The binary gas sorption in the bituminous coal of the Huaibei Coalfield in China

Abstract

Knowledge of the gas sorption characteristics of a coal not only helps to explain the mechanism of enhanced coalbed methane recovery but also provides an important basis for simultaneous coal and gas extraction. In consequence, the pure and binary gas excess sorption capacity of methane, carbon dioxide, and nitrogen of bituminous coal samples derived from the Xutuan Coal Mine in Huaibei coalfield, in Anhui Province in China, was measured using the volumetric method. The fitting analysis of the pure gas Langmuir adsorption model was carried out. The binary gas excess sorption measurement showed that the final sorption capacity of bituminous samples was the same no matter what the gas adsorption order of competitive adsorption and displacement adsorption. Hence, coal gas adsorption is physical adsorption, i.e. the different adsorption and desorption process of gas molecules does not affect the final adsorption amount of coal to each component of gas. Using the fitting parameters obtained by the Langmuir equation, the extended Langmuir equation was used to predict the adsorption capacity for each component of the binary gas. The comparison between predicted adsorption capacity and measured adsorption capacity showed that the extended Langmuir equation can better describe the trend of the adsorption isotherm curves of a binary gas under different pressures. The separation coefficient and displacement coefficient were defined from Langmuir adsorption theory. The separation coefficient involves the proportion of each component in the free phase and the proportion of each component in the adsorption phase. The displacement coefficient involves the displacement ability of gas molecules at adsorption sites by free gas molecules.

Keywords

Bituminous coal gas sorption Langmuir equation binary gas extended Langmuir equation

Introduction

Coal is a highly porous material, and coalbed methane (CBM) is mainly adsorbed in the coal structure, hence the coal acts as both the source and as the reservoir. Natural porous media usually have an extremely complex pore structure with pore sizes that may extend over several orders of magnitude (Cai et al., 2012). As coal has many micropores, cleats, and fissures, the specific surface area of coal is generally 6–15 m²/g (Chen et al., 2013; Qi et al., 2013). As a consequence, coal exhibits a strong adsorption capacity for several gases (Yang et al., 2015) and adsorption gas accounts for more than 90% of the gas stored within the coal (Mastalerz et al., 2004). The goal of gas drainage is to release as much of the adsorbed gas as possible. In the primary coal seam, the gas is in a dynamic equilibrium state of adsorption, desorption, and migration. Reduction of the gas pressure in the coal seam leads to a reduction of its coal gas adsorption capacity.

It has long been recognized that the complex flow processes in porous media depend on the complexity of the microstructure of porous media (Cai et al., 2010). The adsorbed gas detaches from the micropore surfaces and is transmitted to the free gas phase. The free gas is transported first in the micropores of the coal matrix and then into the fissures between the matrix and then through the cleats finally into the drilled holes. Coal gas sorption studies involve an investigation of the gas storage and transport mechanism. Coal gas adsorption capacity is a key characteristic of CBM reserves. Enhanced coalbed methane (ECBM) recovery can be accomplished either by inert gas stripping or by displacement desorption methods (Ruthven, 1984; Yang, 2013) using nitrogen (N₂), carbon dioxide (CO₂), flue gas, compressor gas, and other types of industrial off-gas, which are used as a recovery agent (White et al., 2005). Hence, the process of ECBM recovery involves the adsorption and desorption characteristics of mixed gases. The effectiveness of the operation needs to be confirmed by multicomponent adsorption measurements, as ECBM depends on the relative affinity of the mixture of CO₂ and CH₄ in coal (Kurniawan et al., 2006; Pini et al., 2009). The binary gas sorption study undertaken during the present study provided a research basis for the study of ECBM migration behavior.

According to the trend of increased sorption capacity with the increasing pressure, the solid gas isotherm sorption curves generally are divided into six categories (Brunauer et al., 1940; Sing, 1998). Coal gas adsorption is physical adsorption, and its isothermal sorption curves are mainly Category I and Category II (Karacan and Okandan, 2000; Yang and Saunders, 1985). With regard to the adsorption model for gas in solids, Langmuir (1918) first proposed the single-layer molecular adsorption theory for adsorption sites of gas molecules and solid surfaces and established Langmuir adsorption isotherm equation. The simple form of the Langmuir equation and the clear meaning of the parameters allow it to be widely used in the assessment of CBM reserves. Some studies have shown that the Langmuir equation can be used with satisfactory precision to describe the coal gas sorption isotherm (George and Barakat, 2001; Lin et al., 2016; Wang et al., 2016; Weishauptová and Medek, 1998; Zhang et al., 2014).

When considering the multicomponent gas adsorption of a coal reservoir, the mixed gas adsorption capacity measurement of wet coal undertaken by Fitzgerald et al. (2005) has shown that moisture in the coal sample could cause large errors in the adsorption capacity of each component as predicted by the extended Langmuir (E-L) isotherm equation. Busch et al. (2006a) also found that coal moisture had a great impact on the adsorption capacity of each gas component. The gas adsorption study by Khosrokhavar et al. (2014) on organic carboniferous mudstone showed that the amount of excess carbon dioxide sorption was approximately seven times higher than the methane sorption capacity. Many scholars have found that the coal carbon dioxide sorption capacity was larger than that of methane and nitrogen (Krooss et al., 2002; Ottiger et al., 2008; Pan and Connell, 2007; Zhang et al., 2017, 2016). Clarkson and Bustin (2000) compared the CO₂–CH₄ binary gas sorption capacity on coals with different moisture contents and it was found that moisture had a larger impact on the carbon dioxide sorption capacity than that of methane. The adsorption experiments for CO₂ and CH₄ gas mixtures on coal showed that both CO₂ and CH₄ adsorption capacities performed with gas mixtures were lower than were those determined with pure gases. Thus, these results confirmed that both gases compete to be adsorbed by the coal. The comparative study of flue gas and pure carbon dioxide sorption properties of coal indicated that the flue gas adsorption capacity was much less than that of the carbon dioxide (Mazumder et al., 2006).

The bituminous coal of Xutuan Coal Mine in Huaibei coalfield in China was taken as research object for the present study. On the basis of previous work, a series of pure and binary gas adsorption tests were carried out using a bespoke Gas Adsorption and Strain Testing Apparatus (GASTA). All experiments were performed at 303 K on dry pulverized coal samples. The fitting analysis for a pure gas Langmuir adsorption model was carried out and the fitting parameters were obtained. Then, the binary gas competitive adsorption and displacement adsorption tests were carried out. Finally, based on the fitting parameters of the Langmuir equation for the pure gas, each component gas adsorption capacity was predicted by the E-L equation.

Measurement method

Research background

The Xutuan Coal Mine is located in Mengcheng County, southwest of Suzhou City, in the Anhui province of China. It is in Huaibei coalfield belonging to the Permian coal deposit. The relative gas emission of the mine is reported to be 22 m³/t, and the mine belongs to the high gas coal mine rank. The main coal seams of the mine are coal seam 32 and coal seam 82. The coal sample SA3 was derived from coal seam 32, and the coal sample SA8 was derived from coal seam 82. Samples with a particle size range of 0.25–0.18 mm were prepared in accordance with GB/T 474. Finally, the coal samples were dried completely under anaerobic conditions. The coal petrology parameters of the main coal seams are listed in Tables 1 and 2.

Table 1.

Maceral statistics of sampling coal seam.

Coal samples	Organic component (%)				R_max (%)
Coal samples	Vitrinite	Semivitrinite	Inertinite	Exinite	R_max (%)
SA3	66.93	9.68	14.53	8.86	0.82
SA8	72.96	9.79	12.06	5.19	0.95

Table 2.

The proximate analyses of sampling coal seam.

Coal samples	Mad (%)	Aad (%)	S.d (%)	P.d (%)	Vdaf (%)
SA3	1.51	18.85	0.68	0.0089	35.39
SA8	1.41	17.88	0.53	0.0112	31.93

Note: “Mad” is the moisture content; “Aad” is the ash content, air-drying basis; “S.d” is the sulfur content; “P.d” is the phosphorus content; “Vdaf” is the volatile matter, dry ash-free basis.

Experiment equipment

The binary gas adsorption measurement was finished by the GASTA. A volumetric method is used to calculate the adsorptive capacity of coal samples. Inert gas is used to calibrate the free space volume of the sample chamber. The measured pressure in the chambers is used to calculate the adsorption capacity through the real gas state equation. All experiments were performed at 303 K (30°C) on dry pulverized coal samples.

The pressure range of the reference chamber and the sample chamber was 0–20 MPa. The internal diameter of the chambers was 60 mm and the inner height was 80 mm. The reference chamber, the sample chamber, and their auxiliary pressure transducers are core components of the test apparatus. The components of the apparatus are shown in Figure 1.

Figure 1.

Schematic diagram of the GASTA.

Measurement and calculation method of adsorption capacity

In this investigation, a volumetric method was used to calculate the adsorption capacity. The pressure of the reference chamber and the sample chamber was measured by the pressure transducers. The adsorption capacity was calculated using the real gas state equation. Hence, the adsorption capacity refers to the excess (or Gibbs) adsorption capacity.

The ideal gas state equation is a gas state equation that describes the relationship between the pressure, volume, mass, and temperature. The real gas state is biased from the ideal gas state under different conditions, thus different real gas state equations are established. In this study, the gas state Soave–Redlich–Kwong (SRK) equation was used to calculate the amount of the gas in the fixed volume under a certain pressure. The SRK equation is shown as follows

p = \frac{R T}{(V_{m} - b)} - \frac{α a}{V_{m} (V_{m} + b)}

(1)

where

α = {[1 + (0.48508 + 1.55171 ω - 0.15613 ω^{2}) (1 - \sqrt{T / T_{c}})]}^{2}

a = \frac{0.42747 R^{2} T_{c^{2}}}{P_{c}}

b = \frac{0.08664 R T_{c}}{P_{c}}

and

p

is the gas pressure (MPa),

R

is the gas constant (8.314 J/mol K),

T

is the thermodynamic temperature (K),

V_{m}

is the molar volume (ml/mol),

T_{c}

is the gas critical temperature (K),

P_{c}

is the gas critical pressure (MPa), and

ω

is the gas acentric factor related to the polarity of a gas molecule.

The parameters of $T_{c}$ , $P_{c}$ , $ω$ are only related to the gas molecules. The gas pressure $p$ and the thermodynamic temperature $T$ are measured by the attached sensor. The molar volume $V_{m}$ is calculated by single variable solution of Excel by means of the SRK equation.

For the sorption experiments of pure gas, the inert gas helium, which is not absorbed by coal, is injected into the reference chamber. The injected helium amount is calculated from the calibration volume of the reference chamber and measured pressure through the SRK equation. The valve between the reference chamber and sample chamber is opened after the gas pressure of the reference chamber and the sample chamber reaches equilibrium. The free volume of the sample chamber can be calculated from the injected helium amount and the equilibrium pressure. The same steps then were carried out for methane, carbon dioxide, and nitrogen and the adsorption capacity calculated using the SRK equation, with the fixed sample chamber free volume and measured pressures.

Methodology for binary gas isothermal adsorption measurements

For the binary gas adsorption experiment, the binary gas with a volume ratio of 1:1 first was prepared and introduced into the reference chamber. The next steps were the same with those for the pure gas. In order to obtain the competitive adsorption capacity of each gas into the coal samples, the composition of the exhaust gas after each competitive adsorption experiment was measured. This study used a gas sample bag to collect the exhaust gas and a gas composition analyzer was then used to measure the proportion of CO₂ and CH₄ in the exhaust gas.

The difference between the total amount of injected gas and the amount of free space gas was calculated using the actual gas SRK state equation. The SRK equation of state is used to calculate the molar volume of a pure gas at a certain pressure and temperature. When the gas mixture is calculated using the SRK equation, the equivalent transformation of Figure 2 can be used. A mixed gas with a fixed volume and pressure P is equivalent to having a nonresistant sliding partition around the inside of the container, which to the left side of the partition is CO₂, to the right is CH₄, and the pressure is P. The molar volume of CO₂ and CH₄ at this pressure can be calculated using the SRK equation.

Figure 2.

Calculation of molar volume of mixed gas.

This investigation used the first adsorption equilibrium pressure $P 3$ as an example to illustrate the calculation process for adsorption capacity. The quality of the coal sample was $m$ (g), the reference volume of the reference cylinder was $V r$ (cm³), the free space volume of the sample cylinder was $V s$ (cm³), and the proportion of CO₂ in the tail gas after adsorption equilibrium was $n$ . The pressure of the vacuum reference cylinder after the first injection of CO₂ was $P_{1}$ , the pressure after injection of constant gradient pressurized methane was $P_{2}$ , the pressure after the adsorption equilibrium was $P_{3}$ , and the pressure in the reference cylinder after exhaust sampling was $P_{4}$ .

According to the SRK equation, the molar volume of carbon dioxide ${V m}_{1} ({CO}_{2})$ , ${V m}_{2} ({CO}_{2})$ , ${V m}_{3} ({CO}_{2})$ , ${V m}_{4} ({CO}_{2})$ and the molar volume of methane ${V m}_{1} ({CH}_{4})$ , ${V m}_{2} ({CH}_{4})$ , ${V m}_{3} ({CH}_{4})$ , ${V m}_{4} ({CH}_{4})$ at pressures $P_{1}$ , $P_{2}$ , $P_{3}$ , and $P_{4}$ were calculated using the Excel univariate method. The cylinder system CO₂ injection amount was

V ({CO}_{2}) = V m (STP) \cdot \frac{V r}{{V m}_{1} ({CO}_{2})}

(2)

From the equivalent transformation of Figure 2, the amount of CH₄ injected into the cylinder system can be calculated as

V ({CH}_{4}) = V_{m} (STP) \cdot \frac{V_{r} - \frac{V r}{{V m}_{1} ({CO}_{2})} \cdot {V m}_{2} ({CO}_{2})}{{V m}_{2} ({CH}_{4})}

(3)

and the proportion of gas components can be obtained by the following two equations as

{\begin{array}{l} \frac{V_{f} ({CO}_{2})}{V_{f} ({CO}_{2}) + V_{f} ({CH}_{4})} = n \\ \frac{V_{f} ({CO}_{2})}{V_{m} (STP)} \cdot {V m}_{3} ({CO}_{2}) + \frac{V f ({CH}_{4})}{V m (STP)} \cdot {V m}_{3} ({CH}_{4}) = V r + V s \end{array}

(4)

The amount of free CO₂ in the cylinder system was

V_{f} ({CO}_{2}) = \frac{n (V r + V s) \cdot V m (STP)}{n {V m}_{3} ({CO}_{2}) + {V m}_{3} {(CH}_{4}) - n {V m}_{3} ({CH}_{4})}

(5)

The amount of free CH₄ in the cylinder system was

V_{f} ({CH}_{4}) = \frac{(1 - n) (V r + V s) \cdot V m (STP)}{n {V m}_{3} ({CO}_{2}) + {V m}_{3} ({CH}_{4}) - n {V m}_{3} ({CH}_{4})}

(6)

And the amount of carbon dioxide and methane adsorbed per unit mass of coal was

{\begin{matrix} v_{a} ({CO}_{2}) = \frac{V ({CO}_{2}) - V_{f} ({CO}_{2})}{m} \\ v_{a} ({CH}_{4}) = \frac{V ({CH}_{4}) - V_{f} ({CH}_{4})}{m} \end{matrix}

(7)

In Formulae (2) to (7), the molar volume of the gas under standard conditions was 22.4 × 10³cm³/mol, and the adsorption amount of CO₂ and CH₄ per unit mass of coal sample was $v_{a} ({CO}_{2})$ , $v_{a} ({CH}_{4})$ cm³/g. Thus, the adsorption amount of each sample of coal in the competitive adsorption experiment was obtained.

The method for calculating the adsorptive capacity of the displacement adsorption gas was approximately the same as that for competitive adsorption and therefore is not repeated here. As the displacement adsorption procedure first performs the adsorption test for pure gas, and then the adsorption test for the mixed gas is performed, the cylinder system must be evacuated after the adsorption equilibrium of the mixed gas.

The fitting analysis of the pure gas Langmuir adsorption model

Based on the hypothesis of surface adsorption sites, Langmuir (1918) derived a most popular solid/gas two-phase adsorption model. The Langmuir adsorption isotherm equation is usually expressed as the following formula

\frac{V}{V_{L}} = \frac{P}{P + P_{L}}

(8)

where

V

(ml) is the adsorbed volume at equilibrium pressure

P

(MPa);

V_{L}

is the maximum monolayer capacity, also known as the Langmuir volume (ml); and

P_{L}

is the Langmuir pressure (MPa), which refers to the pressure when the sorbed volume is half of the Langmuir volume

V_{L} / 2

The pure gas experimental data for coal samples SA3 and SA8 were fitted by the Langmuir equation.

The fitting parameters of coal sample SA3 by Langmuir equation are shown in Table 3.

Table 3.

The Langmuir fitting parameters of coal sample SA3.

Test path	$V_{L}$ (cm³/g)	$P_{L}$ (MPa)	Correlation coefficient R²
CO₂ adsorption	35.72	4.36	0.989
CH₄ adsorption	24.39	10.22	0.985
N₂ adsorption	7.41	7.12	0.996

The fitting parameters of coal sample SA8 by Langmuir equation are shown in Table 4.

Table 4.

The Langmuir fitting parameters of coal sample SA8.

Test path	$V_{L}$ (cm³/g)	$P_{L}$ (MPa)	Correlation coefficient R²
CO₂ adsorption	35.72	2.68	0.994
CH₄ adsorption	30.44	9.82	0.992
N₂ adsorption	10.09	5.48	0.997

From the comparison between the experimental data above, it was found that the Langmuir equation can describe properly the isotherm sorption of CO₂, CH₄, and N₂. From the goodness of fit for the data in Tables 3 and 4, the correlation coefficient of the Langmuir equation to the three kinds of gases was greater than 0.985, which meant that the sorption capacity prediction of the Langmuir equation achieved satisfactory results and the Langmuir equation gives significant guidance as to the potential gas reserves in the coal sample(s).

The Langmuir adsorption model assumes that the adsorption sites on the surface of the adsorbent are one to one corresponding to the adsorbate molecules. When the adsorption sites of all adsorbents are occupied by gas molecules, the maximum adsorption capacity of the adsorbent is reached, i.e. the Langmuir volume. According to the fitting data in Tables 3 and 4, coal has different maximum adsorption capacities for different gases. It was determined that the order of V_L of the three gases was CO₂ > CH₄ > N₂.

Adsorption analysis of binary gas

Coal matrix molecules show different adsorption affinity with different gas molecules, which means that coal will show different adsorption characteristics for different gases. The competitive adsorption and displacement adsorption of a binary gas are the main research content in this instance.

Competitive adsorption refers to the process by which the components of the binary gas are adsorbed at the same time. Displacement adsorption refers to the process whereby one gas first is adsorbed and then the other gas is injected to be absorbed by the coal sample. Although the essence of both experiments is binary gas adsorption, the former is an “on the same starting line” competition, and the latter is a “catch up from behind” scenario. In the present study, competitive adsorption and displacement adsorption tests with a 1:1 volume ratio binary gas were carried out on coal sample SA3.

Binary gas adsorption capacity

Comparative analysis of displacement adsorption and competitive adsorption

When the binary gas adsorption determinations had been completed, the binary gas adsorption isotherm curves were plotted (Figure 3).

Figure 3.

The adsorption isotherms of binary CO₂–CH₄ gas.

As shown in Figure 3, the adsorption isotherm curves of competitive adsorption and displacement adsorption were basically overlapped, i.e. the binary gas adsorption capacity on the coal sample was the same. Gas adsorption for coal is a physical reaction of pore surfaces to the gas molecules. The sorption process will not change the pore surface characteristics of the coal. On the other hand, the equilibrium state of the coal gas adsorption is a dynamic equilibrium where the adsorption rate of gas molecules is equal to the desorption rate. In the process of displacement adsorption, methane was first injected into the closed chamber to achieve adsorption equilibrium. After injection of carbon dioxide into the chamber system, the adsorption equilibrium state of the methane gas molecules was broken. At this time, when the methane molecules were desorbed from the microporous surface of the coal, the carbon dioxide molecules, which have more affinity to porous surfaces, will occupy the adsorption sites. Eventually, the displacement adsorption condition will reach the same equilibrium state of competitive adsorption. In fact, the adsorption capacity of the coal sample to each component of the binary gas is related only to its partial pressure. Therefore, the competitive adsorption and displacement adsorption characteristics are only different for the sorption process of the gas molecules and do not affect the final adsorption capacity of coal to the mixture. Other scholars (Yang et al., 2015) have corroborated this conclusion.

Discussion contrasting pure and binary gas adsorption capacity

In order to analyze the contrasting characteristics of binary gas adsorption capacity, the pure gas and binary gas adsorption capacity are plotted in Figure 4.

Figure 4.

Comparison of the characteristics of pure gas and binary gas adsorption. (a) Competitive adsorption and pure gas adsorption and (b) displacement adsorption and pure gas adsorption.

As shown in Figure 4, the shapes of the isothermal adsorption curves for pure gas and binary gas were basically the same, and both of them belong to the type I adsorption curve. Under the same adsorption equilibrium pressure, the total adsorption capacity of the binary gas was higher than that of pure methane and lower than that of pure carbon dioxide. For pure gas adsorption, the ratio of the adsorption capacity of the coal to the two gases was CO₂:CH₄ = 2.6:1. For the volume ratio 1:1 competitive adsorption, the ratio of the adsorption capacity of the coal to the two gases was CO₂:CH₄ = 3.3:1. For the volume ratio 1:1 displacement adsorption, the ratio of adsorption capacity of coal to two gases was CO₂:CH₄ = 3.31:1. The CO₂ and CH₄ adsorption capacity ratio difference of pure gas and binary gas adsorption indicates that carbon dioxide has a stronger adsorption advantage than methane in the binary gas. The adsorption and desorption rates of a gas molecule are involved only in the adsorption equilibrium of the single component gas. For binary gas adsorption, when the adsorbed gas molecules are separated from the adsorption site to form an empty adsorption site, the two different gas molecules compete for the empty adsorption sites. As carbon dioxide shows a higher adsorption affinity for coal, carbon dioxide has an advantage in competitive adsorption and when the binary gas eventually reaches the equilibrium state, carbon dioxide molecules occupy a higher proportion of the adsorption sites.

E-L equation and its prediction analysis

The Langmuir equation, which incorporates also the E-L equation, is the most widely used adsorption prediction model in the multicomponent adsorption field of CBM. Based on the fitting parameters for the pure gas adsorption isotherm curves, combined with the proportion of the binary gas in the state of adsorption equilibrium, the predicted adsorption capacity of coal samples to each component of the binary gas can be obtained from the E-L equation. In this study, the predicted binary gas adsorption capacity was obtained using the E-L equation and there was little difference between the predicted and the measured adsorption capacity.

E-L equation, separation coefficient, and displacement coefficient

Markham and Benton (1931) proposed a multicomponent adsorption model, i.e. the E-L equation based on the Langmuir adsorption theory of single component gas. The E-L equation preserves all the assumptions of the Langmuir adsorption theory for single component gases. It is considered that the adsorption of gas molecules on the surface of an adsorbent on mixed gases is competitive adsorption.

Combined with the fitted parameters of the Langmuir volume and the Langmuir pressure for the pure gas adsorption isotherm, the adsorption capacity of each component at the same temperature can be calculated using equation (7), and the total adsorption capacity is equal to the sum of the adsorption capacity of each component

V_{i} = \frac{\frac{V_{L i} P_{i}}{P_{L i}}}{1 + \sum_{1}^{n} \frac{P_{i}}{P_{L i}}}

(9)

where

V_{i}

is the adsorption capacity of component i,

V_{L i}

is the Langmuir volume of component i,

P_{L i}

is the Langmuir pressure of component i, and

P_{i}

is the partial pressure of component i at the adsorption equilibrium state.

The partial pressure of the mixed gas can be determined from the adsorption equilibrium pressure and the component volume fraction

{\begin{array}{l} P_{i} = P \times y_{i} \\ \sum_{1}^{n} y_{i} = 1 \end{array}

(10)

where

P

is the equilibrium pressure and

y_{i}

is the volume fraction of component i.

The separation coefficient characterizes the relative adsorption ability of the two components in the mixture

a_{i j} = \frac{x_{i} / x_{j}}{y_{i} / y_{j}}

(11)

where

x_{i}

is component i volume fraction of adsorbed phase and

y_{i}

is the free phase volume fraction of component i.

The separation coefficient characterizes the relative adsorption ability of the two components of the binary gas. The separation coefficient is close to 1, indicating that the adsorption ability of the two components is similar. If the separation coefficient is greater than 1, it indicates that the adsorption ability of the component i to the adsorption site is stronger than that of the component j. If the reverse relationship holds good, then the adsorption ability of component j is stronger than that of component i.

From the E-L equation, the expression of the separation coefficient can be transformed into the following equation

a_{i j} = \frac{x_{i} / x_{j}}{y_{i} / y_{j}} = \frac{V_{i} / V_{j}}{y_{i} / y_{j}} = \frac{V_{L i} / P_{L i}}{V_{L j} / P_{L j}}

(12)

As shown in equation (10), the separation coefficient that is derived from the E-L equation is a constant. The separation coefficient characterizes the proportion of the adsorption phase and the free phase in the different components, but it does not show the degree of competition between the two components at the adsorption sites. In order to characterize the degree of competition of the two components at the adsorption sites, that is the capability of one gas’s disturbance to the other gas in the binary gas sorption process, the displacement coefficient may be defined based on the single component adsorption

λ_{i j} = \frac{V_{i} / V_{j}}{V_{P y_{i}}^{i} / V_{P y_{j}}^{j}}

(13)

where

V_{i}

and

V_{j}

are adsorption capacity of components

i

and

j

at the equilibrium pressure of

P

and

V_{P y_{i}}^{i}

is the adsorption capacity of pure component

i

pure gas at the equilibrium pressure of

P y_{i}

By comparing the equilibrium pressure with the behavior of a single component equal to the adsorption amount under the component pressure, the displacement coefficient defines the replacement capacity of the component in the mixture. When the displacement coefficient is greater than 1, compared with the pure gas adsorption, the component $i$ can replace the component $j$ from the adsorbent in binary gas adsorption.

With the Langmuir equation and E-L equation, the expression of the displacement coefficient can be transformed into the following equation

λ_{i j} = \frac{P y_{i} / P_{L i} + 1}{P y_{j} / P_{L j} + 1}

(14)

As shown in equation (12), the displacement coefficient is related to the Langmuir pressure and the partial pressure of the component and is unrelated to the Langmuir volume.

Prediction and analysis of binary gas adsorption by E-L equation

The E-L prediction of the adsorption capacity and the measured binary gas adsorption capacity are presented in Figure 5.

Figure 5.

The measured values of binary gas adsorption and the predicted values of the E-L equation. (a) Competitive adsorption and E-L prediction and (b) displacement adsorption and E-L prediction.

The relative deviation of predicted adsorption capacity and measured adsorption capacity is shown in Tables 5 and 6.

Table 5.

The predicted and measured values for competitive adsorption of CO₂–CH₄.

Equilibrium pressure (MPa)	CO₂ proportion (%)	CH₄ proportion (%)	CO₂ predicted (ml/g)	CO₂ measured (ml/g)	CO₂ relative deviation (%)	CH₄ predicted (ml/g)	CH₄ measured (ml/g)	CH₄ relative deviation (%)
0.663	45	51	2.2190	2.0956	5.9	0.7326	0.8121	−9.8
1.323	47	51	4.2149	4.0112	5.1	1.3323	1.3569	−1.8
2.056	46	51	5.8721	5.5589	5.6	1.8964	1.9234	−1.4
2.827	50	47	7.9633	7.5134	6.0	2.1805	2.2098	−1.3
3.621	51	47	9.5149	9.0864	4.7	2.5543	2.4069	6.1
4.354	52	47	10.7872	10.4817	2.9	2.8401	2.6689	6.4
5.088	50	49	11.4051	10.9911	3.8	3.2558	2.8756	13.2

Table 6.

The predicted and measured values for displacement adsorption of CO₂–CH₄.

Equilibrium pressure (MPa)	CO₂ proportion (%)	CH₄ proportion (%)	CO₂ predicted (ml/g)	CO₂ measured (ml/g)	CO₂ relative deviation (%)	CH₄ predicted (ml/g)	CH₄ measured (ml/g)	CH₄ relative deviation (%)
0.726	0.52	0.46	2.7633	2.3470	17.7	0.7121	0.9476	−24.9
1.425	0.51	0.47	4.8319	4.2580	13.5	1.2971	1.5894	−18.4
2.163	0.51	0.48	6.6718	5.8861	13.3	1.8291	2.1573	−15.2
2.955	0.51	0.48	8.3174	7.6108	9.3	2.2803	2.4199	−5.8
3.684	0.5	0.49	9.4371	9.1240	3.4	2.6940	2.6558	1.43
4.409	0.49	0.5	10.3433	10.1244	2.2	3.0744	2.8874	6.5
5.112	0.49	0.5	11.2471	10.8550	3.6	3.3431	3.1519	6.1

As shown in Figure 5, the trend of the predicted and measured isothermal sorption curves is basically the same and the adsorption capacity of E-L equation prediction generally is a little greater than the measured value. From the data of Tables 5 and 6, it was found that although the relative error of some test points was more than 15%, that of the majority of the test points was less than 10%. The relative error for competitive adsorption was lower than the relative error for displacement adsorption. The predicted adsorption capacity of CO₂ is always greater than the measured adsorption capacity. At lower equilibrium pressure, the predicted adsorption capacity of CH₄ is less than the measured adsorption capacity but at higher equilibrium pressure, the predicted adsorption capacity of CH₄ is greater than the measured adsorption capacity.

Generally speaking, the relative error of the E-L equation in the prediction adsorption capacity is within the control range. Hence, the E-L equation has a direct relationship to the adsorption isotherm curve plot for a mixed gas.

From the data of the Langmuir pressure and Langmuir volume in Table 3, the separation coefficient for CO₂ to CH₄ in coal sample SA3 can be calculated to be 3.43 using equation (10) and the measured separation coefficient is listed in Tables 7 and 8.

Table 7.

Measured separation coefficient under different equilibrium pressures for the competitive adsorption of CO₂–CH₄.

Equilibrium pressure (MPa)	0.663	1.323	2.056	2.827	3.621	4.354	5.088
Separation coefficient $a_{12}$	2.9245	3.2077	3.2043	3.1960	3.4791	3.5497	3.7457

Table 8.

Measured separation coefficient under different equilibrium pressures for the displacement adsorption of CO₂–CH₄.

Equilibrium Pressure (MPa)	0.726	1.425	2.163	2.955	3.684	4.409	5.112
Separation coefficient $a_{12}$	2.1910	2.4689	2.5680	2.9601	3.3668	3.5780	3.5142

As shown in Tables 7 and 8, the measured separation coefficient under different equilibrium pressures was not constant. These data vary at around 3.43, which means that when the binary CO₂–CH₄ free gas ratio is 1:1 the adsorbed phase ratio is 3.43:1.

The displacement coefficient $λ_{12}$ represents the ability of component 1 to replace the component 2 at the adsorption sites, and the contrast basis is the pure gas sorption value. As shown in Tables 9 and 10, all of the displacement coefficients were greater than 1, but the differences were quite small. The greatest displacement coefficient for competitive adsorption was 1.2730, and the greatest displacement coefficient for displacement adsorption was 1.2730 (Table 9). During binary gas adsorption, different components will interfere with each other and will compete for the adsorption sites. Because the displacement coefficient of CO₂ to CH₄ is greater than 1, CO₂ has an advantage over CH₄ in the competition for the adsorption sites, but the advantage of CO₂ to CH₄ is not significant and therefore only a small amount of the CH₄ is displaced.

Table 9.

Measured displacement coefficient under different equilibrium pressures for the competitive adsorption of CO₂–CH₄.

Equilibrium pressure (MPa)	0.663	1.323	2.056	2.827	3.621	4.354	5.088
Displacement coefficient $λ_{12}$	1.0342	1.0719	1.1037	1.1718	1.2203	1.2658	1.2730

Table 10.

Measured displacement coefficient under different equilibrium pressures for the displacement adsorption of CO₂–CH₄.

Equilibrium pressure (MPa)	0.726	1.425	2.163	2.955	3.684	4.409	5.112
Displacement coefficient $λ_{12}$	1.0005	1.0010	1.0015	1.0021	1.0025	1.0028	1.0032

Conclusions

The experimental study of gas sorption characteristics helps not only to explain the mechanism of ECBM but also provides an important basis for simultaneous coal and gas extraction. The bituminous coal of Xutuan Coal Mine in Huaibei coalfield in China was taken as the research object in the present study. A series of pure and binary gas adsorption tests were carried out, using the bespoke GASTA. The main conclusions were as follows:

By comparing the test results, it was confirmed that the Langmuir equation has a good fitting behavior for the adsorption processes of CO₂, CH₄, and N₂, and the fitting degree was greater than 0.985. This confirmed the rationality and relevance of the Langmuir equation to the gas adsorption/desorption process.

The competitive and displacement adsorption mechanisms of a binary gas involve the differences in their adsorption sequence. Their overall adsorption capacity generally remains unchanged. This phenomenon indicates that coal gas sorption is a physical adsorption phenomenon.

Based on the fitting parameters of the pure gas Langmuir equation, binary gas adsorption capacity could be predicted using the E-L equation, which was consistent with the measured test results.

The separation coefficient of the test points and for the Langmuir theory was calculated, respectively. The component ratio of the free phase and the adsorbed phase was considered. Furthermore, it was confirmed that the displacement coefficient was defined by the ability of a component molecule to displace another component molecule from the adsorption sites. The displacement coefficient of CO₂ to CH₄ was greater than 1, and hence, a portion of the adsorbed CH₄ can be displaced by CO₂.

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: This research is supported by National Natural Science Foundation of China (51704274, 51502339, 51704278); the Young Talent Lifting Project from CAST, Beijing Natural Science Foundation (8184082); the Open Projects of State Key Laboratory of Coal Resources and Safe Mining CUMT (SKLCRSM16KF10); the State Key Laboratory Cultivation Base for Gas Geology and Gas Control (Henan Polytechnic University) (WS2017B02); Key Laboratory of Coal-based CO₂ Capture and Geological Storage, Jiangsu Province CUMT (no: 2016B09); and the Priority Academic Programme Development of Higher Education Institutions in Jiangsu Province.

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