Theoretical models to predict gas adsorption capacity on moist coal

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Theoretical models to predict gas adsorption capacity on moist coal Dong Chen, Zhihui Ye, Zhejun Pan, Yuling Tan, and Hui Li Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04190 • Publication Date (Web): 19 Mar 2019 Downloaded from http://pubs.acs.org on March 21, 2019

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Theoretical models to predict gas adsorption capacity on moist coal Dong Chen a, b*, Zhihui Ye b, Zhejun Pan c, Yuling Tan c,d,e, Hui Li b a

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, 102249 b

College of Petroleum Engineering, China University of Petroleum (Beijing), Beijing102200, China

c

CSIRO Energy Flagship, Private Bag 10, Clayton South, VIC 3169, Australia

d

State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China e

University of Chinese Academy of Sciences, Beijing 100049, China

*Corresponding

author. Tel.: +86 010 89732209.

E-mail address: [email protected]

Abstract: The impact of moisture on gas adsorption capacity reduction on coal has been well recognized and empirical correlations are widely used to quantitatively evaluate the moisture effect. However, few studies are found on fundamental modelling of moisture effect on gas adsorption capacity. In this work, two theoretical models on basis of the extended Langmuir theory (EL based) and the ideal adsorbed solution theory (IAS based) were developed to account for the gas adsorption capacity with different pressures and moisture contents. With the parameters determined from the gas adsorption on dry samples and water adsorption on samples under atmospheric condition, both models are able to predict the gas adsorption capacity under combined effect of gas pressure and moisture content. The models were verified through a set of experimental data from a coal sample from Australia and they were further applied to describe the methane adsorption behaviour on a coal sample from New Zealand. The results demonstrate that both models can reasonably predict the gas adsorption capacity on moist coal samples. Although one more parameter is required, the IAS based model could match the experimental data with higher accuracy. The research findings in this work contribute to a better understanding of the fundamentals of gas adsorption characteristics on moist coal.

Keywords: moisture effect; gas adsorption; theoretical model; coal; extended Langmuir model; IAS

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1. Introduction Water in coal normally exists as adsorbed phase on the pore surfaces and as free phase in pores and fractures [1]. Water/moisture would significantly reduce the gas storage capacity, the phenomenon of which has been observed in a number of laboratory measurements [2-11]. To reasonably predict the gas adsorption capacity on moist coal, it is of importance to evaluate the moisture effect on gas adsorption capacity. The impact of moisture on gas adsorption capacity has been well studied experimentally in previous studies. Joubert et al. [3] demonstrated that the methane adsorption capacity on coal decreased linearly with increasing moisture content up to a certain critical value. Based on the experimental data of the Permian coals from the Bowen Basin of Queensland, Australia, Levy et al. [4] reported a similar linear relationship between the methane adsorption capacity and the moisture content. The experimental results from Clarkson and Bustin [5] indicated that the moisture content not only reduced the gas mixture (CO2/methane) adsorption capacity, but also decreased the carbon dioxide selectivity. The strong moisture effect on high-pressure methane and carbon dioxide adsorption capacity reduction was found on Pennsylvanian coals by Krooss et al. [6]. Hildenbrand et al. [7] stated that the moisture content could reduce the gas capacity on Campine Basin coal from Belgium by 60% to 90%. Yao et al. [9] reported that the methane adsorption capacity of coals from Weibei Coalfield, Southeastern Ordos Basin, China, reduced significantly with increasing in moisture content. Moreover, Crosdale et al. [8] found that the methane adsorption capacity decreased with the moisture content in a non-linear form based on the experimental results of low-rank subbituminous coal samples from the Huntly Coalfield, Australia. Similar non-linear relationship between the methane adsorption capacity and the moisture content was also observed by Pan et al. [10] for the bituminous coal cores from the Bulli seam of the Sydney Basin, Australia. The methane and carbon dioxide adsorption data on an Australian subbituminous coal, a German high-volatile bituminous and a German anthracite coal demonstrated that the moisture-induced reduction in CO2 and CH4 sorption capacity decreased with increasing coal rank [11]. All these experimental studies revealed the important role of moisture in reducing gas adsorption capacity. The moisture content change may occur in some circumstances: 1) The moisture content may vary during the gas adsorption measurement; 2) The moisture content may be different under different laboratory conditions; 3) In-situ moisture content in coal may be different from that measured in laboratory. Some field practices have witnessed the alteration of relative humidity during the coal mining, which may correspondingly change the in-situ coal moisture content [12]. Martin [13] stated


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that the decrease of matrix moisture content normally leads to the increase of dustiness during coal mining; 4) During the process of CO2 sequestration in coal seams for enhanced coalbed methane (ECBM) production, the wettability of coal may transfer from water wet to CO2 wet, and hence the moisture content may vary accordingly [14]. Therefore, quantitative evaluation of moisture effect on gas adsorption capacity is important for estimating the gas content for moist coal and it would also allow the comparison of gas adsorption capacity among different coals with moisture effect correction. Several empirical models have been proposed to quantify the moisture effect on gas adsorption capacity on coal. The early linear model was found to be suitable for high rank coals [2-4, 15]. Then a power law equation was proposed by Crosdale et al. [8] to describe the moisture effect on gas adsorption capacity on low rank coal. However, the power law is problematic to describe the moisture effect for coals under lower moisture content conditions. To solve this problem, Chen et al. [16] proposed an exponential relation to quantitatively estimate the gas adsorption capacity in coal under different moisture content levels. Nevertheless, the empirical models for moisture effect on gas adsorption capacity are lack of fundamental background. A theoretical model is required to interpret the relationship between the moisture content and the gas storage capacity fundamentally. In this work, two theoretical models are proposed based on the extended Langmuir (EL) theory and the ideal adsorbed solution (IAS) theory respectively. Both models allow to predict the gas adsorption capacity on moist coal. The models are then calibrated with the experimental data on gas adsorption capacity on moist coal samples. The findings in this work are important for better understanding the moisture effect on gas adsorption capacity. It is noted that the moisture in the coal matrix is considered here, however, the moisture within the fracture network, which would affect relative permeability [17], is not discussed in this study.

2. Model development Methane adsorption on coal is normally considered as the monolayer adsorption under reservoir temperature and pressure conditions, and the Langmuir model is often used to represent the methane adsorption capacity. Differently, water vapor adsorption within the coal micropores forms multilayer of adsorbed molecules [18-19]. Equilibrium moisture content, which can be estimated through the moisture content in a solid under 100% relative humidity condition [20-22], is achieved once the multi-layer moisture adsorption has been formed.


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The BET model assumes that the heat of adsorption of the first layer of adsorbed molecules is decided by the interaction between solid surface and gas (vapor) molecules, and the heat of adsorption for the rest of the layers is equal to the heat of liquefaction, which implied that the interactions are among the adsorbed gas (vapor) molecules [23]. It indicates that only the first layer of the adsorption will interact with solid surface and then alter the surface potential energy. Based on this understanding, previous researchers further verified the coal swelling is mainly caused by the first layer of adsorbed water which changes the surface potential [10, 19]. It indicates the moisture effect on gas adsorption is mainly attributed to the first layer of adsorbed water, since the coal swelling strain is approximately a linear function of the adsorbed gas volume [24]. Therefore, it is assumed that the gas adsorption capacity reduction is mainly influenced by the first layer of adsorbed water. Two approaches based on the extended Langmuir (EL) theory and the ideal adsorbed solution (IAS) theory are proposed to account for the moisture effect on gas sorption capacity reduction. 2.1 EL based model Previous studies have illustrated that the extended Langmuir (EL) isotherm model could reasonably describe the binary (methane-nitrogen and methane-carbon dioxide) and ternary (methane-carbon dioxide-nitrogen) gas adsorption data on moisture-equilibrated coals [25-28]. Similar to extended Langmuir model to binary gas adsorption, the gas adsorption on moist adsorbent can be described as:

ng 

ngL Bg p g 1  Bg p g  Bw pw

(1)

where ng is the gas adsorption amount, ngL and Bg are Langmuir constants for dry gas adsorption, Bw is Langmuir constant for water (first layer) adsorption, pg and pw are gas and water vapor pressures, respectively. Bw in Eq. (1) only refers to the first layer adsorbed water and it can be obtained by matching the first layer of adsorbed water (e.g. obtain the first layer water adsorption in Figure 2 and regress Bw from the first layer water adsorption data in Figure 3). 2.2 IAS based model On basis of solution thermodynamics, another approach to account for the multicomponent adsorption equilibria is the Ideal Adsorption Solution Theory (IAS) proposed by Myers and Prausnitz (1965). The ideal adsorbed solution (IAS) theory [29] assumes that the spreading pressure of each component is equivalent to the multicomponent adsorption. When assuming each component accesses the same surface area, the following relation is obtained:


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

pge

0

 ge  p  p

dp  

pwe

we 1  p  p

0

dp

(2)

e e where pwe is the equilibrium pressure of pure water, p g is the equilibrium pressure of pure gas,  g  p  e is the gas adsorption capacity, and w1  p  is the water (first layer) adsorption capacity.

The gas (methane) adsorption capacity can be estimated by the Langmuir model:

 ge 

ngL Bg p g 1  Bg p g

(3)

According to the BET multilayer adsorption model [29], the amount of first layer adsorption of water can be calculated by [19]:

n cx n cp cx(1  x N )  w1  0 w1 w   nw1 N 1  x  cx(1  x ) 1  x  cx pw  (c  1) pw e w1

(4)

where nw1 is the adsorption capacity of water for a monolayer, c is the pore structure model constant, which is the embodiment of the interaction strength between the adsorbate (methane) and the adsorbent 0 (coal). N is the number of adsorbed layers, and x is the relative humidity, and pw is the water vapor

pressure at saturation. Incorporating Eqs. (3) and (4) into Eq. (2) and integrating, we have:

nw1c   pwe   ngL ln  Bg p  1   ln   c  1 0  1  c  1   pw   e g

(5)

Moreover, the following correlation exists:

pg p ge



pw 1 pwe

(6)

e 0 In Eq. (6), pwe and p g can be solved by Eqs. (5) and (6) simultaneously, and pw equals to

atmospheric pressure (0.101325 MPa). The molar fractions of component gas and water are expressed as:

xg 

pg p ge


(7)

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xw 

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pw pwe

(8)

The total adsorption (WT) is given by:

xg xw 1   e T ngL Bg pg nw1cpwe W 0 e 1  Bg pge pw   c  1 pw

(9)

The gas adsorption capacity (Wg) is then calculated by:

Wg  x g  W T

(10)

3. Model application on the Australian coal The two models developed in Section 2 are applied to describe the experimental data of methane adsorption on the coal sample under different levels of moisture content. The experimental data are collected from Pan et al. [10]. A coal sample from Bulli seam, NSW in Australia, with diameter of 2.54 cm and length of 8.26 cm was used for the experimental measurements [10]. The proximate analysis under air dry basis for the coal as received is summarized as [10]: moisture is 0.9%; volatile matter is 23.7%; fixed carbon is 71.1%; ash is 4.3%. To reduce the coal oxidation rate, the coal core is dried in a 50 ℃ oven with vacuum for more than a week to remove the pre-existing moisture. After the gas adsorption test on the dry sample, the sample was placed in a humidity-controlled chamber to gain moisture. Gas adsorption experiments were performed on the sample with different moisture contents. Detailed experimental procedure and results are referred to Pan et al. [10]. 3.1 Verification of the EL based model The application of the extended Langmuir based model includes two steps: (1) Determine the Langmuir gas adsorption constants ngL and Bg from gas adsorption data on dry coal The methane adsorption capacity data on dry coal sample with increasing gas pressure under 26 ℃ are shown in Figure 1. Using the least square method, the Langmuir gas adsorption constants ngL and Bg are obtained from fitting the experimental data on dry coal: ngL is 1.210 mmol/g and Bg is 0.541 MPa-1. It is noted that the limited data points (four points) would affect the accuracy of model parameters. The uncertainty could be reduced with more data supported.


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1.00 0.80 Gas adsorbed (mmol/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.60 0.40

Data

0.20

Model

0.00 0

1

2

3

4

5

6

Gas pressure (MPa)

Figure 1 Fitting the methane adsorption data on dry Bulli seam coal with Langmuir model (data from [10]) (2) Determine model parameter Bw from moisture adsorption data on coal under atmospheric condition By using several salt solutions, different relative humidity levels are achieved within a sample chamber. Each relative humidity corresponds to a specific moisture content in the coal sample. The detailed information of salt solution, relative humidity and moisture content are listed in Table 1. The water pressure, which is also included in Table 1, is calculated by the product of relative humidity and atmospheric pressure (0.101325 MPa). Table 1 Moisture content levels (after [10]) Salt solution

Relative humidity

Moisture content

Water vapor pressure

K2SO4

97%

8.5%

0.097 MPa

NaCl

75%

5.1%

0.075 MPa

MgCl2

33%

3.3%

0.033 MPa

The moisture adsorption capacity data on coal under atmospheric condition is drawn in Figure 2. Different from the monolayer adsorption of methane, the moisture has a multi-layer adsorption behavior on coal. The BET model as expressed in Eq. (11) can be applied to describe the moisture adsorption capacity on coal as a function of relative humidity.


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  nw1 e w

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cx 1   N  1 x N  Nx N 1 

(11)

1  x  1   c  1 x  cx N 1 

3.5

3.0

Experimental data 2.5

2.0 Total adsorption 1.5 N=4

Adsorption (mmol/g)

1.0 N=4

N=5

N=6

N=5 First layer adsorption

N=6

0.5

0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relative Humidity

Figure 2 Modeling of moisture adsorption data with BET model for Bulli seam coal (after [19]) In this study, the data and modelling results from Pan (2012) are applied. The modeling results are shown in Figure 2 and the parameters used are listed in Table 2. The number of adsorbed layers can be obtained by fitting the data with the BET model. The fitting results suggests that the adsorption of moisture typically forms 4 to 5 layers. Based on the parameters obtained and Eq. (4), the first layer adsorption could be estimated (see Figure 2). The moisture adsorption measurement is under atmospheric condition and thus the gas adsorption effect is negligible. The Langmuir type model as expressed in Eq. (12) could be applied to fit the first layer moisture adsorption data. As shown in Figure 3, the first layer moisture adsorption data are well described by the Langmuir type model. The model parameter Bw values obtained under the three different scenarios are included in Table 2. The results show that the selection of N would significantly affect the parameters, which would in turn changes the modelling results (see Figure 4).


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nw 

nwL Bw pw 1  Bw pw

(12)

where nw is the moisture adsorption amount, nwL and Bw are Langmuir constants for moisture (first layer) adsorption. Table 2 BET and Langmuir type model parameters from moisture adsorption measurement

N

nw1 (mmol/g)

c

Bw (MPa-1)

4

1.372

1.617

9.993

5

1.069

2.749

20.918

6

0.893

5.017

42.013

1.20

Water adsorbed (mmol/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.00 0.80 N=4 N=5 N=6 N=4 Model N=5 Model N=6 Model

0.60 0.40 0.20 0.00 0.00

0.02

0.04

0.06

0.08

Water pressure (MPa)

Figure 3 Modeling of the first layer moisture adsorption with Langmuir type model (data are digitized from the first layer adsorption curves as shown in Figure 2) (3) Prediction of gas adsorption capacity on moist coal With ngL and Bg obtained from gas adsorption on dry coal in Sections (1) and Bw obtained from moisture adsorption at atmospheric condition in Section (2), Eq. (1) can be applied to predict the methane adsorption capacity on moist coal. The modeling results are shown in Figure 4. The three sub-


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figures represent the predicting results when assuming the moisture adsorption layers are 4, 5 and 6 respectively. The results illustrate that the case with 6 moisture adsorption layers could best describe the gas adsorption data under binary influences of gas pressure and moisture content. The extended Langmuir based model is shown to be applicable to predict the methane adsorption capacity on moist coal with parameters from gas adsorption test on dry coal and moisture adsorption on coal at atmospheric condition. 1.00 0%

Gas adsorbed (mmol/g)

0.80

3.3% 5.1%

0.60

8.5% 0% EL

0.40

3.3% EL 5.1% EL

0.20

8.5% EL 0.00 0

1

2

3

4

5

6

Gas pressure (MPa)

(1) N=4 1.00 0% 0.80


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3.3% 5.1%

0.60

8.5% 0% EL

0.40

3.3% EL 5.1% EL

0.20

8.5% EL 0.00 0

1

2

3

4

Gas pressure (MPa)


5

6

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(2) N=5 1.00

0% 3.3%

0.80


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5.1% 0.60

8.5% 0% EL

0.40

3.3% EL 5.1% EL

0.20

8.5% EL 0.00 0

2

4

6

Gas pressure (MPa)

(3) N=6 Figure 4 Prediction of methane adsorption capacity on moist Bulli seam coal with extended Langmuir model (data from [10]) 3.2 Verification of ideal adsorbed solution (IAS) based model The same set of experimental data is applied to verify the ideal adsorbed solution (IAS) based model. The determination of model parameters is the same as (1) and (2) in Section 3.1. The constants for gas adsorption on dry coal are the same as the extended Langmuir type model: ngL is 1.21 mmol/g and Bg is 0.54 MPa-1. Different from the extended Langmuir type model, the constants for moisture adsorption are the adsorption capacity of water for a monolayer ( nw1 ) and the pore structure model constant (c). Three sets of these two parameters obtained by assuming adsorption layers at 4, 5 and 6 are listed in Table 2. The detailed information of water vapor pressure( pw ) and moisture content ( xw ) are listed in Table 1 and the other parameters ( xg , pwe ) can be obtained by applying Eqs. (6) - (8). The modeling results are shown in Figure 5. Consistent with the modeling results obtained by using the EL based model, the best prediction of methane adsorption on moisture samples is achieved by using the IAS based model with six moisture adsorbed layers.


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1.00

0% 3.3%


0.80

5.1% 0.60

8.5% 0% IAS

0.40

3.3% IAS 5.1% IAS

0.20

8.5% IAS 0.00 0

1

2

3

4

5

Gas pressure (MPa)

（1）N=4 1.00

0% 3.3%

0.80


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5.1% 0.60

8.5% 0% IAS

0.40

3.3% IAS 5.1% IAS

0.20

8.5% IAS 0.00 0

1

2

3

Gas pressure (MPa)

（2）N=5


4

5

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1.00

0% 3.3%

0.80 Gas adsorbed (mmol/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5.1% 0.60

8.5% 0% IAS

0.40

3.3% IAS 5.1% IAS

0.20

8.5% IAS 0.00 0

1

2

3

4

5

Gas pressure (MPa)

（3）N=6 Figure 5 Prediction of methane adsorption capacity on moist Bulli seam coal with IAS based model (data from [10]) 3.3 Model comparison Both the EL based model and the IAS based model can achieve the favorable matching results when the moisture adsorption layer is assumed as 6. The best fit results of the EL based and the IAS based model are compared in Table 3. The gas Langmuir constants (ngL and Bg) used by both methods are the same and obtained through matching from dry coal Langmuir fitting with the least square method. The extra parameter Bw in the three parameters EL based model is regressed from matching the moisture adsorption data on coal under atmospheric condition. The average relative error of the prediction results with the EL based model is 8.0%. Table 3 Comparison of modeling results Model

Parameters matching from dry

Parameters obtained from moist adsorption

Average

coal Langmuir fitting

on coal under atmospheric condition

relative error

EL

ngL (mmol/g)

Bg (MPa-1)

Bw (MPa-1)

based

1.210

0.541

42.013

IAS

ngL (mmol/g)

Bg (MPa-1)

nw1 (mmol/g)


8.0% c

1.9%

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based

1.210

0.893

0.541

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5.017

Comparing to the EL based model, the IAS based model has two extra parameters of nw1 and c to fit the experimental data. These two parameters are obtained by matching the moisture adsorption data with the BET model. Although one more parameter is required for the IAS based model, the average relative error reduces to 1.9%. The results demonstrate that both models can reasonably predict the gas adsorption capacity under variable pressures and moisture contents. This indicates that the assumption made, the gas adsorption reduction is mainly affected by the first adsorbed layer of water, is consistent with the test results. However, the moisture adsorbed layers obtained by the two models is close, but slightly different from the modelling results of moisture adsorption data with BET model for Bulli seam coal from [19], in which adsorption layer is considered as 5. The inconformity may be due to the modelling error between the binary adsorption model and single adsorption model. However, it needs to be verified by more experimental data and modelling work.

4. Model application on Zelanian coal In order to test the adaptability to other situations, the two models developed in Section 2 are further applied to match the experimental data of methane adsorption on subbituminous coal from the Huntly Coalfield, New Zealand [8]. Different from the experimental data used in Section 3, the gas adsorption data on dry sample are not available in their experiments. All the gas adsorption capacity measurement are under moist conditions. Therefore, the gas Langmuir constants (ngL and Bg) cannot be regressed using data under dry condition. The three parameters (ngL , Bg and Bw) are obtained by matching the gas adsorption data on moist samples. As shown in Figure 6, the EL based model could reasonably describe the methane adsorption data on the Huntly Coalfield coal with the moisture content varies from 4.6% to 17.7%. The parameter values used in the data fitting are: ngL is 2.261 mmol/g, Bg is 0.263 MPa-1, Bw is 100.049 MPa-1. The ngL and the Bw for the New Zealand coal are about two times of the parameter values obtained from the Australian coal, while Bg is about half.


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1.2

4.6%

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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12.6%

0.8

17.7%

0.6

4.6% EL

0.4

12.6% EL

0.2

17.7% EL

0 0

2

4

6

8

10

Gas pressure (MPa)

Figure 6 Modeling of methane adsorption capacity on moist Huntly Coalfield coal with EL based model (data from [8]) To apply the IAS based model to describe the experimental data, the BET model parameters are determined from the moisture adsorption data (see Table 4) and the data fitting results are illustrated in Figure 7. The ngL and Bg obtained by using the EL based model, the modeling results of the IAS based model are obtained as shown in Figure 8. Similar to the modelling results in Section 3, a better data fitting is achieved by the IAS based model. The difference is that the adsorption layer determined in this case is 3 instead of 6. Though the adsorption layer is less for the Zelanian coal, the nw1 obtained is much larger than that for the Australian coal. The product of adsorption layer and the adsorption capacity of water for a monolayer nw1 is therefore much higher for the Zelanian coal. This is consistent with the experimental condition, that is the equilibrium moisture content for the Zelanian coal is much higher. Table 4 BET model parameters from moisture adsorption measurement

N

nw1 (mmol/g)

c

3

5.739

3.513


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Water adsorbed (mmol/g)

12 Experimental data

10 8

N=3

6 4 2 0 0

0.2

0.4

0.6

0.8

1

Relative humidity

Figure 7 Modeling of moisture adsorption data with BET model for Huntly Coalfield coal (data from [8]) 1.2 4.6%

1.0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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12.6%

0.8

17.7%

0.6

4.6% IAS 0.4 12.6% IAS 0.2

17.7% IAS

0.0 0

2

4

6

8

10

Gas pressure (MPa)

Figure 8 Modeling of methane adsorption capacity on moist Huntly Coalfield coal with IAS based model (data from [8]) The modelling results show that both the EL based and the IAS based models are capable to describe the methane adsorption capacity on moist Huntly Coalfield coal under various pressures. This provides an additional evidence that the models developed in this study are able to estimate the methane adsorption capacity under combined effect of pressure and moisture content.


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5. Discussion The modelling results illustrate that both models could reasonably fit the gas adsorption data on coals under different gas pressures and moisture contents. The limitation of these approaches is that a complete set of experiments including the gas adsorption measurement on dry sample and the water adsorption measurement under atmospheric condition should be available to determine the model parameters. The experimental data for gas adsorption on moist coal could be used to validate the models. Since the models are derived based on the monolayer adsorption of gas, they may not be applicable to CO2 adsorption which may form multilayer adsorption on coal surfaces. But the models might be also applicable to the prediction of methane adsorption capacity on shale, since shale has similar methane adsorption mechanism to coal. There is no strict restriction on water adsorption types, but only the first layer water adsorption curve is used to regress the model parameters.

6. Conclusions In this work, two theoretical models on basis of extended Langmuir theory (EL based) and ideal adsorbed solution theory (IAS based) were proposed to account for the gas adsorption capacity on coals with different pressures and moisture contents. The model parameters can be obtained through matching the gas adsorption data on the dry sample and the water adsorption data on the sample under atmospheric condition. With these parameters, both the EL based and the IAS based model are able to reasonably predict the experimental data under combined influence of gas pressure and moisture content. Although one more parameter is required for the IAS based model than the EL based model, the IAS based model could predict the experimental data with higher accuracy. The research findings in this work contribute to a better understanding of the fundamentals of gas adsorption on moist coals.

Acknowledgement The authors acknowledge the financial support from the National Natural Science Foundation of China (No. 51604283), the Projects of International Cooperation and Exchanges NSFC (No. 51811530306), and the Foundation of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing (No. Z2018096).


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References [1] Chen D, Pan Z, Liu J, Connell L. An improved relative permeability model for coal reservoirs. International Journal of Coal Geology 2013;109:45-57. [2] Ettinger IL, Lidin GD, Dmitriev AM, Zhupakhina ES. Systematic Handbook for the Determination of the Methane Content of Coal Seams from the Seam Pressure of the Gas and the Methane Capacity of the Coal. Institute of Mining, Academy of Sciences 1958, USSR, US Bureau of Mines Translation, (1505). [3] Joubert JI, Grein CT, Bienstock D. Effect of moisture on the methane capacity of American coals. Fuel 1974;53:186-191. [4] Levy JH, Day SJ, Killingley JS. Methane capacities of Bowen Basin coals related to coal properties. Fuel 1997;76:813-819. [5] Clarkson CR, Bustin RM. Binary gas adsorption/desorption isotherms: effect of moisture and coal composition upon carbon dioxide selectivity over methane. International Journal of Coal Geology 2000;42:241-271. [6] Krooss BM, Van Bergen F, Gensterblum Y, Siemons N, Pagnier HJM, David P. High-pressure methane and carbon dioxide adsorption on dry and moisture-equilibrated Pennsylvanian coals. International Journal of Coal Geology 2002;51:69-92. [7] Hildenbrand A, Krooss BM, Busch A, Gaschnitz R. Evolution of methane sorption capacity of coal seams as a function of burial history - a case study from the Campine Basin, NE Belgium. International Journal of Coal Geology 2006;66(3):179-203. [8] Crosdale PJ, Moore TA, Mares TE. Influence of moisture content and temperature on methane adsorption isotherm analysis for coals from a low-rank, biogenically-sourced gas reservoir. International Journal of Coal Geology 2008;76:166-174. [9] Yao Y, Liu D, Tang D, Tang S, Che Y, Huang W. Preliminary evaluation of the coalbed methane production potential and its geological controls in the Weibei Coalfield, Southeastern Ordos Basin, China. International Journal of Coal Geology 2009;78:1-15. [10] Pan Z, Connell LD, Camilleri M, Connelly L. Effects of matrix moisture on gas diffusion and flow in coal. Fuel 2010;89:3207-3217.


Page 19 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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[11] Gensterblum Y, Merkel A, Busch A, Krooss BM. High-pressure CH4 and CO2 sorption isotherms as a function of coal maturity and the influence of moisture. International Journal of Coal Geology 2013;118: 45-57. [12] Su S, Chen H, Teakle P, Xue S. Characteristics of coal mine ventilation air flows. Journal of Environmental Management 2008;86:44-62. [13] Martin CH. Australasian Coal Mining Practice; Monographs, no 12. Australasian Institute of Mining and Metallurgy: Parkville, Vic1986;342. [14] Plug WJ, Mazumder S, Bruining J, Siemons N, Wolf KH. Capillary pressure and wettability behavior of the coal-water-carbon dioxide system at high pressures. International Coalbed Methane Symposium 2006; 0606:1−15. [15] Ozdemir E, Schroeder K. Effect of moisture on adsorption isotherms and adsorption capacities of CO2 on coals. Energy Fuels 2009;23:2821−2831. [16] Chen D, Pan Z, Liu J, Connell LD. Modeling and simulation of moisture effect on gas storage and transport in coal seams. Energy Fuels 2012;26:1695-1706 [17] Chen D, Shi JQ, Durucan S, Korre A. Gas and water relative permeability in different coals: Model match and new insights. International Journal of Coal Geology 2014;122:37-49. [18] Charrière D, Behra P. Water sorption on coals. Journal of Colloid and Interface Science 2010;344:460-467. [19] Pan Z. Modeling of coal swelling induced by water vapor adsorption. Frontiers of Chemical Science and Engineering 2012;6:94-103. [20] Henderson SM. A basic concept of equilibrium moisture. Transactions of the American Society of Agricultural Engineers 1952;1:29-32. [21] Merwe DVD, Campbell QP. An investigation into the moisture absorption properties of thermally dried South African fine coal. Journal of the South African Institute of Mining and Metallurgy 2002;102:417-419. [22] Day S, Sakurovs R, Weir S. Supercritical gas sorption on moist coals. International Journal of Coal Geology 2008;74:203-214. [23] Brunauer S, Emmett PH, Teller E. Adsorption of gases in multimolecular layers. Journal of the American Chemical Society 1938;60:309-319.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 20

[24] Cui X, Bustin RM. Volumetric strain associated with methane desorption and its impact on coalbed gas production from deep coal seams. AAPG Bulletin 2005;89:1181-1202. [25] Ruthven DM. Principles of Adsorption and Adsorption Processes. Wiley, New York 1984;56(4):168-179. [26] Yang RT. Gas Separation by Adsorption Processes. Butterworth, Boston, MA;1987. [27] Arri LE, Yee D, Morgan WD, Jeansonne MW. Modeling coalbed methane production with binary gas sorption. Society of Petroleum Engineers 1992; 459–472. [28] Harpalani S, Pariti UM. Study of coal sorption isotherms using a multicomponent gas mixture. Coalbed Methane Symp 1993;1:151–160. [29] Myers AL, Prausnitz JM. Thermodynamics of mixed-gas adsorption. AIChE Journal 1965;11:121127.


Theoretical models to predict gas adsorption capacity on moist coal

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