Low Subcritical CO2 Adsorption–Desorption Behavior of Intact Bituminous Coal Cores Extracted from a Shallow Coal Seam

This study focuses on improving fundamental understanding of low, subcritical CO2 adsorption–desorption behavior of bituminous coals with the aim to evaluate the utility of shallow-depth coal seams for safe and effective CO2 storage. Comprehensive data and a detailed description of coal–CO2 interactions, e.g., adsorption, desorption, and hysteresis behavior of intact bituminous coals at CO2 pressures <0.5 MPa, are limited. Manometric sorption experiments were performed on coal cores (50 mm dia. and 30- or 60-mm length) obtained from a 30 m deep coal seam located at the Upper Silesian Basin in Poland. Experimental results revealed that the adsorption capacities were correlated to void volume and equilibrium time under low-pressure injection (0.5 MPa). The positive deviation, observed in the hysteresis of adsorption–desorption isotherm patterns, and the increased sample mass at the end of the tests suggested CO2 pore diffusion and condensation. This behavior is vital for assessing low-pressure CO2 injection and storage capabilities of shallow coal seams where confining pressure is much lower than that of the deeper seams. Overall, CO2 adsorption depicts a type II adsorption isotherm and a type H3 hysteresis pattern of the IUPAC classification. Experimental results fitted better to the Brunauer–Emmett–Teller model than the Langmuir isotherm model. CO2 adsorption behavior of intact cores was also evaluated by characteristic curves. It was found that Curve I favored physical forces, i.e., the presence of van der Waals/London dispersion forces to describe the coal–CO2 interactions. However, analysis of Curve II indicated that the changing pressure-volume behavior of CO2 in the adsorbed phase, under low equilibrium pressures, cannot be ignored.


He-pycnometer method; determining the void volume of the reference cell ( ) and the empty sample cell ( )
The void volumes of the reference and sample cells were determined using the gas expansion method and the Boyle's variant of the gas law (PV=ZnRT). The procedures are outlined below. (i) A vacuum pump was used to evacuate the entire adsorption cell apparatus as well as the gas pipelines for 24 hours. Before the test, the tubing that connects the system to the helium gas cylinder was vacuumed for 15 minutes. (ii) The calibration cell (known volume, the volume of calibration cell = m 3 ) was connected to the gas line, and the calibration cell temperature 0.0004892 was maintained at the same temperature as the water tank (298.15 K). To ensure individual isolation, the valves V1, V2, and V3 ( Figure 1) that connected the calibration cell (CC), reference cell (RC), and sample cell (SC) were initially closed. (iii) The calibration cell (CC) was injected with a known volume of He gas (equal to the V cc ) and the pressure data were recorded. Although the pressure readings were stabilised after 120 seconds, around 20 minutes of readings were allowed to monitor any pressure variations caused by indeterminate errors (e.g., leaks, temperature fluctuations). The pressure values were abbreviated as,P cc . (iv) After recording the , valve V1 was opened to expand the He gas into the reference cell (RC) (Figure 1). The pressure readings (referred to as ) were + recorded to determine the volume of the reference cell ( ). (v) The V2 was then opened to allow the He gas to be expanded into the sample cell ( SC). The pressure values (referred to as ) recorded after 20 minutes + + were used to calculate the sample cell volume ( ). When the preceding test was completed. To prepare the system for the next injecti on cycle, the calibration cell (CC) and the helium gas line from the cylinder, RC, a nd SC were evacuated through V3 with a vacuum pump for about 10 minutes.
To eliminate any uncertain experimental mistakes, the aforementioned method from I to (vi) was repe ated three times.

Void volume approximation of the sample cell including a coal sample ( )
Section 2.2 of the main text describes the sample loading and preparation procedures. The experimental approach for calculating the void volume of the sample cell is the same as t he procedures outlined in the section above, from (i) to (v). The only difference was that this time the sample cell (SC) was loaded with a core sample, as seen in Figure 2. The sample cell volume ( ) was calculated using the stable pressure value measured as . + + The volume calculation method is detailed in the following section.

Modified He-Pycnometry volume calculation method
Using the data generated (pressure values) from the He-Pycnometry methods mentioned in the preceding section, the gas law for real/non-ideal gases, Equation (1), was used to compute the volume of the reference cell (V rc ) and sample cell (Vsc). The P-V-T behaviour was considered to reflect the effects of real gas on the molar volume. The following is the calculating technique.
Step 1: To calculate the number of moles injected into the calibration cell.
(1) = where, = The number of moles of He, mol, = Pressure measured from CC, Pa, = Volume of CC =0.0004832 m 3 , Compressibility factor of He, and R = Universal gas = constant = 8.314 Pa m 3 /mol/°K For real gases, the ideal gas law is modified using the compressibility factor to provide a more accurate forecast of cell volume (Smith et al., 2018, Rao, 1997. For the compressibility factor (Z) values, the cubic version of the Peng-Robinson equation of state (PR-EoS) was solved. The values were then compared to compressibility factor (Z) charts to eliminate the deviation error caused by polar gases such as He (Elliot and Lira, 2012;Smith et. al., 2018;Rao, 1997). To calculate the amount of moles, the Z values were inserted in Equation (1).
Step 2: The volume, , was calculated by substituting the number of moles obtained from the foregoing calculations and the pressure values of from section 1.1 in ( ) ( + ) Equation (2). The compressibility factor was estimated for the corresponding measured pressure values of . The reference cell volume was obtained by subtracting from ( + ) . (2) where, V cc = volume of calibration cell, m 3 , V rc = volume of the reference cell, m 3 , and P cc +P rc = pressure measured when the He was in the calibration cell+ reference cell, Pa.
Step 3: Similar procedures, described in Step 2, were followed to calculate the empty sample cell volume ( (Equations 3 and 4). As the ( ) was known from steps 1 and 2 and it ) + can be subtracted from ( ) to determine the empty sample cell volume ( . The sample cell volume with a sample loaded was determined using the same steps as 1 to 3 and referred to as . ( ) is alluded to as (void volume) in the main text (Equations + (1) and (2) of the main text). (3) where, V cc = Volume of calibration cell, m 3 , V rc = Volume of reference cell, m 3 , V sc = Volume of sample cell, m 3 , V scv = Volume of sample cell with sample, m 3 , P cc +P rc +P sc = Pressure measured when the He was in the calibration cell + reference cell + empty sample cell ( Figure  2), Pa, and P cc +P rc +P scv = Pressure measured when the He was in the calibration cell + reference cell + sample cell with sample loaded (Figure 2), Pa.

CO 2 adsorption measurements (Section 2.3)
CO 2 gas adsorption studies were carried out in the same manner as helium gas expansion experiments. By measuring the increasing or decreasing adsorptive gas pressure, the amount of CO 2 adsorbed or desorbed was estimated. The steps are outlined below.
(i) In the sample cell, a known mass of coal sample (SC) was placed. Before the test, the entire system was vacuumed for 24 hours, and the pipeline connecting the system to the CO 2 gas cylinder was evacuated for 15 minutes. (ii) The valves V1, V2 , and V3 ( Figure 3) were closed to isolate the reference and sample cells.
A CO 2 vaporiser was employed to inject the CO 2 in the vapour phase from the cylinder. (iii) By opening the valve V1, a known quantity (n moles) of CO 2 was fed into RC (Figure 3).
The volume of the RC can be calculated using the He-pycnometry volume measurements described in the preceding section. (iv) The gas pressure of RC was measured after filling it with a specified volume of CO 2 . The injected gas's molar volume was determined using the gas law. The following section explains the calculation strategy. The gas was then expanded to the SC by opening the valve V2 (Figure 4). (v) After expanding the gas into SC, the gas pressures in the RC and SC were continually monitored and recorded by an application software provided by the GDS Instruments, UK. The adsorbate gas pressure is decreased in proportion to the rate of adsorption. The sorptive gas was allowed to equilibrate with the sorbent, and the equilibrium gas pressure was identified when the gas pressure values were constant for a minimum of 4 hours. The amount of CO 2 adsorbed was determined by calculating the difference between the number of moles in the gas phase at the beginning of the stage (n moles) and the number of moles at the equilibrium stage (n eq moles).

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(vi) The above steps were repeated in order to inject CO2 in phases at injection pressures ranging from 0.1 MPa kPa to 4.0 MPa.
(vii) The preferential adsorption tests were carried out with an 80% CO2 and 20% methane gas mixture, and the experimental protocols were the same as those described before. To confirm the preferential sorption behaviour of the coal specimens, an Emmerson Xstream gas analyser was coupled in the gas line and located before the reference cell to quantify the change in volume percent.

Calculation procedures for measuring the amount of adsorbed CO 2 in coal samples
The number of moles adsorbed in a kg of coal was obtained by calculating the difference between the number of moles in the gas phase at the beginning of each stage and the number of moles in the gas phase at the time of the equilibrium (Equation 5). where, = Moles adsorbed CO 2 per kg mass of adsorbent mol of CO 2 /kg, Number of moles in RC+SC at the end of each stage (equilibrium).
The number of moles of CO 2 in RC and SC was calculated using the gas law. The P-V-T behaviour was predicted using Peng-Robinson equation of state ( values) (Equation 6). The Peng-Robinson is a modified version of the Redlich-Kwong equation of state (Rao, 1997;and Elliott and Lira, 2012). where, = Compressibility factor, = Equilibrium Pressure, V = Cell Volume, R = Universal Gas constant, T= Temperature, = Critical pressure of CO 2 , = Critical temperature of CO 2 , = Density = PR-EoS parameters, b = Dimensional PR-EoS parameter, = Acentric , α, ϰ factor for CO 2 .
The non-dimensional form of the PR-EoS (Equation 8) was solved to determine the molar volume of the pressures recorded in reference cell. The must be solved for CO 2 vapour/liquid roots to determine the molar volumes of the corresponding states.

CO 2 Desorption experimental procedures
CO 2 desorption experiments were conducted in the same manner as stated in Section 2.2. After the final stage of the adsorption experiment is complete, the valve V2 is closed to isolate the SC from the RC and the pressure in the RC is decreased. Then, valve V2 was opened to connect the RC and SC and enable for equilibrium to be achieved. Pressure increased gradually during desorption when CO 2 molecules were released from the coal surfaces. After achieving equilibrium, the procedures were repeated. Every ten seconds, the change in gas phase pressure during adsorption and desorption was recorded and used to determine the adsorption and desorption rates.

Characteristic curve II:
The molar volume of the adsorbed phase of CO 2 was calculated using Equation (9). where, = Volume available for CO 2 in per kg of coal = Void volume of the sample + maximum volume can occupy on the external surface area (assuming, no multilayer on the surface) + connected and unconnected pore volume (1.5% of the bulk volume of the sample), and = Molar volume of adsorbed phase, m 3 /mol.
Example calculation: = 6.8966×10 -05 m 3 /kg is calculated by summing up (i) measured void volume of the sample by He-pycnometer method (9.17814×10 -06 m 3 ), (ii) maximum volume occupied on the external surface area (calculated using effective contact area of 0.52nm 2 (Atkins et al., 2017) of CO 2 and effective area occupied by CO 2 molecule on coal 0.260 nm 2 (calculated after Pennell, 2002)-this value is negligible, and (iii) the microporous void volume measured using X-ray CT (X-ray computed tomography), which is 1.5% of the bulk volume of the coal. The bulk volume of coal is 0.000111 m 3 /0.1404 kg of coal. The calculated total volume was propagated to a kg of coal as shown in Equation (9a) and substituted in Equation (9).

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To achieve the molar volume or adsorbed phase density, the amount adsorbed for a given equilibrium pressure was replaced into equation (9). Then, ratio is calculated using the molar volume of monolayer adsorption ( = 0.000167 m 3 /mol) calculated from BET (n mon ) isotherm model.
The fugacity values gas phase and adsorbed phase were calculated using Peng-( ) ( ) Robinson equation of state for the corresponding gas pressure.
For example, consider the first data point on the characteristic curve II, the adsorbed phase molar volume of 0.00155 m 3 /mol CO 2 would yield an adsorbed phase fugacity of = =1.35 MPa. The corresponding equilibrium gas phase fugacity is = 0.035 MPa. The ratio of is 0.026. The ratio of is 0.11. Thus, the first data point constructed for the characteristic curve II.
The adsorbed phase fugacity is limited to the liquid phase fugacity of 4.29 MPa. When fugacity ratio of gas phase is equal to 4.29 the adsorption reaches infinite, and condensation sets in. The calculated values for the characteristic curve II are presented in Table S1.