#
CO_{2} Adsorption–Desorption Kinetics from the Plane Sheet of Hard Coal and Associated Shrinkage of the Material

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}desorptions from coals from two Polish mines that differed in petrographic and structural properties. The tests were carried out on spherical and plane sheet samples. On the basis of the sorption tests, the effective diffusion coefficient was calculated on the plane sheet samples based on a proper model. Similar tests were performed on the spherical samples. Mathematical model results for plane sheet samples were compared with the most frequently chosen model for spherical samples. The kinetics of CO

_{2}desorption from plane sheet samples were compared with the kinetics of sample shrinkage. In both samples, the shrinkage was about 0.35%. The size change kinetics and CO

_{2}desorption kinetics significantly differed between the samples. In both samples, the determined shrinkage kinetics was clearly faster than CO

_{2}kinetics.

## 1. Introduction

_{2}(77 K) and CO

_{2}(273 K) as adsorbates. In [8,9,10] the measured coals differed in maceral composition. In the measurement using N

_{2}, a sample with the highest content of vitrinite and low reflectance noted the total pore volume at the level of 26.6 mm

^{3}/g and the specific surface area (SSA) of 15.40 m

^{2}/g, based on the Brunauer, Emmett and Teller model (BET). In the other samples that contained less vitrinite, the pore volumes were much lower (from 1.7 to 1.9 mm

^{3}/g) and the SSA was in the range of 0.31–0.55 m

^{2}/g. In the measurement using CO

_{2}, the values of those parameters were higher and the highest were found in coal of the lowest reflectance. The pore volumes were in the range of 23.8–39.7 mm

^{3}/g and the SSA from 87.9 to 138.2 m

^{2}/g. At work Okolo et al. [11] using N

_{2}, a pore volume at the level of 1.01–1.47 mm

^{3}/g and a SSA (BET) of 2.6–5.7 m

^{2}/g was obtained. Using a CO

_{2}adsorbate, a pore volume at the level of 4.3–5.2 mm

^{3}/g and a SSA of 107–129 m

^{2}/g was obtained, based on the Dubinin-Raduszkiewicz model (DR). Weishauptová and Sýkorová [12] studied the carbon structure by gravimetry method, at 0–0.1 MPa and they used CO

_{2}as the adsorbate at 298 K. They used the Langmuir model and obtained a pore volume of 11.6–17.7 cm

^{3}/g and a SSA of 83–120 m

^{2}/g.

_{4}at the level 0.31 mmolCH

_{4}/g and for pure CO

_{2}—0.65 mmolCO

_{2}/g.

_{2}and CH

_{4}sorption.

_{2}storage in coal or ECBM technology. Due to the fact that the sorption affinity of coal to CO

_{2}is higher than to CH

_{4}, the CO

_{2}adsorption results in swelling of the coal matrix. The values of swelling and shrinkage of the coal matrix caused by CO

_{2}adsorption and desorption are usually 1.5–5 times higher than the values of the same processes in the presence of CH

_{4}[21,22].

_{2}content is emitted from the coal samples with De = 10

^{−9}cm

^{2}/s with equivalent radii in the range of 0.007–0.15 cm (Figure 1a) and 0.007–1.5 cm (Figure 1b). Even in the case of small grains, if the most typical values of effective diffusion coefficients are taken into account, this process can last from several hours for grains below 0.01 cm, through several weeks for millimeter grains, to months and years for centimeter and larger samples. The kinetics of CO

_{2}desorptions depend on the second power of the grain equivalent radius.

## 2. Research Methodology

_{2}adsorption was measured in the relative pressure range: 0 < p/p0 < 0.029. The relative pressure was determined as the ratio of the absolute pressure and the saturation pressure of the gas used. At the preparation stage, the samples were degassed for 12 h at 363 K and then heated for 4 h (368 K). During N

_{2}adsorption, the relative pressure range was 0 < p/p0 <0.996 respectively. Prior to measurement, samples were degassed for 2h (363 K). The LPA measurement involved measuring the volume of the sorbed gas in the sample pore space. On the basis of equilibrium adsorption points, the area of micropores and partly mesopores was characterized in the tested coals. The study determined the total sorption capacity, monolayer and multilayer specific surface area (SSA), pore volume and average pore size and distribution. In the LPA process, Langmuir, Horvath–Kawazoe (HK) [41], density functional theory (DFT) [42] and Dubinina Astakhova (DA) [43] models were used for calculations using CO

_{2}adsorbate, while with the use of N

_{2}adsorbate, Brunauer-Emmett-Teller (BET) [44] and Barrett-Joyner-Halenda (BJH) [45] respectively.

^{−7}Pa) at 353K. On the basis of sorption points, Langmuir sorption isotherms were determined by minimizing the sum of squared deviations (1):

^{3}/g), A is total monolayer capacity, (cm

^{3}/g), B is the inverse of the half pressure, (1/MPa), P is absolute pressure (MPa).

^{−7}Pa) at 353 K.

_{2}to a pressure of 1 MPa. The sample was saturated with CO

_{2}at a given pressure for another 10 days. Then, the pressure in the container was abruptly lowered to atmospheric pressure. The pressure change began desorption and contraction of the sample. Within a few dozen of seconds of the pressure drop, the sample was placed under the laser sensor, which began the measurement of the changes in the sample’s geometry.

_{2}desorption, in the time between the pressure drop in the airtight container and the moment the sample is placed under the laser altimeter (Figure 4a,b), an approximation of the square root curve was performed (2):

## 3. Petrographical and Structural Description of Analyzed Coal

_{2}as the adsorbate, the ultra-micropores and micropores in coal were characterized. N

_{2}was used as the adsorbate to characterize the mesopores. On the basis of equilibrium points of CO

_{2}adsorption, sorption type I isotherm was obtained according to the IUPAC [3]. This shape is similar to the Langmuir isotherm model and is characteristic of microporous materials. N

_{2}adsorption points were consistent with type III isotherm according to IUPAC classification [3]. This shape is typical for low porosity materials. The differences in the shape of CO

_{2}and N

_{2}isotherms result from the different sorption potential of these gases. Nitrogen exhibits weak sorption activity to coal. The kinetic diameter of CO

_{2}is smaller and coal has a higher sorption affinity to the molecules of this gas. Consequently, CO

_{2}is able to permeate into ultra-micropores with diameters as small as 0.4 nm that are inaccessible to nitrogen [48]. CO

_{2}and N

_{2}adsorption isotherms of coal are presented in Figure 5 and the calculation results are shown in Table 2.

_{2}/g, which is higher than in the case of Budryk mine coal (1.117 mmolCO

_{2}/g). The Sobieski mine coal also obtained a higher SSA Langmuir value and a much higher SSA value in terms of micropores (DA model). This value was high compared to typical SSA levels coals [9,17]. The total volume of micro and ultra-micropores in coals, according to the HK theory, was in the range of 0.031 cm

^{3}/g to 0.045 cm

^{3}/g, while according to the DA theory, in the range of 0.06–0.09 cm

^{3}/g, respectively. The average width of the pores accessible to CO

_{2}was 0.67 nm, which corresponds to the range of ultra-micropores in the materials (0–0.8 nm). The characteristic adsorption energy, determined according to DA theory, interpreted as the energy barrier needed to overcome the dispersion forces between adsorbate and coal molecules, was slightly higher in Sobieski mine coal and amounted to 20.70 kJ/mol, while in Budryk mine coal it was 20.11 kJ/mol.

_{2}adsorption. The pore size distribution of the tested coals was determined according to the HK model. It is presented in Figure 6. In Sobieski mine coal with a higher vitrinite content, a larger pore volume was obtained in the entire studied range of micropore diameters. The cumulative pore volume in Sobieski mine was 50% higher than Budryk mine (Figure 6).

_{2}, pore distribution was determined using the BJH model. Also in the range of mesopores (2–50 nm) Sobieski mine had a larger pore volume than Budryk mine in the entire diameter range. The largest volume was found in pores with diameters above 30 nm. It is presented in Figure 7.

## 4. Gas Desorption from the Spherical Coal Sample

_{0}as a result of a step change in external conditions, after which these conditions remain unchanged. The accumulation process is accompanied time changes of the distribution of the cumulative concentration C of the sorbate within grains. If it is assumed that a linear sorption isotherm can be used, the accumulation process can be described using Fick’s second law:

_{e}is effective diffusion coefficient, C is cumulative concentration of the sorbate, D is diffusion coefficient.

_{e}. The value of this coefficient results from the diffusion coefficient value D and the inclination of Henry’s isotherm.

#### 4.1. Mathematical Model of Desorption

#### 4.2. Laboratory Measurements

_{2}saturation in spherical coal samples was analyzed. Interpretations included changes in the mass of coal samples after a quasi-step change in pressure from a vacuum to 0.1 MPa. Direct results of measurements of Sobieski mine coal are presented in Figure 11 and of Budryk mine coal in Figure 12.

## 5. Gas Desorption from the Plane Sheet Coal Sample

#### 5.1. Mathematical Model of Desorption

#### 5.2. Laboratory Measurements

_{2}pressure from vacuum to 1.0 MPa. Prior to that, the samples were prepared in a vacuum for 10 days. Direct results are presented in Figure 13 and Figure 14 and in Table 4.

## 6. Accompanying Coal Shrinkage

_{2}in an external tank and immediately placed under the head of the altimeter. The CO

_{2}desorption process and the accompanying shrinkage were triggered by a step change in the gas pressure from saturation pressure to atmospheric pressure. The recorded changes in the sample size are shown in Figure 15 and Figure 16.

_{2}desorption kinetics. It is also worth noting that for individual coals, shrinkage kinetics is clearly faster than the kinetics of CO

_{2}desorption. Measurement by a gravimetric device assumes that the change in mass is recorded when the gas molecule is bound to the porous material by surface interaction forces. The fact that the recorded shrinkage of the material occurs faster than the change in sorbent mass under the influence of sorption may suggest that the start of surface diffusion (Volmer) and solid diffusion have a slow effect on the cumulative change in sample mass, but significantly change the size of the sample. Figure 17 shows particular types of diffusion in the coal pore system. During surface diffusion and solid diffusion, gas molecules move, but remain in quasi-continuous contact with the sorbent surface.

## 7. Conclusions

_{2}desorption on grain coal samples of a sphere-like shape and a plane sheet shape. The desorption time of gas sorbate from coal depends on the square of the sample size. Sorption tests are usually carried out on small granular samples up to about 1 mm, because such samples ensure the achievement of sorption equilibrium within a few days. However, with such small samples it is difficult to test shrinkage/swelling that result from sorption. The use of plane sheet samples allowed shortening the measurement time to several days, due to the fact that the gas desorption occurred in the geometrically shortest direction (about 1 mm). At the same time, it was possible to observe the coal shrinkage, since the longest sample size of coal was over 20 mm.

_{2}desorption kinetics. Literature review reveals that so far no sorption analysis results have been extrapolated with a Crank model other than for spherical grains.

_{2}desorption from such samples worse than the commonly used unipor model for granular samples. This result may be related to the fact that the roundness of the sieved coal grains is only statistical, while the shape of the plane sheet samples is more consistent with the model shape.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Godyn, K.; Kozusnikova, A. Microhardness of Coal from Near-Fault Zones in Coal Seams Threatened with Gas-Geodynamic Phenomena, Upper Silesian Coal Basin, Poland. Energies
**2019**, 12, 1756. [Google Scholar] [CrossRef] - Godyn, K. Structurally altered hard coal in the areas of tectonic disturbances-an initial attempt at classification. Arch. Min. Sci.
**2016**, 61, 677–694. [Google Scholar] - IUPAC Physical Chemistry Division Commission on Colloid and Surface Chemistry Subcommittee on Characterization of Porous Solids. Recommendations for The Characterization of Porous Solids (Technical Report). Pure Appl. Chem.
**1994**, 66, 1739–1758. [Google Scholar] [CrossRef] - Sing, K.S.W.; Everett, D.H.; Haul, R.A.W.; Moscou, L.; Pierotti, R.A.; Rouquerol, J.; Siemieniewska, T. Reporting Physisorption Data for Gas/Solid Systems with Special Reference to the Determination of Surface Area adn Porosity. Pure Appl. Chem.
**1985**, 57, 603–619. [Google Scholar] [CrossRef] - Mahajan, O.P.; Walker, P.L. Porosity of Coal and Coals Products; The Pensylvania State University: Philadelphia, PA, USA, 1978. [Google Scholar]
- Ettinger, J.L. Solubility of Methane Contained in Coal Deposits. Arch. Min. Sci.
**1990**, 33, 35. [Google Scholar] - Skiba, M.; Młynarczuk, M. Identification of Macerals of the Inertinite Group Using Neural Classifiers, Based on Selected Textural Features. Arch. Min. Sci.
**2018**, 63, 827–837. [Google Scholar] - Wierzbicki, M.; Pajdak, A.; Baran, P.; Zarębska, K. Isosteric heat of sorption of methane on selected hard coals. Przemysl Chemiczny
**2019**, 98, 625–629. [Google Scholar] - Pajdak, A. Parameters of N
_{2}and CO_{2}adsorption onto coal at various temperatures. In Proceedings of the 18th International Multidisciplinary Scientific Geoconference SGEM, Albena, Bulgaria, 30 June–9 July 2018; pp. 633–640. [Google Scholar] - Kudasik, M.; Skoczylas, N.; Pajdak, A. The repeatability of sorption processes occurring in the coal-methane system during multiple measurement series. Energies
**2017**, 10, 661. [Google Scholar] [CrossRef] - Okolo, G.N.; Everson, R.C.; Neomagus, H.W.P.J.; Roberts, M.J.; Sakurovs, R. Comparing the porosity and surface areas of coal as measured by gas adsorption, mercury intrusion and SAXS techniques. Fuel
**2015**, 141, 293–304. [Google Scholar] [CrossRef] - Weishauptová, Z.; Sýkorová, I. Dependence of carbon dioxide sorption on the petrographic composition of bituminous coals from the Czech part of the Upper Silesian Basin, Czech Republic. Fuel
**2011**, 90, 312–323. [Google Scholar] [CrossRef] - Godyn, K.; Dutka, B. The impact of the degree of coalification on the sorption capacity of coals from the Zofiówka Monocline. Arch. Min. Sci.
**2018**, 63, 727–746. [Google Scholar] - Młynarczuk, M.; Skiba, M. The application of artificial intelligence for the identification of the maceral groups and mineral components of coal. Comput. Geosci.
**2017**, 103, 133–141. [Google Scholar] [CrossRef] - Billemont, P.; Coasne, B.; De Weireld, G. Adsorption of carbon dioxide, methane, and their mixtures in porous carbons: Effect of surface chemistry, watercontent, and pore disorder. Langmuir
**2013**, 29, 3328–3338. [Google Scholar] [CrossRef] [PubMed] - Cai, Y.; Liu, D.; Pan, Z.; Yao, Y.; Li, J.; Qiu, Y. Pore structure and its impact on CH4 adsorption capacity and flow capability of bituminous and subbituminous coals from Northeast China. Fuel
**2013**, 103, 258–268. [Google Scholar] [CrossRef] - Pajdak, A.; Kudasik, M.; Skoczylas, N.; Wierzbicki, M.; Teixeira Palla Braga, L. Studies on the competitive sorption of CO2 and CH4 on hard coal. Int. J. Greenh. Gas Control
**2019**, 90, 102789. [Google Scholar] [CrossRef] - Pan, Z.J.; Connell, L. A theoretical model for gas adsorption-induced coal swelling. Int. J. Coal Geol.
**2007**, 69, 243–252. [Google Scholar] [CrossRef] - Liu, S.M.; Harpalani, S. A new theoretical approach to model sorption-induced coal shrinkage or swelling. AAPG Bull.
**2013**, 97, 1033–1049. [Google Scholar] [CrossRef] - Connell, L.; Lu, M.; Pan, Z.J. An analytical coal permeability model for tri-axial strain and stress conditions. Int. J. Coal Geol.
**2010**, 84, 103–114. [Google Scholar] [CrossRef] - Durucan, S.; Ahsanb, M.; Shia, J.-Q. Matrix shrinkage and swelling characteristics of European coals. Energy Procedia
**2009**, 1, 3055–3062. [Google Scholar] [CrossRef] [Green Version] - Seidle, J.P.; Huitt, L.G. Experimental Measurement of Coal Matrix Shrinkage due to Gas Emission and Implications for Cleat Matrix Increases. SPE Pap.
**1995**, 181, 30010. [Google Scholar] - Gawor, M.; Skoczylas, N. Sorption Rate of Carbon Dioxide on Coal. Transp. Porous Media
**2014**, 101, 269–279. [Google Scholar] [CrossRef] - Grabowska, K.; Sosnowski, M.; Krzywanski, J.; Sztekler, K.; Kalawa, W.; Żyłka, A.; Nowak, W. The numerical comparison of heat transfer in a coated and fixed bed of an adsorption chiller. J. Therm. Sci.
**2018**, 27, 421–426. [Google Scholar] [CrossRef] - Li, X.; Nie, B.; Zhang, R.; Chi, L. Experiment of gas diffusion and its diffusion mechanism in coal. Int. J. Min. Sci. Technol.
**2012**, 22, 885–889. [Google Scholar] - Crosdale, P.J.; Beamish, B.B.; Valix, M. Coalbed methane sorption related to coal composition. Int. J. Coal Geol.
**1998**, 35, 147–158. [Google Scholar] [CrossRef] - Harpalani, S.; Schraufnagel, R.A. Shrinkage of coal matrix with release of gas and its impact on permeability of coal. Fuel
**1990**, 69, 551–556. [Google Scholar] [CrossRef] - King, G.R.; Ertekin, T.M. A Survey of Mathematical Models Related to Methaneproduction from Coal Seams, Part 1. Empirical and Equilibrium Sorption Models. In Proceedings of the 1989 Coalbed Methane Symposium, The University of Alabama, Tuscaloosa, AL, USA, 17–20 April 1989; pp. 125–138. [Google Scholar]
- Sercombea, J.; Vidala, R.; Galléb, C.; Adenota, F. Experimental study of gas diffusion in cement paste. Cem. Concr. Res.
**2007**, 37, 579–588. [Google Scholar] [CrossRef] [Green Version] - Staib, G.; Sakurovs, R.; Gray, E.M. Kinetics of coal swelling in gases: Influence of gas pressure, gas type and coal type. Int. J. Coal Geol.
**2014**, 132, 117–122. [Google Scholar] [CrossRef] - Day, S.; Fry, R.; Sakurovs, R. Swelling of coal in carbon dioxide, methane and their mixtures. Int. J. Coal Geol.
**2012**, 93, 40–48. [Google Scholar] [CrossRef] - Otake, Y.; Suuberg, E.M. Temperature dependence of solvent swelling and diffusion processes in coals. Energy Fuels
**1997**, 11, 1155–1164. [Google Scholar] [CrossRef] - Ruckenstein, E.; Vaidyanathan, A.; Youngquist, G. Sorption by solids with bidisperse pore structures. Chem. Eng. Sci.
**1971**, 26, 1305–1318. [Google Scholar] [CrossRef] - Berens, A.; Hopfenberg, H. Diffusion and relaxation in glassy polymer powders: 2. Separation of diffusion and relaxation parameters. Polymer
**1978**, 19, 489–496. [Google Scholar] [CrossRef] [Green Version] - King, G.; Ertekin, T.; Schwerer, F. Numerical simulation of the transient behavior of coal-seam degasification wells. SPE Form. Eval.
**1986**, 1, 165–183. [Google Scholar] [CrossRef] - Busch, A.; Gensterblum, Y.; Krooss, B.; Littke, R. Methane and carbon dioxide adsorption–diffusion experiments on coal: Upscaling and modeling. Int. J. Coal Geol.
**2004**, 60, 151–168. [Google Scholar] [CrossRef] - Staib, G.; Sakurovs, R.; Gray, E. Dispersive diffusion of gases in coals. Part I: Model development. Fuel
**2015**, 143, 612–619. [Google Scholar] [CrossRef] - Skoczylas, N.; Pajdak, A.; Kozieł, K.; Braga, L. Methane emission during gas and rock outburst on the basis of the unipore model. Energies
**2019**, 12, 1999. [Google Scholar] - Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, UK, 1975. [Google Scholar]
- Skoczylas, N.; Kudasik, M.; Topolnicki, J.; Oleszko, K.; Młynarczuk, M. Model studies on saturation of a coal sorbent with gas taking into account the geometry of spatial grains. Przemysl Chemiczny
**2018**, 97, 272–276. [Google Scholar] - Horvath, G.; Kawazoe, K. Method for the calculation of the effective pore size distribution in molecular sieve carbon. J. Chem. Eng.
**1983**, 16, 470–475. [Google Scholar] [CrossRef] - Jagiello, J.; Thommes, M. Comparison of DFT characterization methods based on N
_{2}, Ar, CO_{2}, and H_{2}adsorption applied to carbons with various pore size distributions. Carbon**2004**, 42, 1227–1232. [Google Scholar] [CrossRef] - Dubinin, M.M. Adsorpcja i Porowatość; Wojskowa Akademia Techniczna: Warsaw, Poland, 1975. [Google Scholar]
- Brunauer, S. Physical Adsorption; Princeton University Press: Princeton, NJ, USA, 1945. [Google Scholar]
- Barrett, E.P.; Joyner, L.G.; Halenda, P.P. The determination of pore volume and area distribution in porous substances. I. Computations from nitrogen isotherms. J. Am. Chem. Soc.
**1951**, 73, 373–380. [Google Scholar] [CrossRef] - Pillalamarry, M.; Harpalani, S.; Liu, S. Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs. Int. J. Coal Geol.
**2011**, 86, 342–348. [Google Scholar] [CrossRef] - International Classification of In-Seam Coals; UNECE: Geneva, Switzerland; UN: New York, NY, USA, 1998; p. 41.
- Cui, X.; Bustin, R.M.; Dipple, G. Selective transport of CO
_{2}, CH_{4}and N_{2}in coals: Insights from modeling of experimental gas adsorption data. Fuel**2003**, 83, 293–303. [Google Scholar] [CrossRef] - Airey, E.M. Gas emission from broken coal. An experimental and theoretical investigation. Int. J. Rock Mech. Min. Sci.
**1968**, 5, 475. [Google Scholar] [CrossRef] - Skoczylas, N.; Wierzbicki, M.; Murzyn, T. The influence of temperature of the coal-methane system on sorption capacity of coal, taking into account the kinetics of sorption and diffusion processes. Prace Instytutu Mechaniki Górotworu PAN
**2013**, 15, 75–83. [Google Scholar]

**Figure 1.**The half time of CO

_{2}desorption from coal samples De = 10

^{−9}[cm

^{2}/s] of various equivalent radii in the range of: (

**a**) 0.007–0.15 cm; (

**b**) 0.007–1.5 cm.

**Figure 3.**Registration of changes in the plane sheet sample geometry during desorption: (

**a**) measuring laser head; (

**b**) side view of the sample; top view of the sample.

**Figure 4.**Taking into account changes in the size of coal samples during desorption in the time between the step change in pressure, with the moment of recording the sample geometry: (

**a**) coal from Sobieski mine coal; (

**b**) coal from Budryk mine coal.

**Figure 6.**Pore size distribution of the coals based on method low-pressure gas adsorption (LPA) CO

_{2}(HK model).

**Figure 15.**Kinetics of shrinkage of Sobieski mine coal juxtaposed with CO

_{2}desorption kinetics—plane sheet sample.

**Figure 16.**Kinetics of shrinkage of Budryk mine coal juxtaposed with CO

_{2}desorption kinetics—plane sheet sample.

**Figure 17.**Particular types of diffusion in the coal pore system [50].

Coal | R_{0} | Vitrinite | Inertinite | Liptinite | V^{daf} | A^{d} | W^{t} | ρ_{sk} |
---|---|---|---|---|---|---|---|---|

(%) | (%) | (%) | (%) | (%) | (%) | (%) | (g/cm^{3}) | |

Sobieski mine | 0.71 | 73.7 | 16.8 | 9.5 | 32.35 | 11.54 | 5.35 | 1.44 |

Budryk mine | 0.85 | 62.6 | 27.0 | 10.4 | 30.98 | 8.40 | 1.22 | 1.37 |

CO_{2} Adsorption, 273K | Sobieski Mine | Budryk Mine |
---|---|---|

Langmuir total sorption capacity (mmol/g) | 1.554 | 1.117 |

Langmuir specific surface area (m^{2}/g) | 159.09 | 114.38 |

HK maximum pore volume (cm³/g) | 0.045 | 0.031 |

HK average pore width (nm) | 0.665 | 0.668 |

DFT volume in pores < 0.43 nm, * 10–3 (cm^{3}/g) | 0.96 | 1.80 |

DFT total pore volume ≤ 1.08 nm, * 10–3 (cm^{3}/g) | 32.77 | 24.71 |

DFT pore area > 1.08 nm, (m²/g) | 92.28 | 61.51 |

DFT total pore area ≥ 0.43 nm, (m²/g) | 197.70 | 130.21 |

DA characterization of adsorption energy, (kJ/mol) | 20.70 | 20.11 |

DA volume of micropores (cm³/g) | 0.09 | 0.06 |

DA surface area of micropores (m^{2}/g) | 224.10 | 149.28 |

N_{2} Adsorption, 77K | ||

Sorption capacity (mmol/g) | 0.836 | 0.044 |

BET specific surface area (m²/g) | 15.42 | 0.43 |

BJH total pore volume (cm³/g) | 0.027 | 0.001 |

BJH specific surface area (m²/g) | 10.79 | 0.20 |

BJH average pore diameter (nm) | 9.85 | 27.56 |

Coal | Sorption Capacities | Parameters of the Langmuir Isotherm | Effective Diffusion Coefficient | |||
---|---|---|---|---|---|---|

a(0.1) | a(0.5) | a(1.5) | A | B | De | |

(cm^{3}/g) | (cm^{3}/g) | (cm^{3}/g) | (cm^{3}/g) | (1/MPa) | (cm^{2}/s) | |

Sobieski mine | 11.78 | 39.48 | 61.48 | 86.70 | 1.65 | $3.51\times {10}^{-8}$ |

Budryk mine | 6.24 | 14.18 | 20.89 | 25.46 | 2.76 | $6.58\times {10}^{-9}$ |

_{e}is effective diffusion coefficient.

**Table 4.**Sorption parameters describing CO

_{2}desorption from granular samples and the plane sheet type described by an appropriate mathematical model.

Coal | Sorption Capacity | Effective Diffusion Coefficient | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Spherical Samples | Plane Sheet Samples | Percentage Difference | Spherical Samples | Plane Sheet Samples | Percentage Difference | Spherical Samples | Plane Sheet Samples | |||

a(0.1 MPa), (cm^{3}/g) | (%) | De, (cm^{2}/s) | (%) | RSoS | R^{2} | RSoS | R^{2} | |||

Sobieski mine | 11.55 | 11.78 | 1.95 | $3.51\times {10}^{-8}$ | $3.92\times {10}^{-8}$ | −11.68 | 183 | 0.982 | 125 | 0.989 |

Budryk mine | 6.24 | 6.24 | 0 | $6.58\times {10}^{-9}$ | $7.25\times {10}^{-9}$ | −10.18 | 167 | 0.088 | 97 | 0.995 |

^{2}—coefficient of determination, R-squared.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Skoczylas, N.; Pajdak, A.; Młynarczuk, M.
CO_{2} Adsorption–Desorption Kinetics from the Plane Sheet of Hard Coal and Associated Shrinkage of the Material. *Energies* **2019**, *12*, 4013.
https://doi.org/10.3390/en12204013

**AMA Style**

Skoczylas N, Pajdak A, Młynarczuk M.
CO_{2} Adsorption–Desorption Kinetics from the Plane Sheet of Hard Coal and Associated Shrinkage of the Material. *Energies*. 2019; 12(20):4013.
https://doi.org/10.3390/en12204013

**Chicago/Turabian Style**

Skoczylas, Norbert, Anna Pajdak, and Mariusz Młynarczuk.
2019. "CO_{2} Adsorption–Desorption Kinetics from the Plane Sheet of Hard Coal and Associated Shrinkage of the Material" *Energies* 12, no. 20: 4013.
https://doi.org/10.3390/en12204013