Molecular Dynamics Simulation of Clay Hydration Inhibition of Deep Shale

processes

Article Molecular Dynamics Simulation of Clay Hydration Inhibition of Deep Shale

Yayun Zhang 1,2 and Cong Xiao 3,*

1 State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Beijing 100101, China; [email protected] 2 Sinopec Research Institute of Petroleum Engineering, Beijing 100101, China 3 Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands * Correspondence: [email protected]

Abstract: In the process of the exploitation of deep oil and gas resources, shale wellbore stability control faces great challenges under complex temperature and pressure conditions. It is difficult to reflect the micro mechanism and process of the action of inorganic salt on shale hydration with the traditional experimental evaluation technology on the macro effect of restraining shale hydration. Aiming at the characteristics of clay minerals of deep shale, the molecular dynamics models + + + 2+ of four typical cations (K , NH4 , Cs and Ca ) inhibiting the hydration of clay minerals have been established by the use of the molecular dynamics simulation method. Moreover, the micro dynamics mechanism of typical inorganic cations inhibiting the hydration of clay minerals has been systematically evaluated, as has the law of cation hydration inhibition performance in response to temperature, pressure and ion type. The research indicates that the cations can promote the contraction of interlayer spacing, compress fluid intrusion channels, reduce the intrusion ability of water molecules, increase the negative charge balance ability and reduce the interlayer electrostatic repulsion force. With the increase in temperature, the inhibition of the cations on montmorillonite Citation: Zhang, Y.; Xiao, C. hydration is weakened, while the effect of pressure is opposite. Through the molecular dynam- Molecular Dynamics Simulation of ics simulation under different temperatures and pressures, we can systematically understand the Clay Hydration Inhibition of Deep microcosmic dynamics mechanism of restraining the hydration of clay in deep shale and provide Shale. Processes 2021, 9, 1069. theoretical guidance for the microcosmic control of clay hydration. https://doi.org/10.3390/pr9061069 Keywords: deep shale; clay mineral; inorganic cation; chemical inhibition; molecular dynamic simulation Academic Editor: Andrew S. Paluch

Received: 18 May 2021 Accepted: 17 June 2021 1. Introduction Published: 19 June 2021 With the continuous exploitation of shale gas, the drilling depth is gradually increasing

Publisher’s Note: MDPI stays neutral worldwide, and deep shale gas resources have gradually become the focus of the oil and gas with regard to jurisdictional claims in industry. Meanwhile, with the high-temperature and high-stress environment, the wellbore published maps and institutional affil- collapse of deep shale becomes increasingly serious, i.e., more sudden and destructive, and iations. the sloughing is more severe. Clay minerals are one of the main mineral components of shale. The hydration of clay minerals is one of the main causes of wellbore collapse [1,2]. With the increase in buried depth, the temperature and pressure environment of deep shale will gradually increase. The deterioration of the hydration of clay minerals under high temperature and high pressure is the key factor leading to wellbore collapse of deep Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. shale [3]. Therefore, fully understanding the mechanism of clay hydration expansion and This article is an open access article chemical inhibition is of great strategic significance to realize macro and micro control of distributed under the terms and deep shale hydration, maintain wellbore instability and ensure economic and effective conditions of the Creative Commons development of shale gas. Attribution (CC BY) license (https:// There are two kinds of traditional methods for researching the inhibition mechanism creativecommons.org/licenses/by/ of clay mineral hydration [4,5]. The first is the theoretical analysis based on physical + 4.0/). chemistry theory, in which the main understanding is that the mosaic effect of K and

Processes 2021, 9, 1069. https://doi.org/10.3390/pr9061069 https://www.mdpi.com/journal/processes Processes 2021, 9, 1069 2 of 17

+ NH4 ions on the clay minerals surface fixes the crystal lattice, the surface adsorption of various kinds of inhibitory ions tightens the crystal layer and cationic and surfactant polar groups compress the electric double layer and reduce the charge repulsion between layers. However, the above theoretical analysis is difficult to be verified by experiments and is not intuitive. The second is the experimental characterization methods, mainly including XRD layer spacing, zeta potential, capillary suction timer (CST), cation exchange capacity (CEC) and linear expansion and rolling recovery, as well as various mechanical and chemical coupling macro and micro experimental methods. However, at present, various laboratory test methods are indirect evaluation methods, which characterize the results of inhibitor action. In general, the traditional evaluation methods of the clay hydration inhibition have difficulty in tracking and characterizing the micro process of the inhibitor exerting the chemical inhibition effect in real time, and they ignore the micro dynamic mechanism of the chemical inhibition effect of various treatment agents at the micro-nanoscale on clay hydration. However, the molecular simulation method can obtain the macroscopic properties of the system through atomic-scale simulation, which is widely used in the analysis of hydration mechanism and hydration inhibition process of clay minerals. With the use of Monte Carlo (MC) and molecular dynamics (MD) methods, the hydration characteristics of different montmorillonite (MMT) models (Na-MMT, Mg-MMT) were analyzed, and the applicability of different water molecular models in clay hydration simulation was studied [6–8]. E.S. Boek et al. [9] quantitatively explained the difference in swelling characteristics between Na-MMT and K-MMT and qualitatively analyzed the inhibition mechanism of organic molecules to the clay hydration with the help of grand canonical Monte Carlo (GCMC) and molecular dynamic (MD) methods. They found that PEG molecules can weaken the hydration swelling of clay by affecting the desorption of water molecules. Sposito et al. [10–12] researched the structural characteristics of Li- MMT, Na-MMT and K-MMT hydration through MC methods. Ruth M. Tinnach et al. [13] investigated the diffusion and adsorption behavior of water molecules and ions (Br− and Ca2+) in montmorillonite by molecular dynamics simulation and predicted the average density of ions and water in the clay interlayer region. Laura N. Lammers et al. [14] analyzed the competitive adsorption of Cs and Na at different sites of illite (edge, basal plane and interlayer) by atomic simulation. The hydration characteristics of Na-MMT, K-MMT and Ca-MMT were investigated by MC simulations at higher pressures and temperatures [15]. With the use of MC and MD simulations, the distribution behavior of water molecules and cations in the interlayer region was analyzed [16–19], and the effect of inorganic salts on the mechanical properties of MMT was explored. Anderson et al. [20] investigated the interaction of poly(propylene oxide) diamine, poly(ethylene glycol) and poly(ethylene oxide) diacrylate inhibitor molecules with MMT at 300 K. Zhang et al. [21] used MD simulation to study the structure and dynamic characteristics of water molecules, Na+ and poly(ethylene glycol) (PEG) in the interlayer region of Na-MMT. They found that different PEG molecules exhibit distinct performances in the MMT interlayer. The existence of PEG reduced the mobility of water and counterions, and the formation of the Na+-PEG complex reduced the hydration of Na+. In general, previous reports mainly focused on the structure and dynamic behavior of water and cations in the clay mineral hydration process and partially revealed the inhibition mechanism of clay hydration expansion. However, the microstructure and dynamic response characteristics of the chemical inhibition process of different inhibitory ions were not revealed, and the laws of the chemical inhibition response to different temperatures, pressures, ion types and concentrations were not fully understood. In this paper, based on MD simulation method, according to the characteristics of typical clay minerals contained in deep shale, combined with the types of inorganic salinization inhibitors commonly used in the field, the molecular dynamics models for micro inhibition + + + 2+ evaluation of four typical cations (K , NH4 , Cs and Ca ) inhibiting clay hydration were established. The MD simulations of inhibiting hydration of clay minerals under different temperatures and pressures, types and concentrations of cation ions were carried out. Then, Processes 2021, 9, 1069 3 of 17

the micro mechanism of chemical inhibition effect of typical inorganic salt inhibitors on clay hydration and the temperature and pressure response characteristics were analyzed systematically and deeply.

2. Molecular Dynamics Simulation of Clay Hydration Inhibition 2.1. Simulation Scheme In this paper, molecular dynamics models of typical montmorillonite systems with different interlayer particles (water molecules and inorganic salts) were established, and 72 groups of cationic hydration inhibition molecular dynamics simulations were carried out under different temperature (25, 75, 125 and 150 ◦C) and pressure (0.1, 30, 60 and 90 MPa) conditions, which can be divided into two modes. The simulation scheme of mode 1 is shown in Table1. In mode 1, at 25 ◦C and 0.1 MPa, two systems of Mg-substituted montmorillonite (Mg-Sub-MMT) and Fe-substituted montmorillonite (Fe-Sub-MMT) were used to carry out eight sets of molecular simulations of hydration inhibition. The interlayer domain of montmorillonite contains 72 water + + + 2+ molecules and six electric charges of K , NH4 , Cs and Ca , which represents the formation of two-layer water molecular ﬁlm and the replacement of interlayer exchangeable sodium ions.

Table 1. Mode 1: Simulation scheme for changing the exchangeable cationic.

Systems Interlayer Particles 6 K+ Mg-Sub-MMT Mode 1 6 NH + 25 ◦C 0.1 MPa 4 72 water molecules 6 Cs+ Fe-Sub-MMT 3 Ca2+

The simulation scheme of mode 2 is shown in Table2. In model 2, there are 72 water molecules in the interlayer domain, and the equilibrium cations are the same as the six Na+ ions in the original model, but four kinds of inhibitory cations enter the interlayer domain in the form of saturated inorganic salt solution. At the same time, eight kinds of temperature and pressure conditions were set, including four conditions with constant temperature and variable pressure and four conditions with constant pressure and variable temperature, and 64 groups of inhibitory MD simulations were carried out. The scheme of mode 2 has two objectives: one is to compare the inhibition differences of different types of cations, and the other is to study the temperature and pressure response law of hydration inhibition of different cations.

Table 2. Mode 2: Simulation scheme for changes of saturated inorganic salts under temperature and pressure conditions construction.

Systems Interlayer Particles ◦ Mg-Sub-MMT Constant temperature (25 C) and variable pressure Saturated KCl solution Mode 2 0.1 30 60 90 Saturated NH4Cl solution 72 water molecules + Constant pressure (60 MPa) and variable temperature Saturated CsCl solution + Fe-Sub-MMT ◦ ◦ ◦ ◦ 6Na 25 C 75 C 125 C 150 C Saturated CaCl2 solution

2.2. Model Construction Montmorillonite (MMT) is a clay mineral composed of 2:1 phyllosilicate layers; that is, an alumina (Al2O3) octahedral (O) layer is sandwiched between two silica (SiO2) tetrahedral (T) layers. Due to the existence of isomorphic substitution, MMT is usually negatively charged. Mg2+, Fe2+ or Fe3+ in the octahedral layer is more likely to substitute Al3+. However, the substitution of Al3+ to Si4+ in the tetrahedral layer is relatively rare. In this paper, the Mg-substituted montmorillonite model (Mg-Sub-MMT) and Fe-substituted montmorillonite model (Fe-Sub-MMT) in which Fe2+/Mg2+ replace Al3+ in the octahedron Processes 2021, 9, 1069 4 of 17

Processes 2021, 9, 1069 4 of 17 paper, the Mg-substituted montmorillonite model (Mg-Sub-MMT) and Fe-substituted montmorillonite model (Fe-Sub-MMT) in which Fe2+/Mg2+ replace Al3+ in the octahedron were established. The clay structures refer to the Wyoming MMT model, whose unit cell formulawere established. is Na0.75(Si The7.75Al clay0.25)(Al structures3.5M0.5)O20 refer(OH) to4, thewhere Wyoming M represents MMT model,the substitutional whose unit cat- cell 2+ 2+ ionformula (Mg is and Na 0.75Fe (Si). 7.75TheAl layer0.25)(Al charge3.5M0.5 of)O lattice20(OH) substitution4, where M in represents the supercell the substitutional is −0.75/cell, whichcation is (Mg balanced2+ and Fe by2+ interlayer). The layer cation charge Na of+. lattice substitution in the supercell is −0.75/cell, whichFirstly, is balanced the Mg by-Su interlayerb-MMT and cation Fe- NaSub+.-MMT supercell structures were constructed. Then,Firstly, based on the the Mg-Sub-MMT Metropolis Monte and Fe-Sub-MMT Carlo algorithm supercell, water structures molecules were were constructed. added into theThen, interlayer based on for the theMetropolis construction Monte ofCarlo thealgorithm, Mg-Sub-MMT water moleculesand Fe-Sub were-MMT added hydration into the modelinterlayer with for two the layers construction of water of themolecules. Mg-Sub-MMT In mode and 1, Fe-Sub-MMTall interlayer hydrationNa+ was replaced model with by equaltwo layers charge of of water inhibitory molecules. cations, In mode and the 1, all established interlayer Namodel+ was w replacedith inhibitory by equal cations charge as equilibriumof inhibitory cations cations, is shown and the in established Figure 1 below. model with inhibitory cations as equilibrium cationsIn mode is shown 2, the in corresponding Figure1 below. saturated concentration of inhibitory inorganic salt ions was addedIn mode to the 2, themodel, corresponding and the hydration saturated model concentration of montmorillonite of inhibitory with saturated inorganic con- salt centrationions was added of inorganic to the model,salt solution and the in hydrationthe interlayer model domain of montmorillonite was established with, as shown saturated in Figureconcentration 2 below of (only inorganic the Mg salt-Sub solution-MMT inmodel the interlayer is shown). domain was established, as shown in Figure2 below (only the Mg-Sub-MMT model is shown).

(a) 72-K-Mg-Sub-MMT

(b) 72-NH4-Mg-Sub-MMT

Figure 1. Cont.

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(d) 72-Ca-Mg-Sub-MMT

FigureFigure 1. Initial 1. Initial structure structure of Mg-Sub-MMT of Mg-Sub-MMT with with inhibitory inhibitory cations cation as counterions.s as counterions The water. The moleculeswater molecules in the interlayerin the interlayer are notare shown not inshown the right in the images right ofimages different of different models. models The color. The coding color forcoding the atoms for the is atoms H, white; is H O,, white red; Mg,; O, red green;; Mg Al,, green pink;; Al, Si, gold;pink; K, Si, violet; gold; K N,, violet blue;; Cs, N, deepblue; purple;Cs, deep Ca, purple yellow-green.; Ca, yellow-green.

2.3. Simulation Details Clayff is a special clay mineral force field simulation [22]. Considering that there is no force field information used to describe N element in Clayff, universal force field + (UFF) [23–25] was used in the simulation system involving NH4 , and Clayff was still used in other simulations. Although the accuracy of UFF force field simulation of clay minerals is not as good as Clayff force field, it is also one of the force fields often used by predecessors in the simulation of clay minerals and the simulation accuracy can meet the requirements. UFF force field is a universal force field. The element types cover the whole periodic table of elements, but only diagonal terms and simple harmonic functions are used. The function form is simple, and the parameters are mostly obtained by experimental fitting. QEQ algorithm is used by default for partial charge calculation. The geometry of the MMT model was optimized by the smart minimizer algorithm. The long-range Coulombic interaction was calculated using the Ewald summation method. Each configuration was relaxed in NVT assemblage with Materials Studio (MS) through five decreasing temperature stages with a time step of 0.50 fs. Then, dynamic simulations (a)72-KCl-Mg-Sub-MMT (b)72-NH4Cl-Mg-Sub-MNT

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Processes 2021, 9, 1069 (d) 72-Ca-Mg-Sub-MMT 6 of 17

Figure 1. Initial structure of Mg-Sub-MMT with inhibitory cations as counterions. The water molecules in the interlayer are not shown in the right images of different models. The color coding for the atoms is H, white; O, red; Mg, green; Al, pink; Si, gold; K, violet; Nunder, blue different; Cs, deep temperaturepurple; Ca, yellow and pressure-green. conditions were carried out in the NPT ensemble for 1000 ps. Periodic boundary conditions were used to avoid interface effects.

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(a) 72-KCl-Mg-Sub-MMT (b) 72-NH4Cl-Mg-Sub-MNT

Figure 2. InitialInitial structure structure of Mg Mg-Sub-MMT-Sub-MMT with saturated salt solution solution.. The color color coding coding for for the the atoms atoms is is H H,, white white;; O O,, red red;; MgMg,, green green;; Al,Al, pink;pink; Si,Si, gold;gold; K,K, violet;violet; N,N, blue;blue; Cs,Cs, deep purple;purple; Ca,Ca, yellow-green;yellow-green; Cl,Cl, lavender.lavender.

2.3.3. Results Simulation Details 3.1. MicroClayff Mechanism is a special of clay Cationic mineral Clay force Hydration field Inhibitionsimulation [22]. Considering that there is no forceIn thisfield study, information by comparing used to describe the hydration N element characteristics in Clayff, universal of water force molecules field (UFF) and [23cations–25] afterwas used cations in enterthe simulation the interlayer system region, involving the micro NH mechanism4+, and Clayff of hydrationwas still used inhibi- in othertion effect simulations. of representative Although cations the accuracy was investigated. of UFF force field simulation of clay minerals is not as good as Clayff force field, it is also one of the force fields often used by predecessors in3.1.1. the Interlayersimulation Spacing of clay minerals and the simulation accuracy can meet the requirements. UFFThe interlayerforce field spacing is a universal of the twoforce substituted field. The MMTelement systems types undercover the different whole inhibitory periodic tablecations of iselements, shown in but Table only3. Thediagonal simulation terms resultsand simple of various harmonic inhibitory functions cation are systems used. The in functionthis paper form are is very simple, close and to those the parameters of previous are similar mostly systems, obtained and by the experimental slight difference fitting. is QEQprobably algorithm caused is by used the by difference default infor the partial number charge of double-layercalculation. water molecules and the forceThe ﬁeld geometry and ensemble of the usedMMT in model previous was simulation optimized work. by the smart minimizer algorithm. The long-range Coulombic interaction was calculated using the Ewald summation method. Each configuration was relaxed in NVT assemblage with Materials Studio (MS) through five decreasing temperature stages with a time step of 0.50 fs. Then, dynamic simulations under different temperature and pressure conditions were carried out in the NPT ensemble for 1000 ps. Periodic boundary conditions were used to avoid interface effects.

3. Results 3.1. Micro Mechanism of Cationic Clay Hydration Inhibition In this study, by comparing the hydration characteristics of water molecules and cations after cations enter the interlayer region, the micro mechanism of hydration inhibition effect of representative cations was investigated.

3.1.1. Interlayer Spacing The interlayer spacing of the two substituted MMT systems under different inhibitory cations is shown in Table 3. The simulation results of various inhibitory cation systems in this paper are very close to those of previous similar systems, and the slight difference is probably caused by the difference in the number of double-layer water molecules and the force field and ensemble used in previous simulation work.

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Table 3. Interlayer spacing of MMT under different inhibitory cations.

This Paper Comparative Literature Interlayer Spacing (Å) Mg-Sub-MMT Fe-Sub-MMT Molecular Simulation Experiment Na+ 14.92 14.89 14.7 [26] 14.96 [27] 15.28 [8] 14.7 [28] 15.4 [29] K+ 14.45 14.79 14.31 [30] 15.89–16.83 [31] 15.6 [32] + NH4 72 water molecules 14.75 14.85 - - Cs+ 14.89 14.92 14.88 [30] 15.13 [33] - Ca2+ 15.07 15.31 14.6 [30] 14.73 [33] 15.55 [34]

3.1.2. Distribution of Water Molecules and Ions The relative concentration distribution characteristics of water molecules and cations in the interlayer region after the equilibrium of the hydration inhibition dynamics simulation in Mode 1 are shown in Figures3 and4 below. The relative concentration distribution curve of water molecules showed that the distribution characteristics of water molecules in the interlayer domain did not change + significantly under different inhibitory cations (except NH4 ), and a relatively stable two- layer water molecular film would be formed. Although the two-layer water molecular film + can still be formed in the system with NH4 as the counterions, the concentration curve fluctuates slightly and the peak shape splits, which indicates that the arrangement of the water molecular film in the interlayer becomes not tight at this time, because the addition + of NH4 has a certain destructive effect on the hydrogen bond between water molecules in the two-layer water molecular film. As shown in Figure4, when the inhibitory cations enter the interlayer domain, the peak values of the relative concentration distribution curve of cations in the interlayer domain are closer to the silica surface of the montmorillonite tetrahedral layer than those of the noninhibitory sodium ions. In addition to calcium ions, the distributions of the other three ions in the interlayer domain all showed multimodal properties. Similar to the sodium ion, the calcium ion tends to be far away from the surface of montmorillonite tetrahedron under the condition of 72 water molecules (that is, under the condition of double water molecules) and distributes in the middle of the interlayer domain. Combining with more water molecules, it forms an outer spherical coordination structure. The relative concentration distribution curve shows a strong single peak, and it is more prominent in + + + the Fe-Sub-MMT system. K , NH4 and Cs show obvious multipeak properties in the interlayer domain and are closer to the silica surface, indicating that the three ions are more easily adsorbed by the clay mineral surface than Na+. However, their distribution in the interlayer domain of montmorillonite crystal is not symmetrical, and some peaks are always inclined to one side of the silica surface, which is more obvious in the Fe-Sub-MMT system.

3.1.3. Conduction of Ions and Water Molecules The diffusion coefficients of ions and water molecules in the interlayer domain of the two montmorillonite systems are shown in Figure5 below. Compared with the Na + system, the diffusion coefficient of interlayer water can be reduced to some extent by adding four kinds of inhibitory cations, but the influence degree of each ion is quite different. The most Processes 2021, 9, 1069 7 of 17

Table 3. Interlayer spacing of MMT under different inhibitory cations.

This Paper Comparative Literature Interlayer Spacing (Å) Mg-Sub-MMT Fe-Sub-MMT Molecular Simulation Experiment Na+ 14.92 14.89 14.7 [26] 14.96 [27] 15.28 [8] 14.7 [28] 15.4 [29] K+ 14.45 14.79 14.31 [30] 15.89–16.83 [31] 15.6 [32] NH4+ 72 water molecules 14.75 14.85 - - Cs+ 14.89 14.92 14.88 [30] 15.13 [33] - Ca2+ 15.07 15.31 14.6 [30] 14.73 [33] 15.55 [34]

Through the comparison of the simulation results, it can be found that after adding different inhibitory cations, the interlayer spacing of the two substituted montmorillonite systems is significantly different. Under the conditions of K+, NH4+ and Cs+, the interlayer Processes 2021, 9, 1069 8 of 17 spacing of the two substituted montmorillonite systems is significantly reduced, indicating that these three ions can inhibit the expansion of the montmorillonite crystal layer and promote the contraction of the crystal layer, but the degree of influence is different. The order of inhibition ability of interlayer expansion is K+ > NH2+4+ > Cs+. As for Ca2+, the inter-+ + significant decrease in diffusion ability is in the Ca system, followed by Cs , NH4 and layer spacing of the two substituted montmorillonite systems increases slightly, and the K+. This is because the hydration radius and coordination number of Ca2+ are the largest, increase is more obvious in the Fe-Sub-MMT, which shows that calcium ion has difficulty and more interlayer water molecules are combined to occupy the diffusion channels in in effectively inhibiting the expansion of the MMT crystal layer. the interlayer domain, which leads to the most significant decrease in the diffusion ability 2+ 3.1.2.of waterDistribution molecules of Water in theMolecules Ca system. and Ions Moreover, it can be observed that the inhibitory cationsThe relative have theconcentration same effect distribution in the two characteristics substitution models,of water molecules and the diffusion and cations ability of the in Mg-Sub-MMTthe interlayer region system after decreases the equilibrium slightly of (35% the onhydration average). inhibition On the dynamics other hand, simu- the diffusion lationability in Mode of the 1 fourare shown inhibitory in Figure cationss 3 and in the4 below. interlayer domain changed significantly. Under theThe condition relative concentration of the same distribution water content curve (fixed of water 72 molecules water molecules), showed that except the dis- for calcium tributionions, the characteristics interlayer diffusionof water molecules ability of in the the three interlayer inhibitory domain cations did not is change greater sig- than that of + + + + nificantlysodium under ion, anddifferent the orderinhibitory of diffusion cations (except ability NH is NH4+), 4and> a K rel>atively Cs > stable Na .two According- to layerthe water simulation molecular of cation film would diffusion be formed. in pure Although water, when the two the-layer amount water of molecular charge is the same, filmthe can diffusion still be formed ability in of the ions system is inversely with NH proportional4+ as the counterions, to the radius the concentration of ions. The order of curve fluctuates slightly+ and+ the peak+ shape+ splits, which indicates that the arrangement ion radius is Cs > K > NH4 > Na , so the diffusion ability of the four ions in pure of the water molecular+ + film in+ the interlayer+ becomes not tight at this time, because the water is Cs < K < NH4 < Na . Obviously, in the interlayer domain of montmorillonite, + additionthe diffusion of NH4 abilityhas a certain of these destructive monovalent effect ions on the is quitehydrogen different bond frombetween that water in pure water, moleculeswhich indicates in the two that-layer the water diffusion molecular process film of. cations in the interlayer domain is significantly affected by clay wafer.

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(a) Mg-Sub-MMT

(b) Fe-Sub-MMT FigureFigure 3. Z 3.-axisZ-axis relative relative concentration concentration curves curvesof water of. water.

As shown in Figure 4, when the inhibitory cations enter the interlayer domain, the peak values of the relative concentration distribution curve of cations in the interlayer domain are closer to the silica surface of the montmorillonite tetrahedral layer than those of the noninhibitory sodium ions. In addition to calcium ions, the distributions of the other three ions in the interlayer domain all showed multimodal properties. Similar to the sodium ion, the calcium ion tends to be far away from the surface of montmorillonite tetrahedron under the condition of 72 water molecules (that is, under the condition of double water molecules) and distributes in the middle of the interlayer domain. Combining with more water molecules, it forms an outer spherical coordination structure. The relative concentration distribution curve shows a strong single peak, and it is more prominent in the Fe-Sub-MMT system. K+, NH4+ and Cs+ show obvious multipeak properties in the interlayer domain and are closer to the silica surface, indicating that the three ions are more easily adsorbed by the clay mineral surface than Na+. However, their distribution in the interlayer domain of montmorillonite crystal is not symmetrical, and some peaks are always inclined to one side of the silica surface, which is more obvious in the Fe-Sub-MMT system.

(a) Mg-Sub-MMT

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(b) Fe-Sub-MMT Figure 3. Z-axis relative concentration curves of water.

Processes 2021, 9, 1069 9 of 17 As shown in Figure 4, when the inhibitory cations enter the interlayer domain, the peak values of the relative concentration distribution curve of cations in the interlayer domain are closer to the silica surface of the montmorillonite tetrahedral layer than those of the noninhibitory sodium ions. In addition to calcium ions, the distributions of the other three ions in the interlayer domain all showed multimodal properties. Similar to the sodium ion, the calcium ion tends to be far away from the surface of montmorillonite tetrahedron under the condition of 72 water molecules (that is, under the condition of double water molecules) and distributes in the middle of the interlayer domain. Combining with more water molecules, it forms an outer spherical coordination structure. The relative concentration distribution curve shows a strong single peak, and it is more prominent in the Fe-Sub-MMT system. K+, NH4+ and Cs+ show obvious multipeak properties in the interlayer domain and are closer to the silica surface, indicating that the three ions are more easily adsorbed by the clay mineral surface than Na+. However, their distribution in the interlayer domain of montmorillonite crystal is not symmetrical, and some peaks are al- Processes 2021, 9, 1069 ways inclined to one side of the silica surface, which is more obvious in the Fe-Sub9- ofMMT 17 system.

(b) Fe-Sub-MMT Figure 4. Z-axis relative concentration curves of counterion.

3.1.3. Conduction of Ions and Water Molecules The diffusion coefficients of ions and water molecules in the interlayer domain of the two montmorillonite systems are shown in Figure 5 below. Compared with the Na+ system, the diffusion coefficient of interlayer water can be reduced to some extent by adding four kinds of inhibitory cations, but the influence degree of each ion is quite different. The Processes 2021, 9, 1069 2+ 9 of 17 + + most significant decrease in diffusion ability is in the Ca system, followed by Cs , NH4 + 2+ and K . This is because the hydration radius and coordination number of Ca are the largest, and more interlayer water molecules are combined to occupy the diffusion channels (a) Mg-Sub-MMT in the interlayer domain, which leads to the most significant decrease in the diffusion ability of water molecules in the Ca2+ system. Moreover, it can be observed that the inhibitory cations have the same effect in the two substitution models, and the diffusion ability of the Mg-Sub-MMT system decreases slightly (35% on average). On the other hand, the diffusion ability of the four inhibitory cations in the interlayer domain changed significantly. Under the condition of the same water content (fixed 72 water molecules), except for calcium ions, the interlayer diffusion ability of the three inhibitory cations is greater than that of sodium ion, and the order of diffusion ability is NH4+ > K+ > Cs+ > Na+. According to the simulation of cation diffusion in pure water, when the amount of charge is the same, the diffusion ability of ions is inversely proportional to the radius of ions. The order of ion radius is Cs+ > K+ > NH4+ > Na+, so the diffusion ability of the four ions in pure water is Cs+ < K+< NH4+< Na+. Obviously, in the interlayer domain of montmorillonite, the diffusion ability of these monovalent ions is quite different from that in pure water, which indicates that the diffusion process(b of) Fe cations-Sub-MMT in the interlayer domain is significantly affected by clay wafer. FigureFigure 4. Z 4.-aZ-axisxis relative relative concentration concentration curves curves of counterion of counterion..

3.1.3. Conduction of Ions and Water Molecules The diffusion coefficients of ions and water molecules in the interlayer domain of the two montmorillonite systems are shown in Figure 5 below. Compared with the Na+ system, the diffusion coefficient of interlayer water can be reduced to some extent by adding four kinds of inhibitory cations, but the influence degree of each ion is quite different. The most significant decrease in diffusion ability is in the Ca2+ system, followed by Cs+, NH4+ and K+. This is because the hydration radius and coordination number of Ca2+ are the largest, and more interlayer water molecules are combined to occupy the diffusion channels in the interlayer domain, which leads to the most significant decrease in the diffusion abil- 2+ ity of water molecules in the Ca system. Moreover, it can be observed that the inhibitory cations have the same effect in the two substitution models, and the diffusion ability of the Mg-Sub-MMT(a) Mg system-Sub -decreasesMMT slightly (35% on average).(b) Fe On-Sub the- otherMMT hand, the diffusion ability of the four inhibitory cations in the interlayer domain changed significantly. Figure 5. Diffusion coefﬁcient of counterions and water in different MMT systems. Under the condition of the same water content (fixed 72 water molecules), except for calcium ions, the interlayer diffusion ability of the three inhibitory cations is greater than that 3.2. Response of Cationic Clay Hydration Inhibition to Temperature and Pressure of sodium ion, and the order of diffusion ability is NH4+ > K+ > Cs+ > Na+. According to the simulationIn mode of cation 2, with diffusion temperature in pure rising, water, the when diffusion the performanceamount of charge of water is the molecules same, the after diffusionadding ability saturated of inorganicions is inversely salt solution proportional in the interlayer to the radius domain of was ions. determined, The orderas of shown ion in Figure6 below. It can be found that the water diffusivity still increases signiﬁcantly radius is Cs+ > K+ > NH4+ > Na+, so the diffusion ability of the four ions in pure water is Cs+ with the increase in temperature after adding saturated inhibitory inorganic salt solution < K+< NH4+< Na+. Obviously, in the interlayer domain of montmorillonite, the diffusion at different temperatures. The results show that the addition of cations inhibits the water ability of these monovalent ions is quite different from that in pure water, which indicates diffusivity in the interlayer domain but does not change the overall trend of temperature that the diffusion process of cations in the interlayer domain is significantly affected by clay wafer.

(a) Mg-Sub-MMT (b) Fe-Sub-MMT

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Figure 5. Diffusion coefficient of counterions and water in different MMT systems.

3.2. Response of Cationic Clay Hydration Inhibition to Temperature and Pressure In mode 2, with temperature rising, the diffusion performance of water molecules after adding saturated inorganic salt solution in the interlayer domain was determined, as shown in Figure 6 below. It can be found that the water diffusivity still increases significantly with the increase in temperature after adding saturated inhibitory inorganic salt solution at different temperatures. The results show that the addition of cations inhibits the water Processes 2021, 9, 1069 diffusivity in the interlayer domain but does not change the overall trend of temperature10 of 17 promoting the invasion of water molecules into the interlayer domain. However, compared with the Na+ system without inhibitory salt solution at the same temperature and pressure,promoting the the diffusion invasion coefficient of water molecules of water into molecules the interlayer decreases domain. in However, varying compared degrees after addingwith the salt Na solution.+ system withoutThis shows inhibitory that the salt solutiondegree of at theinhibition same temperature of the saturated and pressure, inhibitory saltthe solution diffusion on coefficient the diffusion of water of water molecules molecules decreases in the in varying interlayer degrees decreases after addingwith the in- creasesalt solution. in temperature. This shows For thatexample, the degree in the of Mg inhibition-Sub-MMT of the system saturated with inhibitory saturated salt KCl solution,solution the onwater the diffusion molecule of waterdiffusion molecules coefficient in the interlayeris 2.41 × decreases10−10 m2/s with at 25 the °C increaseand 60 in MPa. However,temperature. the water For example, diffusivity in thein Mg-Sub-MMT the Mg-Sub system-MMT withsystem saturated without KCl adding solution, inhibitory the −10 2 ◦ solutionwater moleculeis 3.59 × 10 diffusion−10 m2/s. coefficient That is, the is 2.41 reduction× 10 inm the/s diffusion at 25 C and coefficient 60 MPa. of However, the inhibitor the water diffusivity in the Mg-Sub-MMT system without adding inhibitory solution is to water molecules is 32.97%. However, at 150 °C and 60 MPa, the diffusion coefficient of 3.59 × 10−10 m2/s. That is, the reduction in the diffusion coefficient of the inhibitor to −10 −10 2 waterwater molecules molecules decreases is 32.97%. from However, 21.51 × at 10 150 to◦C 13.46 and 60× 10 MPa,m the/s. diffusion The degree coefficient of reduction is 21.51%.of water Comparing molecules decreases the four from kinds 21.51 of inhibitory× 10−10 to salt 13.46 solutions,× 10−10 m it2 is/s. found The degree that the of aver- agereduction degree isof 21.51%.inhibition Comparing of the saturated the four kinds CaCl of2 inhibitorysolution on salt the solutions, diffusion it is abilityfound that of water moleculesthe average is the degree largest, of inhibition followed of by the CsCl, saturated KCl CaCl and2 NHsolution4Cl. on the diffusion ability of water molecules is the largest, followed by CsCl, KCl and NH4Cl.

(a) K+-Na+ (b) NH4+-Na+

Figure 6. Diffusion coefﬁcient of water of MMT system under different counterions and temperatures.

Figure7 shows the relative concentration distribution of inhibitory cations and sodium ions in the Z-axis direction in the interlayer domain when saturated KCl and CsCl solutions are contained in the interlayer domain of the Mg-Sub-MMT system in mode 2, as well as the relative concentration distribution characteristics of sodium ions when no inhibitor is added (marked by Na-0 in the ﬁgure). The distribution peaks of K+ and Cs+ in the interlayer Processes 2021, 9, 1069 11 of 17

Figure 6. Diffusion coefficient of water of MMT system under different counterions and temperatures.

Figure 7 shows the relative concentration distribution of inhibitory cations and sodium ions in the Z-axis direction in the interlayer domain when saturated KCl and CsCl solutions are contained in the interlayer domain of the Mg-Sub-MMT system in mode 2, Processes 2021, 9, 1069 as well as the relative concentration distribution characteristics of sodium ions11 of when 17 no inhibitor is added (marked by Na-0 in the figure). The distribution peaks of K+ and Cs+ in the interlayer domain are closer to the SiO2 tetrahedral surface of montmorillonite crystal than those of Na+. At the same time, compared with the original montmorillonite system domain are closer to the SiO2 tetrahedral surface of montmorillonite crystal than those of + withoutNa+. At adding the same inhibitory time, compared ions, the with main the original peak of montmorillonite Na after addition system is withoutstill near adding the middle ofinhibitory the interlayer ions, thedomain, main peak but ofthe Na peak+ after intensity addition is is significantly still near the middle lower ofthan the that interlayer of the orig- inaldomain, Na+ (Na but-0), the indicating peak intensity that is Na signiﬁcantly+ in the added lower system than that also of has the originala tendency Na+ to(Na-0), transfer to theindicating surface thatof the Na silica+ in the tetrahedron. added system This also distribution has a tendency indicates to transfer that to when the surface the inhibitory of cationsthe silica and tetrahedron. sodium ions This coexist distribution in the interlayer indicates that domain, when the the inhibitory inhibitory cationscations and preferen- tiallysodium adsorb ions coexiston the insilica the interlayersurface of domain, the montmorillonite the inhibitory cations crystal preferentially layer, forming adsorb a more inneron the spherical silica surface coordination of the montmorillonite structure, thus crystal inhibiting layer, forminghydration a more and innerstabilizing spherical the crys- coordination structure, thus inhibiting hydration and stabilizing the crystal layer structure. tal layer structure. Moreover, Na+ migrates to the surface, which further increases the abil- Moreover, Na+ migrates to the surface, which further increases the ability of the cation to itybalance of the cation the negative to balance charge the in negative the crystal charge layer, reducesin the crystal the electrostatic layer, reduces repulsion the electrostatic force repulsionand stabilizes force the and crystal stabilizes layer structure.the crystal layer structure.

(a) K+-Na+

(b) Cs+-Na+ FigureFigure 7. 7. ZZ-axis-axis relative relative concentrationconcentration distribution distribution of counterions.of counterions. The qualitative observation results of the relative concentration curve can be directly evaluated by the change in coordination number between cations and oxygen atoms on the surface of the montmorillonite silicon-oxygen tetrahedron (X-OB). Figure8 shows the Processes 2021, 9, 1069 12 of 17

Processes 2021, 9, 1069 The qualitative observation results of the relative concentration curve can be directly12 of 17 evaluated by the change in coordination number between cations and oxygen atoms on the surface of the montmorillonite silicon–oxygen tetrahedron (X-OB). Figure 8 shows the change inin coordinationcoordination number number between between the the inhibitory inhibitory cations cations in thein the interlayer interlayer domain domain and sodiumand sodium ions ions in the in originalthe original system system and and oxygen oxygen atoms atoms on theon the surface surface of montmorillonite of montmorillo- silicanite silica under under different different temperature temperature conditions. conditions. By comparison,By comparison, it is it found is found that that the the X-OB X- coordinationOB coordination number number increases increases obviously obviously after theafter addition the addition of inhibitory of inhibitory cations, cations, which indicateswhich indicates that the that inhibitory the inhibitory cations cations tend to tend distribute to distribute on the on clay the surface clay surface and form and moreform innermore inner spherical spherical ligands. ligands. The ability The ability of the of four the kinds four kinds of inhibitory of inhibitory cations cations to form to innerform + + + + + +2+ 2+ sphericalinner spherical ligands ligands is Cs >is KCs> > NH K 4> NH> Ca4 >, Ca which, which also reﬂects also reflects the strength the strength of the abilityof the ofability the fourof the kinds four ofkinds cations of cations to stabilize to stabilize the crystal the crystal layer structure.layer structure. At the At same the same time, time, with thewith increase the increase in temperature, in temperature, the X-OB the coordination X-OB coordination number numbe graduallyr gradually decreases, decreases, which indicateswhich indicates that the that increase the increase in temperature in temperature weakens weakens the immobilization the immobilization of the of inhibitory the inhib- cationsitory cations on the on surface the surface of the of montmorillonite the montmorillonite crystal crystal layer, whichlayer, which is not conduciveis not conducive to the hydrationto the hydration inhibition inhibition effect ofeffect the cations.of the cations.

(a) K+-Na+ (b) NH4+-Na+

Figure 8. CN of counterions and O in silicon–oxygensilicon–oxygen tetrahedron surface under different counterionscounterions andand temperatures.temperatures.

When cationscations enterenter intointo the the interlayer interlayer domain, domain, another another important important evaluation evaluation criterion crite- forrion their for their inhibition inhibition effect effect is their is inﬂuencetheir influence on the on mechanical the mechanical properties properties of montmorillonite of montmo- crystals.rillonite crystals. Figures9 Figureand 10s show 9 and the 10 changesshow the in changes the mechanical in the mechanical properties properties of montmorillonite of mont- crystalsmorillonite after crystals the entry after of the four entry kinds of four of inhibitory kinds of inhibitory cations into cations the interlayerinto the interlayer domain, focusingdomain, focusing on the changes on the in changes the crystal in the stiffness crystal (elastic stiffness modulus (elastic and modulus Poisson’s and ratio). Poisson’s ratio).In order to intuitively compare the ability of inhibiting cations to reduce the deterioration effect of mechanical properties of montmorillonite crystal under hydration, this section adds eight groups of mechanical properties under the same temperature and pressure conditions for two kinds of substitution models that have no water molecules in the interlayer, that is, mechanical properties under drying conditions. The reason for choosing to compare the mechanical properties of montmorillonite crystal without water in the interlayer domain is mainly to study whether the addition of inhibitory cations can strengthen

Processes 2021, 9, 1069 13 of 17

the montmorillonite crystal. This investigation allows determining whether the mechanical Processes 2021, 9, 1069 properties of the crystal with inhibitors are better than the original mechanical properties13 of 17 without water or to ensure that the deterioration degree of the mechanical properties of the crystal after hydration is weakened.

(a) K+-Na+ (b) NH4+-Na+

FigureFigure 9. 9.Elastic Elastic modulusmodulus of of MMTMMT crystalscrystals underunder differentdifferent temperatures temperatures and and inhibiting inhibiting cations. cations.

Firstly, the accuracy of the simulation results is veriﬁed by comparing the previous studies on the mechanical properties of montmorillonite crystals with inhibitory cations in the interlayer domain. The calculation results of bulk modulus and shear modulus of crystals with two layers of water molecules and saturated KCl, NH4Cl and CaCl2 in the interlayer domain by Professor Xu [17,35] are 69.16 GPa, 66.59 GPa and 67.83 GPa, 36 GPa, 34.58 GPa and 34.19 GPa respectively (the temperature, pressure and the number of water molecules are unknown). The elastic modulus and Poisson’s ratio calculated based on isotropic assumption are 92.03 GPa, 88.43 GPa and 87.82 GPa, 0.278, 0.278 and 0.284, respectively. These values are similar to the simulation results (E, KCl: 75.76 GPa, NH4Cl: 68.94 GPa, CaCl2: 82.9 GPa; v, KCl: 0.260, NH4Cl: 0.259, CaCl2: 0.257) at 0.1 MPa and 25 ◦C in this paper. The slight difference may be caused by the difference in force ﬁeld parameters, temperature and pressure conditions and the number of water molecules. As shown in Figures9 and 10, at different temperatures, the mechanical properties of montmorillonite crystals are still deteriorated when the saturated inhibitory salt solution is (aadded) K+-Na in+ the interlayer compared with no water molecules(b) NH4+ in-Na the+ interlayer, that is, when there is no hydration, indicating that the addition of inhibitory cations has no strengthening effect on the mechanical properties of montmorillonite crystals and can only reduce the deterioration degree of mechanical properties after hydration. At the same time, the degra- Processes 2021, 9, 1069 13 of 17

(a)K+-Na+ (b) NH4+-Na+

Processes 2021, 9, 1069 14 of 17

dation degree increases with the increase in temperature, which indicates that temperature weakens the ability of cation to maintain the mechanical properties of crystal and reduces its inhibition effect. For example, in the Mg-Sub-MMT system with saturated KCl solution, the degradation degree of the crystal elastic modulus is 15.24% at 25 ◦C, but when the temperature rises to 150 ◦C, the degree of deterioration reaches 39.94%. This is consistent with the effect of temperature on the formation of the inner spherical coordination structure of inhibitory cations on the tetrahedral surface of montmorillonite crystal, both of which indicate that the inhibition of inhibitory cations will be weakened with the increase in temperature. The degradation degree of the mechanical properties of montmorillonite + + 2+ 2+ + + + + (crystalsc) Cs -Na under different temperatures is as follows: (Cad) Ca< Cs-Na < K < NH4 . The average 2+ Figure 9. Elasticdegradation modulus of degree MMT crystals of montmorillonite under different crystal temperatures in the Ca and inhibitingsystem is cations. only 27.46%, followed by 30.79% for Cs+.

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(a) K+-Na+ (b) NH4+-Na+

FigureFigure 10. 10.Poisson’s Poisson’s ratio ratio of of MMT MMT crystals crystals under under different different temperatures temperatures and and inhibiting inhibiting cations. cations.

GenerallyIn order to speaking, intuitively the compare temperature the ability rise is of not inhibiting conducive cations to the to inhibitory reduce the effect deterio- of theration inhibitory effect of cations mechanical in the montmorilloniteproperties of montmorillonite system. The increase crystal under in temperature hydration, weakens this sec- thetion inhibition adds eight of groups cations of on mechanical the hydration properties of montmorillonite under the same by temper reducingature the and inhibitory pressure effectconditions of inhibitory for two cationskinds of on substitution the diffusion models of water that moleculeshave no water in the molecules interlayer in andthe inter- the abilitylayer, ofthat cations is, mechanical to maintain properties the mechanical under drying properties conditions. of the crystal. The reason for choosing to compare the mechanical properties of montmorillonite crystal without water in the inter- 4. Conclusions layer domain is mainly to study whether the addition of inhibitory cations can strengthen the Inmontmorillonite this paper, based crystal on. MD This method, investigation according allows to determining the characteristics whether of typicalthe mechani- clay mineralscal properties contained of the in crystal deep shale, with inhibitors combined are with better the typesthan the of inorganicoriginal mechanical salinization prop- in- hibitorserties without commonly water used or into theensure ﬁeld, that the the molecular deterioration dynamics degree models of the for mechanical micro inhibition proper- + + + 2+ evaluationties of the ofcrystal four typicalafter hydration cations (K is ,weakened. NH4 , Cs and Ca ) inhibiting clay hydration were Firstly, the accuracy of the simulation results is verified by comparing the previous studies on the mechanical properties of montmorillonite crystals with inhibitory cations in the interlayer domain. The calculation results of bulk modulus and shear modulus of crystals with two layers of water molecules and saturated KCl, NH4Cl and CaCl2 in the interlayer domain by Professor Xu [17,35] are 69.16 GPa, 66.59 GPa and 67.83 GPa, 36 GPa , 34.58 GPa and 34.19 GPa respectively (the temperature, pressure and the number of water molecules are unknown). The elastic modulus and Poisson’s ratio calculated based on isotropic assumption are 92.03 GPa, 88.43 GPa and 87.82 GPa, 0.278, 0.278 and 0.284, respectively. These values are similar to the simulation results (E, KCl: 75.76 GPa, NH4Cl: 68.94 GPa, CaCl2: 82.9 GPa; v, KCl: 0.260, NH4Cl: 0.259, CaCl2: 0.257) at 0.1 MPa and 25 °C in this paper. The slight difference may be caused by the difference in force field parameters, temperature and pressure conditions and the number of water molecules. As shown in Figures 9 and 10, at different temperatures, the mechanical properties of montmorillonite crystals are still deteriorated when the saturated inhibitory salt solution is added in the interlayer compared with no water molecules in the interlayer, that is, when there is no hydration, indicating that the addition of inhibitory cations has no strengthening effect on the mechanical properties of montmorillonite crystals and can only reduce the deterioration degree of mechanical properties after hydration. At the same time, the degradation degree increases with the increase in temperature, which indicates that temperature weakens the ability of cation to maintain the mechanical properties of crystal and reduces its inhibition effect. For example, in the Mg-Sub-MMT system with saturated KCl solution, the degradation degree of the crystal elastic modulus is 15.24% at 25 °C, but when the temperature rises to 150 °C, the degree of deterioration reaches 39.94%. This is consistent with the effect of temperature on the formation of the inner spherical coordination structure of inhibitory cations on the tetrahedral surface of montmorillonite crystal, both of which indicate that the inhibition of inhibitory cations will be

Processes 2021, 9, 1069 15 of 17

established. The molecular dynamics simulations of inhibiting hydration of clay minerals under different temperatures, pressures and types and concentrations of cation ions were carried out in order to explore the micro mechanism of the chemical inhibition effect of typical inorganic salt inhibitors on clay hydration and the temperature and pressure response characteristics. The following ﬁndings were obtained: In terms of the micro mechanism of cations inhibiting clay hydration: + + + • The inhibitory cations (K , NH4 and Cs ) promote the contraction of clay interlayer spacing and compress the ﬂow channel of ions and water molecules invading into the MMT interlayer. • The inhibitory cations decrease the diffusivity of water and then weaken its ability to invade the formation. + + + 2+ • When the inhibitory cations (K , NH4 , Cs and Ca ) are added into the interlayer domain, they will transfer to the surface of the crystal layer, resulting in the increase in coordination number with oxygen atoms on the silica surface of clay minerals, the improvement of the ability to balance the negative charge in the interlayer and the reduction in the electrostatic repulsion of the negative charge in the interlayer. In terms of the characteristics of cationic clay hydration inhibition in response to temperature and pressure: • The temperature rise is not conducive to the inhibitory effect of the inhibitory cations in the montmorillonite system. The increase in temperature weakens the inhibition of cations on the hydration of montmorillonite by reducing the inhibitory effect of inhibitory cations on the diffusion of water molecules in the interlayer and the ability of cations to maintain the mechanical properties of the crystal. • The increase in pressure is helpful for the inhibitory cation to exert its inhibitory effect in the montmorillonite system. With the pressure rising, the inhibitory effect of cations on the montmorillonite hydration is enhanced by enhancing the inhibition of the water diffusivity in the interlayer and the ability of cations to maintain the mechanical properties of the crystal. • The inhibitory properties of cations in different crystal lattices of substituted montmorillonites vary greatly. Generally, the cation inhibitory properties of Mg-Sub-MMT are better.

Author Contributions: Conceptualization, Y.Z.; methodology, Y.Z.; software, Y.Z.; validation, Y.Z. and C.X.; formal analysis, Y.Z. and C.X.; investigation, Y.Z.; resources, Y.Z. and C.X.; data curation, Y.Z.; writing—original draft preparation, Y.Z. and C.X.; writing—review and editing, Y.Z. and C.X. Both authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (NSFC) (No. U19B6003-05) and Sinopec Ministry of Science and Technology Project (P18058-2). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data is contained within the article. Acknowledgments: The authors are grateful for financial support to the National Natural Science Foundation of China (NSFC) (No. U19B6003-05) and Sinopec Ministry of Science and Technology Project (P18058-2). Conflicts of Interest: The authors declare no conflict of interest.

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