Competitive adsorption/desorption of CO₂/CH₄ mixtures on anthracite from China over a wide range of pressures and temperatures

Abstract

The adsorption/desorption of CO₂/CH₄ mixtures with three different volume fractions was investigated at 294 K, 311 K, 333 K, and 353 K with pressures of up to 70 bar on anthracite from China using a high-pressure volumetric analyzer (HPVA II-200). For the mixtures, the total excess adsorbed amount decreased as the temperature rose. In addition, it displayed an upward tendency with an increase in the CO₂ fraction in the feed gas. The excess adsorbed amounts of the component gases were calculated on the basis of the composition of the gas phase measured by gas chromatography. For a mixture with a CO₂ fraction of 50%, relatively good adsorptivity for CO₂ was displayed at low pressures (<30 bar), whereas better adsorptivity for CH₄ was displayed at high pressures. When the CO₂ fraction in the feed gas increased from 20% to 50%, the excess adsorbed amount of CO₂ increased dramatically, whereas the excess adsorbed amount of CH₄ decreased slightly (6.3%). When the CO₂ fraction increased from 50% to 80%, the excess adsorbed amount of CO₂ increased substantially, whereas the excess adsorbed amount of CH₄ decreased drastically (42.4%). On the basis of the experimental data, the total excess adsorbed amount can be well simulated by the Ono–Kondo (OK) lattice thermodynamic model with an average deviation of 6.4%. Moreover, the excess adsorbed amounts of the individual components have also been predicted using the OK model.

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1. Introduction

With the consumption of fossil fuels increasing rapidly, the resulting enormous continuous emissions of CO₂ are leading to global warming. Injecting CO₂ into deep coal seams is one of the techniques of carbon capture, utilization and storage (CCUS).^1–7 Moreover, it could enable enhanced coal bed methane (ECBM) recovery and reduce the amount of methane emitted into the atmosphere.⁸ In order to provide relevant data and theoretical guidance for ECBM operations, it is necessary to investigate the adsorption/desorption of CO₂/CH₄ mixtures on coal over a wide range of pressures and temperatures.⁹

In recent years, many experimental studies of the competitive adsorption of CO₂/CH₄ mixtures have been reported. Yu et al.¹⁰ observed that the equilibrium concentration of CH₄ was higher than the initial concentration in the feed gas, which indicated preferential adsorption of CO₂. Merkel et al.¹¹ observed the preferential sorption of CO₂ on coals for gas mixtures with low partial pressures of CO₂ (≈20%). Lee et al.¹² studied the competitive adsorption of CO₂/CH₄ mixtures on dry and wet anthracite at 318 and 338 K and pressures of up to 13 MPa. They found that the CO₂/CH₄ mole ratios of the gas phase in equilibrium were lower than that of the feed gas, which indicated the preferential adsorption of CO₂. However, Majewska et al.¹³ found that coal displayed preferential sorption of CH₄ at 2.6 MPa and exhibited comparable affinities for CH₄ and CO₂ at higher pressures (4.0 MPa). Busch et al.^14–16 found that the preferential sorption behavior was independent of the feed gas composition for CO₂ fractions of between 53% and 92% and preferential adsorption of CH₄ occurred in the pressure range up to 8 MPa. Han et al.¹⁷ found that coal was heterogeneous in chemical composition and physical structure, which may induce differences in its sorption properties. Lafortune et al.¹⁸ performed adsorption experiments with CO₂/CH₄ mixtures on coal and found that whereas adsorption capacities for CO₂ increased with increases in the gas pressure and volume fraction of CO₂ in the mixture, adsorption capacities for CH₄ only increased with the gas pressure. Therefore, research into the adsorption/desorption characteristics of CO₂/CH₄ mixtures has been controversial and further studies via experiments and modeling are needed.

This research focused on the isothermal adsorption/desorption of CO₂/CH₄ mixtures with three different volume fractions on anthracite from China over a wide range of temperatures and pressures. Using a high-pressure volumetric analyzer (HPVA II-200), the adsorption/desorption isotherms of CO₂/CH₄ mixtures were determined in the temperature range from 293 K to 353 K and at pressures of up to 70 bar. The gas phase composition in the adsorption cell after achieving equilibrium was measured and the excess adsorbed amounts of CH₄ and CO₂ at equilibrium were calculated, respectively, during each desorption step. On the basis of the experimental data, the excess adsorbed amounts in the desorption process were described using the Ono–Kondo (OK) lattice model.

2. Experimental section

In this work, a volumetric method was used to measure the adsorption/desorption isotherms of CO₂/CH₄ mixtures. The experimental system was composed of a high-pressure volumetric analyzer (HPVA II-200), a temperature control system, a pressure control system, and a sample analysis system.

2.1 Apparatus

The high-pressure volumetric analyzer (HPVA II-200), which is shown schematically in Fig. 1, uses a static volumetric method to obtain high-pressure adsorption and desorption isotherms. It was produced by Micromeritics Instrument Corporation and has a wide range of operating pressures (vacuum to 200 bar) and broad temperature tolerance (from cryogenic to 500 °C). Dual measurement of free spaces and correction for the non-ideality of the analyzed gas can enhance the accuracy of the isotherm data. The high-pressure transducer provides a full-scale reading accuracy of ±0.04% with a stability of ±0.1% and the low-pressure transducer provides a reading accuracy of ±0.15%.

Fig. 1 (a) Experimental system. (b) HPVA II-200. HP, high-pressure transducer; LP, 1000 torr pressure transducer; T, temperature probe; (1) analysis port valve; (2) vent valve; (3) manifold valve; (4) full vent valve; (5) full vacuum valve; (6) CO₂/CH₄ gas mixture valve; (7) helium gas valve; (8) 1000 torr isolation valve; (9) degas port valve.

The temperature was controlled by a Julabo F12-ED refrigerated/heating circulator, which has a wide temperature range from 253 K to 373 K and a high measuring accuracy of ±0.03 K. The vacuum pump was provided by Edward Corporation (UK) and the ultimate vacuum that could be reached was 3 × 10⁻⁷ MPa. A booster pump (STK-GBD40-Ol) was used to increase the gas pressure to reach the experimental pressure in the adsorption cell. A gas chromatograph (GC7900) was used to determine the gas phase composition in the adsorption cell after achieving equilibrium. The excess adsorbed amounts of the component gases at equilibrium were calculated from the measured composition of the gas phase.

2.2 Analysis and characterization of sample

The gases (binary gases and helium) used in this study were obtained from Dalian Special Gas Co., Ltd. The purity of helium was 99.999% and the CO₂/CH₄ mixtures contained three different volume fractions (20.05% CO₂/79.95% CH₄, 49.80% CO₂/50.20% CH₄, and 80.05% CO₂/19.95% CH₄). In the following paragraphs, these will be simplified as 20% CO₂, 50% CO₂ and 80% CO₂ mixtures.

The coal sample used in this study was a typical anthracite obtained from the Datong coal mine in Shanxi province, China. It was crushed into powder of which the size fraction was 0.25–0.38 mm, and the petrographic analysis is given in Table 1. We used a Micromeritics 3Flex surface characterization analyzer employing a static volumetric method to measure the pore structure of the coal sample. The adsorption and desorption curves of the crushed coal sample are shown in Fig. 2a. Hysteresis was observed during desorption, which indicated that the adsorption pores were mostly open pores. This type of isotherm is commonly dominated by adsorption pores with a large maximum adsorption volume, as well as large values of the BET pore surface area and BJH cumulative pore volume. The BET pore surface area was 80.688 m² g⁻¹. For determination of the pore size distribution, the adsorption branch of the isotherm was used in the BJH method, as shown in Fig. 2b. The cumulative pore volume was 0.113 cm³ g⁻¹ when the pore diameter was between 1.70 nm and 263.70 nm. There existed some micropores (<2 nm), but the average pore diameter was 3.97 nm, which means that the coal sample had a significant amount of mesopores (2–50 nm) in accordance with the pore size classification of the International Union of Pure and Applied Chemistry (IUPAC).

Table 1 Physical properties and pore data of the raw coal used in the experiments^a

Proximate analysis (wt% dry basis)		Ultimate analysis (wt% dry basis)		Petrographic analysis (vol% mmf)		Pore data
a Remarks: SA is the BET surface area (m^2 g^−1); PV is the BJH cumulative adsorption pore volume (cm^3 g^−1); PD is the average pore diameter from the BJH adsorption branch (nm). (a) Adsorption/desorption isotherms (b) pore size distribution.
Ash	37.48	C	50.730	Vitrinite	73.0	SA	80.688
Moisture	0.86	H	2.169	Liptinite	0.0	PV	0.113
Volatiles	10.48	N	7.653	Inertinite	16.2	PD	3.97
Fixed carbon	51.18	O	35.630	Minerals	10.8
		S	0.927	Ro max	3.7

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Fig. 2 Isotherms and pore size distribution results for a coal sample obtained from a N₂ adsorption/desorption test at 77.15 K.

2.3 Adsorption/desorption

The sample cylinder was cleaned using an ultrasonic bath and heated in a drying oven for two hours. The sample weight was measured using a balance with a precision of 0.1 mg. Subsequently, the assembled sample holder was attached to the degas port, where adsorbed moisture was removed. The sample cylinder was evacuated to an ultimate vacuum and then the sample was degassed for 12 hours at 378.15 K. After degassing, the sample holder was attached to the analysis port. The system was purged three times with helium and evacuated to a vacuum. Then a binary gas adsorption/desorption experiment was carried out and isotherm plots were created by the HPVA II automatically. Finally, the excess adsorbed amounts of the gas mixture and individual components were calculated.

2.4 Calculations of adsorbed amounts

The adsorbed amount can be determined from the amount of gas dosed into the adsorption cell and the non-adsorbed amount. In order to determine the non-adsorbed amount, we have to measure the free space, which is the free volume of the adsorption cell excluding coal.

2.4.1 Free space. The free space was measured using a helium expansion method. At the analysis temperature, the sample tube, which is shown in Fig. 3, contains three temperature zones and the free space is divided into three parts. V_xU is the upper stem volume, which is approximately 3.5 cm³, V_xL is the lower stem volume, and V_S is the sample cell volume.

Fig. 3 Structure of the sample tube.

In order to determine V_xL and V_S, two mass balances need to be established, namely, at ambient temperature and the analysis temperature, respectively. At ambient temperature, the entire system (including the dosing manifold and the sample tube) was evacuated. Then, helium was supplied to the dosing manifold (at approximately 0.8 bar) and was finally dosed into the sample tube when equilibrium had been reached. During this analysis, the HPVA II software took readings of temperature and pressure before dosing helium into the sample tube (P_A and T_A), as well as after dosing (P_B and T_B). The total number of moles dosed into the sample tube (n_D) can be calculated using:

where V_LP is the volume of the LP manifold (46.7791 cm³) as provided by the manufacturer of HPVA II and z_A and z_B are gas compressibility factors for the corresponding states provided by the HPVA II software. The free space (V_AFS) is calculated using:

V_AFS = V_xU + V_xL + V_S (2)

For determination of the free space at ambient temperature, it is assumed that V_S and V_xL are at uniform temperature and pressure and it can be stated that:

V_SxL = V_S + V_xL (3)

If the pressure and temperature of the sample cylinder before dosing (P_s0 = 0 and T_s0), as well as after dosing (P_s1 and T_s1), the volume of the upper portion of the stem (V_xU), and the number of moles dosed (n_D) are known, an overall mass balance can be established by eqn (4) to determine V_SxL:

where z_xU0, z_xU1, z_s0 and z_s1 are gas compressibility factors for the corresponding states provided by the HPVA II software. Upon completion of the calculation of free space at ambient temperature, the sample tube was brought to the analysis temperature. Once the pressure and temperature (P_s2 and T_s2) were stable, the number of moles dosed (n′_D) was recorded by the HPVA II software. In comparison with ambient temperature, there was a third temperature zone (T_AM) in the system, because V_S and V_xL were no longer at the same temperature. This requires a new mass balance using eqn (5) to determine V_S and ultimately V_xL:where z_xU2, z_xL2, and z_s2 are gas compressibility factors for the corresponding states provided by the HPVA II software.

2.4.2 Adsorbed amount of gas mixture. In the process of adsorption/desorption, the manifold and sample tubes were evacuated first and then the gas mixture was supplied to the dosing manifold, allowed to reach equilibrium, and finally dosed into the sample tube. The temperature and pressure before dosing (P₁ and T₁), as well as after dosing (P₂ and T₂), were recorded and the amount of gas dosed into the adsorption cell (n_dosed) can be calculated using:where V_HP is the volume of the HP manifold (27.0903 cm³) as provided by the manufacturer of HPVA II and z₁ and z₂ are gas compressibility factors for the corresponding states provided by the HPVA II software.

The amount of the gas mixture that was not adsorbed (n_Nads) can be obtained using the following equation:

where P_S is the pressure of the sample tube, T_S is the temperature of the sample cell, T_xU is the temperature of the upper stem, and z_xU, z_s and z_xL are gas compressibility factors for the corresponding states provided by the HPVA II software.

The adsorbed amount of the gas mixture (n_ads) can be calculated using:

n_ads = n_dosed − n_Nads (8)

2.4.3 Adsorbed amounts of component gases. In the HPVA II measurement procedure, there exists an exhaust process during each desorption step to control the pressure. The gas composition in the adsorption cell after achieving equilibrium was measured during each desorption step, which could be used to calculate the adsorbed amount at each desorption step to improve the accuracy of calculations. The total adsorbed amount at one pressure step (Δn_ads) can be calculated using:

Δn_ads = Δn_dosed − Δn_Nads (9)

where Δn_dosed is the amount dosed from the manifold at that pressure step and Δn_Nads is the non-adsorbed amount at that pressure step. Likewise, the total adsorbed amount at the n^th pressure step (Δn_adsn) can be calculated using:

Δn_adsn = Δn_dosedn − Δn_Nadsn = n_An − n_Bn − n_Nadsn + n_Nadsn−1 (10)

where n_An is the number of moles of gas in the manifold before dosing at the n^th pressure step, n_Bn is the number of moles of gas in the manifold after dosing at the n^th pressure step and n_Nadsn−1 is the number of moles of gas not adsorbed by the sample at the n − 1^st pressure step. The adsorbed amounts of CH₄ and CO₂ at the n^th pressure step (Δn_adsnCH4 and Δn_adsnCO2) can be calculated using:

Δn_adsnCH4 = n_An × y_CH4 + n_Nadsn−1 × y_CH4n−1 − (n_Bn + n_Nadsn) × y_CH4n (11)

Δn_adsnCO2 = Δn_adsn − Δn_adsnCH4 (12)

where y_CH4 is the fraction of CH₄ in the feed gas, y_CH4n is the fraction of CH₄ in the adsorption cell after achieving equilibrium at the n^th pressure step and y_CH4n−1 is the fraction of CH₄ at the n − 1^st pressure step. The excess adsorbed amount of the component gases is the sum of the values for the corresponding steps.

3. Results and discussion

3.1 Total excess adsorbed amount

A repetitive experiment at 311 K was conducted and the total excess adsorbed amounts for the different fractions are shown in Fig. 4. The excess adsorbed amounts of the mixtures exhibited good reproducibility and lie between the excess adsorbed amounts of pure CH₄ and pure CO₂ determined in our earlier study.¹⁹ In the experimental range, when the fraction of CO₂ was higher the excess adsorbed amount of the mixture became larger. Furthermore, adsorption/desorption measurements for CO₂/CH₄ mixtures were conducted at pressures of up to 70 bar on coal samples at 294 K, 311 K, 333 K and 353 K. The total excess adsorbed amounts at different pressures and temperatures are shown in Fig. 5. With an increase in temperature, the excess adsorbed amount decreased, which is the same as the case for the pure gases. The excess adsorption capacity for the CO₂/CH₄ mixture of dry block anthracite increased followed by a sequential decrease with increasing pressure, as shown in Fig. 4 and 5. The maximum excess adsorbed amount decreased with an increase in temperature. According to the relationship between the excess adsorption capacity n_ex and the absolute adsorption capacity n_a, n_ex = n_a(1 − ρ_g/ρ_a), the reason for this can be explained as follows. When the pressure is low, the density of the gas mixture ρ_g is relatively low and n_ex is nearly the same as n_a. With an increase in pressure, ρ_g and n_a increase simultaneously. Because the number of adsorptive sites on the surface of an adsorbent decreases as a result of adsorption, n_a increases to a maximum gradually. When the pressure rises to some extent, CO₂ would enter the supercritical or liquid state and the density ρ_g increases significantly. The increase in ρ_g becomes larger than the increase in n_a; thus, n_ex will decrease. Therefore, the maximum in the excess adsorbed amount may be caused by the increase in the density of the gas mixture. In addition, the pressure corresponding to the maximum excess adsorbed amount decreased with an increase in the CO₂ fraction.

Fig. 4 Total excess adsorbed amounts of different fractions at 311 K. The solid and empty symbols refer to the first and second sets of data, respectively. ◆◇, pure CO₂; ▲△, 80% CO₂/20% CH₄; ●○, 50% CO₂/50% CH₄; ■□, 20% CO₂/80% CH₄; ▼▿, pure CH₄.

Fig. 5 Total excess adsorbed amounts at different pressures and temperatures (■, 293 K; ●, 311 K; ▲, 333 K; ▼, 353 K).

3.2 Excess adsorbed amount of component gases

During the process of desorption, the gas composition in the adsorption cell after achieving equilibrium was measured using gas chromatography during each desorption step. The excess adsorbed amounts of the component gases were calculated using eqn (11) and (12). Reproducibility tests for the excess adsorbed amounts of CH₄, CO₂, and the gas mixtures at 311 K were conducted and the results are shown in Fig. 6, which shows that the excess adsorbed amounts of CH₄ and CO₂ exhibited good reproducibility. The excess adsorbed amount of CO₂ increased with an increase in the CO₂ fraction in the feed gas. When the CO₂ fraction increased to 80%, the excess adsorbed amount of CO₂ was almost twice as large as that of CH₄.

Fig. 6 Reproducibility tests for the excess adsorbed amounts of CH₄, CO₂, and the gas mixtures at 311 K. The solid and empty symbols refer to the first and second sets of data, respectively. ▲△, total; ●○, CO₂; ■□, CH₄.

The excess adsorbed amounts of CH₄ and CO₂ for the different fractions are shown in Fig. 7. For the 80% CO₂ mixture, the excess adsorbed amount of CO₂ made a major contribution to the total excess adsorbed amount of the gas mixture. As the experimental temperature rose, the excess adsorbed amount of CO₂ decreased, which is the same as the case for pure CO₂. Furthermore, the change in the excess adsorbed amount of CH₄ was relatively small, because CH₄ accounted for a small percentage of the feed gas. However, for the 20% CO₂ mixture, the result was the opposite; CH₄ accounted for the major effect. For the 50% CO₂ mixture, at low pressures (<30 bar) the adsorbed amount of CO₂ was larger than that of CH₄ and relatively good adsorptivity for CO₂ was displayed. However, as the pressure increased the adsorbed amount of CO₂ decreased and the adsorbed amount of CH₄ surpassed that of CO₂ gradually, which indicated better adsorptivity for CH₄ at high pressures. The reason for this may be that CO₂ reached adsorption saturation in competition with CH₄ with an increase in pressure, and lost the advantage in the competition. It may also be attributed to the obvious decrease in the excess adsorption of CO₂ with an increase in pressure when the pressure is greater than 30 bar, which was shown in our previous work.¹⁹

Fig. 7 Excess adsorbed amounts of CH₄ and CO₂ for the different fractions. The solid and empty symbols refer to CH₄ and CO₂, respectively. ■□, 293 K; ●○, 311 K; ▲△, 333 K; ▼▿, 353 K.

The excess adsorbed amounts of CH₄ and CO₂ at different temperatures are shown in Fig. 8. It can be seen that the gas phase composition had a great influence on the progress of desorption of the CO₂/CH₄ mixture. When the fraction of CO₂ in the feed gas increased from 20% to 50%, the excess adsorbed amount of CO₂ increased dramatically, whereas the excess adsorbed amount of CH₄ decreased slightly (6.3%). Furthermore, when the CO₂ fraction increased from 50% to 80%, the excess adsorbed amount of CO₂ also increased substantially, whereas the excess adsorbed amount of CH₄ decreased drastically (42.4%). This means that the fraction of CH₄ was relatively high and a small amount of CH₄ was replaced at the beginning of the enhanced recovery of CH₄ by dosing with CO₂. The injected CO₂ was sorbed onto the inner surfaces of coal, which mainly contributed to the increase in the total adsorbed amount. As more CO₂ is injected and the fraction of CH₄ is lower, increasing amounts of CH₄ will be replaced because of the reduction in the partial pressure of CH₄ and the highly selective sorption of CO₂ over CH₄. Therefore, the injection of more CO₂ is needed to promote the operation of ECBM.

Fig. 8 Excess adsorbed amounts of CH₄ and CO₂ at different temperatures. The solid and empty symbols refer to CH₄ and CO₂, respectively. ■□, 80% CO₂/20% CH₄; ●○, 50% CO₂/50% CH₄; ▲△, 20% CO₂/80% CH₄.

4. Modeling

The Ono–Kondo (OK) lattice thermodynamic model was employed to model the adsorption isotherms of gases on coal because of its high accuracy and wide pressure range in engineering calculations.

In this study, the correction for compressibility factors of a non-ideal gas used NIST REFPROP included in the HPVA II software, in which the equation parameters for mixtures composed of natural gas fluids are obtained from the 2008 GERG model.²⁰ Therefore, the bulk phase density of the gas mixture can be calculated via PV = zRT, which is one of the important variables in the Ono–Kondo (OK) lattice model. Sudibandriyo et al.^21,22 evaluated the Ono–Kondo (OK) lattice model for correlating high-pressure supercritical adsorption isotherms in ECBM recovery and CO₂ sequestration. Moreover, they also extended the OK model to the adsorption of gas mixtures on activated carbons and coals. The parameters of the OK model obtained from the adsorption of pure gases were used to predict the adsorption of mixtures. The equality of the chemical potential in the adsorbed and bulk phases for each component leads to the following equilibrium equations for the adsorption of binary gas mixtures:

andwhere x_i is the mole fraction of component i in the adsorbed phase, ε_ij is the fluid interaction energy parameter in the OK model between molecules i and j, ε_is/kT is the fluid–solid interaction energy parameter in the OK model, k is Boltzmann's constant, and z₀ and z₁ are the lattice coordination number and parallel coordination number, respectively. A geometric combination rule was used to calculate the interaction energy between molecules A and B:where the binary interaction parameter for the fluid–fluid interaction energy between dissimilar molecules (C_AB) is obtained by regression fitting. The fractional coverage in the bulk phase (x_i,b) was obtained from the following equation:where ρ_b is the bulk density and the maximum density (ρ_mc) was estimated using the following ideal mixing rule:

For convenience, Sudibandriyo et al.²³ defined the Gibbs adsorption (θ_i) of a fractional component as:

θ_i = n_exi/n_ex (18)

where n_exi is the excess adsorption of component i and n_ex is the total excess adsorption. The absolute component adsorption can be calculated as follows:

x^Abs_B = 1 − x^Abs_A (20)

The Gibbs excess adsorption for each component was calculated using the following expression:

n_exi = 2βC^pure_i(x_i − x_i,b) (21)

where C^pure_i is the maximum adsorption capacity for component i in the pure state and β is calculated as follows:

The parameter E_AB is obtained by regression fitting.

The Ono–Kondo (OK) lattice thermodynamic model can be used to simulate the total excess adsorbed amount and the excess adsorbed amount of an individual component. The model parameters and error analysis are given in Table 2, expressed in terms of the average relative error (ARE). The OK model could predict the total adsorption data and the ARE was 6.4%. However, the predictions for the adsorption of individual components were less accurate and the deviations were larger for the less adsorbed component in the mixture, which is similar to the study findings by Sudibandriyo et al.²¹ The ARE values for the individual components were large, in particular for the gas component with a smaller fraction. The reason for this may be that errors in the measurement of the gas composition and model parameters from sorption data for pure gases would affect the precision of the model for the individual components. The competitive adsorption of gas compositions was not taken into account in the model, which also led to the relatively large deviations.

Table 2 Parameters and error analysis of the Ono–Kondo lattice model for adsorption of CO₂/CH₄^a

	T (K)	NDTS	CAB	EAB	ARE (total)	ARE (CH4)	ARE (CO2)
a NDTS: number of data points estimated; , average relative error.
20% CO2/80% CH4	293.82	8	1.2407	1.4053	3.5%	11.4%	33.7%
	311.08	8	−0.3921	1.1223	6.3%	18.5%	37.9%
	333.21	8	−0.5308	1.0771	7.0%	28.0%	34.0%
	353.23	8	−1.3467	0.9751	6.8%	19.3%	44.0%
50% CO2/50% CH4	293.68	8	2.7435	1.7483	9.2%	30.3%	68.7%
	311.11	8	1.2959	1.3871	8.6%	46.6%	32.3%
	333.17	8	0.6611	1.2932	2.7%	7.1%	13.0%
	353.07	8	0.5601	1.5128	3.4%	11.6%	24.2%
80% CO2/20% CH4	293.82	8	0.6297	1.0618	8.1%	92.2%	27.0%
	311.05	8	−0.3614	1.173	7.0%	23.5%	10.6%
	333.10	8	0.3102	1.3166	8.4%	47.7%	41.4%
	353.18	8	1.007	1.3277	5.7%	28.9%	28.7%

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5. Conclusions

The adsorption/desorption isotherms of CO₂/CH₄ mixtures with three different volume fractions were investigated at 294 K, 311 K, 333 K, and 353 K with pressures of up to 70 bar on anthracite from China using an HPVA II system. The excess adsorbed amounts of the CO₂/CH₄ mixtures and individual components were modelled using the Ono–Kondo (OK) lattice thermodynamic model. The following conclusions can be drawn from this study:

(1) For the mixtures, the total excess adsorbed amount decreased with an increase in the temperature and increased with an increase in the CO₂ concentration in the feed gas. The excess adsorbed amounts of the mixtures lie between the excess adsorbed amounts of pure CH₄ and pure CO₂. Besides, for the 50% CO₂ mixture, relatively good adsorptivity for CO₂ was displayed at low pressures (<30 bar), whereas better adsorptivity for CH₄ was displayed at high pressures.

(2) The gas phase composition had a great influence on the progress of desorption of the CO₂/CH₄ mixture. It can be deduced that the fraction of CH₄ was relatively high and a small amount of CH₄ was replaced at the beginning of the enhanced recovery of CH₄ by dosing with CO₂. The injected CO₂ was sorbed onto the inner surfaces of coal, which mainly contributed to the increase in the total adsorbed amount. As more CO₂ is injected and the fraction of CH₄ is lower, increasing amounts of CH₄ will be replaced because of the reduction in the partial pressure of CH₄ and the highly selective sorption of CO₂ over CH₄. The injection of more CO₂ is needed to promote the operation of ECBM.

(3) The Ono–Kondo (OK) lattice thermodynamic model yielded good agreement with the total excess adsorbed amount of the CO₂/CH₄ mixtures with an ARE of 6.4%. However, the predictions for the adsorption of individual components were less accurate and the deviations were larger for the less adsorbed component in the mixture.

Nomenclature

nD, n′D	Moles dosed into the sample cell at ambient and analysis temperature, mols
TA, PA	Temperature and pressure of helium in the manifold before dosing, K, bar
TB, PB	Temperature and pressure of helium in the manifold after dosing, K, bar
T1, P1	Temperature and pressure of gas mixture before dosing in the manifold, K, bar
T2, P2	Temperature and pressure of gas mixture after dosing in the manifold, K, bar
zA, zB	Helium gas compressibility factors at PA and TA and at PB and TB, respectively
z1, z2	Gas mixture compressibility factors at P1 and T1 and at P2 and T2, respectively
R	Gas constant, cm^3 bar K^−1 mol^−1
VAFS	Volume of free space at ambient temperature, cm^3
VxU	Upper stem volume (approximately 3.5 cm^3)
VxL	Lower stem volume, cm^3
VS	Sample cell volume, cm^3
Ps0	Pressure of sample before dosing, bar
Ts0	Temperature of sample before dosing, K
Ts1	Temperature of sample after dosing at ambient temperature, K
Ps1	Pressure of sample after dosing at ambient temperature, bar
Ts2	Temperature of sample after dosing at analysis temperature, K
Ps2	Pressure of sample after dosing at analysis temperature, bar
zxU0	Gas compressibility factor at Ps0 and TA
zs0	Gas compressibility factor at Ps0 and Ts0
zxL0	Gas compressibility factor at Ps0 and TAM
zxU1	Gas compressibility factor at Ps1 and TB
zs1	Gas compressibility factor at Ps1 and Ts1
zxU2	Gas compressibility factor at Ps2 and TB
zs2	Gas compressibility factor at Ps2 and Ts2
zxL2	Gas compressibility factor at Ps2 and TAM
TAM	Ambient temperature (298 K)
nads	Moles of gas adsorbed by the sample, mol
ndosed	Moles of gas dosed from the manifold, mol
nNads	Moles of gas not adsorbed by the sample, mol
PS	Pressure of the sample tube, bar
TS	Temperature of sample cell, K
TxU	Temperature of upper stem, K
zS	Gas compressibility factor at Ps and Ts
zxL	Gas compressibility factor at Ps and TxL
zxU	Gas compressibility factor at Ps and TxU
Δnads	Moles of gas adsorbed by the sample at one pressure step, mol
Δndosed	Moles of gas dosed from the manifold at one pressure step, mol
ΔnNads	Moles of gas not adsorbed by the sample at one pressure step, mol
Δnadsn	Moles of gas adsorbed by the sample at the n^th pressure step, mol
Δndosedn	Moles of gas dosed from the manifold at the n^th pressure step, mol
ΔnNadsn	Moles of gas not adsorbed by the sample at the n^th pressure step, mol
nAn	Moles of gas in the manifold before dosing at the n^th pressure step, mol
nBn	Moles of gas in the manifold after dosing at the n^th pressure step, mol
ΔnNadsn−1	Moles of gas not adsorbed by the sample at the n − 1^st pressure step, mol
ΔnadsnCH4	Moles of CH4 adsorbed by the sample at the n^th pressure step, mol
ΔnadsnCO2	Moles of CO2 adsorbed by the sample at the n^th pressure step, mol
yCH4n	Fraction of CH4 in the adsorption cell after achieving equilibrium at the n^th pressure step, mol
yCH4n−1	Fraction of CH4 in the adsorption cell after achieving equilibrium at the n − 1^st pressure step, mol
C^purei	Maximum adsorption capacity for component i in its pure state, mol
CAB	Binary interaction parameter for fluid–fluid interaction energy between dissimilar molecules
EAB	Binary interaction parameter for the modified Gibbs adsorption equation
nexi	Excess adsorption of component i, mol
x^Absi	Absolute adsorbed mole fraction of component i, mol
xi	Mole fraction of component i in the adsorbed phase
xi,b	Fraction of sites occupied by molecules of i in the bulk layer of the lattice model
yi	Mole fraction of component i in the gas phase
θi	Gibbs adsorption of fractional component
ρmc	Maximum density, g cm^−3
ρb	Gas-phase density, g cm^−3
ρmc,i	Maximum adsorbed-phase density for component i, g cm^−3
εij	Fluid interaction energy parameter in the OK model between molecules i and j
εis/kT	Fluid–solid interaction energy parameter in the OK model
k	Boltzmann's constant
T	Temperature, K
z0	Lattice coordination number (8)
z1	Parallel coordination number representing the number of primary nearest-neighboring cells in a parallel direction (6)

Acknowledgements

This study was supported by the National Natural Science Foundation of China (51576031, 51436003), the National Key Research and Development Program of China (2016YFB0600804) and the Fundamental Research Funds for the Central Universities (DUT15LAB22).

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