Nanoscale Two-Phase Flow of Methane and Water in Shale Inorganic

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C: Physical Processes in Nanomaterials and Nanostructures

Nanoscale Two-Phase Flow of Methane and Water in Shale Inorganic Matrix Bing Liu, Chao Qi, Xiangbin Zhao, Guilei Teng, Li Zhao, Haixia Zheng, Kaiyun Zhan, and Junqin Shi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06780 • Publication Date (Web): 30 Oct 2018 Downloaded from http://pubs.acs.org on November 2, 2018

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The Journal of Physical Chemistry

Nanoscale Two-Phase Flow of Methane and Water in Shale Inorganic Matrix Bing Liua, Chao Qia, Xiangbin Zhaoa, Guilei Tenga, Li Zhaoa, Haixia Zhenga, Kaiyun Zhana,*, Junqin Shib,* a

School of Science, China University of Petroleum, Qingdao 266580, Shandong, China

b

State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, Shanxi,

China * Corresponding authors: Email：[email protected] Email：[email protected]

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ABSTRACT Both connate water and the injected water through hydraulic fracturing can coexist with methane inside shale nanopores where two-phase flow possibly occurs. Few studies have been pertaining to two-phase flow of water and methane in shale reservoirs at nanoscale. In this work, molecular dynamics (MD) simulations are employed to investigate two-phase flow of water and methane in slit-shaped silica nanopores with hydrophilic surfaces. A sandwich structure of water film-methane-water film or a structure of the methane gas bubble wrapped in water-bridge exists in the nanopore because water wets the surfaces. Darcy’s law breaks down for methane single-phase flow in the nanopore due to the slippage near the surfaces. For two-phase flow of water and methane within the nanopore, water flow pattern varies in the form of water film, water bridge and water pillar at different applied accelerations (different pressure gradients), showing the breakdown of Darcy’s law for water flow. This is attributed to the inhomogeneous number density distribution near the surfaces, which arises from the electrostatic interactions and the hydrogen bonds between water molecules and the surfaces. However, the varied water flow patterns have no effect on methane flow rate, suggesting Darcy’s law holds for methane flow in two-phase flow of water and methane inside the nanopore. This can be explained by the increased friction between methane and fluctuating water films. The results will advance understanding the mechanism of water and gas transport in nanoporous media and the exploitation of shale resources. 1. INTRODUCTION With the increasing energy shortage in conventional reserves, gas production from shale gas reservoirs (SGR) has played an increasingly important role in the North American energy industry and has gradually become a key component in the world’s energy supply1. Compared to 2% in 2000, a rapid growth in shale gas yield reaches 40% of the total gas production in the United States in the past decade. Encouraged by a large reserve and considerable production rate via hydraulic fracturing, several countries involving Canada, Germany and China have started strong development programs to exploit shale gas resources2. This boom has gained increasing attention in gas adsorption and transport in SGR. SGR, substantially different from the conventional gas reservoirs, is composed of both organic matter (e.g., kerogen) and inorganic minerals (e.g., silica) with various proportions3. Core experiments revealed that the average permeability of shale bedrock is 54 nd and approximately 90% are less than 150 nd4. The majority of pores in SGR is the nanopore with size ranging from a few nanometers to several hundred nanometers5-8. Methane as the main component of shale gas is stored in SGR in form of free gas, adsorption gas and dissolved gas, respectively. Previous studies confirmed that about 20%-80% of the total gas in place of SGR is stored in 2


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form of adsorption gas9-11. These findings emphasize the importance of investigating methane flow within shale nanopores, which is crucial for numerical simulation, fracture parameter optimization and gas production prediction in shale gas reservoirs7. The existence of nanopores where fluid molecular distribution is inhomogeneous and surface adsorption is significant12, gives rise to a deviation from the continuum theory for methane flow inside the shale matrix4, 1314.

Methane flow in shale nanopores is a complicated process15 with many coexisting mechanisms1, 16, such as

viscous flow, slip flow, Knudsen diffusion, and surface diffusion12, 17. Moridis18 and Freeman19 comprehensively reviewed gas flow models in SGR considering the four regimes defined by the Knudsen number. Javadpour7 combined slip flow and Knudsen diffusion to describe gas flow in shale. Javadpour4 and Singh20 combined viscous flow and Knudsen diffusion to investigate gas flow in shale. Based on the work from Beskok and Karniadaki, Xiong21 presented a capillary model to study the impact of the adsorbed gas and surface diffusion on shale gas flow. Wu suggested that the surface diffusion of adsorbed methane in nanopores is a significant transport mechanism in SGR17. Jin22 revealed that methane flux in a slit-shaped graphitic nanopore was more than one order of magnitude greater than that obtained from the Knudsen diffusion at low pressure or the HagenPoiseuille equation at high pressure. Wang23 reported that the Klinkenberg effect failed to characterize methane transport through calcite nanoslits and the molecules traveled even slower than the prediction of HagenPoiseuille equation. Jiang24 demonstrated significant variations of atom number density, transport and structural properties of methane nanofluidics near the surfaces considering Poiseuille flow of methane in the rough silicon nano-channel. He25 reported that neglecting the effect of adsorption on methane transport resulted in breakdown of the Knudsen diffusion model in clay nanopores. Although much progress has been achieved in understanding flow behaviors of methane in the shale matrix, insight into flow of methane confined within shale nanopores with water is urgently required. Water can coexist with methane in shale nanopores due to both connate water and the injected water through hydraulic fracturing. This leads to two-phase flow occurring through nanopores in shale formations. For twophase flow in macro- and micro-scale channels, the flow rate of each phase is linearly proportional to the driving force26 when these two phases do not interfere with each other27. One phase effectively decreases the pore area available for the flow of the other. However, two-phase flow in nanopores is expected to differ from that in wider channels caused by the combination of the interactions between the fluids, the significance of viscous and capillary forces, and the pore morphology26, 28-29. Li30 revealed that influence of water on gas flow weakens as the increasing of irreducible water saturation considering methane transport through nanoporous shale with 3



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water. Bui et al.31 demonstrated that the diffusion of methane through the hydrated nanopores is strongly dependent on the solid substrate. Wu et al.29, 32 reported three different flow patterns including single, annular, and stratified for two-phase flows and the linear correlation between flow rate and pressure drop for singlephase flow in silicon nitride nano-channels. Ho33 illustrated that the change in the structure of water significantly influenced methane flow in slit-shaped muscovite nanopores and thus Darcy’s law breaks down. Although much effort has been made to understand two-phase flow in nanopores, the flow mechanisms of water and methane coexisting in shale nanopores are still not clear as well as the impact of water on methane flow. The purpose of the work is to clarify two-phase flow behaviors of water and methane and the effect of water on methane in shale nanopores. To that end, molecular dynamics simulations are performed to investigate the flow of water and methane coexisting in slit-shaped silica nanopores driven by the applied pressure gradients. Through equilibrium molecular dynamics (EMD) simulations, density profiles with respect to slit aperture are calculated to examine the occurrence characteristics of the coexisting water and methane in nanopores. Then nonequilibrium molecular dynamics (NEMD) simulations are carried out to mimic two-phase flow of water and methane induced by the constant pressure gradients. The flow rate as a function of pressure gradient, velocity profiles, and density profiles are determined to examine two-phase flow behaviors of water and methane as well as the influences of water on methane. As a comparison, the single phase flow of methane in nanopores is also investigated. In addition to offering the fundamental science of fluid transport at nanoscale, this work can not only improve gas production prediction and fracture parameter optimization in shale gas reservoirs34, but also provide a wide range of implications relevant to separation and identification of biological and chemical species35, drug delivery36, programmable catalysis37, and reverse osmosis38. 2． MODELS AND METHODOLOGY Silica is one of the major and most important mineral constituent in many shale formations39. A typical shale caprock can be described as quartz-clay rock40. Because sedimentary rocks are initially water saturated and petroleum accumulations form by displacing movable water out of the pore space, a fully hydroxylated silica surface is usually employed to represent geologic conditions39-41. The similar structures are used in the investigation of transport, adsorption and mobility of liquid in nanopores, and the influence of wettability on displacement of nanofluids42-45. Therefore, we constructed the slit-shaped silica nanopore using the hydroxylated

cristobalite surface41, 45. Fig. 1a illustrates the configuration of the simulations containing 2100 water molecules, 700 methane molecules and a slit-shaped silica nanopore. The nanopore consists of two hydroxylated cristobalite surfaces built by attaching a hydrogen atom to each surface oxygen atom to form Si-O-H groups. 4


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The initial dimension of the simulation box is 50.12 × 71.60 × 100 Å3. Periodic boundary conditions are applied in the X and Y directions. The OPLS-AA force field46, the SPC/E model47, and the CLAYFF force field48 are employed to describe methane, water and cristobalite surfaces, respectively. The 12-6 Lennard-Jones potential is used to model van der Waals interactions with a cutoff radius of 10 Å. The Coulombic potential is used to describe the long-range electrostatic interactions with the particle mesh Ewald (PME) method. The LorentzBerthelot mixing rules are applied to describe the interactions between unlike particles. The temperature of the system is held at 343 K by the Nosé-Hoover thermostat49 with a relaxation time of 0.1 ps which is applied to water and methane separately. To ensure that the center-of-mass velocity does not contribute to the fluid temperature, we applied only the velocity components perpendicular to the driving force to calculate the fluid temperature. The fluid temperatures as a function of simulation time are presented in Fig. S1 in Supporting Information. The MD simulations are performed with Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package50. Integration of the equations of motion is carried out with a 1 fs time step. EMD and NEMD simulations are performed in the NVT ensemble. Visualization of the dynamics process is performed in Visual Molecular Dynamics (VMD) software51.

Fig. 1 Schematic diagram of the model. (a) Initial configuration, (b) pressure control configuration and (c) flow configuration. To obtain the desired pressure, a force along the positive Z direction is exerted on the upper surface, as shown in Fig. 1b. Both surfaces are rigid bodies. The bottom surface is fixed and the upper surface can move freely in the Z direction. The pressure can be estimated by

P

Nf LX LY

(1)

where P is the pressure of the system, N is the total number of atoms in the upper surface, LX and LY are the 5



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sizes of the surfaces in the X and Y directions, respectively. In this work, the pressure control is performed for 6 ns and a constant nanopore width is usually obtained after 4 ns. When the pressures are stabilized at 30, 60 and 90 MPa, the corresponding nanopore widths are approximately equal to 45.65, 35.27 and 33.87 Å, respectively. The nanopore width is defined as the shortest center-to-center distance between surface hydrogen atom across the pore volume. Darcy’s law is often employed to describe macroscopically the fluid flowing within a porous media, which is expressed as

Q-

kA



P

(2)

where Q is the flow rate of fluid, k is the permeability, μ is the fluid viscosity, and A is the cross-sectional area of the channel, and P is the pressure gradient. To investigate the two-phase flow in the nanopore, Poiseuille flow simulations are driven by applying an external gravitational field of different magnitude on the fluid in the Y direction21, as shown in Fig.1 c. Applying a constant acceleration, a, is equivalent to impose a pressure gradient on the fluid. The pressure gradient P can be obtained by

n

P  -

N M i 1

i

N AV

i

a

(3)

where the subscript i represents water or methane, Ni is the total number of molecules of fluid i, Mi is the molar mass of molecule of fluid i, NA is the Avogadro constant, and V is the volume of the channel. The consequent simulations begin with the final configurations of the pressure control simulations described above. During the simulations, both surfaces are frozen and treated as rigid. The constant acceleration is exerted on all water and methane molecules inside the nanopore, ranging from 0.020 to 0.251 nm/ps2. In this work, all simulations of the flow are performed for 10 ns. The steady state flow is usually obtained in the first 3 ns. The next 6 ns is used for dynamics calculation. The last 1 ns is used for data extraction and analysis. At the steady state, distribution of water/methane molecules in the nanopore and their average velocity v along the Y-direction remain constant. Flow rate Q can be defined as the number of molecules flowing through the nanopore cross section per unit time per unit area. In this study, Q can be estimated as

Q=

vN V

6


(4)

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To examine the two-phase flow of water and methane, we consider the relationship between flow rate Q in Eq. (4) and the applied acceleration a in Eq. (3). 3． RESULTS AND DISCUSSION 3.1 The structures of water and methane

Fig. 2 Configurations and molecular number density profiles of water and methane at (a) 30 MPa, (b) 60 MPa and (c) 90 MPa. Partial methane molecules at the interface of water and methane are translucent for the convenience of the observation. To study the structures of methane and water in the nanopores, we present configurations and number density profiles after the pressure stabilization in Fig. 2. Originally, methane and water molecules are randomly placed in the nanopores, shown in Fig. 1(a). When the pressure of the system is stabilized, methane and water are separated obviously from each other. Fig. 2a shows a sandwich structure of water film-methane-water film at 30 MPa and the water film structure is similar to Zhang’s studies52. The water film arises from preferential adsorption of water molecules onto the hydrophilic surface compared with methane molecules. This is attributed to the strong electrostatic interaction53 between water and surfaces, and the hydrogen bond54 between water and surface hydroxyl groups. Two distinct peaks in the number density profile of water indicate two adsorption layers of water near each surface. The number density of water is zero in the central region of the nanopore, demonstrating no water located there. The thickness of each water film is about 10 Å. At this distance away from the inner surface, a jump is observed in the number density profile of methane. This implies no methane adsorption layer close to the surface and thus free methane forms between water films in the nanopore. Such free phase of methane is the natural outcome that the water film shields the interaction between the surface and methane. In Fig. 2b, the water films connect with each other in the form of water bridge at 60 MPa. Methane is wrapped in water and forms methane gas bubble. The number density profile of methane demonstrates that no methane molecule exists in the water bridge. The number density of water illustrates that water molecules concentrate near the surfaces and in the water bridge. The minimum thickness of the water bridge is about 17.8 7



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Å. Fig. 2c shows the structures of methane and water in the nanopore are similar to that in Fig. 2b, which is similar to Li’s researches55. The water bridge becomes slightly thicker equal to 18.5 Å due to the reduced size of the nanopore at 90 MPa. The fluctuation in the number density profiles in Fig. 2b and c mainly results from the periodical arrangement of hydroxyl groups on the wall surfaces56. The above analyses show the absence of methane adsorption layer in the nanopore due to the shielding effect of water film on the interaction between the surface and methane. We can expect that methane flow in two-phase flow of water and methane in the nanopore is independent of the surface, while water flow can be affected by the surface and thus perhaps interfering with methane flow. 3.2 Methane flow The dependence between flow rate and acceleration is firstly studied to explore the applicability of Darcy’s equation for methane flow in two-phase flow of water and methane and in single-phase flow of methane, as shown in Fig. 3. It shows a nonlinear relationship between methane flow rate in single-phase flow and the acceleration, demonstrating the breakdown of Darcy’s equation for methane flow57-58. This arises from the strong influence of the surfaces on methane and gas slip at the surface59-62. However, methane flow rate in twophase flow is linearly proportional to the acceleration, indicating Darcy’s equation holds for methane flow. This is attributed to the shielding effect of water film on the interaction between the surface and methane. Methane flow rate in two-phase flow decreases with increasing pressure (decreasing nanopore width) due to the reduction in the effective nanopore area available for methane flow. The slope of the line, as methane fluidity63 defined as the ratio of permeability to viscosity, decreases with increasing pressure, indicating a larger resistance for methane flow in a narrower nanopore. In the narrower nanopore, the water bridge impedes methane flow, and the thicker water film reduces the effective nanopore area for methane flow leading to the decrease in permeability and the increase in viscosity. Therefore, methane fluidity attenuates with the increase in pressure.

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Fig. 3 Methane flow rate as a function of accelerations. The black, red and green lines describe methane flow rate in two-phase flow at 30, 60, and 90 MPa, respectively. The pink curve represents methane flow rate in single-phase flow at 90 MPa. To characterize methane flow behaviors in two-phase flow, we present the velocity and molecular number density profiles of methane at the steady state flow driven by accelerations 0.020, 0.126 and 0.218 nm/ps2 at 30, 60 and 90 MPa in Fig. 4. The average streaming velocity (ASV) is calculated using the bin method64, and the details are provided in the Supporting Information. As predicted by Poiseuille flow, the velocity profiles are parabolic in the central region of nanopores, confirming the relevance of continuum hydrodynamics65. The average streaming velocity (ASV) increases with improving acceleration because of greater kinetic energy of methane molecules with higher acceleration. As the pressure increases, the corresponding ASV decreases in turn. This mainly arises from the greatly reduced effective nanopore area available for methane flow as the nanopore width becomes narrower at higher pressure, as shown by the span of density profiles in Fig. 4. The ASV in Fig. 4a is far greater than that in Fig. 4b and c, showing the nanopore size has an important impact on the flow. The velocity far from the nanopore center gradually goes to zero, indicating no obvious slippage occurs. Fig. 4 also shows the effect of acceleration on methane distribution in nanopores. In Fig. 4a, a small peak of number density appears at an acceleration of 0.020 nm/ps2, implying a small methane adsorption layer forms near the water film. The peak decreases and finally disappears with increasing acceleration, however, the span of the density distribution widens. This is ascribed to the increase in thickness of water-methane interface. Increasing acceleration enhances shearing of fluid, leading to migration of water molecules at water-methane interface. The surface of the water film corrugates, which provides more space available for methane migration. Consequently, the interfacial region between water and methane becomes wider and thus the number density of methane decreases. 9



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In Fig. 4b, as the acceleration increases, the number density of methane first enhances and then decreases, and the span of density distribution first narrows and then widens. This is mainly caused by the water bridge disappearance and the water film thickening. At acceleration of 0.02 nm/ps2, the water film is thinner due to the water bridge. The effective nanopore width available for methane flow is greater, resulting in the wider distribution and the smaller number density. As the acceleration increases to 0.126 nm/ps2, the shearing of fluid greatly strengthens, thereby, rupturing the water bridge and thickening the water film. This leads to the narrower effective nanopore width for methane flow and the increase in number density. At acceleration of 0.218 nm/ps2, the shearing of fluid further improves, giving rise to the dramatic corrugation of the water film. Accordingly, the thickness of water-methane interface becomes wider, thereby, decreasing the number density of methane in the central area of the nanopore. The number density profile of methane and its variation trend with the change in acceleration in Fig. 4c are similar to Fig. 4b. However, methane number density in the central region of nanopore does not change much with the increase in acceleration in Fig. 4c. This possibly indicates that the water bridge still exists but its pattern has changed.

Fig. 4 Methane velocity and density profiles in the Z direction at (a) 30, (b) 60 and (c) 90 MPa. For comparison, we present the velocity profile of single-phase methane flow as a function of the acceleration in Fig. 5. Here, we remove water molecules and add a certain amount of methane molecules to keep the pressure and the nanopore size in agreement with Fig. 2c. Obviously, the velocity profile shows a parabolic shape similar to Fig. 4c. The ASV increases with the increase in acceleration. The velocity near the surface is nonzero, implying the slippage occurs. Based on the work from Li12, the slip length is determined by the velocity profile, shown in Fig. 5. The slippage is positive66-67 and the slip length increases with increasing acceleration. The positive slippage enhances the effective nanopore area available for methane flow, improving the flow rate shown in Fig. 3. The results indicate that the presence of water has an important influence on methane flow in shale nanopores.

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Fig. 5 The velocity profile of single-phase methane flow at different accelerations. Only the slip length at a = 0.020 and a=0.218 nm/ps2 are marked. 3.3 Water flow To examine the effect of water on methane flow in silica nanopores, we investigate water flow behaviors. Fig. 6 shows water flow rate as a function of the acceleration, exhibiting a nonlinear relationship. This indicates that Darcy's law is invalid to describe water flow in two-phase flow of water and methane. A turning point at acceleration of 0.155 nm/ps2 is observed in Fig. 6. Either below or above this point, the flow rate linearly increases with increasing acceleration, but the slope of the line differs. It suggests that the effective permeability of the nanopore is improved at higher accelerations. In addition, water flow rate reduces with increasing acceleration as the acceleration is less than 0.040 nm/ps2 at 60 MPa and greater than 0.218 nm/ps2 at 90 MPa. In these cases, the water bridge between the surfaces disappears and water only exists in the nanopore as the water film. As a result, the water’s movability is weakened, resulting in the reduction in its flow.

Fig. 6 Water flow rate as a function of accelerations at 30, 60 and 90 MPa.

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Fig. 7 (a) Velocity and number density profiles of water as the function of acceleration at 30 MPa. Water configuration at acceleration of (b) 0.126 and (c) 0.218 nm/ps2. Fig. 7a presents the velocity profiles and the number density profiles of water at the steady state flow driven by different accelerations of 0.020, 0.126 and 0.218 nm/ps2 at 30 MPa. Fig. 7b and c show the configurations of water at accelerations of 0.126 and 0.218 nm/ps2, respectively. In Fig. 7, obviously, water is only distributed near the hydrophilic silica surface in the form of a water film. Two peaks of number density occur near each surface, indicating two adsorption layers. Little change in the number density shows the acceleration has little impact on water distribution. The velocity profiles are parabolic and the ASV of water increases with increasing acceleration. The velocity at the first peak of the number density is almost zero for different accelerations, implying a sticking water layer on the surface. The sticking layer reduces the effective nanopore area for twophase flow of water and methane. However, different accelerations induce different degree of surface corrugation of the water film, as shown in Fig. 7b and c. Compared with Fig. 7b, Fig. 7c exhibits more surface uneven protrusions of the water film. The velocity difference between water and methane increases with improving acceleration, as shown in Fig. 7a and Fig. 4a, resulting in the friction enhancement at water-methane interface. This further promotes the corrugation propagation similar to sea waves. Consequently, water molecules in uneven protrusions transport faster, indicating the improvement of permeability and the increase of flow rate. This is the reason that the turning point in flow rate-acceleration curve occurs at 0.155 nm/ps2, as shown in Fig. 6.

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Fig. 8 (a) Velocity and number density profiles of water as the function of acceleration at 60 MPa, and configurations corresponding to accelerations (b) 0.020, (c) 0.126 and (d) 0.218 nm/ps2. Fig. 8a describes the velocity profiles and the number density profiles of water at the steady state flow driven by different accelerations of 0.020, 0.126 and 0.218 nm/ps2 at 60 MPa. The corresponding configurations of water are shown in Fig. 8b, c and d, respectively. In Fig. 8a, the velocity profiles exhibit parabolic shapes and the ASV increases with increasing acceleration. Two obvious peaks appear in each number density profile, indicating two water adsorption layers. Obviously, the peaks first increase and then decrease with increasing acceleration. The increase in peak results from that some water molecules in water bridge are adsorbed to the surface. The decrease in peak is ascribed by the desorption of some water molecules induced by the greater shearing at the larger acceleration. At acceleration of 0.020 nm/ps2, nonzero water number density in the central region indicates presence of the water bridge between surfaces. The bridge spans the entire length of the nanopore along the X direction, as shown in Fig. 8b. However, the velocity profile is parabolic, shown in Fig. 8a, suggesting no slug flow occurs. Details are provided in the Supporting Information. This flow pattern is different from two-phase flow at larger length scales where the slug flow is observed when the gas phase forms large bubbles separated from each other by liquid slugs68. As the acceleration increases, some water molecules escape from the water bridge and are absorbed on the surface. Then the water bridge becomes thinner but still exists between surfaces, and the water film near each surface thickens. Water molecules in the sticking layer increase, which is observed by the increase in the first peak of the number density at acceleration of 0.126 nm/ps2 in Fig. 8a. As a consequence, water flow rate reduces with increasing acceleration when the acceleration is less than 0.040 nm/ps2 in Fig. 6. As the acceleration further increases, the water bridge is destroyed and water only exists in the form of water film near each surface, as shown in Fig. 8c and d. This also can be observed in Fig. 8a where the velocity and the number density are zeros in the central area of the nanopore. Once methane breaks through the water bridge as the acceleration is high enough, water flow is similar to that at 30 MPa. 13



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Fig. 9 (a) Velocity and number density profiles of water as the function of acceleration at 90 MPa, (b) water hole, and configurations corresponding to accelerations (c) 0.126 and (d) 0.218 nm/ps2. Fig. 9a shows the velocity profiles and the number density profiles of water at the steady state flow driven by different accelerations of 0.126, 0.218 and 0.251 nm/ps2 at 90 MPa. The configurations of water at accelerations of 0.218 and 0.251 nm/ps2 are shown in Fig. 9c and d, respectively. Here, the water structure at acceleration of 0.126 nm/ps2 is not given, which is similar to Fig. 8b. In Fig. 9a, the velocity profiles are parabolic and the ASV increases as the applied acceleration improves. Obviously, two peaks appear near each surface for number density profiles, implying the occurrence of two adsorption layers. With the increase in the acceleration, the peaks first decrease and then slightly increase. The velocity near the first adsorption layer is zero for each velocity profile, which means the first adsorption layer as a sticking layer reducing the nanopore area available for the two-phase flow. As the acceleration is greater than 0.126 nm/ps2, methane breaks through the water bridge, illustrated by the water hole shown in Fig. 9b. Gradually, the water bridge in Fig. 8b no longer spans the entire length of the nanopore along the X direction. It spans the entire length of the nanopore along the Y direction like a water pillar surrounded by methane molecules, as shown in Fig. 9c. As the acceleration is greater than 0.218 nm/ps2, the shear effect is enhanced, thereby, destroying the hydrogen bond between water molecules. Eventually, the water pillar disappears and only the water film is present in the nanopore, as shown in Fig. 9d. Consequently, water flow rate reduces at acceleration greater than 0.218 nm/ps2, as shown in Fig. 6. The above analysis further shows that the flow pattern of water strongly depends on the acceleration. In addition, it is observed that the flow rate of water at 30 MPa falls in between those at 60 and 90 MPa. To explain it for simplicity, we take the acceleration of 0.126 nm/ps2 as an example. At 30 and 60 MPa, water in the nanopore exists in the form of the water film. The average streaming velocity at 30 MPa is greater than that at 60 MPa, as shown in Fig. 7a and Fig. 8a. In addition, the size of the nanopore at 30 MPa is larger than that at 60 MPa, indicating a larger effective space for water flow at 30 MPa. Thus, the flow rate of water at 30 MPa is greater than that at 60 MPa. At 90 MPa, water presents in the form of the water bridge in the nanopore. Fig. 9a 14


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shows a non-zero velocity of water in the central region of the nanopore, implying that the water molecules located in the central region of the water bridge participate in the flow. This part of the water molecule contributes significantly to the flow rate of water through the nanopore. Consequently, the flow rate of water at 90 MPa is the greatest, although the size of the nanopore is the smallest among 30, 60 and 90 MPa.

4.

CONCLUSIONS

MD simulations are conducted to investigate the two-phase flow of water and methane inside shale inorganic nanopores formed by hydrophilic cristobalite plates. The effects of the bulk pressure and the driving pressure gradient on two-phase flow of water and methane are systematically studied. These effects are understood by exploring molecular spatial distribution, flow rate, flow velocity and corresponding flow configurations. Due to the preferential adsorption of water molecules onto the inner surfaces and the shielding effect of water film between methane and the surfaces, a stable sandwich structure of water film-methane-water film was formed in the low pressure region, and the methane gas bubble is wrapped by the water bridge at higher pressures. For the single-phase flow of methane, the flow rate increases nonlinearly with increasing acceleration, which indicates the invalidity of the Darcy’s equation. This is attributed to the slippage of methane near the surface. In the twophase flow of water and methane case, the shielding effect of water film on the interactions between methane and the surfaces would appear, leading to the flow rate of methane linear enhancement with increasing acceleration. In other word, the Darcy’s law holds for methane flow in two-phase flow of water and methane inside the nanopore. It is noteworthy that the flow pattern of water strongly affects the methane distribution in nanopores despite no effect on methane flow rate. In addition, the water flow in two-phase flow does not satisfy Darcy's equation at different water configuration. The presence of water bridge may considerably enhances the flow rate of water. On the other hand, when the water bridge is broken by methane and a water film is formed, the water flow rate would decrease due to the change of water configuration. Furthermore, it is shown that the velocity gap between methane and water increases continously with the increasing the acceleration, and the undulation of the water film is strengthened, which leads to the friction between methane and water improvement, further hinders the flow of methane and may block the slippage of methane at the surface. Although we limit ourselves to the two-phase liquid of water and methane transport inside cristobalite hydrophilic bilayers, our argument should be applicable to the flow of fluid at nanoscale in biological, chemical, medical, and physical fields. Furthermore, our results are also expected to serve as guidelines to flow behavior for exploitation of oil and gas in aqueous environment. 15



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ACKNOWLEDGMENT This work was financially supported by the PetroChina Innovation Foundation (2017D-5007-0206), Natural Science Foundation of Shandong Province (ZR2018MA027), China University of Petroleum (East China), Innovation Project (18CX05005A) and Natural Science Foundation of China (NSFC) (61605251). SUPPORTING INFORMATION Temperature as a function of simulation time, the calculation of average streaming velocity, and detailed explanation of no slug flow for water at a = 0.002 nm/ps2.

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Table of Contents Graphic

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Nanoscale Two-Phase Flow of Methane and Water in Shale Inorganic

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