Evolutions in the Elastic Constants of Ca-Montmorillonites with H2O

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Evolutions in the Elastic Constants of Ca-Montmorillonites with HO/CO Mixture under Supercritical Carbon Dioxide Conditions 2

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Weina Zhang, Haixiang Hu, Xiaochun Li, and Zhi Ming Fang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10648 • Publication Date (Web): 24 Jan 2017 Downloaded from http://pubs.acs.org on January 31, 2017

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The Journal of Physical Chemistry

Evolutions in the Elastic Constants of Ca-Montmorillonites with H2O/CO2 Mixture under Supercritical Carbon Dioxide Conditions Wei. N. Zhang, a, b Hai. X. Hu, a Xiao. C. Li, *, a Zhi. M. Fang a a

State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of

Rock and Soil Mechanics, the Chinese Academy of Science, Xiaohongshan, Wuchang, Wuhan, 430071,P.R.China b

University of Chinese Academy of Sciences, Beijing, 100049, China.

*Corresponding Author: X.C. Li; Email address: [email protected]

ABSTRACT. Clay mineral plays a crucial role in determining permeability and affecting mechanical properties of caprock formations in geologic carbon sequestration (GCS) and enhanced oil recovery (EOR) engineering. In the corresponding environment, CO2-H2O intercalation not only causes swelling or shrinkage of clay mineral but also results in affecting mechanical properties of mineral. However, influence of quantitative CO2/H2O adsorption on mechanical properties of clay still remains unknown. This work investigated evolutions of elastic 1

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properties of Ca-MMT with variable CO2-H2O component using molecular dynamic method. Elastic coefficients Cij, bulk modulus K, shear modulus G, Young’s modulus Eii and Poisson’s ratio Eij were correlated to qualified adsorption of CO2-H2O mixture. We obtained the following conclusions: (1) in-plane elastic constants, bulk modulus, shear modulus and Young’s modulus E33 had distinct correlation with the profile of d001spacing as a function of H2O content at fixed CO2 content; (2) no distinct evolution profile was found in Poisson’s ratio as a function of CO2 or H2O content; (3) we revealed that the mixture of CO2/H2O caused decrease in strength of clay mineral; and (4) varying ranges of all elastic constant were summarized for clay- CO2-H2O considered in this work.

1. Introduction. Geologic carbon sequestration (GCS) has been proposed as a promising option to reduce anthropogenic CO2 emissions into the atmosphere.1 In GCS, supercritical CO2 (scCO2) is injected into deep geological formations and prevented from escaping by low permeable caprock formations with high clay mineral content.2-3 In long term GCS, leakage of CO2 through caprock formations is determined by permeability after capillary breakthrough pressure is exceeded.4 In addition, scCO2 is used to enhance the CH4 production rate by expanding micro fracture within the shale rocks. In a word, assessing CO2-rock interactions is a necessary part of these engineering processes.5 As clay mineral consists most of the caprock formations and plays an important role 2


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in determining the permeability of caprock formations in GCS and shale rock in gas reservoir, it is necessary to understand the mechanical properties of naturally occurring clay mineral. Moreover, concerning about the characteristics of the reservoir environment, it is of crucial importance to investigate the impact of CO2-H2O adsorption on mechanical properties of clay mineral. Recent experimental and simulated studies demonstrated that CO2 could enter into interlayer of clay6-7 and focused on interactions of CO2 with H2O on clay surface.8-9 Furthermore, CO2 adsorption causes swelling or shrinking strain on d001 spacing.10-12 Particularly, some researchers stated that the evolution of d001 spacing would result in further changes in solid volume, porosity and permeability of caprock formations.12-14 Besides indirect structural changes in porosity and permeability of shale or mud rock, direct changes in mechanical properties of hydrated clay with H2O adsorption has also attracted interest of some researchers. However, it still remains a challenge of measuring fundamental mechanical properties of clay minerals considering their affinity for H2O /CO2 and layered structure. Mondol et al.15 achieved five basic elastic parameters (bulk and shear modulus, Young’s modulus, Poisson’s ratio and Lame constants) by an indirect way of compacting porosity. Although Prasad16 and Kopycinska-Müller et al.17 obtained Young’s modulus using atomic force acoustic microscopy (AFAM), they failed to describe anisotropic property of clay mineral. In contrast to difficulty in experimental methods, molecular simulation can estimate

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mechanical properties of dehydrated and hydrated clay mineral from atomic scale. Recently, Zartman et al.18 calculated elastic constants of layered silicates including dehydrated montmorillonite (MMT) under a wide range of stress loading using semiempirical classical molecular dynamics (MD). Mazo et al.19 presented MD results of Na-MMT with variable H2O content and found that interlayer H2O significantly altered Young’s modulus perpendicular to clay lamellae. More recently, Ebrahimi et al.20 investigated the influence of interlayer H2O on nanoscale elastic mechanical properties of Na-MMT by means of MD method. Carrier et al.21 performed MD simulations on calculating mechanical properties of Na-MMT and Ca-MMT. The results showed that elastic coefficients were extremely sensitive to H2O content. Moreover, the results confirmed that the decrease of in-plane elastic coefficients was caused by the swelling of d001 spacing after H2O molecules intercalating into the interlayer of clay. However, influence of quantitative CO2/H2O adsorption on mechanical properties of clay still remains unknown. Accordingly, the interest of the current work lies in the influence of quantitative scCO2-H2O adsorption on mechanical properties of Ca-MMT under GCS condition. We computed basic elastic constants, namely full set of stiffness coefficients Cij, bulk modulus K, shear modulus G, Young’s modulus Eii and Possion’s ratio Eij, for Ca-MMT with variable component of scCO2-H2O. Moreover, we summarized varying ranges of these basic elastic constants within the

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adsorption component considered in this work at super critical condition of CO2 (P=10 MPa, T=304.5 K). 2. Simulation details. 2.1 Models and system setup The atomic models were developed from the X-ray diffraction patterns of Ca-MMT studied by Vaini et al.22 In our simulations, we modified their unit cell from Al4Si8O24Ca2 to Ca0.375(Si7.75Al0.25)( Al3.50Mg0.50)O20(OH)4·m CO2·n H2O where m and n represent the number of CO2 and H2O molecules per unit cell. The initial configuration consisted of two layers where each layer includes 4a×2b×1c times of unit cell. Isomorphic octahedral Al3+/Mg2+ contributed the 67% of total charge and tetrahedral Si4+/Al3+ substitutions contributed the remaining charge in the clay lamellae.23-24 The resulting layer charge of 12 e was balanced by 6 interlayer Ca2+. Variable H2O and CO2 molecules with Ca2+ were randomly intercalated into the interlayer determined by Monte Carlo (MC) calculations using Metropolis method. The MC simulations include 100000 equilibrated steps and 100000 productive steps. Equilibrated steps of MC varying from 1000 to 150000 were tested to determine the appropriate steps. Figure SI-1 explains that the minimum energy will reach convergence after 100000 steps. Therefore, we selected 100000 steps as the equilibrated steps of MC and equal step as the productive steps of MC. The configuration with the minimum energy was set as the initial configuration of MD. As

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a start of MD simulation, we performed fully geometry optimization on each model under supercritical condition of CO2 (T=304.5 K, P=10 MPa). The following MD relaxation included 500 ps NPT equilibrated and 500 ps NVT productive stages using a time step of 0.5 fs. The last half frames of the NVT MD simulation were used to determine the lattice parameters (see Table SI-1and Table SI-2) and calculate the mechanical properties. Temperature was controlled by a Nóse-Hoover-Langevin (NHL) thermostat 25 with a parameter of 0.5 ps and pressure was controlled by a Berendsen barostat26 with a parameter of 1ps, respectively. Coulomb term was determined by Ewald summation method in an accuracy of 0.0001 kcal/mol. The cutoff distance of 12.0 Å was applied for van der Waals term. Periodic boundary conditions were used to avoid interface effects. MC and MD simulations were carried out in Forcite module in Material Studio 6.0. Clayff force field, developed by Cygan et al.,27-28 was applied for calculating interactive energy and forces between atoms. In order to investigate the influence of variable H2O and CO2 intercalation on the changes of mechanical properties of Ca-MMT, elastic constants of Ca-MMT with two series of adsorption component were calculated: (1) elastic constants varying as a function of n H2O from 0 to 8 with m=0, 0.5 and 1 CO2 per unit cell; (2) elastic constants varying as a function of m CO2 from 0 to 1 with n=3, 4 and 5 H2O per unit cell. In the former component series, the maximum H2O intercalation, 8 H2O molecules per unit cell in the Ca-MMT, was based on MD simulations reported by

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Zhang et al.29 In the latter series, structures of 0 and 1 CO2 molecules per unit cell were based on DFT-MD simulations reported by Schaef et al.30 According to the range of two series of adsorption component, the increasing step of added H2O and CO2 is 1 and 0.125 molecules per unit cell, respectively. For the convenience of depiction, we used m-n to represent a system with m CO2 and n H2O molecules per unit cell. A case of 1-6 CO2-H2O component after MD equilibration was displayed in Figure SI-2. 2.2 Methods for calculating the elastic constants. We used a constant strain method31 to calculate the stiffness constants. The constant strain method obtains the tensors via minimizing the energy of the system and deforming the cell parameters in twelve directions in order. The strain varies from -0.01 to 0.01 and the strain step is 0.004 along each direction. The detail derivation process is from function (2) to (5) in the section 2 from our previous work.32 Approximate bulk modulus K and shear modulus G were obtained by the Voigt-Reuss-Hill method.33 The stress-strain relations derive the corresponding Young’s modulus Eii, Poisson's Ratio Eij:

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 11 11  E22  22  22  E33  33  33  E12   11  22  E13   11  33  E23   22  33 E11 

(1)

3. Results and discussion. 3.1 Validation of models. We offered validation of our models from two aspects: d001 spacing and elastic coefficients. For d001 spacing, we compared our simulated values of 0-4 and 0-8 component (determining 1W and 2W hydrated state, respectively) with other simulated results6, 29-30, 34-37 and experimental results25, 30, 37-39 in Table SI-3. Figure 1a showed the changes in d001 spacing as a function of H2O content with fixed number of CO2 (m=0, 0.5 and 1) intercalated into interlayer. At a content of H2O alone (m=0), increasing H2O content yielded a stepwise profile of d001 spacing, which is similar to the profile of Na-MMT with pure H2O adsorption.40 Special emphasis is placed on the scenarios with m=0.5 and 1 CO2 molecules per unit cell. After CO2 entered into interlayer region, adding H2O content still generated a stepwise profile of d001 spacing.

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Figure 1. d001 spacing as a function of (a) H2O content and (b) CO2 content. Gray blocks represent the d001 spacing for the corresponding 1W and 2W hydrated states of Ca-MMT. As for elastic coefficients, to our best knowledge, it is unavailable to compare results of Ca-MMT with the same CO2-H2O component with other simulated results or experimental data. Therefore, we only compared elastic coefficients of 1W and 2W hydrated system with available reference results of hydrated clay without CO219, 21, 41 as shown in Table 1. In general terms, elastic coefficients were classified into two types: in-plane coefficients and out-of-plane coefficients. In-plane coefficients, including C11, C12, C22 and C66, correspond to strain mainly occurring in clay lamellae. While out-of-plane coefficients, including C33, C13, C23, C44 and C55, correspond to strain involving deformation of interlayer. According to Table 1, our simulated in-plane coefficients are in good agreement with reported values by Carrier et al.21 However, our simulated out-of-plane coefficients differ much from the values 9



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computed by Carrier et al. These discrepancies may be explained by the difference of two methods of calculating elastic coefficients: we directly calculated elastic coefficients via constant strain method, while Carrier et al. did their work via elastic bath method. Although the elastic bath method can accelerates the convergence, the selected stiff bath affects the precise of the results at different temperature. Table SI-4 compares the values of Cij at 0K with the values at ~300 K calculated in Carrier’s et al. method and our method. Regarding the values calculated by Carrier et al., the temperature has a significant impact on the out-of-plane coefficients (including C33, C13, C23, C44 and C55). While, by comparing the values calculated in our method (without elastic bath), we found that temperature affects little on the out-of-plane coefficients. The largest discrepancy is found in C33 calculated by Carrier et al. and us. According to the results of Carrier et al., the value of C33 at 300 K is six times larger than the value at 0 K. By contrast, the related discrepancy of our calculated C33 is less than 1GPa. Our calculated results indicate that the elastic coefficients are nearly not affected by the temperature over the range of 0-304.5 K. This conclusion is in agreement with the statement of Mazo et al.19 who stated that the elastic coefficients of MMT changes weakly with the temperature over the range of 300 - 350 K. Moreover, our results are within the range of experimental results by means of UPV. Compared to results of Carrier et al., our calculated C33, C13, C44 are more close to the interpreted values (denoted by Cijs ) estimated from the UPV measurement.41 Large

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discrepancies are mostly resulted by finite length scale of simulation model.20 Ensemble average values with standard deviations for elastic coefficients were displayed in Figure 2 and Figure 3. Table 1. Elastic coefficients of 1W and 2W Ca-MMT with pure H2O. Carrier et al.21

Ortega et al.41

1W

2W

UPV

225.84 ±4.55 195.49 ±2.29

211.5

186.8

13.8-46.1 44.9

C12

101.02 ±4.26 84.96 ±2.09

98.3

88.6

6.9-17.8

21.7

C13

12.55 ±3.33

1.3

4.5

6.1-24.3

18.1

C22

264.44 ±4.75 225.32 ±2.42

209.1

177.6

N.A.

N.A.

C23

11.06 ±3.66

10.76 ±1.40

1.3

3.5

N.A.

N.A.

C33

23.88 ±4.18

31.49 ±1.03

4.9

6.0

11.5-30.4 24.2

C44

8.68 ±4.74

6.50 ±0.20

0.6

0.7

2.9-8.9

3.7

C55

13.94 ±4.17

9.05 ±0.40

0.7

1.5

N.A.

N.A.

C66

56.57 ±2.69

48.30 ±0.73

63.4

51.7

N.A.

N.A.

Cij

This work

(GPa)

1W

C11

2W

10.61 ±1.36

Csij

3.2 Influence of CO2/H2O mixture adsorption on elastic coefficients. 3.2.1 Variation of elastic constants as a function of H2O content at fixed CO2 content. Figure 2 showed all elastic coefficients for Ca-MMT with variable H2O content for the selected number of CO2 per unit cell (m=0, 0.5 and 1). For 0-0 CO2-H2O composition, the driest Ca-MMT has the highest stiffness along all directions. Elastic coefficients sharply dropped from the maximum values as soon as few H2O molecules entered into the interlayer region. For example, C11, a member of in-plane coefficients 11



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in Figure 2a, dropped from 297.36 GPa for dry clay to 210.11 GPa, 226.77 GPa and 211.32 GPa for 0-1, 0.5-1and 1-1 system, respectively. C33, a member of out-of-plane coefficients in Figure 2c, dropped from 71.18 GPa to 32.13 GPa, 27.40 GPa and 20.74 GPa in the order of 0-1, 0.5-1and 1-1 system. Before Ca-MMT exposure to pure H2O (m=0 CO2), it was strong ionic bonds that connected clay lamellae. After clay exposure to pure H2O, interlayer H2O molecules began to form weak hydrogen bonding networks instead of ionic bonds to connect clay lamellae. The increasing number of H-bonds with H2O intercalation (see Figure SI-3) can prove the conclusion. Regarding this transition, hydrated clay was much softer than dry clay in any direction. Figure 2a and 2b displayed that in-plane coefficients showed similar evolution pattern as a function of variable H2O content at m=0.5 and 1 CO2 per unit cell (red and blue lines). For reference of C11 (see Figure 2a), all systems with m=0, 0.5 and 1 CO2 per unit cell exhibited stepwise decreasing trend as a function of H2O. Besides, C12 and C66 showed significantly decreasing trend with increasing H2O intercalation. After clay exposure to CO2-H2O mixture, interlayer CO2 might replace some H2O and play a similar role of H2O which interacted with clay surface. In addition, evolutions of in-plane elastic coefficients relied on the d001 profile. C12 and C66 began to decrease with the increasing H2O content after 2.73 mmol H2O /g clay corresponding to the 1W hydrated state (see Figure 2b). Meanwhile, CO2 12


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intercalation attenuated the increasing scope. For m=0 CO2 component, C12 jumped from 93.90 GPa at 1.36 mmol H2O /g clay to 104.47 GPa at 2.73 mmol H2O /g clay. Then, it exhibited a gradually decreasing trend with increasing H2O content. In contrast, for clay with m=1 CO2 in unit cell, C12 slightly increased from 98.82 GPa to 102.72 GPa at 2.73 mmol H2O /g clay. After a gradual decreasing stage, it stabilized at around 82.0 GPa after 9.54 mmol H2O /g clay.

Figure 2. Changes in elastic coefficients as a function of H2O content at m=0 (black square), 0.5 (red circle) and 1 (blue triangle) CO2 per unit cell. Gray blocks denote 1W and 2W hydrated states.

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3.2.2 Variation of elastic constants as a function of CO2 content at fixed H2O content. Table SI-5 summarized varying ranges for Cij of hydrated Ca-MMT compared with dehydrated Ca-MMT with adsorption of 0-1.36 mmol CO2/g dehydrated clay at H2O content of 3, 4, and 5 H2O molecules per unit cell. In-plane coefficients of hydrated clay could reduce as much as around 31%-35% of dehydrated clay. Special attention should be paid on the component of 0.875-5 CO2 - H2O because this system determined all down bounds of in-plane coefficients. Up bounds, determined by m CO2-3 H2O component, was 79 % - 88 % of dehydrated clay. Basically, down and up bounds, determined by m-5 and m-3 component, were hardly relevant to CO2 content. Meanwhile, as already shown in Figure 1, d001 spacing relied slightly fluctuated with increasing CO2 content at fixed H2O content. As regards out-of-plane coefficients, it was difficult to recognize obvious correlation with neither d001 spacing nor CO2 content. We just concluded correlative varying range based on out-of-plane coefficients of dehydrated Ca-MMT. C33, varying from 28% at 1-1 CO2-H2O component to 48% at 0.5-2 CO2-H2O component, decreased most among C11, C22 and C33 related to principle stress and strain. It implied principle stress and strain occurring vertical to interlayer space which endured loadings in company with clay lamellae. Accordingly, CO2/H2O mixture had significant influence on C33. By contrast, C66 varied in magnitude between 67% and 88% of dehydrated Ca-MMT, which decreased least among three shearing coefficients (C44, C55, and C66). 14


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The significant difference was also caused by the participation of interlayer space. For C44 and C55, they indicated correlation between shear stress and strain involving soft interlayer space. As regards C66, it expressed correlation between shear stress and strain of stiff lamellae.

Figure 3. Changes in elastic coefficients as a function of CO2 content at n=3 (black square), 4 (red circle) and 5 (blue triangle) H2O per unit cell. 3.3 Bulk modulus and shear modulus. Figure 4a displayed bulk modulus K varying as a function of H2O content at fixed CO2 content (m=0, 0.5 and 1). By comparing with evolution pattern of d001 spacing, K 15



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showed distinct correlation with d001. Regarding 0 CO2 – n H2O component, K sharply decreased from 84.9 GPa (0 mmol H2O /g clay) to 75.2 GPa (1.27 mmol H2O /g clay mmol H2O /g clay starting to form 1W hydrate state). With increasing sorbed H2O after 2.73 mmol H2O /g clay, K showed a flat decreasing trend. Decreasing speed accelerated within the range of 4.09-8.17 mmol H2O/g clay determining 2W hydrated stated. Finally, K increased to 51.4 GPa at 10.90 mmol H2O/g clay. After exposure to scCO2 (0.5-n and1-n component), K still showed an obvious correlation with d001 spacing. As shown in Figure 4a, K firstly exhibited maximum value at 2.73 mmol H2O/g clay (corresponding to 1W hydrated state) and then kept decreasing until H2O content reached 8.18 mmol H2O/g clay (corresponding to 2W hydrated state). The trend of G was similar to K which was shown in Figure 4c. For reference, as shown in Figure 5a and 5c, both K and G significantly decreased as soon as few H2O molecules (at 2.73 mmol H2O/g clay) intercalated, appeared temporary plateau before 2W hydrated state formed (lower than 6.81 mmol H2O/g clay) and finally showed plateau at higher H2O content (higher than 8.18 mmol H2O/g clay).These features implied that the evolution pattern of K and G, as a function of H2O at fixed CO2 content, behaved similar manner with that of d001 as a function of H2O content (see Figure 1a). In parallel, evolution pattern of G, as a function of CO2 at fixed H2O content (n=3, 4 and 5), was also similar with K (see Figure 4b and 4d). In case of m-3 CO2-H2O component, the minimum of both modulus appeared at 0.34 mmol CO2 /g clay. After 16


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an accelerative period, they both showed a plateau between 0.85 mmol CO2 /g clay and 1.36 mmol CO2 /g clay. However, there was no common feature of changes in neither K nor G as a function of CO2 intercalation at fixed H2O content. We compared related K and G values to the ones of dehydrated clay and summarized the corresponding results in Table SI-6. For changing range of modulus for Ca-MMT with variable H2O content at fixed CO2 molecules, K varied from 54% to 89% of dehydrated clay and G varied from 39% to 69% of dehydrated clay. Both maximum and minimum values occurred in 0-1 and 0-7 CO2-H2O component, respectively. As for systems with variable CO2 content at fixed H2O content, the varying range of K was from 54% at 1.19 mmol CO2 /g clay with 5 H2O molecules per unit cell to 70% at 0.17 mmol CO2 /g clay with 4 H2O molecules per unit cell.

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Figure 4. Bulk modulus K and shear modulus G changing as a function of variable H2O content with fixed CO2 (left column); (b) variable CO2 content with fixed H2O (right column). 3.4 Young’s modulus. Figure 5 and Figure SI-4 exhibited varying trend of Young’s modulus (denoted by Eij) for clay with variable CO2-H2O component. There was no obvious evolution pattern of in-plane modulus, namely E11 and E22, except for fluctuating with increasing sorbed H2O or CO2. For systems with variable H2O content at fixed CO2 content (m=0, 0.5 and 1), however, Figure 5c and Figure 1a indicated correlation of E33 with d001 spacing. A local maximum value appeared at 2.73 mmol H2O / g clay related to the 18


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formation of 1W hydrated state, followed by a flat interim period between 1W and 2W hydrated state (from 4.09 to 6.81 mmol H2O / g clay). A local minimum value appeared at 8.18 or 9.54 mmol H2O / g clay within 2W hydrated range. As for systems with variable CO2 content at fixed H2O content (n=3, 4 and 5), similar correlation was only found in systems with high H2O content (m-5 CO2-H2O component). As shown in Figure SI-4c and Figure 1b, the first local minimum and the maximum values of E33 appeared at 0.34 and 1.36 mmol H2O / g clay, respectively. Table SI-7 summarized varying range of Young’s modulus for clay with variable CO2-H2O component. Although, there was no obvious evolution pattern of E11 and E22, CO2-H2O adsorption reduced Young’s modulus compared with dehydrated clay indeed. Additionally, E22 decreased less than E11. This might be contributed to the difference in topology of lamellae along X-axis and Y-axis.42 As shown in Figure SI-5, lamellae had a complete topology structure of Al-O octahedral.

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Figure 5. Young’s modulus: (a) E11, (b) E11 and (c) E33 varying as a function of H2O content at m=0 (black square), 0.5 (red circle) and 1(blue triangle) CO2 per unit cell. 3.5 Poisson’s ratio. No distinct evolution pattern could be concluded concerning about the changes in Poisson’s ratio (denoted by Eij) as a function of H2O or CO2 content as shown in Figure 6 and Figure 7. However, we concluded some regularity by comparing 20


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Poisson’s ratio related to different directions of deformation. For systems with variable H2O content at fixed CO2 (m=0, 0.5 and 1), it was obvious that E21 (Figure 6b) was smaller than E12 (Figure 6a) which indicated that lamella was softer along X-axis than Y-axis. This was resulted by incomplete topology structure along X-axis. E12 varied from 0.1 to 0.4, while E21 varied from 0.3 to 0.5 in the same system. This feature kept consistent with Young’s modulus which E22 was smaller than E11 (discussed in section 3.4). Regarding out-of-plane Poisson’s ratio, E13 varied from 0.2 to 0.5 (Figure 6c) which was higher than E31 (Figure 6d) varying from 0.05 to 0.3 at the same component. Especially, E23 (Figure 6e) was about an order of magnitude higher than E32 (Figure 6f) at the same component. Figure 7 implied that systems with variable CO2 content at fixed H2O (n=3, 4 and 5) had similar features as discussed above. The details of varying ranges of Poisson’s ratio as a function of CO2 and H2O were summarized in Table SI-8.

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Figure 6. Anisotropic Poisson’s ratio as a function of H2O content at m=0 (black square), 0.5 (red circle) and 1 (blue triangle) CO2 per unit cell.

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Figure 7. Anisotropic Poisson’s ratio as a function of CO2 content at n=3 (black square), 4 (red circle) and 5 (blue triangle) H2O per unit cell. 4. Conclusions. In the present work, correlations of elastic coefficients Cij, bulk modulus K, shear modulus G, Young’s modulus Eii and Poisson’s ratio Eij with qualified adsorption of CO2-H2O mixture have been studied through MD method. Moreover, varying ranges 23



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of these elastic constants were summarized under the condition of super critical CO2 (P=10 MPa, T=304.5 K). The main conclusions are as follows: (1) We revealed that the mixture of CO2/H2O caused decrease in strength of clay mineral along either in-plane direction or out-of-plane direction. This could be easily found in varying ranges of elastic coefficients, bulk modulus, shear modulus and Young’s modulus, which were summarized in Table SI-5 to Table SI-7. (2) For systems with fixed CO2 content (m=0. 0.5 and 1), in-plane elastic constants, bulk modulus, shear modulus and Young’s modulus E33 had distinct correlation with the profile of d001spacing as a function of H2O. For instance of bulk modulus for 1-n CO2-H2O component (see Figure 4a), K firstly exhibited maximum value at 2.73 mmol H2O/g clay and then kept decreasing until H2O content reached 8.18 mmol H2O/g clay. The two H2O content corresponded to 1Wand 2W hydrated state, respectively. (3) C33 decreased most among three elastic coefficients (C11, C22 and C33) related to principle stress and strain. Meanwhile, C66 decreased least among three shearing coefficients (C44, C55 and C66). The difference was dependent on the participation of interlayer space. Therefore, influence of CO2/H2O adsorption was more significant on the elastic coefficients related to interlayer space. (4) No distinct evolution profile was observed in Poisson’s ratio as a function of CO2 or H2O. A common feature of Poisson’s ratio was that E21 was smaller than E12. This 24


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was resulted by incomplete topology structure along X-axis direction (see Figure SI-5). Besides, Ei3 was larger than E3i (i=1 and 2) which was caused by the swelling deformation of interlayer space. The present work aided in understanding mechanical properties of clay- CO2-H2O system in GCS and EOR engineering. Our next work is to study on changes of clay deriving from competitive adsorption of CO2/CH4 which is of crucial importance for shale gas recovery. ASSOCIATED CONTENT Additional simulation methods and supplementary data are included in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *

Email address: [email protected]

Author Contributions The manuscript was written through contributions of all authors. Funding Sources This work is supported by the National Natural Science Foundation of China (NSFC-41472236). 25



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Notes The authors declare no competing financial interest. References (1) IPCC, Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. 2007. (2) Bachu, S., Review of CO2 Storage Efficiency in Deep Saline Aquifers. Int. J. Greenhouse Gas Control 2015, 40, 188-202. (3) Altman, S. J.; Aminzadeh, B.; Balhoff, M. T.; Bennett, P. C.; Bryant, S. L.; Cardenas, M. B.; Chaudhary, K.; Cygan, R. T.; Deng, W.; Dewers, T. et al. Chemical and Hydrodynamic Mechanisms for Long-Term Geological Carbon Storage. J. Phys. Chem. C 2014, 118, 15103-15113. (4) Busch, A.; Alles, S.; Gensterblum, Y.; Prinz, D.; Dewhurst, N. D.; Raven, M. D.; Stanjek, H.; Krooss, B. M. Carbon Dioxide Storage Potential of Shales. Int. J. Greenhouse Gas Control 2008, 2, 3, 297-308. (5) Gaus, I. Role and Impact of CO2–Rock Interactions During CO2 Storage in Sedimentary Rocks. Int. J. Greenhouse Gas Control 2010, 14, 73-89.

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Evolutions in the Elastic Constants of Ca-Montmorillonites with H2O

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