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Oil displacement by supercritical CO2 in a water cut dead-end pore: Molecular dynamics simulation
Journal Pre-proof Oil displacement by supercritical CO2 in a water cut dead-end pore: Molecular dynamics simulation Yalin Luan, Bing Liu, Peng Hao, Kaiyun Zhan, Jianlin Liu PII:
S0920-4105(19)31313-0
DOI:
https://doi.org/10.1016/j.petrol.2019.106899
Reference:
PETROL 106899
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 25 July 2019 Revised Date:
22 November 2019
Accepted Date: 31 December 2019
Please cite this article as: Luan, Y., Liu, B., Hao, P., Zhan, K., Liu, J., Oil displacement by supercritical CO2 in a water cut dead-end pore: Molecular dynamics simulation, Journal of Petroleum Science and Engineering (2020), doi: https://doi.org/10.1016/j.petrol.2019.106899. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Abstract: Exploitation of residual oils inside the micro/nano-pores in the reservoir is one perpetual goal of Enhancing oil recovery (EOR), which presents a big challenge for both advanced technologies and fundamental theories. In the current study, we make a comprehensive molecular dynamics (MD) simulation on the displacement process of trapped oils inside a water cut dead-end pore driven by supercritical CO2 molecules. First, the whole displacement process is fully demonstrated by snapshots of MD simulation. Next, the collapse details of the water film between carbon dioxide and octane are simulated, where the hydrogen bonds and the evolution of ruptured hole are discussed. Thirdly, the configuration of the oil-water interface is computed and analyzed by the Laplace equation. Fourthly, the displacement mechanism of octane by carbon dioxide is explained according to the energy principle. These findings can strengthen our understandings on the details of the residual oil displacement in rocks, which may provide some inspirations on the oil recovery enhancement.
Oil displacement by supercritical CO2 in a water cut dead-end pore: molecular dynamics simulation Yalin Luana, Bing Liub, Peng Haoc, Kaiyun Zhanb, Jianlin Liu a, *
a
Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
b
c
School of Science, China University of Petroleum (East China), Qingdao 266580, China
College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China
*
Corresponding author:
Jianlin Liu, E-mail: [email protected].
Abstract: Exploitation of residual oils from the micro/nanopores in the reservoir is one perpetual goal of Enhancing oil recovery (EOR), which presents a big challenge for both advanced technologies and fundamental theories. In the current study, we make a comprehensive molecular dynamics (MD) simulation on the displacement process of trapped oils inside a water cut dead-end pore driven by supercritical CO2 molecules. Firstly, the whole displacement process is fully demonstrated by snapshots of MD simulation. Next, the collapse details of the water film between carbon dioxide and octane are simulated, where the hydrogen bonds and the evolution of ruptured hole are discussed. Thirdly, the configuration of the oil-water interface is computed and analyzed by the Laplace equation. Fourthly, the displacement mechanism of octane by carbon dioxide is explained according to the energy principle. These findings can strengthen our understandings on the details of the residual oil displacement in rocks, which may provide some inspirations on the oil recovery enhancement.
Keywords: supercritical CO2; dead-end pore; oil displacement; molecular dynamics; energy analysis
1. Introduction Enhancing oil recovery (EOR) is an unremitting pursuit in the field of petroleum exploitation, which strongly challenges the advanced technologies and fundamental theories. In many eastern old oil fields with a high water amount, the oil recovery factor can only amount to 35%, and the residual oils almost account 2/3 of the whole reservoir. To expel the residual oils out of the pores or cracks in the reservoir, numerous oil-displacing agents have been developed and applied (Chen et al., 2010; Wu et al., 2012; Yuan et al., 2012), including nanoparticles, surfactants, and carbon dioxide, etc. Among them, carbon dioxide injection could enhance the oil recovery up to 8~14% on the original oils in place (Rogers and Grigg, 2000), as it can make the oils swell, reduce the oil viscosity, increase the oil density, and enhance the vaporization and extraction portions of oils (Holm and Josendal, 1974). It is well known that, in the moderate and low water cut stage, oil phases are mostly distributed in terms of a continuous state. However, after entering the extra high water-cut stage, the residual oil distribution possesses the characteristic of "overall dispersion and partial enrichment", i.e. the oil phase mainly exists in the micro/nanopores in a discontinuous state, such as the dead-end residual oil, pore throat residual oil, clustered residual oil, oil film and isolated oil (Zhu et al., 2017). Therefore many investigations based on experiments and numerical simulations have been carried out on the oil displacement inside the pores. For example, Campbell and Orr (1985) performed the experiment with a 2D pore networks etched in glass plates using high-pressure CO2 floods, and they found that CO2 is capable of displacing the oil effectively. In succession, they conducted another experiment including a round glass-typed dead-end pore with the characteristic size of millimeter, and it was found that the CO2 molecules contact the trapped oils by diffusing through water, and thus the oils
are swelled by CO2 (Campbell and Orr, 1985; Yu et al., 2015). Grogan and Pinczewski (1987) also declared that the molecular diffusion of CO2 plays a dominant role in the recovery of water flood residual oil. Following similar equipment by Campbell and Orr (1985), Bijeljic et al. (2002) developed a numerical model on the dead-end pore by virtue of the Fick’s first law. They claimed that the water film rupture time is affected by the existence of CO2 when injecting mixed gases into oils. In what follows, Riazi et al. (2011) used the second Fick’s law to establish another mathematical model with a higher accuracy, in order to simulate the experimental results by Campbell and Orr (1985) with water considered or not. In their study, the effects of such parameters as CO2 density, initial oil volume, diffusion coefficients of CO2 in water and oil, and the water layer length on the oil swelling were fully discussed. Similarly, Mirazimi and Rostami (2017) did a set of microscopic visualization experiments related with the dead-end pore, and then they injected mixed gases in the horizontal direction outside the water. What’s more, they built an improved mathematical model based on the work of Bijeljic et al. (2002) to estimate the water rupture time during displacement, and the result is in close agreement with the experimental data. It should be mentioned that, when the temperature and pressure exceed 31°C and 7.1 MPa respectively, CO2 will be at the supercritical state. Riazi et al. (2011) conducted the visual oil displacement experiment by injecting CO2 at both subcritical (gaseous state) and supercritical conditions. Compared with the supercritical CO2, the gaseous state CO2 has a lower solubility in water, and a higher interfacial tension between CO2 and oil. It is difficult for the gaseous CO2 molecules to diffuse through water into the oil phase, and they cannot cause the swelling and vaporization of oils (Riazi et al., 2009). As a result, supercritical CO2 is normally chosen as the injected gas due to its unique properties, including the large diffusion coefficient of similar to gas,
and high dissolving capability similar to liquid (Mondal and De, 2015; Zanganeh et al., 2015). Different from the experimental setup of Campbell and Orr (1985), Cui et al. (2017) carried out the micro-visualization experiment related with a glass etching dead-end pore under a high temperature (82.5 °C) and high pressures (15 MPa, 20 MPa and 25 MPa, respectively). The results also show that, the thicker the water film is, the longer the mixture of oil and carbon dioxide reaches the miscible phase. Although much effort has been devoted on the displacement of oil by CO2 in a dead-end pore, the detailed process is not clear due to the limitation of experimental techniques, especially at nanoscale. Therefore the current study is directed towards a full understanding on the process how CO2 displaces residual oils inside a nanopore, in which the MD simulation is chosen as a tool. This advanced simulation skill can replace part of the experiments, fully demonstrating the dynamic evolution of the components in one system. The popular MD technique has proved that it is an efficient tool to simulate the current molecular system, including carbon dioxide, octane, water, silica and graphene. Another advantage on MD is that it can be correlated with the macroscopic thermodynamics parameters, such as energy, entropy and enthalpy. This article is organized as follows. In Section 2, we give the detailed illustrations on the simulation model and methodology based on MD. In Section 3, simulation results and discussion are illustrated. First, the whole displacement process is demonstrated by snapshots of MD simulation. Next, the rupture of the water film is simulated, where the hydrogen bonds and the evolution of collapsed hole are discussed. Thirdly, the configuration of the oil-water interface is computed and analyzed based on the Laplace equation. Fourthly, the displacement mechanism of octane by carbon dioxide is explained on the basis of energy principle. Finally, conclusions follow up in Section 4.
2. Model and methodology As shown in Fig. 1, a molecular dynamics (MD) model is established to probe the process and microscopic details of supercritical CO2 driving oils in a dead-end pore, and the top end of the pore is covered by a water film. Refer to the Cartesian coordinate system O-XYZ, where point O is the origin. As sedimentary rocks are initially water saturated and they have already been hydroxylated, oil droplets can cluster to push water out of the pores; and for modeling, a full hydroxylated silica surface is abstracted to represent the real geologic conditions (Skelton et al., 2011). The hydrophilic silica surface in this model is created by cleaving the bulk crystal of α -quartz along the [0 0 1] direction, and then H atoms are manually added on the fresh silica surface. The H atoms are linked with the O atoms, and finally form Si-O-H groups (Koretsky et al., 1998). In the modeling process, an 85×50×75 Å3 sized α -quartz block with a 30×50×55 Å3 sized aperture or pore is built, as schematized in Fig. 1. Then a dead-end pore model including trapped oils (represented by octane molecules, C8H18) is demonstrated, and a water film with the thickness of approximately 13Å on top of the pore is added. In addition, the water molecules are randomly distributed out of the nanopore. Finally, some supercritical CO2 molecules originally arranged randomly outside the water are injected into the system, which are pressed by a thin layer of graphene plate. In Fig. 1, there are totally 3060 CO2 molecules, 1620 water molecules, and a silica nanopore filled with 270 octane molecules (C8H18) in the system. The silica wall is fixed, which is set as a rigid body. The initial dimension of the simulation box is 85×50×240 Å3, and periodic boundary conditions are applied in X and Y directions. Various classical force fields, including the three-site EPM2 (Harris and Yung, 1995), the SPC/E
model (Mark and Nilsson, 2001), OPLS-AA force field (Jorgensen et al., 1984), and the CLAYFF force field (Cygan et al., 2004) have been proposed to describe the interactions among carbon dioxide, water, octane, and α -quartz surfaces. The plate-like structure, graphene, has no gravity and no charge, and thus it serves as a tool for applying pressures on the oil-water system. The bonded potential consists of bond stretching, angular bending, dihedral angle torsion, out-of-plane interactions and crossed terms; in which the non-bonded potential is composed of the long-range electrostatic interaction and the short-range van der Waals (vdW) interaction. To get a higher computational efficiency, the long-range electrostatic interactions are calculated by the particle– particle particle-mesh (PPPM) solver instead of Ewald summation (Chilukoti et al., 2014; Luty et al., 1994). The 6-12 Lennard-Jones potential is applied to describe the vdW terms and a cutoff radius of 9.5 Å (Firouzi et al., 2014) is adopted. In the present model, all-atom MD simulations are performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) free software package (Plimpton, 1995), and the visualization of the dynamics process is realized in Visual Molecular Dynamics (VMD). Firstly, each molecule is structurally optimized and then the optimization of potential energy on the initial configuration is carried out. The time step is set as 1 fs for the whole MD simulation. The octane and water are then relaxed via the Nosé−Hoover thermostat at 363.15 K (Feng et al., 2016) for 200 ps with CO2 molecules fixed in place. If the statistical average values of related physical qualities, such as total energy, temperature, and pressure, become time-independent, it can be assumed that the equilibrium state has been achieved (Wang et al., 2015). Eventually, we exert pressures on the graphene plate on top of the carbon dioxide to propel them downwards. Throughout the whole process, the graphene plate does not participate in the reaction, but it keeps the pressure of
the system always being 30 MPa. Altogether 14000 ps EMD and NEMD simulations of NVT computations are conducted for data collection. It should be mentioned that, although the temperature and pressure can affect the oil displacement, herein we choose their values which are closer to the real conditions of oil reservoir, where its depth is around from 2500 to 3000 km.
3. Results and discussion 3.1. Overall simulation results on the displacement The typical snapshots on the displacement process of supercritical carbon dioxide interacting with water and oils are displayed in Fig. 2. The original configuration after relaxation is that, octane molecules inside the nanopore are covered by a layer of water molecules, and CO2 molecules are randomly distributed outside the water-octane system. When the system pressure reaches 30 MPa, the simulation result shows that the position of the graphene sheet has only a slight fluctuation at its equilibrium position, and the snapshots are shown in Fig. 2(a) to (f). When the time t=305 ps, it is shown in Fig. 2(a) that, many CO2 molecules have been dissolved in water, whose colors are deepened for visibility, indicating that supercritical CO2 has a strong diffusive capability into water. Then when t=605 ps, some CO2 molecules quickly accumulate at the oil-water interface, as shown in Fig. 2(b). The diffusion goes on, and when t=1235 ps, it can be observed that more CO2 molecules are dissolved in water and have arrived at the oil-water interface. There are even part of the CO2 molecules adsorbed on the silica surface, and the atom O in CO2 and hydroxyl hydrogen in SiO2 can form the H-bond, which is marked by the red frame enlarged in Fig. 2(c). As shown in Fig. 2(d), when t=1710 ps, once the water film ruptures and the water channel or hole is thus formed, some CO2 molecules can rapidly gather near the hole and the hole continues to expand. When the hole on
the water film is large enough for the transportation of the octane molecules, they will go out of the quartz nanopore through this water channel. It is noticed from Fig. 2(e) that, when t=1795 ps, many octane molecules have clustered at the water channel. As shown in Fig. 2(f), when the time t=2020 ps, a lot of octane molecules have diffused out of the blind pore, where the numbers of carbon dioxide and octane are much bigger than those in Fig. 2(e). In Fig. 2(d), (e) and (f), part of the water channel has been magnified in red circles, where details of the accumulation of octane and carbon dioxide at the water channel can be identified. We also simulated the stage after 2020 ps, where more CO2 molecules come into the nanopore and more octane molecules go outside, and there are no new phenomena. In what follows, we will make the detailed illustrations on the displacement of oils driven by carbon dioxide in the nanopore.
3.2. Water film: hydrogen bond and hole As the supercritical CO2 has a polar molecule with two active and considerably strong bond dipoles (Raveendran et al., 2005), it is capable of being partially miscible with water. According to our statistics, when t=210 ps only a few CO2 molecules are dissolved in the water film with the depth of 4 Å, and when t=305 ps, the molecules have diffused into the middle layer of the water film, with the depth of about 11 Å. What’s more, with just 100 ps passing by, the amount of CO2 molecules dissolved in water has doubled. To illustrate how CO2 molecules enter and then cause the failure of the water film, the rupture details are shown by Fig. 3 in a top view. Our conventional experience tells us that water always appears as a whole substance without gaps. However, as shown in Fig. 3(a), there are actually some
clearings or gaps among water molecules, in which the CO2 molecules are randomly scattered among them. Compared with Fig. 3(a), it seems that there are a bit more holes in water with time going on, and they tend to cluster around the previous gap, as shown in Fig. 3(b). At the same time, there is a clear tendency for CO2 molecules to gather near the center, and the hole in the middle becomes bigger with more CO2 molecules accumulating there. After some time, the small holes will merge into a bigger one, and more holes appear when t=1704 ps, as shown in Fig. 3(c). It is displayed in Fig. 3(d) that, when t=1706 ps, the hole of the water film expands to a big enough value. In this case, more CO2 molecules come into the pore, and then an extraction passage for oils begins to form, as shown in Fig. 3(d). The formation of holes on the water film is attributed to the hydrogen bond breakage caused by the CO2 molecules, as shown in Fig. 3(e) to (h), where t=1700 ps, 1702 ps, 1704 ps and 1706 ps respectively. In these figures, the blue circles represent the places where the hydrogen bonds have broken. Evidently, the number of hydrogen bonds NH in water decreases over this period, as shown in Fig. 4(a). In the simulation, if the distance between the O–O atoms is less than 3 Å, and the angle of H–O–O atoms is less than 20°, the number of hydrogen bonds will be counted. When t=1700 ps, the hydrogen bonds are broken only at the center where the holes are small and where the CO2 molecules accumulate. With the aggregation of much more CO2 molecules near the center, the holes are getting bigger. It should be noted that, there are only fewer hydrogen bonds in the same position when t=1702 ps and t=1704 ps. The channel becomes significantly obvious when t=1706 ps, and the area of the hole expands rapidly accompanied with the rupture of water film. This phenomenon is very similar to the principle of stress concentration in solid mechanics, where the dangerous point is just at the location where the stress is highest. The area evolution law on the
hole during the expansion process can be expressed by the data-fitting of the curve in Fig. 4(b), which is expressed as a piecewise function 0 ( 0 ≤ t ≤ 1705 ps ) S (t ) = t – –2.69 × 108 e 134.73 + 890 (1705 < t ≤ 2500 ps )
(1)
3.3. Configuration of the oil-water interface The next issue for the CO2 molecules is their accumulation on the oil-water interface, as shown in Fig. 2(b) to (f). This tendency is the same as the previous simulation result, where it was claimed that the interfacial tension difference between the CO2-H2O and C8H18-H2O interfaces leads to this accumulation (Liu et al., 2016). The simulation result in Fig. 5 shows that, for the CO2 molecules, the ratio between the number of CO2 molecules on the oil-water interface, NO-W, and that inside water, NW, is getting bigger and bigger, especially after the water film collapses at t=1700 ps. When the time comes to t=8100 ps, the ratio NO-W/NW has exceeded 90%, which means that most of the CO2 molecules are accumulating at the oil-water interface. This behavior indicates that, the property of the interface is a bit special, which differs from the bulky materials, and we then concentrate on the morphology of the oil-water interface. Due to the accumulation of carbon dioxide molecules, there is an obvious variation on the configuration of the oil-water interface. With more carbon dioxide molecules dissolved in water and accumulating at the oil-water interface, the surface area of the whole water film increases. For example, the surface area value is 24218.23, 24496.58 and 24814.12 Ų, corresponding to the time t=565, 1075 and 1675 ps, respectively. As shown in Fig. 6, the roughness of the water-oil interface becomes stronger, i.e. with the increase of the CO2 molecules aggregation, the surface morphology
becomes more irregular. As a result, the shape of the meniscus, i.e. the oil-water interface will be regulated by the accumulation of CO2, and the curvature of the meniscus increases with the molecule number accumulated at the interface. In practice, the curvature of the oil-water interface can be geometrically expressed as C=
1
ρ
=−
cos θ , R
(2)
where ρ is the curvature radius, ߠ is the contact angle between the vertical line (silica wall) and tangential line of the oil-water interface at the triple contact point, and R is the width of the nanopore, as schematized in Fig. 6. As the curvature has changed, the contact angle changes accordingly, based on Eq. (2). Then the Laplace-Young equation reads
∆p = γ WOC ,
(3)
where ∆p is the Laplace pressure difference across the oil-water interface, and γ WO is the interfacial tension between oil and water. It is determined from Eq. (3) that, the change of the curvature may be governed by two variables, i.e. the Laplace pressure difference, and the interfacial tension between oil and water. From the microscopic view, this curvature alteration is caused by the accumulation of CO2 molecules at the oil-water interface, which can induce the change of the Laplace equation and interfacial tension. For illustration, the radial distribution function g(r) on the octane-octane is depicted in Fig. 7, and r is the radius of the circular area for calculation. It shows that after the peak, all the curves of g(r) decrease with the increase of the radius. The curve indicates that the coordination number around each octane molecule decreases and the octane molecule distribution becomes looser. This phenomenon tells us that, when the CO2 molecules are dissolved in octane, the volume of oils inside the pore expands. The volume expansion of octane in the nanopore can certainly increase the pressure, and thus alter the Laplace pressure difference to modulate the
oil-water interface. In addition, it can be observed in Fig. 8(a) that, when t=525 ps, the carbon dioxide molecules at the oil-water interface tend to arrange their postures to adapt to the interface shape. After some time, such as when t=1500 ps, the molecules at the interface modulate their postures and tend to become perpendicular to the interface, as shown in Fig. 8(b). Evidently, this posture modulation may provide extra space for more CO2 molecules to accumulate there, and to promote CO2 molecules into oils. This may be one of the reasons for roughness enhancement at the interface. It is clear that, this arrangement of CO2 molecules may be similar to the case of a cell entry of one-dimensional nanomaterials by its tip recognition and rotation (Shi et al., 2011).
3.4. Energy analysis As mentioned above, residual oils are initially confined in the silica nanopore and adsorbed on its inner surface. Many experiments (Cui et al., 2017) and simulations (Liu et al., 2016; Makimura et al., 2013) show that carbon dioxide molecules can pierce into the water-oil interface, and diffuse into the octane, as demonstrated in Fig. 2. As a consequence, the CO2 molecules detach oils from the surface, which plays a significant role in CO2 EOR. The underlying mechanism of displacement can be explained from the viewpoint of interaction energy between molecules. As shown in Fig. 9(a), at the very beginning, the pore is full of octane, and the interaction energy between SiO2 and octane is calculated as E=–380 kcal/mol while that between SiO2 and CO2 is zero, where the negative sign means the interplay is attractive between two substances (Fermeglia et al., 2003). As more and more CO2 molecules go into the pore and attach on the silica surface, the adsorption ability of the silica surface to oil becomes much weaker, as the interaction energy between them becomes smaller and
smaller and finally attains to zero. On the contrary, the attraction energy between CO2 and silica E becomes gradually bigger, whose value changes from zero to –520 kcal/mol, and the adsorption of CO2 on the silica surface nearly reaches the state of saturation, as shown in Fig. 9(a). The interaction energy difference manifests that the attraction of SiO2–C8H18 is weaker than that of SiO2–CO2, and a natural conclusion can be drawn is that, octane is prone to be replaced by CO2. From the viewpoint of thermodynamics, the whole evolution of the system including SiO2, CO2, Oil and H2O depends on its free energy, and the equilibrium state must be that with lowest free energy when the external work is zero. The Helmholtz free energy is expressed as F=U–TS,
(4)
where U is the potential energy of the system, T is the temperature and S is the entropy. The total potential energy originates from the short range van der Waals (vdW) interaction energy and the long-range electrostatic interaction energy, which can be written as 15
U = ∑Ui ,
(5)
i
where the 15 terms are composed of the interaction energies of the graphene plate, the silica, the carbon dioxide molecules, the water molecules and the octane molecules; and the remaining 10 terms are the result of combinatorial arrangement of the above 5 energies. For the current system, when the pressure reaches 30 MPa, the displacement of the plate is very small via the simulation result, so that the input work is close to zero. The computational results in Fig. 9(b) show that the potential energy of the system U decreases with time increasing, and the entropy S must increase according to the second law of thermodynamics. As a consequence, at the condition of constant temperature and constant pressure, we can ascertain that the free energy of the whole system keeps decreasing with time, i.e. dF<0. It is suggested that the system tends to evolve to the state with a smaller free energy,
and the oil displacement process can happen.
3.5. Potential applications Obviously, the previous simulations show that the injected CO2 molecules can enhance the displacement of oils, and the oil recovery factor at nanoscale can be computed. It can be defined as
R1 =
N1 − N 2 , N1
(6)
where N2 is the number of residual octane molecules after displacement, and N1 is the number of original octane molecules in the pore. In the calculation, N1 is equal to 270. The subfigure in Fig. 10 indicates that the number of residual oil molecules N2 decreases and finally reaches to a stable value of 48, and this tendency is consistent with the previous simulation (Fang et al., 2018). As a consequence, it is shown in Fig. 10 that, when t=1705 ps, the oil recovery factor becomes bigger than zero. Moreover, the value of the oil recovery factor increases with the time, and it can finally attain to the value as high as 82%. From the macroscopic viewpoint, the oil recovery factor in the process of oil displacement is defined as
R2 =
V1 − V2 , V1
(7)
where V1 is the initial volume of the oil, and V2 is the volume expelled by water or some other solutions. The reported results on the oil recovery experiment show that the value of R2 is normally in the range of 40%–70% due to different methods and geological conditions. Especially, a recent experiment shows that the oil recovery factor driven by CO2 can amount to 94% (Cui et al., 2017), which is higher than our simulation result.
Although the pores at nanoscale and macroscale are geometrically similar, the results from MD cannot be enlarged proportionally to get the macroscopic values according to their geometric similarity, as the physical mechanisms are different. It can be imagined that, for the macroscopic experiment, the adsorption effect of the silicon surface is small, while at nanoscale this effect becomes comparatively larger due to the interaction between the molecules and solid surface. This is the well-known surface effect, and it can be conjectured that the oil recovery factor is smaller than that at macroscale. What’s more, the oil recovery factor can be determined by many parameters, such as molecular interaction among different liquids (CO2, C8H18, H2O), density of liquids, wettability of the pore, geometry of the pore, roughness of the pore, velocity and pressure of liquids, temperature and humidity, etc. It is also seen that the current geometric model in our simulation is not the same from the previous setup at macroscale (Cui et al., 2017). Another possible reason may be attributed to the difference between the experimental setup (Cui et al., 2017) and our simulation model, where the directions of the pressure are distinct. Besides these, the components of octane in our simulation and the macroscopic experiment are different. Regardless of these differences, the two values on the oil recovery factor are at the same order, and the experiment at macroscale has the same tendency with our simulation result at nanoscale. In order to correlate the MD simulation result with the macroscopic experiment, the multiscale simulation technique must be explored for the next step.
4. Conclusions In conclusion, a comprehensive study based on MD simulation is performed to probe the displacement of residual oils trapped in a dead-end nanopore which is enveloped by a water film,
where the oils are driven by the supercritical carbon dioxide molecules. The main conclusion is that the excellent diffusion capacity of CO2 plays a key role in the whole molecule motion. Firstly, when the carbon dioxide molecules diffuse into the water film, the hydrogen bonds are broken, and there is a collapsed hole formed, which becomes the channel for CO2 going into the pore. Secondly, when sufficient CO2 molecules aggregate at the oil-water interface, the roughness of the interface is enhanced. Thirdly, the curvature of the oil-water interface becomes bigger, where one reason is that the accumulation of CO2 molecules on the interface alters the interfacial tension, and the other is that the swelling of oils caused by the invasion of CO2 inside the pore. Fourthly, it is observed that the alignment of oil molecules on the oil-water interface can spontaneously modulate their postures to more easily pierce into the water film. Next, the displacement mechanism is also explained by the energy principle. The interaction energy between CO2 and silica is bigger than that between octane and silica, and this fact makes CO2 favorable to detach the oil from silica. Moreover, the whole evolution process of the system can be formulated by the energy principle. At last, we calculate the oil recovery factor, which can amount to the value as high as 82%. It should be mentioned that, there are some practical factors which should be further considered in simulation, such as the roughness of the pore surface, the geometry of the pore, the temperature and pressure effects, which deserve to be examined in future studies. Regardless of these issues, our findings can strengthen the understandings on the details of the residual oil displacement in rocks, which may provide some inspirations on the oil recovery enhancement. In order to get a quantitative correlation between the MD and macroscopic experiment, we hope to develop a multiscale simulation technique in the near future.
Acknowledgements This project was supported by the National Natural Science Foundation of China (11672335 and 11972375).
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298 K. J. Phys. Chem. A. 105, 9954–9960. Mirazimi, S., Rostami, B., Ghazanfari, M.H., et al., 2017. Water film rupture in blocked oil recovery by gas injection: experimental and modeling study. Chem. Eng. Sci. 161, 288–298. Mondal, S., De, S., 2015. CO2 based power cycle with multi-stage compression and intercooling for low temperature waste heat recovery. Energy. 90, 1132–1143. Plimpton, S., 1995. Fast parallel algorithms for short–range molecular dynamics. J. Comput. Phys. 117, 1–19. Raveendran, P., Ikushima, Y., Wallen, S.L., 2005. Polar attributes of supercritical carbon dioxide. Acc. Chem. Res. 38, 478–485. Riazi, M., Sohrabi, M., Jamiolahmady, M., et al., 2009. Direct observation of CO2 transport and oil displacement mechanisms in CO2/water/oil systems. In: 15th European Symposium on Improved Oil Recovery, Paris, France. Riazi, M., Jamiolahmady, M., Sohrabi, M., 2011. Theoretical investigation of pore-scale mechanisms of carbonated water injection. J. Petrol. Sci. Eng. 75, 312–326. Rogers, J.D., Grigg, R.B., 2000. A literature analysis of the WAG injectivity abnormalities in the CO2 process. In: SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma. Shi, X., Annette, V.D.B., Hurt, R.H., 2011. Cell entry of one-dimensional nanomaterials occurs by tip recognition and rotation. Nature Nanotechnology. 6, 714–719. Skelton, A.A., Fenter, P., Kubicki, J.D., et al., 2011. Simulations of the quartz(101̅1)/water interface: a comparison of classical force fields, Ab initio molecular dynamics, and X-ray reflectivity experiments. J. Phys. Chem. C. 115, 2076–2088. Wang, S., Feng, Q., Javadpour, F., et al., 2015. Oil adsorption in shale nanopores and its effect on
recoverable oil–in–place. In. J. Coal Geol. 147–148, 9–24. Wu, J., He, J., Torsater, O., et al., 2012. Effect of nanoparticles on oil-water flow in a confined nanochannel: a molecular dynamics study. In: SPE Annual Technical Conference and Exhibition, Noordwijk, The Netherlands. Yu, W., Lashgari, H.R., Wu, K., et al., 2015. CO2 injection for enhanced oil recovery in Bakken tight oil reservoirs. Fuel. 159, 354–363. Yuan, Q., Sun, C.Y., Yang, X., et al., 2012. Recovery of methane from hydrate reservoir with gaseous carbon dioxide using a three-dimensional middle-size reactor. Energy. 40 (1), 47–58. Zanganeh, P., Dashti, H., Ayatollahi, S., 2015. Visual investigation and modeling of asphaltene precipitation and deposition during CO2 miscible injection into oil reservoirs. Fuel. 160, 132– 139. Zhu, G.P., Yao, J., Zhang, L., et al., 2017. Pore-scale investigation of residual oil distributions and formation mechanisms at the extra-high water-cut stage. Chin. Sci. Bull. 62, 2553–2563 (in Chinese with English abstract).
Figure captions
Figure 1 Overall configuration diagram with dimensions of the dead-end pore. Color codes for atoms are, purple: CO2; cyan: water; grey: octane; yellow, silicon; red, oxygen; and white, hydroxyl hydrogen (Hh).
Figure 2 The whole displacement of oils by carbon dioxide inside a nanopore at (a) t=305 ps, (b) t=605 ps, (c) t=1235 ps, with a snapshot of Hydrogen bond formed between the silica surface and CO2 molecules when t=1235 ps. The H-bond is highlighted as a red dashed line between the oxygen from CO2 (in purple) and the hydroxyl hydrogen from SiO2 (in white) inside the red frame. In succession, (d) t=1710 ps, (e) t=1795 ps, and (f) t=2020 ps. The enlarged views of water film clearings have been marked by the red circles in (d), (e) and (f) respectively.
Figure 3 Details (top View) of carbon dioxide diffusing into the water film at (a) t=1700 ps, (b) t=1702 ps, (c) t=1704 ps, and (d) t=1706 ps, and snapshots (top View) of hydrogen bonds in the water film at (e) t=1700 ps, (f) t=1702 ps, (g) t=1704 ps and (h) t=1706 ps. The blue circles highlight where the hydrogen bonds have been broken and the hydrogen bond is highlighted as a purple dashed line between the oxygen (in red) and hydrogen (in white).
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Figure 4 Hydrogen bond number and hole area of the water film. (a) Number of hydrogen bonds in water decreases with CO2 dissolved in water. (b) Area of the main hole on the water film increases with the increase of time (1705 ps < t ≤ 2500 ps )
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Figure 5 Ratio between the number of CO2 at the oil-water interface to that in water. The subfigure shows the number of CO2 dissolved in water NW and that of CO2 accumulated at the oil-water interface NO-W.
Figure 6 Configurations of the roughness, the shape of the meniscus of the oil-water interface at (a) t=565 ps, (b) t=1075 ps and (c) t=1675 ps respectively in which ρ is the curvature radius, ߠ is the contact angle between the vertical line (silica wall) and tangential line of the oil-water interface at the triple contact point, and R is the radius of the nanopore.
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Figure 7 Radial distribution function of octane-octane at t=535 ps, 1505 ps, 2250 ps and 4250 ps, respectively.
Figure 8 Alignment of octane molecules at the oil-water interface, at (a) t=525 ps when CO2 at the oil-water interface tend to adapt to the interface shape and (b) t=1500 ps when CO2 tend to become perpendicular to the interface.
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Figure 10 Oil recovery factor driven by CO2 with respect to the time, where the subfigure gives the molecule number of residual octane molecules.
The whole displacement process is fully demonstrated by snapshots of MD simulation.
The hydrogen bonds and the evolution of ruptured hole on the water film are discussed.
The configuration of the oil-water interface is computed and analyzed by the Laplace equation.
The displacement mechanism of octane by carbon dioxide is explained according to the energy principle.
Author Contribution Statement
Yalin Luan: Methodology, Software Bing Liu: Conceptualization, Methodology, Software Peng Hao: Software, Validation Kaiyun Zhan: Software Jianlin Liu: Conceptualization, Methodology, Writing-Reviewing and Editing
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0920-4105(19)31313-0
DOI:
https://doi.org/10.1016/j.petrol.2019.106899
Reference:
PETROL 106899
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 25 July 2019 Revised Date:
22 November 2019
Accepted Date: 31 December 2019
Please cite this article as: Luan, Y., Liu, B., Hao, P., Zhan, K., Liu, J., Oil displacement by supercritical CO2 in a water cut dead-end pore: Molecular dynamics simulation, Journal of Petroleum Science and Engineering (2020), doi: https://doi.org/10.1016/j.petrol.2019.106899. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Abstract: Exploitation of residual oils inside the micro/nano-pores in the reservoir is one perpetual goal of Enhancing oil recovery (EOR), which presents a big challenge for both advanced technologies and fundamental theories. In the current study, we make a comprehensive molecular dynamics (MD) simulation on the displacement process of trapped oils inside a water cut dead-end pore driven by supercritical CO2 molecules. First, the whole displacement process is fully demonstrated by snapshots of MD simulation. Next, the collapse details of the water film between carbon dioxide and octane are simulated, where the hydrogen bonds and the evolution of ruptured hole are discussed. Thirdly, the configuration of the oil-water interface is computed and analyzed by the Laplace equation. Fourthly, the displacement mechanism of octane by carbon dioxide is explained according to the energy principle. These findings can strengthen our understandings on the details of the residual oil displacement in rocks, which may provide some inspirations on the oil recovery enhancement.
Oil displacement by supercritical CO2 in a water cut dead-end pore: molecular dynamics simulation Yalin Luana, Bing Liub, Peng Haoc, Kaiyun Zhanb, Jianlin Liu a, *
a
Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
b
c
School of Science, China University of Petroleum (East China), Qingdao 266580, China
College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China
*
Corresponding author:
Jianlin Liu, E-mail: [email protected].
Abstract: Exploitation of residual oils from the micro/nanopores in the reservoir is one perpetual goal of Enhancing oil recovery (EOR), which presents a big challenge for both advanced technologies and fundamental theories. In the current study, we make a comprehensive molecular dynamics (MD) simulation on the displacement process of trapped oils inside a water cut dead-end pore driven by supercritical CO2 molecules. Firstly, the whole displacement process is fully demonstrated by snapshots of MD simulation. Next, the collapse details of the water film between carbon dioxide and octane are simulated, where the hydrogen bonds and the evolution of ruptured hole are discussed. Thirdly, the configuration of the oil-water interface is computed and analyzed by the Laplace equation. Fourthly, the displacement mechanism of octane by carbon dioxide is explained according to the energy principle. These findings can strengthen our understandings on the details of the residual oil displacement in rocks, which may provide some inspirations on the oil recovery enhancement.
Keywords: supercritical CO2; dead-end pore; oil displacement; molecular dynamics; energy analysis
1. Introduction Enhancing oil recovery (EOR) is an unremitting pursuit in the field of petroleum exploitation, which strongly challenges the advanced technologies and fundamental theories. In many eastern old oil fields with a high water amount, the oil recovery factor can only amount to 35%, and the residual oils almost account 2/3 of the whole reservoir. To expel the residual oils out of the pores or cracks in the reservoir, numerous oil-displacing agents have been developed and applied (Chen et al., 2010; Wu et al., 2012; Yuan et al., 2012), including nanoparticles, surfactants, and carbon dioxide, etc. Among them, carbon dioxide injection could enhance the oil recovery up to 8~14% on the original oils in place (Rogers and Grigg, 2000), as it can make the oils swell, reduce the oil viscosity, increase the oil density, and enhance the vaporization and extraction portions of oils (Holm and Josendal, 1974). It is well known that, in the moderate and low water cut stage, oil phases are mostly distributed in terms of a continuous state. However, after entering the extra high water-cut stage, the residual oil distribution possesses the characteristic of "overall dispersion and partial enrichment", i.e. the oil phase mainly exists in the micro/nanopores in a discontinuous state, such as the dead-end residual oil, pore throat residual oil, clustered residual oil, oil film and isolated oil (Zhu et al., 2017). Therefore many investigations based on experiments and numerical simulations have been carried out on the oil displacement inside the pores. For example, Campbell and Orr (1985) performed the experiment with a 2D pore networks etched in glass plates using high-pressure CO2 floods, and they found that CO2 is capable of displacing the oil effectively. In succession, they conducted another experiment including a round glass-typed dead-end pore with the characteristic size of millimeter, and it was found that the CO2 molecules contact the trapped oils by diffusing through water, and thus the oils
are swelled by CO2 (Campbell and Orr, 1985; Yu et al., 2015). Grogan and Pinczewski (1987) also declared that the molecular diffusion of CO2 plays a dominant role in the recovery of water flood residual oil. Following similar equipment by Campbell and Orr (1985), Bijeljic et al. (2002) developed a numerical model on the dead-end pore by virtue of the Fick’s first law. They claimed that the water film rupture time is affected by the existence of CO2 when injecting mixed gases into oils. In what follows, Riazi et al. (2011) used the second Fick’s law to establish another mathematical model with a higher accuracy, in order to simulate the experimental results by Campbell and Orr (1985) with water considered or not. In their study, the effects of such parameters as CO2 density, initial oil volume, diffusion coefficients of CO2 in water and oil, and the water layer length on the oil swelling were fully discussed. Similarly, Mirazimi and Rostami (2017) did a set of microscopic visualization experiments related with the dead-end pore, and then they injected mixed gases in the horizontal direction outside the water. What’s more, they built an improved mathematical model based on the work of Bijeljic et al. (2002) to estimate the water rupture time during displacement, and the result is in close agreement with the experimental data. It should be mentioned that, when the temperature and pressure exceed 31°C and 7.1 MPa respectively, CO2 will be at the supercritical state. Riazi et al. (2011) conducted the visual oil displacement experiment by injecting CO2 at both subcritical (gaseous state) and supercritical conditions. Compared with the supercritical CO2, the gaseous state CO2 has a lower solubility in water, and a higher interfacial tension between CO2 and oil. It is difficult for the gaseous CO2 molecules to diffuse through water into the oil phase, and they cannot cause the swelling and vaporization of oils (Riazi et al., 2009). As a result, supercritical CO2 is normally chosen as the injected gas due to its unique properties, including the large diffusion coefficient of similar to gas,
and high dissolving capability similar to liquid (Mondal and De, 2015; Zanganeh et al., 2015). Different from the experimental setup of Campbell and Orr (1985), Cui et al. (2017) carried out the micro-visualization experiment related with a glass etching dead-end pore under a high temperature (82.5 °C) and high pressures (15 MPa, 20 MPa and 25 MPa, respectively). The results also show that, the thicker the water film is, the longer the mixture of oil and carbon dioxide reaches the miscible phase. Although much effort has been devoted on the displacement of oil by CO2 in a dead-end pore, the detailed process is not clear due to the limitation of experimental techniques, especially at nanoscale. Therefore the current study is directed towards a full understanding on the process how CO2 displaces residual oils inside a nanopore, in which the MD simulation is chosen as a tool. This advanced simulation skill can replace part of the experiments, fully demonstrating the dynamic evolution of the components in one system. The popular MD technique has proved that it is an efficient tool to simulate the current molecular system, including carbon dioxide, octane, water, silica and graphene. Another advantage on MD is that it can be correlated with the macroscopic thermodynamics parameters, such as energy, entropy and enthalpy. This article is organized as follows. In Section 2, we give the detailed illustrations on the simulation model and methodology based on MD. In Section 3, simulation results and discussion are illustrated. First, the whole displacement process is demonstrated by snapshots of MD simulation. Next, the rupture of the water film is simulated, where the hydrogen bonds and the evolution of collapsed hole are discussed. Thirdly, the configuration of the oil-water interface is computed and analyzed based on the Laplace equation. Fourthly, the displacement mechanism of octane by carbon dioxide is explained on the basis of energy principle. Finally, conclusions follow up in Section 4.
2. Model and methodology As shown in Fig. 1, a molecular dynamics (MD) model is established to probe the process and microscopic details of supercritical CO2 driving oils in a dead-end pore, and the top end of the pore is covered by a water film. Refer to the Cartesian coordinate system O-XYZ, where point O is the origin. As sedimentary rocks are initially water saturated and they have already been hydroxylated, oil droplets can cluster to push water out of the pores; and for modeling, a full hydroxylated silica surface is abstracted to represent the real geologic conditions (Skelton et al., 2011). The hydrophilic silica surface in this model is created by cleaving the bulk crystal of α -quartz along the [0 0 1] direction, and then H atoms are manually added on the fresh silica surface. The H atoms are linked with the O atoms, and finally form Si-O-H groups (Koretsky et al., 1998). In the modeling process, an 85×50×75 Å3 sized α -quartz block with a 30×50×55 Å3 sized aperture or pore is built, as schematized in Fig. 1. Then a dead-end pore model including trapped oils (represented by octane molecules, C8H18) is demonstrated, and a water film with the thickness of approximately 13Å on top of the pore is added. In addition, the water molecules are randomly distributed out of the nanopore. Finally, some supercritical CO2 molecules originally arranged randomly outside the water are injected into the system, which are pressed by a thin layer of graphene plate. In Fig. 1, there are totally 3060 CO2 molecules, 1620 water molecules, and a silica nanopore filled with 270 octane molecules (C8H18) in the system. The silica wall is fixed, which is set as a rigid body. The initial dimension of the simulation box is 85×50×240 Å3, and periodic boundary conditions are applied in X and Y directions. Various classical force fields, including the three-site EPM2 (Harris and Yung, 1995), the SPC/E
model (Mark and Nilsson, 2001), OPLS-AA force field (Jorgensen et al., 1984), and the CLAYFF force field (Cygan et al., 2004) have been proposed to describe the interactions among carbon dioxide, water, octane, and α -quartz surfaces. The plate-like structure, graphene, has no gravity and no charge, and thus it serves as a tool for applying pressures on the oil-water system. The bonded potential consists of bond stretching, angular bending, dihedral angle torsion, out-of-plane interactions and crossed terms; in which the non-bonded potential is composed of the long-range electrostatic interaction and the short-range van der Waals (vdW) interaction. To get a higher computational efficiency, the long-range electrostatic interactions are calculated by the particle– particle particle-mesh (PPPM) solver instead of Ewald summation (Chilukoti et al., 2014; Luty et al., 1994). The 6-12 Lennard-Jones potential is applied to describe the vdW terms and a cutoff radius of 9.5 Å (Firouzi et al., 2014) is adopted. In the present model, all-atom MD simulations are performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) free software package (Plimpton, 1995), and the visualization of the dynamics process is realized in Visual Molecular Dynamics (VMD). Firstly, each molecule is structurally optimized and then the optimization of potential energy on the initial configuration is carried out. The time step is set as 1 fs for the whole MD simulation. The octane and water are then relaxed via the Nosé−Hoover thermostat at 363.15 K (Feng et al., 2016) for 200 ps with CO2 molecules fixed in place. If the statistical average values of related physical qualities, such as total energy, temperature, and pressure, become time-independent, it can be assumed that the equilibrium state has been achieved (Wang et al., 2015). Eventually, we exert pressures on the graphene plate on top of the carbon dioxide to propel them downwards. Throughout the whole process, the graphene plate does not participate in the reaction, but it keeps the pressure of
the system always being 30 MPa. Altogether 14000 ps EMD and NEMD simulations of NVT computations are conducted for data collection. It should be mentioned that, although the temperature and pressure can affect the oil displacement, herein we choose their values which are closer to the real conditions of oil reservoir, where its depth is around from 2500 to 3000 km.
3. Results and discussion 3.1. Overall simulation results on the displacement The typical snapshots on the displacement process of supercritical carbon dioxide interacting with water and oils are displayed in Fig. 2. The original configuration after relaxation is that, octane molecules inside the nanopore are covered by a layer of water molecules, and CO2 molecules are randomly distributed outside the water-octane system. When the system pressure reaches 30 MPa, the simulation result shows that the position of the graphene sheet has only a slight fluctuation at its equilibrium position, and the snapshots are shown in Fig. 2(a) to (f). When the time t=305 ps, it is shown in Fig. 2(a) that, many CO2 molecules have been dissolved in water, whose colors are deepened for visibility, indicating that supercritical CO2 has a strong diffusive capability into water. Then when t=605 ps, some CO2 molecules quickly accumulate at the oil-water interface, as shown in Fig. 2(b). The diffusion goes on, and when t=1235 ps, it can be observed that more CO2 molecules are dissolved in water and have arrived at the oil-water interface. There are even part of the CO2 molecules adsorbed on the silica surface, and the atom O in CO2 and hydroxyl hydrogen in SiO2 can form the H-bond, which is marked by the red frame enlarged in Fig. 2(c). As shown in Fig. 2(d), when t=1710 ps, once the water film ruptures and the water channel or hole is thus formed, some CO2 molecules can rapidly gather near the hole and the hole continues to expand. When the hole on
the water film is large enough for the transportation of the octane molecules, they will go out of the quartz nanopore through this water channel. It is noticed from Fig. 2(e) that, when t=1795 ps, many octane molecules have clustered at the water channel. As shown in Fig. 2(f), when the time t=2020 ps, a lot of octane molecules have diffused out of the blind pore, where the numbers of carbon dioxide and octane are much bigger than those in Fig. 2(e). In Fig. 2(d), (e) and (f), part of the water channel has been magnified in red circles, where details of the accumulation of octane and carbon dioxide at the water channel can be identified. We also simulated the stage after 2020 ps, where more CO2 molecules come into the nanopore and more octane molecules go outside, and there are no new phenomena. In what follows, we will make the detailed illustrations on the displacement of oils driven by carbon dioxide in the nanopore.
3.2. Water film: hydrogen bond and hole As the supercritical CO2 has a polar molecule with two active and considerably strong bond dipoles (Raveendran et al., 2005), it is capable of being partially miscible with water. According to our statistics, when t=210 ps only a few CO2 molecules are dissolved in the water film with the depth of 4 Å, and when t=305 ps, the molecules have diffused into the middle layer of the water film, with the depth of about 11 Å. What’s more, with just 100 ps passing by, the amount of CO2 molecules dissolved in water has doubled. To illustrate how CO2 molecules enter and then cause the failure of the water film, the rupture details are shown by Fig. 3 in a top view. Our conventional experience tells us that water always appears as a whole substance without gaps. However, as shown in Fig. 3(a), there are actually some
clearings or gaps among water molecules, in which the CO2 molecules are randomly scattered among them. Compared with Fig. 3(a), it seems that there are a bit more holes in water with time going on, and they tend to cluster around the previous gap, as shown in Fig. 3(b). At the same time, there is a clear tendency for CO2 molecules to gather near the center, and the hole in the middle becomes bigger with more CO2 molecules accumulating there. After some time, the small holes will merge into a bigger one, and more holes appear when t=1704 ps, as shown in Fig. 3(c). It is displayed in Fig. 3(d) that, when t=1706 ps, the hole of the water film expands to a big enough value. In this case, more CO2 molecules come into the pore, and then an extraction passage for oils begins to form, as shown in Fig. 3(d). The formation of holes on the water film is attributed to the hydrogen bond breakage caused by the CO2 molecules, as shown in Fig. 3(e) to (h), where t=1700 ps, 1702 ps, 1704 ps and 1706 ps respectively. In these figures, the blue circles represent the places where the hydrogen bonds have broken. Evidently, the number of hydrogen bonds NH in water decreases over this period, as shown in Fig. 4(a). In the simulation, if the distance between the O–O atoms is less than 3 Å, and the angle of H–O–O atoms is less than 20°, the number of hydrogen bonds will be counted. When t=1700 ps, the hydrogen bonds are broken only at the center where the holes are small and where the CO2 molecules accumulate. With the aggregation of much more CO2 molecules near the center, the holes are getting bigger. It should be noted that, there are only fewer hydrogen bonds in the same position when t=1702 ps and t=1704 ps. The channel becomes significantly obvious when t=1706 ps, and the area of the hole expands rapidly accompanied with the rupture of water film. This phenomenon is very similar to the principle of stress concentration in solid mechanics, where the dangerous point is just at the location where the stress is highest. The area evolution law on the
hole during the expansion process can be expressed by the data-fitting of the curve in Fig. 4(b), which is expressed as a piecewise function 0 ( 0 ≤ t ≤ 1705 ps ) S (t ) = t – –2.69 × 108 e 134.73 + 890 (1705 < t ≤ 2500 ps )
(1)
3.3. Configuration of the oil-water interface The next issue for the CO2 molecules is their accumulation on the oil-water interface, as shown in Fig. 2(b) to (f). This tendency is the same as the previous simulation result, where it was claimed that the interfacial tension difference between the CO2-H2O and C8H18-H2O interfaces leads to this accumulation (Liu et al., 2016). The simulation result in Fig. 5 shows that, for the CO2 molecules, the ratio between the number of CO2 molecules on the oil-water interface, NO-W, and that inside water, NW, is getting bigger and bigger, especially after the water film collapses at t=1700 ps. When the time comes to t=8100 ps, the ratio NO-W/NW has exceeded 90%, which means that most of the CO2 molecules are accumulating at the oil-water interface. This behavior indicates that, the property of the interface is a bit special, which differs from the bulky materials, and we then concentrate on the morphology of the oil-water interface. Due to the accumulation of carbon dioxide molecules, there is an obvious variation on the configuration of the oil-water interface. With more carbon dioxide molecules dissolved in water and accumulating at the oil-water interface, the surface area of the whole water film increases. For example, the surface area value is 24218.23, 24496.58 and 24814.12 Ų, corresponding to the time t=565, 1075 and 1675 ps, respectively. As shown in Fig. 6, the roughness of the water-oil interface becomes stronger, i.e. with the increase of the CO2 molecules aggregation, the surface morphology
becomes more irregular. As a result, the shape of the meniscus, i.e. the oil-water interface will be regulated by the accumulation of CO2, and the curvature of the meniscus increases with the molecule number accumulated at the interface. In practice, the curvature of the oil-water interface can be geometrically expressed as C=
1
ρ
=−
cos θ , R
(2)
where ρ is the curvature radius, ߠ is the contact angle between the vertical line (silica wall) and tangential line of the oil-water interface at the triple contact point, and R is the width of the nanopore, as schematized in Fig. 6. As the curvature has changed, the contact angle changes accordingly, based on Eq. (2). Then the Laplace-Young equation reads
∆p = γ WOC ,
(3)
where ∆p is the Laplace pressure difference across the oil-water interface, and γ WO is the interfacial tension between oil and water. It is determined from Eq. (3) that, the change of the curvature may be governed by two variables, i.e. the Laplace pressure difference, and the interfacial tension between oil and water. From the microscopic view, this curvature alteration is caused by the accumulation of CO2 molecules at the oil-water interface, which can induce the change of the Laplace equation and interfacial tension. For illustration, the radial distribution function g(r) on the octane-octane is depicted in Fig. 7, and r is the radius of the circular area for calculation. It shows that after the peak, all the curves of g(r) decrease with the increase of the radius. The curve indicates that the coordination number around each octane molecule decreases and the octane molecule distribution becomes looser. This phenomenon tells us that, when the CO2 molecules are dissolved in octane, the volume of oils inside the pore expands. The volume expansion of octane in the nanopore can certainly increase the pressure, and thus alter the Laplace pressure difference to modulate the
oil-water interface. In addition, it can be observed in Fig. 8(a) that, when t=525 ps, the carbon dioxide molecules at the oil-water interface tend to arrange their postures to adapt to the interface shape. After some time, such as when t=1500 ps, the molecules at the interface modulate their postures and tend to become perpendicular to the interface, as shown in Fig. 8(b). Evidently, this posture modulation may provide extra space for more CO2 molecules to accumulate there, and to promote CO2 molecules into oils. This may be one of the reasons for roughness enhancement at the interface. It is clear that, this arrangement of CO2 molecules may be similar to the case of a cell entry of one-dimensional nanomaterials by its tip recognition and rotation (Shi et al., 2011).
3.4. Energy analysis As mentioned above, residual oils are initially confined in the silica nanopore and adsorbed on its inner surface. Many experiments (Cui et al., 2017) and simulations (Liu et al., 2016; Makimura et al., 2013) show that carbon dioxide molecules can pierce into the water-oil interface, and diffuse into the octane, as demonstrated in Fig. 2. As a consequence, the CO2 molecules detach oils from the surface, which plays a significant role in CO2 EOR. The underlying mechanism of displacement can be explained from the viewpoint of interaction energy between molecules. As shown in Fig. 9(a), at the very beginning, the pore is full of octane, and the interaction energy between SiO2 and octane is calculated as E=–380 kcal/mol while that between SiO2 and CO2 is zero, where the negative sign means the interplay is attractive between two substances (Fermeglia et al., 2003). As more and more CO2 molecules go into the pore and attach on the silica surface, the adsorption ability of the silica surface to oil becomes much weaker, as the interaction energy between them becomes smaller and
smaller and finally attains to zero. On the contrary, the attraction energy between CO2 and silica E becomes gradually bigger, whose value changes from zero to –520 kcal/mol, and the adsorption of CO2 on the silica surface nearly reaches the state of saturation, as shown in Fig. 9(a). The interaction energy difference manifests that the attraction of SiO2–C8H18 is weaker than that of SiO2–CO2, and a natural conclusion can be drawn is that, octane is prone to be replaced by CO2. From the viewpoint of thermodynamics, the whole evolution of the system including SiO2, CO2, Oil and H2O depends on its free energy, and the equilibrium state must be that with lowest free energy when the external work is zero. The Helmholtz free energy is expressed as F=U–TS,
(4)
where U is the potential energy of the system, T is the temperature and S is the entropy. The total potential energy originates from the short range van der Waals (vdW) interaction energy and the long-range electrostatic interaction energy, which can be written as 15
U = ∑Ui ,
(5)
i
where the 15 terms are composed of the interaction energies of the graphene plate, the silica, the carbon dioxide molecules, the water molecules and the octane molecules; and the remaining 10 terms are the result of combinatorial arrangement of the above 5 energies. For the current system, when the pressure reaches 30 MPa, the displacement of the plate is very small via the simulation result, so that the input work is close to zero. The computational results in Fig. 9(b) show that the potential energy of the system U decreases with time increasing, and the entropy S must increase according to the second law of thermodynamics. As a consequence, at the condition of constant temperature and constant pressure, we can ascertain that the free energy of the whole system keeps decreasing with time, i.e. dF<0. It is suggested that the system tends to evolve to the state with a smaller free energy,
and the oil displacement process can happen.
3.5. Potential applications Obviously, the previous simulations show that the injected CO2 molecules can enhance the displacement of oils, and the oil recovery factor at nanoscale can be computed. It can be defined as
R1 =
N1 − N 2 , N1
(6)
where N2 is the number of residual octane molecules after displacement, and N1 is the number of original octane molecules in the pore. In the calculation, N1 is equal to 270. The subfigure in Fig. 10 indicates that the number of residual oil molecules N2 decreases and finally reaches to a stable value of 48, and this tendency is consistent with the previous simulation (Fang et al., 2018). As a consequence, it is shown in Fig. 10 that, when t=1705 ps, the oil recovery factor becomes bigger than zero. Moreover, the value of the oil recovery factor increases with the time, and it can finally attain to the value as high as 82%. From the macroscopic viewpoint, the oil recovery factor in the process of oil displacement is defined as
R2 =
V1 − V2 , V1
(7)
where V1 is the initial volume of the oil, and V2 is the volume expelled by water or some other solutions. The reported results on the oil recovery experiment show that the value of R2 is normally in the range of 40%–70% due to different methods and geological conditions. Especially, a recent experiment shows that the oil recovery factor driven by CO2 can amount to 94% (Cui et al., 2017), which is higher than our simulation result.
Although the pores at nanoscale and macroscale are geometrically similar, the results from MD cannot be enlarged proportionally to get the macroscopic values according to their geometric similarity, as the physical mechanisms are different. It can be imagined that, for the macroscopic experiment, the adsorption effect of the silicon surface is small, while at nanoscale this effect becomes comparatively larger due to the interaction between the molecules and solid surface. This is the well-known surface effect, and it can be conjectured that the oil recovery factor is smaller than that at macroscale. What’s more, the oil recovery factor can be determined by many parameters, such as molecular interaction among different liquids (CO2, C8H18, H2O), density of liquids, wettability of the pore, geometry of the pore, roughness of the pore, velocity and pressure of liquids, temperature and humidity, etc. It is also seen that the current geometric model in our simulation is not the same from the previous setup at macroscale (Cui et al., 2017). Another possible reason may be attributed to the difference between the experimental setup (Cui et al., 2017) and our simulation model, where the directions of the pressure are distinct. Besides these, the components of octane in our simulation and the macroscopic experiment are different. Regardless of these differences, the two values on the oil recovery factor are at the same order, and the experiment at macroscale has the same tendency with our simulation result at nanoscale. In order to correlate the MD simulation result with the macroscopic experiment, the multiscale simulation technique must be explored for the next step.
4. Conclusions In conclusion, a comprehensive study based on MD simulation is performed to probe the displacement of residual oils trapped in a dead-end nanopore which is enveloped by a water film,
where the oils are driven by the supercritical carbon dioxide molecules. The main conclusion is that the excellent diffusion capacity of CO2 plays a key role in the whole molecule motion. Firstly, when the carbon dioxide molecules diffuse into the water film, the hydrogen bonds are broken, and there is a collapsed hole formed, which becomes the channel for CO2 going into the pore. Secondly, when sufficient CO2 molecules aggregate at the oil-water interface, the roughness of the interface is enhanced. Thirdly, the curvature of the oil-water interface becomes bigger, where one reason is that the accumulation of CO2 molecules on the interface alters the interfacial tension, and the other is that the swelling of oils caused by the invasion of CO2 inside the pore. Fourthly, it is observed that the alignment of oil molecules on the oil-water interface can spontaneously modulate their postures to more easily pierce into the water film. Next, the displacement mechanism is also explained by the energy principle. The interaction energy between CO2 and silica is bigger than that between octane and silica, and this fact makes CO2 favorable to detach the oil from silica. Moreover, the whole evolution process of the system can be formulated by the energy principle. At last, we calculate the oil recovery factor, which can amount to the value as high as 82%. It should be mentioned that, there are some practical factors which should be further considered in simulation, such as the roughness of the pore surface, the geometry of the pore, the temperature and pressure effects, which deserve to be examined in future studies. Regardless of these issues, our findings can strengthen the understandings on the details of the residual oil displacement in rocks, which may provide some inspirations on the oil recovery enhancement. In order to get a quantitative correlation between the MD and macroscopic experiment, we hope to develop a multiscale simulation technique in the near future.
Acknowledgements This project was supported by the National Natural Science Foundation of China (11672335 and 11972375).
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Figure captions
Figure 1 Overall configuration diagram with dimensions of the dead-end pore. Color codes for atoms are, purple: CO2; cyan: water; grey: octane; yellow, silicon; red, oxygen; and white, hydroxyl hydrogen (Hh).
Figure 2 The whole displacement of oils by carbon dioxide inside a nanopore at (a) t=305 ps, (b) t=605 ps, (c) t=1235 ps, with a snapshot of Hydrogen bond formed between the silica surface and CO2 molecules when t=1235 ps. The H-bond is highlighted as a red dashed line between the oxygen from CO2 (in purple) and the hydroxyl hydrogen from SiO2 (in white) inside the red frame. In succession, (d) t=1710 ps, (e) t=1795 ps, and (f) t=2020 ps. The enlarged views of water film clearings have been marked by the red circles in (d), (e) and (f) respectively.
Figure 3 Details (top View) of carbon dioxide diffusing into the water film at (a) t=1700 ps, (b) t=1702 ps, (c) t=1704 ps, and (d) t=1706 ps, and snapshots (top View) of hydrogen bonds in the water film at (e) t=1700 ps, (f) t=1702 ps, (g) t=1704 ps and (h) t=1706 ps. The blue circles highlight where the hydrogen bonds have been broken and the hydrogen bond is highlighted as a purple dashed line between the oxygen (in red) and hydrogen (in white).
1150 (a)
NH
1100 1050 1000 0
1200
500
(b)
1000 S (Å2)
1000 1500 2000 2500 t (ps)
800
1 2
600 400
1, Measured Value 2, Fitted Value
200 0 1600 1800 2000 2200 2400 2600 t (ps)
Figure 4 Hydrogen bond number and hole area of the water film. (a) Number of hydrogen bonds in water decreases with CO2 dissolved in water. (b) Area of the main hole on the water film increases with the increase of time (1705 ps < t ≤ 2500 ps )
120 t=1705 ps
80 200 2
60 NCO
NO-W/NW (%)
100
40
t=1705 ps
150 100
20
1
1, Nw 2, NO-W
50 2 0
0 0
0
3000
6000
9000
t (ps)
12000
15000
3000 6000 9000 12000 15000 t (ps)
Figure 5 Ratio between the number of CO2 at the oil-water interface to that in water. The subfigure shows the number of CO2 dissolved in water NW and that of CO2 accumulated at the oil-water interface NO-W.
Figure 6 Configurations of the roughness, the shape of the meniscus of the oil-water interface at (a) t=565 ps, (b) t=1075 ps and (c) t=1675 ps respectively in which ρ is the curvature radius, ߠ is the contact angle between the vertical line (silica wall) and tangential line of the oil-water interface at the triple contact point, and R is the radius of the nanopore.
1, t=535 ps 2, t=1505 ps 3, t=2250 ps 4, t=4250 ps
g (r)
15 10
1 2 3
5 4
0
0
5
10 r (Å)
15
Figure 7 Radial distribution function of octane-octane at t=535 ps, 1505 ps, 2250 ps and 4250 ps, respectively.
Figure 8 Alignment of octane molecules at the oil-water interface, at (a) t=525 ps when CO2 at the oil-water interface tend to adapt to the interface shape and (b) t=1500 ps when CO2 tend to become perpendicular to the interface.
E (kcal/mol)
0
(a)
1
-200
1, C8H18/SiO2 2, CO2/SiO2
-400
2
-600
t=1705 ps
0
t=4830 ps
3000 6000 9000 12000 15000 t (ps)
U (kcal/mol)
12407200 (b)
12406800
12406400
12406000 0
3000
6000
9000
12000 15000
t (ps) Figure 9 Energy diagrams. (a) Interaction energy between C8H18 and SiO2, and that between CO2 and SiO2. (b) Total potential energy evolution with respect to the time.
100 t=1705 ps
60
300 250 N2
R1 (%)
80
40
200 Residual C8H18
150 100
20
t=1705 ps
50 0
0
0
3000
6000 9000 t (ps)
12000 15000
3000 6000 9000 12000 15000 t (ps)
Figure 10 Oil recovery factor driven by CO2 with respect to the time, where the subfigure gives the molecule number of residual octane molecules.
The whole displacement process is fully demonstrated by snapshots of MD simulation.
The hydrogen bonds and the evolution of ruptured hole on the water film are discussed.
The configuration of the oil-water interface is computed and analyzed by the Laplace equation.
The displacement mechanism of octane by carbon dioxide is explained according to the energy principle.
Author Contribution Statement
Yalin Luan: Methodology, Software Bing Liu: Conceptualization, Methodology, Software Peng Hao: Software, Validation Kaiyun Zhan: Software Jianlin Liu: Conceptualization, Methodology, Writing-Reviewing and Editing
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: