Molecular-Scale Considerations of Enhanced Oil Recovery in Shale

With only less than 10% recovery, the primary production of hydrocarbon from shale reservoirs has redefined the energy equation in the world. Similar to conventional reservoirs, Enhanced Oil Recovery (EOR) techniques could be devised to enhance the current recovery factors. However, shale reservoirs possess unique characteristics that significantly affect the fluid properties. Therefore, we are adopting a molecular simulation approach that is well-suited to account for these effects to evaluate the performance of three different gases, methane, carbon dioxide and nitrogen, to recover the hydrocarbons from rough pore surfaces. Our hydrocarbon systems consists of either a single component (decane) or more than one component (decane and pentane). We simulated cases where concurrent and countercurrent displacement is studied. For concurrent displacement (injected fluids displace hydrocarbons towards the production region), we found that nitrogen and methane yielded similar recovery; however nitrogen exhibited a faster breakthrough. On the other hand, carbon dioxide was more effective in extracting the hydrocarbons when sufficient pressure was maintained. For countercurrent displacement (gases are injected and hydrocarbons are produced from the same direction), methane was found to be more effective, followed by carbon dioxide and nitrogen. In all cases, confinement reduced the recovery factor of all gases. This work provides insights to devise strategies to improve the current recovery factors observed in shale reservoirs.


Introduction
While abundant, shale formations are unique and serve as unconventional hosts for hydrocarbons [1]. In recent times, a shale revolution has redefined the energy equation in the world [2]. Although the hydrocarbon content of these reservoirs was known for long, the economic developments of these reservoirs became possible only by the coupling of multi-stage hydraulic fracturing with horizontal drilling [3][4][5]. This coupling overcomes the ultra-low permeability nature of the shale by providing highly conductive pathways connecting the natural fractures. However, the current recovery factors are less than 10%, even with the most efficient completion schemes [6,7].
Enhanced oil recovery techniques have been widely-used in conventional reservoirs [8,9]. Some provide pressure maintenance and others improve the hydrocarbon mobility by tuning the interfacial and physical properties of the reservoir fluids [10]. In contrary to conventional reservoirs, the interconnectivity between shale wells does not always warrant a field-wide design of EOR operations [11,12]. Alternatively, single-well approaches have been proposed [13,14]. Zhang et al. [15] numerically evaluated the efficiency of cyclic methane injection considering both the molecular diffusion and nano-confinement effects. Their results suggest implementing a cyclic injection strategy during the early stages of production. On the other hand, Meng et al. [16] evaluated the efficiency of carbon dioxide cyclic injection, and they experimentally observed more than 30% increase in the recovery.
On the other hand, CO 2 injection disrobes the hydrocarbon from the pore surface, which enhances the extraction of heavier components.
Fluid behavior and phase properties deviate from the bulk behavior under confinement [48][49][50]. Consequently, confinement affects the efficiency of the gases to extract liquid hydrocarbons and requires revisiting both the design and the operation to account for the confinement effects. We used molecular dynamics to evaluate the performance of various gases for enhancing the hydrocarbon recovery from shale formations. We organized the rest of this article as follows: the methodology section briefly presents the modeling approach and the simulation details, and the results section discusses the impact of confinement and operational parameters on the performance of different gases. The main findings are summarized in the conclusions section.

Methods
In this section, we briefly present the modeling approach and the simulation details.

Modeling Approach
Molecular dynamics rely on decoupling between the nucleus and electron motions. While the nucleus motion is classically treated through Newton's mechanics, the effects of the electron motions are considered through partial charges placed on the molecular structure. The force field is a set of equations that describe the molecular interactions and includes intermolecular and intramolecular interactions. Intermolecular interactions describe the interactions among atoms from different molecular entities and include both the Van der Waals (VDW) and electrostatics interactions. While the Lenard Jones potential (Equation (1)) is one of the widely-used models to model the VDW interactions, electrostatic interactions are modeled by Coulomb's law (Equation (2)). On the other hand, the intramolecular interactions maintain the molecular entity and include the bond, angle, dihedral and improper interactions. Given the initial configuration of the system and the molecular interactions, where ε is the depth of the potential well (dimensions: ML 2 T −2 ), σ is the distance at which the potential energy is zero (dimension: L), Q is the atomic charge (dimension: AT) and 0 is the permittivity of free space (dimensions: M −1 L −3 T 4 A 2 ).

Simulation Details
We used graphite to represent the pore material, decane and pentane to represent the hydrocarbons and carbon dioxide, respectively, and nitrogen and methane to represent the EOR's gases. We elected to simulate rough solid surfaces, which realistically capture the complexity of the porous media. As shown in Figure 1, our system consists of a silt pore connected to a reservoir containing the EOR's gas. This reservoir is constrained by a wall that acts as a fixed boundary or constant-rate boundary. In addition, a production region is defined on the other side of the pore. The whole simulation matrix is shown in Table 1. The dimensions of the simulation cell are lx = 504 Å, ly = 42.6 Å and lz = 90/70 Å. The solid substrate comprise three sheets of graphite. We used equal molar gas density for all gases. Note that equal gas densities do not correspond to equal fluid pressures, as shown in Figure 2. (c) the EOR gas equilibration; (d) the system extended to include a production region, where the pore was opened for production and a constant-velocity wall is allowed; (e) the system after 0.1 ns; (f) the system after 0.5 ns; (g) the system after 1 ns. Color code: red is graphite, blue is gas and yellow is hydrocarbon.  We used the OPLS_UA force field [52] to model the hydrocarbon interactions and united-atom force fields for the EOR's gases as detailed in Table 2. We used Moltemplate software to set up the initial system [53] and LAMMPS to run all the simulations [54]. We started by annealing the hydrocarbons inside the pore for 0.1 ns using canonical ensemble and then equilibrating the EOR's gas for 0.1 ns. After that, the simulation was extended to include a production region (an extra 250 Å in the x-direction). In this scenario, we simulated concurrent displacement, where both the injected fluid and hydrocarbons are moving in the same directions. For constant-rate boundary cases, we applied a constant velocity of 0.0002 Kcal/mole-Angstrom on the wall. We ran the simulation for 1 ns and recorded the hydrocarbon production. We created rough surfaces by carving out grooves inside the solid substrate. We used the Lorentz-Berthelot mixing rules to model the cross interactions. We used the Nosé-Hoover thermostat with a damping parameter of 100 time steps. We also simulated the Huff and Puff process, where the EOR's gas is kept in contact with the hydrocarbon system for 10 ns. After that, the region of the EOR's gas is evacuated to allow the hydrocarbon recovery. This scenario depicts countercurrent displacement. We recorded the production for another 5 ns.

Results
In the section, we discuss the results of our single, binary and confined systems.

Concurrent Displacement
We used the recovery factor as a quantitative measure of the gas efficiency to extract the hydrocarbons from the pore. We estimated the recovery factor by normalizing the number of hydrocarbon molecules leaving the systems by the total number of hydrocarbon molecules in the system. Figures 3 and 4 present the performance of different gases to extract single-component hydrocarbon systems with and without constant-rate injection. We observed that both nitrogen and methane yielded similar recovery factors with and without injection. However, nitrogen exhibited faster breakthrough and displacement compared to carbon dioxide and methane, respectively. We could attribute this behavior to the miscibility of each gas in the hydrocarbons [55]. Given that the solubility of nitrogen in decane is only 15% of that of carbon dioxide at 5 MPa and 50 • C with more than six times minimum miscibility pressure at a temperature of 343.2 K, nitrogen had a stable displacement front and in turn a faster breakthrough [56][57][58][59][60]. In addition, we observed lower recovery rates for all gases without injection. However, the reduction in the case of CO 2 was the most significant, where the breakthrough was not achieved.  On the other hand, carbon dioxide had better results than the rest with continuous injection and worse than the rest without injection. This could be attributed to the superior adsorption and diffusion characteristics of supercritical CO 2 , which allow the extraction of the trapped hydrocarbons in the pore grooves [61,62]. While carbon dioxide could not achieve the breakthrough without the injection, it did not induce a phase separation. Li et al. [63] experimentally and numerically compared the performance of miscible and immiscible CO 2 displacement using the recovery factor. In our case, we believe that the miscibility was initially achieved; however there was no pressure to maintain the miscible front.
Herein, our hydrocarbon system is a multi-component system with a 50:50 mixture of pentane and decane. Figure 5 presents the results of the multi-component systems. Regardless of the boundary conditions, more pentane was extracted compared to decane. Similar to the single-component systems, both nitrogen and methane had similar recovery factors. However, methane and nitrogen had the same displacement speed. In addition, CO 2 still yielded a relatively slower and better performance with constant-rate injection. However, it failed to reach the breakthrough without the injection. It is worth noting that the methane performance was quite different than in the single-component system, especially regarding the displacement speed. This behavior could be attributed to a stable displacement front caused by diluting the decane with pentane. Therefore, there is limited room for methane solubility before phase separation. On the other hand, the pentane presence did not affect the carbon dioxide performance. As the pore width decreased, we observed that the displacement of hydrocarbons became slower. Figure 6 presents the gas performance to extract single-component systems from confined pores (2 nm). For constant-rate injection scenarios, nitrogen started to displace the hydrocarbons faster than the rest. However, both methane and carbon dioxide eventually yielded better recovery rates. We observed a no-production period for all gases at the start, which was shorter for nitrogen. This period might be attributed to the stronger adsorption hydrocarbons experienced as the pore size decreases. Theoretically, higher capillary pressure is required for gases to enter smaller pores. However, our results suggest that both cases, with and without injection, start to displace hydrocarbons around the same time. This behavior could be attributed to the compressibility of the injected fluid. Even though we did not observe significant impacts on the boundary conditions in the early stages, significant effects were observed later on. It is worth noting that the curve shape of the recovery factor of confined pores differs from the one observed from large pores. In confined pores, we observed more of a convex shape compared to the linear response observed in large pores. In addition, the breakthrough is more transitional instead of the abrupt change observed in large pores. Both observations suggest a stronger adsorption of hydrocarbons on the pore surface under confinement. On the other hand, less recovery is observed without injection. Both methane and carbon dioxide did not reach the breakthrough. However, methane had a slightly better recovery than carbon dioxide.

Countercurrent Displacement
In this section, we simulate the performance of the gases to extract single-component hydrocarbon systems. The gases were soaked in contact with the hydrocarbon system for 10 ns, while the hydrocarbons were extracted from the pore to the EOR's gas region. Figure 7 presents the results of the Huff and Puff simulations. During the soaking time, CH 4 was the most effective in extracting the hydrocarbon, followed by CO 2 and then N 2 . As the puff process started, a large influx of hydrocarbons left the pore. We observed that some of the hydrocarbons returned back to the pore for 5 nm cases, especially with nitrogen or methane. While similar behavior was observed for 2 nm pores, less recovery was observed for all gases. In addition, the CO 2 s performance was relatively improved compared to the methane. While reduced compared to the concurrent displacement, the countercurrent displacement's recovery factors were in line with field observations and recent molecular simulation studies [64,65]. The superiority of CO 2 over N 2 has been previously experimentally and numerically reported. However, we found that CH 4 outperformed all of them in this scenario. This behavior could be attributed to the better vaporization characteristics of methane [66,67]. Field recommendations include using CO 2 for multi-well EOR operations and CH 4 for single-well EOR operations. In addition, the injection pressure significantly affects the CO 2 performance. Consequently, pressure support should be maintained throughout the operations. While valid, these recommendations were derived based on single-pore simulations with single or binary component hydrocarbons. However, the heterogeneity of the porous media and the complexity of the crude oil mixture might dramatically affect the EOR operations. Therefore, further research is required to quantify the impact of these factors along with more integrated lab and field pilots.

Conclusions
In this study, we have conducted a comprehensive molecular simulation study to examine the efficiency of carbon dioxide, nitrogen and methane to extract hydrocarbons from organic rough pores. We found that: • Confinement enhances the adsorption of hydrocarbons to the pore surface, which hinders both concurrent and counter-current displacements.

•
All gases are more efficient in displacing hydrocarbons in concurrent displacement relative to counter-current displacement. While the recovery factors observed in counter-current displacements are usually less than 20%, the concurrent displacement could reach up to 90%. • Nitrogen usually exhibited faster breakthrough regardless of the hydrocarbons' type, pore size and the boundary conditions for the concurrent displacement. Interestingly, the limited diffusion and miscibility of nitrogen in hydrocarbons led to faster recovery in the case of concurrent displacement, while the opposite was observed for counter-current displacement. On the other hand, methane yielded better recovery for counter-current displacement.

•
Carbon dioxide proved more efficient in extracting the hydrocarbons from rough pores (from the grooves) if enough pressure was maintained. Having favorable adsorption characteristics and capability to improve the hydrocarbon mobility, carbon dioxide provides the best candidate. However, constant pressure support is needed to overcome the unstable displacement front.

Conflicts of Interest:
The authors declare no conflict of interest.