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Fluid Phase Equilibria 360 (2013) 456– 465

Contents lists available at ScienceDirect

Fluid Phase Equilibria

j our na l ho me pa ge: www.elsev ier .com/ locate / f lu id

ethane and carbon dioxide adsorption in clay-like slit pores byonte Carlo simulations

hehui Jina, Abbas Firoozabadia,b,∗

Reservoir Engineering Research Institute, United StatesYale University, United States

r t i c l e i n f o

rticle history:eceived 28 June 2013eceived in revised form7 September 2013ccepted 21 September 2013vailable online 29 September 2013

eywords:

a b s t r a c t

Shale is composed of two distinct permeable media: (1) inorganic, and (2) organic. Both media may con-tribute to the amount of hydrocarbon and non-hydrocarbon species in shale. In this work, we investigatesorption in clay minerals which may constitute most of the inorganic matter in shale. We represent theinorganic matter by the montmorillonite clays with different charges for different atoms. Sorption ofmethane and carbon dioxide is investigated by Monte Carlo simulations. In this work, we assume thatmethane is structureless and CO2 is assumed to have structure and we assign partial charges to its atoms.Our results indicate that charge affects the orientation of CO2 molecules close to the surface and plays

halelay

an important role in CO2 sorption. Methane sorption is found to be mainly a function of surface area. Wealso incorporate cation exchange in clay description and model its effect on sorption. Cation exchangeincreases CO2 sorption at low pressure significantly and as pressure increases, the effect becomes lesspronounced. Cation exchange also affects orientation of CO2 molecules near the surface. Results fromour simulation are expected to provide insight into phase behavior in clays, a major constituent of shale

media.

. Introduction

Shale gas is an important unconventional energy resource; itas had a game changing effect on natural gas supply in the US inecent years. Despite the huge impact, we know very little on someundamental aspects related to the phase behavior and local speciesistribution in shale permeable media. The fluid samples from shale

ight oil formations may be highly undersaturated. However, whenroduction starts, the ratio of gas to liquid may increase signifi-antly. Such a phase behavior is drastically different from that inonventional formations. The modeling of phase behavior in shaleas and shale light oil formations provides knowledge related toell production rate. In the literature, there is neither a molecu-

ar model nor a macroscopic-based model that can describe phaseehavior in shale formation.

One of the challenges in the shale gas and shale light oil forma-ions is well productivity and gas-in-place (GIP) estimation [1]. Theontribution of the adsorbed gas to the total GIP can be as much

s 60% [2]. However, there is currently no sound theory to pre-ict the sorbed gas in shale media mainly due to complex naturef shale media. Shale is comprised of two distinct parts: inorganic

∗ Corresponding author at: Reservoir Engineering Research Institute, Unitedtates. Tel.: +1 650 326 9259.

E-mail address: af@rerinst.org (A. Firoozabadi).

378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.fluid.2013.09.047

© 2013 Elsevier B.V. All rights reserved.

and organic materials. The organic material is mainly composedof kerogen, which is a mixture of organic chemical compounds. Astudy [3] suggests that gas sorption and gas solubility in organicmaterials may provide bulk of the gas-in-place in shale gas reser-voirs. The common belief is that the amount of adsorbed gas isproportional to the content of organic matter. A number of paperspresent data relating a correlation between methane sorption tothe total organic content of organic-rich shales [3–5].

A few studies have shown that the clay mineral compositionand its micropore structure also affect gas sorption of organic-rich shales [6–8]. There are indications that clay minerals affectsorption in clay-rich shales [9–11]; sorption in clay-rich shales canbe comparable to that of total-organic-carbon (TOC) shales. Clayminerals have micropore-to-mesopore structures which providesurface area for gas adsorption depending on the pore structuresand clay chemical compositions. The surface area of shale rocks isin the range of 5–50 m2/g [3]. The surface area of clay minerals isreported to be in the range of 10–25 m2/g [12]. The surface areasin shale and clay minerals are, therefore, comparable. The clay-richshales provide a significant portion of mesoporosity [3]; we may nottherefore predict the GIP in shales only based on the TOC contents.Experimental work [13] has shown that pores of 1–2 nm width in

the interlayers of clay minerals provide the adsorption sites forgases due to large surface area. In this microscopic scale, the proper-ties of species are greatly different from that in bulk. Unlike simplecarbonaceous porous media, clay minerals exhibit morphological

dx.doi.org/10.1016/j.fluid.2013.09.047http://www.sciencedirect.com/science/journal/03783812http://www.elsevier.com/locate/fluidhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.fluid.2013.09.047&domain=pdfmailto:af@rerinst.orgdx.doi.org/10.1016/j.fluid.2013.09.047

Z. Jin, A. Firoozabadi / Fluid Phase Equilibria 360 (2013) 456– 465 457

F ef. [3s

di[m

wtspTotictoetloZastot(alCI

srgwhsltcrbat

ig. 1. The schematic representation of 2:1 layer type clay minerals obtained from Rpheres depict Si and the large solid spheres are Al.

isorder and heterogeneous chemistry. Such chemical heterogene-ty will likely affect gas sorption and sorbed gas phase equilibrium14]. Currently the underlying mechanisms of gas sorption in clay

inerals are not well understood.Extensive molecular simulation studies [15–18] are reported on

ater adsorption and swelling in clay minerals. However, gas sorp-ion in clay minerals has been rarely studied. Most of molecularimulations of gas sorption are focused on the activated-carbon slitores [19–23], where chemical heterogeneity may not be relevant.he chemical heterogeneity of the pores may have significant effectn gas sorption under confinement [14,24–26]. Unlike the conven-ional carbonaceous materials, due to mineralogy [27], gas sorptionn clay minerals not only depends on pore structure but also on thehemical heterogeneity. Experimental research has demonstratedhe efficacy of intercalating gas molecules in clays [28]. There arenly a handful of molecular simulations on gas sorption in clay min-rals. Cygan et al. [29] used NpT and NVT molecular dynamics (MD)o investigate carbon dioxide intercalation mechanism in the inter-ayer of montmorillonite clays and the effect of molecular flexibilityn diffusion rate of CO2 in water by a flexible force field. Yang andhang [19] used MD in an NVT ensemble to study the structurend diffusion of dense CO2 in clay-like slit pores. The effect of poretructure and chemical heterogeneity on gas sorption and struc-ure in clay minerals has yet to be investigated. A drawback of NpTr NVT ensemble simulations is that they cannot provide gas con-ent in clays. In this work, we use the grand canonical Monte CarloGCMC) simulations to investigate the effect of clay pore structurend chemical heterogeneity on methane and CO2 sorption in clay-ike slit pores. Methane is the main constituent of natural gases.arbon dioxide can be potentially sequestered in shale formations.

t is also found in the subsurface together with methane.Clays are generally made of large particles formed by stacks of

heets [30]. Similar to gas sorption modeling in carbonaceous mate-ials, we assume that the inter-pore interactions are negligible andas adsorbs in nanometer slit-like pores. The solid surface in ourork has a structure and charge of the montmorillonite clay whichas two tetrahedral sheets fused to an octahedral sheet [31] ashown in Fig. 1. Two of the octahedral positions of the montmoril-onite clay are filled by the trivalent Al atoms; such an electroneu-ral 2:1 clay mineral is called pyrophyllite [32]. Montmorillonitelays consist of negatively charged silicate layers with Si atoms

eplaced by Al atoms in the tetrahedral sheet and Al atoms replacedy Mg atoms in the octahedral sheet [32]. The negative chargesre compensated by interlayer counterions [15,32]. The focus ofhis work is on gas sorption in a neutral slit-like aluminum-silicate

1]. The open spheres represent O, the shaded spheres represent OH, the small solid

mineral and slit-like montmorillonite clay mineral with cationexchange. We use a full atomistic pore structure of clay by duplicat-ing the unit cell of montmorillonite clay proposed by Skipper et al.[33]. This unit cell has been widely used in molecular simulationsof water and hydrate formation in clay minerals [15,32,34–36].Methane molecule is simulated by single-site Lennard–Jones parti-cles and CO2 molecule is modeled by three-site particles explicitlyconsidering the short-range van der Waals and long-range elec-trostatic interactions. By incorporating these features, our GCMC isexpected to provide the effect of both pore structure and chemicalheterogeneity on gas sorption in clay-like slit pores.

The remainder of this paper is organized as follows. In Section2, we introduce the molecular simulation methods and define themolecular models. In Section 3, we investigate methane and CO2sorption in clay-like slit pores with various pore sizes and bulkpressures of the gas molecules. In Section 4, we summarize thekey conclusions and discuss implications.

2. Simulation method

2.1. Model

We use a fixed solid surface of montmorillonite clay as a 2:1clay mineral. The neutral montmorillonite has the unit-cell formulaSi8Al4O20(OH)4 [15]. The simulation cell contains two 32-clay unitcells resulting in a clay patch of 4.224 nm × 3.656 nm with a thick-ness of 0.656 nm separated by a fixed distance to represent a claynanopore. In molecular dynamics simulations [19], two half-layersof the solid sheets have been used to investigate the structure ofdense carbon dioxide in a clay-like slit pore. But in a simulationstudy of water adsorption in montmorillonite clays, it has beenshown that the two-clay-sheets provide more accurate results thanthe one-clay-sheet, especially at small basal spacings [32]. The pos-itions and charges of the sites in the unit cell of the clay are shownin Table 1 [33]. The positions and charges from Ref. [33] are widelyused in simulations of water adsorption in clay and validated bycomparing simulations to experimental data [32,35,36]. The unitcell that constitutes the clay sheet in our work is shown in Table 1.

For montmorillonite clay with cation exchange, the unit cell for-mula is Na0.75(Si7.75Al0.25)(Al3.5Mg0.5)O20(OH)4 [32]. Based on this

formula, each of our clay sheets with 32 unit cells have 16 iso-morphous trivalent Al atoms replaced by divalent Mg atoms inthe octahedral sheet, 8 isomorphous replacements of tetravalentSi atoms by trivalent Al atoms in the tetrahedral sheet, and 24

458 Z. Jin, A. Firoozabadi / Fluid Phase Equilibria 360 (2013) 456– 465

Table 1Atomic positions and effective charges in the unit cell [33] and charges in CO2 [40].

Atom x (nm) y (nm) z (nm) q (e)

O 0.264 0.0 0.328 −0.8O 0.132 0.228 0.328 −0.8O 0.396 0.228 0.328 −0.8O(OH) 0.0 0.0 0.106 −1.7175H(OH) 0.08815 0.0 0.1434 0.7175Si 0.264 0.152 0.273 1.2Si 0.0 0.305 0.273 1.2O 0.264 0.152 0.106 −1.0O 0.0 0.305 0.106 −1.0Al 0.44 0.152 0.0 3.0Al 0.44 −0.152 0.0 3.0O 0.0 0.457 0.328 −0.8O 0.396 0.685 0.328 −0.8O 0.132 0.685 0.328 −0.8O(OH) 0.264 0.457 0.106 −1.7175H(OH) 0.35215 0.457 0.1434 0.7175Si 0.0 0.609 0.273 1.2Si 0.264 0.762 0.273 1.2O 0.0 0.609 0.106 −1.0O 0.264 0.762 0.106 −1.0Al 0.704 0.609 0.0 3.0Al 0.704 0.305 0.0 3.0O 0.088 0.914 −0.328 −0.8O 0.22 0.686 −0.328 −0.8O −0.044 0.686 −0.328 −0.8O(OH) 0.352 0.914 −0.106 −1.7175H(OH) 0.26385 0.914 −0.1434 0.7175Si 0.088 0.762 −0.273 1.2Si 0.352 0.609 −0.273 1.2O 0.088 0.762 −0.106 −1.0O 0.352 0.609 −0.106 −1.0O 0.352 0.457 −0.328 −0.8O −0.044 0.229 −0.328 −0.8O 0.22 0.229 −0.328 −0.8O(OH) 0.088 0.457 −0.106 −1.7175H(OH) −0.00015 0.457 −0.1434 0.7175Si 0.352 0.305 −0.273 1.2Si 0.088 0.152 −0.273 1.2O 0.352 0.305 −0.106 −1.0O 0.088 0.152 −0.106 −1.0

cc

iomi

TtoL

u

wrL

�

ε

t

Table 2LJ parameters of methane, CO2, sodium ion and atoms of clay.

Atom ε (K) � (nm)

MethaneCH4 [39] 148.0 0.373

Carbon dioxideC [40] 28.129 0.2757O [40] 80.507 0.3033

ClayH [41,42] 0 0O [41,42] 78.18 0.3166Si [41,42] 47.803 0.3951Al [41,42] 32.707 0.4112Mg [43] 32.707 0.4112

Sodium ion

C(CO2) 0.6512O(CO2) −0.3256

ompensating monovalent sodium ions in the interlayer region. Thelay with cation exchange is discussed in Ref. [32].

Unlike NpT ensemble simulations used to study swelling behav-or of clay minerals [17,18,37], the clay structure is fixed inur simulations. For simplicity, sheets are considered as rigidolecules; bending potential is not considered for clay sheets [38]

n our work.The potential model used for methane molecule is from the

raPPE force field [39]. For methane sorption in clay minerals,he interactions between methane and atoms of clay and withther methane molecules are described by the pairwise-additiveennard–Jones (LJ) 12–6 potentials,

LJ(rij) = 4εij

[(�ijrij

)12−

(�ijrij

)6], (1)

here rij, εij, and �ij are the separation, LJ well depth, and LJ size,espectively. Unlike interactions are computed using the standardorentz–Berthelot combining rules

ij =�ii + �jj

2, (2)

ij =√

εiiεjj. (3)

The potential model used for CO2 molecules is fromhe flexible three-site EPM2 model [40], which includes the

Na [41,42] 62.90 0.2801

bond-bending potential, the short-range LJ potential, and thelong-range Coulomb potential. The bond-bending potential ubendingof each CO2 molecule is given as [40]:

ubending(�) =12

k�(� − �0)2, (4)

where k� = 1236 kJ/mol/rad2 is the bond-bending force constant, �is the bond-bending angle between O C O atoms, and �0 = � radis the equilibrium bond-bending angle. The pairwise additiveLennard–Jones and Coulomb potentials are used to compute theinteractions of clay–clay, clay–CO2, and CO2–CO2:

u(rij) = uLJ + uC = 4εij

[(�ijrij

)12−

(�ijrij

)6]+ qiqj

4�ε0rij, (5)

in which qi is the partial charge of the site. In Table 1, wealso provide partial charges of CO2 molecules. The conventionalLorentz–Berthelot combining rules are applied to obtain the LJparameters. The LJ parameters of atoms of clay and sodium ionsare based on the Dreiding [41,42] force-field. The data of the Dreid-ing force field do not include the parameters for the Mg atoms. Weassign to Mg the same LJ parameters as in Al [43]. The charges ofsodium ion and Mg atom are +1e and +2e, respectively. All the LJparameters are listed in Table 2. The short-range LJ interactions aretruncated at a distance of 1.07 nm. We place an empty space in thesimulation cell along the z direction with a length much larger thanLx or Ly and use the three-dimensional Ewald summation with thecorrection term [44,45] to account for the long-range electrostaticinteractions and the slab geometry.

2.2. Simulations

The simulations of sorption of methane and CO2 molecules areperformed in the grand canonical (�VT) ensemble. The simulationcell is placed in a rectangular box with periodicity in the x and ydirections. The box size in the x direction is Lx = 4.224 nm, in they direction is Ly = 3.656 nm. The length in the z direction is deter-mined by the pore size of the clay and the vacuum. The pore size H isdefined as the distance between the inner planes of the two sheets.The schematic representations of the clay nanopores without cationexchange and with cation exchange are shown in Figs. 2 and 3,respectively.

For simulations of methane molecules in clay nanopores, in eachMC cycle, a trial random displacement is applied to all methane

molecules and a methane molecule is randomly removed from orinserted into the simulation box at equal probability dependingon the chemical potential of the methane reservoir outside. Forsimulations of CO2 molecules in clay, in addition to the MC moves

Z. Jin, A. Firoozabadi / Fluid Phase Equilibria 360 (2013) 456– 465 459

Fig. 2. The schematic representation of the structure of clay nanopore withoutcation exchange. The red spheres are O atoms, the white spheres are H atoms, theyov

aCrcCCeim

FTapfi

ellow spheres are Si atoms, and light blue spheres are Al atoms. (For interpretationf the references to color in this figure legend, the reader is referred to the webersion of this article.)

bove, in every MC cycle, a trial random rotation is applied to allO2 molecules. We employ a biased MC algorithm to insert andemove CO2 molecules [15]. The vibrational degree of freedom ofarbon dioxide is not incorporated in the insertion and removal ofO2 molecules. However, we incorporate the bond bending effect in

O2 molecule insertion/deletion. In simulations of clay with cationxchange, a trial random displacement is applied to the sodiumons in each MC cycle. The chemical potentials of methane and CO2

olecules in the exterior reservoir are obtained from the Widom

ig. 3. The schematic representation of the structure of clay with cation exchange.he red spheres are O atoms, the white spheres are H atoms, the yellow spheresre Si atoms, light blue spheres are Al atoms, light green spheres are Mg atoms, andurple spheres are Na+ ions. (For interpretation of the references to color in thisgure legend, the reader is referred to the web version of this article.)

Fig. 4. The sorption isotherms of methane and CO2 in clay nanopores with pore sizeH = 1 nm.

insertion method [46] in canonical (NVT) ensemble without clayminerals. The MC moves are implemented by using the Metropolisalgorithm [47]. The simulation consists of 0.1 million MC cycles perabsorbate molecule for equilibrium and 0.5 million MC cycles perabsorbate molecule for sampling of the density profiles.

3. Results and discussions

We present the sorption isotherm of methane and carbon diox-ide in clay nanopores and density distribution for different poresizes and bulk densities. All of the simulations are performed atsystem temperature T = 298.15 K.

The sorption isotherms of methane and CO2 in clay nanoporeswith pore size H = 1 nm are presented in Fig. 4. The average gasweight density �ave in clay nanopores is given as:

�ave = 1H

H∫0

�(z)dz, (6)

where �(z) is the weight density at distance z from one of the claysurface sheets. For CO2 molecules, cation exchange increases gassorption in clay nanopores, especially at low pressures. With cationexchange, CO2 molecules are strongly sorbed in clay nanoporeswith a small pore size even at a low bulk pressure. For clay withoutcation exchange, CO2 sorption increases significantly as pressureincreases and gas sorption reaches plateau due to densely packedCO2 molecules in the pores. The high sorption of CO2 in claynanopores with small pore sizes can be attributed to strong elec-trostatic interactions and correlations due to the two clay surfaces.On the other hand, cation exchange reduces methane sorption inclay nanopores. In contrast to CO2 molecules, the methane–clay andmethane–ion interactions are from the non-electrostatic LJ interac-tions. For a small pore size (H = 1 nm), due to the strong correlationsbetween the two walls, the sorption of methane quickly approachesa plateau as the bulk pressure increases. The ions slightly reducemethane sorption, but the shapes of methane sorption isothermwith or without cation exchange are similar. In general, the sorp-tion of methane is much less than that of carbon dioxide. CO2 is acharge neutral molecule and has zero dipole moment, but it has a

strong quadrupole moment [24], which increases sorption coupledwith the charged clay atoms. In contrast to CO2, methane has a zeroquadrupole moment [48], thus the sorption of methane is muchless than that of CO2. Similar phenomena have also been reported

460 Z. Jin, A. Firoozabadi / Fluid Phase Eq

FH

om

isicwssnccmc

FH

ig. 5. The sorption isotherms of methane and CO2 in clay nanopores with pore size = 4 nm.

n gas sorption in metal-organic frameworks [49,50] and clay rockaterials [12,51].The sorption isotherms of methane and CO2 in clay nanopores

n a pore of size H = 4 nm are presented in Fig. 5. In contrast to poreize of H = 1 nm, the difference between methane and CO2 sorptionncreases with the bulk pressure. This is because in large pores, theorrelations between the two walls on methane sorption becomeeak, while the long-range electrostatic interactions affect CO2

orption in clay nanopores. As bulk pressure increases, methaneorption reaches a plateau indicating that methane sorption in clayanopores is aided by surface adsorption and sorption capacity in

lay minerals is closely related to surface area [6]. Similar to Fig. 4,ation exchange slightly decreases methane sorption but the twoethane sorption isotherms have identical shapes. This is not the

ase for CO2 sorption in clay nanopores: cation exchange enhances

ig. 6. The weight density distributions of methane and carbon dioxide molecules at bul = 1 nm, (b) H = 2 nm, (c) H = 3 nm, and (d) H = 4 nm.

uilibria 360 (2013) 456– 465

CO2 sorption. Cations in the nanopores increase CO2 sorption. Com-pared to the pore size of H = 1 nm, CO2 sorption in a pore of sizeH = 4 nm gradually increases with bulk pressure increase. This isbecause the long-range electrostatic interactions between CO2 andclay induce not only strong surface adsorption but also pore fillingin the middle of pores.

We present the weight density distributions of methane and car-bon dioxide molecules at bulk pressure P = 40 bar in clay nanoporeswithout cation exchange with varying pore sizes in Fig. 6. While thedensity profiles of methane only have one peak, the density dis-tributions of CO2 molecules have two peaks: CO2 molecules firstadsorb on the surfaces of clay and a second layer of adsorptionforms. This is probably due to the fact that the system tempera-ture T = 298.15 K is higher than the critical temperature of methane(190.56 K), but slightly lower than that of CO2 (304.14 K). In smallpores (H = 1 nm), both CO2 and methane molecules are highlypacked due to strong correlations between the two walls. Whilethe properties of methane molecules in the middle of the porereach bulk limit for a pore width of H = 2 nm, the properties ofCO2 molecules in the middle of the pore approach the bulk onlyas the pore size increases. In other words, the correlation lengthof CO2–clay is longer than that of methane–clay. As the poresize increases, the correlation between the two surfaces becomesweaker and the density of CO2 molecules in the middle of the poresapproach bulk limit.

In Fig. 7, we present the density distributions of methaneand CO2 molecules in clay nanopores with cation exchange atbulk pressure P = 40 bar. The sorption of CO2 molecules is signif-icantly enhanced due to the sodium ions in the clay interlayer.On the other hand, methane sorption is not significantly affectedby cation exchange. Cation exchange significantly increases theCO2/methane sorption ratio. In contrast to Fig. 6, we observe that

the two peaks in CO2 density profiles with cation exchange are bothstronger than that of CO2 without cation exchange. This is becausecations further increase CO2 sorption. In contrast to CO2, methane-ion interactions are non-electrostatic, thus the effect of ions in

k pressure P = 40 bar in clay nanopores without cation exchange with pore size (a)

Z. Jin, A. Firoozabadi / Fluid Phase Equilibria 360 (2013) 456– 465 461

6, but

ntfie

mpt

F(

Fig. 7. The same as Fig.

anopores are negligible. Comparing Figs. 6 and 7, we observe thathe increase in CO2 sorption with cation exchange is due to strongerrst and second adsorption layers than that of CO2 without cationxchange.

The density profiles of oxygen and carbon atoms of CO2olecules in clay nanopores without cation exchange in different

ore widths at bulk pressure P = 40 bar are presented in Fig. 8. Inhe proximity of surface, the carbon atom density profiles have

ig. 8. The density profiles of oxygen and carbon atoms of CO2 molecules in clay nanopob) H = 2 nm, (c) H = 3 nm, and (d) H = 4 nm.

with cation exchange.

only one peak. The oxygen atom density profiles have two peaksfor CO2 molecules. The distribution of carbon and oxygen atomsresults in a small “bump” in the weight density profiles of CO2 nearthe clay surfaces as shown in Fig. 4, which implies that the CO2

molecules are not parallel to the surfaces. Previous studies [20–22]on CO2 adsorption in carbon nanopores report CO2 molecules tobe parallel to the surface. The orientation of CO2 molecules in claynanopores is, therefore, due to the surface charge.

res without cation exchange at bulk pressure P = 40 bar with pore size (a) H = 1 nm,

462 Z. Jin, A. Firoozabadi / Fluid Phase Equilibria 360 (2013) 456– 465

F ar in H

q

S

wmep

ig. 9. The orientation order parameters of CO2 molecules at bulk pressure P = 40 b = 3 nm, and (d) H = 4 nm.

The orientation of the CO2 molecules in the pore space can beuantified using the orientation-order parameter S(z) [52,53]:

(z) = 1.5〈cos2 ˛〉 − 0.5, (7)

here ̨ is the angle between the head-to-tail vector of the CO2olecule and the z axis and the bracketed term represents the

nsemble average of the MC simulations. When all molecules areerpendicular to the clay surface, the orientation-order parameter

Fig. 10. The same as Fig. 9, bu

clay nanopores without cation exchange of pore size (a) H = 1 nm, (b) H = 2 nm, (c)

is 1, if they are parallel to the surface, the value is −0.5 and whenthey are randomly oriented the value is 0.

Fig. 9 presents the orientation-order parameter of CO2molecules at bulk pressure P = 40 bar in various pore widths with-out cation exchange. In the proximity of surfaces, many of the

CO2 molecules in clay nanopores are more perpendicular to thesurface. Such behavior has been reported in the study of struc-ture of dense carbon dioxide in clay-like slit pores [19]. When apore is small (H ≤ 3 nm), the orientation of CO2 molecules does not

t with cation exchange.

Z. Jin, A. Firoozabadi / Fluid Phase Equilibria 360 (2013) 456– 465 463

F ange, H( nd ligr this a

rtopb

ws

ig. 11. The snapshot of CO2 molecules at P = 40 bar in clay (a) without cation exchd) with cation exchange, H = 4 nm. The gray spheres are C, the red spheres are O, aeferences to color in this figure legend, the reader is referred to the web version of

each bulk limit because of strong long-range electrostatic interac-ions from the two walls. For large pores (H = 4 nm), the orientationf CO2 molecules becomes the bulk limit in the middle of theores, because the correlation between charges of the two surfaces

ecomes weaker.

We present the orientation-order parameter of CO2 moleculesith cation exchange at bulk pressure P = 40 bar in various pore

izes in Fig. 10. In contrast to Fig. 9, the orientation of CO2 molecules

Fig. 12. The same as Fig. 6, but a

= 1 nm, (b) with cation exchange, H = 1 nm, (c) without cation exchange, H = 4 nm,ht blue spheres are Na. The structure of clay is omitted. (For interpretation of therticle.)

is more parallel in proximity of surfaces. This is because the sodiumions are attracted to the surface and the presence of sodium ionseases CO2 molecules to lay parallel to the surface. For pore sizeH ≥ 3 nm, the properties of CO2 molecules in the middle of the pore

approach the bulk limit.

To have a better understanding of the structure of CO2 moleculein various pores, we present snapshots of CO2 molecules in Fig. 11.In a small pore (H = 1 nm), CO2 molecules are mainly attracted to the

t bulk pressure P = 100 bar.

464 Z. Jin, A. Firoozabadi / Fluid Phase Equilibria 360 (2013) 456– 465

but a

cmwtoncea

mcttaapcoFtthOispfcddataoia

Fig. 13. The same as Fig. 7,

lay surface in the proximity of the surface. The orientations of CO2olecules with cation exchange are closer to parallel at the surface,hile CO2 molecules in a clay without cation exchange is closer

o perpendicular at the surface. For a larger pore (H = 4 nm), therientation of CO2 molecules remains the same as in the small poreear the surface. However, in contrast to CO2 molecules withoutation exchange, we observe a stronger second layer with cationxchange. In both the 1 and 4 nm pore sizes, sodium ions are mainlyttracted to the clay due to the negatively charged clay sheets.

The weight density distributions of methane and carbon dioxideolecules at bulk pressure P = 100 bar in clay nanopores without

ation exchange in different pore sizes are presented in Fig. 12. Athis pressure, methane is in the supercritical region and CO2 is inhe bulk liquid state. The density of CO2 in the middle of the pores isbout the same at H = 3 and 4 nm. There is a weak second methanedsorption layer; the second layer of CO2 molecules becomes moreronounced. The first layer of CO2 adsorption is affected by thelay charge and CO2–clay dispersive interactions. The second layerf adsorption is due to clustering of CO2 molecules. In contrast toig. 6, with the bulk pressure increase in Fig. 12, the first adsorp-ion layer of CO2 density profiles becomes somewhat stronger, buthe major contribution to CO2 sorption in larger pores (H ≥ 2 nm) atigher pressure is from the pore filling in the middle of the pores.n the other hand, as the pressure increases, there is an increase

n adsorption layer of methane density profiles. The weight den-ity distributions of methane and carbon dioxide molecules at bulkressure P = 100 bar in clay nanopores with cation exchange at dif-erent pore sizes are presented in Fig. 13. In contrast to Fig. 12, withation exchange, stronger first and second adsorption layer of CO2ensity profiles are observed, while in large pores (H ≥ 3 nm) CO2ensities approach bulk limit in the middle of the pores. This isn indication that CO2 molecules can accumulate around cationso further increases CO2 sorption. However, at high pressure, the

dsorption layer of CO2 screens the charges of cations and the effectf cations on CO2 molecule accumulation in the middle of the poress negligible. Therefore, pore filling in the middle of the pores isided by the first and second adsorption layer of CO2. Similar to

t bulk pressure P = 100 bar.

Fig. 7, the effect of cation exchange on methane density distribu-tions is insignificant.

4. Conclusions

Our investigation reveals that methane adsorption in clay min-eral is dominated by the dispersive clay–methane interactions andas the pore size increases, the sorption mainly occurs in the proxim-ity of the clay surface. This is because the dispersive interactions arerelatively short-ranged. The system temperature selected is higherthan the critical temperature of methane; as a result the densityprofile of methane in clay has only one peak near the surface anda weak second peak forms only at high bulk reservoir pressures.Our work implies that the sorption of methane in clay nanopores ismainly dominated by the surface area of the pores, since a secondadsorption layer does not form in methane sorption. This result isin line with recent experiments [6].

The charge of clay is the main contribution to the sorptionof CO2 molecules. The cation exchange of clay minerals furtherincreases sorption of CO2 molecules. The clay charge results in alarge difference in methane and CO2 sorption in clay minerals inline with experiments [12,51]. The clay charge contributes to thenon-parallel orientation behavior of CO2 molecules near the claysurfaces. With cation exchange, the first layer of adsorption is eas-ily filled by CO2 molecules and CO2 molecules become parallel tothe clay surface near the wall. In general, the sorption of CO2 inclay starts with the formation of the first layer of adsorption nearthe clay surface and as the bulk pressure increases, then a lessprominent second layer of adsorption forms. At low pressure, CO2sorption is dominated by surface and cation charges which forma strong adsorption layer. As pressure increases, CO2 sorption isfurther enhanced by the pore filling in the middle of the pores.

The main conclusion from this work is that the clay atom

charges and cation exchange affect sorption and orientation of CO2molecules in clay minerals, while methane sorption is dominatedby dispersive clay–methane interactions and sorption is related tothe surface area of the clay minerals. As an important component

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f shale rocks, gas sorption in clays may not be neglected. Our sim-lation results provide a fundamental understanding toward thestimation of gas-in-place study in the clay media of the shale. Welan to expand the work on clay to include the effect of water onorption of carbon dioxide and methane. The picture will be com-leted when we expand our research into phase behavior to includerganic materials in shale.

cknowledgement

This work was supported by member companies of the Reservoirngineering Research Institute. Their support is greatly appreci-ted.

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Methane and carbon dioxide adsorption in clay-like slit pores by Monte Carlo simulations1 Introduction2 Simulation method2.1 Model2.2 Simulations

3 Results and discussions4 ConclusionsAcknowledgementReferences