Molecular Dynamics Simulation of Diffusion of Shale Oils in

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Molecular Dynamics Simulation of Diffusion of Shale Oils in Montmorillonite Hui Wang, Xiaoqi Wang, Xu Jin, and Dapeng Cao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b01660 • Publication Date (Web): 11 Apr 2016 Downloaded from http://pubs.acs.org on April 17, 2016

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The Journal of Physical Chemistry

Molecular Dynamics Simulation of Diffusion of Shale Oils in Montmorillonite Hui Wang 1, Xiaoqi Wang 2, Xu Jin 2 and Dapeng Cao *1 1

State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China 2

Research Institute of Petroleum Exploration and Development, PetroChina, Beijing 100083, People’s Republic of China * Email: [email protected]

Abstract The shale oil is an important unconventional resource gathered in shales with nano-scale pores. In this work molecular dynamics simulations were performed to investigate the diffusion of shale oil in the clay-rich shale. Montmorillonite model was used to represent the clay-rich shale, and octane was used as a shale oil model. Results show that the diffusion coefficient of shale oils is extremely small in the basal spacing of 2.8 nm, and with the increase of basal spacing, the diffusion coefficient increases by several order of magnitudes. This observation indicates that once the shale oils flow from microscopic pores into the mesoscopic pores, it would accompany with the decrease of oil density and extreme increase of diffusion coefficient, which is very beneficial for exploitation of shale oils. However, it is still difficult to exploit the oil molecules adsorbed in the microscopic pore. Besides, by exploring the effect of chain length of oil molecule on the diffusion, we found that the shorter chain oils are beneficial for exploitation. It is expected that these simulation results provide useful reference and important fundamentality for the investigation of shale oils.

1

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1. Introduction With the rapid consumption of conventional fossil fuels of coal, petroleum and natural gas, it is necessary to develop alternative unconventional energy sources to meet future energy needs.1 It is estimated that China holds (223-263)×108 t of unconventional oil resources.2 Shale oil, as an unconventional resource, has received much attention recently, because it is a considerable amount of potential energy.1 Thus, many researchers have focused their attention on the exploitation of shale oil.3-6 Zhou et al. studied the extracting shale oil via supercritical carbon dioxide.3 Moreover, some researchers also explored the oil shale pyrolysis (or retorting) over the years.1, 4, 7-8 Shale oil is mature oil gathered in organic-rich shales with nano-scale pores.9 Therefore, the macroscopic flow mechanics theory is not suitable for the study on shale oil reserves and production.10 Recently, molecular simulation, as a useful alternative technique, has been widely used to provide a reasonable explanation and to predict the thermophysical properties of nano-scale systems,11-12 including reservoir engineering, gas production and hydrocarbon processing.13-14 Collell et al. performed molecular dynamics（MD） simulation of hydrocarbons permeating through a molecular model representative of oil-prone type II kerogen.15 Ru et al. modeled the average molecular structure of kerogen by experimental and computational studies.16 Welch et al. used the MD simulations to study the retrograde phase behavior of ethane/heptane mixtures in nanopores.17 Although there are abundant shale oil resources, one of the most challenges in exploiting oils from reservoirs stem is their low permeability.17 In fact, the permeability of shale oil is closely related to the 2


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diffusion of shale oil in the shale nanopores. So, it is very significant to explore the diffusion behavior of shale oil in the nanoscale pore, which can reveal the microscopic diffusion mechanism of shale oils and help optimize exploitation conditions of shale oils. 2. Methodology 2.1. Models In the exploitation process of the shale oils, understanding the diffusion behavior of the oil molecules in the hierarchical pore systems containing micropore and mesopore (as illustrated in Figure 1) is still a great challenge, because it involves in the studies at atom and molecular levels. Generation of fracture makes the oil molecules flow (or diffuse) toward the low pressure zone,18 which refers to the fact that the oil molecules will diffuse from micropore to mesopore, as shown in Figure 1. So, we simulated the diffusion behavior of shale oil in the pores of different scales. The constituents of shale mainly include organic matter, inorganic minerals, and other components.19 The organic matter is mainly composed of kerogen, which is a mixture of organic chemical compounds. Inorganic clay minerals are layered aluminnosilicates,20 and they are also an important component of shale. Montmorillonite is a typical 2:1 layer type clay mineral which consists of alumiminum octahedral sheets sandwiches between two silicon tetrahedral sheets.21 In the montmorillonite model, Al atoms can be replaced by Mg atoms in the octahedral sheet and the negative charges are compensated by interlayer counterions.22 The interlayer pores of swelling clays are an ideal environment to study the fundamental properties of confined fluids, especially for shale oil and gas.23 So, we used the montmorillonite as the model of the clay-rich shale to study the diffusion of shale oil. The 3



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chemical formula of montmorillonite model is Ca0.5(Al3Mg)Si8O20(OH)4 with dimensions of x = 5.18 Å, y = 8.98 Å. The length in the z direction is changed with the basal spacing of the montmorillonite. The majority of shale oil is light oil, with an oil density of 0.70−0.85 g/cm3,

9

so we used the octane to represent the shale oil. The force field

parameters for the montmorillonite model were taken from CLAYFF force field,24-25 which has been successfully applied to clay mineral systems.26-27 The united-atom (UA) model was used to represent octane, which can reduce the computational cost without losing accuracy, and the force filed was taken from TraPPE-UA force field.28 The bond length of octane was fixed at 1.54 Å. Bond angle bending was described by a harmonic potential (with an equilibrium bond angle of 114°) and the dihedral angles were governed by OPLS united-atom torsional potential.28 The montmorillonite model is fixed in the simulations, so the bending and torsion potential is not considered for clay sheets. Intramolecular interactions were described by Lennard-Jones (LJ) potential and the LJ cross interaction parameters were obtained by the Lorentz−Berthelot mixing rules 1

( σ ij = (σ ii + σ jj ) 2 and ε ij = (ε iiε jj ) 2 ). All the potential parameters are shown in Table 1. 2.2. Simulation methods NVT MD simulations were employed to study the diffusion of shale oil in the clay-rich shale. The simulation box contains 20 (5×4×1) unit cells. Initially, we put some octane molecules in the pore of each unit cell (as shown in Figure 1), and optimized the initial structures by minimizing the energy. The system was equilibrated for 2 ns, and the molecular configurations were stored every 10000 steps for final result analysis in the following 6 ns. The time step of 1 fs was implemented. A cutoff radius of 12 Å was used 4


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to calculate the interactions between the oil and the shale without the long-range corrections. The periodic boundary conditions were applied along x and y directions. During simulations, the shale atoms were kept fixed. To decrease the statistical error of the calculations, ten independent runs were performed to obtain the ensemble average.29-30 All the MD simulations were performed by LAMMPS program.31 Because the concentration of oils may influence the diffusion, we also studied the behavior of shale oils of different concentrations by changing the number of particles in each unit cell. Finally, we also explored the influence of temperature on the diffusion of octane in shale. The self-diffusivity, Ds(c), describes the mobility of the tagged particles and can be calculated from the mean-squared displacement (MSD) by the following equation.29-30

11  t → ∞ 6t N 

DS ( c ) = lim

k =1

∑ r (t ) − r (0) k

k

N

2

  

where c is concentration, rk (t ) is the position of the k molecule at time t, and N is the number of molecules.

3. Results and Discussion As shown in Figure 1, six octane molecules are initially arranged randomly in each unit cell (marked as Case I), and total 120 octane molecules are in the supercell. Figure 2 shows the self-diffusion coefficients (Ds) of octane molecules at different basal spacings. At the basal spacing of 2.8 nm, the Ds of octane is 7.6 ×10-8 cm2/s at 310 K. When the basal spacing increases to 3.8 nm, 10 nm and 50 nm, the Ds increases to 2.1×10-5 cm2/s, 7.3×10-5 cm2/s and 4.0×10-4 cm2/s, respectively. That is to say, with the increase of basal spacing, the Ds of shale oil increases several order of magnitudes, which means that increasing the pore size is an efficient method for exploitation of the shale oil. This 5



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observation also confirms the reasonableness of pressure fracturing in exploitation of shale gas and oils. In addition, we studied the influence of temperature on the Ds. When the temperature increases from 310 K to 400 K, the Ds of octane in different pore sizes has an increase of different degrees, as shown in Figure 2. The uncertainties of diffusion coefficients are also calculated. The uncertainties are basically smaller than 5%, so we did not add the error bar to the corresponding Figures. Generally, the oil content in shale is often different, especially for different resources. When the shale oil flows from microscopic pore to mesoscopic pore, it will often accompany with the decrease of oil density in the pores. Therefore, we also simulated another case in which each unit cell was put three octane molecules (marked as Case II). Figure 3 shows the Ds of octane at Case II, and they are 5.4×10-5, 6.7×10-5, 9.2×10-5 and 8.5×10-4 cm2/s at basal spacing of 2.8 nm, 3.8 nm, 10 nm and 50 nm at 310 K, respectively. When the oil content reduced to half, the Ds increased more than twice compared to Case I. Definitely, the increment by oil contents is greatly smaller than the one by pore size. The oil content shows a smaller effect on Ds compared to the pore size. Therefore, the pore size is a most key factor determining the diffusion behavior of shale oils. Simulation snapshots of octane at basal spacing of 3.8 nm at 400 K are presented in Figure 4 for visualization purposes. The Case II is shown in Figure 4a and Case I is shown in Figure 4b. We can see that the octane molecules and Ca2+ randomly occupy the whole pore. To better understand the microscopic confirmations, Figure 5 shows the contour plot of the probability density of octane in the montmorillonite. In Case II, most molecules are adsorbed on the pore surface, and the center of the pore has less molecules due to the 6


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affinity decrease of pore surface (Figure 5a), which is beneficial for diffusion behavior of shale oils. On the contrary, in Case I, the oil molecules are closely filled in the middle of the pore besides partial molecules adsorbed on the pore surface, which leads to the diffusion decrease of shale oils. To better understand the microscopic structure of octane in different pore sizes, density distributions of octane at different basal spacing of montmorillonite at 400 K are displayed in Figure 6. Figure 6a shows three distinct peaks which are symmetric with respect to the pore center at the basal spacing of 2.8 nm in Case I, which the octane molecules are in a highly packed state. However, with the increase of pore size, the density of oil molecules in shale would decrease, which is beneficial for diffusion behavior of shale oils. Instead, these molecules are mainly adsorbed on the pore surface in the relative large pores. We can see from Figure 6 that the diffusion of oil molecules within the contact layer may be closely related to the local diffusion of contact layer. Here, the first layer of oils adsorbed on the pore surface is defined as the contact layer. In order to explore the behavior of octane in the contact layer, we counted the average number of octane molecules in different layers. Figure 7 shows the average number of molecules in the contact layer vs basal spacing of montmorillonite. We can see that the average number of molecules in the basal spacing of 2.8 nm, 3.8 nm, 10 nm and 50 nm is 49.0, 41.1, 36.8 and 36.1, respectively. It should be noted that among these molecules, not all atoms of these molecules are in the contact layer. So, we also counted how many atoms of each molecule were in the contact layer. In Figure 7, different colors stand for the cases of different atom numbers in contact layer. We believe that if the half atoms of an oil molecule are adsorbed 7



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on the contact layer, the oil molecule is mainly adhesive on the pore surface. The smaller is the basal spacing, the more the oil molecules adsorbed on the contact layer, which definitely leads to the slow diffusion of the octane in small pore. Previous studies32-35 indicate that the diffusions in different directions are different for the confined fluids. In order to investigate the influence of confinement on the diffusion coefficients, we also separately calculated the diffusions in the directions perpendicular and parallel to the pore walls. The diffusion coefficient in the perpendicular direction to the pore walls ( Ds⊥ ) is calculated by

∆z 2 (t ) = 2 Ds⊥ t , where

∆z 2 (t )

represents the

mean square displacement in the z-direction as a function of time (t). The diffusions in the parallel direction to the pore walls ( Ds ) can be calculated by where ∆x 2 (t ) + ∆y 2 (t )

∆x 2 (t ) + ∆y 2 (t ) = 4 Ds t ,

represents the mean square displacement in the xy-plane as a

function of time (t). We just take Case I at 400 K as an example, and the calculated results are shown in Figure 8. We can see that the Ds is larger than the Ds⊥ because of the confinement on the z-direction. For example, the Ds in the basal spacing of 10.0 nm is 3.2×10-4 cm2/s, while the Ds⊥ is 4.7×10-5 cm2/s and the Ds is 2.2×10-4 cm2/s. That is to say, the Ds is about seven times of the Ds⊥ due to the confinement of z direction. In fact, Ds is the weighted average of Ds and Ds⊥ . Obviously, Ds basically describes the diffusion of shale oils. The above researches explore the cases where the pore contains the fixed number oil molecules. In fact, the diffusion of shale oils with fixed density in the different basal spacing of montmorillonite may be another important case. Figure 9 shows the Ds of octane at the fixed density at different basal space of montmorillonite. The density of 8


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octane at 400 K and 600 bar is fixed at 0.682 g/cm3, which was taken from NIST Chemistry WebBook.36 The results in Figure 9 show that the Ds of octane in the basal spacing of 2.8, 3.8, 10.0, 30 and 50.0 nm is 3.0×10-5, 3.6×10-5,7.2×10-5, 9.4 ×10-5 and 1.4×10-4 cm2/s, respectively. With the increase of basal spacing, the Ds of octane is also increased. The Ds of octane in the basal spacing of 50.0 nm increased fourfold compared with that in the basal spacing of 2.8 nm, indicating increasing the pore size is still a key factor to increase the diffusion of the shale oil. In order to explore the influence of chain lengths on the Ds, we also studied the diffusion coefficients of hexane at different basal spacing of montmorillonite. The density of hexane is fixed at 0.64 g/cm3 at 400 K and 600 bar. Figure 10 shows the results of Ds. The Ds of hexane in the basal spacing of 2.8, 3.8, 10.0, 30 and 50.0 nm is 5.3×10-5, 6.6× 10-5, 9.1×10-5, 1.7 ×10-4 and 2.2×10-4 cm2/s, respectively. With the increase of basal spacing, the Ds of octane increases almost linearly. The Ds of hexane in the basal spacing of 50.0 nm increased threefold compared with that in the basal spacing of 2.8 nm. Compared with the Ds of octane, the Ds of hexane is higher than that of octane in the same basal spacing of montmorillonite, which means that the oils with shorter chain is beneficial for exploitation.

4. Conclusions We have used the molecular dynamics simulation to study the diffusion of shale oil in the clay-rich shale, which is an important unconventional resource gathered in shales with nano-scale pores. Montmorillonite was used as the model to represent the clay-rich shale and the octane was used to represent the shale oil. The effects of temperature, basal 9



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spacing and shale oil density on the self-diffusion coefficients of shale oil were studied. Results indicate that the increase of temperature can improve the diffusion coefficient of shale oil, and with the increase of basal spacing, the diffusion coefficient of shale oil is increased by several order of magnitudes. In particular, the diffusion coefficient of shale oil in the basal spacing of 50.0 nm increased fourfold compared to that in the basal spacing of 2.8 nm, which indicates that increasing the pore size is an efficient method for exploitation of the shale oil.

Based on the contour plots of the probability densities and

the densities distribution of octane in the montmorillonite, we found that most molecules are inclined to diffuse near the pore surface, so the density near the pore surface is much higher than the middle of the pore, which reveals the difficulty of exploiting shale oils at microscopic level. Besides, by exploring the effect of chain length of oil molecule on the diffusion, we found that the shorter chain oils are beneficial for exploitation. It is expected that these simulation results provide useful guidance and important fundamentality for the investigation of shale oil.

Acknowledgements This work is supported by NSF of China (No. 91334203, 21274011), National 863 Program (2013AA031901) and Outstanding Talents Plan from BUCT.

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counterion-intercalated montmorillonite from first-principles calculations. Comput. Mater. Sci. 2015, 96, Part A 051503, 134-139. (28) Martin, M. G.; Siepmann, J. I., Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes. J. Phys. Chem. B 1998, 102, 2569-2577. (29) Wang, H.; Cao, D., Diffusion and Separation of H2, CH4, CO2 and N2 in Diamond-Like Frameworks. J. Phys. Chem. C 2015, 119, 6324-6330. (30) Yang, Z.; Cao, D., The Effect of Li-Doping on Diffusion and Separation of Hydrogen and Methane in Covalent Organic Frameworks. J. Phys. Chem. C 2012, 116, 12591-12598. (31) Plimpton, S., Fast parallel algorithms for short-range molecular dynamics. J. Compt. Phys 1995, 117, 1-19. (32) Kumar, P.; Buldyrev, S. V.; Starr, F. W.; Giovambattista, N.; Stanley, H. E., Thermodynamics, structure, and dynamics of water confined between hydrophobic plates. Physical Review E 2005, 72, 051503. (33) Han, S.; Kumar, P.; Stanley, H. E., Absence of a diffusion anomaly of water in the direction perpendicular to hydrophobic nanoconfining walls. Physical Review E 2008, 77, 030201. (34) Chen, M.; Lu, X.; Liu, X.; Hou, Q.; Zhu, Y.; Zhou, H., Slow dynamics of water confined in Newton black films. Phys. Chem. Chem. Phys. 2015, 17, 19183-19193. (35) Cao, D.; Zhang, X.; Chen, J.; Yun, J., Local Diffusion Coefficient of Supercritical Methane in Activated Carbon by Molecular Simulation, Carbon, 2003, 41, 2696-2689 (36) Lemmon, E. W.; McLinden, M. O.; Friend, D. G., Thermophysical Properties of Fluid Systems. In NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds.;National Institute of Standards and Technology: Gaithersburg MD 2009.

Table 1. Force Field Parameters for shale oil and clay molecules

atom

ε/kB (K)

σ (Å)

q (e) 13



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

octane clay

CH3 98 CH2 46 hydroxyl hydrogen hydroxyl oxygen 78.26 bridging oxygen 78.26 bridging oxygen with 78.26 octahedral substitution tetrahedral silicon 0.000926 tetrahedral aluminum 0.000669 aqueous calcium ion 50.36 octahedral magnesium 0.00045

3.75 3.95

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3.17 3.17

0 0 0.425 -0.95 -1.05

3.17

-1.1808

3.30 4.27 2.87 5.26

2.1 1.575 2 1.36

Figure 1. The model of initial configuration of shale oil in the montmorillonite.

14


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1E-3

2

Ds (cm /s)

1E-4 1E-5 310 K 340 K 370 K 400 K

1E-6 1E-7 2

4

6 8 10 49 50 51 Basal spacing (nm)

Figure 2. Diffusion coefficients of octane in montmorillonites of different basal spacings. Six molecules were put in each unit cell. Different colors stand for different temperatures.

1E-3 2

Ds (cm /s)

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


310 K 340 K 370 K 400 K

1E-4

2

4

6 8 10 46 48 50 Basal spacing (nm)

Figure 3. Diffusion coefficients of octane in montmorillonites of different basal spacings. Three molecules were put in each unit cell. Different colors stand for different temperatures.

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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 16 of 20

Figure 4. Snapshot of octane at basal spacing of 3.8 nm and T=400 K. (a) Three molecules were put in each unit cell, (b) Six molecules were put in each unit cell. Green: Ca2+, grey: CH3,CH2, red: O, yellow: Si, pink: Al.

Figure 5. Contour plots of the probability densities of octane at basal spacing of 3.8 nm and T=400 K. (a) Three molecules were put in each unit cell, (b) Six molecules were put in each unit cell.

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Page 17 of 20

2.0

(a)

3.0

(b) 1.6 Density (g/cm )

2.0

3

Density (g/cm3)

2.5

1.5 1.0 0.5

1.2 0.8 0.4 0.0

0.0 0

1

2

3

4

0

1

2

z (nm)

3 z (nm)

4

5

(d)

(c)

1.2

3

3

Density (g/cm )

1.2 Density (g/cm )

0.8 0.4

0.8 0.4 0.0

0.0 0

2

4

6 z (nm)

8

10

12

0

2

4

48

50

52

z (nm)

Figure 6. Local density distributions of octane in montmorillonites of different basal spacing at T=400 K. Six molecules were put in each unit cell. (a) 2.8 nm, (b) 3.8 nm, (c) 10 nm, (d) 50 nm.

number of molecules

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


50 45 40 35 30 25 20 15 10 5 0

1 2 3 4 5 6 7 8

2.8nm 3.8nm 10nm

50nm

basal spacing Figure 7. The number of octane molecules in the contact layer of montmorillonites. The different colors stand for the number of atoms of each octane molecule in the contact layer.

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1E-3

1E-4 2

Ds (cm /s)

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

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1E-5

Ds || Ds

1E-6

⊥

Ds 1E-7 2

4

6

8

10

49 50 51

Basal spacing (nm) Figure 8 Diffusion coefficients of octane in montmorillonites of different basal spacings and T=400 K. Six molecules were put in each unit cell. The square stands for the Ds, the circle stands for Ds , and the triangle stands for Ds⊥ .

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Page 19 of 20

-4

1.5x10

3

density =0.682 g/cm -4

2

Ds (cm /s)

1.2x10

400 K,600 bar

-5

9.0x10

-5

6.0x10

-5

3.0x10

0

10 20 30 40 Basal spacing (nm)

50

Figure 9. Diffusion coefficients of octane in montmorillonites of different basal spacings.

-4

2.5x10

3

density=0.64 g/cm 400K, 600 bar

-4

Ds (cm /s)

2.0x10 2

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


-4

1.5x10

-4

1.0x10

-5

5.0x10

0

10 20 30 40 Basal spacing (nm)

50

Figure 10. Diffusion coefficients of hexane in montmorillonites of different basal spacings.

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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

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Table of Contents Graphics

Molecular Dynamics Simulation of Diffusion of Shale Oils in Montmorillonite Hui Wang, Xiaoqi Wang, Xu Jin and Dapeng Cao

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Molecular Dynamics Simulation of Diffusion of Shale Oils in

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