Influence of Self-Generated Electric Field on Coexisting Patterns of

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C: Physical Processes in Nanomaterials and Nanostructures

Water Film or Water Bridge? Influence of Self-Generated Electric Field on Coexisting Patterns of Water and Methane in Clay Nanopores You-zhi Hao, Xiaotian Jia, Zhiwei Lu, Detang Lu, and Peichao Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b06519 • Publication Date (Web): 21 Aug 2019 Downloaded from pubs.acs.org on August 23, 2019

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The Journal of Physical Chemistry

Water Film or Water Bridge? Influence of Self-Generated Electric Field on Coexisting Patterns of Water and Methane in Clay Nanopores Youzhi Hao,† Xiaotian Jia,† Zhiwei Lu,‡ Detang Lu,†* and Peichao Li§* †

Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China.

‡

Viterbi School of Engineering, University of Southern California, Los Angeles, CA, 90089, USA

§School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620,

China. *

Email address: [email protected] (D. Lu), [email protected] (P. Li).

ABSTRACT

Water always occurs in gas shales, especially during the treatment of shale gas hydraulic fracturing. In sharp contrast to the prevailing view that water film is ubiquitous in shale formations, we observed an unusual phenomenon that water bridge instead of water film dominates in some illite and kaolinite slit pores, when we are investigating the coexisting pattern of water and methane inside shale nanopores using molecular dynamics simulations. The network orientation structure and hydrogen bond of water molecules are analyzed and the results indicate that appearance of water bridge is attributed to the strong internal, self-generated electric field induced by surface charge contrast between different pore surfaces. Four factors can significantly influence this self-generated electric field strength: pore surface chemistry, mineral type, pore shape, and pore size etc. When the pore size is within several nanometers, a small charge difference could induce strong electric field and change S1

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the structural properties of water clusters. The water film or water bridge inside shale nanopores alters the hydraulic diameter of the pore and the fluid flow pattern. These findings may provide a better and microscopic insight of the water-gas flow behavior and the electric field inside clay nanopores.

1.

INTRODUCTION

Shale gas is stored in deep shale formations and served as important unconventional energy. Clay minerals (illite, kaolinite, montmorillonite etc.) along with quartz and kerogens are main components of shale formations.1-5 The main gas component of shale gas is methane (CH4).6 In shale gas development, horizontal drilling and water-based hydraulic fracturing are key methods to extract more gas; the former introduces large amounts of water into the shale reservoirs to create more fractures.7-8 Therefore, interactions between water and shale rock, especially structure of water cluster impose significant impact shale gas recovery and well management. Various water structures such as ordered water layers, small droplets, thin films, or capillary bridges can be formed when water drops on a solid surface.9 In experiments, Fuchs et al.10-11 observed a floating water bridge when high voltage is applied to water filling in two separate glass beakers. Through Raman scattering measurements on floating water bridges, Ponterio et al.12 found that electric fields could change the OH-stretching band, i.e. the local environment of water molecules. In simulations, Ho et al.13 proposed that water bridges across the pores can be formed by the capillary force in slit pores using molecular simulations. Chen et al.14 obtained water bridges connecting two substrate plates through restraining water molecules by external electric field using molecular simulations, similar to experiments by Fuchs et al.10-11 Celebi et al.15 modified surface carbon charges S2


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of graphene slit pore to investigate the influence of generated electric field on transport properties of water, but did not observe water bridge. In theory, Aerov16 proposed that the water bridge is supported by its surface tension and the electric field prevents water bridge breaking into separate drops to reduce its surface energy. Namin et al.17 proposed that water bridge is hold up against gravity by dielectric tension and surface tension using experiments. Tokunaga and Wan18 proposed that heterogeneous water film thickness and water film flow is important in fractures. Li et al.19 proposed that water exist mainly as water film in larger pores and two separated water films which are at close contact distance at the pore throats will connect each other to form a bridge. Li et al.20 proposed that the total surface interactions inside capillaries are higher than that inside slits, which leads to an easier condensation and thicker film thickness in capillaries. Liu et al.21 found that water bridge by capillary-bridge forces due to the dramatic corrugation of water films could appear when high accelerations are applied to water-methane flow in cristobalite slit pore using molecular dynamics simulations. Therefore, the structure of water clusters inside nanopores is generally treated as water films with possibly small amount of capillary bridges in many literatures. Currently, direct experimental evidence on the behavior of methane and water inside clay nanopore is rare. To the best of our knowledge, the effects of illite or kaolinite slit pores considering edge surfaces on the structure and dynamics of water have not been previously reported in the literature. In this work, we focus on illite and kaolinite nanopores to investigate the coexistence state of water and gas inside these pores.

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MODELS AND METHODOLOGY

The simulation system consists of water and methane confined in illite and kaolinite nanopores. Four factors are taken into account when modeling the pores: (1) pore shapes: generally categorized as slit and cylindrical, with some other irregular shapes, such as oval, cone, wedge, and inkbottle in shale formations;22-23 (2) pore surface chemistry: basal surface or edge surfaces. Clay particles or tablets are generally less than 1 um in size, exhibiting basal or edge surfaces.24-26 There are no difference between illite’s up and down basal surfaces, but for kaolinite, two kinds of basal surfaces (one with outmost oxygens and one with outmost hydrogens) exist. According to Hartman-Perdock’s periodic bond chain theory,27 the edge surfaces can be categorized as “A&C chain” and “B chain” edge surfaces (see our previous work26). The determination and partial charge of edge surfaces can refer to literatures.28-31 (3) mineral species that form the pore: illite or kaolinite; (4) pore size: nanopores are abundant in shale gas reservoirs, with pore sizes ranging from a few nanometers to several hundred nanometers.1, 32-34 The shale nanopores are modelled by slit pore and cylindrical pore, both with constant cross-section area. The illite are modelled with chemical formula K2[Si7Al](Al3Mg)O20(OH)4 and kaolinite with Al2Si2O5(OH)4. Two factors: metal ion substitution of octahedral Al3+ and tetrahedral Si4+ by Mg2+ or Al3+, and cutting edge surfaces are considered when modelling illite pores.26 For kaolinite pores, only cutting edge surfaces are considered. Because of isomorphic metal ions substitutions or cations adsorption, net charge is often present on the outmost surfaces35 and will be neutralized with some mobile potassium ions (K+) during the simulations. According to this, we built five clay pore models (1) illite basal slit pore (2) illite A&C chain edge slit pore (3) illite B chain edge slit pore; (4) illite cylindrical pore with inner basal and edge surface and (5) kaolinite basal slit pore. S4


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The interatomic potentials for clay atoms and ions are modelled by CLAYFF force field.26,36 Methane molecule is described by all-atom CVFF37-38 and water molecule by flexible SPC force field. The hydroxyl bond and angle inside clay crystals are described by harmonic potentials.36 We performed molecular dynamics simulations using LAMMPS.39 At initial state, the water and methane molecules are filled into the pore space, each accounts for half of the pore spaces. The skeleton structural atoms of illite & kaolinite (Al, Mg, Si, and O) are kept rigid to their crystal coordination, except that the hydroxyl H atoms and the cations K+ are mobile with thermal motions. 3.

RESULTS AND DISCUSSION

3.1. Coexisting Patterns of Water and Methane. As shown in Figure 1ac, several water bridges that connect upper and lower pore surfaces are formed inside illite basal and kaolinite basal slit pores. The distribute characteristics of water bridge can be viewed from the side and top view of the spreading patterns of water island in Figure 1bd. In the illite cylindrical pore, only water film exists as shown in Figure 2a. Compared with basal slit pores, water film dominates inside A&C chain or B chain slit pores (Figure 2bcde). When the pore size is less than 2 nm, water bridge forms only when there are adequate water molecules as shown in Figure 2fg. But this type of water bridge (Figure 2fg) is formed due to water inter-molecular attraction, because we observed that water molecular orientations are random, so this water bridge belongs to capillary bridge. We increase the pore size and found that water bridge still exist in basal slit pores but diminishes in A&C or B chain slit pores. Based on these simulations, there are strong adhesions of water molecules to spread onto the clay surface to form water film. But inside basal slit pore, these water films tend to shrink to form water bridge.

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Figure 1. Water bridges in (a,b) illite and (c,d) kaolinite slit pores from side view and top view, respectively. Color scheme: yellow, silicon; pink, aluminum; green, magnesium; red, oxygen; cyan, carbon; purple, potassium; white, hydrogen.

Figure 2. Water films in 5 nm illite (a) cylindrical pore, (b) A&C chain and (c) B chain slit pores. Water films in 2 nm illite (d) A&C chain and (e) B chain slit pores with less water molecules. Water bridges 2 nm illite (f) A&C chain and (g) B chain slit pores with more water molecules.

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3.2. Forming Process of Water Bridge. To investigate how the water bridge forms, we take the 50 nm illite basal slit pore as an example to show the detailed formation process of water bridge as shown in Figure 3.

Figure 3. The formation process of water bridge in 50 nm illite basal slit pore. At initial state, water and methane molecules are artificially placed in separate half of the pore space. As time progresses, the water molecules begin to move the opposite surface, and form a cone-like shape. When the tip of cone-like water clusters connects the opposite pore surface, more water molecules from the left pore surface begin to travel along the cone-like pillar to the opposite site, transform the cone-like pillar into a cylindrical pillar, and finally a stable water bridge is formed. The formation process indicates that the water molecules are driven by some kind of force or pressure gradient. 3.3. Pore-Filling Patterns. Water bridge or water film influences the pore-filling patterns: the water layer grows axially in the direction of the pore axis where water film dominates, while radially towards S7



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the pore center where water bridge appears. Compared with water film, the water bridge leaves more pore surface area for methane molecules to adsorb directly. Water film acts as water channels and water bridge acts as water pillars. There exist different transport pathways for methane molecules inside water film nanopores and water bridge nanopores. In addition, we found that methane transport is hindered by water bridges when we examine the diffusion coefficients of water and methane inside different illite pores (Table S1 in Supporting Information). As water saturation increases in cylindrical pore, A&C or B chain slit pores, water bridge will appear due to water inter-molecular attractions but not due to electric field as shown in Figure 2fg. 3.4. Hydrogen Bond Number and Dipole Orientation Distributions. To inspect water bridges, the water structures are firstly analyzed through (1) change of hydrogen bond number and (2) distributions of water dipole orientation. A hydrogen bond is determined by the following geometric criterion (1) distance between the donor oxygen and the acceptor oxygen < 3.5 Å; (2) the angle donor– hydrogen-acceptor < 20. From the calculations, we found a decrease of hydrogen bond per atom (1.08 in illite basal slit pore) compared with bulk water (3.64 using SPC flexible water model). The decrease of the hydrogen bond could be associated with the changes of water dipole orientations or intermolecular distances. Therefore, we continue to check the water dipole orientation distributions described by the orientation angle θ defined as between water dipole vector and the pore surface vertical vector (inset in Figure 4a). θ becomes 0° and 180° when the water dipole vector is parallel to and pointing to the pore surface, respectively.

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Figure 4. Histogram of water molecular orientation angle distribution at (a) initial random state and (b) equilibrium state. Inset: definition of water molecular orientation. As shown in Figure 4a, at initial state (or as bulk phase), water molecular shows random orientations in the pore space. After equilibrium, θ resides within 0° ~ 40° (most between 0° ~ 25°) as shown in Figure 4b, indicating that most water molecules are highly aligned with pore surface’s vertical direction. Combined with the analysis of hydrogen bond number changes of water clusters, we found that water hydrogen bond network is greatly destroyed by some kind of force. 3.5. Self-Generated Electric Field Inside Nanopores. Inspired by the work of Fuchs et al.10-11 and Ponterio et al.,12 we suspect the water bridge is possibly induced by electrostatic interactions, namely the electric field. The suspect is based on that electric field could influence water structures. HeadGordon et al.40 thought that the external electric field can completely destroy the local tridimensional arrangement of the water network, giving rise to the formation of linear chain-like structures of dipolar water molecules aligned along the field axis. However, where does the electric field come from, since we do not introduce any external electric field in these simulations? To address this assumption, we computed the electric field inside these clay nanopores by numerically measuring the electrostatic S9



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force on test elementary particle with charge e by probing through the three dimensional grids of the empty pores without any water or methane molecules. We also calculated the electric field in filled pores with the existence of water & methane molecules at equilibrium.

Figure 5. The calculated electric fields depicted by scaled vectors inside 3 nm illite slit pores: (a) empty basal pore, (b) empty A&C chain pore, and (c) empty B chain pore without any water or methane molecules; (d) filled basal pore, (e) filled A&C chain pore, and (f) filled B chain pore with water & methane molecules at equilibrium. The corresponding slit pore structures are presented in (g) basal pore, (h) A&C chain pore, and (i) B chain pore. The lengths of electric field vectors are scaled by a scale factor to accommodate within the graph. The magnitude and direction of the self-generated electric fields inside a 3 nm illite basal slit pore, A&C chain slit pore, and B chain slit pore are shown in Figure 5. The average electric field strength is 16.24 V/nm, 0.90 V/nm, and 0.71 V/nm inside empty basal, A&C chain, and B chain slit pores, respectively (Table S2 in Supporting Information). These results show that the empty basal slit pore S10


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generates strong and directional electric field that points from low-density K+ surface to high-density K+ surface (Figure 5ag). For A&C chain or B chain slit pores, the electric field vectors also point from one pore surface to the opposite side (Figure 5bchi). The electric fields exhibit high anisotropy in the vicinity of pore surfaces in edge surface (A&C chain or B chain) slit pores as shown in Figure 5bc. This difference is related with the basal and edge surface structures and their adsorbed metal ion distributions.

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Figure 6. The components along x/y/z three directions of electric field vectors in 3 nm empty illite slit pores: (a) basal slit pore, (b) A&C chain slit pore, and (c) B chain slit pore. (d) the comparison of electric field strengths inside various illite slit pores with the influence of water & methane molecules at equilibrium.

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The distribution of electric field components along x/y/z three directions in 3 nm empty illite pores and the comparison of electric field strengths inside various illite slit pores with the influence of water & methane molecules at equilibrium is depicted in Figure 6. Since the positions of probe atom in each pore is different, in order to compare the electric field values in different pores, these electric field values in each pore are arranged in descending order and the horizontal axis in Figure 6 is just the sequence row number of the order. As shown in Figure 6abc, the electric field strength vertical to the pore surface is much larger and symmetric than that parallel to the pore surface inside basal slit pores. In A&C chain or B chain slit pores, the electric field strength vertical to the pore surface is comparable but still larger than that parallel to the pore surface. The average electric field components values are provided in Table S2 in Supporting Information. These results indicate that these internal electric fields tend to point from one surface to another. The influence of filled water & methane molecules on the electric field in the pores are cindered. Figure 5def shows the electric field vectors in filled pores, and Figure 6d depicts the comparison of electric field strengths inside empty and filled pores. There are two points we need to pay attention: 1) since we insert the probe atom uniformly in the three-dimensional pore space with full of fluid molecules, it may occur that the position of the probe atom resides too close or even overlap with the fluid molecules (in fact, it occurs). These extremely close distance leads the calculated electric field values at this position extremely large according to Coulomb's law, which can be seen in Figure 5def and Figure 6d. From the latter half of the curves that shows the low-fluctuated electric fields, the electric field strength follows the order of Ebasal >EA&C chain >EB chain, consistent with that in pores S12


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without any fluid molecules. 2) Part of the electric field vectors have random directions and did not toward a single direction, which is affected by water molecules, but most of the electric field vectors still point to the pore vertical direction. Note that as shown in Figure 6d by the latter part of the curves, the difference of electric field strengths between empty and filled pores is small which indicates that the existence of filled fluid molecules has limited influence on electric field at most positions in pores. In the case of water bridge in basal slit pore, the water dipole orientation distribution changes from random to aligned, this change cancelled part of the self-generated electric field strength as shown in Figure 6d. Therefore, the electric fields inside the pores are self-generated and intrinsic, while the role of fluid molecules is that they affect the nearby electric field by distance and overall electric field by their entire molecular dipole orientations. Cramer et al.41 investigated the sudden formation of water pillar arising from water droplet on a polar surface when the exerted electric field exceeds 1.2 V/nm. Skinner et al.42 found that electric field at 1.0 V/nm can cause significant structural anisotropy (directional-dependence) of water molecules while electric field at 1×10-3 V/nm cannot. In our simulations, the electric field strength in A&C or B chain slit pore is less than 1.0 V/nm, which is not strong enough to induce stable water bridges. However, the strength of electric field inside basal slit pore is several times higher than that in A&C chain or B chain slit pore at same pore size. The electric field strength in the basal slit pore is about 16.2 V/nm and much larger than 1.2 V/nm, which could form water bridges. 3.6. Imbalanced Surface Charges inside Clay Nanopores. In these nanopores, the generating of electric field is mainly attributed to the higher density of K+ on one surface than that on other surface

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of illite, and the distinct surfaces structures of kaolinite. Since clay minerals can retain a significant amount of metal ions,43 these ions could distribute locally and chemically stable as proved in our simulations on the clay particle surfaces which could cause imbalanced surface charges. In slit pores, the upper and lower pore surface acts as cathode and anode like electrodes. The long-range electrostatic interactions can extend tens of nanometers, therefore the water in the nanopores center may be out control of pore surface van der Waals forces, but still under the influence of Coulomb forces. Then the water bridge or water film is determined by the tendency of water spreading on the pore surface via hydrophilic attractions versus the vertical moving toward the other side surface via electric interactions. 3.7. Influence of Pore Size on Water Bridge. The electric field strength in the pore zone decreases with increasing pore size, thereby impair the formation of water bridge. However, to what extent of pore size the water bridge will collapse and be unsustainable? In order to investigate this, we increase the pore size until 100 nm as shown in Figure 7.

Figure 7. The influence of pore size (50 ~ 100 nm) on the formation of water bridge inside illite basal slit pores.

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In the case of illite basal slit pores, water bridge can hardly be formed when pore size exceeds 80 nm as shown in Figure 7. The average electric field strength is calculated to be 1.009 V/nm and 0.895 V/nm inside 80 nm and 90 nm illite basal slit pores, respectively. This indicates that the water bridge requires electric field higher than 0.895V/m or even to 1.0 V/nm. This electric value is consistent with the conclusion of Cramer et al.41 and Skinner et al.,42 that the electric field with about 1×109 V/m can align the water network of hydrogen bond to the direction of electric field. Chen et al.14 also observed that by exerting a horizontal electric field 1.0 V/ nm, a nanoscale water bridge leaps across the gaps parallel or perpendicular to the electric field. Therefore, the electric field strength decreases as the pore size increases until not strong enough to support the water bridge. 3.8. Cation Locations in Micropores. The locations of K+ cations influence the surface charge contrast thus the water cluster shapes. As proved in our simulations, although these K+ ions are mobile with thermostat, they are mostly located firmly inside pores that exceeds 2 nm. Here, we examine the pores that is less than 2 nm, i.e. the micropore.

Figure 8. Location changes of mobile K+ ions inside (a) 1 nm empty illite basal slit pore, (b) 2 nm illite basal slit pore with only methane molecules, and (c) 2 nm illite basal slit pore with both water and methane molecules. As shown in Figure 8a, in 1 nm empty micropores (without water or methane), we observed some K+ ions move onto the other side of the pore surfaces due to the strong influence of potential overlap of surface atoms. In Figure 8b, a 2 nm illite pore, the K+ ions are hardly influenced by the methane S15



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molecules with zero dipole moments. But the K+ ions can be influenced and expelled by water molecules to the other side of pore surface as shown in Figure 8c. The change of K+ locations can alter the surface charge distributions and weakens the formation of water bridge. While in basal slit pores, some K+ ions are carried to neighbor sites or opposite surface sites, in edge slit pores, some K+ ions are expelled to the accessible interlayer pore space by water molecules. In our simulations, we observed that the water molecules have little influence on the location of K+ ions in pores larger than 2 nm. 4.

CONCLUSIONS

In summary, water bridge is evident in illite or kaolinite basal slit pores, while water film is obvious in cylindrical pores and edge surface slit pores. The exact appearance of water bridge or water film is determined by the surface charge contrast or by water saturations. The surface charge contrast between different nanopore surfaces could generate strong electric field that induces water bridge. The surface charge contrast is influenced by the imbalanced surface metal cations distributions, pore shapes, pore size, and surface chemistries. But with the water saturation increasing in cylindrical pores or edge surface slit pores, water bridge could also occur due to inter-molecular attractions which is also capillary bridge that is not influenced by external electric field. The self-generated electric fields inside clay nanopores are calculated and certain pores that have high voltages (over 1.0V/nm) can form water bridges. The electric fields inside the pores are self-generated and intrinsic, while the role of fluid molecules is that they affect the nearby electric field by distance and overall electric field by entire molecular dipole orientations. The gas transport can be enhanced or greatly reduced by the presence of water films or water bridges, respectively. Compared with water film, the water bridge significantly S16


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reduces the surface area occupied by water molecules, thereby leaves more surface area for CH4 molecules. These findings may provide a better and microscopic understanding of water-gas flow behavior and the electric field inside clay nanopores. ASSOCIATED CONTENT Supporting Information The Supporting Information includes: (1) Diffusion coefficients of methane inside different nanopores with water bridge or water film; (2) Average values of electric field components along x/y/z directions in illite slit pores. AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (D. Lu) *E-mail: [email protected] (P. Li). ORCID Youzhi Hao: 0000-0002-7622-4858 Detang Lu: 0000-0002-4571-0810 Peichao Li: 0000-0001-5295-3805 Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work was financially supported by the National Science and Technology Major Project (2017ZX05009005-002) and the CAS Strategic Priority Research Program (Grant No. XDB100304002). We are thankful to Dr. Jianlong Kou for his helpful suggestions on this work.

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Influence of Self-Generated Electric Field on Coexisting Patterns of

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