Displacement of Methane by Coadsorbed Carbon Dioxide Is

Article pubs.acs.org/JPCC

Displacement of Methane by Coadsorbed Carbon Dioxide Is Facilitated In Narrow Carbon Nanopores Piotr Kowalczyk,*,† Piotr A. Gauden,‡ Artur P. Terzyk,‡ Sylwester Furmaniak,‡ and Peter J. F. Harris§ †

Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P.O. Box U1987, Perth, 6845 Western Australia, Australia ‡ Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, 87-100 Torun, Poland § Centre for Advanced Microscopy, University of Reading, Whiteknights, Reading RG6 6AF, United Kingdom S Supporting Information *

ABSTRACT: By using simulation methods, we studied the adsorption of binary CO2−CH4 mixtures on various CH4 preadsorbed carbonaceous materials (e.g., triply periodic carbon minimal surfaces, slit-shaped carbon micropores, and Harris’s virtual porous carbons) at 293 K. Regardless of the different micropore geometry, two-stage mechanism of CH4 displacement from carbon nanospaces by coadsorbed CO2 has been proposed. In the first stage, the coadsorbed CO2 molecules induced the enhancement of CH4 adsorbed amount. In the second stage, the stronger affinity of CO2 to flat/ curved graphitic surfaces as well as CO2−CO2 interactions cause the displacement of CH4 molecules from carbonaceous materials. The operating conditions of CO2-induced cleaning of the adsorbed phase from CH4 mixture component strongly depend on the size of the carbon micropores, but, in general, the enhanced adsorption field in narrow carbon ultramicropores facilitates the nonreactive displacement of CH4 by coadsorbed CO2. This is because in narrow carbon ultramicropores the equilibrium CO2/CH4 selectivity (i.e., preferential adsorption toward CO2) increased significantly. The adsorption field in wider micropores (i.e., the overall surface energy) for both CO2 and CH4 is very similar, which decreases the preferential CO2 adsorption. This suppresses the displacement of CH4 by coadsorbed CO2 and assists further adsorption of CH4 from the bulk mixture (i.e., CO2/CH4 mixing in adsorbed phase).

I. INTRODUCTION Recent experimental studies of the competitive adsorption of CO2 and CH4 on coal seams have revealed that CO2 molecules injected into carbonaceous pores displace preadsorbed CH4 molecules, thereby offering an enhancement of CH4 recovery.1−3 This scenario, also known as enhanced coalbed methane recovery (ECBM),4−10 seems to be an attractive method to reduce the amount of anthropogenic CO2. This is because the injection of CO2 into methane-rich coal seams (or other geological formations, such as: depleted oil and gas fields, unmineable coal, etc.) seems to enhance CH4 recovery by a factor of two to three times over that achieved in simple desorption by pressure drawdown.1 Therefore, the cost of CO2 geosequestration can be offset by ECMB. Coal is a complex heterogeneous sedimentary organic rock made of fossilized plant matter and incorporated inorganic matter.11−13 The maceral compositions indicate the botanic precursors and depositional histories for a coal and are divided into three groups:11 “vitrinite” (remains of various plant matter such as bark, stems, roots, etc.), “liptinite” (cuticles, spores, resin, and algal remains), and “inertinite” (oxidized plant material, fungal remains, fossilized char, coal, etc.). Various molecular representations for the structure of coal have been proposed.12 However, it is commonly accepted that coal is a 3-D macromolecular network structure consisting of polyaromatic © 2012 American Chemical Society

and alkyl-substituted aromatic units linked by covalent and noncovalent bonds (hydrogen bonds, van der Waals interactions, electrostatic interactions, and π−π interactions).12 The number/type of functional groups attached to the macromolecular network, the amount of preadsorbed water, and the content of mineral ash strongly depend on the origin of the coal.11,14,15 Notice, that even for the same mine the coal structure and adsorption properties depend on the depth (i.e., they are function of increased stress). Therefore, it is necessary to simplify the complex structure of coal to gain some basic insight into its adsorption/elastic properties. Let us consider the porosity of coals. It is commonly known that coal is predominantly composed of carbonaceous micropores smaller than 2 nm in diameter and mesopores ranging between 2 and 50 nm, with micropores making the largest contribution into the adsorption capacity.16−18 Narrow carbonaceous micropores of irregular shapes and various topologies are partially/completely filled by guest molecules, such as CH4 and higher molecular weight hydrocarbons. Those molecules are trapped in narrow micropores by the enhanced adsorption potential (i.e., surface forces). Therefore, to first Received: March 23, 2012 Revised: June 1, 2012 Published: June 6, 2012 13640

dx.doi.org/10.1021/jp302776z | J. Phys. Chem. C 2012, 116, 13640−13649

The Journal of Physical Chemistry C

Article

distance-dependent site−site interaction potential. Depending on the type of the site, uij(r) is given by a pairwise dispersion or electrostatic interaction energy. We assumed that the dispersion energy of interaction is given by the (12,6) Lennard-Jones equation41−44

approximation carbonaceous materials are good candidates to study the adsorption/coadsorption properties of some coals, such as anthracite. Note that the carbon content in anthracite is between 92 and 98%.11 Although we acknowledge the importance of H 2 O sorption in coals and activated carbons,19−27 this effect is not considered in this article. To gain some basic insight into the mechanism of nonreactive CH4 displacement from small carbonaceous micropores upon injection of CO2, we focus on the adsorption of binary CO2−CH4 mixtures on selected CH4 preadsorbed carbonaceous materials, including: triply periodic carbon minimal surfaces (Schwarz’s Primitive and Schoen’s Gyroid carbon minimal surfaces),28−31 slit-shaped carbon micropores,32−36 and Harris’s virtual porous carbons (VPCs)37−40 at 293 K. Intuitively, one should expect that CO2 molecules gradually displace preadsorbed CH4 ones from carbonaceous micropores. This is because both CO2−CO2 interactions as well as the interactions of CO2 molecules with flat/curved graphitic fragments (i.e., surface energy) are greater as compared with their CH4 counterparts.1 Therefore, upon adsorption of the binary CO 2 −CH 4 mixtures on CH 4 preadsorbed carbonaceous materials, the composition of the binary mixture in micropores will be continuously enriched with CO2 mixture component until the complete displacement of preadsorbed CH4 molecules. Note that following to this generally accepted scenario an increase in the partial pressure of CO2 in the bulk mixture should result in a monotonic decrease in the pore density of preadsorbed CH4 fluid. The bulk mixture enriched with recovered CH4 can then be used as a viable energy source. The molecular simulations performed here help us to understand the general mechanism of the binary CO2−CH4 mixture adsorption on CH4 preadsorbed carbonaceous materials at 293 K. We would like to answer the following question: how the enhanced solid−fluid potential in narrow carbon micropores will impact the displacement of preadsorbed CH4 upon coadsorption of CO2. It is important to point out that in our modeling we assumed fast equilibration between the bulk mixture and the carbonaceous material (i.e., we excluded any high-energetic kinetic barriers limiting the diffusion of mixture components from the bulk mixture to the micropores). The real materials, including coals, do not always fulfill this condition.1,11 However, to the best of our knowledge, the microscopic mechanism of CH4 displacement from fully accessible carbonaceous micropores upon CO2 coadsorption has not been investigated so far, and this is the primary goal of the current work.

uijA,B

j

(2) A,B

and ε , were A,B

Table 1. Lennard-Jones Parameters and Partial Charges for the Three-Site Carbon Dioxide Model51 a CO2

σff (Å)

εff/kB (K)

lCO (Å)

q (e)

C: 2.824 O: 3.026 C−O: 2.925

C: 28.68 O: 82.0 C−O: 48.495

1.162

O: −0.332 C: 0.664

a C−O denotes LJ parameters obtained from Lorentz−Berthelot mixing rule.41,42 lCO is the C−O bond length.

Table 2. Lennard-Jones Parameters and Partial Charges for the Five-Site Methane Model47 a CH4

σff (Å)

εff/kB (K)

lCH (Å)

q (e)

C: 3.4 H: 2.65 C−H: 3.025

C: 55.055 H: 7.901 C−H: 30.6

1.09

C: −0.66 H: 0.165

C−H denotes LJ parameters fitted to experimental data. lCH is the C−H bond length.

a

We modeled electrostatic force via the Coulomb law of electrostatic potential41−44

uiA,B ,j

A B 1 qi qj = 4πε0 rijA,B

(3)

where ε0 is the permittivity of free space (ε0 = 8.85419 × 10−12 C2 N−1 m−2), qAi denotes the value of the point charge i on the molecule A, qBj denotes the value of the point charge j on the molecule B, and rA,B ij is the distance between two charges i and j on the molecules A and B, respectively. The values of the point charges were taken from Tables 1 and 2. The applied force fields were validated against known experimental data in a series of our previous works.45−47 II.II. Carbonaceous Porous Materials: Solid−Fluid Interactions. Triply periodic carbon minimal surfaces as well as VPCs were modeled by fully atomistic representation. The structures of the unit cell for two studied carbonaceous triply minimal surfaces (see Figure 1), that is, Schwarz’s P-surface (P denotes primitive) and Schoen’s G-surface (G denotes gyroid), were taken from previous works.28−30 These stable periodic graphitic structures (known also as “Schwarzites”) with negative curvature analogous to zeolites were theoretically predicted in 1991. Energetic calculations showed that Schwarzites carbon structures are more stable than C60 buckminsterfullerene. This stability comes from the fact that in the heptagonal or octagonal carbon rings there is very little mechanical strain, thus preserving the sp2-like nature of graphite. The ordered channels and labyrinths of model Schwarzites structures are attractive for potential separation

∑ ∑ uij(rijA,B) i

= 4ε

⎛ A,B ⎞6 ⎤ ⎟ ⎜σ ⎟ ⎥ ⎢⎜ r A,B ⎟ − ⎜ r A,B ⎟ ⎥ ⎝ ij ⎠ ⎦ ⎣⎝ ij ⎠ 12 A,B ⎞

The parameters of the potential, that is, σ taken from Tables 1 and 2.

II. SIMULATION DETAILS II.I. Potential Models: Fluid−Fluid Interactions. In the current work we used fully atomistic representation for CO2 and CH4. In the atomistic simulations, we expressed the intermolecular potential between two molecules A and B as a sum of site−site terms41−44 U A,B(q) =

⎡⎛

A,B⎢⎜ σ

(1)

where the sum is taken over all sites i of the molecule A and the sites j of the molecule B, q ≡ {rAi − rBj }i,j is the set of separations between each atom in the molecule A and each atom in the A B molecule B, rA,B ij = ∥ri − rj ∥ is the distance between two sites i and j on the molecules A and B, respectively, and uij(r) denotes 13641



Article

Figure 1. Structures of the unit cell for two carbonaceous triply minimal surfaces: Schwarz’s P-surface (a) and Schoen’s G-surface (b).29,30 Similar to zeolites, Schwarzites carbon structures are characterized by negative curvature.

of fluid mixtures. Two samples of Harris’ VPCs (S00 and S24) were taken from our previous works37−39 (see Figures 1S−3S in the Supporting Information). The solid−fluid interactions were computed from eq 2 by summing all dispersion interactions between carbon atoms and Lennard-Jones dispersion sites of adsorbate molecules. Here we assumed that all studied carbonaceous materials are uncharged. As previously, for carbon atoms, we used (12,6) Lennard-Jones parameters from Steele’s work: σ = 0.34 nm, ε/kB = 28.0 K.48,49 (For details, see section IS in the Supporting Information.) For calculation of solid−fluid potential in studied slit-shaped carbon micropores, we used structureless Steele’s 10−4−3 potential.48,49 The total adsorbate-carbon potential is a superposition of potentials exerted by opposing pore walls

Figure 2. Schematic illustration of our computer experiment. Pure CH4 fluid is preadsorbed on the studied carbonaceous material at 293 K (left panel). Partial pressure of CH4 controls the amount of preadsorbed CH4. Then, we are injecting a small amount of CO2 into pure CH4 fluid (right panel). The partial pressure of CO2 controls the composition of the binary CO2−CH4 mixture because the partial pressure of CH4 is kept fixed. The mixture is then equilibrated, and its composition in carbonaceous micropores is recorded and analyzed. Gradual increasing of CO2 partial pressure in the binary CO2−CH4 mixture allows us to study the CO2-induced cleaning of adsorbed phase from CH4 mixture component.

the studied porous carbonaceous material (see Figure 2). Note that the binary CO2−CH4 mixture is not in direct contact with carbonaceous material. Instead, the correct equilibrium composition of adsorbed phase is guaranteed by the Metropolis GCMC moves.41,42 After equilibration, the composition of the adsorbed mixture is further recorded and analyzed. Note that gradually increasing the partial CO2 pressure in the bulk mixture makes it possible to study the microscopic mechanism of CH4 displacement from studied representative carbonaceous materials. All studied carbonaceous materials were kept rigid during all computer experiments in the GCMC. This simplification is reasonable because we investigated the equilibrium properties of adsorbed mixtures. For triply periodic carbon minimal surfaces and VPCs, we imposed periodic boundary conditions along x, y, and z directions. As others,50 for slit-shaped carbon micropores, we used two periodic dimensions (x and y). In all computer experiments, CO2 and CH4 molecules were kept rigid. This is because the applied force-field parameters were adjusted to rigid model of CO2 and CH4.47,51 The Monte Carlo steps (in our simulations) consist of a grand canonical (Widom) insertion/deletion move and of a translational/ rotation move. The details of these moves can be found elsewhere.41,42,50 To attain microscopic reversibility and detailed balance, the translation/insertion/deletion move was selected with equal probability of 1/3. In each GCMC step, the mixture component was selected with equal probability. In all GCMC simulations, 108 configurations were used, of which we discarded the first 5 × 107 to guarantee equilibration. The stability of the simulation results was confirmed by additional longer runs of 5 × 108 configurations. Absolute value of adsorption (i.e., pore density) and potential energy was

M A

U (q) =

∑

[us(ziA )

+ us(H −

ziA )]

i=1

(4)

where q ≡ is the set of separations between each LJ dispersion site on molecule A and pore walls, M is the number of dispersion sites of the molecule A (for CO2 M = 3, whereas for CH4 M = 5), H denotes the slit-shaped carbon pore width, and us(x) is modeled by the 10−4−3 potential48,49 {zAi ,H−zAi }i=1,2,...,M

⎡ σ ⎞10 ⎛ σ ⎞4 sf ⎟ 2 ⎢2⎛ ⎜ us(x) = 2πρε σ Δ − ⎜ sf ⎟ sf sf s ⎝x⎠ ⎢⎣ 5 ⎝ x ⎠ ⎞⎤ ⎛ σsf4 ⎟⎥ −⎜ 3 ⎝ 3Δ(x + 0.61Δ) ⎠⎥⎦

(5)

−3

where ρs = 114 nm is the density of carbon atoms, Δ = 0.335 nm denotes the distance between carbon planes in graphite, and σsf and εsf denote LJ solid−fluid collision diameter and well depth, respectively. For all studied carbonaceous materials, the solid−fluid Lennard-Jones parameters were computed from Lorentz−Berthelot mixing rule.41,42 (For details, see section IS attached to the Supporting Information.) II.III. Simulation Protocol. Our computer experiment is schematically presented in Figure 2. We used Monte Carlo simulations in grand canonical ensemble (GCMC) 41,42 implemented to mimic the displacement experiment. First, we preadsorbed CH4 molecules in micropores of the studied carbonaceous materials. The assumed partial pressure of CH4 mixture component in the bulk phase controls the amount of preadsorbed CH4. Next, we inject a small amount of CO2 into bulk CH4 and equilibrate the resulting mixture in contact with 13642



Article

Figure 3. Upper panel: CO2 partial pressure variation of CH4 pore density in Schwarz’s Primitive (left panel) and Schoen’s Gyroid (right panel) carbon minimal surfaces. Middle panel presents composition of the binary CO2−CH4 mixture in both carbonaceous materials. Bottom panel displays CH4 pore density variation of the total potential energy of confined mixture. For all panels, studied partial pressures of CH4 are displayed in the right middle panel.

computed using energy/particle fluctuations in grand canonical ensemble.50

into the bulk mixture (i.e., an increasing of CO2 partial pressure) causes an enhancement of CH4 content in both studied carbonaceous materials. (See Figure 3 and the middle panel in Figure 4.) Surprisingly, some additional CH 4 molecules are pumped from the bulk mixture into carbonaceous micropores. It seems reasonable that adsorbed CO2 molecules can be treated as a part of the external field that overall enhances the solid−fluid interactions with bulk CH4 molecules. However, note that enhancement of CH4 adsorption is slightly higher on the P carbon minimal surface compared with the G one. This result can be easily explained by the fact that the P carbon sample contains wider carbon micropores (see pore size distributions54 displayed in Figure 5). In wider micropores, the equilibrium CO2/CH4 selectivity at zero coverage is reduced. We will discuss this point in detail later for simpler slit-shaped pore geometry. Further injecting of CO2 molecules into the bulk mixture results in gradual displacement of CH4 from carbonaceous micropores. (See the bottom panel in Figure 4.) That is why for both studied porous materials we observe clear maxima in Figure 3 (see upper and middle panels). As expected, at higher CO2 partial pressures in the binary mixture, the stronger affinity of CO2 to curved graphitic minimal surfaces as well as CO2−CO2 interactions causes the displacement of CH4 molecules from studied materials (i.e.,

III. RESULTS AND DISCUSSION We begin our analysis by studying the microscopic mechanism of the binary CO2−CH4 mixture adsorption on preadsorbed CH4 triply periodic carbon minimal surfaces. Note that these carbonaceous materials are a good representation of ordered porous carbons. In fact, Schoen’s G carbon surface predicted theoretically in 199130 has been already synthesized.52 Curved minimal carbon surfaces were also found in low-density carbonaceous materials such as glassy carbons.53 Surprisingly, for both P and G carbon minimal surfaces, we found a nonmonotonic relation between the partial pressure of CO2 in the bulk mixture and the adsorbed amount of CH4. Let us analyze in detail the results displayed in Figures 3 and 4. If the partial pressure of CO2 in the bulk mixture is negligible, then the amount of preadsorbed CH4 is constant. Obviously, we get more preadsorbed CH4 if its partial pressure in the bulk mixture is higher, as is presented in Figure 3. At low CO2 partial pressures, carbonaceous material contains only preadsorbed CH4 because the activities of adsorbed CO2 molecules in the bulk mixture are very small. Further injecting of CO2 molecules 13643



Article

Figure 5. Comparison of the histograms of pore diameters computed from the method of Bhattacharya and Gubbins54 (the data recalculated with resolution of 0.05 nm) for the Schoen’s Gyroid (upper panel) and Schwarz’s Primitive (bottom panel) carbon minimal surfaces.

micropores. It has been shown that coals, carbide-derived porous carbons,33,36 ordinary porous carbons,32 and activated carbon fibres55−58 contain slit-shaped carbon micropores of various sizes. Regardless of the different micropore geometry, we have found a very similar trend. First, at low CO2 partial pressures in the binary CO2−CH4 mixture, adsorbed CO2 molecules induced the enhancement of CH4 storage in comparison with adsorption of pure CH4 fluid (i.e., the amount of preadsorbed CH4). For higher partial pressures of CO2 in the bulk mixture, we observe a displacement of CH4 molecules from the studied silt-shaped carbon micropores (see Figure 6). As for triply periodic carbon minimal surfaces, we notice that the pore size is crucial to control the amount of CH4 in adsorbed phase. To quantify our theoretical results, we propose to describe the variation of the CH4 pore density with the CO2 partial pressure in the bulk mixture by the following resonancetype relation

Figure 4. Microscopic snapshots of the binary CO2−CH4 mixtures adsorbed in Schwarz’s Primitive carbon minimal surface. In all presented snapshots, the CH4 partial pressure of 0.1 MPa was kept fixed in the bulk mixture. The assumed CO2 partial pressures are: 1.0 × 10−6 (upper panel), 0.01 (middle panel), and 4.0 MPa (bottom panel). Upper panel shows the configuration of preadsorbed CH4. Middle panel corresponds to the maximum of CH4 storage induced by coadsorbed CO2. Finally, bottom panel presents the adsorbed mixture enriched in CO2 mixture component.

CO2-induced cleaning of the adsorbed phase from CH4 mixture component). Moreover, we observe an interesting degeneracy phenomenon, where two different values of the total potential energy of the adsorbed mixture correspond to the same content of CH4 in the adsorbed phase. To the best of our knowledge, this is the first report showing such interesting behavior of fluid mixture confined on the nanoscale. The higher potential energy state of adsorbed molecules corresponds to the pore fluid phase enriched in CH4, whereas the lower potential energy state of adsorbed molecules corresponds to the pore fluid phase enriched in CO2. The analysis of theoretical results clearly shows that CO2-induced enhancement of CH4 adsorption as well as displacement of preadsorbed CH4 depends on the carbon pore size (compare Figures 3 and 5). This observation could have important implications in enhanced coalbed methane recovery. To study CO2-induced enhancement and displacement of CH4 from carbonaceous micropores, we replaced the model triply periodic carbon minimal surfaces by slit-shaped carbon

ρCH = f0 {(ω 2 − x 2)2 + ω 2γ 2}−1/2 4

(6)

where x ≡ ln(P), P denotes CO2 partial pressure in the binary CO2−CH4 mixture, and ρCH4 is the CH4 pore density. The parameters f 0, ω, and γ controls the position and height of the maximum CH4 storage. Note that for γ = (2ω)1/2 the curve is monotonic. Although eq 6 is purely empirical, it gives precise value of the CO2 partial pressure corresponding to the maximum of CH4 pore density. From practical viewpoint, this information is very important because this point defines the minimum CO2 partial pressure that has to be overcome to induce the displacement of preadsorbed and adsorbed CH4. We computed the maximum enhancement of CH4 in the adsorbed phase from the following expression 13644



Article

Figure 6. Upper panel: CO2 partial pressure variation of CH4 pore density in two slit-shaped carbon micropores of pore width 1.31 (left panel) and 0.66 nm (right panel). Middle panel presents composition of the binary CO2−CH4 mixture in studied slit-shaped carbon micropores. Bottom panel displays CH4 pore density variation of the total potential energy of confined mixture. For all panels, studied partial pressures of CH4 are displayed in the right middle panel.

⎛ρ ⎞ αCH4 = ⎜⎜ max − 1⎟⎟ ·100% ⎝ ρmin ⎠

for both CH4 and CO2 with solid−fluid parameters published by Neimark et al.59,60 Although, this is strong simplification, especially for rod-shaped CO2 molecules, we believe that the fundamental physics behind studied phenomenon is correctly captured. As would be expected, in wider carbon micropore the solid−fluid potentials for CH4 and CO2 are very similar, as is depicted in Figure 8. Only close to the micropore walls the carbon-CO2 potential is slightly deeper as compared with the carbon-CH4 one. In the remaining micropore space, the solid− fluid potential profiles are indistinguishable (i.e., the adsorption at infinite dilution is not selective toward CO2 or CH4). In contrast, in narrower carbon ultramicropore, the differences between carbon-CO2 and carbon-CH4 potential profiles are enhanced and span the entire pore space, which indicates the stronger affinity of CO2 to this ultramicropore (i.e., the equilibrium CO2/CH4 selectivity at zero coverage is enhanced). Therefore, the displacement of preadsorbed CH4 from narrower ultramicropore occurs easier (i.e., at low partial pressure of CO2 in the bulk mixture) as compared with wider micropore (see Figure 6). Therefore, it is evident that enhanced adsorption field in carbon ultramicropores facilitates the nonreactive displacement of CH4 by coadsorbed CO2. The enhancement of the equilibrium CO2/CH4 selectivity, given at zero coverage by the ratio of Henry’s constants,50 αCO2/CH4 =

(7)

Here αCH4 is given in [%], ρmax denotes the maximum CH4 pore density induced by adsorbed CO2, and ρmin is the CH4 pore density corresponding to zero partial pressure of CO2 in the binary CO2−CH4 mixture. Obviously, αCH4 = 0 at low CO2 partial pressures in the bulk mixture because CO2 molecules are not adsorbed on carbonaceous materials. Figure 7 depicts the use of eqs 6 and 7 in analysis of theoretical results. Interestingly, the CO2-induced enhancement of CH4 storage is significant in wider carbon micropores. For example, in slitshaped carbon micropore of pore size 1.61 nm and CH4 partial pressure of 0.026 MPa, we can store 14 times more CH4 with adsorbed CO2 as compared with adsorption of pure CH4 fluid. (See Table 3.) At the same time, we need higher partial pressure of CO2 in the binary CO2−CH4 mixture to induce the displacement of CH4 molecules from micropores. To explain these results, we need to analyze the differences between the carbon−CO2 and carbon−CH4 interaction potentials for selected pore sizes. Therefore, we computed solid−fluid potential profiles for two studied slit-shaped carbon micropores (see Figure 8). For simplicity, we assumed the spherical model 13645



Article

Figure 8. Carbon-CH4 (blue dashed lines) and carbon-CO2 10−4−3 Steele48,49 (black solid lines) potential profiles computed for two studied slit-shaped carbon micropores. The effective slit-shaped pore width was computed from, H = Hg − σss, where Hg denotes geometrical pore size and σss = 0.34 nm. The solid−fluid parameters were taken from previous studies (Neimark et al.59,60).

Figure 7. Maximum enhancement of CH4 storage in slit-shaped carbon ultramicropore (pore width of 0.66 nm) at 293 K. CH4 pore density of 1.58 mmol cm−3 (i.e., the adsorbed amount of preadsorbed CH4) corresponds to the adsorption from the pure CH4 at 0.26 MPa and 293 K. Maximum CH4 pore density of 3.85 mmol cm−3 is found for the CO2 partial pressure of 0.157 MPa in the bulk mixture. (See eq 6.) The maximum enhancement of CH4 storage computed from eq 7 is ∼144%. Black line shows the fit of the proposed resonance-type relation given by eq 6 to the simulation results.

Figure 9 depicts simulation results for two different samples of VPCs. This model of carbon microstructure introduced by Harris et al.37,38 has been successfully applied to explain different fundamental problems of adsorption science.61,62 The simulation results shown in Figure 9 are in line with those computed for triply periodic carbon minimal surfaces and slitshaped carbon micropores. However, they highlight the important aspect of the current work, namely, the impact of the pore size distribution on the enhancement and displacement of CH4 from carbonaceous materials upon the adsorption of the binary CO2−CH4 mixture. Sample S24 consists of various carbon micropores with pore sizes lower than 1 nm (see Figure 10). In contrast, sample S00 contains a significant fraction of wider micropores with pore sizes greater than 1 nm. That is why to induce the displacement of CH4 molecules from S00 sample we need higher CO2 partial pressure in the bulk mixture. At the same time, we notice that adsorbed CO2 molecules significantly enhanced the CH4 adsorbed amount (see the left middle panel in Figure 9). In conclusion, we have presented the first comprehensive study of the binary CO2−CH4 adsorption on various CH4 preadsorbed carbonaceous materials at 293 K. Taking into account simulation results, we postulate the two-stage mechanism of CH4 displacement from carbon nanospaces by coadsorbed CO2. In the first stage, the coadsorbed CO2 molecules induced the enhancement of CH4 storage. Enhanced CH4 adsorbed amount can be easily explained by the fact that adsorbed CO2 molecules increase the overall external potential field attracting some additional CH4 molecules from the bulk mixture to carbon nanospaces. It is worth pointing out that our theoretical results are in line with recent combined experimental and theoretical study of CO2 adsorption on H 2 O preadsorbed Cu-BTC metal−organic framework (MOF).63 Yazaydin et al.63 showed that preadsorbed H2O molecules enhance the CO2 uptake. Moreover, preadsorbed H2O molecules confined in Cu-BTC MOF nanopores significantly altered the equilibrium selectivity of CO2 over N2 and CH4. Conducted molecular simulations revealed that unusual enhancement of both CO2 uptake and CO2/N2 (and CO2/CH4) equilibrium separation factor is due to the

Table 3. Maximum CO2-Induced Enhancement of CH4 Storage in Selected Slit-Shaped Carbon Micropores (see eq 7) and Studied CH4 Partial Pressures in the Binary CO2− CH4 Mixturea slit-shaped carbon pore width, (nm) 0.66

0.86

1.31

1.61

CH4 partial pressure, (MPa)

CO2 partial pressure corresponding to maximum of CH4 storage, ω (MPa)

maximum enhancement of CH4 storage, αCH4 (%)

0.026 0.1 0.26 0.46 1.37 0.026 0.1 0.26 0.46 1.37 0.026 0.1 0.26 0.46 1.37 0.026 0.1 0.26 0.46 1.37

0.28 0.22 0.16 0.12 0.05 0.59 0.52 0.42 0.35 0.18 1.74 1.6 1.42 1.28 0.94 2.8 2.7 2.5 2.3 1.9

702.6 300.8 143.8 83.6 18.8 1183.3 549.2 288.6 183.7 59.3 1365.2 646.8 357.9 240.7 100.4 1429.5 678.1 376.9 256.6 109.9

a

Note that CO2 partial pressure corresponding to maximum of CH4 storage (see ω in eq 6) is the starting point of CH4 displacement from slit-shaped carbon micropores.

KCO2/KCH4, is a key to desorb efficiently the preadsorbed CH4 molecules. 13646



Article

Figure 9. Upper panel: CO2 partial pressure variation of CH4 pore density in S00 (left panel) and S24 (right panel) virtual porous. Middle panel presents composition of the binary CO2−CH4 mixture in studied carbonaceous materials. Bottom panel displays CH4 pore density variation of the total potential energy of confined mixture. For all panels, studied partial pressures of CH4 are displayed in the right middle panel.

porous materials. They inherently contain mixture of narrow and wider carbonaceous pores.16−18 From our results, we make the following general conclusion: the more narrow ultramicropores a host material has, the more efficient the enhanced methane recovery is. Clearly, similar results are expected when we replace CO2 with other molecule, say X. However, we argue that if X molecule has higher affinity to carbon micropores than CO2, then we expected the better efficiency of the CH4 recovery (i.e., higher amount of desorbed CH4). This is because X/CH4 separation factor is greater as compared with CO2/CH4. This interesting aspect of the current work will be considered in our future works.

enhanced electrostatic interactions of CO2 with preadsorbed H2O molecules. As pointed by Yazaydin et al.,63 the electrostatic interactions between CO2 quadrupolar moment and the electric field gradient of the Cu-BTC MOF are increased when H2 O molecules are preadsorbed. Our theoretical results showed that CO2 induces the enhancement of the CH4 uptake in carbonaceous nanopores at 293 K. However, this enhancement results mainly from the dispersion van der Waals interactions between CO2 and CH4. The electrostatic interactions between CO2 and CH4 are very weak because CH4 has no permanent electric quadrupolar moment. In the second stage, the stronger affinity of CO2 to flat/curved graphitic surfaces as well as CO2−CO2 interactions cause the displacement of CH4 molecules from carbonaceous materials. Under fixed thermodynamic conditions, the distribution of pore sizes is a crucial parameter controlling the CH4 adsorbed amount. This is because in narrow carbon micropores the equilibrium CO2/CH4 separation factor is enhanced by the surface energy. Finally, we would like to put some comment about real enhanced coalbed methane experiment. We showed that even for assumed fast equilibration the injection of CO2-enriched industrial mixtures to carbonaceous micropores with preadsorbed CH4 is a complex phenomenon. This is because to displace the preadsorbed CH4 one needs to know the thermodynamic conditions and the pore size distribution of host material. Note that coals are structurally heterogonous

IV. CONCLUSIONS We have presented the first comprehensive study of the binary CO2−CH4 adsorption on various CH4 preadsorbed carbonaceous materials at 293 K. From our computer experiments, we proposed two-stage mechanism of CH4 displacement from carbon nanospaces by coadsorbed CO2. In the first stage, the coadsorbed CO2 molecules induced the enhancement of CH4 adsorbed amount. This is because the adsorbed CO2 molecules enhanced the overall adsorption field that drag some additional CH4 from the bulk mixture to the micropores. In the second stage, the stronger affinity of CO2 to flat/curved graphitic surfaces as well as CO2−CO2 interactions cause the displacement of CH4 molecules from carbonaceous materials. Pore size is a key factor controlling both stages. The enhanced adsorption 13647



■

Article

ASSOCIATED CONTENT

S Supporting Information *

Structures of the unit cell for two studied samples of VPCs. The discussion of the Lorentz−Berthelot mixing rules and the additional simulation details. The material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +61 8 9266 7800. E-mail: [email protected]. au. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS P.K. acknowledges partial support by the Office of Research & Development, Curtin University of Technology, grant CRF10084. P.K. acknowledges partial support by the Australian Academy of Science, Scientific Visits to Japan 2011-12 Grant. P.A.G., A.P.T., and S.F. acknowledge the use of the computer cluster at Poznan Supercomputing and Networking Centre as well as the Information and Communication Technology Centre of the Nicolaus Copernicus University (Torun, Poland). P.K. acknowledges the use of the iVEC Epic supercomputer.

■

REFERENCES

(1) Shi, J. Q.; Mazumder, S.; Wolf, K. H.; Durucan, S. Transp. Porous Media 2008, 75, 35−54. (2) Busch, A.; Gensterblum, Y.; Krooss, B. M.; Siemons, N. Int. J. Coal Geol. 2006, 66, 53−68. (3) Ceglarska-Stefanska, G.; Zarebska, K. Fuel Process. Technol. 2002, 77−78, 423−429. (4) Ottiger, S.; Pini, R.; Storti, G.; Mazzotti, M. Langmuir 2008, 24, 9531−9540. (5) Pini, R.; Storti, G.; Mazzotti, M. Adsorption 2011, 17, 889−900. (6) Tambach, T. J.; Mathews, J. P.; Bergen, F. V. Energy Fuels 2009, 23, 4845−4847. (7) Durucan, S.; Shi, J. Int. J. Coal Geol. 2009, 77, 214−221. (8) Ozdemir, E. Int. J. Coal Geol. 2009, 77, 145−152. (9) Mazzotti, M.; Pini, R. J. Supercrit. Fluids 2009, 47, 619−627. (10) White, C. M.; Smith, D. H. Energy Fuels 2005, 19, 659−724. (11) van Krevelen, D. W. Coal: Typology, Chemistry, Physics, Constitution; Elsevier Science: Amsterdam, 1993. (12) Marzec, A. Fuel Process. Technol. 2002, 77−78, 25−32. (13) Milligan, J. B.; Thomas, K. M.; Crelling, J. C. Energy Fuels 1997, 11, 364−371. (14) Narkiewicz, M. R.; Mathews, J. P. Energy Fuels 2009, 23, 5326− 5246. (15) Narkiewicz, M. R.; Mathews, J. P. Energy Fuels 2008, 22, 3104− 3111. (16) Clarkson, C. R.; Bustin, R. M. Fuel 1996, 75, 1483−1489. (17) Bustin, R. M.; Clarkson, C. R. Int. J. Coal Geol. 1998, 38, 3−26. (18) Radlinski, A. P.; Mastalerz, M.; Hinde, A. L.; Hainbuchner, M.; Rauch, H.; Baron, M.; Lin, J. S.; Fan, L.; Thiyagarajan, P. Int. J. Coal Geol. 2004, 59, 245−271. (19) Charriere, D.; Behra, P. J. Colloid Interface Sci. 2010, 344, 460− 467. (20) Mahajan, O. P.; Walker, P. L. Fuel 1971, 50, 308−317. (21) Furmaniak, S.; Gauden, P. A.; Terzyk, A. P.; Rychlicki, G. Adv. Coll. Interf. Sci. 2008, 137, 82−143. (22) Brennan, J. K.; Thomson, K. T.; Gubbins, K. E. Langmuir 2002, 18, 5438−5447. (23) Ohba, T.; Kanoh, H.; Kaneko, K. J. Phys. Chem. B 2004, 108, 14964−14969. (24) Pierce, C.; Smith, R. N.; Wiley, J. W.; Cordes, H. J. Am. Chem. Soc. 1951, 73, 4551−4557.

Figure 10. Comparison of the histograms of pore diameters computed from the method of Bhattacharya and Gubbins54 (the data recalculated with resolution of 0.05 nm) for the S24 (upper panel) and S00 (bottom panel) virtual porous carbon samples.

field in carbon ultramicropores facilitates the nonreactive displacement of CH4 by coadsorbed CO2. This is because in carbon ultramicropores the equilibrium CO2/CH4 separation factor is increased as compared with wider micropores. The real coal sample is a not-pure dry defect-free carbon skeleton. It may contain the preadsorbed water, oxygen-containing functional groups, carbon surface defects, heteroatoms, surface partial charges, mineral contaminations, and so on. How all of these factors affect the CO2 coadsorption and coalbed CH4 recovery is a very difficult question to answer. However, taking into account current simulation results, we speculate that all factors enhancing the CO2/CH4 equilibrium selectivity should increase the efficiency of coalbed CH4 recovery. Therefore, we speculate that preadsorbed water, oxygen-containing functional groups, carbon surface defects, heteroatoms, and surface partial charges are factors that overall enhance the CO2 /CH 4 equilibrium selectivity. This is because the quadruple moment of CO2 induces the specific interactions with partial charges either dispersed on the carbon surface or preadsorbed water molecules. It is difficult to make prediction about the impact of the mineral contaminates (such as ash) on the CO2/CH4 equilibrium selectivity. First of all, mineral contaminates can reduce the volume of adsorption space and in this way decrease the adsorbed amount from a gas phase. Mineral contaminates contain mainly metal oxides. Therefore, the CO 2 /CH 4 equilibrium selectivity can be enhanced by ash. However, full understanding of displacement of CH4 by coadsorbed CO2 from various coal samples needs further theoretical and experimental research. 13648



Article

(25) Kaneko, K.; Ohba, T.; Ohkubo, T.; Utsumi, S.; Kanoh, H.; Yudasaka, M.; Iijima, S. Adsorption 2005, 11, 21−28. (26) Furmaniak, S.; Gauden, A. P.; Terzyk, A. P.; Rychlicki, G.; Wesolowski, R.; Kowalczyk, P. J. Colloid Interface Sci. 2005, 290, 1−13. (27) Brennan, J. K.; Bandosz, T. J.; Thomson, K. T.; Gubbins, K. E. Colloids Surf., A 2001, 187−188, 539−568. (28) Kowalczyk, P.; Holyst, R.; Terrones, M.; Terrones, H. Phys. Chem. Chem. Phys. 2007, 9, 1786−792. (29) Mackay, A. L. Nature 1985, 314, 604−606. (30) Mackay, A. L.; Terrones, H. Nature 1991, 352, 762. (31) Lijma, S.; Ichihashi, T.; Ando, Y. Nature 1992, 356, 776−778. (32) Franklin, R. E. Acta Crystallogr. 1951, 4, 253−261. (33) Chmiola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P.; Taberna, P. L. Science 2006, 313, 1760−1763. (34) Kowalczyk, P.; Gauden, P. A.; Terzyk, P. A.; Furmaniak, S. Phys. Chem. Chem. Phys. 2010, 12, 11351−11361. (35) Kowalczyk, P.; Tanaka, H.; Holyst, R.; Kaneko, K.; Ohmori, T.; Miyamoto, J. J. Phys. Chem. B 2005, 109, 17174−17183. (36) Gogotsi, Y.; Dash, R. K.; Yushin, G.; Yildirim, T.; Laudisio, G.; Fischer, J. E. J. Am. Chem. Soc. 2005, 127, 16006−16007. (37) Harris, P. J. F.; Tsang, S. C. Philos. Mag. A 1997, 76, 667−677. (38) Harris, P. J. F. Int. Mater. Rev. 1997, 42, 206−218. (39) Terzyk, A. P.; Furmaniak, S.; Harris, P. J.; Gauden, P. A.; Wloch, J.; Kowalczyk, P.; Rychlicki, G. Phys. Chem. Chem. Phys. 2007, 9, 5919−5927. (40) Terzyk, A. P.; Furmaniak, S.; Gauden, P. A.; Harris, P. J. F.; Wloch, J.; Kowalczyk, P. J. Phys.: Condens. Matter 2007, 19, 406208− 406224. (41) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, U.K., 1987. (42) Frenkel, D.; Smit, B. Understanding Molecular Simulation FromAlgorithms To Applications; Academic Press: London, 1996. (43) Kowalczyk, P.; Gauden, P. A.; Ciach, A. J. Phys. Chem. B 2009, 113, 12988−12998. (44) Kowalczyk, P.; Gauden, P. A.; Ciach, A. J. Phys. Chem. B 2011, 115, 6985−6994. (45) Kowalczyk, P. Phys. Chem. Chem. Phys. 2012, 14, 2784−2790. (46) Kowalczyk, P.; Furmaniak, S.; Gauden, P. A.; Terzyk, A. P. J. Phys. Chem. C 2010, 114, 21465−21473. (47) Terzyk, A. P.; Furmaniak, S.; Gauden, P. A.; Kowalczyk, P. Adsorpt. Sci. Technol. 2009, 27, 281−296. (48) Steele, W. A. The Interaction of Gases with Solid Surfaces; Pergamon: Oxford, U.K., 1974. (49) Steele, W. A. Surf. Sci. 1973, 36, 317−352. (50) Nicholson, D.; Parsonage, N. G. Computer Simulation and theStatistical Mechanics of Adsorption; Academic Press: London,1982. (51) Nguyen, T. X. Characterization of Nanoporous Carbons, Ph.D.Thesis, The University of Queensland: Brisbane, Australia, 2006. (52) Zhang, F.; Meng, Y.; Gu, D.; Yan, Y.; Yu, Ch.; Tu, B.; Zhao, D. J. Am. Chem. Soc. 2005, 127, 13508−13509. (53) Peterson, T. C.; Snook, I. K.; Yarovsky, I.; McCulloch, D. G.; O’Malley, B. J. Phys. Chem. C 2007, 111, 802−812. (54) Bhattacharya, S.; Gubbins, K. E. Langmuir 2006, 22, 7726− 7731. (55) Tanaka, A.; Iiyama, T.; Ohba, T.; Ozeki, S.; Urita, K.; Fujimori, T.; Kanoh, H.; Kaneko, K. J. Am. Chem. Soc. 2010, 132, 2112−2113. (56) Kanoh, H.; Zamma, A.; Setoyama, N.; Hanzawa, Y.; Kaneko, K. Langmuir 1997, 13, 1047−1053. (57) Kowalczyk, P.; Gun’ko, V. M.; Terzyk, A. P.; Gauden, P. A.; Rong, H.; Ryu, Z.; Do, D. D. App. Surf. Sci. 2003, 206, 67−77. (58) Nguyen, T. X.; Cohaut, N.; Bae, J. S.; Bhatia, S. K. Langmuir 2008, 24, 7912−7922. (59) Yang, K.; Lu, X.; Lin, Y.; Neimark, A. V. Energy Fuels 2010, 24, 5955−5964. (60) Ravikovitch, P. I.; Vishnyakov, A.; Russo, R.; Neimark, A. V. Langmuir 2000, 16, 2311−2320. (61) Furmaniak, S.; Terzyk, A. P.; Gauden, P. A.; Marks, N. A.; Powels, R. C.; Kowalczyk, P. J. Colloid Interface Sci. 2011, 360, 211− 219.

(62) Furmaniak, S.; Terzyk, A. P.; Gauden, P. A.; Harris, P. J. F.; Kowalczyk, P. J. Phys.: Condens. Matter 2010, 22, 085003−085013. (63) Yazaydin, A. O.; Benin, A. I.; Faheem, S. A.; Jakubczak, P.; Low, J. J.; Willis, R. R.; Snurr, R. Q. Chem. Mater. 2009, 21, 1425−1430.

13649


Displacement of Methane by Coadsorbed Carbon Dioxide Is

Recommend Documents