temperature and upon mild oxidation at 300 °C have been analysed by means of mercury porosimetry, Nitrogen adsorption, X-Ray Diffraction, Raman spectroscopy and Electron Paramagnetic Resonance. The samples included carbons with increasing level of graphitic order: three chars derived from two bituminous coals and a lignite, a synthetic carbon and a graphitized coke. The experimental characterization allows to classify the materials according to different structural parameters, including porosity, surface area, degree of graphitization and paramagnetic activation of the carbonaceous surface. A correlation with the rank of the analysed materials is observed. For the graphitized coke, oxidation leads to more crystalline order and enhancement of the paramagnetic signal. A similar increase in the paramagnetic activity is observed for the Lignite char. On the other hand, for the higher rank, bituminous and synthetic chars, mild oxidation leads to a slight expansion of the amorphous carbon and loss of paramagnetic activity. The differences are rationalized in terms of formation of new carbon-oxygen complexes on the graphitized coke and on the Lignite char, and redistribution of already existing complexes for the higher-rank coals. This investigation complements previous X-ray photoelectron spectroscopy measurements.

Characterisation of the Contaminants Generated from a Large-Scale Ex-Situ Underground Coal Gasification Study Using High-Rank Coal from the South Wales Coalfield

This paper presents an analysis of contaminants generated from large-scale, laboratory-based, underground coal gasification (UCG) experiments using a high-rank coal from the South Wales Coalfield. The experiments were performed at atmospheric and elevated pressures (30 bar) by varying the oxidants’ composition. The experiments were designed to predict the amount of produced water and contaminants generated at each stage of the operating conditions. The mass balance of water supplied and produced in the experiments was accounted for. Chemical analyses of produced water, char and ash contents were performed to quantify the inorganic and organic chemical parameters. Most of the contaminant concentrations in the produced water from the 30-bar pressure experiment were lower than the concentrations generated from the atmospheric pressure experiment. The measured concentrations of the inorganic chemical species and the inorganic parameters of the coal seam water from the South Wales Coalfield were used in theoretical calculations to predict the dominant equilibrium species concentrations in a hypothetical scenario of effluent contaminated groundwater. The biodegradation of organic contaminants such as phenol, benzene and sorbed fractions of inorganic contaminants from the produced water on iron oxide in the ash residue was predicted using existing biotransformation kinetics and surface complexation models, respectively. The biodegradation of phenol and benzene would be a slow process even at optimum conditions and the iron oxide left in the cavity can act as a sorbent for a few inorganic species. The evidence from the present study suggests future work towards (i) developing an appropriate water treatment process during gas cleaning, (ii) operational procedure (pressure and proportions of oxidant) and (iii) developing UCG-specific experimental prediction of contaminant transportation and transformation kinetics.Graphical abstract

Oxy-coal combustion in a 30 kWth pressurized fluidized bed: Effect of combustion pressure on combustion performance, pollutant emissions and desulfurization

Oxy-coal combustion with pressurized fluidized beds has recently emerged as a promising carbon capture and storage (CCS) technology for coal-fired power plants. Although a large number of energy efficiency analyses have shown that an increase in combustion pressure can further increase the net plant efficiency, there are few experimental studies of pressurized oxy-coal combustion conducted on fluidized bed combustors/boilers with continuous coal feeding. In this study, oxy-coal combustion experiments with lignite and anthracite were conducted with a 30 kWth pressurized fluidized bed combustor within the pressure range of 0.1 MPa to 0.4 MPa. The investigation focused on the elucidation of the impacts of combustion pressure on the combustion performance, pollutant emissions and desulfurization of oxy-coal combustion in fluidized beds. The results showed that an increase in pressure increased the combustion efficiency and combustion rate of coal particles, and the promoting effect of pressure increase was more significant for the high rank coal with smaller particle size and the high O2 concentration atmosphere. For both coals, NOx emissions decreased with pressure but N2O emissions increased with pressure and accounted for a considerable part of the nitrogen oxide pollutants under high pressure oxy-coal combustion conditions. The pressure had insignificant impact on the SO2 emissions of oxy-coal combustion but an increase in pressure enhanced the direct desulfurization of limestone.

The Impact of Coal’s Petrographic Composition on Its Suitability for the Gasification Process: The Example of Polish Deposits

In this paper, we discuss the impact of the rank of coal, petrographic composition, and physico-chemical coal properties on the release and composition of syngas during coal gasification in a CO2 atmosphere. This study used humic coals (parabituminous to anthracite) and lithotypes (bright coal and dull coal). Gasification was performed at temperatures between 600 and 1100 °C. It was found that the gas release depends on the temperature and rank of coal, and the reactivity increases with the increasing rank of coal. It was shown that the coal lithotype does not affect the gas composition or the process. Until 900 °C, the most intense processes were observed for higher rank coals. Above 1000 °C, the most reactive coals had a vitrinite reflectance of 0.5–0.6%. It was confirmed that the gasification of low-rank coal should be performed at temperatures above 1000 °C, and the reactivity of coal depends on the petrographic composition and physico-chemical features. It was shown that inertinite has a negative impact on the H2 content; at 950 °C, the increase in H2 depends on the rank of coal and vitrinite content. The physicochemical properties of coal rely on the content of maceral groups and the rank of coal. An improved understanding these relationships will allow the optimal selection of coal for gasification.

Numerical Simulation of Matrix Swelling and Its Effects on Fracture Structure and Permeability for a High-Rank Coal Based on X-ray Micro-CT Image Processing Techniques

The adsorption gas of coal matrix will cause its swelling, change the fracture structure, and further affect the permeability of coal seam. In this study, CT image processing technology was used to...

Experimental comparison of CO2, N2, and CH4 permeability of water saturated coals of different ranks

ABSTRACT Coalbed methane is a kind of highly efficient and clean energy source. The permeability of coal seam affects the application of gas extraction. There are so many factors affecting gas permeability, such as gas pressure, temperature, moisture content, confining pressure, and coal rank. We experimentally investigated gas permeability of three different coals at four different temperatures (23°C, 34°C, 45°C, and 60°C) and three different moisture contents (dry, medium moisture and moisture-saturated coals). Injection gas pressure varied from 1 MPa to 6 MPa (up to 8 MPa for N2) at constant axial confining pressure of 9 MPa. The results show that under constant axial and confining pressure conditions, with the increase of gas injection pressure, the permeability of N2 and CH4 shows a “V”-shaped change trend, that is, “inflection point”; CO2 permeability decreases with the increase of gas injection pressure. The permeability of coal core samples decreases with increasing temperature, caused by thermal expansion, decrease of gas absorption and increase of porosity. As the temperature rises, the decline gradually flattens. The permeability of coal core samples decreases with the increase of moisture content, related to moisture and gas competitive adsorption, coal porosity reduction. The permeability of high rank coal is lower than the medium rank coal under the same experimental conditions, caused by the pore structure of coal sample.

Research on the fractal characteristics of the micro/nano-mesoscopic pore structure of high-rank coal under impact loads

ABSTRACT To reveal the mechanism of impact load on coal micropores and improve the extraction efficiency of high-rank coal gas, a separate Hopkinson pressure bar (SHPB) impact test system was used to simulate the shock and stress waves of the impact stress in different attenuation processes. Based on mercury intrusion and low-temperature liquid nitrogen test data before and after impact, fractal theory was applied to study the micropore fractal characteristics of high-rank coal in different directions before and after impact in the Chengzhuang Mine. The results show that pores smaller than or equal to 100 nm based on mercury intrusion data and pores larger than or equal to 100 nm based on low-temperature liquid nitrogen data do not follow fractal rules. Impact loads reduce the seepage and adsorption pore fractal dimensions. Although the seepage and adsorption pore fractal dimensions do not decrease with increasing impact load, a minimum fractal dimension occurs. The impact load corresponding to the minimum seepage and adsorption pore fractal dimensions in the same direction is the same. Impact loads increase gas migration velocities of the seepage pores, reduce the adsorption capacity of the adsorption pores, and promote gas desorption. The research results are important for determining the optimal drainage hole layout and examining the impact cracking and infiltration mechanism.

Diffusion characteristics of methane in various rank coals and the control mechanism

The methane diffusion behavior is one of the key factors that influence the production potential of coalbed methane (CBM) reservoirs. In this study, low temperature nitrogen, carbon dioxide adsorption and methane isotherm adsorption experiments for various rank coal samples were carried out to investigate the characteristics of pore size distribution and gas adsorption-diffusion behavior. A mathematical model similar to the Langmuir equation was established to describe the methane diffusion in coals. The variation law of the Langmuir effective diffusion coefficient (DL) with coal rank and its influencing factors, control mechanism were analyzed. With the increase of coal rank, the development degree of micropore rises, and both the specific pore volume and specific surface area first decrease and then increase. The diffusion coefficient of methane in coals generally rises with the rise of pressure. The Langmuir volume rises with the rise of Ro,m (maximum vitrinite reflectance with oil). The influence of moisture and coal molecular structure on gas diffusion varies with coal rank. The moisture content has a more significant influence on the gas diffusion in the medium-rank coals than in the low- and high-rank coals. The outcomes may deepen our understanding of gas transport in coals and benefit the exploration of CBM.

Experimental study of coal fracture dynamics under the influence of cyclic freezing\u2013thawing using shear elastic waves

Cyclic freezing–thawing can lead to fracture development in coal, affecting its mechanical and consumer properties. To study crack formations in coal, an ultrasonic sounding method using shear polarized waves was proposed. Samples of three coal types (anthracite, lignite and hard coal) were tested. The research results show that, in contrast to the shear wave velocity, the shear wave amplitude is extremely sensitive to the formation of new cracks at the early stages of cyclic freezing–thawing. Tests also show an inverse correlation between coal compressive strength and its tendency to form cracks under temperature impacts; shear wave attenuation increases more sharply in high-rank coals after the first freezing cycle. Spectral analysis of the received signals also confirmed significant crack formation in anthracite after the first freeze–thaw cycle. The initial anisotropy was determined, and its decrease with an increase in the number of freeze–thaw cycles was shown. The data obtained forms an experimental basis for the development of new approaches to preserve coal consumer properties during storage and transportation under severe natural and climatic conditions.

Multifractal Analysis in Characterizing Adsorption Pore Heterogeneity of Middle- and High-Rank Coal Reservoirs.

Nanopore heterogeneity has a significant effect on adsorption, desorption, and diffusion processes of coalbed methane. The adsorption pore size distribution heterogeneity was calculated by combining N2 with CO2 adsorption data, and factors affecting multifractal and single-fractal dimensions were studied. The results indicate that pore size distribution of micropores (with pore diameters smaller than 2 nm) and meso–macro-pores (with pore diameters between 2 and 100 nm) in coal samples exhibit typical multifractal behavior. The overall heterogeneity of micropores in high-rank coal samples is higher than that in the middle-rank coal samples. The low-probability measure areas control the overall heterogeneity of pores with diameters of 0.40–1.50 nm. The high-probability measure area heterogeneity and spectral width ratio have a higher linear correlation with coal rank and pore structure parameters than those of low-probability measure areas. Heterogeneity of high-probability measure areas and overall pore size distribution are controlled by pores with diameters of 0.72–0.94 nm. Multifractal parameters of meso–macro-pores have no clear relationship with coal rank. The pore volume of 2–10 nm diameter shows a good linear correlation with heterogeneity of low-probability measure areas, and pores of this diameter range are the key interval that affected pore size distribution heterogeneity. The single-fractal dimension obtained using the Frenkel–Halsey–Hill (FHH) model shows a positive linear correlation with heterogeneity of the low-probability measure areas. It indicates that this parameter can effectively characterize the pore size distribution heterogeneity of low-probability measure areas in meso–macro-pores.