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
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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
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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
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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
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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
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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
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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.
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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
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The Journal of Physical Chemistry C
■
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
dx.doi.org/10.1021/jp302776z | J. Phys. Chem. C 2012, 116, 13640−13649
The Journal of Physical Chemistry C
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
dx.doi.org/10.1021/jp302776z | J. Phys. Chem. C 2012, 116, 13640−13649