Competitive Sorption of CO2 with Gas Mixtures in Nanoporous Shale

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Competitive Sorption of CO with Gas Mixtures in Nanoporous Shale for Enhanced Gas Recovery from Density Functional Theory Jinlu Liu, Shun Xi, and Walter G Chapman Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00410 • Publication Date (Web): 27 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

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Competitive Sorption of CO2 with Gas Mixtures in Nanoporous Shale for Enhanced Gas Recovery from Density Functional Theory Jinlu Liu, Shun Xi, and Walter G. Chapman∗ Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, TX, 77005, United States E-mail: [email protected]

Abstract CO2 competitive sorption with shale gas under various conditions from simple to complex pore characteristics is studied using a molecular density functional theory (DFT) which reduces to perturbed chain-statistical associating fluid theory (PCSAFT) in bulk fluid region. The DFT model is first verified by grand canonical Monte Carlo (GCMC) simulation in graphite slit pores for pure and binary component systems at different temperatures, pressures, pore sizes and bulk gas compositions for methane/ethane with CO2 . Then the model is utilized in multicomponent systems which include CH4 , C2 H6 , and C3+ components of different compositions. It is shown that selectivity of CO2 decreases with increases in temperature, pressure, nanopore size, and average molecular weight of shale gas. Extending the model to more realistic situations, we consider the impact of water present in the pore and consider the effect of permeation of fluid molecules into the kerogen that forms the pore walls. The water-graphite interaction is calibrated with contact angle from molecular simulation data from the literature. The kerogen pore model prediction of gas absolute sorption

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is compared with experimental and molecular simulation values in the literature. It is shown that the presence of water reduces the CO2 adsorption but improves the CO2 selectivity. The dissolution of gases into the kerogen matrix also leads to increase of CO2 selectivity. The effect of kerogen type and maturity on the gas sorption amount and CO2 selectivity is also studied. The associated mechanisms are discussed to provide fundamental understanding for gas recovery by CO2 .

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Introduction Shale is a widely distributed unconventional resource for natural gas production. As hydrocarbons are trapped in the source rock, commercially viable gas production from shale can only be realized by horizontal drilling and hydraulic fracturing, which creates large fractures in the formation for gas molecules to flow from source rocks to wellbores. Because of the strong adsorption and absorption of hydrocarbons in source rocks, the recovery factor of hydrocarbons from shale is still limited. One of the current interests is the injection of carbon dioxide (CO2 ) in exchange of CH4 to improve the natural gas recovery and simultaneously sequester CO2 to mitigate the CO2 emission problem. Enhanced gas recovery (EGR) by CO2 injection benefits from the facts that CO2 has a high affinity to organic matter, high density and low viscosity, which make the CO2 injection, gas production and CO2 storage an integrated and promising process. Reservoir simulations have shown the improvement in recovery factor largely depends on the petrophysical properties and fracturing conditions of a reservoir, so understanding the parameter dependency of CO2 EGR performance is meaningful for real process design. Shale gas is recognized to have multiple storage mechanisms in the formation, which include free gas in fractures and macropores, adsorbed gas on pore surfaces and nanopores and dissolved gas in organic matter. The storage in organic matter is considered to contribute the most to total storage and the sorption amount of gas depends largely on the total organic carbon (TOC) content. A significant proportion of pores in organic matter are in nanoscale and gas molecules adsorb strongly on nanopore surfaces. Depending on the interactions of different molecules with organic matter surfaces, competitive adsorption among mixtures happen. As CO2 exhibits a stronger interaction with pore surfaces than CH4 , the preferential adsorption of CO2 makes the key role in displacing the adsorbed shale gas. The ultimate potential of gas recovery by CO2 displacement is often investigated in lab environments on core samples or insoluble organic matter kerogen using isothermal gas adsorption measurements. 1,2 Measurements have shown a higher adsorption amount of CO2 3


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over CH4 , 3 a "U-shape" dependence of CO2 sorbed amount on organic matter maturity, 4 swelling of matrix with gas adsorption 5,6 and reduction in adsorbed amount due to moisture. 7 Empirical correlations of gas sorption capacity dependency on organic matter type and maturity can be determined based on collections of measurements of different samples 8 to provide valuable knowledge for pure gas adsorption, but multicomponent sorption data is still limited. To understand the fundamental mechanism of CO2 displacing shale gas, microscale studies are necessary to reveal the thermodynamics and transport of gas mixtures in pores. Molecular simulation proves to be an effective approach to understand microscale phenomena. To simulate an organic nanopore, graphite is initially selected to form a nanopore. By using grand canonical Monte Carlo(GCMC) simulation, the adsorption of CO2 and CH4 and their mixtures has been studied for two decades either on graphite slit pores or carbon nanotubes. 9–13 As the organic matter in shale is complex in chemical and structural composition, modifications on the simplified graphite pore model have been applied to understand how the functional groups like N-, S- and O- containing groups affect the adsorption capacity and CO2 selectivity. 14 It is found that these functional groups as active sites have higher attraction energies to gas molecules and enhance the gas adsorption. 15 A significant advance in modeling the organic matter is to take into account the chemical and physical properties of kerogen from elemental and functional group analysis. 16,17 The modeled kerogen molecules have been utilized by many researchers for simulation of gas adsorption and transport in packed kerogen matrix of different maturities and moisture levels. 18–20 These studies are representative mostly for gas mixture behavior in subnano scale pores. Kerogen molecules are fixed and the matrix swelling effect is not directly simulated. To take into account the hierarchical pore size distribution, simulations are expanded in length scale and meso-micropores can be constructed by using blocks of kerogen matrix 21–24 to form slit pores or creating spherical pores inside the kerogen matrix by dummy particle insertion 25 or cutter atom insertion. 26 Despite the advancement in molecular simulation models, it should be 4


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noted that results from simulations can only represent the localized phenomena in real shale matrix because the pore connectivity from subnanoscale to macroscale, the distribution of organics in inorganics have not been rigorously considered yet. In spite of the progress in molecular simulations, few attempts have been made for modeling the CO2 competitive adsorption with shale gas by a molecular theory. Molecular density functional theory (DFT) is a versatile approach to model inhomogeneous fluids with the same accuracy as molecular simulation. A few studies in the literature are available for CO2 adsorption in carbon slit pores with direct comparison with molecular simulation, 7,27 in which CO2 is modeled as a spherical Lennard-Jones (L-J) molecule with a modified potential model. Jin and Firoozabadi 28 modeled the CO2 adsorption and dissolution in bitumen by using the free energy model from Peng-Robinson Equations of State (EoS). Modeling CO2 as a sphere is not so sufficient as the linear shape and quadrupole moments make it challenging to describe the CO2 bulk phase behavior by a L-J sphere. Interfacial Statistical Associating Fluid Theory (iSAFT) of Tripathi and Chapman 29 and Jain et al. 30 has the advantage of describing molecules with different size and shape, which has been used for various complex inhomogeneous fluids. 31–36 It can reduce to SAFT-based EoS in the bulk and parameters from the EoS can be applied. Using a DFT approach, the computational time is greatly reduced in comparison with simulation and more importantly, systems which involve trace components can be naturally studied whereas sampling problems arise for low concentration components in molecular simulation. Hydrocarbons and CO2 will dissolve in the organic matter such as kerogen and bitumen and swell the matrix, which creates a third gas storage environment apart from free gas phase and adsorbed gas phase. The effect of permeable kerogen matrix on CO2 selective sorption in nanopores is not included in previous theory studies. In some molecular simulation studies, 21–24 the positions of kerogen molecules are fixed during insertion of gas molecules, which makes the sorption process essentially surface adsorption of molecules. This approach is not completely representative of the experimentally measured sorption isotherms due to the lack 5


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of swelling of kerogen matrix. 37,38 Kerogen, as the primary source of oil and gas, originates from the biological degradation of living matter. Without any defined structure, kerogen is believed to have a three dimensional cross-linked network. A molecular modeling method of nanoporous kerogen has been developed in our previous work, 39 in which we model kerogen as a cross-linked polymer with asphaltene molecules as building blocks. Two slabs of kerogen form a nanosized pore( Figure 1(b)), which allows molecules to adsorb on the pore surface and absorb in the kerogen matrix. This article is organized as follows. The DFT model is firstly verified by GCMC simulation in graphite slit pores for pure and binary component systems at different temperatures, pressures, pore sizes and bulk compositions. Then the model is utilized to predict the CO2 adsorption selectivity in multicomponent systems for two different shale gases. The influence of shale gas composition, temperature and pressure on CO2 selectivity is discussed. Subsequently, we model the CO2 /CH4 adsorption in pores under more realistic conditions, in which we consider different levels of moisture in the pore and the effect of gas dissolution in the organic matrix. We show the presence of water inside a nanopore greatly reduces the CO2 adsorption but increases the CO2 selectivity with respect to methane. The presence of organic matter kerogen also increases the CO2 selectivity. Based on these results, we expect the efficiency of CO2 enhanced gas recovery largely depends on the organic matter content and maturity of the reservoir. We show that molecular scale modeling through DFT is a promising and efficient method that facilitates understanding the fundamental mechanisms for increased recovery by CO2 injection.

Methods In this section, we first present the two modeled systems: an impermeable graphite pore and a permeable kerogen pore. Next, molecular DFT, which is applied throughout the study from simple to complex systems, is outlined with explanations of the free energy model.

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Then, we explain how the model parameters are determined. Finally, we briefly introduce the molecular simulation method which is used for pure and binary component systems to validate the theory results.

Slit pore model: impermeable graphite pore and permeable kerogen pore

CO2 H CH4

Δ (a) Impermeable Graphite Pore

(b) Permeable Kerogen Pore

Figure 1: Schematic representation of the two nanopore models in this work. For the graphite pore model, molecules cannot penetrate the graphite pore wall, while for the kerogen pore model, molecules dissolve in the kerogen matrix. In this subsection, we describe the modeled systems for nanoscale pores in shale. Graphite pores (Fig 1(a)) are usually used as a model system for fluids in shale reservoirs and lots of molecular simulation studies have been done for fluids confined in graphite pores. The pore size H is defined as the center to center distance between the two first layers of graphite walls. There are a few studies in the literature modeling CO2 with CH4 in comparison with molecular simulation, however, none of them has modeled CO2 as a polyatomic molecule and achieved good agreement with molecular simulation both for pure component and mixtures. 7,27 In this study, we model CO2 as a polyatomic molecule with parameters from the 7


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PC-SAFT equation of state 40 and compare the DFT calculation with that from GCMC simulation. To understand how the fluid dissolution in the kerogen matrix can affect the adsorption selectivity of CO2 , we modify the pore walls to be kerogen that are permeable to molecules (Fig 1(b)). Kerogen is modeled as a cross-linked network of asphaltene-like molecules as in our previous studies. This is accomplished by combining a PC-SAFT EoS model with the Flory-Huggins theory for crosslinked polymers are combined to formulate this model. Model parameters are determined from experimental measurements of kerogen swelling in different solvents. Interactions between kerogen and fluid components are accounted for explicitly – attraction leads molecules dissolve into the matrix and also adsorb onto the kerogen pore wall. Compared to an impermeable graphite pore, the permeable pore wall is expected to reduce the confinement effect and result in less dense packing of fluid inside the pore.

Molecular DFT method Potential models Consistent with the PC-SAFT EoS model, 40 molecules are modeled as chains of hard sphere beads bonded at contact (Figure 2) that also interact with van der Waals attraction modeled by a modified square well potential as given by Chen and Kreglewski 41    ∞       3ε u(r) =   −ε       0

r < (σ − s1 ) (σ − s1 ) ≤ r < σ

(1)

σ ≤ r < λσ r ≥ λσ

where u(r) is the pair potential, r is the radial distance between two segments, σ is the temperature-independent segment diameter, ε is the depth of the potential well, and λ is the reduced well width. A ratio of s1 /σ = 0.12 is suggested by Chen and Kreglewski. Then for

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non-associating molecules, three model parameters are needed, which are the temperatureindependent segment diameter σ, the depth of the potential , and the number of segments per chain m.

non-associating molecules (alkanes and CO2) B

A

θA

A

𝑟

θB

B

water with two association sites

Figure 2: Molecular models for non-associating hydrocarbons and CO2 and water molecule with two association sites. The hydrogen bonding between molecules such as water is modeled by a directional attractive potential between association sites as in Figure 2. An orientationally dependent square well potential is used to model the association between two sites:

φassoc AB (r, θA , θB ) =

   −εassoc , AB

r < rcut ; θA < θcut ; θB < θcut

  0,

(2)

otherwise

where εassoc denotes the association energy between site A on one segment and site B on AB another segment.rcut is the cutoff distance within which association can occur. θ is the angle between the vector pointing from the center of a segment to the center of one association site on this segment and the vector pointing from the center of one segment to another. Association occurs when both θB and θA are smaller than the cutoff angle θcut .

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Free energy functionals The focus of this work is to produce a molecular model to predict the competitive sorption of CO2 and shale gas competitive adsorption under a range of conditions. To focus on the results, we briefly describe the theory and equations and direct readers to certain literature or Supplementary Information for details. In molecular density functional theory applied in a grand canonical ensemble, where temperature, volume and chemical potentials of each component are set, the density distributions of each component is solved through minimization of the grand free energy:

Ω[ρ(r)] = A

total

[ρ(r)] −

N Z X

ρi (r)[µbulk − Viext (r)]dr i

(3)

i=1

δ Ωsf [ρ(r)] = 0 for i = 1, 2, ..., N δ ρi (r) equilibrium

(4)

where Atotal [ρ(r)] is the total intrinsic Helmholtz free energy functional, ρi (r) is the is the bulk chemical potential of component i density distribution of component i and µbulk i and N is the total number of components. In the bulk, the free energy functional reduces to the free energy from PC-SAFT EoS 40 for associating fluids, which is a sum of ideal gas, hard sphere, chain, dispersion and association contributions. The hard sphere part accounts for the volume exclusion effect of the reference fluid, and the white-bear version of fundamental measure theory is applied. The reference hard spheres form chains by complete tangential association at the contact distance, which was developed by Tripathi and Chapman. 29 For the dispersion part, a weighted density approximation method by Sauer and Gross 42 is used, which approximates the local free energy density by the bulk free energy evaluated at a locally weighted density. The equations corresponding to the non-associative contributions could be found in our previous work 43–45 and here we only provide the equations for association, which was originally developed by Segura et al.. 46

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Atotal [ρ(r)] = Aid [ρ(r)] + Ahs [ρ(r)] + Ach [ρ(r)] + Adisp [ρ(r)] + Aassoc [ρ(r)]

(5)

This free energy functional allows us to model inhomogeneous mixtures of polyatomic molecules with hydrogen bonding. The association free energy functional was first proposed by Chapman, 47 which is an inhomogeneous form of Wertheim perturbation theory for associating molecules. 48–51 The equations are given by Segura et al. 46 in studying hard sphere fluids with association sites,

βAassoc [ρ(r)] =

Z dr

N X

" ρi (ri )

i=1

X A∈Γ(i)

(i)

χ (ri ) 1 (i) ln(χA (ri ) − A + 2 2

# (6)

(i)

where χA (ri ) is the fraction of segment i not bonded at site A at position r. It is obtained from

 (i)

Z

χA (r1 ) = 1 +

dr2

N X

−1 ρj (r2 )

j=1

X

(j) χB (r2 )∆Ai Bj (r1 , r2 )

(7)

B∈Γ(j)

(i)

which means χA (ri ) is determined by all the bonding conditions of sites that site A can bond to over the entire domain. ∆Ai Bj (r1 , r2 ) is the "association strength" defined by ij ∆Ai Bj (r1 , r2 ) = 4πκ[exp(βεass Ai Bj ) − 1]y (r1 , r2 )

(8)

where κ is a constant geometric factor accounting for the available bonding volume between molecules, y ij (r1 , r2 ) is the inhomogeneous cavity correlation function between segment i and j and is approximated by the geometric mean of the hard sphere pair correlation functions at contact positions at r1 and r2 , 1/2 y ij (r1 , r2 ) = g hs (ρi (r1 ))g hs (ρj (r2 ))

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(9)

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and the average densities ρi (r1 ) are approximated by 3 ρi (r1 ) = 4πσi3

Z dr2 ρi (r2 )

(10)

|r2 −r1 |>σi

For fluids near a graphite surface, the fluid-wall interaction is modeled by the Steele 10-4-3 potential, 52

Vj10−4−3 (z) where ρs = 0.114 Å

−3

= 2πρs ∆s σsj

2

σsj 4 2 σsj 10 σsj 4 − − εsj 5 z z 3∆(z + 0.61∆)3

(11)

is the carbon atom density, δs = 3.35 Å is the separation distance

between two graphite layers, σsj and sj are the segment diameter and interaction energy that √ are estimated from the Lorentz−Berthelot mixing rules, σsj = (σs + σj )/2 and εsj = εs εj , where σs and σj are the carbon atom diameter (σs = 3.345 Å) and segment diameter of the component and εs and εj are the interaction energies for solid−solid (s /kb = 28 K) and fluid−fluid interactions, respectively. For fluids in between two surfaces, the external potential includes contributions of both walls, i.e. Vjext (z) = Vj10−4−3 (z) + Vj10−4−3 (H − z). In studying the influence of pre-adsorbed water and permeable kerogen pore wall, we apply variations of the basic DFT. The mass conservation of water is achieved by applying the equation from Malijevsk` y and Jackson 53 only to water. Details can be found in Part IIB. For a permeable kerogen pore, we apply the model parameters that were presented in our previous work. 39 The model and parameters can be found in the Supplementary Information for interested readers. Model parameters As the free energy of the DFT model reduces to the free energy in the PC-SAFT EoS, parameters are directly taken from Gross and Sadowski. 40 CO2 is modeled as a non-polar molecule and H2 O is modeled as a molecule with one electron donor and one electron acceptor or one A site and one B site. Lorentz-Berthlot mixing rule is applied for interactions between 12


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√ two different molecules for dispersion interactions, i.e. εij = (1 − kij ) εi εj . The binary interaction parameter kij for alkanes and CO2 were taken from Gross and Sadowski. 40 A temperature dependent kij over the range 300 K < T < 550 K is applied for CH4 or CO2 with H2 O, which are given by Eqn. 12 and 13. kij ’s are fit to the experimental data of solubilities of CH4 in water 54–59 and CO2 in water. 60–66 The fitting of kij and the resulted solubilities can be found in Supplementary Information(SI). kijH2 O−CH4 (T ) = −1.00634 × 10−6 T 2 + 9.30847 × 10−4 T − 0.193479

(12)

kijH2 O−CO2 (T ) = −3.49629 × 10−6 T 2 + 3.36332 × 10−3 T − 0.701767

(13)

Table 1: PC-SAFT parameters for fluid molecules in this work substance Mw[g/mol] m CH4 16.043 1.0000 C 2 H6 30.07 1.6069 C 3 H8 44.096 2.0020 n-C4 H10 58.123 2.3316 n-C6 H14 86.177 3.0576 N2 28.01 1.2053 CO2 44.01 2.0729 H2 O 18.015 1.0656

σ[Å] 3.7039 3.5206 3.6184 3.7086 3.7983 3.3130 2.7852 3.0007

/kb [K] 150.03 191.42 208.11 222.88 236.77 90.96 169.21 366.51

AB /kb [K]

κAB

2500.7

0.034868

Table 2: Binary interaction kij parameters for PC-SAFT used in this work CH4 C2 H6 C3 H8 n-C4 H10 n-C6 H14 N2 CO2 H2 O

CH4 0

C 2 H6 0 0

C3 H8 0 0 0

n-C4 H10 0.022 0 0.003 0

13

n-C6 H14 0.021 0 0 0 0

N2 0.1 0.1 0.1 0.1 0.119 0


CO2 H2 O 0.065 Equation 12 0.095 0.109 0.12 0.12 0.1 0 Equation 13 0

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GCMC simulation in a graphite pore Monte Carlo molecular simulation was performed in the grand canonical ensemble using the simulation package TOWHEE. 67,68 Temperature, volume and chemical potentials are the input state variables in the grand canonical ensemble. TraPPE United-Atom force field for methane, ethane 69 and carbon dioxide 70 is used. A slit shaped graphite pore is modeled by Steele 10-4-3 potential 52 with the pore-fluid interaction parameters determined by LorentzBerthelot rule (see Table 3 for force field parameters). At each temperature, simulation for pure CH4 , C2 H6 and CO2 in bulk phase is firstly performed in the grand canonical ensemble to verify the bulk fluid ρ − P relations with NIST data. 71 Meanwhile the relations between chemical potential and pressure are also calculated. Using these bulk chemical potentials as input, we simulate gas adsorption on graphite at various pressures and pore sizes. For binary mixtures, however, calculation of chemical potentials at high CO2 concentration is challenging with electrostatic interactions being especially important. The sampling for chemical potential is very inefficient and the chemical potential is almost always incorrect. 72 Since PC-SAFT accurately models the thermodynamic properties of CO2 even at high concentrations, we use the chemical potential for CO2 from PC-SAFT as input to the simulations. It is then verified that using the CO2 chemical potential from PC-SAFT, the simulations produce the correct pressure and concentrations for a bulk mixture in the grand canonical ensemble. Table 3: TraPPE force field parameters for CH4 , C2 H6 and CO2 69,70 atom /kb [K] σ[Å] q (e) methane CH4 148 3.73 0 ethane -CH3 98 3.75 0 carbon dioxide C 27 2.8 0.7 O 79 3.05 -0.35

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Results and Discussion Part I: DFT model verification for pure and binary component systems In this section, we compare adsorption isotherm predictions from DFT with GCMC simulation either from this work or from literature for pure component systems of CH4 , C2 H6 and CO2 and mixtures of CH4 /CO2 and C2 H6 /CO2 in graphite pores. Figure 3a shows that for pure components, excellent agreement between theory and simulation is achieved especially for CH4 and C2 H6 . Smaller pores (3 nm) show higher density at low pressures because the adsorbed layers take a higher fraction of the total pore volume compared to larger pores (5 nm). When the pressure is high enough, however, density inside the pores become liquid-like. The average density in a larger pore becomes higher, because the fraction of void volume near the wall (approximately one molecular diameter thickness) is greater for a smaller pore. The adsorbed structure at various state points can be found in Figure 4. For methane, DFT predicts almost exactly the same density profiles with that from molecular simulation because the molecular diameter in PC-SAFT EoS is close to that in simulation. The overall adsorption of ethane is well predicted by the theory and the density profile is in good agreement with simulation results. Because the intermolecular force model in simulation is different from that in the DFT, the density oscillations have different spacing. In Figure 3a, the average mass density of CO2 is much higher than C2 H6 and CH4 , which is expected since CO2 has a high molecular weight and mass density. Nevertheless, the preferential adsorption of CO2 cannot be concluded from single component adsorption. In Figure 3b, CO2 adsorption over a large range of temperatures from DFT is compared with reported simulation from Gu et al., 13 who used the TraPPE force field for CO2 . The agreement with simulation data of excess adsorbed amount, which is defined by Eqn 14, in a 1.5 nm pore is excellent. The theory over predicts the excess adsorption below 10 MPa for lower temperatures, but the pressures where maximum excess adsorption occurs are well 15


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predicted. Z

H

Γ=

ρ(z) − ρbulk dz

(14)

0

As the major interest of this work is CO2 competitive adsorption with other components, we also verify the binary adsorbed fluid property predicted by theory for CO2 /CH4 and CO2 /C2 H6 mixtures. Figure 5 shows the binary mixture adsorption at 328 K at lower pressure of 5 MPa and higher pressure of 50 MPa in two pore sizes of 3 nm and 5 nm. The bulk composition of each specified condition is varied. We see the overall agreement of DFT prediction and our molecular simulation results is very good. Better agreement is seen for CO2 /CH4 mixture while DFT over predicts the density of CO2 and C2 H6 in the CO2 /C2 H6 mixture. As expected the adsorbed density is higher for smaller pore sizes and higher pressures. At low pressure of 5 MPa, the difference between 3 nm and 5 nm pore density is significant while at high pressure of 50 MPa, the difference is negligible. This is because at high pressures, the fluids reach the maximum packing inside the pore regardless of the pore size and there is little potential for them to be more densely packed. In Figure 5, the intersection of CH4 or C2 H6 density with CO2 density at the same condition indicates the same adsorbed amount for the two components. A lower CO2 fraction at this point means higher selectivity of CO2 with respect to CH4 or C2 H6 with selectivity in binary mixture adsorption defined as

Si =

xi /(1 − xi ) yi /(1 − yi )

(15)

where xi and yi are the mole fractions of component i in the adsorbed phase and bulk phase, respectively. The selectivity of CO2 with respect to CH4 is higher at low pressure and in small pore sizes, with CO2 always more preferentially adsorbed. The stronger interaction of CO2 with a graphite surface makes it preferentially adsorbed at low pressure. As pressure increases, CO2 and methane are adsorbed in similar amounts and the maximum packing is reached at high pressure. The selectivity then reaches a constant at high pressures. This 16


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1 0.9

CO2

0.8

T(K) 298 298 328 328 328 328 328 328

density [g/cm3]

0.7

0.6 0.5

Pore size (Å) 30 50 30 50 30 50 30 50

DFT

GCMC

C2H6

0.4 0.3

CH4

0.2 0.1

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Pressure [MPa] (a) 30

Excess adsorbed amount [kmol/m3]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Temperature (K) 315 323 348 360 400 500 600 850

315 K to 850 K

25

20

DFT

Simulation

15

10

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0 0

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Pressure [MPa] (b)

Figure 3: (a)Pure CO2 , CH4 and C2 H6 adsorption isotherms of different temperatures and pore sizes in comparison with GCMC simulation; (b)Excess adsorption isotherms of CO2 in a 1.5 nm graphite pore in comparison with simulation by Gu et al. 13 17 ACS Paragon Plus Environment

Langmuir

3.5

2.5

2.5

GCMC

Pressure (MPa) DFT 0.26 1.25 3.40

2.0

reduced density/ ρσ3

Pressure (MPa) DFT 5.87 31.23 84.94

3.0

reduced density/ ρσ3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2.0 1.5 1.0

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z/Å

z/Å

(a)

(b)

Figure 4: Comparison of density profiles from GCMC simulation and DFT (a) methane (b) ethane is more clearly shown in Figure 6a, where DFT calculations are compared with molecular simulation from Kurniawan et al. 27 with a constant bulk composition of CO2 /CH4 = 1/1 at different temperatures in a 1.5 nm pore. The maximum adsorption selectivity is successfully predicted at pressures between 5 to 10 MPa. The same maximum adsorption selectivity pressure has also been predicted by Huang et al. 18 and Zhang et al.. 73 Figure 6b shows the adsorbed CO2 fraction versus the bulk CO2 fraction at different pressures ranging from 0.1 to 20 MPa. Consistent with the maximum selectivity pressure range in Figure 6a, the deviation of CO2 pore fraction from bulk fraction reaches a maximum at intermediate pressures of 5 and 10 MPa both from theory and simulation. Much difference is seen in Figure 5b for the CO2 /C2 H6 mixture. At lower pressures, both the theory and molecular simulation predicts the selectivity of CO2 with respect to C2 H6 less than 1 and at higher pressures, the selectivity is close to 1, which means CO2 has no preferential adsorption over C2 H6 . This is because the attraction between ethane and graphite is stronger than CO2 and graphite and DFT captures this effect correctly. We will discuss the prominent effect of heavy component fraction on the CO2 selectivity in later predictions from DFT. 18


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20000

CH4

CO2

density [mol/m3]

15000

Pore size(Å) 50 30 50 30 50 30 50 30

Pressure(MPa) 5 5 50 50 5 5 50 50

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GCMC

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15000

density [mol/m3]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

10000

5000

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CO2 bulk fraction (b)

Figure 5: (a) CO2 /CH4 and (b) CO2 /C2 H6 adsorption in 3 nm and 5 nm pores at two constant pressures of 5 MPa and 50 MPa in varying bulk compositions from DFT (lines) and GCMC (points). Temperature is kept constant at 328 K. 19


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5.5

1.0

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0.9

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CO2 fraction (pore)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(xCO2/xCH4) / (yCO2/yCH4)

Langmuir

4.0 3.5 3.0 2.5 2.0

Temperature (K) 308 318 328 338 348

1.5 1.0 0.5

DFT

GCMC

0.7 0.6

0.5 0.4 Pressure (bar) 1 10 50 100 200

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(a)

(b)

Figure 6: CO2 selectivity with respect to methane in a 1.5 nm pore (a) at different bulk temperatures and pressures for a CO2 /CH4 (1:1) mixture; (b) at different pressures and bulk CO2 fractions at T = 318 K. The points are simulation data by Kurniawan et al. 27 The comparisons with molecular simulation verify the accuracy of DFT in predicting the adsorption density and selectivity. Next in this work, we will explore the parameter space of temperature, pressure, pore size and gas composition to gain understanding of how CO2 selectivity depends on these parameters. As the graphite pore model is very idealized, we also investigate how the presence of water and organic matter influence the CO2 selectivity.

Part II: Prediction of CO2 adsorption selectivity in nanopores at various conditions As the DFT model is well verified by molecular simulation from various sources, in this section we make predictions on multicomponent systems where molecular simulations find challenges in handling trace components. We first study the adsorption of different shale gas mixtures with CO2 at various temperature and pressure combinations which represent the physical conditions at different geological depths. The pore size effect is also studied. Then the pore wall properties are altered to be either pre-wet by water or permeable to fluid molecules. The altered pore conditions represent more realistic situations in real organic rich shale gas 20


Page 21 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

reservoirs. These studies provide fundamental understanding of CO2 preferential adsorption behavior in nanopores. The maximum adsorption selectivity condition is preferred for CO2 enhanced gas recovery and the maximum adsorption amount should be selected for CO2 geological sequestration in shale reservoirs. A. Effect of gas composition, geological depth and pore size In Part I we have shown CO2 is preferentially adsorbed from a CO2 /CH4 mixture but not from a CO2 /C2 H6 mixture. This raises questions for CO2 adsorption selectivity with shale gas mixtures. While methane is the major component in shale gas, ethane, propane and even C6+ are also present in the gas. When the fraction of heavy components is high, preferential adsorption of CO2 will be inhibited by heavy hydrocarbons and the efficiency of enhanced gas recovery will be affected. DFT has the advantage in studying multicomponent mixtures with trace components, which are not usually studied by molecular simulation. Here we take two sample gases 74 and examine how the adsorption selectivity changes as a function of temperature/pressure and pore size in graphite slit pores. A comparison with simple CO2 /CH4 is made to show how gas composition changes the CO2 selectivity. Different temperature/pressure combinations are studied to represent different geological depths, i.e., temperature increases by 30 K and pressure increases by 15 MPa for every 1 km depth. 75,76 Figure 7a shows the DFT prediction of CO2 adsorption selectivity from mixtures of CO2 /CH4 with fixed bulk CO2 fraction of 0.5. Adsorption selectivity of CO2 is always larger than 1, but selectivity becomes insignificant beyond a pore size of about 10 nm. As temperature and pressure increases, the selectivity of CO2 drops significantly. The same phenomenon is also reported by Zhang and Cao 77 in organic-inorganic mixed matrix nanopores and by Zhang et al. 14 in functional group rich organic slit pores. Low temperature and pressure conditions were thus recommended for CO2 enhanced gas recovery. Heavy components compete with CO2 adsorption and suppress the CO2 selectivity depending on the original gas in place composition. Shale gas compositions also vary for 21


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different plays. 74 To study the composition variation effect on the CO2 adsorption selectivity, we choose compositions of unprocessed shale gas from Eagle Ford and Appalachian play (Table 4) and predict the selectivity of CO2 with respect to shale gas mixture. The mole fraction of CO2 in the bulk mixture is kept constant as 0.5. C4+ and C6+ components are represented by butane and hexane, respectively. The same (T,P) conditions were studied as in Figure 7b and reduction in CO2 selectivity is seen for all the conditions. Because of the higher fraction of heavy component in Eagle Ford shale gas, CO2 selectivity is very low even for lowest temperature and pressure condition. For the two highest (T,P) conditions, CO2 selectivity drops below 1 for large pore sizes for both gases. This finding shows that the effectiveness of CO2 EGR depends on the reservoir (T,P) condition and gas composition. A few percentage of heavy components (C3+) will result in noticeable reduction in CO2 selectivity and diminish the CO2 injection efficiency. Table 4: Shale gas compositions Component CH4 C 2 H6 C 3 H8 C4+ C6+ CO2 N2

mole fraction (%) Eagle Ford Appalachian 74.6 79.1 13.8 17.7 5.4 0.6 4.5 0 0.5 0 1.5 0.1 0.2 2.5

B. Effect of pore water content Water is generated during the conversion of organic matter to oil and gas. Interaction of water with pores is more complex than that of non-polar compounds with pores. Water tends to accumulate in clay pores due to strong electrostatic interaction with minerals and adsorption sites with polar functional groups. The presence of water results in a decrease of gas sorption capacity due to a decrease in accessible pore volume and also due to the occupation of high surface energy adsorption sites. 8 CO2 geological storage or EGR is affected by in situ water 22


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2.5

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CO2 selectivity (mol CO2 / mol shale gas)

4.5

CO2 selectivity (mol CO2 / mol CH4)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

selectivity

2.5

2.0 1.5 1.0

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shale gas

2.1

Appalachian

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1.7

Eagle Ford

1.5

T(K) 310 340 400 460 310 340 400 460

Pressure (MPa) 15 30 60 90 15 30 60 90

CO2 selectivity

1.3 1.1 0.9

0

25

50

75

100

125

0

Pore size [Å]

25

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125

Pore size [Å]

(a)

(b)

Figure 7: Adsorption selectivity of CO2 with respect to (a) CH4 and (b) Eagle Ford and Appalachian shale gas in different temperature and pressures as a function of pore size of graphite slit pores. CO2 bulk fraction is always kept at 50%. or water remaining after hydraulic fracturing. In this section, we shed light on this problem from theory prediction. The system we consider is the simplest case, where there is no functional group or clay mineral on the pore surface. Water amount inside the pore is fixed in DFT calculation to study the adsorption of CO2 or CO2 /CH4 at different bulk pressures. Water is modeled to interact with a graphite surface through dispersion interaction only. Studies by molecular simulations show water has a contact angle of around 90°on graphite 78 . 79 In DFT we calculate the contact angle of a water droplet on a surface through Young’s equation: γlv cos θ = γsv − γsl

(16)

where γlv , γsv and γsl are the liquid-vapor, solid-vapor and solid-liquid interfacial tensions, respectively. The solid-vapor interfacial tension is much lower than solid-liquid interfacial tension, 78 so it is treated to be negligible here. The contact angle can then be determined from the other two values. The solid-liquid interfacial tension is determined by the difference between grand potential at the interface and the grand potential of bulk water. Werder et al. 79 and Jaffe et al. 80 both showed the contact angle of water is correlated with the water23


Langmuir

graphite dispersion interaction energy. In DFT, this corresponds to the well depth of the external potential. Figure 8a shows a collection of MD simulation of water droplet on graphite surface by Werder et al.. 79 We correlate cos θ with the binding energy 80 using the dataset both from molecular simulation and DFT calculations. As can be seen, the dataset from DFT follows the linear relation similarly with MD simulation with a slightly different slope. We then choose the binding energy parameter that gives θ = 90°. The density distribution of water near the graphite surface is then compared with that from MD simulation. 78,79 We see a reasonable prediction of the first layer of water on the graphite surface and larger oscillation of water layers from the second layer. The frequency of oscillation is also overestimated by DFT. 1.0

3.5

correlation from simulations: y = -0.2185x - 1.4415 R² = 0.9661

3.0

DFT (contact angle = 90 degrees)

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MD simulation 1 MD simulation 2

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correlation from DFT: y = -0.1877x - 1.2577 R² = 0.9998

cos(θ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2.0

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-5

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z / σH2O

binding energy [kJ mol-1]

(a)

(b)

Figure 8: (a) Correlation of contact angle of water on a surface with binding energy from simulation data (collected by Werder et al. 79 ) and DFT calculation; (b) water density profile on graphite at a contact angle of 90°. Simulation data 1 and 2 are from Werder et al. 79 and Jaffe et al., 80 respectively. After the water interaction energy with graphite is determined, we apply the mass conservation algorithm by Malijevsk` y and Jackson 53 to examine if the structure of CO2 is correctly predicted with water present. Jin and Firoozabadi 81 used GCMC simulation to study the CO2 adsorption in a clay pore with pre-loaded water. Since water has a zero contact angle with the clay surface, we adjust the water-graphite binding energy as in Figure 8a to compare 24


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4000 density [kg/m3]

(Jin and Firoozabadi, 2014)

3500

density [kg/m3]

3000 2500 2000

No water

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z [nm] Figure 9: CO2 density distribution at different water pore densities when water purely wets the surface at T = 298.15 K and P = 100 bar. The molecular simulation result from Jin and Firoozabadi 81 is inserted as a comparison.

4.0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

CO2 (0.2 g/ml)

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Figure 10: (a) Density distributions of water and CO2 at different water content shown in parentheses in the pore; (b) Density distributions of water, CO2 and CH4 at different water content shown in parentheses. T = 298.15 K, P = 100 bar. 25


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the density distribution with Jin and Firoozabadi’s simulation. 81 Figure 9 shows the CO2 density distribution at different water densities at 298.15 K and 100 bar. DFT shows overall very good agreement with molecular simulation. Similar with molecular simulation, CO2 has only minor adsorption on the graphite surface when water is present and forms layers at the water-CO2 interface. Different from molecular simulation, DFT predicts the water-CO2 interface more distant from the wall surface and a higher density in the center of the pore when water density is 0.6 g/ml. This means less mixing between CO2 and water is predicted by DFT. In contrast to the water-wet surface scenario, we find for a graphite surface, CO2 is adsorbed on the graphite surface as shown in Figure 10a. The reduction of CO2 adsorption is due to the decrease in volume available for CO2 and limited solubility of CO2 in water, which is also found from molecular simulation and experimental studies. 82–84 The reduced CO2 adsorption with pre-adsorbed water of different concentrations can be found in SI. When CO2 and CH4 both adsorb in the pore (Figure 10b), phase separations are different in the pore depending on the water density. When water density is 0.4 g/ml or 0.6 g/ml, only a waterrich phase and a CO2 /CH4 -rich phase are formed. However, when water density decreases to 0.2 g/ml, CO2 is rich both near the graphite surface and in the center of the pore. CH4 has a higher average density in the center of the pore than near the surface. This is because CH4 interacts less strongly with the graphite surface than CO2 , and also CH4 prefers a CO2 rich phase due to its higher solubility in CO2 than in water. The competitions among multicomponent fluid-fluid interactions and fluid-wall interactions make the solubilities change significantly compared to bulk fluid. When the CO2 and CH4 mixture adsorb in the pore with different water content(Figure 11), the largest adsorption of CO2 occurs at low temperature and high pressure when water density is 0.2 g/ml. This implies that a small amount of water can enhance the adsorption of CO2 . The density profiles shown in Figure 10b predict that water divides the 3 nm pore into three subnanoscale pores. CO2 is confined between either water-water or water-graphite 26


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pores. Densities in these subnanoscale pores are then higher than that in the original pore.

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Langmuir

0.2

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Figure 11: Adsorption density of CO2 from a binary CO2 /CH4 (1:1) mixture in a 3 nm graphite pore pre-loaded by different amounts of water at different temperatures (310 - 460 K) and different pressures (15 - 90 MPa). Figure 12 shows the CO2 selectivity at various conditions shown previously. The selectivity of CO2 increases as water density increases. This increase results from the different solubilities of CO2 and CH4 in water. The pore is essentially modified by water to have higher preference to CO2 . An increase in CO2 selectivity is also reported by other researchers for modeled coal, 26 kerogen 18,22 and clays. 85 It was also shown that water is preferentially absorbed in the kerogen matrix rather than being adsorbed on the pore surface. 22

27


Langmuir

10

no water water density = 0.2 g/ml water density = 0.4 g/ml water density = 0.6 g/ml

8

x CO2 / xCH4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Figure 12: Selectivity of CO2 with respect to CH4 from a binary CO2 /CH4 (1:1) mixture in a 3 nm graphite pore pre-loaded by different amounts of water. C. Effect of fluid dissolution to kerogen matrix As shown in Figure 1(b), the pore walls, which are composed of kerogen, can be permeable to hydrocarbons and CO2 . CO2 has a different solubility in kerogen matrix from the hydrocarbons and exhibits a different selectivity in the matrix from when it is in the pore. It is thus of great interest and significance to quantify this effect from a molecular theory. An equation of state for the pore wall – kerogen, which based on PC-SAFT for cross-linked polymers and asphaltene, was developed in our previous work 39 and shows good agreement with experiments for kerogen swelling ratios when various solvents dissolve in kerogen. We then utilize the parameters (as provided in the Supplementary Information) to study the CO2 sorption in different types of kerogen. We firstly calculate the absorption selectivity of CO2 over CH4 from binary mixtures at 318 K and compare with that from molecular simulation results on compact kerogen matrix. Figure 13a shows the selectivity of CO2 over CH4 as they are absorbed in a Type II kerogen in the middle of the oil window. Using the molecular 28


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model for kerogen, selectivity of CO2 over CH4 is predicted in semiquantatitive agreement with molecular simulation, which shows the difference of CO2 /kerogen and CH4 /kerogen interactions are captured in a physical manner by the model. As the kerogen structure is fully fixed in molecular simulation, molecules mainly adsorb on the surface area of kerogen matrix. The subnanoscale of pores in matrix facilitates a high adsorption selectivity of CO2 . To understand the difference between selectivities in a nanopore and in a compact matrix, we compare the sorption selectivity of CO2 in kerogen matrix with that in different sized graphite pores for an equimolar CO2 /CH4 mixture at the same temperature ( Figure 13b) . We see at high pressures, CO2 selectivity is similar with a pore of 2.70 nm. However, the monotonic decay of selectivity with increasing pressure resembles that for graphite pores larger than 3 nm. The microporosity in kerogen only ranges from 1 - 20 %, so there is a non-neglegible volume for gas storage. The different selectivities of gas inside the matrix and in a graphite pore demonstrate the necessity of considering gas dissolution to matrix. 6

6

H = 1.26 nm H = 1.62 nm H = 1.98 nm H = 2.34 nm H = 2.70 nm H = 3.36 nm H = 5.52 nm H = 6.60 nm Type IIB kerogen

bulk CO2 fraction = 0.2 bulk CO2 fraction = 0.4

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4

CO2 selectivity

4

CO2 selectivity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

3

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Figure 13: (a)Selectivity of CO2 over CH4 in a Type II - middle of oil window kerogen (named IIB in kerogen parameter table in S.I.) matrix at T = 318 K. Kerogen matrix model prediction is compared with molecular simulation from Huang et al.. 86 (b)Comparison of CO2 sorption selectivity of an equimolar CO2/CH4 mixture in Type II kerogen and graphite pores of different pore sizes at T = 318 K. Within the permeable kerogen pore model, we are able to quantify the absolute sorption 29


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

per unit of kerogen matrix by including the porosity information. As kerogen becomes mature into the gas window, the H/C ratio decreases and microporosity increases due to gas generation from kerogen, which has been recognized by simulation and experimental studies. 2,18 As quantified on atomistic kerogen models by helium probe method, 18 the enterable pore (>4Å) porosities for three types of kerogens – immature Type I Green River kerogen (GRK), immature Type II kerogen and immature Type III kerogen – of decreasing H/C ratios of 1.53, 1.17 and 0.87 are 1.1 %, 1.8 % and 6.1 %, respectively. We take parameters for our model kerogens that have a similar H/C ratio (1.53, 1.24 and 1.04) and assume the corresponding porosities for the three types of kerogens. The pore size is fixed to be 4 Å representing the enterable pores. With such assumptions, we compare the sorption of pure CH4 and CH4 /CO2 mixture with experiments and simulations. Figure 14 shows the absolute CH4 sorption isotherms on Type II kerogens of increasing maturity. As expected, the amount of absolute sorption increases as maturity increases due to the increase in pore volume. The model predictions are in reasonable agreement with experiment, given the fact that samples from our models and the referenced experiments are different. It can be concluded that the permeable kerogen pore model is reasonable to quantify the loadings of molecules on microporous kerogen. In Figure 15 the loadings of CH4 and CO2 are also reasonably predicted in comparison with simulation. The difference is largely attributed to the difference in matrix properties – in molecular simulation, the predicted loadings all come from gas adsorption on surfaces of enterable pores, whereas the model accounts for the mixing of matrix with gases. This results in different characteristics of isotherms. Simulation predicts a more steep increase in sorption amounts at low pressure and reaches plateau quickly at higher pressure, which is different from experiments actually. 37,38 Selectivities predicted from theory are higher than simulation due to the large amount of CO2 sorption, as shown in Figure 16. The pressure where maximum selectivity occurs is in good agreement with simulation. To study how the dissolution of gases affect the overall selectivity of CO2 with respect to shale gas, we apply the model to a CO2 and shale gas (Eagle Ford gas as shown in 30


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1.60

CH4 excess sorption [mmol/g]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Type I_GRK_immature(DFT) Toarcian_Type II_middle of oil window (DFT)

1.40

Toarcian_Type II_end of oil window (DFT) early oil window 1 (exp)

1.20

early oil window 2 (exp) middle oil window 1 (exp)

1.00

middle oil window 2 (exp) gas window 1 (exp) gas window 2 (exp)

0.80 0.60 0.40 0.20 0.00 0

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14

16

Pressure [MPa]

Figure 14: Comparison between DFT model predicted and experimentally determined 2 absolute CH4 sorption isotherms on different types of kerogen at 338 K. Table 4) mixture with the CO2 mole fraction equal to 0.5. A uniform pore size of 3 nm and a porosity of 15 % is assumed for the three types of kerogen particles with an increasing maturity. A graphite pore of 3 nm is also used for the same mixture for comparison. This is a rough assumption as the deformation of pores due to increased loadings of molecules is not considered. Studies by Yang et al. 87,88 have shown the volumetric strain due to surface adsorption of CH4 and CO2 can be modeled by molecular DFT and relating the pore deformation to solvation pressures and elastic modulus of the material. As is shown in Figure 17, CO2 has a higher selectivity in nanoporous kerogen in comparison with graphite pore, though the selectivity is much lower than for a CO2 /CH4 mixture as in Figure 16. As kerogen becomes more mature, the selectivity of CO2 increases, which is of the same trend in the previous simulation done by Huang et al.. 18 As was shown by a more detailed analysis of our model, 39 the fractionation effect of kerogen on a fluid mixture becomes stronger as kerogen matures, thus dissolution of gases causes the overall CO2 selectivity to be higher for a more mature kerogen. A low kerogen micro and mesoporosity will intensify the fractionation effect of kerogen on free gases as the fraction of dissolved gases is higher. The presence of 31


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organic matter is expected to facilitate the gas recovery with CO2 injection and also the sequestration of CO2 . This effect has also been demonstrated from lab experiments of both static and dynamic CO2 contact with a Bakken shale sample, 89 where a very high recovery factor is obtained. This was explained by the high microporosity associated with organic matter and high affinity of CO2 with organic matter. 0.8

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Figure 15: Absolute adsorption isotherms of CH4 and CO2 in the binary (1:1) mixtures on kerogen models of different organic types at 338 K. Lines are predictions from DFT model and points are from molecular simulation of Huang et al.. 18 (a) CH4 (b) CO2 .

Conclusions Displacement of shale gas by injecting CO2 is favorable for improving the gas recovery factor and simultaneously sequestrating CO2 . Understanding the displacing mechanism from an equilibrium sorption point of view is essential for improving the gas recovery prediction and designing optimized operation strategies. In this work, we have applied a molecular density functional theory which reduces to the PC-SAFT EoS for bulk fluids to study the competitive sorption of CO2 with pure and mixed gases under various conditions, i.e. temperatures, pressures, gas composition, pore sizes, dry versus moist, and impermeable graphite versus permeable kerogen pores. The theory shows advantage in studying multicomponent systems 32


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Figure 16: CO2 /CH4 sorption selectivity on kerogen models. Lines are predictions from DFT model and points are from molecular simulation of Huang et al.. 18

CO2 selectivity

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1.45 1.43 1.41 1.39 1.37 1.35 1.33 1.31 1.29 1.27 1.25 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70

increasing maturity

Kerogen IIA Kerogen IIB Kerogen IIC

graphite pore 0

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Figure 17: Sorption selectivity of CO2 over Eagle Ford shale gas in nanoporous kerogen of 15 % porosity (up) and graphite pores(down) at T = 328 K. The inserted graph shows the simulated adsorption selectivity from Huang et al. 18 for three kerogen samples of increasing maturity for equimolar CO2 /CH4 .

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with trace components for a complex reservoir fluid while retaining the accuracy of explicitly describing molecular size and shape, fluid-fluid and fluid-solid interactions. Our composite kerogen model enables accurate modeling of sorption in the kerogen matrix and adsorption in nanopores. The major findings from this study can be summarized as follows: • The molecular density functional theory is well validated by GCMC simulation in graphite nanosized pores for pure CH4 , C2 H6 , and CO2 , and also for binary mixtures of CH4 /CO2 and C2 H6 /CO2 . Both theory and simulation show that CO2 is always preferentially adsorbed compared to CH4 but not for C2 H6 . • Consideration of the minor components (C2+) in shale gas is necessary as heavy components (C3+) strongly affect the overall selectivity of CO2 because of their stronger interactions with pore surfaces. The increase of temperature, pressure as well as pore size all have negative effects on the CO2 selectivity. • Presence of water trapped in the pore will greatly reduce the adsorbed amount of CO2 because of the decrease in available pore volume for CO2 . However, when CO2 is mixed with CH4 , selectivity of CO2 over CH4 in the pore is enhanced by water because of the higher solubility of CO2 in water. At low pore water concentrations, the amount of adsorbed CO2 even increases compared to a dry graphite pore because of an enhanced pore - fluid interaction energy which is induced by water. • Dissolution of gases to organic matter also elevates the CO2 selectivity. Predictions from our permeable kerogen pore model are directly compared with experimental measurement of CH4 and molecular simulation of CH4 /CO2 sorption with reasonable agreement in describing the absolute sorption and CO2 selectivity for kerogen of different maturities. In conclusion, molecular density functional theory for polyatomic molecules in combination with our new method of kerogen molecular modeling scheme 39 provides a powerful 34


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framework for understanding CO2 phase behavior with shale gas and water. Detailed structure information in molecular scale and subsequent linkings to meso- and macro-scale observations are both practical. In view of the high efficiency of solving for fluid properties, this model and method is promising to predict overall sorption and molecular distribution of gas mixtures in shale reservoirs.

Acknowledgement The authors thank the Robert A. Welch Foundation (Grant No. C-1241) and the American Chemical Society Petroleum Research Fund (No. ACS-PRF58859-ND6) for financial support. The authors also thank Prof. George Hirasaki, Dr. Philip Singer, Dr. Dilip Asthagiri, Zeliang Chen and Arjun Valiya Parambathu for insightful discussions.

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Competitive Sorption of CO2 with Gas Mixtures in Nanoporous Shale

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