Microscopic Mechanism for the Displacement of Shale Oil by CO₂ in Organic Nanopores

Abstract

The effective displacement of the shale oil from organic nanopores plays a significant role in development of the shale oil reservoirs. In order to deeply understand the microscopic displacement mechanism of alkane of shale oil by CO₂ in organic nanopores, microscopic pore model of organic matter and molecular model of CO₂ and n-dodecane were established to investigate the influences of key parameters on the displacement process by using the Monte Carlo and molecular dynamics simulation method. The instantaneous adsorption of molecules demonstrates that the displacement of n-dodecane and the adsorption of CO₂ are proportional to the increase of the injection pressure of CO₂ as well as the pore size. In addition, the results also show that the adsorption capacity of CO₂ first increases and then decreases with the increase of the temperature, which indicates that the optimum temperature exists for the adsorption of CO₂. This work can provide critical insights into understanding the microscopic displacement mechanism of shale oil by CO₂ in organic nanopores in shale oil reservoirs and lay a solid foundation for the CO₂ flooding in the shale oil reservoir and the CO₂ storage.

1. Introduction

With the increasing demand for energy in the world and the gradual depletion of conventional oil and gas resources, it is an inevitable trend to seek another unconventional alternative energy in the future. Generally, shale oil is a very typical unconventional resource, and thus can be regarded as an important alternative energy source [1,2,3].

During the six periods of Early Silurian, Late Devonian, Late Carboniferous to Early Permian, Late Jurassic, Cretaceous, and Oligocene-Miocene, shale was widely deposited worldwide. During the formation period of the four sets of shale strata, the Upper Jurassic, Oligocene-Miocene, Cretaceous and Upper Devonian, the global temperature and humidity were relatively high, which was favorable for the formation and preservation of type I–II organic matter. The oil is mainly enriched in these layers, accounting for 87.83% of the total resources [3].

In recent years, shale oil is increasingly playing an important role in the energy supply, and then the adsorption and resolution of shale oil in nanopores has drawn extensive attention [4,5].Wang et al. [6] employed molecular dynamics (MD) simulation to study adsorption behavior of shale oil within nanoscale carbonaceous slits in shale system and they found that the adsorption portion of liquid n-alkanes always consists of multimolecular layers, and the thickness of each layer is approximately 0.48 nm under shale reservoir conditions. Based on N₂ and CO₂ composited adsorption isotherms, Wang et al. [7] established a simplified pillar-layer model to investigate CH₄ adsorption behavior and competitive adsorption effect between CO₂ and CH₄ and they concluded that CO₂ has stronger competitive adsorption ability than CH₄. Pang et al. [5] employed the experimental and analytical method to investigate the gas adsorption in organic nanopores and they insisted that the gas adsorption decreased greatly in organic nanopores due to the effect of the moisture. Lately, Hazra et al. [8] used the low-pressure adsorption techniques to study the adsorption-desorption isotherms of the organic-rich Permian shales and they indicated that a strong positive relationship may be exist between the pore radius and the difference in volumes of gas. Memon et al. [9] adopted two supercritical CO₂ fracturing tests and low-pressure N₂ adsorption experiments to stimulate the supercritical CO₂-shale interactions during fracturing and they concluded that adsorption swelling can make the reduction of fracture aperture. The topics of the above literature mainly focus on the adsorption and resolution of shale oil in nanopores, the displacement of the shale oil from organic nanopores or inorganic nanopores by CO₂ is not taken into consideration.

The displacement of the shale oil from organic nanopores or inorganic nanopores by CO₂ has been extensively studied by many researchers [10,11,12]. Severson et al. [13] employed Monte Carlo method to study the effects of temperature and the length of carbon chain on the adsorption properties of alkanes in nanopores and found that the adsorption of alkanes with long-chain at high temperature is similar to that of alkanes with short-chain at low temperature. Lately, Pathak et al. [14] presented the adsorption and desorption of methane and CO₂ in methane-CO₂-kerogen system and concluded that CO₂ can effectively displace shale gas trapped in shale nanopores. Wang et al. [15] studied the storage morphology of linear alkanes in nanopores formed from organic by molecular dynamics simulation, and suggested that several adsorption layers of alkanes exist on the surface of nanopores and the thickness of the adsorption layer is about 0.42 nm. However, in the above literature, the effects of temperature, pore size, pressure and other comprehensive conditions on the adsorption mechanism in organic nanopores of shale reservoir are not studied. Recently, Haghshenas et al. [16] proposed the compositional simulation model to study the effect of fluid component adsorption on the displacement of oil by the CO₂ huff-n-puff performance and they concluded that the lower saturation pressure may be better to obtain the better results than that with the higher saturation pressure fluid. Liu et al. [17] used the molecular simulations to investigate the competitive adsorption behavior of hydrocarbon(s)/CO₂ mixtures in a double-nanopore system and they concluded that the CH₄ will be easily adsorbed in nanopores as the decrease of the pressure due to the stronger adsorption capacity of CO₂ on organic pore surface. Zhu et al. [18] conducted an experiment to illustrate the effect of different factors (such as shale properties, n-alkanes type and temperature) on the adsorption and dissolution behaviors of CO₂ and n-alkane mixtures in shale reservoirs. The above study of Liu et al. [17] and Zhu et al. [18] provided a guideline for quantitatively characterizing the effect of the injection pressure of CO₂ on the displacement of shale oil in this work.

To further analyze the effect of the injection pressure of CO₂, pore size and temperature on the displacing process of shale oil by CO₂, Grand Canonical Monte Carlo method and molecular dynamics method are employed to construct the graphene pore model with a vacuum layer. Based on that, the displacement of typical alkanes and the adsorption capacity of CO₂ are further discussed in detail. In addition, the optimum injection pressure of CO₂, pore size and temperature for the displacement of shale oil by CO₂ are determined, which can provide a new idea for the CO₂ flooding in the shale oil reservoir and the CO₂ storage.

2. Simulation System

2.1. Model Construction

(1)

Single crystal cell structure of graphene was imported from the database of Materials Studio and thus the Graphene monolayer lamellae can be constructed. Then the pores-vacuum layers and supercell graphene pore model was built by the Super Cell in the database of Materials Studio respectively.

(2)

In pores of graphene, n-dodecane molecular are injected and the force field of n-dodecane was distributed by the Dreiding force field [19,20]. Subsequently, Atom Based was used to obtain the sum method of Van der Waals’ force and the electrostatic force in isochoric-isothermal ensemble (NVT). And then, the simulations are run by periodic boundary. The schematic for the pore structure of n-dodecane adsorbed is shown in Figure 1.

(3)

The pre-adsorption simulation of n-dodecane molecules in graphene pores was further conducted to obtain the stable adsorption configuration of n-dodecane. After that, CO₂ molecules with different injection pressures were added into the pore model to simulate and study the dynamic displacing process of n-dodecane molecules by CO₂ [21,22].

2.2. Optimization of Computational Model

Before the displacing simulation, structural model of graphene, CO₂ molecular model and n-dodecane molecular model should be optimized to obtain the energy minimization. Based on that, the optimized models are employed to conduct the molecular simulation [23]. The optimization steps of the computational models (including the structural model of graphene, CO₂ molecular model and n-dodecane molecular model) are as follows:

(4)

The SMART option in Task Geometry Optimization under the Forcite module of Molecular Dynamics was selected to optimize the geometry of the constructed model, and then the stable graphene slit structure was obtained;

(5)

The COMPASS force filed was selected to stimulate the force field and the sum method of Atom based was used to obtain the Van der Waals’ force;

(6)

The optimization of CO₂ molecular model and n-dodecane molecular model are similar to that of the structural model of graphene.

2.3. Calculation Method

Generally, the adsorption and free states of CO₂ and n-dodecane molecules in graphene pores are based on the interactional force between atoms and molecules. In this work, L-J potential energy model is adopted to analyze the potential energy between molecules and the potential energy of each molecule is listed in

Table 1. L-J potential energy of each molecule used in this work.

Site	σ/nm	(ε/KB)/K
CO2	0.363	242.0
C (CNT)	0.350	35.26
C12H26	0.785	715

. Meanwhile, to describe the Van der Waals’ force in the system, the following potential-energy function is employed,

$$U(ij)=4{\epsilon }_{ij}[{(\frac{{\sigma }_{ij}}{r_{ij}})}^{12}-{(\frac{{\sigma }_{ij}}{r_{ij}})}^6]+\frac{q^i{q}^j}{r_{ij}}$$

(1)

where r_ij represents the distance between the i-th particle and the j-th particle. qⁱ and q^j are the electric charge of i-th particle and j-th particle, respectively. ε is the the energy action parameter and σ is the dimensional action parameter.

2.4. Modeling Scheme

In this work, to simulate the dynamic displacing process of shale oil by CO₂ in pores of graphene, the long chain atom model and three-point hard-sphere linear model are used to represent n-dodecane molecule and CO₂ molecule, respectively. Meanwhile, the interactional forces between the CO₂ molecule, n-dodecane molecule and graphene slits are calculated by the L-J potential energy model. In order to simulate the effect of CO₂ displacing shale oil under different injection pressure of CO₂, different pore size and different temperature, Grand Canonical Monte Carlo (GCMC) method is further used. The simulation steps are as follows:

(1)

n-dodecane molecules must be adsorbed in pores of graphene in advance, and the adsorption capacity of n-dodecane molecules depends on the differential pressure of n-dodecane;

(2)

CO₂ molecules with differential pressures are injected into organic nanopores that reached stable adsorption state. And when the adsorption of CO₂ reached equilibrium state in pores, the injection of CO₂ should be stopped immediately;

(3)

The displacement capacity of n-dodecane and the adsorption capacity of CO₂ in pores are calculated when the adsorption equilibrium state is obtained;

(4)

Through the above simulation steps, single factor control variate method can be adopted to analyze the effects of injection pressure of CO₂, pore size and temperature on the displacement of n-dodecane and the adsorption of CO₂.

3. Results and Discussion

In this section, the effects of some parameters, such as the injection pressure of CO₂, pore size and temperature, on the displacement of shale oil by CO₂ are discussed in detail.

3.1. Injection Pressure of CO₂

In order to investigate the effect of the injection pressure of CO₂ on the displacement of shale oil, the molecular simulation process of this section is as follows,

(1)

The pore size of the pore model is fixed at 40 Å and the simulated temperature is set at 373 K and the differential pressure of n-dodecane is set at 30 MPa;

(2)

Before the molecular simulation, n-dodecane should be adsorbed on the pore wall in advance. After that, CO₂ is injected into the pore and the injection pressure of CO₂ gradually increases from 0 MPa to 90 MPa;

(3)

When the dynamic displacing process reached equilibrium, the displacement of n-dodecane and the adsorption of CO₂ were further analyzed with the increase of the injection pressure of CO₂.

Figure 2, Figure 3 and Figure 4 mainly show the instantaneous adsorption of molecules under the injection pressure of CO₂ at 0 MPa, 50 MPa and 90 MPa, respectively. In order to calculate the displacement of shale oil, the following equation is employed,

$$N_d=N_t-N_p$$

(2)

where N_d is the number of n-dodecane molecules displaced by CO₂. N_t is number of n-dodecane molecules absorbed in the pores when the injection pressure of CO₂ is 0 MPa. N_p is the number of n-dodecane molecules absorbed in the pores under differential CO₂ injection pressures.

In Figure 2a, the yellow spheres represent n-dodecane molecules, and the red and gray spheres are carbon dioxide molecules. As can be seen from Figure 2a, carbon dioxide molecules cannot be naturally adsorbed into pores, in which are fully absorbed by n-dodecane molecules in the surface of pores. When the injection pressure of CO₂ increases to some degree (such as 50 MPa, shown in Figure 2b), some n-dodecane molecules gradually enter into pores while some carbon dioxide molecules absorbed in the surface of pores tend to desorb and become free-state at the same time. When the injection pressure of CO₂ increases to 90 MPa (shown in Figure 2c), n-dodecane molecules completely desorb from pores and become free state, while at the same time, the surface of pores is almost absorbed by carbon dioxide molecules, which indicates that the adsorption capacity of CO₂ is much stronger than that of n-dodecane under reservoir conditions and the adsorbed shale oil can be fully displaced by CO₂ when the injection pressure of CO₂ is large enough.

Based on Equation (2), the displacement of n-dodecane and the adsorption of CO₂ can be calculated, shown in Figure 3. As can be seen from Figure 3, the displacement of n-dodecane can be more sensitive when the injection pressure of CO₂ is smaller than 60 MPa. Taking relation between the displacement of n-dodecane and the injection pressure of CO₂ as an example, when the injection pressure of CO₂ increases from 10 MPa to 40 MPa, the displacement of n-dodecane accordingly increase from 13.93 mol/uc to 48.93 mol/uc with an increasing ratio of 251.26%. When the injection pressure of CO₂ increases from 60 MPa to 90 MPa, the increasing ratio is only 9.69%. This phenomenon indicates that the absorbed shale oil is mainly displaced when the injection pressure of CO₂ is smaller than 60 MPa. Meanwhile, when the injection pressure of CO₂ is less than 20 MPa, the adsorption of CO₂ rises sharply as the increase of the injection pressure. For instance, the adsorption of CO₂ rises from 368.36 mol/uc to 488.65 mol/uc with an increasing ratio of 32.66% when the injection pressure of CO₂ accordingly increases from 10 MPa to 20 MPa, while the increasing ratio is only 0.38% when the injection pressure of CO₂ increases from 80 MPa to 90 MPa. The underlying cause for this phenomenon may be that the interactional force between the carbon dioxide molecules and the surface of pores tends to increase with the growth of the injection pressure of CO₂. From the above phenomenon, we can conclude that the displacement of shale oil by CO₂ is positively correlated with the injection pressure of CO₂ and CO₂ can be stored in shale reservoirs when the injection pressure of CO₂ is larger than 20 MPa, which can provide new thought for carbon dioxide storage.

3.2. Pore Size

In order to comprehensively investigate the influence of the pore size on the displacement of shale oil by CO₂, the pore size ranges from 20 Å to 60 Å and the instantaneous adsorption of molecules are displayed in Figure 4. Meanwhile, the displacing process of n-dodecane is assumed to be constant temperature to avoid the influence of temperature (T = 373 K). Generally, reservoir pressure plays a significant role in the adsorption of n-dodecane in pores and thus we should study the influence of pore size on the adsorption of n-dodecane under different reservoir pressures, shown in Figure 5.

It can be seen from Figure 4, adsorption layers exist on the surface of pores while the thickness of adsorption layers are significantly various when the pore size is different. Generally, the adsorption of molecules in the surface of pores increases exponentially with the increase of the pore size and thus the thickness of adsorption layers will be greatly increased. This phenomenon can be explained by that with the increase of the pore size, the interaction between molecules gradually increases, and the molecular motion becomes more severe, which increases the probability of collision between n-dodecane molecules and pores. Meanwhile, due to the collision between n-dodecane molecules and pores, n-dodecane molecules will be desorbed from the surface of pores and accordingly CO₂ will be adsorbed into the corresponding pores.

As can be observed from Figure 5, the adsorption of n-dodecane is proportional to the pore size for a fixed injection pressure of CO₂. From Figure 5, we can find that the increase of the adsorption of n-dodecane is slightly different when the pore size has an equal increase. For example, at P_iCO2 = 10 MPa, the adsorption of n-dodecane increases from 60.35 mol/uc to 75.66 mol/uc with an increasing ratio of 25.37% when the pore size accordingly increases from 20 Å to 30 Å while the increasing ratio can up to 51.53% if the pore size increases from 50 Å to 60 Å, which indicates that the larger the pore size is, the easier the adsorption of n-dodecane obtains. Meanwhile, as the increase of the injection pressure of CO₂, the increasing degree of n-dodecane tends to be weakened with the increase of the pore size. For instance, at P_iCO2 = 50 MPa, when the pore size increases from 20 Å to 30 Å, the increasing ratio of the adsorption of n-dodecane is only 20. 41% while under the same condition, the increasing ratio of the adsorption can up to 47.88% at P_iCO2 = 20 MPa. In addition, when the pore size is fixed at 60 Å, the adsorption of n-dodecane increases first and then decrease with the increases of the injection pressure of CO₂, while for other cases, the adsorption of n-dodecane decreases with the increase of the injection pressure, shown in Figure 5. The underlying cause for this phenomenon may be that, for a pore large enough, the small amount of injected CO₂ has difficulty to move to the pore wall to displace adsorbed n-dodecane considering the great distances of CO₂ molecules to the wall. The total bulk pressure, including the bulk pressure of n-dodecane would be increased, which bring higher adsorption amount of n-dodecane. With injection pressure increasing, more CO₂ molecules appear in the pore, and there is higher opportunity to reach the pore wall to replace adsorbed n-dodecane. As a result, the adsorption of n-dodecane would decrease.

Generally, the displacement of shale oil by CO₂ always depends on the adsorption of CO₂ and thus the effect of the pore size on the adsorption of CO₂ should be discussed in detail, shown in Figure 6. As can be seen from Figure 6, when the pore size ranges from 20 Å to 50 Å, the increase of the adsorption capability of CO₂ becomes slowly with the increase of the pore size, while when the pore size increases from 50 Å to 60 Å, the adsorption capability of CO₂ increases rapidly. For example, at P_iCO2 = 10 MPa, the adsorption capability of CO₂ increases from 312.66 mol/uc to 333.25 mol/uc with an increasing ratio of 6.59% when the pore size accordingly increases from 20 Å to 30 Å, while the increasing ratio can reach 22.64% when the pore size increases from 50 Å to 60 Å. This phenomenon implies that when the pore size of shale matrix reaches 60 Å by hydraulic fracturing or acid fracturing technology, the production of shale oil can increase dramatically due to the huge increase of the adsorption of CO₂. Meanwhile, when the injection pressure of CO₂ is greater than 20 MPa, the effect of the pore size on the adsorption of CO₂ tends to be stable, showing that the adsorption curves of different pore sizes are parallel to each other.

After that, the effect of the pore size on the displacement of n-dodecane under the CO₂ injection pressure of 60 MPa is discussed in Figure 7. As displayed in Figure 7, the displacement of n-dodecane increased with the increase of pore size, and the increasing degree tends to be strengthened when the pore size changes from 30 Å to 40 Å. The displacement capacity of n-dodecane increases from 43.97 mol/uc to 50.16 mol/uc when the pore size accordingly increases from 20 Å to 30 Å with an increasing ratio of 14.07%, while the increasing ratio is 43.38% when the pore size increases from 30 Å to 40 Å. From the above phenomenon, we can conclude that the larger the pore size is, the easier the displacement of shale oil by CO₂ is.

3.3. Temperature

In this section, we mainly discuss the effect of temperature on the displacement of the shale oil by CO₂. In order to fully reveal the effect of the temperature on the displacement of the shale oil, the pore size of the pore model is fixed at 40 Å and the differential pressure is assumed to be equal to 30 MPa.

The displacement of n-dodecane by CO₂ at different temperatures can be visually observed by analyzing the instantaneous adsorption of molecules, shown in Figure 8. At T = 353 K (Figure 8b), the adsorption capacity of n-dodecane in the surface of pores is obviously smaller than that at T = 333 K (Figure 8a), while the adsorption capacity of n-dodecane is similar to that of CO₂. Further, when we compare the instantaneous adsorption at T = 373 K (Figure 8c) and the instantaneous adsorption at T = 393 K (Figure 8d), we can observe that the adsorption of CO₂ is dominant and n-dodecane exists in the free state in pores. In particular, as can be seen from Figure 8d (T = 393 K), only a small amount of n-dodecane is adsorbed into the surface of pores, which implies that n-dodecane molecular are almost displaced by CO₂ under the above situation. In addition, when the temperature is fixed at T = 413 K (Figure 8e), we can find that all n-dodecane molecular originally adsorbed in the surface of pores are completely displaced, which can be explained by that the higher the temperature is, the higher the kinetic energy is, and thus the displacement of n-dodecane by CO₂ is accelerated.

Similarly, Figure 9 mainly illustrates the effect of the temperature on the adsorption of n-dodecane and Figure 10 is on the influence of the temperature on the adsorption of CO₂. As can be seen from Figure 9, the temperature is conducive to the adsorption of n-dodecane, which can be explained by that the higher the temperature is, the less energy the n-dodecane molecular need to adsorb into the surface of pores. However, the influence of the temperature on the adsorption of n-dodecane tends to be weakened with the increase of the injection pressure. For example, at P_iCO2 = 20 MPa, the adsorption capacity of n-dodecane decreases from 101 mol/uc to 90 mol/uc with a dropping ratio of 12.22% when the temperature decreases from 393 K to 373 K, while at P_iCO2 = 70 MPa, the dropping ratio is only 9.52% under the same condition.

From Figure 10, we can observe that when the temperature is lower than 393 K, the increase of the temperature is conductive to the adsorption of CO₂, while when the temperature is above 393 K, the adsorption capacity of CO₂ will be slightly reduced, which indicates that the optimum temperature for the adsorption of CO₂ is 393 K. The underlying cause for this phenomenon may be that when the temperature is over 393 K, Brownian movement of CO₂ will be greatly enhanced and thus more energy is needed to make CO₂ adsorbed into the surface of pores. Meanwhile, the effect of temperature on the adsorption of CO₂ is various at different injection pressures. For example, at P_iCO2 = 10 MPa, the adsorption capacity of CO₂ increases from 352.66 mol/uc to 368.36 mol/uc when the temperature accordingly increases from T = 333 K to T = 373 K with an increasing ratio of 4.45%, while at P_iCO2 = 60 MPa, the increasing ratio can up to 16.47% under the same condition. This phenomenon indicates that the effect of temperature on the adsorption of CO₂ is more sensitive under medium-high injection pressure.

Further, the effect of the temperature on the displacement of n-dodecane is displayed in Figure 11. As illustrated in Figure 11, we can observe that the displacement capacity of n-dodecane by CO₂ is stronger at higher temperature. And, when the temperature of shale oil reservoir is lower than 373 K, the displacement capacity of n-dodecane increases dramatically. For instance, when the temperature increases from T = 333 K to T = 373 K, the displacement capacity of n-dodecane increases from 28.97 mol/uc to 60.42 mol/uc with an increasing ratio of 108.56%, while the increasing ratio is only 16.57 % when the temperature increases from T = 373 K to T = 413 K. Based on that phenomenon, we can conclude that there is an optimal temperature that the maximum displacement capacity of shale oil by CO₂ can be obtained from the perspective of economic production.

4. Conclusions

In this work, Grand Canonical Monte Carlo and molecular dynamics methods are used to study the microscopic displacing process of n-dodecane by CO₂ in shale oil reservoirs. Based on the discussion on the displacement of n-dodecane and the adsorption capacity of CO₂ under different conditions, the following conclusions can be obtained:

(1)

The adsorption capacity of CO₂ is much stronger than that of shale oil under reservoir conditions, which indicates that shale oil can be effectively displaced by CO₂. And, the displacement capacity of shale oil by CO₂ and the adsorption capacity of CO₂ show a positive correlation with the injection pressure of CO₂.

(2)

The larger the pore size, the stronger the capacity to store shale oil and the easier it is for CO₂ to displace the shale oil. Moreover, when the pore size ranges from 20 Å to 50 Å, the adsorption capacity of n-dodecane decreases with the the injection pressure of CO₂. When the pore size reaches 60 Å, the adsorption capacity of n-dodecane fist increases under pressure less than 10 MPa and then decreases as the pressure increases larger than 10 MPa.

(3)

The adsorption capacity of CO₂ is highly sensitive to temperature. The adsorption capacity of CO₂ increases first and then decreases with the increase of the temperature and the highest adsorption capacity appeared at the temperature of 393 K, while the displacement capacity of n-dodecane increases with the increase of temperature. Overall, higher temperature is more favorable for the displacement of shale oil by CO₂.