Displacement Mechanism of Oil in Shale Inorganic Nanopores by

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Displacement mechanism of oil in shale inorganic nanopores by supercritical carbon dioxide from molecular dynamics simulations Bing Liu, Chao Wang, Jun Zhang, Senbo Xiao, Zhiliang Zhang, Yue Shen, Baojiang Sun, and Jianying He Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b02377 • Publication Date (Web): 14 Dec 2016 Downloaded from http://pubs.acs.org on December 19, 2016

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Energy & Fuels

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Displacement mechanism of oil in shale inorganic nanopores by

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supercritical carbon dioxide from molecular dynamics simulations

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Bing Liu a, b,*, Chao Wang a, Jun Zhang a, Senbo Xiao b, Zhiliang Zhang b, Yue Shen a, Baojiang

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Sun c, Jianying He b,*

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a

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

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b

NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian University of

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Science and Technology (NTNU), Trondheim, 7491, Norway

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c

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China

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

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* Corresponding authors:

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Email：[email protected]

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Email：[email protected]

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1

ACS Paragon Plus Environment

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ABSTRACT: Supercritical CO2 (scCO2), as an effective displacing agent and clean fracturing

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fluid, exhibits a great potential in enhanced oil recovery (EOR) from unconventional reservoirs.

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However, the microscopic translocation behavior of oil in shale inorganic nanopores, has not been

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well understood yet in the scCO2 displacement process. Herein, non-equilibrium molecular

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dynamics (NEMD) simulations were performed to study adsorption and translocation of

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scCO2/dodecane in shale inorganic nanopores at different scCO2 injection rates. The injected

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scCO2 preferentially adsorb in proximity of the surface and form layering structures due to

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hydrogen bonds interactions between CO2 and -OH groups. A part of scCO2 molecules in the

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adsorption layer retain the mobility, due to the cooperation of slippage, Knudsen diffusion, and

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imbibition of scCO2. The adsorbed dodecane are separated partly from the surface by scCO2, as a

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result the competitive adsorption between scCO2 and dodecane, and thus enhancing the mobility

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of oil and improving oil production. In the scCO2 displacement front, interfacial tension (IFT)

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reduction and dodecane swelling enhance the mobilization of dodecane molecules, which plays

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the crucial role in the CO2 EOR process. The downstream dodecane, adjacent to the displacement

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front, are found to aggregate and pack tightly. The analysis of contact angle, meniscus and

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interfacial width shows that the small scCO2 injection rate with a large injection volume is

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favorable for CO2 EOR. The morphology of meniscus changes in the order convex-concave-CO2

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entrainment with the increase of the injection rate. The microscopic insight provided in this study

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is helpful to understand and effectively design CO2 exploitation of shale resources.

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KEYWORDS: shale inorganic nanopore, adsorption and translocation, scCO2 displacement,

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injection rate

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2


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1. INTRODUCTION

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The growing demand for crude oil has inspired the innovative technologies to develop enhanced

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oil recovery (EOR) methods involving the injection of CO2, N2, hydrocarbon gases or chemicals

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into oil reservoirs. Among these EOR methods, CO2 EOR has become increasingly important

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because CO2 flooding can effectively improve the oil recovery factor (RF) and considerably

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mitigate greenhouse gas emissions. 1 The oil recovery rate can be enhanced by 8-16% of the OOIP

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through CO2 tertiary processes. 2, 3 CO2 injection, in contrast to water flooding, is recognized as a

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promising agent to EOR in shale reservoirs due to favorable properties such as low viscosity and

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high injectivity.4 Gamadi et al. studied cyclic CO2 injection for improving oil recovery and

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observed a maximum increase of recovery from 33% to 85%.5 CO2, as the clean fracturing fluid,

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can create better fractured networks compared to water.6, 7

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The commonly-recognized oil recovery mechanisms include oil viscosity reduction, oil swelling,

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interfacial tension (IFT) reduction, and light-hydrocarbons extraction.8, 9 The CO2 EOR process is

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quite different for shale reservoirs because CO2 is expected to flow through natural and produced

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fractures rather than the non-fractured rock matrix. Hawthorne et al. showed that mobilization of

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light oil components into CO2 is a dominant recovery process rather than dissolution of CO2 into

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bulk oil.10 Alharthy et al. indicated that molecular diffusion and advective mass migration across

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the fracture-matrix interface are the main mechanisms for incremental production of oil in shale

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nanopore.11 Tovar et al. reported that the main recovery mechanism is the vaporization of the

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hydrocarbons into CO2.12 Wang et al. found that the dissolution of CO2 induces an increase in

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oil/gas relative permeability due to the reduced viscosity of CO2 saturated oil phase.13 However, it

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is difficult to speculate the exact mechanism based on experiments due to the universal existence

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of nanopores in shale 2-100nm.14-17 In nanopores, microstructural, dynamical and thermophysical

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behavior of the confined fluids differ dramatically from their bulk counterparts. The transport

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properties in nanochannel is significantly affected by the width of channel, system temperature,

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hydrophobicity/hydrophilicity, and roughness of wall.18-20 The stress anisotropy is also observed in

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a fluid confined in a nanochannel.21 These behaviors result from the molecular asymmetry

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between fluid-fluid and fluid-solid interactions displaying inhomogeneous density distributions of

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the local fluid, which can be demonstrated by molecular simulation techniques.22-24 Thu et al. 3


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investigated structural and dynamic properties of pure propane and the relation between structure

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and dynamics of CO2-C4H10 mixtures in slit-shaped silica pores using molecular dynamics (MD)

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simulations.25, 26 Wu et al.27 and Yuan et al.28 investigated displacement of methane with CO2 in

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carbon nanochannels from MD simulations. Jin et al. studied methane flow in shale nanopores by

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non-equilibrium molecular dynamics (NEMD) simulations.29 Wang et al. investigated octane

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transport in shale inorganic nanopores from NEMD simulations.30 The results showed that much

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progress has been achieved in adsorption and transport of oil or gas in nanopores. However, it

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remains challenging for adsorption, migration, interfacial and confinement properties of scCO2/oil

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during the CO2 driving oil transport process inside shale nanopores.

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In this work, non-equilibrium molecular dynamics (NEMD) simulations were performed to

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study the microscopic mechanism of scCO2 displacing oil inside the shale inorganic nanopore.

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Firstly, we investigate the adsorption and transport of scCO2 in the nanopore. Then, we examine

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detachment and translocation of dodecane in the nanopore. In addition, we study the effects of IFT

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and oil volume swelling on oil migration in the nanopore. Finally, we investigated the effect of

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injection rate on the transport of scCO2 and dodecane in the nanopore. Our results would help to

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understand and design effective CO2 exploitation of shale resources as well as provide physical

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insight into CO2 storage, nanoscale fluid flow, and surface cleaning.

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2. MODELS and METHODOLOGY

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To construct MD simulation models, the nanopore with a diameter of 30 Å was created by

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digging a cylindrical hole in a cristobalite supercell31, 32 in the size of 42.96 × 42.96 × 153 Å. The

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nanopore with hydroxylated surfaces of silica was fixed in all simulations. Initially, 90 dodecane

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molecules represent oil which were placed inside the left end of the nanopore. An equilibrium MD

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simulation was carried out for 2000 ps to obtain a steady-state distribution of oil in the nanopore

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(supporting information Figure. S1). Then the nanopore was connected with 2197 CO2 molecules,

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which randomly distributed in a cuboid system with edge dimension of 42.96 × 42.96 × 106 Å3.

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Periodic boundary conditions (PBC) were applied in three dimensions. A vacuum of 26 Å long

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was constructed along the z direction to eliminate the boundary effect33. The created model is

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shown in Figure. 1.

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All MD simulations were performed using LAMMPS software34 in the NVT ensemble with a

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time step of 1fs. The Nosé-Hoover thermostat35, 36 was employed to control the temperature at 318 4


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K. The nanopore was modeled with the consistent valence force field (CVFF)32, 37. CO2 was

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modeled with the EPM2 model which was successfully demonstrated to reproduce critical point of

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CO2 in experiment.38, 39 The dodecane representing oil was modeled by the CHARMM force

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field40, 41. The cutoff of non-bonded interaction was set to be 9.5 Å. Long-range electrostatic

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interaction was calculated using the Ewald summation method42, 43. The precision of calculation

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was 0.0001. The nonbond energy Eij between two atoms i and j was the sum of Lenard-Jones (LJ)

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and electrostatic potential energy:

Eij = 103

qi q j rij

 σ ij + 4ε ij    rij 

12 6   σ ij    −     r     ij  

(1)

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where qi and qj were the charges of the atoms i and j, respectively; rij represented the separation

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between two atoms i and j; and εij and σij represented the LJ potential well depth and the

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zero-potential distance. The interaction between different types of atoms was determined by the

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Lorentz-Berthelot rule: σij = (σii + σjj)/2 and εij = (εii εjj)1/2. σ and ε values employed in the interaction

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calculations were given in Table 1 of supporting information.

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NEMD simulations were performed to simulate the process of dodecane displaced by scCO2 in

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the nanopore. A rigid graphene sheet was placed at the left side of scCO2, and moved at rates of 2,

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4, 6, 8 and 10m/s in the z direction, which drove scCO2 to enter into the nanopore and displace

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dodecane molecules. Corresponding to the injection rates, the simulations time were 4.0, 2.0, 1.5,

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1.0 and 0.8 ns, respectively.

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Figure. 1. The MD simulation model. (A) Plane view of atomistic cristobalite cylindrical nanopore with diameter D=3nm. (B) Dodecane

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molecule (marked in red color) and CO2 molecule (marked in blue color). (C) 90 dodecane molecules inside the nanopore. (D) The model

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of CO2- dodecane in nanopore.

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3. RESULTS and DISCUSSIONS

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3.1 Adsorption and transport of CO2

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To characterize the adsorption of CO2, in Figure 2(A), we report results for the radial number

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profiles of CO2 in the nanopore at the injection rate of 2 m/s for 100, 800, 1000 and 1500 ps,

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respectively. The profile exhibits two well defined peaks at 14 Å and 11 Å, indicating the formation of

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two adsorbed monolayers of CO2 in the range of 9 Å to the nanopore surface. The ordering

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construction at 14 and 11Ǻ is a result of the small dimensions of the nanochannel as described in works

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of Giannakopoulos44 and Holland45. The time evolution of the profile shows the increase in the CO2

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number in the first layer (14 Å), the second layer (11 Å), and the central area of the pore. This is well

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understood because the movable graphite plate squeezes more and more CO2 into the nanopore as time

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is longer. However, the peaks of two adsorbed layers, especially for the first layer, increase rapidly

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compared to the central area. The increment in these three regions is evidently observed to follow the

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sequence the first layer > the second layer > the central area. It indicates that CO2 molecules

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preferentially adsorb in proximity of the surface, form layering structures, and subsequently fill the

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nanopore. It suggests that two typical stages, before and after pore filling, are involved in the

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adsorption process.

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The strong layering of CO2 molecules in the nanopore, clearly depicted as higher peaks in the

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corresponding radial profiles, depends on the nature of the solid surface and CO2. This behavior results

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from the favorable hydrogen bonds formed by O atoms in CO2 with H atoms in -OH groups. Moreover,

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supercritical CO2 becomes more polar albeit CO2 is normally nonpolar. This also enhances the

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electrostatic interaction between CO2 and the surface, leading to more CO2 adsorbing on the surface. In

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this work, a hydrogen bond is defined to exist if the O-O distance is less than 3.5 Å and simultaneously

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the angle of H-O-O is less than 30°46. To visualize the hydrogen bond, a typical snapshot is described

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by the inserted Figure 2a. It shows the formation of hydrogen bonds between CO2 and the hydroxylated

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surface located at different positions. Inserted Figure 2b depicts time evolution of the number of

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hydrogen bonds. It is evident that the number of hydrogen bonds increases with time, demonstrating

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the strong interaction between CO2 and the surface responsible for the adsorption of CO2, consistent 6


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with the tendency in Figure 2(A).

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To visualize transport of CO2 molecules, the typical snapshots for CO2 in the nanopore are provided

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in Figure 2(B). It shows that CO2 molecules advance faster along the hydroxylated surface than in the

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nanopore center. To quantify CO2 migration in the nanopore, the velocity profiles of CO2 in the

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nanopore as a function of the distance from the solid surface are presented in Figure 2(C) at 1000 and

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2000 ps. Two symmetrical distinct peaks of the velocity profiles occur in the vicinity of the solid

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surface, showing CO2 molecules move forwards faster along the solid surface than in the center of the

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nanopore. The steric hindrance of dodecane molecules results in that the CO2 velocity in the central

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area slows down. However, the results also show that the adsorbed CO2 molecules are not immobile but

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still retain their mobility. Non-zero CO2 velocity on the surface means the slip effect contributing to the

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flow enhancement of CO2 near the surface. Knudsen diffusion also improves the migration of adsorbed

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CO2 due to much smaller nanopore size than the mean free path of CO2 molecules29. In addition, the

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hydroxylated surface is CO2-philic due to that CO2 can displace water from the surface with silanol

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groups.

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injection rate on adsorption, we present the radial profiles of CO2 molecules in the nanopore at different

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injection rates with same injection volume, as shown in Figure 2(D). Two peaks occur at 14 Å and 11 Å,

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indicating two adsorbed layer structures for CO2 molecules and no effect of injection rate on the

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location of the adsorbed layer. Peak heights of the profiles decrease with the increase in the injection

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rate, suggesting that CO2 adsorption enhances at low injection rate and weakens at high rate. Because

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of constant injection volume and cross section area of the nanopore, low injection rate means low CO2

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loading per unit time, low injection pressure, and long interaction time between CO2 and the surface.

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The influence of temperature on the adsorption number of CO2 is investigated as shown in supporting

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information Figure S2. It is found that two adsorbed layers of CO2 on the surface occurring at 14 Å and

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11 Å, but temperature has no evident effect on the location of the adsorbed layer. In addition, the peaks

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decrease with the increase of temperature. This can be ascribed to the higher mobility of CO2 at high

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temperature and thus the fewer number of CO2 intend to adsorb on the rock. Similar results have been

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previously reported by Giannakopoulos et al44. Thus, at low injection rate, more CO2 molecules

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strongly adsorb on the solid surface. While at high injection rate, more CO2 molecules migrate in the

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central area of the nanopore, reducing the adsorption on the solid surface.

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This aids imbibition of CO2 into the hydroxylated nanopore.

7


To investigate the effect of

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Figure 2. (A) Radial distribution of number density of CO2 at gas injection rate of 2 m/s at 100, 800, 1000, and 1500ps; Inserted Figure (a)

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depicts the adsorption configuration of CO2 molecules around silanol groups on silica surface in which the yellow, red, blue and white

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sphere represent silicon, oxygen, carbon and hydrogen atoms, respectively; Inserted Figure (b) shows the number of H-bond between CO2

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and the surface with time. (B) The snapshots of CO2 transport in shale pore at 400ps and 1000ps. (C) The velocity profiles of CO2

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transport at 1000ps and 2000ps. Red dash lines represent the position of CO2/rock interface; (D) Radial distribution of number density of

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CO2 at different gas injection rate.

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To study the effect of the injection rate on the velocity profile, the velocity profiles of CO2 at the

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rates of 2, 4 and 8 m/s are calculated, respectively, as shown in Figure S3 of supporting information. It

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shows that curvature of parabola decreases with the increase of injection rate. Obviously, with the

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increase in the injection rate, the velocity of CO2 in the central area of the pore increases rapidly while

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the velocity of CO2 near the surface decreases especial for the larger injection rate of 8 m/s. The similar

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results have also been reported by Duan48 et al. It indicates that CO2 molecules preferentially adsorb in

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proximity of the surface and subsequently fill the nanopore. Therefore, two typical stages, before and

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after pore filling, are involved in the adsorption process. We can infer that the flow in the central area

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of the nanopore will be dominant when it reaches saturated adsorption and steady flow state. The

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results reveal that adsorption of fluids on the surface plays a significant influence on their transport in a 8


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nanopore.

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3.2 Detachment and transport of dodecane

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3.2.1 Detachment of dodecane

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In Figure 3(A), we report the radial profiles of molecular number for dodecane in the nanopore at

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100, 800, 1000 and 1500 ps, as CO2 injection rate is 2 m/s. There is a distinct peak at 13 Å

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corresponding to the adsorbed dodecane layer. The peak of the adsorbed layer decreases with CO2

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injection time, implying parts of adsorbed dodecane molecules are gradually detached from the surface.

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The detached dodecane molecules transfer to the central area of the nanopore and thus increases the

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amount of dodecane there, shown by the rising curves of the central area. To visualize the dodecane

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detachment from the surface due to CO2, the representative snapshots for adsorbed dodecane molecules

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in green at 1, 30, 50, 150 ps are presented in Figure 3(B). It shows that parts of adsorbed dodecane

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molecules are separated further away from the surface and migrate towards the central area of the

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nanopore. With the increase in dodecane molecules detached from the surface, moveable oil in the

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nanopore improves. This results in the enhancement of oil recovery during the exploiting process.

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Therefore, CO2 detaching oil from the surface plays a significant role in CO2 EOR.

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The dodecane detachment is highly linked to the adsorption of CO2 on the surface. Comparing

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Figure 3(A) with Figure 2(A), we observe the dodecane peak is always farther from the surface than the

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peak of the first adsorption layer of CO2, also indicating preferential CO2 adsorption on the surface.

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Then, the average adsorption strength of CO2 to the hydroxylated surface plays a crucial role in

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dodecane detachment or dodecane transport process. To evaluate the average adsorption strength of

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CO2 molecules, we calculate the interaction energy between CO2 molecules and the nanopore surface

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from equation (2)49.

Eco2 / rock =

213

214 215

where E co

2 / rock

Etotal − ( Eco2 + Erock )

(2)

N co2

is the interaction energy between CO2 molecules and the surface, N co is the number

of CO2 molecules,

2

E co2 and Erock represent the energy of CO2 and the rock surface, and

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E total denotes the total energy of the system containing CO2. Similarly, we can calculate the interaction

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energy between dodecane and the surface to characterize the average adsorption strength of dodecane

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molecules. Inserted figure in Figure 3(A) depicts the variation of the interaction energy of surface-CO2 9


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and that of surface-dodecane. It can be found that the interaction energy between CO2 and surface

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increases with CO2 injection time, in agreement with the trend of increasing hydrogen bonds in inserted

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Figure 2b. It indicates the enhancement of CO2 adsorption on the surface. However, the interaction

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energy between dodecane and surface reduces, meaning the extent of dodecane adsorption on the

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surface decreases. After 2300 ps, the interaction energy between CO2 and surface is larger than that

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between dodecane and surface. It suggests that the capability of CO2 to adsorb on the surface is

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stronger than dodecane. It is a favorable effect on the dodecane detachment.

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3.2.2 Transport of dodecane

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From above analysis of dodecane detachment, we conclude that one of transport mechanisms for oil

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in shale is that adsorbed dodecane molecules are detached partly from the surface and migrate into the

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central area of the nanopore. To further visualize transport of dodecane molecules inside the nanopore,

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several typical snapshots for the process of CO2 displacing oil at injection rate of 2 m/s are presented in

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Figure 3(C). It shows that dodecane molecules move to the right of the nanopore and are gradually

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expelled from the nanopore.

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When the movable graphite plate moves to the right, it compresses CO2 to generate a driving force

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inducing the transport of oil droplet inside the nanopore. With the CO2 molecules filling the nanopore

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and occupying the cavity space, the equilibrium of dodecane breaks. The interactions between CO2 and

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the solid surface, and between CO2 and dodecane dominate the structure and the transport of dodecane

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within the nanopore. The structural variation of oil droplet is also observed in Figure 3(C), showing

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two distinct zones. One is formed in the displacement front, where CO2 is miscible with dodecane. The

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other is the downstream oil zone adjacent to the displacement front. To evaluate the structure of oil

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droplet, the axial density distribution of dodecane molecules is plotted in Figure 3(D). It shows that the

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density peak positions shift to the right of the z axis, indicating movement of the oil droplet toward the

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right side of the nanopore. For the part of oil droplet in the miscible zone, the density distribution

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shows an increasing span of the curve and a decreasing peak. It indicates the oil volume swelling and

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the interfacial variation, which have a significant influence on oil recovery (we will discuss it in section

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3.3). For the part of oil droplet in the downstream oil zone, the density distribution shows a constant

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span of the curve and an increasing peak. It indicates that dodecane molecules adjacent to the

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displacement front aggregate and pack tightly, resulting in the formation of oil column. This is mainly

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caused by the attractive interaction among dodecane molecules, and the driving force resulting from the 10


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oil swelling in the miscible zone and CO2 flooding. Therefore, the dodecane molecules adjacent to the

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displacement front migrate forward in the form of oil column within the nanopore, which is beneficial

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to the displacement of oil droplet. In addition, the RDF between C atoms in different dodecane

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molecules in the downstream oil zone, reported in Figure S4 in the supporting information, exhibits the

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increasing peak and area below the curve with time. The result indicates the higher coordinate number

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(dodecane) around a dodecane molecule and thus the tighter distribution for dodecane molecules.

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256 257

Figure 3. (A) Radial distribution of number density of CO2 at gas injection rate of 2 m/s at 100, 800, 1000, and 1500ps; Inserted Figure

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shows the interaction energy between CO2 and the surface (black line), and that between dodecane and the surface (red line); (B)

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Snapshots of the process of CO2 detach dodecane in the nanopore at 1, 30, 50, 150ps; (C) Snapshots of CO2 displacing dodecane at gas

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injection rate 2m/s at (a) 1, (b) 200, (c) 500, and (d) 5000ps; and (D) Density distribution of dodecane molecules (a) in the miscible zone

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and (b) in the oil zone at 1, 500 and 1000 ps at the injection rate of 2 m/s.

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3.2.3 Effect of injection rate on detachment and transport of dodecane

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To quantitatively describe the effect of injection rate on detachment and transport of dodecane, we

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calculate the radial number density, the axial number density and the transport distance of center of

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mass (COM) for oil droplet at different injection rates, as shown in Figure 4(A), Figure 4(B) and Figure 11


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4(C), respectively.

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Figure 4(A) shows that a distinct peak always occurs at 13 Å for the injection rate of 4, 6, 8 or 10

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m/s, which lowers with the decrease in the injection rate. At the injection rate of 2 m/s, no distinct peak

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occurs in the vicinity of the surface. The results show that small injection rate is of benefit to the

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detachment of dodecane molecules adsorbed on the surface, while high injection rate is adverse to

271

separate dodecane molecules from the surface. It implies that more residual oil molecules will remain

272

in the nanopore at the higher injection rate, resulting in the loss of oil during the exploiting process.

273

Combining Figure 4(A) with Figure 2(D), we may expect that entrainment or breakthrough of CO2 will

274

occur at higher injection rate. In this case, CO2 bubble moves steadily and leaves behind a thin oil film

275

close to the surface. The thickening residual oil film in the presence of mass transfer leads to a loss in

276

the oil recovery.

277

278 279

Figure 4. (A) Radial distribution of number density of dodecane at different gas injection rate; (B) Number density distribution of

280

dodecane in the axial direction of the nanopore at different CO2 injection rates; (C) Displacement of COM of dodecane droplet at CO2

281

injection rate from 2 to10 m/s.

12


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Figure 4(B) shows that the peak of the axial number density decreases and the span of the curve

283

increases when decreasing the injection rate from 10 to 2 m/s. It indicates looser packing and wider

284

distribution region for dodecane molecules within the nanopore at smaller injection rate. The peak

285

position shifts to the right of the z axis, implying that the displacement distance of the oil droplet

286

increases with the decrease in the injection rate. The results demonstrate that smaller injection rate is

287

preferable to oil displacement in CO2 flooding, which is also confirmed by Figure 4(C). The figure

288

shows the biggest displacement of COM of oil droplet at the injection rate of 2 m/s as CO2 injection

289

volume is constant. Therefore, a small injection rate with a large gas volume is favorable to CO2 EOR.

290

3.3 Interfacial behavior of CO2 and dodecane

291

3.3.1 Interface between CO2 and dodecane

292

The interfacial behavior, playing an important role in studying two-phase flow, dominates the

293

efficiency of CO2 EOR lying on the achievement of the miscibility front between CO2 and oil.50 Figure

294

5(A) shows the formation of the miscible zone as well as the variation of its width as a function of time.

295

The formation of the miscible zone consists of three processes: (1) detached dodecane molecules

296

migrate into CO2; (2) bulk dodecane molecules dissolve in CO2; and (3) CO2 penetrate into bulk

297

dodecane. The processes (1) and (2) indicate the translocation of dodecane molecules in the direction

298

opposite to the flow direction, compressing the domain through which CO2 molecules permeate into

299

dodecane at the displacement front. This lowers the penetration of CO2 into dodecane, imparting

300

stability to a displacement process in oil recovery. Thus mobilization of dodecane molecules into CO2

301

has a crucial effect on this zone or interface rather than dissolution of CO2 into bulk dodecane.

302

We calculate the width of the interfacial region to examine the variation of the interface between

303

CO2 and dodecane during CO2 flooding process, as shown in Figure 5(A). The interfacial region is

304

established by the “10-90” interfacial width characterized by the distance L between two surfaces at the

305

10% and 90% of the dodecane density along the z axis.51 It is shown that the interfacial widths at 100

306

ps and 800 ps for the injection rate of 2 m/s are L1 = 20 Å and L2 = 50 Å, respectively. The obvious

307

increase in the interfacial width means the extension of the coexistent region of CO2 and dodecane,

308

leading to the reduction in IFT. The lower IFT improves the transport of dodecane molecules, which is

309

favorable for EOR. We also calculate the receding contact angle of oil droplet to examine the

310

morphology of the interfacial meniscus52, reported in Figure 5(B). The contact angle θ is calculated by

311

equation (3). 13


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θ = tan −1 ( 312

r 2 − h2 ) 2rh

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（3）

313

where r is the radius of the nanopore, and h is the height of the meniscus53, as shown in Figure 5(B).

314

The contact angle is plotted in Figure 5(B), showing a nearly constant value of 175° due to the

315

hydroxylated surface is oleophobic.

316 317

Figure 5. (A) The snapshot of the miscible zone; Density profile of CO2-doecane system at injection rate of 2m/s; The label L1, L2 is the

318

“10-90” interface width at T=100ps and 800ps; (B) Representative meniscus profile: the line shows the circular fit and the contact angle;

319

Contact angle θ between the dodecane droplet and the surface at different CO2 injection rate with time.

320

3.3.2 Oil swelling

321

When CO2 is injected into oil-bearing reservoirs, interactions between CO2 and oil will induce

322

favorable effects on the oil recovery, such as oil volume swelling, oil viscosity decrease and miscible

323

CO2-oil. To investigate oil volume swelling stimulated by CO2, several snapshots are reported in Figure

324

6(A), showing the variation of dodecane volume at injection rate of 2 m/s. It is observed that three

325

processes contribute to the oil volume expansion, including that (1) adsorbed dodecane molecules are

326

separated from the surface migrating into the displacement front; (2) upstream dodecane molecules

327

adjacent to the interface disturbed by CO2 disentangle and dissolve into CO2, offering available space

328

for CO2 diffusion and thus enhancing their miscibility; and (3) adsorbed dodecane molecules in the

329

downstream front are detached from the surface and subsequently move to the central area of the

330

nanopore, providing available space for the back dodecane molecules. Volume swelling offers an

331

additional driving to expel the downstream oil toward the right of the nanopore. On the other hand, it 14


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332

reduces oil viscosity and thus improving oil mobility. To characterize the enhanced mobility, we

333

calculate the self-diffusion coefficients of dodecane at different time using the mean-squared

334

displacement approach based on the Einstein relation54, reported in Figure 6(B). The result shows that

335

the self-diffusion coefficient increases as the time, indicating the increased mobility of dodecane, as

336

expected.

337 338

Figure 6. (A) Snapshots of the process of CO2 swelling dodecane in the nanopore at 300 and 800 ps; (B) Diffusion efficient of dodecane

339

at injection rate of 2m/s at different time; RDF of (C) C(dodecane)-C(dodecane) and (D) C(dodecane)-C(CO2) at CO2 injection rate of 2

340

m/s at 500, 1000, 1500 and 2000 ps.

341

The volume swelling embodies oil molecule disentanglement and loose distribution in the presence

342

of CO2, which can be described by the radial distribution function (RDF). Figure 6(C) and (D) depict

343

the RDFs between C atoms in different dodecane molecules and that between CO2 and dodecane,

344

respectively. Figure 6(C) shows that the peak of RDF and the area below the curve decrease with time.

345

It suggests the decrease in the coordinate number (dodecane) around one dodecane molecule or the

346

loose distribution of dodecane molecules. Opposite tendency is observed in Figure 6(D), showing that

347

the coordinate number (CO2) around one dodecane molecule increases with time. The results imply that 15


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348

more and more CO2 accumulate around dodecane molecules, resulting in the larger average separation

349

between dodecane molecules. The larger separation among dodecane molecules indicates a reduced oil

350

viscosity and enhanced oil mobility.

351

3.3.3 Effect of injection rate on the interface between CO2 and dodecane

352 353

Figure 7. (A) Contact angle θ between the dodecane droplet and the surface at different scCO2 injection rate with time; (B) Snapshots of

354

the meniscus curvature at the same injection volume of CO2 but different injection rates of 2, 4, 6, 8, and 10 m/s; (C) Density profile of

355

CO2-doecane system at injection rate of 2m/s and 8m/s; (D) RDF of C(dodecane)-C(dodecane) at different CO2 injection rate. The

356

inserted snapshots of CO2 displacing oil at the same injection volume but different injection rate (a) 10 and (b) 2 m/s.

357

To study the influence of injection rate on the interface between CO2 and dodecane, we firstly

358

calculate the receding contact angle of oil droplet at different injection rates, reported in Figure 7(A).

359

The corresponding snapshots describing the meniscus morphology are presented in Figure 7(B). In

360

order to investigate whether the vacuum area in the right hand side of the simulation model would

361

influence the morphology of meniscus or not, we have made a complement to the initial model. The

362

results show that the vacuum space has little or no influence on the morphology of meniscus when

363

there is enough amount of oil in the nanopore (supporting information Figure S5). Figure 7(A) shows 16


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364

that the contact angle is always larger than 150° due to hydrophilicity of the hydroxylated surface; it is

365

independent of time at constant injection rate; it decreases with the increasing rate due to the

366

weakening adsorption and migration of CO2 along the surface as the injection rate increases. Figure

367

7(B) shows that high injection rate attenuates the convex extent of interfacial meniscus. The results

368

imply a tendency for the morphology of meniscus that it would alter in the order convex-concave-CO2

369

entrainment when the injection rate gradually increases (supporting information Figure S6).

370

Then we calculate the interfacial width at the rate of 2 m/s and 8 m/s with same injection volume,

371

plotted in Figure 7(C). It shows the effect of injection rate on IFT. The interfacial widths at 2 m/s and 8

372

m/s are equal to L1 = 50 Å and L2 = 25 Å, respectively. L1 is wider than L2, indicating the lower IFT for

373

L1 than that for L2. Therefore, IFT increases with the increasing injection rate, unfavorable for the

374

translocation of dodecane molecules within the nanopore. We also calculate the RDF between C atoms

375

in different dodecane molecules to examine the effect of injection rate on oil volume swelling, plotted

376

in Figure 7(D). It shows that a small injection rate is of benefit to the expansion of oil volume. The

377

peak of RDF and the area below the curve decrease with the injection rate, indicating that the

378

coordinate number around a dodecane molecule also decreases with the injection rate. Consequently,

379

dodecane molecules distribute loosely and the average separation between them increases at smaller

380

CO2 injection rate. This can be observed by comparing the configurations at 10 and 2 m/s inserted in

381

Figure 7(D). Because of constant injection volume at different rates, more sufficient interaction

382

between CO2 and dodecane at the small injection rate improves the mobilization of upstream dodecane

383

molecules into CO2, which enhances the volume swelling of dodecane. The volume swelling of

384

upstream dodecane provides additional energy to expel the downstream dodecane towards the right of

385

the nanopore.

386

4. CONCLUSIONS

387

In this study, NEMD simulations were carried out to study the microscopic mechanisms of

388

scCO2 displacing oil confined in the shale nanopore at different injection rates. The injected scCO2

389

preferentially adsorbs on the hydroxylated surface and form layering structures due to hydrogen

390

bonds between CO2 and -OH groups. However, many adsorbed CO2 molecules still retain their

391

mobility, which may be caused by slippage, Knudsen diffusion and imbibition of scCO2. Adsorbed

392

dodecane molecules are partly detached from the surface resulting from the competitive

393

adsorption between scCO2 and dodecane, which leads to more moveable oil and thus increasing 17


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394

oil production. The miscible zone is formed by the dodecane molecules separated from the surface,

395

bulk dodecane molecules dissolved in CO2 phase, and CO2 molecules penetrating into dodecane

396

phase. Thus, mobilization of dodecane molecules into CO2 has an important effect on CO2 EOR.

397

The formation of the miscible zone results in IFT reduction and oil volume expansion, which

398

enhance the mobility of oil and have a dominant role in scCO2 driving process. Adjacent to the

399

displacement front, the downstream dodecane molecules aggregate and pack tightly, migrating in

400

the form of oil column favorable to CO2 EOR. With the increase of CO2 injection rate, the contact

401

angle of dodecane phase decreases, the Meniscus convex reduces, and the interfacial width

402

increases. The results reveal that the small injection rate with a large volume is favorable to CO2

403

EOR. The morphology of meniscus may alter in the order convex-concave-CO2 entrainment when

404

the injection rate gradually increases. The findings are benifitial to understand and design effective

405

CO2 exploitation of shale resources as well as may provide physical insight into CO2 storage,

406

nanoscale fluid flow, biological molecules translocation, and so on.

407

ACKNOWLEDGMENT

408

This

409

(2014D-5006-0211), the National Natural Science Foundation of China (U1262202), the

410

Fundamental Research Funds for the Central Universities (14CX05022A, 15CX08003A), the

411

National Basic Research Program of China (2014CB239204, 2015CB250904), and the Shandong

412

Provincial Natural Science Foundation, China (ZR2014EEM035). The Research Council of

413

Norway, Det Norske Oljeselskap ASA, and Wintershall Norge AS are acknowledged for funding

414

support via WINPA project (Nano2021 and Petromaks2234626/O70).

415

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work

was

financially

supported

by

the

Petro

China

Innovation

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Displacement Mechanism of Oil in Shale Inorganic Nanopores by

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