Subscriber access provided by NEW YORK UNIV
Article
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
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
1
Displacement mechanism of oil in shale inorganic nanopores by
2
supercritical carbon dioxide from molecular dynamics simulations
3
Bing Liu a, b,*, Chao Wang a, Jun Zhang a, Senbo Xiao b, Zhiliang Zhang b, Yue Shen a, Baojiang
4
Sun c, Jianying He b,*
5
a
School of Science, China University of Petroleum, Qingdao 266580, Shandong, China
6
b
NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian University of
7
Science and Technology (NTNU), Trondheim, 7491, Norway
8
c
9
China
School of Petroleum Engineering, China University of Petroleum, Qingdao 266580, Shandong,
10
* Corresponding authors:
11
Email:
[email protected] 12
Email:
[email protected] 13
1
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
14
ABSTRACT: Supercritical CO2 (scCO2), as an effective displacing agent and clean fracturing
15
fluid, exhibits a great potential in enhanced oil recovery (EOR) from unconventional reservoirs.
16
However, the microscopic translocation behavior of oil in shale inorganic nanopores, has not been
17
well understood yet in the scCO2 displacement process. Herein, non-equilibrium molecular
18
dynamics (NEMD) simulations were performed to study adsorption and translocation of
19
scCO2/dodecane in shale inorganic nanopores at different scCO2 injection rates. The injected
20
scCO2 preferentially adsorb in proximity of the surface and form layering structures due to
21
hydrogen bonds interactions between CO2 and -OH groups. A part of scCO2 molecules in the
22
adsorption layer retain the mobility, due to the cooperation of slippage, Knudsen diffusion, and
23
imbibition of scCO2. The adsorbed dodecane are separated partly from the surface by scCO2, as a
24
result the competitive adsorption between scCO2 and dodecane, and thus enhancing the mobility
25
of oil and improving oil production. In the scCO2 displacement front, interfacial tension (IFT)
26
reduction and dodecane swelling enhance the mobilization of dodecane molecules, which plays
27
the crucial role in the CO2 EOR process. The downstream dodecane, adjacent to the displacement
28
front, are found to aggregate and pack tightly. The analysis of contact angle, meniscus and
29
interfacial width shows that the small scCO2 injection rate with a large injection volume is
30
favorable for CO2 EOR. The morphology of meniscus changes in the order convex-concave-CO2
31
entrainment with the increase of the injection rate. The microscopic insight provided in this study
32
is helpful to understand and effectively design CO2 exploitation of shale resources.
33
KEYWORDS: shale inorganic nanopore, adsorption and translocation, scCO2 displacement,
34
injection rate
35
2
ACS Paragon Plus Environment
Page 2 of 20
Page 3 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
36 37
1. INTRODUCTION
38
The growing demand for crude oil has inspired the innovative technologies to develop enhanced
39
oil recovery (EOR) methods involving the injection of CO2, N2, hydrocarbon gases or chemicals
40
into oil reservoirs. Among these EOR methods, CO2 EOR has become increasingly important
41
because CO2 flooding can effectively improve the oil recovery factor (RF) and considerably
42
mitigate greenhouse gas emissions. 1 The oil recovery rate can be enhanced by 8-16% of the OOIP
43
through CO2 tertiary processes. 2, 3 CO2 injection, in contrast to water flooding, is recognized as a
44
promising agent to EOR in shale reservoirs due to favorable properties such as low viscosity and
45
high injectivity.4 Gamadi et al. studied cyclic CO2 injection for improving oil recovery and
46
observed a maximum increase of recovery from 33% to 85%.5 CO2, as the clean fracturing fluid,
47
can create better fractured networks compared to water.6, 7
48
The commonly-recognized oil recovery mechanisms include oil viscosity reduction, oil swelling,
49
interfacial tension (IFT) reduction, and light-hydrocarbons extraction.8, 9 The CO2 EOR process is
50
quite different for shale reservoirs because CO2 is expected to flow through natural and produced
51
fractures rather than the non-fractured rock matrix. Hawthorne et al. showed that mobilization of
52
light oil components into CO2 is a dominant recovery process rather than dissolution of CO2 into
53
bulk oil.10 Alharthy et al. indicated that molecular diffusion and advective mass migration across
54
the fracture-matrix interface are the main mechanisms for incremental production of oil in shale
55
nanopore.11 Tovar et al. reported that the main recovery mechanism is the vaporization of the
56
hydrocarbons into CO2.12 Wang et al. found that the dissolution of CO2 induces an increase in
57
oil/gas relative permeability due to the reduced viscosity of CO2 saturated oil phase.13 However, it
58
is difficult to speculate the exact mechanism based on experiments due to the universal existence
59
of nanopores in shale 2-100nm.14-17 In nanopores, microstructural, dynamical and thermophysical
60
behavior of the confined fluids differ dramatically from their bulk counterparts. The transport
61
properties in nanochannel is significantly affected by the width of channel, system temperature,
62
hydrophobicity/hydrophilicity, and roughness of wall.18-20 The stress anisotropy is also observed in
63
a fluid confined in a nanochannel.21 These behaviors result from the molecular asymmetry
64
between fluid-fluid and fluid-solid interactions displaying inhomogeneous density distributions of
65
the local fluid, which can be demonstrated by molecular simulation techniques.22-24 Thu et al. 3
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
66
investigated structural and dynamic properties of pure propane and the relation between structure
67
and dynamics of CO2-C4H10 mixtures in slit-shaped silica pores using molecular dynamics (MD)
68
simulations.25, 26 Wu et al.27 and Yuan et al.28 investigated displacement of methane with CO2 in
69
carbon nanochannels from MD simulations. Jin et al. studied methane flow in shale nanopores by
70
non-equilibrium molecular dynamics (NEMD) simulations.29 Wang et al. investigated octane
71
transport in shale inorganic nanopores from NEMD simulations.30 The results showed that much
72
progress has been achieved in adsorption and transport of oil or gas in nanopores. However, it
73
remains challenging for adsorption, migration, interfacial and confinement properties of scCO2/oil
74
during the CO2 driving oil transport process inside shale nanopores.
75
In this work, non-equilibrium molecular dynamics (NEMD) simulations were performed to
76
study the microscopic mechanism of scCO2 displacing oil inside the shale inorganic nanopore.
77
Firstly, we investigate the adsorption and transport of scCO2 in the nanopore. Then, we examine
78
detachment and translocation of dodecane in the nanopore. In addition, we study the effects of IFT
79
and oil volume swelling on oil migration in the nanopore. Finally, we investigated the effect of
80
injection rate on the transport of scCO2 and dodecane in the nanopore. Our results would help to
81
understand and design effective CO2 exploitation of shale resources as well as provide physical
82
insight into CO2 storage, nanoscale fluid flow, and surface cleaning.
83
2. MODELS and METHODOLOGY
84
To construct MD simulation models, the nanopore with a diameter of 30 Å was created by
85
digging a cylindrical hole in a cristobalite supercell31, 32 in the size of 42.96 × 42.96 × 153 Å. The
86
nanopore with hydroxylated surfaces of silica was fixed in all simulations. Initially, 90 dodecane
87
molecules represent oil which were placed inside the left end of the nanopore. An equilibrium MD
88
simulation was carried out for 2000 ps to obtain a steady-state distribution of oil in the nanopore
89
(supporting information Figure. S1). Then the nanopore was connected with 2197 CO2 molecules,
90
which randomly distributed in a cuboid system with edge dimension of 42.96 × 42.96 × 106 Å3.
91
Periodic boundary conditions (PBC) were applied in three dimensions. A vacuum of 26 Å long
92
was constructed along the z direction to eliminate the boundary effect33. The created model is
93
shown in Figure. 1.
94
All MD simulations were performed using LAMMPS software34 in the NVT ensemble with a
95
time step of 1fs. The Nosé-Hoover thermostat35, 36 was employed to control the temperature at 318 4
ACS Paragon Plus Environment
Page 4 of 20
Page 5 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
96
K. The nanopore was modeled with the consistent valence force field (CVFF)32, 37. CO2 was
97
modeled with the EPM2 model which was successfully demonstrated to reproduce critical point of
98
CO2 in experiment.38, 39 The dodecane representing oil was modeled by the CHARMM force
99
field40, 41. The cutoff of non-bonded interaction was set to be 9.5 Å. Long-range electrostatic
100
interaction was calculated using the Ewald summation method42, 43. The precision of calculation
101
was 0.0001. The nonbond energy Eij between two atoms i and j was the sum of Lenard-Jones (LJ)
102
and electrostatic potential energy:
Eij = 103
qi q j rij
σ ij + 4ε ij rij
12 6 σ ij − r ij
(1)
104
where qi and qj were the charges of the atoms i and j, respectively; rij represented the separation
105
between two atoms i and j; and εij and σij represented the LJ potential well depth and the
106
zero-potential distance. The interaction between different types of atoms was determined by the
107
Lorentz-Berthelot rule: σij = (σii + σjj)/2 and εij = (εii εjj)1/2. σ and ε values employed in the interaction
108
calculations were given in Table 1 of supporting information.
109
NEMD simulations were performed to simulate the process of dodecane displaced by scCO2 in
110
the nanopore. A rigid graphene sheet was placed at the left side of scCO2, and moved at rates of 2,
111
4, 6, 8 and 10m/s in the z direction, which drove scCO2 to enter into the nanopore and displace
112
dodecane molecules. Corresponding to the injection rates, the simulations time were 4.0, 2.0, 1.5,
113
1.0 and 0.8 ns, respectively.
114 5
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
115
Figure. 1. The MD simulation model. (A) Plane view of atomistic cristobalite cylindrical nanopore with diameter D=3nm. (B) Dodecane
116
molecule (marked in red color) and CO2 molecule (marked in blue color). (C) 90 dodecane molecules inside the nanopore. (D) The model
117
of CO2- dodecane in nanopore.
118
3. RESULTS and DISCUSSIONS
119
3.1 Adsorption and transport of CO2
120
To characterize the adsorption of CO2, in Figure 2(A), we report results for the radial number
121
profiles of CO2 in the nanopore at the injection rate of 2 m/s for 100, 800, 1000 and 1500 ps,
122
respectively. The profile exhibits two well defined peaks at 14 Å and 11 Å, indicating the formation of
123
two adsorbed monolayers of CO2 in the range of 9 Å to the nanopore surface. The ordering
124
construction at 14 and 11Ǻ is a result of the small dimensions of the nanochannel as described in works
125
of Giannakopoulos44 and Holland45. The time evolution of the profile shows the increase in the CO2
126
number in the first layer (14 Å), the second layer (11 Å), and the central area of the pore. This is well
127
understood because the movable graphite plate squeezes more and more CO2 into the nanopore as time
128
is longer. However, the peaks of two adsorbed layers, especially for the first layer, increase rapidly
129
compared to the central area. The increment in these three regions is evidently observed to follow the
130
sequence the first layer > the second layer > the central area. It indicates that CO2 molecules
131
preferentially adsorb in proximity of the surface, form layering structures, and subsequently fill the
132
nanopore. It suggests that two typical stages, before and after pore filling, are involved in the
133
adsorption process.
134
The strong layering of CO2 molecules in the nanopore, clearly depicted as higher peaks in the
135
corresponding radial profiles, depends on the nature of the solid surface and CO2. This behavior results
136
from the favorable hydrogen bonds formed by O atoms in CO2 with H atoms in -OH groups. Moreover,
137
supercritical CO2 becomes more polar albeit CO2 is normally nonpolar. This also enhances the
138
electrostatic interaction between CO2 and the surface, leading to more CO2 adsorbing on the surface. In
139
this work, a hydrogen bond is defined to exist if the O-O distance is less than 3.5 Å and simultaneously
140
the angle of H-O-O is less than 30°46. To visualize the hydrogen bond, a typical snapshot is described
141
by the inserted Figure 2a. It shows the formation of hydrogen bonds between CO2 and the hydroxylated
142
surface located at different positions. Inserted Figure 2b depicts time evolution of the number of
143
hydrogen bonds. It is evident that the number of hydrogen bonds increases with time, demonstrating
144
the strong interaction between CO2 and the surface responsible for the adsorption of CO2, consistent 6
ACS Paragon Plus Environment
Page 6 of 20
Page 7 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
145
with the tendency in Figure 2(A).
146
To visualize transport of CO2 molecules, the typical snapshots for CO2 in the nanopore are provided
147
in Figure 2(B). It shows that CO2 molecules advance faster along the hydroxylated surface than in the
148
nanopore center. To quantify CO2 migration in the nanopore, the velocity profiles of CO2 in the
149
nanopore as a function of the distance from the solid surface are presented in Figure 2(C) at 1000 and
150
2000 ps. Two symmetrical distinct peaks of the velocity profiles occur in the vicinity of the solid
151
surface, showing CO2 molecules move forwards faster along the solid surface than in the center of the
152
nanopore. The steric hindrance of dodecane molecules results in that the CO2 velocity in the central
153
area slows down. However, the results also show that the adsorbed CO2 molecules are not immobile but
154
still retain their mobility. Non-zero CO2 velocity on the surface means the slip effect contributing to the
155
flow enhancement of CO2 near the surface. Knudsen diffusion also improves the migration of adsorbed
156
CO2 due to much smaller nanopore size than the mean free path of CO2 molecules29. In addition, the
157
hydroxylated surface is CO2-philic due to that CO2 can displace water from the surface with silanol
158
groups.
159
injection rate on adsorption, we present the radial profiles of CO2 molecules in the nanopore at different
160
injection rates with same injection volume, as shown in Figure 2(D). Two peaks occur at 14 Å and 11 Å,
161
indicating two adsorbed layer structures for CO2 molecules and no effect of injection rate on the
162
location of the adsorbed layer. Peak heights of the profiles decrease with the increase in the injection
163
rate, suggesting that CO2 adsorption enhances at low injection rate and weakens at high rate. Because
164
of constant injection volume and cross section area of the nanopore, low injection rate means low CO2
165
loading per unit time, low injection pressure, and long interaction time between CO2 and the surface.
166
The influence of temperature on the adsorption number of CO2 is investigated as shown in supporting
167
information Figure S2. It is found that two adsorbed layers of CO2 on the surface occurring at 14 Å and
168
11 Å, but temperature has no evident effect on the location of the adsorbed layer. In addition, the peaks
169
decrease with the increase of temperature. This can be ascribed to the higher mobility of CO2 at high
170
temperature and thus the fewer number of CO2 intend to adsorb on the rock. Similar results have been
171
previously reported by Giannakopoulos et al44. Thus, at low injection rate, more CO2 molecules
172
strongly adsorb on the solid surface. While at high injection rate, more CO2 molecules migrate in the
173
central area of the nanopore, reducing the adsorption on the solid surface.
47
This aids imbibition of CO2 into the hydroxylated nanopore.
7
ACS Paragon Plus Environment
To investigate the effect of
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
174 175
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)
176
depicts the adsorption configuration of CO2 molecules around silanol groups on silica surface in which the yellow, red, blue and white
177
sphere represent silicon, oxygen, carbon and hydrogen atoms, respectively; Inserted Figure (b) shows the number of H-bond between CO2
178
and the surface with time. (B) The snapshots of CO2 transport in shale pore at 400ps and 1000ps. (C) The velocity profiles of CO2
179
transport at 1000ps and 2000ps. Red dash lines represent the position of CO2/rock interface; (D) Radial distribution of number density of
180
CO2 at different gas injection rate.
181
To study the effect of the injection rate on the velocity profile, the velocity profiles of CO2 at the
182
rates of 2, 4 and 8 m/s are calculated, respectively, as shown in Figure S3 of supporting information. It
183
shows that curvature of parabola decreases with the increase of injection rate. Obviously, with the
184
increase in the injection rate, the velocity of CO2 in the central area of the pore increases rapidly while
185
the velocity of CO2 near the surface decreases especial for the larger injection rate of 8 m/s. The similar
186
results have also been reported by Duan48 et al. It indicates that CO2 molecules preferentially adsorb in
187
proximity of the surface and subsequently fill the nanopore. Therefore, two typical stages, before and
188
after pore filling, are involved in the adsorption process. We can infer that the flow in the central area
189
of the nanopore will be dominant when it reaches saturated adsorption and steady flow state. The
190
results reveal that adsorption of fluids on the surface plays a significant influence on their transport in a 8
ACS Paragon Plus Environment
Page 8 of 20
Page 9 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
191
nanopore.
192
3.2 Detachment and transport of dodecane
193
3.2.1 Detachment of dodecane
194
In Figure 3(A), we report the radial profiles of molecular number for dodecane in the nanopore at
195
100, 800, 1000 and 1500 ps, as CO2 injection rate is 2 m/s. There is a distinct peak at 13 Å
196
corresponding to the adsorbed dodecane layer. The peak of the adsorbed layer decreases with CO2
197
injection time, implying parts of adsorbed dodecane molecules are gradually detached from the surface.
198
The detached dodecane molecules transfer to the central area of the nanopore and thus increases the
199
amount of dodecane there, shown by the rising curves of the central area. To visualize the dodecane
200
detachment from the surface due to CO2, the representative snapshots for adsorbed dodecane molecules
201
in green at 1, 30, 50, 150 ps are presented in Figure 3(B). It shows that parts of adsorbed dodecane
202
molecules are separated further away from the surface and migrate towards the central area of the
203
nanopore. With the increase in dodecane molecules detached from the surface, moveable oil in the
204
nanopore improves. This results in the enhancement of oil recovery during the exploiting process.
205
Therefore, CO2 detaching oil from the surface plays a significant role in CO2 EOR.
206
The dodecane detachment is highly linked to the adsorption of CO2 on the surface. Comparing
207
Figure 3(A) with Figure 2(A), we observe the dodecane peak is always farther from the surface than the
208
peak of the first adsorption layer of CO2, also indicating preferential CO2 adsorption on the surface.
209
Then, the average adsorption strength of CO2 to the hydroxylated surface plays a crucial role in
210
dodecane detachment or dodecane transport process. To evaluate the average adsorption strength of
211
CO2 molecules, we calculate the interaction energy between CO2 molecules and the nanopore surface
212
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
216
E total denotes the total energy of the system containing CO2. Similarly, we can calculate the interaction
217
energy between dodecane and the surface to characterize the average adsorption strength of dodecane
218
molecules. Inserted figure in Figure 3(A) depicts the variation of the interaction energy of surface-CO2 9
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
219
and that of surface-dodecane. It can be found that the interaction energy between CO2 and surface
220
increases with CO2 injection time, in agreement with the trend of increasing hydrogen bonds in inserted
221
Figure 2b. It indicates the enhancement of CO2 adsorption on the surface. However, the interaction
222
energy between dodecane and surface reduces, meaning the extent of dodecane adsorption on the
223
surface decreases. After 2300 ps, the interaction energy between CO2 and surface is larger than that
224
between dodecane and surface. It suggests that the capability of CO2 to adsorb on the surface is
225
stronger than dodecane. It is a favorable effect on the dodecane detachment.
226
3.2.2 Transport of dodecane
227
From above analysis of dodecane detachment, we conclude that one of transport mechanisms for oil
228
in shale is that adsorbed dodecane molecules are detached partly from the surface and migrate into the
229
central area of the nanopore. To further visualize transport of dodecane molecules inside the nanopore,
230
several typical snapshots for the process of CO2 displacing oil at injection rate of 2 m/s are presented in
231
Figure 3(C). It shows that dodecane molecules move to the right of the nanopore and are gradually
232
expelled from the nanopore.
233
When the movable graphite plate moves to the right, it compresses CO2 to generate a driving force
234
inducing the transport of oil droplet inside the nanopore. With the CO2 molecules filling the nanopore
235
and occupying the cavity space, the equilibrium of dodecane breaks. The interactions between CO2 and
236
the solid surface, and between CO2 and dodecane dominate the structure and the transport of dodecane
237
within the nanopore. The structural variation of oil droplet is also observed in Figure 3(C), showing
238
two distinct zones. One is formed in the displacement front, where CO2 is miscible with dodecane. The
239
other is the downstream oil zone adjacent to the displacement front. To evaluate the structure of oil
240
droplet, the axial density distribution of dodecane molecules is plotted in Figure 3(D). It shows that the
241
density peak positions shift to the right of the z axis, indicating movement of the oil droplet toward the
242
right side of the nanopore. For the part of oil droplet in the miscible zone, the density distribution
243
shows an increasing span of the curve and a decreasing peak. It indicates the oil volume swelling and
244
the interfacial variation, which have a significant influence on oil recovery (we will discuss it in section
245
3.3). For the part of oil droplet in the downstream oil zone, the density distribution shows a constant
246
span of the curve and an increasing peak. It indicates that dodecane molecules adjacent to the
247
displacement front aggregate and pack tightly, resulting in the formation of oil column. This is mainly
248
caused by the attractive interaction among dodecane molecules, and the driving force resulting from the 10
ACS Paragon Plus Environment
Page 10 of 20
Page 11 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
249
oil swelling in the miscible zone and CO2 flooding. Therefore, the dodecane molecules adjacent to the
250
displacement front migrate forward in the form of oil column within the nanopore, which is beneficial
251
to the displacement of oil droplet. In addition, the RDF between C atoms in different dodecane
252
molecules in the downstream oil zone, reported in Figure S4 in the supporting information, exhibits the
253
increasing peak and area below the curve with time. The result indicates the higher coordinate number
254
(dodecane) around a dodecane molecule and thus the tighter distribution for dodecane molecules.
255
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
258
shows the interaction energy between CO2 and the surface (black line), and that between dodecane and the surface (red line); (B)
259
Snapshots of the process of CO2 detach dodecane in the nanopore at 1, 30, 50, 150ps; (C) Snapshots of CO2 displacing dodecane at gas
260
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
261
and (b) in the oil zone at 1, 500 and 1000 ps at the injection rate of 2 m/s.
262
3.2.3 Effect of injection rate on detachment and transport of dodecane
263
To quantitatively describe the effect of injection rate on detachment and transport of dodecane, we
264
calculate the radial number density, the axial number density and the transport distance of center of
265
mass (COM) for oil droplet at different injection rates, as shown in Figure 4(A), Figure 4(B) and Figure 11
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
266
4(C), respectively.
267
Figure 4(A) shows that a distinct peak always occurs at 13 Å for the injection rate of 4, 6, 8 or 10
268
m/s, which lowers with the decrease in the injection rate. At the injection rate of 2 m/s, no distinct peak
269
occurs in the vicinity of the surface. The results show that small injection rate is of benefit to the
270
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
ACS Paragon Plus Environment
Page 12 of 20
Page 13 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
282
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
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
θ = tan −1 ( 312
r 2 − h2 ) 2rh
Page 14 of 20
(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
ACS Paragon Plus Environment
Page 15 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
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
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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
ACS Paragon Plus Environment
Page 16 of 20
Page 17 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
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
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 18 of 20
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
REFERENCES
416 417 418 419 420 421 422 423 424 425 426
work
was
financially
supported
by
the
Petro
China
Innovation
Foundation
(1) Aycaguer, A.-C.; Lev-On, M.; Winer, A. M. Energy Fuels 2001, 15, 303-308. (2) Nobakht, M.; Moghadam, S.; Gu, Y. Energy Fuels 2007, 21, 3469-3476. (3) Nobakht, M.; Moghadam, S.; Gu, Y. Fluid Phase Equilib. 2008, 265, 94-103. (4) Zhang, C.; Oostrom, M.; Grate, J. W.; Wietsma, T. W.; Warner, M. G. Environ. Sci. Technol. 2011, 45, 7581-7588. (5) Gamadi, T. D.; Elldakli, F.; Sheng, J. SPE/AAPG/SEG Unconventional Resources Technology Conference, 2014, 1922690. (6) Ishida, T.; Aoyagi, K.; Niwa, T.; Chen, Y.; Murata, S.; Chen, Q.; Nakayama, Y. Geophys. Res. Lett. 2012, 39. (7) Tudor, R.; Poleschuk, A. J. Can. Pet. Technol. 1996, 35. (8) Wang, S.; Chen, S.; Li, Z. Energy Fuels 2015, 30, 54-62. 18
ACS Paragon Plus Environment
Page 19 of 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470
(9) Cao, M.; Gu, Y. Fluid Phase Equilib. 2013, 356, 78-89. (10) Hawthorne, S. B.; Gorecki, C. D.; Sorensen, J. A.; Steadman, E. N.; Harju, J. A.; Melzer, S. SPE Unconventional Resources Conference Canada, 2013, 167200. (11) Alharthy, N.; Teklu, T.; Kazemi, H.; Graves, R.; Hawthorne, S.; Braunberger, J.; Kurtoglu, B. SPE Annual Technical Conference and Exhibition, 2015, 175034. (12) Tovar, F. D.; Eide, O.; Graue, A.; Schechter, D. S. SPE Unconventional Resources Conference, 2014, 169022. (13) Wang, R.; Lv, C.; Zhao, S.; Lun, Z.; Wang, H.; Cui, M. SPE Asia Pacific Enhanced Oil Recovery Conference, 2015, 174590. (14) Wang, S.; Feng, Q.; Javadpour, F.; Yang, Y.-B. J. Phys. Chem. C 2016, 120, 14260-14269. (15) Saidian, M.; Prasad, M. Fuel 2015, 161, 197-206. (16) Kuila, U.; Prasad, M. Geophys. Prospect. 2013, 61, 341-362. (17) Hantal, G. r.; Brochard, L.; Dias Soeiro Cordeiro, M. N. l.; Ulm, F. J.; Pellenq, R. J.-M. J. Phys. Chem. C 2014, 118, 2429-2438. (18) Sofos, F.; Karakasidis, T.; Liakopoulos, A. International Journal of Heat and Mass Transfer 2009, 52, 735-743. (19) Giannakopoulos, A.; Sofos, F.; Karakasidis, T.; Liakopoulos, A. International Journal of Heat and Mass Transfer 2012, 55, 5087-5092. (20) Liakopoulos, A.; Sofos, F.; Karakasidis, T. E. Microfluidics and Nanofluidics 2016, 20, 1-7. (21) Hartkamp, R.; Ghosh, A.; Weinhart, T.; Luding, S. J. Chem. Phys. 2012, 137, 044711. (22) Argyris, D.; Cole, D. R.; Striolo, A. Langmuir 2009, 25, 8025-8035. (23) Sofos, F. D.; Karakasidis, T. E.; Liakopoulos, A. Phys. Rev. E 2009, 79, 026305. (24) Malani, A.; Ayappa, K.; Murad, S. J. Phys. Chem. B 2009, 113, 13825-13839. (25) Le, T.; Striolo, A.; Cole, D. R. J. Phys. Chem. C 2015, 119, 15274-15284. (26) Le, T.; Striolo, A.; Cole, D. R. Chemical Engineering Science 2015, 121, 292-299. (27) Wu, H.; Chen, J.; Liu, H. J. Phys. Chem. C 2015, 119, 13652-13657. (28) Yuan, Q.; Zhu, X.; Lin, K.; Zhao, Y.-P. Phys. Chem. Chem. Phys. 2015, 17, 31887-31893. (29) Jin, Z.; Firoozabadi, A. J. Chem. Phys. 2015, 143, 104315. (30) Wang, S.; Javadpour, F.; Feng, Q. Fuel 2016, 171, 74-86. (31) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. Langmuir 2010, 26, 10872-10881. (32) Coasne, B.; Fourkas, J. T. J. Phys. Chem. C 2011, 115, 15471-15479. (33) Collell, J.; Galliero, G.; Vermorel, R.; Ungerer, P.; Yiannourakou, M.; Montel, F.; Pujol, M. J. Phys. Chem. C 2015, 119, 22587-22595. (34) Plimpton, S. J. Comput. Phys. 1995, 117, 1-19. (35) Hoover, W. G. Phys. Rev. A 1985, 31, 1695. (36) Nosé, S. J. Chem. Phys. 1984, 81, 511-519. (37) Qamhieh, K.; Wong, K.-Y.; Lynch, G. C.; Pettitt, B. M. Int. J. Numer. Anal. Mod. 2009, 6, 474. (38) Harris, J. G.; Yung, K. H. J. Phys. Chem. 1995, 99, 12021-12024. (39) Senapati, S.; Berkowitz, M. L. J. Phys. Chem. B 2003, 107, 12906-12916. (40) Goldsmith, J.; Martens, C. C. J. Phys. Chem. Lett. 2009, 1, 528-535. (41) de Lara, L. S.; Michelon, M. F.; Miranda, C. R. J. Phys. Chem. B 2012, 116, 14667-14676. (42) Toukmaji, A. Y.; Board, J. A. Comput. Phys. Commun. 1996, 95, 73-92. (43) Nymand, T. M.; Linse, P. J. Chem. Phys. 2000, 112, 6152-6160. (44) Giannakopoulos, A. E.; Sofos, F.; Karakasidis, T. E.; Liakopoulos, A. Microfluid. Nanofluid. 19
ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
471 472 473 474 475 476 477 478 479 480 481 482 483 484 485
2014, 17, 1011-1023. (45) Holland, D. M.; Lockerby, D. A.; Borg, M. K.; Nicholls, W. D.; Reese, J. M. Microfluid. Nanofluid. 2015, 18, 461-474. (46) Luzar, A.; Chandler, D. J. Chem. Phys. 1993, 98, 8160-8173. (47) Dickson, J. L.; Gupta, G.; Horozov, T. S.; Binks, B. P.; Johnston, K. P. Langmuir 2006, 22, 2161-2170. (48) Duan, C.; Zhou, F.; Jiang, K.; Yu, T. Int. J. Heat Mass Transfer 2015, 91, 1088-1100. (49) Fang, T.; Shi, J.; Sun, X.; Shen, Y.; Yan, Y.; Zhang, J.; Liu, B. J. Supercrit. Fluids 2016, 113, 10-15. (50) Green, D.; Willhite, G. Soc. Pet. Eng. 1998. (51) Liu, B.; Shi, J.; Wang, M.; Zhang, J.; Sun, B.; Shen, Y.; Sun, X. J. Supercrit. Fluids 2016, 111, 171-178. (52) Li, X.; Fan, X. Int. J. Greenhouse Gas Control 2015, 36, 106-113. (53) De Coninck, J.; Blake, T. Annu. Rev. Mater. Res. 2008, 38, 1-22. (54) Gerek, Z. N.; Elliott, J. R. Ind. Eng. Chem. Res. 2010, 49, 3411-3423.
486
20
ACS Paragon Plus Environment
Page 20 of 20