Molecular Simulations on Adsorption and Diffusion of CO2 and CH4 in

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Molecular simulations on adsorption and diffusion of CO2 and CH4 in moisture coals Jinxuan Han, A.Kh. Bogomolov, E.Yu. Makarova, Zhaozhong Yang, Yanjun Lu, and Xiaogang Li Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02898 • Publication Date (Web): 27 Nov 2017 Downloaded from http://pubs.acs.org on November 27, 2017

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Energy & Fuels

Molecular simulations on adsorption and diffusion of CO2 and CH4 in moisture coals Jinxuan Han

a,*

, Alexander Kh. Bogomolov a, Elena Yu. Makarova a, Zhaozhong Yang b, Yanjun

Lu a, Xiaogang Li b a

Department of Geology, Moscow State University Lomonosov, Moscow 119991, Russian

Federation b

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest

Petroleum University, Chengdu 610500, China

KEYWORDS: Coalbed methane, Adsorption, Diffusion, Moisture, Molecular simulation

ABSTRACT Most of coalbed methane (CBM) reservoirs contain moisture that can have an impact on adsorption and diffusion of CBM, so moisture content is an important factor that affects CBM production. CO2 can be used to improve CBM production on site. Combined with these two points, regulations of CH4 adsorption and diffusion are sought at different conditions when CO2 is injected into coal seams with moisture. Slit pores with different moisture contents (1%, 2%, 4% and 6%) and random model are established. Molecular simulations are carried out, respectively, from 0MPa-10MPa at 293.15K, 303.15K and 313.15K. Relative to CO2, the interaction of CH4

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and -C-C- is weaker, indicating that CO2 can adsorb more steadily on the surface of coal. Water molecules preferentially adsorb on the oxygen functional groups, and then water molecules adsorb each other with hydrogen bond to form clusters that can interfere with the adsorption and diffusion of CO2 and CH4. Due to the influence of functional group, hydrogen bond and micropore filling, the adsorption capacity of H2O can increase steeply at very low pressure. The phenomenon is not beneficial to the CBM exploitation.

1. INTRODUCTION China has huge coalbed methane (CBM) reserves, and the CBM reserves in the coal seams deeper than 1000 m accounts for 61.2% of the total reserves 1. Therefore, the development of CBM reserves has become an important trend. In addition to hydraulic fracturing, gas injection is also currently being used to recover enhanced CBM (ECBM) 2-11. ECBM technique is based on the competitive adsorption. To achieve large-scale field applications of ECBM and improve the efficiency of the ECBM process, the effects of the injected gases on CBM reservoirs must be first understood. In addition to that, most of CBM reservoirs contain moisture that can significantly affect gas adsorption and diffusion in coal seams. Moisture content is a first-order control on the gas adsorption capacity, especially in low-rank coals, and its impact on gas adsorption is much greater than that of temperature or maturity

12-13

. The gas adsorption capacity decreases with increasing moisture content until a

“limiting moisture content” is reached

12-13

. Beyond the limiting moisture content, the gas

adsorption capacity remains constant 5, 12-14.


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According to entropy calculations, water condensed in capillaries behaves as a liquid, and gas will dissolve in the condensed water

13, 15

molecules confined to a nanospace is ice-like

. Iiyama et al. showed that the structure of water 13, 16

. Alcaniz-Mongue et al. confirmed that liquid

water adsorbed in the pore space of carbon materials behaves as a solid throughout the whole range of micropore sizes

13, 17

. Micropores are the majority in coal seams. Hence, this structure

similar to ice will keep gas from diffusing in micropores. To further study characteristics of adsorption and diffusion of CH4 and CO2 at different moisture contents, molecular simulations are carried out, and simulation results are deeply analyzed. This can provide scientific and theoretical guidance for the construction and design of field tests. 2. SIMULATION DETAILS Monte Carlo method is used in this paper, and Metropolis method and grand canonical ensemble (VTµ) are used to simulate the adsorption process of gases. In the simulation process of diffusion, canonical ensemble (NVT) and microcanonical ensemble (NVE) are successively used to obtain optimized diffusion model, and then analysis of diffusion is conducted. The software of Materials Studio (MS) is applied in this paper. The coal molecular model put forward by W. Fuchs and modified by Krevelen 18 (Figure 1) is used to establish slit pores with different pore sizes 1nm, 2nm and 4nm, respectively. For establishing models with different moisture contents, numbers of water molecules in the unit cell are calculated (Table 1), and then slit pores with absolute moisture content 1%, 2%, 4% and 6%, respectively, are established. Figure 2 shows molecular models of coal with different pore size at 6% moisture content. Besides, taking the operation capability of the computer into account, the fragment with oxygen functional


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groups (Figure 3a) is extracted from the coal molecule to establish the random model (Figure 3b), which can highlight the heterogeneity of micopores (especially the random distribution of functional groups on the coal surface) and contribute to the intensive study on H2O adsorption in micropores. The random model can increase the compactness of coal molecules and well show the forming process of water clusters in micropores. The adsorbates (H2O, CO2 and CH4) are optimized by the Forcite module. In the simulation, the forcefield type is pcff, and the charges are forcefield assigned. The summation method of electrostatic is Ewald, while van del Waals is Atom based. The van del Waals potential is described by the Lennard-Jones 9-6 potential. The simulation temperatures are, respective, 293.15K, 303.15K and 313.15K, and the pressure is from 0MPa to 10MPa. In the simulation process, the pressure will be transferred to the fugacity that expresses the effective pressure of real gas.

Figure 1. Optimized Fuchs model modified by Krevelen

a) d=1nm

b) d=2nm

c) d=4nm

Figure 2. Slit pores with different pore size at 6% moisture content


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Table 1. Number of water molecules corresponding different moisture contents in unite cell Number of water molecules (molecules/u.c) Pore size (nm) 1%

2%

4%

6%

1

40

79

159

238

2

60

118

236

354

4

97

191

383

574

a)

b)

Figure 3. a) The fragment with oxygen functional groups; b) Random model of coal In the simulation process of adsorption, absolute adsorption capacity and excess adsorption capacity are obtained, respectively. Absolute adsorption capacity includes bulk phase in the pore as well as adsorbed phase that exists on the walls of pore, while excess adsorption capacity only refers to the adsorbed phase. The relationship can be shown as: N ( e) = N ( a ) - V p ⋅ ρ

(1)

Such that N(e) is the excess adsorption capacity; N(a) is the absolute adsorption capacity; Vp is the pore volume of adsorbent; ρ is the density of adsorbate at one temperature and pressure.


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The software of Aspen can be used to calculate the density ρ. The pore volume Vp can be obtained from Atom Volume & Surfaces in MS. In the simulation process of diffusion, curves of mean square displacement (MSD) and Einstein method are used to obtain the diffusion coefficient, and the formula of Einstein method is as follows 19: 1 d D= lim 6N dt

2

N

∑  r ( t ) − r ( 0 ) i

i

(2)

i =1

Such that D is diffusion coefficient; N is numbers of adsorbates; t is simulation time; ri(t) and ri(0) are positon vectors at t and initial time, respectively. Based on curves of MSD, linear regression is carried out, and the slope k is obtained, therefore, diffusion coefficient D can be simplified as: D =

k 6

(3)

Micropore diffusion and surface diffusion will happen when gas molecules diffuse in micropores of coal, but gas adsorption is mainly controlled by micropore diffusion, therefore, even if surface diffusion exists, diffusion coefficient can be directly expressed by coefficient D of micropore diffusion

20

. According to pore size and mean free path of molecules (MMFP),

micropore diffusion can be divided into molecular diffusion and Knudsen diffusion. MMFP of gas at different temperatures, pressures, and pore sizes can be calculated by formula (4), and then values of MMFP compare with pore sizes. Finally, diffusion type of gas can be determined. When pore size is greater than MMFP, molecular diffusion will happen, while the opposite is Knudsen diffusion.


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λ =

1 2πd 2 n

n =

N V

(4)

(5)

Such that λ is MMFP; d is diameter of molecule; n is molecular concentration; N is molecular numbers; V is free space volume.

3. RESULTS AND DISCUSSIONS 3.1 The influence of moisture content Figure 4 shows that with the increase of moisture content, absolute and excess adsorption capacities of CO2 and CH4 gradually decrease. Compared with adsorption in dry coal, adsorption capacities in moisture coal significantly decrease. That is because water molecules will preferentially adsorb on the oxygen functional groups (Figure 5), and then water molecules adsorb each other with hydrogen bond to form clusters (Figure 6 and Figure 7), which will interfere with the adsorption of CO2 and CH4. As is shown in Figure 5, H2O firstly chooses the site with oxygen molecule to adsorb. H2O is polar molecule, and the polarity of oxygen functional group from strong to weak is carboxyl (-COOH), aldehyde group (-CHO), carbonyl (-C=O-) and carbon-oxygen single bond (-C-O-), so the interaction between H2O and oxygen functional group weakens in turn. The isosteric adsorption heat qst is, respective, 30.644kJ/mol, 14.705kJ/mol, 12.929kJ/mol and 12.293kJ/mol. The sequence of H2O adsorption is -COOH＞ -CHO＞-C=O-＞-C-O-. CO2 and CH4 are nonpolar molecules, so they preferentially choose the nonpolar site (-C-C-) to adsorb. -COOH with strong polarity can impact on the chosen adsorption site of CO2 as a


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result of the greater electric susceptibility relative to CH4, so CO2 will adsorb on the nonpolar site (-C-C-) that is in adjacent -COOH. The isosteric adsorption heat between CO2 and fragment with -COOH is the highest. Compared with -COOH, other oxygen functional groups have less impact for CO2 adsorption. Relative to CO2, the interaction of CH4 and -C-C- is weaker, indicating that CO2 can adsorb more steadily on the surface of coal. That is why CO2 can be used to substitute for CH4 to increase the CBM production. As is discussed above, water molecules preferentially adsorb on the oxygen functional groups, and then water molecules will choose adsorbed water molecules as the secondary sites to adsorb with hydrogen bond, which can be seen from Figure 6. The slit pore with heterogeneity is different from the model composed of graphite with homogeneity, so the number of water molecules from the center of the slit pore is unsymmetrical change. Water molecules mainly adsorb on the wall of slit pore at low pressure, but as the pressure rises, the middle of slit pore is gradually occupied by the increased water molecules, indicating that multilayer adsorption happens with hydrogen bond. The simulated results are consistent with the conclusions from previous researches 21, 22.

14

11

2%-absolute-1nm-303.15K-CO2 4%-absolute-1nm-303.15K-CO2

12

6%-absolute-1nm-303.15K-CO2

11

0%-excess-1nm-303.15K-CO2 1%-excess-1nm-303.15K-CO2

10

2%-excess-1nm-303.15K-CO2

9


8


2%-absolute-1nm-303.15K-CH4 4%-absolute-1nm-303.15K-CH4

10

Adsorption capacity (mmol/g)

13

0%-absolute-1nm-303.15K-CH4 1%-absolute-1nm-303.15K-CH4

12

0%-absolute-1nm-303.15K-CO2 1%-absolute-1nm-303.15K-CO2

15


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7 6 5 4 3

6%-absolute-1nm-303.15K-CH4 0%-excess-1nm-303.15K-CH4

9

1%-excess-1nm-303.15K-CH4 2%-excess-1nm-303.15K-CH4

8 7

4%-excess-1nm-303.15K-CH4 6%-excess-1nm-303.15K-CH4

6 5 4 3 2

2

1

1

0

0 0

1

2

3

4

5

6

7

0

1

2

3

4

5

Fugacity (MPa)

Fugacity (MPa)

a) CO2

b) CH4


6

7

8

9

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Figure 4. Adsorption capacities of CO2 and CH4 at different moisture contents Molecular fragment

H2 O

CO2

CH4

with -C=O-

qst=12.929kJ/mol

qst=11.069kJ/mol

qst=9.054kJ/mol

with -C-O-

qst=12.293kJ/mol

qst=11.328kJ/mol

qst=9.217kJ/mol

with -COOH

qst=30.644kJ/mol

qst=12.657kJ/mol

qst=9.923kJ/mol

with -CHO

qst=14.705kJ/mol

qst=11.278kJ/mol

qst=9.409kJ/mol

Figure 5. The adsorption sites of H2O, CO2 and CH4 in coal fragments with different oxygen functional groups To further reveal the influence of water on CO2 and CH4 adsorption, the snapshots of water clusters formation at 293.15K are shown in Figure 7. With the increase of water molecule


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numbers, the bulk of water cluster gradually grow (illustrated in Figure 7 in yellow) until the integration happens among water clusters. Water molecules form clusters with hydrogen bond followed by capillary condensation 21, 23. Figure 8 shows the isosteric adsorption heat at different numbers of water molecules. As the water molecule number increases, the isosteric adsorption heat gradually increases. When just one water molecule adsorbs on the surface of coal, the isosteric adsorption heat is 38.556kJ/mol that is lower than the heat of water condensation 45kJ/mol, while water molecules add to 5, the isosteric adsorption heat has increased to 44.199kJ/mol that indicates that water molecules have begun to condense. When water molecules are 40, the isosteric adsorption heat has reached 56.643kJ/mol that is related to the formation of water cluster. Although the energy of water-carbon interaction is very small compared to the energy of hydrogen bond

24

, water clusters in micropores may interact with

surrounding pore walls, which results in the relatively high heat

24

. The curve of heat obtained

shows that strong interactions exist among water molecules, which is the reason of cluster formation. The simulation result is similar to the study results of water adsorption on carbons 22, 23

. The more water molecules in cluster are, the lower the potential of the cluster is

23

. Though

activated carbon is not coal, they have similar elementary composition, molecular structure and pore size distribution, therefore, the results are correlated to some extent. The existence of water in coal micropores certainly will have an impact on the gas adsorption. Reduced degree is introduced to better explain the influence of moisture content on gas adsorption. The equation of reduced degree is as follows:


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R=

1 n N d ,i − N m ,i ∑ N n i =1 d ,i

(6)

Such that R is reduced degree; Nd,i is adsorption capacity of dry coal at pressure i; Nm,i is adsorption capacity of moisture coal at pressure i. As is shown in Table 2, with the increase of moisture content, the reduced degree of CO2 and CH4 adsorption capacity gradually increase, and there is a larger reduction in the adsorption that corresponds to the volume of adsorbed water. Moreover, reduced degree of excess adsorption capacity is greater than that of absolute adsorption capacity, which indicates that more water molecules in the form of adsorbed state exist in micropores than those in the form of bulk phase.

50 0.02MPa 0.06MPa 0.1MPa 0.2MPa 0.4MPa 1MPa

40

Number of molecules

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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30

20

10

0 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Distance from center (nm)

Figure 6. Number of water molecules from the center of the slit pore at 293.15K

0 H2O molecule

20 H2O molecules


40 H2O molecules

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60 H2O molecules

80 H2O molecules

100 H2O molecules

Figure 7. The snapshots of water cluster formation at 293.15K (Random coal structure is hidden). 60

293.15K 58

Isosteric adsorption heat (kJ/mol)

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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56 54 52 50 48 46 44 42 40 38 0

5

10

15

20

25

30

35

40

45

Water molecule numbers (molecules/u.c)

Figure 8. Isosteric adsorption heat at different numbers of water molecules Table 2. Average reduced degree of CO2 and CH4 adsorption capacity at 303.15K and different moisture contents in 1nm slit pore Reduced degree Component

Absolute adsorption capacity

Excess adsorption capacity

1%

2%

4%

6%

1%

2%

4%

6%

CO2

6.34%

11.72%

19.21%

28.27%

9.25%

18.12%

29.37%

42.48%

CH4

5.63%

8.79%

18.15%

29.15%

6.93%

10.69%

22.47%

36.12%


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For further explaining the effect of water, CO2 and CH4 diffusions at different moisture content are carried out. The simulation results are shown in Table 3. With the increase of moisture content, diffusion coefficients of CO2 and CH4 significantly decrease, but at the same condition the diffusion coefficient of CO2 is always greater than that of CH4. That is because the diffusion space of gas becomes smaller due to adsorbed water molecules, while CO2 with smaller diameter will be dominant in the small space, and besides that, CO2 can spread more easily in water. Water can not only occupy the pore space to hinder the diffusion channel of gas, but also make the coal matrix swell due to its adsorption 25, 26.

Table 3. Diffusion coefficients of CO2 and CH4 at different moisture contents (1nm slit pore-8MPa-303.15K) D (×10-8m2/s) Component 0%

1%

2%

4%

6%

CO2

0.870

0.805

0.705

0.592

0.363

CH4

0.847

0.722

0.582

0.383

0.262

In general, for the study on the adsorption swelling of coal matrix, most researchers just consider the influence of gas, but ignore the role of water as inherent factor. As is shown in Table 4, the volumetric swelling strain increases with the increase of moisture content

25, 26

. When the

range of moisture content is from 1% to 6%, the swelling strain increases from 0.49% to 1.39% 25, 26

, indicating that water adsorption resulting in swelling of coal matrix. From macroscopic

perspective, the matrix swelling can make the pore become narrow and reduce the permeability


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of gas, while microscopically saying, it can improve the collision frequency of gas molecules and increase the diffusion resistance. In addition, water clusters that can be formed in micropores will block the diffusion space as is explained above, therefore, the behavior on reduced adsorption is owing to the diffusion problem of gas molecules entering the narrow pores.

Table 4. Swelling strain at different moisture contents 25, 26 1%

2%

4%

6%

0.49%

0.80%

1.17%

1.39%

3.2 The influence of pressure As is well known, with the increase of pressure, the adsorption capacity gradually increases. Therefore, the depressurization is the main way to promote the methane desorption from coal seams. However, in moisture coal seams exist complex situations due to the influence of water. Figure 9 shows that the adsorption capacity of H2O steeply increases from 0 to 0.1MPa, and then the adsorption capacity has a slow change that presents stable state. To further analyze the characteristics of water adsorption, the fugacity range less than 0.1MPa will be subdivided in the simulation process to reveal the influence of H2O on methane production when the bottom hole pressure reaches the utmost pressure 0.1MPa. The simulated result is shown in Figure 10. The adsorption capacity begins to increase slowly at around 50KPa, and the variation trend tends to be stable. When the fugacity is less than 8.8KPa, the adsorption capacity is very low, but from 8.8KPa to 16.7KPa the adsorption capacity bumps up, and then continues to increase. The phenomenon is related to the influence of functional group, hydrogen bond and micropore filling. Functional groups firstly govern the adsorption of H2O, and then water-water interactions


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enhance so that more water molecules assemble with hydrogen bond. In addition, micropores with strong adsorption potential can make the number of adsorbed water molecules increase sharply at low pressure. However, the structure and density of the condensate in micropores are different from the common liquid 20, so more details need be in-depth studied. Know then, when the pressure cone of depression, refers to the funnel shaped zone where the pressure drops dramatically with the fluid towards the bottom hole, is formed in coal seams, and even the bottom hole pressure reaches the atmospheric pressure, the negative effect of water (even very little water) on gas output is difficult to be eliminated. Moreover, it is difficult for CO2 as substitute to effectively enter micropores to increase CBM production. Though the simulation results are more considered as the qualitative analysis, the variation trend is in accord with the experimental results

27

that are carried out on activated carbon fibers. Some classical concepts

and methods from material science and adsorption science maybe bring new spring for the CBM exploration.

35

30


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25

20

15

10

5

Subdivided area 0 0

1

2

3

4

5

6

7

8

9

Fugacity (MPa)

Figure 9. Adsorption capacities of H2O in 2nm slit pore at 303.15K


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30

25


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20

15

10

5

0 0

10

20

30

40

50

60

70

80

90

100

Fugacity (KPa)

Figure 10. The adsorption isotherm of subdivided area As is well known, high pressure is disadvantage to the diffusion of gas. As the pressure rises, MMFP of CO2 and CH4 almost decreases at 303.15K (Table 5), which indicates that high pressure can increase the collision frequency of gas molecules so that gas diffusion is hindered. MMFP of CO2 at 8MPa is slightly greater than that at 6MPa, which may be related to the subcritical state of CO2, indicating that the diffusion of CO2 is more sensitive to the pressure change at subcritical state.

Table 5. MMFP of CO2 and CH4 in 1nm slit pore at 303.15K and different pressures (moisture content 2%) λ (nm) Component 2MPa

4MPa

6MPa

8MPa

10MPa

CO2

0.402

0.364

0.329

0.339

0.328

CH4

0.385

0.314

0.289

0.266

0.264

3.3 The influence of temperature


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6

7

6

5



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5

4

3

2

293.15K-absolute-1nm-2%-CO2 303.15K-absolute-1nm-2%-CO2

1

4

3

293.15K-absolute-1nm-2%-CH4

2

303.15K-absolute-1nm-2%-CH4 293.15K-excess-1nm-2%-CH4

1

303.15K-excess-1nm-2%-CH4

293.15K-excess-1nm-2%-CO2 303.15K-excess-1nm-2%-CO2 0

0 0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

8

9

Fugacity (MPa)

Fugacity (MPa)

a) CO2

b) CH4

Figure 11. Adsorption capacities of CO2 and CH4 at 293.15K and 303.15K As the temperature rises, the absolute adsorption capacities of CO2 and CH4 all decrease, but the variation trends of excess adsorption are different (Figure 11). The excess adsorption capacity of CO2 experiences the process of increase-decrease-smooth (Figure 4a and Figure 11a), which is related to the change of bulk density and adsorbed density. The CO2 excess adsorption capacity gradually increases at low fugacity. However, when the fugacity continues to rise, the increase of CO2 bulk density cannot be ignored, and the gap between bulk density and adsorbed density becomes narrow, which results in the decrease of excess adsorption capacity 28. When the CO2 bulk density approaches the adsorbed density, and the density difference tends to be stable, the smooth begins to appear. The crossover can be seen in the curves of CO2 excess adsorption capacity, which is perhaps affected by the property of CO2 as a result of the density change. In a word, the variation trends of simulated results are in accordance with previous results of other researchers

12, 28-31

. The curves of CH4 excess adsorption are different from that of CO2 (Figure

11b). As the fugacity rises, the CH4 excess adsorption capacity slightly decreases, but the


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reduced degree at 293.15K is greater than that at 303.15K. The bulk density is closer to the adsorbed density at low temperature and high pressure, so the variation of CH4 excess adsorption capacity at 293.15K is more evident. Diffusion coefficients of CO2 and CH4 in 1nm slit pore at different temperatures are shown in Table 6. With the increase of temperature, diffusion coefficients of CO2 and CH4 increase gradually, but diffusion coefficient of CH4 is less than that of CO2. To further considerate the influence of temperature on gas diffusion, Arrhenius equation is used to calculate activation energy of the gas diffusion. The equation is as follows:

D = D0 exp(−

Ea ) RT

(7)

Such that D0 is preexponential factor; Ea is activation energy; R is ideal gas constant. Activation energies of CO2 and CH4 are shown in Table 7. Activation energy of CO2 is about 2 times that of CH4, which indicates that CO2 is more sensitive to temperature, and the system constituted by CO2 and coal is more dependent on temperature.

Table 6. Diffusion coefficients of CO2 and CH4 in 1nm slit pore at 8MPa and different temperatures (moisture content 2%) D (×10-8m2/s) Component 293.15K

303.15K

313.15K

CO2

0.676

0.705

0.854

CH4

0.578

0.582

0.641


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Table 7. Activation energies of CO2 and CH4 diffusion Component

Fitting formula

Ea (kJ/mol)

CO2

y=-1026.09x-15.33

8.53

CH4

y=-542.77x-17.13

4.51

3.4 The influence of pore size With the increase of pore size, absolute and excess adsorption capacities gradually decrease (Figure 12). Table 8 shows that as the pore size increases, the isosteric heat of adsorption gradually decreases, indicating that the influence of surrounding pore walls on gas adsorption gradually weakens, and gas molecules adsorbed on the surface is more unstable, which can make adsorption capacity and liberated heat less. As the pore size increases, diffusion coefficients of CO2 and CH4 significantly increase (Table 9). With the increase of pore size, MMFP of CO2 and CH4 gradually increases, but MMFP is always less than the pore size (Table 9), so the main way of diffusion is molecular diffusion. 8

10

1nm-absolute-303.15K-2%-CH4

1nm-absolute-303.15K-2%-CO2 2nm-absolute-303.15K-2%-CO2

9


7


4nm-absolute-303.15K-2%-CO2

8

1nm-excess-303.15K-2%-CO2



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7


6 5 4 3 2 1

1nm-excess-303.15K-2%-CH4

6

2nm-excess-303.15K-2%-CH4 4nm-excess-303.15K-2%-CH4

5 4 3 2 1

0

0 0

1

2

3

4

5

6

7

0

1

2

Fugacity (MPa)

3

4

5

6

7

Fugacity (MPa)

a) CO2

b) CH4

Figure 12. Adsorption capacities of CO2 and CH4 at different pore sizes


8

9

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Table 8. Isosteric adsorption heat of CO2 and CH4 at 303.15K and different pore sizes (moisture content 2%) Isosteric adsorption heat (kJ/mol) Component 1nm

2nm

4nm

CO2

19.90

15.80

13.75

CH4

15.63

12.41

10.58

Table 9. Diffusion coefficients and MMFP of CO2 and CH4 at different pore sizes (303.15K-8MPa-moisture content 2%) D (×10-8m2/s)

λ (nm)

Component 1nm

2nm

4nm

1nm

2nm

4nm

CO2

0.705

1.757

4.522

0.339

0.415

0.667

CH4

0.582

2.082

4.800

0.266

0.345

0.524

4. CONCLUSIONS H2O can strongly adsorb on the carboxyl, while the interaction between H2O and -C-O- is the weakest. The sequence of H2O adsorption is -COOH＞-CHO＞-C=O-＞-C-O-. As the water molecule number increases, the isosteric adsorption heat gradually increases. Water molecules preferentially adsorb on the oxygen functional groups, and then water molecules adsorb each other with hydrogen bond to form clusters in micropores. Water clusters can block the diffusion space, so the behavior on reduced adsorption is owing to the diffusion problem of gas molecules


Page 21 of 25

entering the narrow pores. The adsorption capacity of H2O increases steeply at very low pressure, which is related to the influence of functional group, hydrogen bond and micropore filling. CO2 and CH4 are nonpolar molecules, so they preferentially choose the nonpolar site (-C-C-) to adsorb. -COOH with strong polarity can impact on the chosen adsorption site of CO2 as a result of the greater electric susceptibility relative to CH4, so CO2 will adsorb on the nonpolar site (-C-C-) that is in adjacent -COOH. Relative to CO2, the interaction of CH4 and -C-C- is weaker, indicating that CO2 can adsorb more steadily on the surface of coal. The excess adsorption capacity of CO2 experiences the process of increase-decrease-smooth, which is related to the change of bulk density and adsorbed density. The bulk density is closer to the adsorbed density at low temperature and high pressure, so the variation of CH4 excess adsorption capacity is more evident in this state.

ASSOCIATED CONTENT Supporting Information

CO 2 CH 4

lnD

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T -1 ( K - 1 )

Figure 13. Curves of lnD changing with T-1. Fitting formulas in Table 7 are obtained according to the curves.


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Fugacity can be calculated as the equation:

fi =β i ⋅ Pi

(8)

Such that fi is fugacity; Pi is pressure. Fugacity coefficients (Table 10) can be obtained via the software of Aspen.

Table 10. Fugacity coefficients β at different temperatures and pressures β293.15K

β303.15K

β313.15K

Pressure (MPa) H2 O

CO2

CH4

H2 O

CO2

CH4

H2 O

CO2

CH4

1

0.84

0.94

0.98

0.85

0.95

0.98

0.86

0.95

0.98

2

0.74

0.89

0.95

0.73

0.90

0.96

0.73

0.91

0.96

3

0.78

0.83

0.93

0.77

0.85

0.94

0.76

0.86

0.95

4

0.80

0.78

0.91

0.79

0.80

0.92

0.78

0.82

0.93

5

0.81

0.73

0.89

0.80

0.75

0.90

0.80

0.78

0.91

6

0.82

0.67

0.88

0.81

0.71

0.89

0.81

0.74

0.90

7

0.82

0.67

0.86

0.82

0.66

0.87

0.81

0.70

0.89

8

0.83

0.67

0.84

0.82

0.65

0.86

0.82

0.65

0.87

9

0.83

0.67

0.82

0.83

0.65

0.84

0.82

0.61

0.86

10

0.84

0.67

0.81

0.83

0.65

0.83

0.83

0.57

0.85

AUTHOR INFORMATION Corresponding Author *E-mail address: [email protected]


Page 23 of 25

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ACKNOWLEDGMENT This work was conducted with support from the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation at Southwest Petroleum University. We thank Pro. Yang Zhaozhong and associate Pro. Li Xiaogang for their helpful complete this work.

ABBREVIATIONS CBM, coalbed methane; ECBM, enhanced coalbed methane; MS, materials studio; MSD, mean square displacement; MMFP, mean free path of molecules.

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