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CH4 competitive sorption: Implications for CO2 sequestration and enhanced CH4 recovery
Journal of Petroleum Science and Engineering 183 (2019) 106460
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Kerogen deformation upon CO2/CH4 competitive sorption: Implications for CO2 sequestration and enhanced CH4 recovery
T
Liang Huanga,b,∗, Zhengfu Ninga,∗∗, Qing Wanga, Rongrong Qia, Zhilin Chenga, Xiaojun Wua, Wentong Zhanga, Huibo Qinc a
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, PR China Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, CA 94720-1462, United States c State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing), Beijing, 102249, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Kerogen deformation CO2/CH4 competitive adsorption CO2 sequestration and enhanced gas recovery Molecular simulation Poromechanical model
The low permeability of kerogen governs the storage and production of shale gas. The flexible kerogen constantly experiences mechanical deformation induced by reservoir environment and complex interplay with geofluids. However, the kerogen deformation associated with CH4/CO2 competitive sorption remains poorly understood. In this work, the effect of preloaded moisture on the deformation of kerogen with different organic types was investigated with molecular dynamics simulation. The kerogen deformation upon CH4/CO2 competitive sorption was quantified with the combination of grand canonical Monte Carlo simulations and poromechanics theory. The effects of various factors and their corresponding contributions were discussed in detail. The effects of kerogen deformation on CH4/CO2 diffusion were studied. Some implications for CO2 sequestration and enhanced gas recovery (CS-EGR) were proposed. Our results verify the theoretical feasibility of CS-EGR in shale gas reservoir. CO2 is observed to have a higher affinity with kerogen and a lower diffusion coefficient compared with CH4, facilitating it to replace CH4 and retain in the kerogen matrix. The rising CO2 composition can induce larger kerogen swelling, thus opening fluid flow pathways and increasing shale gas production. There are optimum moisture content and reservoir pressure corresponding to the maximum effective pore size in kerogen. It could be feasible to enhance the efficiency of CS-EGR by manipulating the reservoir moisture and CO2 injection timing. Thermal stimulation in deep shale reservoir may not be efficient for CS-EGR. CH4/CO2 competitive sorption can induce significant swelling of kerogen. The flexible nature of kerogen should be considered to improve the evaluation on both gas-in-place and CO2 storage capacity.
1. Introduction As one of the most potential substitutes for conventional fossil resources, shale gas has gained increasing attention due to its considerable resource abundance, environmental friendliness and high utilization efficiency (Kerr, 2010; Cueto-Felgueroso and Juanes, 2013; Paylor, 2017). The production of shale gas has experienced sharp expansion with the development of techniques such as horizontal well and hydraulic fracturing. It is estimated that the shale gas production can take up more than 45% of the total natural gas production in the U.S. by 2035 (Stevens, 2012). However, note that the current recovery factor for most shale gas reservoirs is still less than 20% (U.S. Energy Information, 2013). The low recovery factor can be mainly attributed to the presence of amorphous kerogen in shale reservoir.
∗
Kerogen, the major part of shale organic matter, is an amorphous matter insoluble in organic solvents. It is not only the source of hydrocarbons, but also the main storage space for hydrocarbons due to abundant nanopores and specific surface areas (Wang et al., 2015). The hydrocarbons trapped in kerogen nodules can account for 50% of the total shale gas (Wang and Reed, 2009). Also, the complexity of nanoporous network in kerogen results in extremely low permeability of shale matrix, which contributes to the difficulty in gas desorption and production (Holmes et al., 2017; Wang et al., 2017a,b; Zhang et al., 2018a; Sun et al., 2019). In addition to physically heterogeneous nanochannels, kerogen also possesses surface heterogeneity due to the presence of heteroatom functional groups (Psarras et al., 2017; Wang et al., 2017a,b). The polar groups including carboxylic and hydroxylic groups enable moisture uptake by kerogen (Gensterblum et al., 2013;
Corresponding author. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, PR China. Corresponding author. E-mail addresses: [email protected] (L. Huang), [email protected] (Z. Ning).
∗∗
https://doi.org/10.1016/j.petrol.2019.106460 Received 23 February 2019; Received in revised form 17 August 2019; Accepted 31 August 2019 Available online 02 September 2019 0920-4105/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Kerogen units and models used in this work. (a) kerogen unit for type IA with a chemical formula of C251H385O13N7S3; (b) kerogen model for type IA with 6 units; (c) kerogen type IIA with a chemical formula of C252H294O24N6S3; (d) kerogen model for type IIA with 6 units; (e) kerogen type IIIA with a chemical formula of C233H204O27N4; (f) kerogen model for type IIIA with 7 units. Atom representations: black for carbon atoms, gray for hydrogen atoms, red for oxygen atoms, yellow for sulfur atoms, and blue for nitrogen atoms. The moisture content is 2.4 wt % in the three kerogen models. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
are closely correlated with the organic type of kerogen, which is governed by the biological source and the depositional environment. In recent years, CO2 sequestration and enhanced gas recovery (CSEGR) has been proposed as one potential strategy in shale gas
Hu et al., 2014). The loaded moisture can not only compete with gas for adsorption sites, interfere with the dynamic kerogen-gas interaction, but also block the nanochannels for fluid flow (Zhang et al., 2018b,c; Sun et al., 2018a,b). The innate physiochemical properties of kerogen 2
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2. Computational methodology
reservoirs, which can increase the shale gas production and mitigate the CO2 emission simultaneously (Aljamaan et al., 2017). Although the technique has not yet been commercialized, many attempts have been conducted to gain insights into the microscopic interplay between kerogen and CH4/CO2 mixtures by molecular simulations (Sun et al., 2017; Huang et al., 2017a, 2018a,b,c). However, the previous studies are based on the assumption of fixed kerogen structure, ignoring the dynamic nature of kerogen (Wu and Firoozabadi, 2018). As a soft nanoporous matter, kerogen constantly experiences mechanical deformation induced by subsurface stress environment and interplay with geofluids. Recently, the flexibility of kerogen upon gas sorption has aroused intense interest in the literature. Although kerogen sample is subject to swelling upon gas adsorption in experiment (Zhao et al., 2017, 2018; Wu et al., 2019a,b), the quantification of volumetric strain remains a big challenge because of the difficulty in kerogen extraction and the small deformation of kerogen. Heller and Zoback (2014) adopted activated carbon to represent organic matter in shale, but only measured a volumetric strain on the magnitude of 10−3 upon gas adsorption. To date, there is no experimental report on kerogen deformation induced by gas sorption. Some researchers have devoted efforts into kerogen flexibility associated with gas sorption by molecular simulation. Pathak et al. (2018) studied the swelling of kerogen by performing annealing simulations on the system of kerogen and fixed CH4/CO2 components, which cannot represent the coupling between gas sorption and kerogen swelling. Tesson and Firoozabadi (2018) utilized a hybrid grand canonical Monte Carlo (GCMC) method based on molecular dynamics (MD) simulation (MD-GCMC) to study CH4 sorption in a flexible kerogen model. Although kerogen was flexible, the volume of the kerogen model was fixed due to the use of NVT ensemble (constant molecular number, volume and temperature). Ho et al. (2018) also adopted a hybrid MD-GCMC method but with NPT ensemble (constant molecular number, pressure and temperature) to study kerogen swelling induced by CH4 and CO2 sorption. Their simulations were conducted at zero effective stress condition to observe the maximum swelling of kerogen, different from the stress paths in reservoir conditions. Therefore, the kerogen deformation associated with gas sorption using molecular simulations is still in a preliminary stage and remains to be further improved. Alternatively, some authors have devoted theoretical efforts to unifying fluid sorption and mechanical deformation within porous framework (Brochard et al., 2012a; Carmeliet et al., 2012; Kulasinski et al., 2015). Brochard et al. (2012b) developed a poromechanical model to assess the sorption-induced deformation in solids extended to micropores. This model has successfully described the interplay between sorption and deformation in microporous solids such as coal (Brochard et al., 2012b) silicon (Coasne et al., 2014) and kerogen (Sui and Yao, 2016; Huang et al., 2019). Despite of previous efforts, kerogen deformation associated with CH4/CO2 sorption remains to be unraveled. The effect of preloaded moisture on kerogen deformation is still poorly understood. In our recent work (Huang et al., 2019), we gained insights into kerogen deformation upon CH4/CO2 sorption and water loading for the first time. In this work, we extend the research to kerogen deformation induced by CH4/CO2 competitive sorption. MD simulations were performed to characterize the moisture induced deformation of kerogen with different organic types, while the combination of GCMC simulations and poromechanics theory was utilized to quantify the kerogen deformation induced by CH4/CO2 competitive sorption. The effects of organic type, moisture content, CO2 composition, pressure, temperature and geological depth on kerogen deformation were discussed. We shed lights on the coupling deformation mechanisms of kerogen by decomposing the contribution from pressure, temperature, geological depth and total sorption amount. The effects of kerogen deformation on CH4/CO2 diffusion were explored. Also, the implications of our results for CS-EGR were discussed.
2.1. Construction of kerogen models In this work, we focus on three immature types of kerogen (IA, IIA and IIIA in Fig. 1), covering sources of both conventional and unconventional hydrocarbon resources. Kerogen IA is typical of hydrogenrich kerogen correlated with oil shale retorting and shale oil. Kerogen IIA is representative source of conventional hydrocarbon resources. Kerogen IIIA is also regarded as important contributing source of conventional oil and gas resources. The chemical structures of the three kerogen units were developed by Ungerer et al. (2014) based on analytical experimental data. The elemental compositions, lattice parameters and functional groups of these kerogen units are in good agreement with the derived results from 13C NMR spectroscopy, X-ray photoelectron spectroscopy and S-XANES data (Kelemen et al., 2007). In this work, we combine geometry optimization, annealing dynamics and successive MD simulations to bring the three kerogen units into three-dimensional condensed phases. Geometry optimization was first performed on the kerogen units to obtain the relaxed configurations with local minimum energy. In geometry optimization, the smart minimization algorithm was adopted with a fine convergence criterion. The short-range cutoff distance for non-bonded interaction was 15.5 Å. Subsequently, annealing dynamics, including 10 cycles with temperature first increasing from 300 to 800 K and then decrease back, were conducted to search for the configurations with global minimum energy. The simulation under each temperature point was carried out with the NVT ensemble, and a total simulation time of 400 ps was executed for the annealing process. These relaxed kerogen units were then put into an amorphous cell with initial density of 0.1 g/cm3 (Ungerer et al., 2014; Huang et al., 2017b). Successive MD simulations were thereafter performed to further relax the kerogen structures (Huang et al., 2017b, 2018d). Structure relaxation at high temperature was first performed with NVT ensemble at 800 K for 400 ps. Then MD simulations with NPT ensemble were conducted at 20 MPa with a stepwise decreasing temperature from 800 to 300 K (Huang et al., 2017b, 2018d). The simulation time was determined by checking the convergence of the kerogen densities. Finally, these configurations of kerogen models were relaxed at 300 K and 0.1 MPa for 2000 ps to obtain the stable structures. 2.2. Computational details All the simulations in this work were performed using the Materials Studio package (Materials Studio, 2012). The COMPASS force field (Sun, 1998) was adopted to describe the non-bonded dispersion-repulsion interactions between atomic pairs and the intramolecular interactions in kerogen units. This force field has been proven to provide fairly consistent predictions for structural and thermodynamic properties of both inorganic and organic materials (Huang et al., 2018b; Sui and Yao, 2016). The cutoff radius for short-range pair interaction is 15.5 Å, meeting the criterion that the cutoff distance should be smaller than the half length of the minimum dimension of the simulation box. The barostat and thermostat methods are Berendsen (Berendsen et al., 1984) and Nosé-Hoover (1985) respectively. The long-range Coulombic interactions are summed by the Ewald method. The fluid molecules including H2O, CH4 and CO2 are represented by full-atom models with point charge on each Lennard-Jones center (Wang and Huang, 2019). To study the effect of moisture content on kerogen deformation, the kerogen models with various moisture contents were built. These moisture contents (0–4.8 wt%) were determined based on previous experimental investigations (Gasparik et al., 2013) and simulation work (Zhang et al., 2014). The moisture induced deformation was investigated using the MD simulation with NPT ensemble, in which both the kerogen structures and the simulation box can change during the relaxation simulation. The simulation time for each NPT run is 5000 ps 3
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Ottiger et al. (2008) and Brochard et al. (2012b). In this model, the total sorption including the adsorption amounts and the absorption amounts are used. In our recent work (Huang et al., 2019), we have validated this model by matching the predicted kerogen swelling upon CH4/CO2 sorption with documented data from molecular simulation. To distinguish the effect of adsorption and absorption on kerogen deformation, the excess adsorption amount is converted from the total sorption amount by,
ne = n − υρ
(3)
where n e is the excess adsorption amount, n is the total sorption amount, ρ is the bulk gas density, and υ is the free pore volume of kerogen model. The excess adsorption is utilized to quantify the deformation of kerogen induced by gas adsorption. To study the effect of kerogen deformation on fluids diffusion, the self-diffusion coefficients of CH4/CO2/H2O are calculated with the Einstein equation (Tesson and Firoozabadi, 2018),
D=
with a time step of 1 fs. The kerogen deformation is quantified with the definition of volumetric strain,
V − V0 V0
(1)
where Vε is the volumetric strain, V and V0 are the box volume of kerogen models with and without moisture, respectively. The free pore volumes in the flexible kerogen structure were detected using the probe insertion method with the Connolly algorithm (Connolly, 1983). To be consistent with measurements, the radius of helium (1.3 Å) was assigned for the probe molecule to compute the porosity. The pore size distribution (PSD) of kerogen model represents the incremental pore volume as a function of pore width. We increased the Connolly diameter of probe molecule stepwise from 0.1 to 6.2 Å to detect the pore volume corresponding to the probe molecule. PSD was then computed by differentiating the free pore volumes with respect to different diameters of probe molecule. The deformation of kerogen models induced by CH4/CO2 competitive sorption was investigated by the combination of molecular simulation and poromechanics model. The sorption amounts for CH4 and CO2 in the mixtures were simulated with the GCMC method. The kerogen structures were kept fixed during the sorption process to match the condition of zero strain. For each pressure point, a total of 6 × 107 Monte Carlo steps are performed, wherein the first 3 × 107 steps are utilized to guarantee the adsorption equilibration, while the remaining steps are utilized to compute the statistical adsorption amount. The sorption amounts were then combined with the extended poromechanical model proposed by Brochard et al. (2012b) to provide a quantitative estimate of kerogen deformation. This extended model takes into account the effect of pressure, temperature, adsorption and absorption,
Vε = −
CCH4 P + K K
∫
fCH4 0
CCO2 nCH4 RT dfCH4 + K fCH4
∫
fCO2 0
N
∑ ⟨ [ri (t ) − ri (0)]2 ⟩ i=1
(4)
where D is the self-diffusion coefficient of fluid species, N is the number of molecules for studied species, ri (t ) is the position of the particle i at N time t . ∑i = 1 ⟨ [ri (t ) − ri (0)]2 ⟩ is defined as the mean square displacement (MSD). The MSD is proportional to t m with m < 1 in the early stage of relaxation simulation. After sufficient equilibrium, the normal diffusion (m = 1) is reached, which can be described by the Einstein equation (Wu et al., 2019a,b). In this work, we performed successive NPT (1000 ps), NVT (1000 ps) and NVE (10000 ps) simulations to collect trajectory data for computing the self-diffusion coefficients of fluid molecules.
Fig. 2. Volumetric strain of kerogen as a function of moisture content at 30 MPa and 318 K. The error bars are estimated based on 10 blocks using the block averaging method.
Vε =
1 d lim 6N i →∞ dt
3. Results and discussion 3.1. Effect of moisture and organic type on kerogen deformation 3.1.1. Kerogen volumetric swelling Fig. 2 shows the volumetric strain of kerogen with different organic types as a function of moisture content. The volumetric strain of these immature kerogen models presents a linearly increasing trend as moisture content rises. The kerogen swelling induced by moisture is governed by the water volumes added into the kerogen skeletons. Chen et al. (2018) adopted molecular simulation to study the water sorption and induced swelling in flexible nanoporous polymer. They also observed that the water induced swelling was linearly proportional to the water loading amount. Fig. 2 also shows that the moisture induced deformation is in the order of kerogen IA > IIA > IIIA. At the moisture content of 4.8 wt %, the volumetric strain for kerogen IIIA is 1.64 ± 0.08%, while that for kerogen IIA and IA is 3.33 ± 0.19% and 5.63 ± 0.39%, respectively. To date, little study on kerogen swelling induced by moisture has been reported. Some researchers have put efforts on coal swelling induced by moisture and gas adsorption. Fry et al. (2009) measured the moisture induced swelling on coal and found the swelling decreased as the coal rank rose. Day et al. (2011) concluded by measurement that the maximum swelling induced by CH4 adsorption in the highest rank coal was twice smaller than that in the lowest rank sample. The effect of organic type on moisture induced kerogen swelling is similar to the measured effect of coal rank on coal swelling. The maximum volumetric strain induced by moisture in our kerogen models ranges between 1.64 ± 0.08–5.63 ± 0.39%, close to the reported range (0.5–5%) on coal samples (Fry et al., 2009). The effect of organic type on kerogen swelling can be attributed to discrepancy in physicochemical structures between different kerogen models. For one thing, the chemical structure of kerogen unit with higher organic type, containing more aromatic clusters and less aliphatic chains, is stiffer than that with lower
nCO2 RT dfCO2 fCO2 (2)
where P is bulk pressure, K is bulk modulus, CCH4 and CCO2 are fluid coupling coefficient, nCH4 and nCO2 are total sorption amount in kerogen models at zero strain, fCH4 and fCO2 are fluid fugacity, T is temperature, R is universal constant. In this work, the values of K = 2.65 GPa, CCH4 = 6.05, CCO2 = 7.06 were adopted, as documented in the work of 4
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Fig. 3. Kerogen structure change due to sorption-induced swelling. (a) Kerogen cell size as a function of volumetric strain. (b) Kerogen matrix density as a function of volumetric strain. (c) Kerogen porosity as a function of volumetric strain. (d) Kerogen void fraction as a function of volumetric strain.
volumetric strain (Fig. 3c). This indicates that the outward expansion of kerogen matrix outweighs the inward expansion. The outward expansion can be attributed to the repulsive force between the preloaded water molecules and the kerogen matrix. The increasing amplitude of porosity is kerogen IA (9.5–14.5%) > IIA (11.5–14.6%) > IIIA (19.4–19.8%), which is related to the flexibility of kerogen units and the averaged pore size of kerogen models. Note that kerogen swelling is simulated at zero effective stress in this work. The inward expansion may be more pronounced for realistic kerogen in confined state at reservoir conditions. Although water molecules can induce an increasing porosity, they can also occupy some pore spaces. The void volume is defined as the remaining pore spaces in kerogen models with preloaded water molecules, which takes into account both the pore swelling effect and the pore occupation effect. Contrary to porosity, void fraction in our kerogen models shows a decreasing trend with increasing volumetric strain (Fig. 3d). This observation suggests the pore occupation effect of preloaded water molecules outweighs the induced pore swelling effect. The decreasing amplitude of void fraction is kerogen IA < IIA < IIIA, which is opposite to the change in porosity. Fig. 4 presents the void volume distribution (VSD) and specific surface area distribution in the kerogen models. Due to the limitation of kerogen size, the range of VSD in our kerogen models is narrow, similar to the reported VSD in kerogen by molecular simulation (Pathak et al., 2018). The narrow VSD is comparable with the measured micropore size distributions on kerogen by CO2 adsorption experiments (Rexer et al., 2014). In this work, we focus on the change of kerogen
organic type (Fig. 1). Thus, it is more difficult for kerogen IIIA to deform compared with kerogen IA and IIA. For another, the kerogen model with higher organic type has a larger average pore size. Water molecules located in the middle of pores can exert a smaller repulsive force to the kerogen skeleton. The two factors result in a smaller volumetric strain for kerogen IIIA than that for kerogen IA and IIA. The moisture induced volumetric strain presents an accepted divergence under different configurations using the block averaging method. The largest uncertainty was observed to be 6.84% for kerogen IA at the moisture content at 4.8 wt %. 3.1.2. Change of kerogen nanoporous structure Fig. 3 shows the change of kerogen structure associated with kerogen swelling. The cell size of kerogen model presents a linearly increasing correlation with the volumetric strain (Fig. 3a). The cell size ranges from 33.5 to 34.1 Å for kerogen IA model, from 32.5 to 32.8 Å for kerogen IIA model, and from 32.7 to 32.9 Å for kerogen IIIA model. These cell sizes are larger than the reported typical size (25 Å) that can reproduce most of structural and thermodynamic properties of realistic kerogen (Ungerer et al., 2014). The density of kerogen matrix shows a linearly decreasing dependence on the volumetric strain (Fig. 3b). As kerogen swells, the matrix expands outward, resulting in a more loose structure. In addition to outward expansion, the deformable kerogen matrix can also swell inward, which causes the complexity of the change of porous structure with kerogen swelling. A linear increase of porosity is observed in our kerogen models with the increase of 5
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Fig. 4. Void volume and specific surface area distribution. (a) Void volume distribution in kerogen IA. (b) Specific surface area distribution in kerogen IA. (c) Void volume distribution in kerogen IIA. (d) Specific surface area distribution in kerogen IIA. (e) Void volume distribution in kerogen IIIA. (f) Specific surface area distribution in kerogen IIIA.
volumetric strain. By comparing the VSDs for flexible kerogen models at the moisture content of 2.4 wt % and 4.8 wt %, we can observe that some bigger enterable voids are divided into smaller voids with further increasing moisture loading. This is also confirmed by the void distribution in Fig. 5b and c. By contrast, Fig. 5d,e,f show the change of pore distribution in kerogen with increasing moisture content, which is only affected by pore swelling effect. The increase of pore size is observed with kerogen swelling, since the effect of water occupation is not considered. Therefore, the effect of moisture on the kerogen void spaces is governed by both the pore swelling and pore occupation induced by water molecules.
nanostructure to study the effect of moisture induced deformation. In Fig. 4a,b,c,d, sharp peaks are observed around the maximum void sizes in kerogens. The sharp peaks are attributed to the significant change of probed void volumes in kerogens when the diameter of probe molecule increases to be larger than the maximum void sizes. By comparing the VSDs for rigid and flexible kerogen models at the moisture content of 2.4 wt %, we can observe that some smaller enterable voids are expanded into bigger voids with moisture induced swelling. This observation can be clearly confirmed by the void distribution in Fig. 5a and b. The expansion amplitude in void size is in the order of kerogen IA > IIA > IIIA, consistent with the sequence of moisture induced 6
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Fig. 5. Void and pore distribution in kerogen IIA. (a) Void in rigid structure with 2.4 wt % moisture content. (b) Void in flexible structure with 2.4 wt % moisture content. (c) Void in flexible structure with 4.8 wt % moisture content. (d) Pore in dry structure. (e) Pore in flexible structure with 2.4 wt % moisture content. (f) Pore in flexible structure with 4.8 wt % moisture content. Void and pore volume, shown in green, is probed by helium (d = 0.26 nm). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
to a larger kerogen swelling. The volumetric strain first increases to the maximum and then decreases as pressure further rises for kerogen IA and IIA. At higher pressure, the volumetric strain is expected to be negative, corresponding to kerogen shrinkage. For kerogen IIIA, the maximum volumetric strain has not yet been reached because of its high sorption capacity. According to the poromechanics theory, kerogen deformation induced by pressure results from both sorption-induced swelling and pressure-induced compression. Fig. 7 shows the contribution of the two factors to pressure induced deformation. Opposite effect is observed for the two factors on the volumetric strain of kerogen. Compared with pressure compression, sorption swelling dominates the contribution to kerogen deformation. The sorption swelling effect weakens while the pressure compression effect strengthens as pressure increases. The contribution of pressure compression effect is in the order of kerogen IA > IIA > IIIA, which is closely related to the flexibility of kerogen units.
3.2. Kerogen coupling deformation upon gas competitive sorption 3.2.1. Sorption-compression coupling deformation induced by pressure Fig. 6 shows the volumetric strain of dry kerogen models immersed in CH4/CO2 mixtures. Contrary to the moisture induced deformation, the kerogen deformation induced by CH4/CO2 competitive sorption is in the order of kerogen IA < IIA < IIIA. This trend is correlated with the kerogen porosity (kerogen IA < IIA < IIIA). At the same pressure, a higher porosity facilitates the sorption of more gas molecules, leading
3.2.2. Sorption-swelling coupling deformation induced by temperature Fig. 8 shows the effect of temperature on kerogen deformation and the contribution of temperature swelling effect and sorption reduction effect. In Fig. 8a, the kerogen deformation upon CH4/CO2 competitive sorption declines as temperature increases. Although temperature effect can swell kerogen skeleton, kerogen sorption capacity reduces as temperature rises, leading to deceasing kerogen deformation. In Fig. 8b, we can observe that sorption reduction effect plays a major role in temperature induced kerogen deformation. The contribution of temperature swelling effect gradually rises with increasing pressure. While the contribution of sorption reduction effect initially increases sharply and then decreases to reach a plateau (~70%) as pressure rises. The contribution of temperature swelling effect weakens as temperature increases, consistent with that of sorption reduction effect when pressure is below 20 MPa.
Fig. 6. Volumetric strain of dry kerogen upon CH4/CO2 competitive sorption as a function of pressure at the CO2 composition of 0.5 and 318 K. 7
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Fig. 7. Contribution of compression effect and sorption effect to volumetric strain induced by pressure at the CO2 composition of 0.5 and 318 K.
increasing pressure. At 50 MPa, the adsorption effect can even lead to kerogen shrinkage, the overall kerogen swelling is fully governed by the absorption effect at this pressure condition.
3.2.3. Pressure-temperature coupling deformation induced by geological depth Fig. 9a shows the effect of geological depth on kerogen deformation upon CH4/CO2 competitive sorption. The volumetric strain follows a linearly decreasing trend with the increase of geological depth. The effect of geological depth consists of both the pressure effect and the temperature effect. As discussed above, the pressure effect results in an increasing volumetric strain, while the temperature effect leads to a decreasing volumetric strain. Fig. 9a indicates that the temperature effect plays a major role in kerogen deformation upon CH4/CO2 competitive sorption induced by geological depth. Fig. 9b presents the contribution of pressure effect and temperature effect to the volumetric strain. The positive pressure effect decreases while the negative temperature effect increases as the geological depth increases.
3.2.5. Effect of moisture content and CO2 composition Fig. 11 presents the effect of moisture content and CO2 composition on the volumetric strain of kerogen IIIA upon CH4/CO2 competitive sorption. The gas induced volumetric strain declines as the moisture content increases. The moisture loaded into the kerogen skeleton occupies some polar adsorption sites and pore volumes, reducing the sorption capacity of kerogen for gas molecules. Note that, as we show in section 3.1, the moisture can also induce kerogen swelling, contributing to larger pore volumes. The moist kerogen is already partly swelled before gas sorption. Therefore, the coupling deformation of kerogen induced by both the moisture uptake and gas sorption should be further studied. The volumetric strain induced by CH4/CO2 competitive sorption initially rises sharply and then increases gently with the increase of CO2 composition. This indicates that kerogen has a larger affinity with CO2 compared with CH4. The sorption loading of gas molecules increases with increasing CO2 composition, resulting in a larger volumetric strain.
3.2.4. Adsorption-absorption coupling deformation induced by sorption The kerogen deformation upon CH4/CO2 competitive sorption consists of both adsorption effect and absorption effect. Fig. 10 shows the contribution of the two effects. The adsorption induced volumetric strain initially rises to the maximum and then declines with increasing pressure. While the absorption induced volumetric strain shows a continuously increasing trend as pressure rises. The adsorption effect plays a major role in sorption induced deformation at low pressure, while the absorption effect gradually dominates the contribution with
Fig. 8. (a) Effect of temperature on the volumetric strain of dry kerogen IIIA at the CO2 composition of 0.5. (b) Contribution of temperature swelling effect and sorption reduction effect to kerogen deformation induced by temperature. 8
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Fig. 9. (a) Effect of geological depth on the volumetric strain of dry kerogen IIIA at the CO2 composition of 0.5. (b) Contribution of temperature effect and pressure effect to kerogen deformation induced by geological depth.
3.3. Effect of kerogen deformation on fluid diffusion Kerogen experiences constantly mechanical deformation under reservoir conditions, which significantly affects the percolation of geofluids. In the section, we design three scenarios to study the effect of kerogen deformation on CH4/CO2/H2O diffusion. In scenario (a), CH4 and CO2 molecules diffuse in fixed dry kerogen IIIA model. In scenario (b), the dry kerogen is allowed to deformation, while in scenario (c), the kerogen is firstly moisture equilibrated at the moisture content of 2.4 wt %. Table 1 lists the self-diffusion coefficients of CH4/CO2/H2O molecules in the three scenarios. In this work, we focus on the differences of self-diffusion coefficients between fluid molecules and various scenarios instead of the actual values. By comparing scenario (a) and (b), we can observe that CH4/CO2 self-diffusion coefficients increase when kerogen becomes flexible. This indicates that kerogen deformation induced by CH4/CO2 competitive sorption open the diffusion paths for both CH4 and CO2. By comparing scenario (b) and (c), we observe that CH4/CO2 self-diffusion coefficients rise with the loading of water molecules, suggesting the effect of moisture induced pore swelling outweighs the effect of pore occupation by water molecules at this moisture condition. Also, the self-diffusion coefficient of CO2 has a larger increase than that of CH4, which indicates the effect of pore swelling induced by moisture uptake preferentially facilitates the diffusion of CO2. CH4 is observed to diffuse faster than CO2 in the three scenarios. This can be attributed to that kerogen has a higher affinity
Fig. 10. Volumetric strain induced by adsorption effect and absorption effect for dry kerogen IIIA upon CH4/CO2 competitive sorption at the CO2 composition of 0.5 and 318 K.
Fig. 11. (a) Effect of moisture content on the volumetric strain of kerogen IIIA upon CH4/CO2 competitive sorption at the CO2 composition of 0.5 and 318 K. (b) Effect of CO2 composition on the volumetric strain of dry kerogen IIIA upon CH4/CO2 competitive sorption at 318 K. 9
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Table 1 Self-diffusion coefficients of fluid molecules in the kerogen skeleton.a System
DCH₄ (m2/s)
DCO₂ (m2/s)
DH₂O (m2/s)
Fixed dry kerogen with CH4 & CO2 Swelling dry kerogen with CH4 & CO2 Swelling moist kerogen (2.4 wt %) with CH4 & CO2
3.1 ± 0.7 × 10−11 5.9 ± 0.6 × 10−11 6.1 ± 0.8 × 10−11
1.4 ± 0.5 × 10−11 2.0 ± 0.5 × 10−11 5.0 ± 0.6 × 10−11
– – 5.1 ± 0.7 × 10−11
a
The deviations are derived from three different kerogen configurations.
compression. With the desorption and production of shale gas, the reservoir pressure declines, which can increase the kerogen swelling. Therefore, injecting CO2 into reservoir when the reservoir pressure drops to around the optimum pressure could improve the efficiency of CS-EGR. The kerogen swelling decreases with increasing temperature, which indicates thermal stimulation can reduce the fluid flow pathways in shale kerogen, thus damping the efficiency of CS-EGR. The kerogen swelling is inversely proportional to the geological depth. Shallow shale reservoir should be preferentially evaluated on suitability for CS-EGR.
with CO2, as well as H2O, compared with CH4. The self-diffusion coefficients of fluid molecules in kerogen matrix are in the order of 10−11, which is in the same order of magnitude with that of CO2 in coal reported by Wu et al. (2019a,b) (6.8 × 10−11–2.33 × 10−10), Zhang et al. (2016) (3 × 10−11–1.5 × 10−10) and Zhao et al. (2016) (5.4 × 10−11). The self-diffusion coefficient is sensitive to the porous skeleton, fluid species, temperature and pressure conditions. The low diffusion coefficients can be attributed to the slowing effect, as reported by previous studies (Krishna and van Baten, 2010), where the thermal and dynamic motion of the slowest molecules can damp the diffusion of the fasted molecules. This slowing effect can result in a reduction of diffusion coefficient by an order of magnitude (Kucukpinar and Doruker, 2003; Viswanathan et al., 2011).
4. Conclusions Kerogen deformation with preloaded moisture was quantified with MD simulations, while kerogen deformation upon CH4/CO2 competitive sorption was quantified with the combination of GCMC simulations and poromechanics theory. The main conclusions are summarized as follows.
3.4. Implications for CS-EGR This work sheds lights on kerogen deformation upon CH4/CO2 competitive sorption. In this section, we discuss the potential application of these results in fields associated with CS-EGR. Our results show that there is a strong chemo-mechanical coupling in kerogen associated with CH4/CO2 competitive sorption. Gas sorption can induce significant swelling of kerogen, thus increasing the sorption capacity of kerogen. This indicates that the assumption of fixed kerogen structure cannot capture the realistic interplay between kerogen and geofluids. Also, the dynamic nature of kerogen should be taken into account to improve the evaluation on both gas-in-place and CO2 storage capacity in shale reservoirs associated with CS-EGR. CO2 is observed to have a higher affinity with kerogen and a lower diffusion coefficient compared with CH4, which facilitates it to replace CH4 and retain in the kerogen matrix. The rising CO2 composition can induce larger kerogen swelling, generating more nanochannels in the kerogen matrix. The low permeability of kerogen plays a major role in shale gas percolation. The injecting CO2 can open fluid flow pathways in the complex nanoporous network of kerogen, thus increasing the shale gas production. The kerogen deformation is greatly affected by the moisture content. Moisture by itself can linearly increase the volumetric strain of kerogen with increasing moisture uptake. However, moisture can also result in a decrease of gas sorption amount, reducing the gas induced swelling. At low moisture content, the effective pore size, as well as the gas diffusion coefficient, increases with the moisture content. While at high moisture condition, the pore occupation induced by moisture uptake plays a major role, leading to a decrease of the effective pore size. We can manipulate the moisture content in kerogen to obtain the maximum kerogen swelling, which can facilitate the injection of CO2 and production of CH4. For kerogen with low original moisture content like type III kerogen or high mature kerogen, it can be theoretically feasible to enhance the efficiency of CS-EGR by increasing the reservoir moisture. To accomplish this purpose, we can first inject CO2 to produce artificial fractures in the reservoir, and then inject slick water to carry proppants and increase moisture contents. Also, steam injection is another potential technique to increase the reservoir moisture. The effect of pressure shows that there is an optimum pressure corresponding to the maximum kerogen swelling. This result provides implication for the injection timing of CO2 associated with CS-EGR in shale gas reservoir. The original shale reservoir is under high pressure
1. The moisture induced swelling is in the order of kerogen IA > IIA > IIIA.There is an optimum moisture content corresponding to the maximum effective pore size. The efficiency of CSEGR could be enhanced by manipulating the reservoir moisture. Potential techniques include hybrid CO2-water fracturing and steam injection. 2. The adsorption effect plays a major role in kerogen deformation upon CH4/CO2 sorption at low pressure, while the absorption effect gradually dominates the contribution with increasing pressure. 3. Kerogen swelling upon CH4/CO2 sorption decreases with increasing geological depth. Shallow shale reservoir is more potentially suitable for CS-EGR. 4. The temperature effect outweighs the pressure effect in kerogen deformation induced by geological depth. Kerogen swelling decreases as temperature rises. Thermal stimulation in deep shale reservoir may not improve the efficiency of CS-EGR. 5. The volumetric strain initially increases and then decreases with rising pressure. Conducting CS-EGR around the optimum pressure corresponding to the maximum swelling is suggested. 6. CO2 has a higher affinity with kerogen and a lower diffusion coefficient compared with CH4. The rising CO2 composition can induce larger kerogen swelling, which generates more nanochannels in kerogen matrix thereby enhancing shale gas production. Notes The authors declare no competing financial interest. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51774298 and 51504265) and the Science Foundation for the Excellent Youth Scholars of China University of Petroleum (Beijing) (Grant No.2462015YQ0223). Computer time for this study was provided by the HP High Performance Computing Cluster of the State Key Laboratory of Heavy Oil Processing at China University of Petroleum (Beijing). We also appreciate the support of China Scholarship Council (CSC No. 201806440095). 10
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11
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Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Kerogen deformation upon CO2/CH4 competitive sorption: Implications for CO2 sequestration and enhanced CH4 recovery
T
Liang Huanga,b,∗, Zhengfu Ninga,∗∗, Qing Wanga, Rongrong Qia, Zhilin Chenga, Xiaojun Wua, Wentong Zhanga, Huibo Qinc a
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, PR China Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, CA 94720-1462, United States c State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing), Beijing, 102249, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Kerogen deformation CO2/CH4 competitive adsorption CO2 sequestration and enhanced gas recovery Molecular simulation Poromechanical model
The low permeability of kerogen governs the storage and production of shale gas. The flexible kerogen constantly experiences mechanical deformation induced by reservoir environment and complex interplay with geofluids. However, the kerogen deformation associated with CH4/CO2 competitive sorption remains poorly understood. In this work, the effect of preloaded moisture on the deformation of kerogen with different organic types was investigated with molecular dynamics simulation. The kerogen deformation upon CH4/CO2 competitive sorption was quantified with the combination of grand canonical Monte Carlo simulations and poromechanics theory. The effects of various factors and their corresponding contributions were discussed in detail. The effects of kerogen deformation on CH4/CO2 diffusion were studied. Some implications for CO2 sequestration and enhanced gas recovery (CS-EGR) were proposed. Our results verify the theoretical feasibility of CS-EGR in shale gas reservoir. CO2 is observed to have a higher affinity with kerogen and a lower diffusion coefficient compared with CH4, facilitating it to replace CH4 and retain in the kerogen matrix. The rising CO2 composition can induce larger kerogen swelling, thus opening fluid flow pathways and increasing shale gas production. There are optimum moisture content and reservoir pressure corresponding to the maximum effective pore size in kerogen. It could be feasible to enhance the efficiency of CS-EGR by manipulating the reservoir moisture and CO2 injection timing. Thermal stimulation in deep shale reservoir may not be efficient for CS-EGR. CH4/CO2 competitive sorption can induce significant swelling of kerogen. The flexible nature of kerogen should be considered to improve the evaluation on both gas-in-place and CO2 storage capacity.
1. Introduction As one of the most potential substitutes for conventional fossil resources, shale gas has gained increasing attention due to its considerable resource abundance, environmental friendliness and high utilization efficiency (Kerr, 2010; Cueto-Felgueroso and Juanes, 2013; Paylor, 2017). The production of shale gas has experienced sharp expansion with the development of techniques such as horizontal well and hydraulic fracturing. It is estimated that the shale gas production can take up more than 45% of the total natural gas production in the U.S. by 2035 (Stevens, 2012). However, note that the current recovery factor for most shale gas reservoirs is still less than 20% (U.S. Energy Information, 2013). The low recovery factor can be mainly attributed to the presence of amorphous kerogen in shale reservoir.
∗
Kerogen, the major part of shale organic matter, is an amorphous matter insoluble in organic solvents. It is not only the source of hydrocarbons, but also the main storage space for hydrocarbons due to abundant nanopores and specific surface areas (Wang et al., 2015). The hydrocarbons trapped in kerogen nodules can account for 50% of the total shale gas (Wang and Reed, 2009). Also, the complexity of nanoporous network in kerogen results in extremely low permeability of shale matrix, which contributes to the difficulty in gas desorption and production (Holmes et al., 2017; Wang et al., 2017a,b; Zhang et al., 2018a; Sun et al., 2019). In addition to physically heterogeneous nanochannels, kerogen also possesses surface heterogeneity due to the presence of heteroatom functional groups (Psarras et al., 2017; Wang et al., 2017a,b). The polar groups including carboxylic and hydroxylic groups enable moisture uptake by kerogen (Gensterblum et al., 2013;
Corresponding author. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, PR China. Corresponding author. E-mail addresses: [email protected] (L. Huang), [email protected] (Z. Ning).
∗∗
https://doi.org/10.1016/j.petrol.2019.106460 Received 23 February 2019; Received in revised form 17 August 2019; Accepted 31 August 2019 Available online 02 September 2019 0920-4105/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Kerogen units and models used in this work. (a) kerogen unit for type IA with a chemical formula of C251H385O13N7S3; (b) kerogen model for type IA with 6 units; (c) kerogen type IIA with a chemical formula of C252H294O24N6S3; (d) kerogen model for type IIA with 6 units; (e) kerogen type IIIA with a chemical formula of C233H204O27N4; (f) kerogen model for type IIIA with 7 units. Atom representations: black for carbon atoms, gray for hydrogen atoms, red for oxygen atoms, yellow for sulfur atoms, and blue for nitrogen atoms. The moisture content is 2.4 wt % in the three kerogen models. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
are closely correlated with the organic type of kerogen, which is governed by the biological source and the depositional environment. In recent years, CO2 sequestration and enhanced gas recovery (CSEGR) has been proposed as one potential strategy in shale gas
Hu et al., 2014). The loaded moisture can not only compete with gas for adsorption sites, interfere with the dynamic kerogen-gas interaction, but also block the nanochannels for fluid flow (Zhang et al., 2018b,c; Sun et al., 2018a,b). The innate physiochemical properties of kerogen 2
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2. Computational methodology
reservoirs, which can increase the shale gas production and mitigate the CO2 emission simultaneously (Aljamaan et al., 2017). Although the technique has not yet been commercialized, many attempts have been conducted to gain insights into the microscopic interplay between kerogen and CH4/CO2 mixtures by molecular simulations (Sun et al., 2017; Huang et al., 2017a, 2018a,b,c). However, the previous studies are based on the assumption of fixed kerogen structure, ignoring the dynamic nature of kerogen (Wu and Firoozabadi, 2018). As a soft nanoporous matter, kerogen constantly experiences mechanical deformation induced by subsurface stress environment and interplay with geofluids. Recently, the flexibility of kerogen upon gas sorption has aroused intense interest in the literature. Although kerogen sample is subject to swelling upon gas adsorption in experiment (Zhao et al., 2017, 2018; Wu et al., 2019a,b), the quantification of volumetric strain remains a big challenge because of the difficulty in kerogen extraction and the small deformation of kerogen. Heller and Zoback (2014) adopted activated carbon to represent organic matter in shale, but only measured a volumetric strain on the magnitude of 10−3 upon gas adsorption. To date, there is no experimental report on kerogen deformation induced by gas sorption. Some researchers have devoted efforts into kerogen flexibility associated with gas sorption by molecular simulation. Pathak et al. (2018) studied the swelling of kerogen by performing annealing simulations on the system of kerogen and fixed CH4/CO2 components, which cannot represent the coupling between gas sorption and kerogen swelling. Tesson and Firoozabadi (2018) utilized a hybrid grand canonical Monte Carlo (GCMC) method based on molecular dynamics (MD) simulation (MD-GCMC) to study CH4 sorption in a flexible kerogen model. Although kerogen was flexible, the volume of the kerogen model was fixed due to the use of NVT ensemble (constant molecular number, volume and temperature). Ho et al. (2018) also adopted a hybrid MD-GCMC method but with NPT ensemble (constant molecular number, pressure and temperature) to study kerogen swelling induced by CH4 and CO2 sorption. Their simulations were conducted at zero effective stress condition to observe the maximum swelling of kerogen, different from the stress paths in reservoir conditions. Therefore, the kerogen deformation associated with gas sorption using molecular simulations is still in a preliminary stage and remains to be further improved. Alternatively, some authors have devoted theoretical efforts to unifying fluid sorption and mechanical deformation within porous framework (Brochard et al., 2012a; Carmeliet et al., 2012; Kulasinski et al., 2015). Brochard et al. (2012b) developed a poromechanical model to assess the sorption-induced deformation in solids extended to micropores. This model has successfully described the interplay between sorption and deformation in microporous solids such as coal (Brochard et al., 2012b) silicon (Coasne et al., 2014) and kerogen (Sui and Yao, 2016; Huang et al., 2019). Despite of previous efforts, kerogen deformation associated with CH4/CO2 sorption remains to be unraveled. The effect of preloaded moisture on kerogen deformation is still poorly understood. In our recent work (Huang et al., 2019), we gained insights into kerogen deformation upon CH4/CO2 sorption and water loading for the first time. In this work, we extend the research to kerogen deformation induced by CH4/CO2 competitive sorption. MD simulations were performed to characterize the moisture induced deformation of kerogen with different organic types, while the combination of GCMC simulations and poromechanics theory was utilized to quantify the kerogen deformation induced by CH4/CO2 competitive sorption. The effects of organic type, moisture content, CO2 composition, pressure, temperature and geological depth on kerogen deformation were discussed. We shed lights on the coupling deformation mechanisms of kerogen by decomposing the contribution from pressure, temperature, geological depth and total sorption amount. The effects of kerogen deformation on CH4/CO2 diffusion were explored. Also, the implications of our results for CS-EGR were discussed.
2.1. Construction of kerogen models In this work, we focus on three immature types of kerogen (IA, IIA and IIIA in Fig. 1), covering sources of both conventional and unconventional hydrocarbon resources. Kerogen IA is typical of hydrogenrich kerogen correlated with oil shale retorting and shale oil. Kerogen IIA is representative source of conventional hydrocarbon resources. Kerogen IIIA is also regarded as important contributing source of conventional oil and gas resources. The chemical structures of the three kerogen units were developed by Ungerer et al. (2014) based on analytical experimental data. The elemental compositions, lattice parameters and functional groups of these kerogen units are in good agreement with the derived results from 13C NMR spectroscopy, X-ray photoelectron spectroscopy and S-XANES data (Kelemen et al., 2007). In this work, we combine geometry optimization, annealing dynamics and successive MD simulations to bring the three kerogen units into three-dimensional condensed phases. Geometry optimization was first performed on the kerogen units to obtain the relaxed configurations with local minimum energy. In geometry optimization, the smart minimization algorithm was adopted with a fine convergence criterion. The short-range cutoff distance for non-bonded interaction was 15.5 Å. Subsequently, annealing dynamics, including 10 cycles with temperature first increasing from 300 to 800 K and then decrease back, were conducted to search for the configurations with global minimum energy. The simulation under each temperature point was carried out with the NVT ensemble, and a total simulation time of 400 ps was executed for the annealing process. These relaxed kerogen units were then put into an amorphous cell with initial density of 0.1 g/cm3 (Ungerer et al., 2014; Huang et al., 2017b). Successive MD simulations were thereafter performed to further relax the kerogen structures (Huang et al., 2017b, 2018d). Structure relaxation at high temperature was first performed with NVT ensemble at 800 K for 400 ps. Then MD simulations with NPT ensemble were conducted at 20 MPa with a stepwise decreasing temperature from 800 to 300 K (Huang et al., 2017b, 2018d). The simulation time was determined by checking the convergence of the kerogen densities. Finally, these configurations of kerogen models were relaxed at 300 K and 0.1 MPa for 2000 ps to obtain the stable structures. 2.2. Computational details All the simulations in this work were performed using the Materials Studio package (Materials Studio, 2012). The COMPASS force field (Sun, 1998) was adopted to describe the non-bonded dispersion-repulsion interactions between atomic pairs and the intramolecular interactions in kerogen units. This force field has been proven to provide fairly consistent predictions for structural and thermodynamic properties of both inorganic and organic materials (Huang et al., 2018b; Sui and Yao, 2016). The cutoff radius for short-range pair interaction is 15.5 Å, meeting the criterion that the cutoff distance should be smaller than the half length of the minimum dimension of the simulation box. The barostat and thermostat methods are Berendsen (Berendsen et al., 1984) and Nosé-Hoover (1985) respectively. The long-range Coulombic interactions are summed by the Ewald method. The fluid molecules including H2O, CH4 and CO2 are represented by full-atom models with point charge on each Lennard-Jones center (Wang and Huang, 2019). To study the effect of moisture content on kerogen deformation, the kerogen models with various moisture contents were built. These moisture contents (0–4.8 wt%) were determined based on previous experimental investigations (Gasparik et al., 2013) and simulation work (Zhang et al., 2014). The moisture induced deformation was investigated using the MD simulation with NPT ensemble, in which both the kerogen structures and the simulation box can change during the relaxation simulation. The simulation time for each NPT run is 5000 ps 3
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Ottiger et al. (2008) and Brochard et al. (2012b). In this model, the total sorption including the adsorption amounts and the absorption amounts are used. In our recent work (Huang et al., 2019), we have validated this model by matching the predicted kerogen swelling upon CH4/CO2 sorption with documented data from molecular simulation. To distinguish the effect of adsorption and absorption on kerogen deformation, the excess adsorption amount is converted from the total sorption amount by,
ne = n − υρ
(3)
where n e is the excess adsorption amount, n is the total sorption amount, ρ is the bulk gas density, and υ is the free pore volume of kerogen model. The excess adsorption is utilized to quantify the deformation of kerogen induced by gas adsorption. To study the effect of kerogen deformation on fluids diffusion, the self-diffusion coefficients of CH4/CO2/H2O are calculated with the Einstein equation (Tesson and Firoozabadi, 2018),
D=
with a time step of 1 fs. The kerogen deformation is quantified with the definition of volumetric strain,
V − V0 V0
(1)
where Vε is the volumetric strain, V and V0 are the box volume of kerogen models with and without moisture, respectively. The free pore volumes in the flexible kerogen structure were detected using the probe insertion method with the Connolly algorithm (Connolly, 1983). To be consistent with measurements, the radius of helium (1.3 Å) was assigned for the probe molecule to compute the porosity. The pore size distribution (PSD) of kerogen model represents the incremental pore volume as a function of pore width. We increased the Connolly diameter of probe molecule stepwise from 0.1 to 6.2 Å to detect the pore volume corresponding to the probe molecule. PSD was then computed by differentiating the free pore volumes with respect to different diameters of probe molecule. The deformation of kerogen models induced by CH4/CO2 competitive sorption was investigated by the combination of molecular simulation and poromechanics model. The sorption amounts for CH4 and CO2 in the mixtures were simulated with the GCMC method. The kerogen structures were kept fixed during the sorption process to match the condition of zero strain. For each pressure point, a total of 6 × 107 Monte Carlo steps are performed, wherein the first 3 × 107 steps are utilized to guarantee the adsorption equilibration, while the remaining steps are utilized to compute the statistical adsorption amount. The sorption amounts were then combined with the extended poromechanical model proposed by Brochard et al. (2012b) to provide a quantitative estimate of kerogen deformation. This extended model takes into account the effect of pressure, temperature, adsorption and absorption,
Vε = −
CCH4 P + K K
∫
fCH4 0
CCO2 nCH4 RT dfCH4 + K fCH4
∫
fCO2 0
N
∑ ⟨ [ri (t ) − ri (0)]2 ⟩ i=1
(4)
where D is the self-diffusion coefficient of fluid species, N is the number of molecules for studied species, ri (t ) is the position of the particle i at N time t . ∑i = 1 ⟨ [ri (t ) − ri (0)]2 ⟩ is defined as the mean square displacement (MSD). The MSD is proportional to t m with m < 1 in the early stage of relaxation simulation. After sufficient equilibrium, the normal diffusion (m = 1) is reached, which can be described by the Einstein equation (Wu et al., 2019a,b). In this work, we performed successive NPT (1000 ps), NVT (1000 ps) and NVE (10000 ps) simulations to collect trajectory data for computing the self-diffusion coefficients of fluid molecules.
Fig. 2. Volumetric strain of kerogen as a function of moisture content at 30 MPa and 318 K. The error bars are estimated based on 10 blocks using the block averaging method.
Vε =
1 d lim 6N i →∞ dt
3. Results and discussion 3.1. Effect of moisture and organic type on kerogen deformation 3.1.1. Kerogen volumetric swelling Fig. 2 shows the volumetric strain of kerogen with different organic types as a function of moisture content. The volumetric strain of these immature kerogen models presents a linearly increasing trend as moisture content rises. The kerogen swelling induced by moisture is governed by the water volumes added into the kerogen skeletons. Chen et al. (2018) adopted molecular simulation to study the water sorption and induced swelling in flexible nanoporous polymer. They also observed that the water induced swelling was linearly proportional to the water loading amount. Fig. 2 also shows that the moisture induced deformation is in the order of kerogen IA > IIA > IIIA. At the moisture content of 4.8 wt %, the volumetric strain for kerogen IIIA is 1.64 ± 0.08%, while that for kerogen IIA and IA is 3.33 ± 0.19% and 5.63 ± 0.39%, respectively. To date, little study on kerogen swelling induced by moisture has been reported. Some researchers have put efforts on coal swelling induced by moisture and gas adsorption. Fry et al. (2009) measured the moisture induced swelling on coal and found the swelling decreased as the coal rank rose. Day et al. (2011) concluded by measurement that the maximum swelling induced by CH4 adsorption in the highest rank coal was twice smaller than that in the lowest rank sample. The effect of organic type on moisture induced kerogen swelling is similar to the measured effect of coal rank on coal swelling. The maximum volumetric strain induced by moisture in our kerogen models ranges between 1.64 ± 0.08–5.63 ± 0.39%, close to the reported range (0.5–5%) on coal samples (Fry et al., 2009). The effect of organic type on kerogen swelling can be attributed to discrepancy in physicochemical structures between different kerogen models. For one thing, the chemical structure of kerogen unit with higher organic type, containing more aromatic clusters and less aliphatic chains, is stiffer than that with lower
nCO2 RT dfCO2 fCO2 (2)
where P is bulk pressure, K is bulk modulus, CCH4 and CCO2 are fluid coupling coefficient, nCH4 and nCO2 are total sorption amount in kerogen models at zero strain, fCH4 and fCO2 are fluid fugacity, T is temperature, R is universal constant. In this work, the values of K = 2.65 GPa, CCH4 = 6.05, CCO2 = 7.06 were adopted, as documented in the work of 4
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Fig. 3. Kerogen structure change due to sorption-induced swelling. (a) Kerogen cell size as a function of volumetric strain. (b) Kerogen matrix density as a function of volumetric strain. (c) Kerogen porosity as a function of volumetric strain. (d) Kerogen void fraction as a function of volumetric strain.
volumetric strain (Fig. 3c). This indicates that the outward expansion of kerogen matrix outweighs the inward expansion. The outward expansion can be attributed to the repulsive force between the preloaded water molecules and the kerogen matrix. The increasing amplitude of porosity is kerogen IA (9.5–14.5%) > IIA (11.5–14.6%) > IIIA (19.4–19.8%), which is related to the flexibility of kerogen units and the averaged pore size of kerogen models. Note that kerogen swelling is simulated at zero effective stress in this work. The inward expansion may be more pronounced for realistic kerogen in confined state at reservoir conditions. Although water molecules can induce an increasing porosity, they can also occupy some pore spaces. The void volume is defined as the remaining pore spaces in kerogen models with preloaded water molecules, which takes into account both the pore swelling effect and the pore occupation effect. Contrary to porosity, void fraction in our kerogen models shows a decreasing trend with increasing volumetric strain (Fig. 3d). This observation suggests the pore occupation effect of preloaded water molecules outweighs the induced pore swelling effect. The decreasing amplitude of void fraction is kerogen IA < IIA < IIIA, which is opposite to the change in porosity. Fig. 4 presents the void volume distribution (VSD) and specific surface area distribution in the kerogen models. Due to the limitation of kerogen size, the range of VSD in our kerogen models is narrow, similar to the reported VSD in kerogen by molecular simulation (Pathak et al., 2018). The narrow VSD is comparable with the measured micropore size distributions on kerogen by CO2 adsorption experiments (Rexer et al., 2014). In this work, we focus on the change of kerogen
organic type (Fig. 1). Thus, it is more difficult for kerogen IIIA to deform compared with kerogen IA and IIA. For another, the kerogen model with higher organic type has a larger average pore size. Water molecules located in the middle of pores can exert a smaller repulsive force to the kerogen skeleton. The two factors result in a smaller volumetric strain for kerogen IIIA than that for kerogen IA and IIA. The moisture induced volumetric strain presents an accepted divergence under different configurations using the block averaging method. The largest uncertainty was observed to be 6.84% for kerogen IA at the moisture content at 4.8 wt %. 3.1.2. Change of kerogen nanoporous structure Fig. 3 shows the change of kerogen structure associated with kerogen swelling. The cell size of kerogen model presents a linearly increasing correlation with the volumetric strain (Fig. 3a). The cell size ranges from 33.5 to 34.1 Å for kerogen IA model, from 32.5 to 32.8 Å for kerogen IIA model, and from 32.7 to 32.9 Å for kerogen IIIA model. These cell sizes are larger than the reported typical size (25 Å) that can reproduce most of structural and thermodynamic properties of realistic kerogen (Ungerer et al., 2014). The density of kerogen matrix shows a linearly decreasing dependence on the volumetric strain (Fig. 3b). As kerogen swells, the matrix expands outward, resulting in a more loose structure. In addition to outward expansion, the deformable kerogen matrix can also swell inward, which causes the complexity of the change of porous structure with kerogen swelling. A linear increase of porosity is observed in our kerogen models with the increase of 5
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Fig. 4. Void volume and specific surface area distribution. (a) Void volume distribution in kerogen IA. (b) Specific surface area distribution in kerogen IA. (c) Void volume distribution in kerogen IIA. (d) Specific surface area distribution in kerogen IIA. (e) Void volume distribution in kerogen IIIA. (f) Specific surface area distribution in kerogen IIIA.
volumetric strain. By comparing the VSDs for flexible kerogen models at the moisture content of 2.4 wt % and 4.8 wt %, we can observe that some bigger enterable voids are divided into smaller voids with further increasing moisture loading. This is also confirmed by the void distribution in Fig. 5b and c. By contrast, Fig. 5d,e,f show the change of pore distribution in kerogen with increasing moisture content, which is only affected by pore swelling effect. The increase of pore size is observed with kerogen swelling, since the effect of water occupation is not considered. Therefore, the effect of moisture on the kerogen void spaces is governed by both the pore swelling and pore occupation induced by water molecules.
nanostructure to study the effect of moisture induced deformation. In Fig. 4a,b,c,d, sharp peaks are observed around the maximum void sizes in kerogens. The sharp peaks are attributed to the significant change of probed void volumes in kerogens when the diameter of probe molecule increases to be larger than the maximum void sizes. By comparing the VSDs for rigid and flexible kerogen models at the moisture content of 2.4 wt %, we can observe that some smaller enterable voids are expanded into bigger voids with moisture induced swelling. This observation can be clearly confirmed by the void distribution in Fig. 5a and b. The expansion amplitude in void size is in the order of kerogen IA > IIA > IIIA, consistent with the sequence of moisture induced 6
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Fig. 5. Void and pore distribution in kerogen IIA. (a) Void in rigid structure with 2.4 wt % moisture content. (b) Void in flexible structure with 2.4 wt % moisture content. (c) Void in flexible structure with 4.8 wt % moisture content. (d) Pore in dry structure. (e) Pore in flexible structure with 2.4 wt % moisture content. (f) Pore in flexible structure with 4.8 wt % moisture content. Void and pore volume, shown in green, is probed by helium (d = 0.26 nm). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
to a larger kerogen swelling. The volumetric strain first increases to the maximum and then decreases as pressure further rises for kerogen IA and IIA. At higher pressure, the volumetric strain is expected to be negative, corresponding to kerogen shrinkage. For kerogen IIIA, the maximum volumetric strain has not yet been reached because of its high sorption capacity. According to the poromechanics theory, kerogen deformation induced by pressure results from both sorption-induced swelling and pressure-induced compression. Fig. 7 shows the contribution of the two factors to pressure induced deformation. Opposite effect is observed for the two factors on the volumetric strain of kerogen. Compared with pressure compression, sorption swelling dominates the contribution to kerogen deformation. The sorption swelling effect weakens while the pressure compression effect strengthens as pressure increases. The contribution of pressure compression effect is in the order of kerogen IA > IIA > IIIA, which is closely related to the flexibility of kerogen units.
3.2. Kerogen coupling deformation upon gas competitive sorption 3.2.1. Sorption-compression coupling deformation induced by pressure Fig. 6 shows the volumetric strain of dry kerogen models immersed in CH4/CO2 mixtures. Contrary to the moisture induced deformation, the kerogen deformation induced by CH4/CO2 competitive sorption is in the order of kerogen IA < IIA < IIIA. This trend is correlated with the kerogen porosity (kerogen IA < IIA < IIIA). At the same pressure, a higher porosity facilitates the sorption of more gas molecules, leading
3.2.2. Sorption-swelling coupling deformation induced by temperature Fig. 8 shows the effect of temperature on kerogen deformation and the contribution of temperature swelling effect and sorption reduction effect. In Fig. 8a, the kerogen deformation upon CH4/CO2 competitive sorption declines as temperature increases. Although temperature effect can swell kerogen skeleton, kerogen sorption capacity reduces as temperature rises, leading to deceasing kerogen deformation. In Fig. 8b, we can observe that sorption reduction effect plays a major role in temperature induced kerogen deformation. The contribution of temperature swelling effect gradually rises with increasing pressure. While the contribution of sorption reduction effect initially increases sharply and then decreases to reach a plateau (~70%) as pressure rises. The contribution of temperature swelling effect weakens as temperature increases, consistent with that of sorption reduction effect when pressure is below 20 MPa.
Fig. 6. Volumetric strain of dry kerogen upon CH4/CO2 competitive sorption as a function of pressure at the CO2 composition of 0.5 and 318 K. 7
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Fig. 7. Contribution of compression effect and sorption effect to volumetric strain induced by pressure at the CO2 composition of 0.5 and 318 K.
increasing pressure. At 50 MPa, the adsorption effect can even lead to kerogen shrinkage, the overall kerogen swelling is fully governed by the absorption effect at this pressure condition.
3.2.3. Pressure-temperature coupling deformation induced by geological depth Fig. 9a shows the effect of geological depth on kerogen deformation upon CH4/CO2 competitive sorption. The volumetric strain follows a linearly decreasing trend with the increase of geological depth. The effect of geological depth consists of both the pressure effect and the temperature effect. As discussed above, the pressure effect results in an increasing volumetric strain, while the temperature effect leads to a decreasing volumetric strain. Fig. 9a indicates that the temperature effect plays a major role in kerogen deformation upon CH4/CO2 competitive sorption induced by geological depth. Fig. 9b presents the contribution of pressure effect and temperature effect to the volumetric strain. The positive pressure effect decreases while the negative temperature effect increases as the geological depth increases.
3.2.5. Effect of moisture content and CO2 composition Fig. 11 presents the effect of moisture content and CO2 composition on the volumetric strain of kerogen IIIA upon CH4/CO2 competitive sorption. The gas induced volumetric strain declines as the moisture content increases. The moisture loaded into the kerogen skeleton occupies some polar adsorption sites and pore volumes, reducing the sorption capacity of kerogen for gas molecules. Note that, as we show in section 3.1, the moisture can also induce kerogen swelling, contributing to larger pore volumes. The moist kerogen is already partly swelled before gas sorption. Therefore, the coupling deformation of kerogen induced by both the moisture uptake and gas sorption should be further studied. The volumetric strain induced by CH4/CO2 competitive sorption initially rises sharply and then increases gently with the increase of CO2 composition. This indicates that kerogen has a larger affinity with CO2 compared with CH4. The sorption loading of gas molecules increases with increasing CO2 composition, resulting in a larger volumetric strain.
3.2.4. Adsorption-absorption coupling deformation induced by sorption The kerogen deformation upon CH4/CO2 competitive sorption consists of both adsorption effect and absorption effect. Fig. 10 shows the contribution of the two effects. The adsorption induced volumetric strain initially rises to the maximum and then declines with increasing pressure. While the absorption induced volumetric strain shows a continuously increasing trend as pressure rises. The adsorption effect plays a major role in sorption induced deformation at low pressure, while the absorption effect gradually dominates the contribution with
Fig. 8. (a) Effect of temperature on the volumetric strain of dry kerogen IIIA at the CO2 composition of 0.5. (b) Contribution of temperature swelling effect and sorption reduction effect to kerogen deformation induced by temperature. 8
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Fig. 9. (a) Effect of geological depth on the volumetric strain of dry kerogen IIIA at the CO2 composition of 0.5. (b) Contribution of temperature effect and pressure effect to kerogen deformation induced by geological depth.
3.3. Effect of kerogen deformation on fluid diffusion Kerogen experiences constantly mechanical deformation under reservoir conditions, which significantly affects the percolation of geofluids. In the section, we design three scenarios to study the effect of kerogen deformation on CH4/CO2/H2O diffusion. In scenario (a), CH4 and CO2 molecules diffuse in fixed dry kerogen IIIA model. In scenario (b), the dry kerogen is allowed to deformation, while in scenario (c), the kerogen is firstly moisture equilibrated at the moisture content of 2.4 wt %. Table 1 lists the self-diffusion coefficients of CH4/CO2/H2O molecules in the three scenarios. In this work, we focus on the differences of self-diffusion coefficients between fluid molecules and various scenarios instead of the actual values. By comparing scenario (a) and (b), we can observe that CH4/CO2 self-diffusion coefficients increase when kerogen becomes flexible. This indicates that kerogen deformation induced by CH4/CO2 competitive sorption open the diffusion paths for both CH4 and CO2. By comparing scenario (b) and (c), we observe that CH4/CO2 self-diffusion coefficients rise with the loading of water molecules, suggesting the effect of moisture induced pore swelling outweighs the effect of pore occupation by water molecules at this moisture condition. Also, the self-diffusion coefficient of CO2 has a larger increase than that of CH4, which indicates the effect of pore swelling induced by moisture uptake preferentially facilitates the diffusion of CO2. CH4 is observed to diffuse faster than CO2 in the three scenarios. This can be attributed to that kerogen has a higher affinity
Fig. 10. Volumetric strain induced by adsorption effect and absorption effect for dry kerogen IIIA upon CH4/CO2 competitive sorption at the CO2 composition of 0.5 and 318 K.
Fig. 11. (a) Effect of moisture content on the volumetric strain of kerogen IIIA upon CH4/CO2 competitive sorption at the CO2 composition of 0.5 and 318 K. (b) Effect of CO2 composition on the volumetric strain of dry kerogen IIIA upon CH4/CO2 competitive sorption at 318 K. 9
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Table 1 Self-diffusion coefficients of fluid molecules in the kerogen skeleton.a System
DCH₄ (m2/s)
DCO₂ (m2/s)
DH₂O (m2/s)
Fixed dry kerogen with CH4 & CO2 Swelling dry kerogen with CH4 & CO2 Swelling moist kerogen (2.4 wt %) with CH4 & CO2
3.1 ± 0.7 × 10−11 5.9 ± 0.6 × 10−11 6.1 ± 0.8 × 10−11
1.4 ± 0.5 × 10−11 2.0 ± 0.5 × 10−11 5.0 ± 0.6 × 10−11
– – 5.1 ± 0.7 × 10−11
a
The deviations are derived from three different kerogen configurations.
compression. With the desorption and production of shale gas, the reservoir pressure declines, which can increase the kerogen swelling. Therefore, injecting CO2 into reservoir when the reservoir pressure drops to around the optimum pressure could improve the efficiency of CS-EGR. The kerogen swelling decreases with increasing temperature, which indicates thermal stimulation can reduce the fluid flow pathways in shale kerogen, thus damping the efficiency of CS-EGR. The kerogen swelling is inversely proportional to the geological depth. Shallow shale reservoir should be preferentially evaluated on suitability for CS-EGR.
with CO2, as well as H2O, compared with CH4. The self-diffusion coefficients of fluid molecules in kerogen matrix are in the order of 10−11, which is in the same order of magnitude with that of CO2 in coal reported by Wu et al. (2019a,b) (6.8 × 10−11–2.33 × 10−10), Zhang et al. (2016) (3 × 10−11–1.5 × 10−10) and Zhao et al. (2016) (5.4 × 10−11). The self-diffusion coefficient is sensitive to the porous skeleton, fluid species, temperature and pressure conditions. The low diffusion coefficients can be attributed to the slowing effect, as reported by previous studies (Krishna and van Baten, 2010), where the thermal and dynamic motion of the slowest molecules can damp the diffusion of the fasted molecules. This slowing effect can result in a reduction of diffusion coefficient by an order of magnitude (Kucukpinar and Doruker, 2003; Viswanathan et al., 2011).
4. Conclusions Kerogen deformation with preloaded moisture was quantified with MD simulations, while kerogen deformation upon CH4/CO2 competitive sorption was quantified with the combination of GCMC simulations and poromechanics theory. The main conclusions are summarized as follows.
3.4. Implications for CS-EGR This work sheds lights on kerogen deformation upon CH4/CO2 competitive sorption. In this section, we discuss the potential application of these results in fields associated with CS-EGR. Our results show that there is a strong chemo-mechanical coupling in kerogen associated with CH4/CO2 competitive sorption. Gas sorption can induce significant swelling of kerogen, thus increasing the sorption capacity of kerogen. This indicates that the assumption of fixed kerogen structure cannot capture the realistic interplay between kerogen and geofluids. Also, the dynamic nature of kerogen should be taken into account to improve the evaluation on both gas-in-place and CO2 storage capacity in shale reservoirs associated with CS-EGR. CO2 is observed to have a higher affinity with kerogen and a lower diffusion coefficient compared with CH4, which facilitates it to replace CH4 and retain in the kerogen matrix. The rising CO2 composition can induce larger kerogen swelling, generating more nanochannels in the kerogen matrix. The low permeability of kerogen plays a major role in shale gas percolation. The injecting CO2 can open fluid flow pathways in the complex nanoporous network of kerogen, thus increasing the shale gas production. The kerogen deformation is greatly affected by the moisture content. Moisture by itself can linearly increase the volumetric strain of kerogen with increasing moisture uptake. However, moisture can also result in a decrease of gas sorption amount, reducing the gas induced swelling. At low moisture content, the effective pore size, as well as the gas diffusion coefficient, increases with the moisture content. While at high moisture condition, the pore occupation induced by moisture uptake plays a major role, leading to a decrease of the effective pore size. We can manipulate the moisture content in kerogen to obtain the maximum kerogen swelling, which can facilitate the injection of CO2 and production of CH4. For kerogen with low original moisture content like type III kerogen or high mature kerogen, it can be theoretically feasible to enhance the efficiency of CS-EGR by increasing the reservoir moisture. To accomplish this purpose, we can first inject CO2 to produce artificial fractures in the reservoir, and then inject slick water to carry proppants and increase moisture contents. Also, steam injection is another potential technique to increase the reservoir moisture. The effect of pressure shows that there is an optimum pressure corresponding to the maximum kerogen swelling. This result provides implication for the injection timing of CO2 associated with CS-EGR in shale gas reservoir. The original shale reservoir is under high pressure
1. The moisture induced swelling is in the order of kerogen IA > IIA > IIIA.There is an optimum moisture content corresponding to the maximum effective pore size. The efficiency of CSEGR could be enhanced by manipulating the reservoir moisture. Potential techniques include hybrid CO2-water fracturing and steam injection. 2. The adsorption effect plays a major role in kerogen deformation upon CH4/CO2 sorption at low pressure, while the absorption effect gradually dominates the contribution with increasing pressure. 3. Kerogen swelling upon CH4/CO2 sorption decreases with increasing geological depth. Shallow shale reservoir is more potentially suitable for CS-EGR. 4. The temperature effect outweighs the pressure effect in kerogen deformation induced by geological depth. Kerogen swelling decreases as temperature rises. Thermal stimulation in deep shale reservoir may not improve the efficiency of CS-EGR. 5. The volumetric strain initially increases and then decreases with rising pressure. Conducting CS-EGR around the optimum pressure corresponding to the maximum swelling is suggested. 6. CO2 has a higher affinity with kerogen and a lower diffusion coefficient compared with CH4. The rising CO2 composition can induce larger kerogen swelling, which generates more nanochannels in kerogen matrix thereby enhancing shale gas production. Notes The authors declare no competing financial interest. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51774298 and 51504265) and the Science Foundation for the Excellent Youth Scholars of China University of Petroleum (Beijing) (Grant No.2462015YQ0223). Computer time for this study was provided by the HP High Performance Computing Cluster of the State Key Laboratory of Heavy Oil Processing at China University of Petroleum (Beijing). We also appreciate the support of China Scholarship Council (CSC No. 201806440095). 10
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