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Molecular simulations of methane adsorption behavior in illite nanopores considering basal and edge surfaces You-zhi Hao, Lan-Feng Yuan, Peichao Li, Wenhui Zhao, Daolun Li, and Detang Lu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b00070 • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 31, 2018

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TITLE

Molecular simulations of methane adsorption behavior in illite nanopores considering basal and edge surfaces ∥

Youzhi Hao,† Lanfeng Yuan,‡ Peichao Li,§ Wenhui Zhao,‡ Daolun Li, and Detang Lu†* †

Department of Modern Mechanics, ‡Department of Physical Chemistry, University of Science and Technology

of China, Hefei 230026, China. §

School of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China.

∥

Department of Mathematics, Hefei University of Technology, Hefei 230009, China.

*

E-mail address: [email protected] (D. Lu)

ABSTRACT

Adsorption properties of methane (CH4) impose great influences on shale gas exploration and development. Surface chemistry characteristics of nanopores are key factors in adsorption phenomena. The clay pores in shale formations exhibit basal surface and edge surfaces (mainly as A&C chain surface and B chain surface in illite). Seldom researches relating CH4 adsorption on clay edge surfaces are carried out despite their distinct surface chemistries. In this work, the adsorption of CH4 confined in nanoscale illite slit pores with basal and edge surfaces were investigated by grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. The adsorbed phase density, adsorption capacity, adsorption energy, isosteric heat of adsorption and adsorption sites were calculated and analyzed. The simulated adsorption capacity compares favorably with the available experimental data. The results show that the edge surfaces have weaker van der Waals interactions than the basal surfaces. The adsorption capacity follows the order of basal surface > B chain surface > A&C chain surface, however, the differences of adsorption capacity between these surfaces are small thus edge surfaces cannot be 1 / 35

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ignored in shale formation. Additionally, we confirmed that the adsorbed phase has thickness around 0.9 nm. The pore size determines the interaction overlap strength on the gas molecules and the threshold value of pore size is about 2 nm. The preferential adsorption sites locate differently on edge and basal surfaces. These findings could provide deep insights into CH4 adsorption behavior in natural illite-bearing shales. Key words: shale gas; adsorption; nanopore; illite; edge surface; GCMC; MD

1.

INTRODUCTION

Since the energy shortage is becoming a global issue critically, shale gas has attracted intense attention for its large storage, clean burning as a fuel, and rapid successful commercial development in recent years.1 By extracting shale gas, the U.S. natural gas industry was rejuvenated and the four decade embargo on crude oil was lifted in 2015 by the boom production of shale gas.2 In China, great efforts are also being made to the exploration of shale gas and significant progresses have been achieved until now.3,4 As originally generated from thermogenesis kerogen materials, CH4 is the primary shale gas component that occupies up to 90%.5 CH4 is supposed to be stored in three phases, i.e. free phase (or called bulk phase), adsorbed phase in pores, and dissolved phase in organic matters.6 Gas adsorption due to the guest-host interactions plays a significant role in assessing the gas resource, evaluating economic feasibility, optimizing later-stage production, and maximizing gas recovery in shale reservoirs. The percentage of adsorbed gas was estimated from 20% to 85%.7 Adsorbed gas is important in determining Gas-In-Place (GIP) in shale gas reservoirs, and the long-term shale gas development.8. Adsorption can also change the effective interatomic forces between the surface atoms and consequently change the surface energy and the surface stress when atoms or molecules are physically adsorbed on a solid surface. 9-11. In shale gas reservoirs, organic matters (kerogen, bitumen) and inorganic matters (clay minerals, quartz, carbonite etc.) coexist. The organic matters account for 1 - 10% while the clay minerals and quartz content account 2 / 35


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for 70~90%,12,13 the ratio of clay minerals to quartz varies in different shale gas reservoirs.14 Clay minerals as fine-grained, clastic sedimentary silicates15 are ubiquitous in the shale formations. Illite, kaolinite, and montmorillonite are typical phyllosilicates that most commonly found as the main clay minerals in shale formations.8,16-19 Comparing with quartz, the grain size of clay minerals is much smaller,20 clay minerals tend to form microscopic particles and contribute largely to the pore surface area. Clay minerals were found to adsorb considerable and comparable amount of CH4 in experimental measurements at various temperatures and pressures.19,21-23 Nanopores are abundant in shale gas reservoirs, with pore sizes ranging from a few nanometers to several hundred nanometers. From the pore size distribution of various shale plays defined by the pore surface area from porosimetry analyses, the pores with width lower than 10 nm make dominant contribution to pore surface area.8,21,24,25 Generally, the pore shapes in shale can be categorized as slit and cylindrical, with some other irregular shapes, such as oval, cone, wedge, and inkbottle.26,27 In view of slit pores occupying a vast majority of clay pore networks,28 we focus on investigating the adsorption characteristics of CH4 in slit pores. The clay pores are mainly formed by extremely fine structured, aggregated clay flakes (AlO-O), bridging O atoms coordinated to tetrahedral Si and octahedral Al atoms (>AlO-O-SiSi-O). The structure also carries additional types of surface O atoms resulting from isomorphic substitutions of Si4+ by Al3+, and Al3+ by Mg2+. The exact protonation scheme depends on the pH of environment.61 Here, the surface relaxation tends toward the neutralization of unsaturated valence on individual surface groups, the exposed edge O atoms were protonated in accordance with the expected protonation state at near neutral pH (≈6.5) environment.61-63 We use ‘Oe’ to denote the edge oxygens. Specifically, as shown in Figure 1bc, the tetrahedral >Si-Oe and >AlT-Oe were assigned a single proton, the octahedral >AlO-Oe and >MgO-Oe were doubly protonated, and the >SiT-Oe-AlO< were not protonated. The edge Mg2+ is protonated with two H atoms for Mg-substituted clay edge according to Newton, et al.64 In CLAYFF force field, the ion substitutions cause a recalculation of the partial charges of oxygens, decided by its chemical environment.45 The partial charges for illite atoms including the effect of ion substitutions have been included in CLAYFF.45 However, the partial charge for edge oxygens is not given in CLAYFF. Recently, Tournassat et al. and Lammers et al. investigated the partial charge of edge oxygens illite based on the CLAYFF compatible bond valence method.63,65 In this work, we use this bond valence method based on the bond environment considering the substitution and protonation scheme for edge oxygen atoms. The exact calculation procedure is referred to Lammers et al.63 The calculated edge oxygens partial charge is presented in Table 2. 2.3. Pore structure & simulation details We built three clay pore models based on the types of the illite substrates surface which include basal surface

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(Figure 2ad), A&C chain surface (Figure 2be), and B chain surface (Figure 2cf). The slit pore was constructed with two parallel illite substrates confined in a three dimensional orthorhombic simulation cell. The illite substrates of A&C chain, B chain surfaces were cleaved along the corresponding bond chain directions as mentioned above. The parallel substrates form a slit-like nanopore. The A&C chain slit pore consists of 8 layers of illite that exposes their edge surface pointing inner ward to the pore, while the B chain slit pore consists of 6 layers of illite that exposes their B chain surface pointing inner ward to the pore. The in-plane lengths of the pore substrates are 7.8 ⨯ 8.9 nm for basal slit pore, 8.2 nm ⨯ 7.9 nm for A&C chain slit pore, and 7.2 nm ⨯ 5.9 nm for B chain slit pore. The total surface areas of the basal, A&C chain, and B chain slit pore are 138.84 nm2, 129.56 nm2, and 84.96 nm2, respectively. The vertical length depends on the choice of pore size. The pore size is defined as the vertical distance between the center of nearest atoms that belong separately to the upper and lower pore surfaces as shown in Figure 2. Specially, in the case of A&C chain slit pore, the pore size is not well defined because of the surface roughness, we define the pore size as the distance between the protruded tetrahedral edge oxygens as shown in Figure 2b. The molecular simulations were performed using the open source molecular simulation software LAMMPS 66. The GCMC method, which can exchange the gas number to equilibrium with outer gas reservoirs, was used to improve the understanding of adsorption in microporous media. It is especially suitable for simulations of mixtures and inhomogeneous systems.67 In GCMC, the chemical potentials of the gas (µ), the volume (V), and the temperature (T) of the system are fixed.68 In this work, the reservoir bulk gas pressure (P) and the fugacity coefficient (f) instead of chemical potential (µ) were used in the GCMC accepting criterion.68 The fugacity coefficients of CH4 at different thermodynamic conditions were from Holley et al.69 The simulations were performed using GCMC in µVT ensemble, assisted by MD to keep the system well thermostat and equilibrated. Specifically, the GCMC can produce the expected number of CH4 molecules under selected reservoir temperature

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and pressure; however, the manipulated full-atom gas molecules by GCMC can cause system temperature into large fluctuations (the relative velocity of all atoms in the molecule is zero, this may result in inserted molecules that are systematically too cold). Then MD is necessary in assisting the simulation cell in thermal equilibrium with the imaginary reservoir by fully thermostat the system and guides the system to explore more phase spaces during the time interval when GCMC is paused, thus ensuring the system remains in µVT ensemble. Here, we give the detailed calculation procedure as follows. In the first place, the negative charges caused by the edge surface and substitutions were balanced by the potassium cations (K+). Then the coordinates of H atoms in hydroxyls of illite were fully optimized based on the hydroxyl bond potential of water according the CLAYFF force field. In subsequent simulations, the skeleton structural atoms (Al, Mg, Si, and O) of illite were kept rigid to their crystal coordination, except that hydroxyl H+ and the cation K+ were allowed to be mobile with thermal motions. Cross parameters between unlike atom types in Lennard-Jones potentials are calculated through Lorentz-Berthelot mixing rule (arithmetic mean for σ, and geometric mean for ε ).70,71 Periodic boundary conditions were used in order to avoid finite size effect. The cutoff distance rcut-off for the short-range interactions was set to 1.5 nm and the minimum image convention was satisfied. The interactions longer than rcut-off are omitted in both energy and force computations. The long-range coulomb interaction potential is computed using particle-particle/particle-mesh (PPPM) algorithm72 with Ewald accuracy of 1 × 10-4. The bond interactions involving H atoms in CH4 molecules were constrained using rigid-body algorithm in LAMMPS.73 For each simulation, the GCMC move consists of 5 × 106 insertions, deletions, rotations, and translations of CH4 molecules for equilibration (without any bond/angle MC moves). The first 3 × 106 moves were discarded, and statistics were taken over the rest MC moves. In MD, the newton’s equation of motion as solved using the Verlet algorithm with a 2 fs time step and the Nose-Hoover thermostat was employed to regulate the temperature. We carried a series of CH4 adsorption in basal, A&C chain,

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and B chain slit pores at different pore sizes, pressures, and temperatures. The pore size ranges from 1.0 nm to 5.4 nm, the pressure ranges from 1 to 30 MPa, and the temperature ranges from 293 K to 393 K which are consistent with thermal conditions in shale reservoirs.8,21,24,25 The total simulation time is 10 ns, the first 5 ns were used to equilibrate the system and the last 5 ns were used to collect CH4 trajectories for analysis.

3.

RESULTS AND DISCUSSION

The equilibrium states are reached when the system energy and pore gas amount fluctuate around their mean value over time. Although the K+ ions are thermostated and mobile, they are preferentially located tightly within the specific sites on the pore surface and almost not influenced by the surrounding CH4 molecules during the simulations. 3.1. Total adsorption, absolute adsorption, and excess adsorption The GCMC yields the total gas that would enter the pore systems from ideal gas reservoir. The total gas consists of free gas and adsorbed gas in dynamic equilibration, while the adsorbed gas can be further described in terms of absolute adsorption and excess adsorption. The absolute adsorption is defined as the quantity of gas present only in an adsorbed phase. The excess adsorption (also known as Gibbs adsorption) is additional amount of gas adsorbed in the pore system compared with the amount of gas in the same pore volume in the absence of pore systems.74 The excess adsorption can be measured directly by:

nexc = ntot − ρ g v pore

(2)

where nexc is the excess adsorption, ntot is the total amount of gas in the pore, ρg is the bulk gas density that can be estimated by gas equation of state, and vpore is the total pore volume that is available to the gas that also ignores the adsorption phase volume. In experimental procedure, the absolute adsorption nabs and the excess adsorption nexc can be related by: 11 / 35


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nexc = nabs − va ρ g = nabs −

nabs

ρa

ρg

(3)

 ρg  = nabs  1 −   ρa  where ρa is the adsorbed phase density, and va is the adsorbed phase volume. The nabs can be estimated via nexc from:

nabs = nexc

ρa

(4)

ρa − ρ g

In eq (3) and eq (4), ρa and va are unknown parameters determined by the adsorbed phase which is unable to probe by experiments especially at supercritical conditions in shale gas reservoirs. Many experiments report adsorption data as absolute adsorption by assigning ρa constant values to convert nexc to nabs.75,76 However, in molecular simulations, we can distinguish the adsorbed phase from the free phase through the structural features of density profiles that represent the gas distribution across the pore space.77 3.2. Gas distributions in the pore space The pore size and pressure are important factors that should be taken into consideration. Figure 3 and Figure 4 report the CH4 density profiles across the pore space with relation to pressure and pore size, respectively. The density profiles for the centroid atom C of CH4 molecule were obtained by using statistical bins with thickness of 0.01 nm parallel to the walls and time averaged over many simulation snapshots after system reaching equilibrium. In Figure 3, the temperature is 333 K, and the pore size is 3 nm, while the pressure ranges from 1 to 30 MPa. The thermal conditions in Figure 4 are P = 10 MPa, T = 333 K, with the pore size changes from 1.0 to 5.4 nm. Then we continue to examine the structural features in Figure 3 and Figure 4 to distinguish the adsorbed gas and free gas, respectively. 12 / 35


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3.2.1. Molecular density profile with pressure

The pressure interests us because during shale gas exploration, the pressure drops quickly and thus significantly affects the adsorption behavior. From Figure 3, several features can be derived: (1) two peaks (one higher, one normal) are presented remarkably near the pore surface, this morphology of curves is a phenomenon reported by many simulations,40,41,78-80 a direct evidence that adsorption occurs. The reason for adsorption is the interactions between the pore surface atoms and nearby gas atoms are much stronger than that between the gas molecules themselves.81 The value of the first closest peak near to the clay surface is several times larger than the central zone value, indicating that CH4 molecules accumulate intensely near the pore surface. (2) The free gas density is equal to the bulk density at the same pressure, this further confirms that the simulation models and parameters are reasonable and provide a correct description of the adsorption mechanism on the molecular level. (3) The density profiles curves are asymmetric, especially for the basal slit pore and the A&C chain slit pore. This is due to the imbalance distribution of mobile K+ ions covered on the different opposite surfaces that can be seen in Figure 2. The presence of K+ ions near the surface decreases the adsorption of CH4 that is further explained in section 3.6. (4) At lower pressures (< 5 MPa), only the first layer is formed; as the pressure exceeds 5 MPa, a second layer arises. The CH4 molecules are most strongly adsorbed in the first layer of adsorption and loosely adsorbed in the second layer, and then falls into free phase. (5) In contrast to the basal surface or the B chain surface that have smooth pore surface, the A&C chain density curves have ‘shoulder-like’ curvature due to its surface roughness and follow along the surface geometry structure (Figure 3b). (6) The CH4 molecules are more organized and aligned as evident by the sharper peak of the density curve as pressure increases. The valley goes below the free phase density, lower and lower along with pressure increasing. This means that the gas molecules are more patterned as pressure increases. The asymmetry of the peak also indicates that the CH4 molecules lean toward 13 / 35


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the pore surface. For clarity, we choose one density profile from each clay model with augmented views of adsorbed phase and free phase boundary indicated by the lines as shown in Figure 3d. A distance of about one kinetic diameter of CH4 starting from the end of first adsorption layer to the surface and between two adsorption layers exists as shown in Figure 3d. Each adsorption layer width (dpeak in Figure 3d) is roughly one kinetic diameter of CH4 (0.38 nm according to Ismail et al.82). The distance between the first and the second peaks is also equal to the kinetic diameter of CH4 as shown in Figure 3d, and also roughly equal to the σ value of united-atom CH4 molecule in Lennard-Jones potential.83 An excluded region (shown in Figure 3d) with about 0.12~0.14 nm wide between the pore surface atom and the CH4 molecules is found. We need to add this distance of exclude region from the pore atoms to the width of adsorption layer curve as the adsorption layer thickness. Xiong et al.84 assumed that the first adsorption layer contributed to the adsorption and ignored the contributions of the other layers. In our work, we extend the adsorption layer to the tail of the second layer with peak in the density profiles. The reason is that the gas molecules in the second layer are still moderately influenced by the adsorbent atoms42. In this way of handling, the thickness of adsorbed phase is the distance starting from the pore surface atoms extend to the end of second layer indicated by the dash line in Figure 3d that estimated to around 0.9 nm. This value is close to the measured value of 0.7 – 0.9 nm for CH4 adsorption in mesoporous silica materials.85 The adsorbed amount is obtained by the summation of the accumulated CH4 molecules that belong to this adsorbed phase region.

3.2.2. Molecular density profile with pore size

There are several features of the molecular density curves with relation to pore size in Figure 4. The density peak value and width near the pore surfaces can indicate if there are potential overlaps exerted by two pore surfaces on gas molecules and the adsorbed layer thickness. In pores less than 2 nm, there are two layers forming clearly, 14 / 35


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similar to the larger pores, but the layers are prevented from forming normally as shown by the low density of the peaks in Figure 4. In addition, we can hardly find any signs of free gas. As the pores become smaller, gas molecules residing within such pores become more influenced by the potential superimposed effect of the enclosed pore surface.86,87 The pore tends to “squeeze” the molecule to a very little space that leaves no space for free gas. This phenomenon is also reported by Kadoura et al.40 With the increase of pore size, the peak values lower until 2 nm as indicated by the tendency arrows in Figure 4abc. It indicates that when the pore size exceeds 2 nm, the adsorption affinity becomes weaker due to the short range features of interatomic interactions. This finding is consistent with Chen et al. that the pore size threshold which interaction energy overlaps is about 2 nm.42 3.3. Comparison with experiments The best way to examine the simulation results is to compare them with available experimental data. The simulation results cannot be normalized by the adsorbent weight but should be normalized by the specific surface area SBET of the adsorbent.88 The adsorption capacity at a given pore size is linearly related with SBET as reported by experiments.8,89 We choose two values, 1.4 nm and 3 nm as the simulation pore sizes since adsorption is related with pore size as discussed in section 3.2.2. The 1.4 nm pore contains adsorbed gas and no free gas, while the 3 nm pore has distinguishable free phase. The simulated adsorption capacities (cm3/g) with pore size of 1.4 nm and 3 nm along with the comparison with experimental data from Ji et al.8, Liu et al.90, and Fan et al.91 are presented in Figure 5a. Ji et al. published the experimental adsorption isotherm data of CH4 adsorption on illite-dominated rocks at 338 K with pressure up to 12.5 MPa and SBET = 7.1 m2/g. The experimental data were fitted and represented by the Langmuir isotherm92 with Langmuir parameter VL = 1.77 cm3/g, PL = 6.75 MPa.8 Liu et al. published the experimental adsorption isotherm data based on CH4 adsorption using pure illite samples at temperature of 333 K and pressure up to 18 MPa.90 The measured SBET = 11.2 m2/g, VL = 2.22 cm3/g, and PL = 3.1 MPa.90. Fan et al.91

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conducted experimental CH4 adsorption on illite sample with pressure up to 20 MPa at 333 K with VL = 3.46 cm3/g, PL = 3.41 MPa, SBET = 17.5 m2/g (from Dogan et al.93). We note that the adsorption in Ji, Zhang et al.’s experiment was supposed to be absolute adsorption since it is modelled by the Langmuir equation while excess adsorption cannot. For clarity, we present experimental data from Ji et al., Liu et al., and Fan et al. at with our simulation results at 333 K in the same Figure 5a, since the temperature difference of 5 K is rather small. Additionally, for comparability, all the experimental data were re-normalized by the SBET value of 11.2 m2/g. As shown in Figure 5a, the adsorption curves predict the general tendency of the experimental data. The basal slit pores have slightly higher absolute adsorption than B chain and A&C chain slit pores. However, the difference is not significant, indicating that the edge surface pores contribute comparable adsorption to the total adsorption. The absolute adsorption follows the order of basal > B chain >A&C chain. The reason is that CH4 as a highly symmetry molecule, it is not sensitive to the charge distributions (the lowest non-zero moment of CH4 is octupole moment); instead CH4 is more sensitive to the van der Waals interactions. Because the metal ions (Mg2+, Al3+, Si4+) and H have much lower Lennard-Jones parameter ε as compared with O, K atoms in CLAYFF which leads CH4 more attracted to O, K atoms. The basal surfaces have higher density of O, K atoms and therefore have slightly higher adsorption that than of edge surfaces. The simulated data are higher than experimental data at pore size of 3 nm, but the adsorption amount decreases by a certain amount at 1.4 nm pores. The simulations is larger than experiment at higher pressure (larger than 20 MPa) and goes lower than experiment at lower pressure, the same trend is also observed by Zhai et al.16 Therefore, the simulation results are reasonable and acceptable. The reasons of molecular simulations not matching exactly with experiment are due to: (1) using a single pore size in the simulation is not sufficient, because natural illite shales have variable pore size distributions. (2) The simulation focus on the slit pores, it does not build the

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complex pore structures such as connectivity, tortuosity etc. (3) The natural illite samples are not as ideal as that used in the simulation, some lattice imperfections, surface irregularities and disorder may exist in these samples. (4) Some experimental uncertainties exist, such as the treatment of buoyancy effects in a gravimetric adsorption experiment.50 Additionally, Figure 5b presents the simulated excess adsorption isotherms of different slit pore models with pore size of 1.4 nm and 3 nm, additionally with comparison with simulation data from Chen et al.42 of basal illite surface in 2 nm slit pore. The excess adsorption isotherms are normalized by SBET = 11.2 m2/g as measured by Liu et al.90 to have consistent unit of cm3/g. The excess adsorption in our simulation matches well with simulation data from Chen et al.42 on illite basal surface. As shown in Figure 5b, the excess adsorption of different pore sizes increases to a maximum and then decreases with pressure. The excess adsorption capacity follows the order of basal surface > B chain surface > A&C chain surface, consistent with Figure 5a. The excess adsorption is determined by the relative increase rate of the adsorbed phase density and the free gas density. The maximum excess adsorption occurs around 15 MPa that agrees favorably with simulations from Chen et al.,42 and Xiong et al.94,95 The increase rate of CH4 adsorbed phase density begins to be slower than that of free phase density when pressure exceeds 15 MPa. 3.4. Effect of pore size and temperature on adsorption From the discussion above in section 3.2.2, we know that adsorption is related with the pore size. Here, we examined the effect of the pore size and temperature on absolute and excess adsorption and present it in Figure 6. The adsorption capacities in Figure 6 are normalized by SBET = 11.2 m2/g as measured by Liu et al.90 to have consistent unit of cm3/g. As shown in Figure 6a, the absolute adsorption increases while the excess adsorption decreases with the pore size. The micropores (< 2 nm) have more excess adsorption due to the potential

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overlapping as discussed before. Increase tendency of absolute adsorption capacity exists as the pore size increases from 1.0 nm, through 1.4 nm and reaches 2.0 nm. When the pore size is larger than 2 nm, the adsorption remains almost invariant. Although CH4 molecules are influenced by the strong overlapping potential exerted by the smaller pores,87 the adsorbed phase is confined and cannot be fully shaped, while the larger pores have more space that can accommodate more gas. The gas density decreases with temperature under identical conditions, leading absolute and excess adsorptions reversely related with the temperature as shown in Figure 6b. This is consistent with the gas adsorption capacity decreases with the rise in temperature.96 3.5. Isosteric heat of adsorption Gas adsorption is an exothermal process, and the isosteric heat of adsorption characterizes the adsorption heat released during the adsorption process. The isosteric heat of adsorption is very sensitive to the adsorbent microstructure and thus considered as an indicator of the interaction strength between adsorbates and adsorbents.97 The formula to calculate isosteric heat of adsorption in GCMC is from Nicholson98 and Palace Carvalho99 which stated that it can be obtained from the fluctuations of adsorbate number and the system energy: qst = k BT −

UN − U N

2

− N

N

(5)

2

where qst is isosteric heat of adsorption, kB is Boltzmann constant, T is temperature, U is system potential energy, and N is the number of adsorbate molecules. We calculated qst on the basal, A&C chain and B chain surfaces in 2 nm slit pore at 333 K with pressures and presented the results in Figure 7. The isosteric heat of adsorption qst decreases first then increases with pressure. A reasonable explanation is that at low pressure, gas molecules are preferentially adsorbed to the low energy positions since the illite surfaces are heterogeneous which results high qst. With the process of adsorption, these preferential low energy positions are gradually occupied and gas molecules

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begin to adsorb on high energy positons, thus qst decreases. As more gas molecules are adsorbed at high pressures, the interaction between gas molecules becomes stronger and increases the value of qst.100,101 The calculated qst values also indicate that basal surface has stronger physisorption affinity than edge surfaces, and B chain surface has larger physisorption affinity than A&C chain surface with slight differences, which is consistent with the order of adsorption capacity (basal > B chain > A&C chain). 3.6. Adsorption sites The adsorption site is where adsorbate molecules tend to reside in with respect to the adsorbent pore surface. In this work, the adsorption sites are probed by one CH4 molecule that hovers 0.5 nm above and rolls over the pore surface, and then the interaction energy contour in the xy plane is recorded as shown in Figure 8. As shown in Figure 8, the darker blue color represents lower interaction energy between CH4 molecule and the pore surface. From the contour color, compared with the surface atom patterns, we find the most favorable adsorption sites in basal surface locate at the center of those quasi-hexagonal rings consist of six tetrahedral surface oxygens (Figure 8a). When these quasi-hexagonal sites are adsorbed by K+ ions, the favorable adsorption sites shift to the center of the four quasi-hexagonal center-located K+ ions (Figure 8b), the positions of K+ ions and CH4 are mutual exclusive. The most favorable and stable adsorption sites locate above the grooves that formed by the Al-O-Si which the O is not protonated in A&C chain surface (Figure 8c), and near the octahedral in B chain surface (Figure 8d). To inspect the packed pattern of CH4 molecules in the adsorbed layers on the illite pore surfaces, we extract one molecular simulation snapshot of the first and the second layer on the basal pore surface without K+ in Figure 9ab. We also performed calculation of the corresponding time averaged density map for the first and the second layer as shown in Figure 9cd. We can see that at every moment, CH4 molecules do not locate specifically on the lowest adsorption site due to the thermal motions. This can also be explained that physisorption is reversible and is

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non site-specific.102 However, the time averaged density map of the first adsorption layer (Figure 9c) showed that CH4 molecules locate on the preferential sites, consist with the analysis in Figure 8a. In contrast to the first adsorption layer, the preferential sites of second adsorption layer are irregular and unpredictable (Figure 9d), because they are also affected by the first adsorption layer, and the interaction with the pore surface atoms is greatly reduced. 3.7. Adsorbed phase density As mentioned before, the adsorbed phase density ρa is an important parameter that connects the excess and absolute adsorption in experiments. However, ρa cannot be measured or derived directly from experiments; it is rather unclear for experimentalist to know which state (liquid or gas) the adsorption region belongs, especially under supercritical condition in shale gas reservoirs. There are many discussions on the determination on ρa. A commonly used approximation is the liquid density value of 0.421 g/cm3 at the atmospheric pressure boiling point.75,76 The 0.375 g/cm3 density of CH4 gas measured at extremely high pressures is also used in experiment measurements.103 Another approach is to extrapolate the linear region of the excess adsorption isotherm to intersect with pressure axis at Pintersect, then ρa is the bulk gas density from EOS at this pressure Pintersect.74 All these approaches are based on limited experimental data and ρa are treated as constant.87 In this section, we will discuss ρa based on our simulation results. As mentioned above, we calculated the adsorbed phase volume from the surface extending to the distance of adsorption region. Using absolute adsorption divided by the adsorbed phase volume, we calculated ρa with pressure at specific temperature, compared with ρa from other works and present it in Figure 10. As shown in Figure 10, the simulated free gas density matches well with the bulk gas density calculated from EOS. The adsorbed phase volume remains constant, while ρa dynamically changes at different thermal conditions. The bulk density increases nearly linear with pressure. ρa follows the order

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of basal > B chain > A&C chain. ρa is much lower than the liquid density of CH4 (0.421 g/cm3) or the density at extremely high pressure (0.375 g/cm3) that assumed in experiments. This also indicates that the adsorbed CH4 is not liquefied, as supported by the CH4 is in supercritical state in shale reservoir conditions (>critical temperature of -189 K). Our simulations propose that the ρa dynamically changes from 0.016 to 0.233 g/cm3 as pressure increases from 1 to 30 MPa. The adsorbed phase density is assumed 0.21 - 0.46 g/cm3 fitted by SDR model by Pan et al.104. Riewchotisakul et al.105 predicted CH4 adsorbed phase density ρads = 0.1057*ln(P)-0.4629, where P is in the unit of psi at 353 K using molecular dynamics simulation of methane in carbon nanotubes. Zhang et al.106 calculated the ρa of CH4 on dry and moist coal as a function of pressure at 308 K as shown in Figure 10. It can be seen that this adsorbed phase density is a little larger than our results since coal have higher affinity to methane than clays. Liang et al.107 and Xiong et al.84 adopted empirical equation proposed by Ozawa et al.108 to get ρa at specific temperature and ignores pressure dependence. The equation is ρ ad = ρb exp(−0.0025 × (T − Tb ))

(6)

where ρb is the methane density at a boiling point (0.4224 g/cm3), T is the experiment temperature in K, and Tb is the methane boiling point temperature at an atmospheric pressure (111.7 K). Using Ozawa et al.’s equation at 333 K, ρad = 0.243 g/cm3. This value is much smaller than the liquid methane density and closer with our simulation results of ρad (0.016 - 0.233 g/cm3) at higher pressures, the difference is that Ozawa’s equation ignores the influences of the pressure. In summary, the evaluation of ρa needs correction based on the thermal conditions. These simulation data provide a useful reference for converting excess adsorption to absolute adsorption in experiments according to eq (4).

4.

CONCLUSIONS

In this work, GCMC combined with MD simulations were conducted to investigate the adsorption properties 21 / 35


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of pure CH4 on dry illite slit nanopores considering various factors such as edge surface chemistry, pressure, pore size, and temperature. The absolute and excess surface adsorptions are derived based on the features of density profiles of CH4 across the pore space. The simulation results show reasonable agreement with the experimental data on natural illite-rich samples. The main conclusions are drawn: (1) Molecular simulations give a direct and clear description of the CH4 distribution in the pore space. The gas accumulation at the pore surface is an obvious adsorption phenomenon. We distinguished the adsorbed phase from the free phase based on the density profiles. (2) The adsorbed phase has thickness around 0.9 nm and contains one adsorption layer at low pressure ( B chain surface > A&C chain surface, as evidenced by the isosteric heat of adsorption. However, the adsorption capacity differences between these surfaces are small. The edge surface pores have comparable adsorption capacity with basal surface pore thus cannot be ignored especially in shale formations. The preferential adsorption sites locate differently based on these clay surfaces. (4) The pore size determines the interaction overlap strength on the gas molecules. The threshold pore size is around 2 nm. The gas in adsorbed phase dominates in the slit micropores that are less than 2 nm. Absolute adsorption increases while the excess adsorption decreases with the pore size. Micropores have more excess adsorption but less absolute adsorption than mesopores (> 2nm). (5) The adsorption decrease with temperature as adsorption is exothermal process. (6) The adsorbed phase density increases with pressure, but it is much lower than the CH4 liquid density at normal boiling point and the adsorbed phase is clearly not liquefied. These findings may provide useful information for understanding the gas adsorption behavior in nanoscale clay pores. In the future work, we hope to explore the adsorption of CH4 in clay minerals while considering the edge surfaces in the presence of water, because water cannot be avoided especially during the hydraulic fracturing process and the clay

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minerals have hydrophilic nature.

ASSOCIATED CONTENT

Supporting Information The Supporting Information includes (1) the structural data (volume and surface) of the illite pore structures (Table S1), (2) The CLAYFF force field parameters for illite atoms (Table S2), (3) The basal, A&C chain and B chain slit pore models in xyz format, and (4) The running script in LAMMPS used in this work as txt file. This material is available free of charge via the Internet at ***

AUTHOR INFORMATION

Corresponding Author * Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China. E-mail: [email protected]. ORCID Detang Lu: 0000-0002-4571-0810 Youzhi Hao: 0000-0002-7622-4858 Peichao Li: 0000-0001-5295-3805 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS

This work was financially supported by the CAS Strategic Priority Research Program (XDB10030402), CNPC-CAS Strategic Cooperation Research Program (2015A-4812), and National Science and Technology Major 23 / 35


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Project (2017ZX05009005-002, 201Su6ZX05053). These simulations were performed at the Supercomputing Center at University of Science and Technology of China.

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(79) Nguyen, C. V.; Phan, C. M.; Ang, H. M.; Nakahara, H.; Shibata, O.; Moroi, Y., Molecular dynamics investigation on adsorption layer of alcohols at the air/brine interface. Langmuir 2015, 31 (1), 50-56. (80) Li, Z. F.; Van Dyk, A. K.; Fitzwater, S. J.; Fichthorn, K. A.; Milner, S. T., Atomistic molecular dynamics simulations of charged latex particle surfaces in aqueous solution. Langmuir 2016, 32 (2), 428-441. (81) Vadakkepatt, A.; Dong, Y.; Lichter, S.; Martini, A., Effect of molecular structure on liquid slip. Phys. Rev. E 2011, 84 (6). (82) Ismail, A. F.; Khulbe, K. C.; Matsuura, T., Gas separation membranes. Springer: 2015. (83) Mosher, K.; He, J. J.; Liu, Y. Y.; Rupp, E.; Wilcox, J., Molecular simulation of methane adsorption in microand mesoporous carbons with applications to coal and gas shale systems. Int. J. Coal. Geol. 2013, 109, 36-44. (84) Xiong, J.; Liu, X.; Liang, L.; Zeng, Q., Adsorption of methane in organic-rich shale nanopores: An experimental and molecular simulation study. Fuel 2017, 200, 299-315. (85) Chiang, W. S.; Fratin, E.; Baglion, P.; Chen, J. H.; Liu, Y., Pore size effect on methane adsorption in mesoporous silica materials studied by small-angle neutron scattering. Langmuir 2016, 32 (35), 8849-8857. (86) Xiong, J.; Liu, X.; Liang, L.; Zeng, Q., Methane adsorption on carbon models of the organic matter of organic-rich shales. Energy Fuels 2017, 31 (2), 1489-1501. (87) Heller, R.; Zoback, M., Adsorption of methane and carbon dioxide on gas shale and pure mineral samples. Journal of Unconventional Oil and Gas Resources 2014, 8, 14-24. (88) Chen, G.; Lu, S.; Zhang, J.; Xue, Q.; Han, T.; Xue, H.; Tian, S.; Li, J.; Xu, C.; Pervukhina, M., Keys to linking GCMC simulations and shale gas adsorption experiments. Fuel 2017, 199, 14-21. (89) Wang, Y.; Zhu, Y. M.; Liu, S. M.; Zhang, R., Pore characterization and its impact on methane adsorption capacity for organic-rich marine shales. Fuel 2016, 181, 227-237. (90) Liu, D.; Yuan, P.; Liu, H.; Li, T.; Tan, D.; Yuan, W.; He, H., High-pressure adsorption of methane on montmorillonite, kaolinite and illite. Appl. Clay Sci. 2013, 85, 25-30. (91) Fan, E.; Tang, S.; Zhang, C.; Guo, Q.; Sun, C., Methane sorption capacity of organics and clays in high-over matured shale-gas systems. Energy Exploration & Exploitation 2014, 32 (6), 927-942. (92) Langmuir, I., The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc. 1918, 40 (9), 1361-1403. (93) Dogan, M.; Dogan, A. U.; Yesilyurt, F.; Alaygut, D.; Buckner, I.; Wurster, D. E., Baseline studies of the Clay Minerals Society special clays: specific surface area by the Brunauer Emmett Teller (BET) method. Clays Clay Miner. 2007, 55 (5), 534-541. (94) Xiong, J.; Liu, K.; Liu, X.; Liang, L.; Zeng, Q., Molecular simulation of methane adsorption in slit-like quartz pores. RSC Advances 2016, 6 (112), 110808-110819. (95) Xiong, J.; Liu, X.-J.; Liang, L.-X.; Zeng, Q., Investigation of methane adsorption on chlorite by grand canonical Monte Carlo simulations. Petroleum Science 2017, 14 (1), 37-49. (96) Li, G.; Meng, Z., A preliminary investigation of CH 4 diffusion through gas shale in the Paleozoic Longmaxi Formation, Southern Sichuan Basin, China. J. Nat. Gas. Sci. Eng. 2016. (97) Vuong, T.; Monson, P., Monte Carlo simulation studies of heats of adsorption in heterogeneous solids. Langmuir 1996, 12 (22), 5425-5432. (98) Nicholson, D., Computer simulation and the statistical mechanics of adsorption. Academic Press: 1982. (99) Palace Carvalho, A. J.; Ferreira, T.; Estêvão Candeias, A. J.; Prates Ramalho, J. P., Molecular simulations of nitrogen adsorption in pure silica MCM-41 materials. Journal of Molecular Structure: THEOCHEM 2005, 729 (1-2), 65-69.

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(100) Tang, X.; Ripepi, N.; Valentine, K. A.; Keles, C.; Long, T.; Gonciaruk, A., Water vapor sorption on Marcellus shale: measurement, modeling and thermodynamic analysis. Fuel 2017, 209, 606-614. (101) Wang, Z.; Li, Y.; Liu, H.; Zeng, F.; Guo, P.; Jiang, W., Study on the Adsorption, Diffusion and Permeation Selectivity of Shale Gas in Organics. Energies 2017, 10 (1), 142. (102) Clarkson, C. R.; Haghshenas, B. In Modeling of supercritical fluid adsorption on organic-rich shales and coal, SPE Unconventional Resources Conference-USA, 2013; Society of Petroleum Engineers: 2013. (103) Yee, D.; Seidle, J. P.; Hanson, W. B., Gas sorption on coal and measurement of gas content: chapter 9. 1993. (104) Pan, L.; Xiao, X. M.; Tian, H.; Zhou, Q.; Cheng, P., Geological models of gas in place of the Longmaxi shale in Southeast Chongqing, South China. Mar. Petrol. Geol. 2016, 73, 433-444. (105) Riewchotisakul, S.; Akkutlu, I. Y., Adsorption-Enhanced Transport of Hydrocarbons in Organic Nanopores. SPE Journal 2016. (106) Zhang, J. F.; Clennell, M. B.; Dewhurst, D. N.; Liu, K. Y., Combined Monte Carlo and molecular dynamics simulation of methane adsorption on dry and moist coal. Fuel 2014, 122, 186-197. (107) Liang, L. X.; Luo, D. X.; Liu, X. J.; Xiong, J., Experimental study on the wettability and adsorption characteristics of Longmaxi Formation shale in the Sichuan Basin, China. J. Nat. Gas. Sci. Eng. 2016, 33, 1107-1118. (108) Ozawa, S.; Kusumi, S.; Ogino, Y., Physical adsorption of gases at high pressure. IV. An improvement of the Dubinin—Astakhov adsorption equation. J. Colloid Interface Sci. 1976, 56 (1), 83-91.

List of tables Table 1. Lennard-Jones potential parameters and partial charges for rigid all-atom CH4 model based on CVFF force field. The force field parameters for illite atoms are from CLAYFF and provided in Table S1. Atom type

ε (kcal/mol)

σ (nm)

q (e)

C (CH4)

0.160

0.3474

-0.4000

H (CH4)

0.010

0.2450

0.1000

Table 2. The partial charges of edge oxygen (Oe) based on bond valence coordination calculation edge oxygen

q (e)

edge oxygen

q (e)

>AlO-Oe-H

-1.18750

>SiT-Oe-H

-0.9500

>MgO-Oe-H

-1.31833

>AlT-Oe-H

-1.06875

>AlO-Oe-H2

-0.6125

>AlO-Oe-SiT

-1.2875

>MgO-Oe-H2

-0.743330

>MgO-Oe-SiT

-1.41833

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Energy & Fuels

List of figures

Figure 1. (a) The crystal structure of illite with one octahedral Al3+ substituted by Mg2+ and one tetrahedral Si4+ substituted by Al3+; (b) A&C chains edge surface, and (c) B chain edge surface with edge oxygen protonation schemes (gray H atoms). The edge surfaces are viewed along the direction of A&C ((110) or (11 0̅ )) and B bond chains (010), respectively. Color scheme: yellow, silicon; pink, aluminum; green, magnesium; red, oxygen; purple, potasium; white, hydrogen; gray, protonation hydrogen.

pore size

pore size

pore size

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 30 of 35

Figure 2. Illustration of molecular model of illite (a) basal slit pore, (b) A&C chain slit pore and (c) B chain slit pore with adsorbate CH4 in equilibrium state (from orthographic view) and (d) basal slit pore, (e) A&C chain slit pore, (f) B chain slit pore (from pespective view). Color scheme: yellow, silicon; pink, aluminum; green, magnesium; red, oxygen; purple, potasium; cyan, carbon; white, hydrogen.

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Page 31 of 35

(b) basal

0.7 0.6 mass density (g/cm3)

0.35

1 MPa 5 MPa 10 MPa 15 MPa 20 MPa 25 MPa 30 MPa

0.5 0.4 0.3 0.2

0.15 0.10

1.5

2.0

2.5 3.0 distance (nm)

B chain

3.5

1.0

4.0

(d)0.7


0.45 0.40 0.35

1.5


3.0

30 MPa (basal) 30 MPa (B chain) 30 MPa (A&C chain)

adsorbed gas

0.6

3.5

4.0

adsorbed gas

≈0.38 nm ≈0.38 nm

mass density (g/cm3)

1.0


0.20

0.00

0.0

0.50

0.25

0.05

0.1

(c)


A&C chain

0.30 mass density (g/cm3)

(a)

0.30 0.25 0.20 0.15

0.5

first adsorption layer

0.4

second adsorption layer

0.3 pore surface

pore surface

free gas

0.2

0.10

0.1

0.05

d peak d peak

d peak d peak 0.0

0.00 1.5

2.0

2.5

3.0 distance (nm)

3.5

4.0

4.5

exclusive region

1.0

1.5

exclusive region

2.0


3.5

4.0

Figure 3. Time averaged CH4 density profiles of illite (a) basal slit pores, (b) A&C chain slit pores and (c) B chain slit pores at pore size of 3 nm with different pressures. (d) The comparasion of density profiles of basal, A&C chain, and B chain slit pores at 30 MPa, with analysis on the morphologies of these curves. The temperature is 333 K. The horizonal axis represents the distance to the lower boundary of the simulation box.

basal

0.4

pore size = 2 nm

peak tendency

1.0 nm 1.4 nm 2.0 nm 2.4 nm 3.4 nm 4.4 nm 5.4 nm

0.3

0.2

(b)

A&C chain pore size = 2 nm

0.20 mass density (g/cm3)

(a)


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

Energy & Fuels

peak tendency

1.0 nm 1.4 nm 2.0 nm 2.4 nm 3.4 nm 4.4 nm 5.4 nm

0.15

0.10

0.05

0.1

0.00

0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 distance (nm)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 distance (nm)

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Energy & Fuels

(c)0.30

B chain


1.0 nm 1.4 nm 2.0 nm 2.4 nm 3.4 nm 4.4 nm 5.4 nm

pore size = 2 nm

peak tendency

0.25 0.20 0.15 0.10 0.05 0.00 1

2

3

4 5 distance (nm)

6

7

8

Figure 4. Time averaged CH4 density profiles of illite (a) basal, (b) A&C chain, and (c) B chain slit pores with different pore sizes at 333 K, 10 MPa along the direction normal to the clay surface. The horizonal axis represents the distance to the lower boundary of the simulation box.

2.5 absolute adsorption (cm3/g)

(b) 0.8

experiment (Liu, Yuan et al. 2013) experiment (Ji, Zhang et al. 2012) experiment (Fan, Tang et al. 2014) simulation (3.0 nm - basal) simulation (3.0 nm - A&C chain) simulation (3.0 nm - B chain) simulation (1.4 nm - basal) simulation (1.4 nm - A&C chain) simulation (1.4 nm - B chain)

3.0

2.0

0.7 excess adsorption (cm3/g)

(a)

1.5 1.0

0.6 0.5 0.4 simulation ( 3.0 nm - basal) simulation ( 3.0 nm - A&C chain) simulation ( 3.0 nm - B chain) simulation ( 1.4 nm - basal) simulation ( 1.4 nm - A&C chain) simulation ( 1.4 nm - B chain) simulation (Chen et al., 2016, 2nm basal)

0.3 0.2

0.5

0.1 0.0 0

5

10

15

20

25

0.0

30

0

5

Pressure (MPa)

10

15 20 Pressure (MPa)

25

30

Figure 5. (a) Comparison between the experimental adsorption data from Ji et al.,8 Liu et al.,90 and Fan et al.91 on illite samples with simulated adsorption isotherms of illite slit pores with pore size of 1.4 nm and 3 nm at 333 K. The hollow symbols represent extended experimental data from fitting Langmuir equation that were not measured experimentally at higher pressures. (b) The simulated excess adsorption isotherms with pressure of 333 K, pore size of 1.4 nm and 3 nm, respectively. In addition with the simulation data of excess adsorption from Chen et al.42 in 2 nm illite slit pore with basal surface. All the adsorption isotherms are normalized by SBET = 11.2 m2/g as measured by Liu et al.90

(a)1.50

(b)1.8

absolute adsorption - basal absolute adsorption - A&C chain absolute adsorption - B chain excess adsorption - basal excess adsorption - A&C chain excess adsorption - B chain

1.6 adsorption capacity (cm3/g)

1.25 adsorption capacity (cm3/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

Page 32 of 35

absolute adsorption - basal absolute adsorption - A&C chain absolute adsorption - B chain excess adsorption - basal excess adsorption - A&C chain excess adsorption - B chain

1.00

0.75

0.50

1.4 1.2 1.0 0.8 0.6 0.4 0.2

0.25 1

2

3 4 Pore size (nm)

5

6

280

300

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320

340 360 Temperature (K)

380

400

Page 33 of 35

Figure 6. (a) Pore size dependence (333 K, 10 MPa) and (b) temperature denpendence (3 nm pore, 10 MPa) of simulated adsorption capacity in different illite slit pores. The adsorption capacity is normalized by the BET surface area of 11.2 m2/g as measured on illite sample by Liu et al to have consistent unit of cm3/g. 2.0 Isosteric heat of adsorption (kcal/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

Energy & Fuels

basal A&C chain B chain

1.9

1.8

1.7

1.6

0

5 Pressure (MPa)

10

Figure 7. The calculated isosteric heat of adsorption (kcal/mol) of basal surface, A&C chain surface, and B chain surface in 2 nm slit pore at 333 K with different pressures.

Figure 8. Contour plots of the interaction energy bewteen one CH4 molecule and (a) basal pore surface (covered without K+ ions), (b) basal pore surface (covered with K+ ions), (c) A&C chain pore surface, and (d) B

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Energy & Fuels

chain pore surface. Insets: molecular illustration of the location of the preferential adsorption sites on the pore surfaces.

(c)

CH4 number

first adsorption layer (time averaged)

(d)

second adsorption layer (time averaged)

0.07300

CH4 number 0.03630

4.0

4.0 0.06472

0.03309

3.5

3.5 0.05645

0.02987

3.0

3.0

2.5 0.03990

2.0

0.02666

Y (nm)

0.04817

Y (nm)

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 34 of 35

2.5 0.02345

2.0

0.03163

1.5

0.02024

1.5 0.02335

1.0

0.01507

0.5

0.006800

0.0 0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.01702

1.0

0.01381

0.5

0.01060

0.0 0.5

X (nm)

1.0

1.5

2.0

2.5

3.0

3.5

X (nm)

Figure 9. Molecular simulation snapshot of the distribution of (a) the first adsorption layer, (b) the second adsorption layer CH4 molecules on the basal pore surface without K+ ions in xy plane at 30 MPa. The time averaged distribution map of CH4 on the basal pore surface without K+ ions in xy plane at pressure of 30 MPa, (c) the first adsorption layer, (d) the second adsorption layer, only part of the xy plane is shown for clarity. Color scheme for (a)(b): yellow, silicon; pink, aluminum; green, magnesium; red, oxygen; purple, potasium; white, hydrogen.

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Page 35 of 35

0.45 0.40 0.35 mass density (g/cm3)

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

Energy & Fuels

0.30 0.25 0.20 0.15

adsorbed phase - basal adsorbed phase - A&C chain adsorbed phase - B chain bulk gas density from EOS free phase - basal free phase - A&C chain free phase - B chain Riewchotisakul, 2016 Zhang et al. 2014 Ozawa et al. 1976 Yee et al. 1993 liquid density

0.10 0.05 0.00 0

5

10

15

20

25

30

Pressure (MPa)

Figure 10. Adsorbed phase density ρa and free phase density with relation to pressure in 3 nm illite slit pores at 333 K with different pore surfaces, compared with bulk gas density and values from other works.

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Molecular Simulations of Methane Adsorption ... - ACS Publications

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