Abstract
This paper presents the experimental and theoretical investigations of the sorption of water vapour in hard coal samples from Polish collieries (Sośnica, Jaworzno and Pniówek). Analysis of the sorption isotherm of water molecules gives information on specific interactions with surface groups, especially oxygen radicals. Detailed considerations of experimental results and theoretical simulation estimates let us to indicate changes in the surface composition for the different samples of coals and its dependency on the petrography or metamorphism.
Introduction
Understanding the sorption of gases, related to the exploitation of coal seams, is essential when explaining the mechanism of gas deposition in the coal seams (Baran et al., 2013; Czerw et al., 2016) and its relationship with outbursts of rocks and gases in mines (Skoczylas and Wierzbicki, 2014). To a large extent, the structure of hard coal, containing the aromatic cyclic, hydrogenated or aliphatic chain concentrations exhibits an apolar behaviour. The defects and concentrations of condensed aromatic groups are mostly apolar, due to the presence of π-electrons located in the benzene rings. The polarity of hard coals is largely determined by the presence of reactive oxygen-containing groups, partly nitrogen and sulphuric groups (Ceglarska-Stefańska et al., 1997; Li et al., 2012; Lodewyckx et al., 2006). Oxygen is present in the organic substance of coal in the form of reactive hydroxyl, metoxyl, carboxyl and carbonyl groups. There are also oxygen-containing non-reactive compounds, ether compounds (linear or cyclic) and compounds where oxygen is present in the aromatic core. In the process of carbonisation, the oxygen content in the coal structure will decrease and other groups will gain preponderance. Hydroxyl groups are strongly reactive oxygen groups which, when bonded with aromatic compounds, behave like acidic phenols and when bonded to aliphatic chains, exhibit the properties of alcohol groups. The number of those groups tends to decrease with the carbon content C. The ratio of oxygen content in hydroxyl groups to the total amount of oxygen, as a function of the oxidation level is investigated in the works by Brown and Wyss (1955). The value OOH/OTotal in relation to the carbon content (89% by weight) is equal to 38%. For higher carbon content, the value of this ratio falls to 10%, or below. According to the authors, the ratio of hydroxyl oxygen to the total oxygen for those coal is stabilised because the majority of transitions occurring in the process of carbonisation takes place on the edges (reactive groups) whilst the inner core of the porous structure remains unchanged. For carbon contents in excess of 85–86% by weight or for oxygen content 8% (transition point), the ratio of hydroxyl to total oxygen decreases, which is indicative of an entirely different mechanisms of carbonisation, i.e. thorough condensation of aromatic rings.
Analytic tests have revealed that large amounts of metoxyl groups (Given, 1960) are present in low rank coals, with carbon content below 81.5%. They are associated both with aromatic and aliphatic groups. It was found out that in high rank coals only 0.4% of the elemental oxygen is present in arylometoxyl groups. Carboxyl groups are found in hard coals, though in relatively small numbers (1.5% maximum), but they are present in low rank coals. Hard coals with carbon content C in excess of 83% contain trace amounts of carbonyl groups. Carbonyl groups are present in most of the coals regardless of their rank, though their content is rather low (up to 0.8%). Similar to COOH groups, these groups make the coal surface acidic. One has to bear in mind that carboxyl and carbonyl groups can be formed from aliphatic hydrocarbons, in the processes of slow oxidation of hard coals (Grzybek et al., 1997; Švábová et al., 2012).
A number of surface properties of coal, particularly those relating to sorption, are associated with the presence of hydrophilic groups formed from oxygen and nitrogen atoms. Hydrophilic groups can have a heterocyclic structure, though they are mostly in the form of hydrophilic reactive oxygen groups. These groups can be bonded with aliphatic chains, but typically they are directly bonded to crystallites of condensed benzene rings. The actual content of those groups in hard coals is closely associated with the coal rank, being a residue of chemical components of plants, containing cellulose and lignin (Marzec, 1986). In the case of these groups, the change of reactivity is manifested by the value of the wetting heat, particularly in sorption processes (Allardice and Evans, 1971). The concentration of oxygen polar groups can be determined by chemical analysis methods, the IR analysis, measurements of wetting heat and sorption tests using water and methanol vapours. Results obtained by analytical methods vary significantly depending on the applied procedure. As reported in literature (Brennan et al., 2001; Charrière and Behra, 2010; Collins et al., 2006; Cossarutto et al., 2001; Foley et al., 1997; Gensterblum et al., 2014; Guo and Kantzas, 2009; McCutcheon et al., 2001; Pan, 2012; Sun et al., 2008), low rank coals tend to sorb considerable amounts of water whilst the middle- and high rank coals contain a decidedly smaller number of sorbed molecules of this sorbate. Hard coal is a sorbent with relatively good sorption capacity, particularly with respect to polar compounds with a simple structure (such as water, methyl alcohol, alternately carbon dioxide or methane). Water molecules exhibiting a polar nature can interact with numerous energetic sites, particularly hydroxyl and carbonyl groups, mostly forming hydrogen bonds. Sorption capacity of water vapour can be treated as an indicator of the presence of oxygen groups in hard coals.
Multiple sorption model
The theoretical analysis of the sorption isotherms is based on the copolymeric model of coal structure. This model assumes the composition of coal with five main components (Jodłowski and Wójcik, 2013):
arene domains – rigid, complex structures built with plates of condensed benzene rings, connected each other; number of benzene rings in plate together with number of plates in the domain are in relation to coalification degree of the coal; interconnected chains – bulk structure of aliphatic, alicyclic or heterocyclic chains connected each other composing 3D structure with cross-junctions (either with arene domains); free chains – unconnected chains with statistical dominant longitude of several atoms of carbon (typically 16 atoms); pores – empty spaces in the bulk of coal, generally places remaining after the desorption of water, methane or carbon dioxide either compositions in the neighbourhood of function groups having different size; mineral admixtures – additions with origin of the coal bed of different size and composition, generally its influence on sorption process is neglected.
Compounds 1 and 2 compose the macromolecular network which is the limitedly rigid, bulk structure called macromolecular phase. This phase is filled by the free chains. This unconnected chains are called molecular phase of coal. The idea of copolymeric model is schematically presented in Figure 1.

Schematic representation of the components of coal structure (Jodłowski and Ziółkowska, 2017).
The way of molecule location in the sorption system is presented in Figure 2. The molecule of sorbate is evaporated to the hypothetical vacuum and in the next step located on the surface in the liquid-like state (adsorption) or to the bulk (absorption) with energy of condensation calculated from the Berthelot Rule (Jodłowski et al., 2007). The molecule changes the location without changing the chemical potential Δµ = 0.

Hypothetical way of sorbate molecule location in the sorption system (Jodłowski and Ziółkowska, 2017).
Detailed thermodynamic considerations are made basing on the copolymeric model of coal as well as fundamental law
The assumption is made that the pores of size comparable to the size of sorbate molecule (submicropores) has the main significance for the sorption, because the surface area of coal is generally enclosed in this kind of pores. Thus the sorption space is divided into the subsystems:
absorption – pores doesn’t exist and are built while sorption goes with defeat of cohesion energy of coal substance; adsorption – pores having size of molecule diameter and bigger are filled using cohesion energy, for bigger pores additional model extension (LBET (Milewska-Duda et al., 2000) and family of models (Duda et al., 2010)); expansion – whole phenomena taking place in the pores of size lower than diameter of sorption molecules, complicated relation of cohesion–adhesion energy appears in this region.
Sorption process is a priori divided into 11 subsystems depend on pores size (R = 0 for absorption, R = 1 for adsorption and nine intermediate subsystems). Sorption system is characterized by the medium radius of pores RB which describes the size of pores in which the balance of cohesion and adhesion energy appears.
Sorbate molecules doesn’t fit perfectly to the pores, thus Z parameter describes the contact quality of the molecules to the coal matter segments. Z = 1 describes perfect contact (appears rather in absorption) and Z = 0 means lack of contact. This correction parameter on the energy of adsorption is divided to two regions ZA for pores smaller than RB and ZB for pores bigger than RB. Nine subprocesses are the effect of normal (Gauss) distribution of pores volume or capacity in which middle one means the average radius of pores RB (the peak of distribution) and four compartments of default width (mathematical function) on both sides of this dominant submicropore dimension. It is described by the approximate formula
Region I of formula (2) depict absorption, II describe non-ideal contact of molecule and coal component i submicropores Rha lower than dominant radius RB, III calculates the non-ideal contact correction for submicropores Rha bigger than dominant radius RB and IV is pure adsorption on the surface. ZA and ZB are coefficient of non-ideal contact in smaller and bigger pores, respectively, Cpa and CpA are coefficients of specific interactions (polar surface groups) in smaller and bigger pores, respectively.
Sorption process is a priori divided into 11 subsystems that depend on pore size (R = 0 for absorption, R = 1 for adsorption and nine intermediate subsystems). Sorption system is characterized by the medium radius of pores Rha which describes the size of pores in which the balance of cohesion and adhesion energy appears.
Sorbate molecules doesn’t fit perfectly to the pores, thus Z parameter describes the contact quality of the molecules to the coal matter segments. Z = 1 describes perfect contact (appears rather in absorption) and Z = 0 means lack of contact. This correction parameter on the energy of adsorption is divided to two regions ZA for pores smaller than Rha and ZB for pores bigger than Rha.
MSM gives us the possibility to achieve the description of pores using developed equation LBET, which describes adsorption in pores even for stacks different from BET theory. (Jodlowski GS et al., 2007) detailed thermodynamical analysis of the energy of contacts allows to the estimation of volume of pores Vh and pores capacity Vhad.
As described above, the geometrical parameters of the coal structure together with energy of sorption (cohesion and adhesion) give us the base to further consideration on the sorption system properties.
Simulation experiment consists of a number of simulation steps, starting from changing of chosen parameter of the sorption system (e.g. Rha, ZA, ZB, Vh, etc. – see description under Table 5). The effect of simulation, i.e. theoretical sorption isotherm is compared to empirical points of measured isotherm. Next changes of parameters are made in further steps after the confrontation, until the satisfy fitting of theoretical isotherm and empirical one is obtained. Certainly, all parameters have thermodynamical meaning and manipulations are made in the range of data appropriate for the coal sample with given carbon content. So, parameters describing coal composition (in the copolymeric model point of view) are unchangeable while simulation experiments are lead.
Experimental
Materials and methods
The results of the measurements of sorption of the water vapours on the samples of hard coals from the following coal mines: Jaworzno Coal Mine, bed 209 (sample J), Sośnica Coal Mine, bed 413 (sample S) and Pniówek Coal Mine, bed 360/1 (sample P) are presented. The samples were prepared in the Department of Mining Aerology of the Central Institute of Mining (Katowice, Poland), following the PN-90/G-04502 Polish standard. The sorption experiments were carried out at 303 K, on the grain fraction 0.125–0.250 mm, using fluid micro-burettes equipment. Prior to measurements the samples were degassed to 10−3 Pa, with additional He washing during degassing. Chemical, technological and petrographic parameters of the studied coals are shown in Tables 1 and 2. Coal samples are designated by the letters: P, S, J.
Chemical and technological analyses of the coals studied.
Petrographic analysis of the coals studied.
Microstructure testing
Tests were conducted with the use of a polarisation microscope POLMI A, supported by observations using an OLYMPUS microscope, typically used when handling very small objects. Coals were subjected to X-ray analysis by the Debye-Sherrer’s powder method.
Coal sample from the colliery Jaworzno
The analysis of the coal substance does not reveal any easily identifiable mineral admixtures. Only in the fusinite, filling the intermolecular space, and in two sites within the sample, there are small concentrations of a crypto-crystalline, very low-birefringent mineral substance. It may represent poorly crystallised minerals of the SiO2 groups or some clay matter. This supposition will have to be verified by X-ray and perhaps scanning electron microscope/energy-dispersive X-ray spectroscopy (SEM/EDS) tests. X-ray analyses reveal significant amounts of caolinite with a well-ordered structure (polytype 1T) and trace amounts of iron sulphide (pyrite and/or marcasite).
Coal sample from the colliery Pniówek
Mineral substance is present in trace amounts, mostly impregnating the macropores in macerals, such as fusinite. Microscopic analyses reveal the minerals similar to the SiO2 groups (chalcedony, microcrystalline quartz), or to carbonates. An admixture of clay matter distributed within the organic substance is also possible, mostly in brighter microlamines. X-ray analyses do not reveal any mineral phases in the amounts identifiable by the X-ray diffraction (XRD) method.
Coal sample from the colliery Sośnica
The analysis reveals an admixture of mineral matter (over 10%), uniform distributed within the coal substance and containing mostly carbonate minerals with diverse microscopic features: possibly siderite or representatives of the dolomite-ankerite group. These minerals tend to concentrate in one corner of the specimen, intermingled with the coal substance and inlaid with fusinite producing mixed-type formations of the carbominerite type and fill in the micro-cracks, forming irregular aggregates and irregular spherulites about 0.8 mm in diameter. At some points the carbonates are accompanied by opaque ore minerals resembling framboidal pyrite and in the proximity and within the suspected siderite there are red-brown iron oxides or hydroxides. No clay substance was found. X-ray analyses does not reveal the presence of such amounts of mineral matter that would be identifiable by the XRD method.
Coal from the colliery Pniówek (coal seam 360) has the highest carbon content (over 80%) and the highest ash content, falling in the range 3–4%. Among lower rank coals, the coal from the colliery Sośnica (coal seam 413) contains about 70% of carbon and its ash content is considerable (about 14%). Coal from the colliery Jaworzno, coal seam 209, is the lowest rank coal (carbon content C = 57.83%) and has a large moisture content (11.11%).
Porosimetric testing of coals
The mercury porosimetry methods were employed to determine the volume and surface areas of pores in the investigated coal samples. Porosimetric measurements were taken with the Pascal 140 and Pascal 440 porosimeters. Porosimetric test data suggest that coal from the colliery Jaworzno has the highest total porosity and the coal from the colliery Pniówek – the lowest (Table 3). Density of coals was measured with the Accu Pyc Micrometrics 1330 device. The results are summarised in Table 4.
Results of porosity investigation: total volume of pores and porosity for coals from individual mines.
The real densities of investigated coal samples and calculated porosity data.
Results and discussion
Experimental data (shown in Figure 3) suggest that the coal rank is associated with the change in concentration of functional groups on the coal surface, which is responsible for major changes of the degree of polarity of investigated coals. First adsorbed molecules begin to act as sorption sites for further sorbate molecules and the process leads to the formation of isolated clusters. Water dipoles can then interact with energetic sites, particularly the hydroxyl and carbonyl groups, forming hydrogen bonds. The highest sorption capacity is reported for coals with large oxygen contents and relatively low carbon contents, which may be attributable to high concentrations of hydroxyl groups. Medium rank coals display low sorption capacity and these are mostly coals with large contents of aliphatic and alicyclic hydrocarbons. The surface in these coals is found to be strongly hydrophobic. High rank coals (anthracites, semi-anthracites) exhibit a marked increase of the polar sorption sites, which is the consequence of their graphite-like structure, with numerous free π-electrons.

Sorption of water vapour on coal samples.
The concave isotherm pattern in the low pressure range is attributable to the fact that adsorption energy of the molecule in the first layer is larger than adsorption energy in further layers. The actual shape of the sorption isotherm obtained for a high-rank coal is explained by lower energy of adsorption of molecules in the first layer compared to the energy of condensation associated with interactions between the molecules in the first, second and further layers.
The patterns of H2O sorption isotherms indicate that the energy of adsorbate–adsorbent interactions is low and that the adsorbate–adsorbate processes play a significant role (Furmaniak et al., 2008; Liu et al., 2017; Terzyk et al., 2010). The absence of an inflection point in the low coverage regions on sorption isotherms for coals is typical of hydrophobic porous coals. It is reasonable to suppose the dual mechanism of sorption. At first, in the low coverage regions, sorption takes place mostly in the adsorption sites where molecules with a non-uniform distribution of free-electron density (dipole, quadrupoles and those with multiple bonds) get adsorbed in a specific manner. Once they are blocked by previously adsorbed molecules, the free sorption space will emerge and will be filled in the subsequent stages of the sorption process, under the action of dispersion forces. These molecule-adsorption site interactions add to the dispersion forces, which leads to enhanced energy of adsorption. Specific interactions occur when there is large surface concentration of oxygen groups. The influence of the coal rank on sorption capacity can be explained by reduced mobility of macromolecular chains in the coal copolymer in higher-rank coals. Sorbate molecules under the action of a strong force field of a porous adsorbent whose structural components have a limited mobility will block the access to some portion of pores, thus hindering adsorption. Water molecules, being adsorbed on the first adsorption sites, get deformed and, when unable to overcome the mobility barrier of the chains of the coal substance, may become the sites where water associates will be formed. The degree of association is chiefly dependent on the concentration of adsorbed water molecules in the sorbent’s field of forces. Hence the degree of association has a small value at the onset of the adsorption process, and then tends to increase as the adsorption space gets filled. The actual patterns can be attributable to penetration of individual sorbate molecules into new sorption spaces formed due to deformations of the coal bulk network. The difference in sorbate concentrations between the regions occupied by previously adsorbed water molecules and the new sorption space will result in their displacement, revealing the role of the absorption process. Sorption capacity with respect to water vapours depends in the first place on the coal rank, though the influence of coal petrography must not be disregarded.
Modelling results for water vapour
The fitting of the theoretical isotherms to empirical data are presented in Figures 4 to 6. The original measured sorption isotherm points are recalculated to the bigger number accordingly for better presentation of the shape of the curve.

Sorption isotherms of water vapour on the J coal sample.

Sorption isotherms of water vapour on the P coal sample.
Theoretical total sorption (Figure 4) fits acceptably well with the empirical points and adsorption is the dominant phenomenon in whole sorption process. Little overestimation appears in the medium relative pressure region and underestimation in lower relative pressure one. Sigmoidal shape of the isotherm indicates the occurrence of molecule aggregates, which is caused by polar interaction of water and surface groups together with aggregation of BET type. The tendency of absorption curve corresponds to the hydrophobic character of the coal substance. The absorption level increases little just in the higher relative pressure zone probably as an effect of a little number functional groups enclosed in the coal mass. Expansion (cohesive–adhesive process) rather doesn’t appear in this sorption system.
Recalculation of the experimental curve to the bigger number of points goes wrong in starting region in this case. The possible cause is irregularity in the further zone; third and fourth points of experimental curve are little lower in the comparison to the tendency from other points. The experimental isotherm is added to the chart in the aim of comparison to simulated curves. The expansion in the system P coal sample – water is of weak significance. Even absorption is a sub-process of lower significance than adsorption. So, one could state that the system is nearly adsorptional and whole phenomena occur on the surface of the coal. Sigmoidal shape of isotherm is related to the aggregation of water molecules. This shape is not satisfactorily fitted by the theoretical curve and need to be improved a little. Estimates given by the model are reasonable (see Table 5) even with this defect.
Expansion practically is on the observable level in the sorption system water vapour – S coal sample (Figure 6). Absorption is also of a little significance. So, this system is an example of multi sorption (whole phenomena appears and have a significance in the sorption process). Worse quality of simulation is probably caused by the tendency to the condensation of water in the mesopores under the sorption process. MSM Model doesn’t calculate strictly this region of the isotherm in specific conditions and very well fitting is impossible to reach. The Rha parameter cannot be estimated with big certainty in such a case but the theoretical parameters obtained from simulation are generally reasonable.
Chosen parameters of sorption systems obtained for water vapour as a sorbate.
Rha: characteristic pore radius relative to molecule radius in which correction parameters Z change its property (description in the text above); ZA: energy correction coefficient describes the contact of molecule and coal substance quality for pores smaller than Rha; ZB: energy correction coefficient describes the contact of molecule and coal substance quality for pores bigger than Rha; Vh: total pore volume depicted as the number of sorbate moles; Vhsub: volume of submicropores; Vhad: volume of bigger pores accessible for sorbate molecules; χad: unitless energetic parameter describing adsorption energy (adsorption enthalpy ΔHad= χad⋅RT); χab: unitless energetic parameter describing absorption energy; δC: cohesion energy density; parameter describing the cohesion energy of coal substance, given by Hombach and van Krevelen (van Krevelen, 1961); exp/sorp(0.8): expansion to sorption ratio by the relative pressure p/p0 = 0.8; abs/sorp(0.8): absorption to sorption ratio by the relative pressure p/p0 = 0.8; CpA: unitless parameter characterizing the presence of polar group on the surface of coal; value of the parameter bigger than one is related to specific interactions of sorbate and coal surface (whole parameters are unitless, except volume).

Sorption isotherms of water vapour on the S coal sample.
Simulation experiment leads to the estimation of several parameters describing the coal structure and sorption system. Chosen parameters describing sorption systems are collected in Table 5.
There is no clear relation of the characteristic, relative radius of pores Rha to the carbon content in coal samples. Rha values are comparable to the water molecule, which is the effect of pore origin from water and methane desorption. Water is regarded as a polar substance and this property could produce the effect results in worse fitting of water molecule to the submicropores (ZA is near but lower than one). Simultaneously, water molecules interact with surface groups (parameter CpA), which results in building of aggregates in their neighbourhood and gives an effect in the decrease of ZB parameter. Some parts of water molecule contact are not to coal substance but to another water molecule resulting in significant decrease of adsorption energy coefficient χad despite the fact of relatively high sorption level.
The geometrical factors ZA and ZB values changeability vs. carbon content is irregular. Surprising are values for J and S samples, where the contact of sorbate molecule to the coal substance is very weak in the adsorption system.
Sorption capacity of pores Vhsub + Vhad decrease with carbon content is observed. In whole systems sorption capacity exceeds the pore volume Vh. This phenomenon is commonly connected to the polar properties of water and in the consequence building of aggregates in the neighbourhood of surface groups. Adsorption energy parameter χad increase with carbon content as an effect of growth of the aromatic substance content in coal matter – π-electrons could interact with water and surface is less apolar.
Expansion is negligible sub-process in whole sorption systems (see exp/sorp(0.8) at Table 5) and absorption ratio decrease with carbon content (see abs/sorp(0.8) at Table 5). Second tendency is expected because the content of molecular phase (elastic) decrease to macromolecular advantage (rigid one).
Conclusions
In the context of research data, when considering the influence of the coal rank on sorption of the water vapour the following aspects have to be addressed:
- concentration of surface adsorption sites – oxygen groups – and their influence on specific sorption of water molecules (low coverage area); - the influence of coal texture – well developed mesoporosity forms a free adsorption space to be filled with sorbate molecules bonded by dispersive interactions. Here water molecule associates (clusters) are formed as a result of strong adsorbate–adsorbate interactions (hydrogen bonds) – the medium and high coverage zones; - the influence of degree of metamorphism (coal rank), coalification, carbon content C, chemical structure on mobility of macromolecular chains of the coal copolymer – sorbate molecules bonded by strong sites block the entrance to the pores, thus precluding their participation in the process of adsorption. Potential deformations of the coal substance foster the formation of a new sorption space (medium and high coverage range). Deposition of water molecules in those regions may involve absorption. Sorption capacity coal with respect to water vapour is largely dependent on the coal rank and petrography is found to play some role too.
The novelty of this paper is that the multiple sorption model is applied in the description of H2O sorption isotherm in the case of higher-rank coals; for the first time the model was applied to investigate the behaviour of the sample J (borderline composition between lignite and bituminous coals) and the results were compared with those obtained for higher-rank coals giving good agreement.
High sorption capacity of the coal sample J is not exclusively attributed to surface interactions between H2O and polar centres on the sample’s surface, also involving the formation of clusters followed by sorbate diffusion to the carbon matrix interior, which leads to swelling. Results obtained for the sample J confirm that in the high range of relative pressures the proportion of volumetric absorption is significantly higher, which implies a major role of volumetric processes in sorption, responsible for swelling of the carbon materials at pressures nearing the saturated vapour pressure. In the case of higher-rank coals (samples P and S), water sorption is a surface process (a cluster model), which is evidenced by low values of absorption isotherms.
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: a part of the AGH-UST research project No 11.11.210.374.
