Molecular Dynamics Study of Carbon Dioxide Storage in Carbon-Based Organic Nanopores

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1 Molecular Dynamics Study of Carbon Dioxide Storage in Carbon-Based Organic Nanopores Mohammad Kazemi and Ali Takbiri-Borujeni, West Virginia University Copyright 2016, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Dubai, UAE, September This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract With large scale production of gas from shale resources, large volumes of pore space have been vacated. Therefore, there is a large capacity for storage of carbon dioxide in these resources. Furthermore, due to the higher affinity of the organic matter to carbon dioxide compared to methane, injection of carbon dioxide can replace the adsorbed methane and therefore, enhances the recovery of natural gas. The objective for this work is to investigate the sorption (adsorption of carbon dioxide and desorption of methane) in carbonbased organic channels using Molecular Dynamics (MD) simulations. In this study, adsorption isotherms of methane and carbon dioxide are compared by performing grand canonical Monte Carlo (GCMC) simulations in identical setups of carbon channels. Excess and absolute adsorption isotherms of these gases are plotted and compared. Furthermore, the surface selectivity of carbon dioxide over methane is computed to determine the competitive adsorption of these two gases. To simulate the displacement process, MD simulations of displacement of methane molecules with carbon dioxide molecules in presence and absence of pressure gradients are performed. The results are compared for different values of gas pressures and pressure gradients. According to the results, adsorption capability of carbon dioxide is found to be higher than that of methane under the same pressure and temperature. The selectivity values of carbon dioxide over methane is found to be higher than the ones for pressure range of 100 to 200 atm, which shows that carbon dioxide molecules have higher affinity to the surface compared with methane. It is also found that carbon dioxide molecules replace adsorbed methane molecules due to their higher affinity to the surface. Concentration of methane sharply decreases as carbon dioxide molecules are introduced in the channel. The results show that the amount of carbon dioxide storage and methane production rate increases as injection pressure increases. The results in this study can impact on the research and development of new tools for both candidate selection (selection of the sites for carbon dioxide storage) and development of predictive models for estimating of the amount of carbon dioxide intake. Introduction Burning fossil fuels emits numerous amount of carbon dioxide that leads to irreversible climate changes. Furthermore, the world energy demand will increase by 50% by 2040 and this causes more emissions to

2 2 atmosphere (Sieminski, 2014). Carbon capture and sequestration (CCS) in depleted shale gas reservoirs provides an opportunity for underground storage of the carbon dioxide. Carbon dioxide affinity to the organic matter of shale compared to methane molecules makes its storage feasible in shale. Furthermore, injecting the carbon dioxide into the shale reservoirs can cause desorption of the trapped methane molecules (mostly found in adsorbed phase) and replacement with the carbon dioxide molecules. This process is called enhanced shale gas recovery. Current understanding of the competitive adsorption/desorption process of carbon dioxide and methane and its impact on the efficiency of CCS is still insufficient. In this study, competitive sorption process of carbon dioxide/methane in carbon-based organic nanopores is simulated by performing molecular dynamics simulations. There have been several studies on carbon dioxide storage and enhanced gas recovery in shale reservoirs. Cygan et al. (2012) carried out molecular simulations to study the molecular interactions in interlayer of montmorillonite. Their investigation showed that molecular dynamics simulations have the accuracy to predict the carbon carbon capture mechanisms in complex natural materials. Godec et al. (2013) investigated the enhanced gas production using reservoir simulations and found that 7% incremental enhanced gas production can be achieved by to carbon dioxide injection. They also found that Marcellus shale has the capacity of storing 55 billion tones (Gt) of carbon dioxide. However, they noted that lack of knowledge in sorption process of methane and carbon dioxide is one of uncertainties in their estimations. Liu and Wilcox (2012) performed grand canonical Monte Carlo (GCMC) simulations by including oxygen-containing functional groups to graphite and found that these groups can enhance the adsorption of carbon dioxide. They also studied the selectivity of carbon dioxide over methane. Based on their results, the selectivity of carbon dioxide over methane decreases as pressure increases. Sun et al. (2013) developed a dual-porosity mathematical model to investigate the sequestration of carbon dioxide. Their study showed that higher carbon dioxide injection pressure can highly improve natural gas production. Firouzi and Wilcox (2012) performed nonequilibrium molecular dynamics simulations of flow of methane and carbon dioxide in a three-dimensional carbon-based pore network. They investigated the effect of porosity in pore network on the permeability. The objective for this work is to study the storage of carbon dioxide in carbon-based organic nanopores. In this study, MD simulations are performed to investigate the adsorption and displacement of methane molecules with carbon dioxide. Adsorption of methane and carbon dioxide and also selectivity values of carbon dioxide over methane are computed. Furthermore, to study the storage of carbon dioxide in the molecular level, two types of displacements of methane molecules with carbon dioxide are considered: displacements with introducing carbon dioxide at the channel entrance in the absence of pressure gradient and displacements in presence of pressure gradients. Computational Methodology Moltemplate molecular builder software (Jewett et al., 2013) is used to create a graphite channel attached to two control volumes (or reservoirs). The graphite channels consist of three graphite layers, each nm apart. The distance between two adjacent carbon atoms in the same graphite layer is Direct connection of two control volumes causes high fluctuations in the pressures in the reservoirs. Therefore, two graphite layers are placed at two ends of control volumes to avoid direct connection between two control volumes to apply the periodic boundary conditions in all directions (Fig. 1). The length of the left (downstream) and right reservoirs (upstream) and also the channel height are chosen to be 2 nm. In order to consider the surface roughness, carbon atoms are deleted from the most inner layers (layers with direct contact with that gas molecules (Fig. 2).

3 3 Figure 1 Simulation setup for the 2 nm channel. The channel length is 40 nm. "H" and "L" represent the high and low pressure reservoirs, respectively. Figure 2 Surface of the graphite channel. The TraPPE model (Martin and Siepmann, 1998) is used to simulate the gases (methane and carbon dioxide). The charges of carbon and hydrogen atoms are not considered. Lennard-Jones (LJ) pairwise additive potential field is employed to represent the gas molecules interaction as, (1) where rij, εij, and σij are separation distance, strength of interaction, and LJ well depth, respectively. Unlike interactions are determined using the Lorentz-Berthelot combining rules, (2) (3) The separation distance (σ) and strength (ε) parameters for all gases are shown in following table. A cutoff distance of 10 A is considered for all simulations. Simulation Method In order to simulate flow of gases in the graphite channel, DCV-GCMD method (Heffelfinger and van Swol, 1994; Xu et al., 1998) is employed. In DCV-GCMD simulations, molecular dynamics (MD) moves are combined with GCMC insertion and deletion of molecules in two control volumes. The MD simulation time integration of equation of motion are performed using Verlet velocity algorithm with a time step of 3 fs (femtoseconds). The pressure inside the control volumes is kept constant using adequate number of GCMC insertion and deletion. The probability of inserting a molecule is determined as, (4) where is the absolute activity at temperature T, λ is the de Broglie wavelength, μ is the chemical potential, and kb is the Boltzmann constant. Potential energy change resulting from insertion and

4 4 deletion of molecules is represented by ΔU, volume of control volume is VCV, and number of molecules in control volume is NCV. Inserted molecules were assigned a velocity using Maxwell-Boltzmann distribution. The probability of deleting a molecule is, (5) Table 1 Interatomic potential parameters Interaction ε, kcal/mol σ (A) Reference CH4-CH Muser and Berne (1996) C-C Saito et al. (2001) CO2-CO Kurniawan et al. (2006) The inserted molecules are assigned based on specified reservoir temperature (300 K). The driving force for gas molecules movement are the pressure or chemical potential difference between the two reservoirs (L and H). The wall and fluid temperatures are kept constant at 300 K in NVT (constant number of molecules, constant volume and constant temperature) ensemble. All the simulations are performed using Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) (Plimpton, 1995) and Visual Molecular Dynamics (VMD) (Humphrey et al., 1996) is used for visualization. Results and Discussion Adsorption isotherms In order to determine adsorption isotherms of methane and carbon dioxide, grand canonical Monte Carlo (GCMC) simulations are performed. Adsorption isotherms are determined at 350 K for a pressure range of 10 to 330 atm. Density profiles of methane and carbon dioxide in the channel are shown in Figs. 3. At 10 atm (blue lines), two sets of density peaks are observed; the first peaks (approximately at z = 7 and 33 A), represents the gas molecules adsorbed to the two-layered graphite sections of the channel (sections of the channel where the carbon atoms are taken out) (Fig. 2). The second peaks (approximately at z = 12.5 and 28.5 A) demonstrate the density of gas molecules adsorbed to the three-layered sections of the surface, where no carbon atoms are removed from the surface. As pressure increases, values of density at the first, second, and third peaks and also the density at the middle of the channel increase.

5 5 Figure 3 Density profiles of carbon dioxide and methane across the channel (a) Carbon dioxide and (b) Methane. At pressures lower than 90 atm, two carbon dioxide layers can be observed (Fig. 3a). However, as pressure increases (90 atm and higher), third layers are formed; At 330 atm, fourth sets of density peaks are formed. For methane (Fig. 3b), formation of the third layer occurs at higher pressures compared to that of carbon dioxide and once it forms, the difference between the density of the third layer with that in the second layer is less significant compared to carbon dioxide. For instance, the ratios of the densities of third layer to density in middle of channel for carbon dioxide and methane at 330 atm are 1.4 and 1.1, respectively. In order to investigate the adsorption behavior of the gases, usually two quantities are defined. Absolute adsorption is defined as total amount of gas adsorbed to the solid walls. Excess adsorption is the amount of gas in absence of walls subtracted from amount of gas in adsorbed phase (Gumma and Talu, 2010). The absolute and excess loading quantities (moles of adsorbed molecules per unit volume of gas in terms of mmol/cm3) at 350 K are demonstrated in Fig. 4. The absolute loadings of both gases increase as pressure increases. For both gases, rate of increase of absolute loading with pressure decreases as pressure increases. For the pressure range tested, absolute adsorption values for carbon dioxide are higher than those for methane. Figure 4 Absolute and excess adsorption isotherms of methane and carbon dioxide

6 6 The excess loading of methane increases with pressure to reach a maximum value at an optimum pressure and then slightly decreases. Similarly, the carbon dioxide loading increases and saturates around 130 atm and then reduces slightly; however, a jump in excess loading is observed between 200 and 250 atm. The behavior of methane isotherms is similar to Langmuir isotherm for the pressure range tested. This can be confirmed by looking at the density profiles of methane in Fig. 3b. Methane densities in the third peaks (one layer away from the three-layered sections of the surface) are not significantly high compared with the densities on the wall (first and second peaks). For carbon dioxide, a behavior similar to BET isotherms (Brunauer et al., 1938) can be observed. The density profiles of carbon dioxide (Fig. 3a) also confirm that its adsorption is of multilayer nature. Selectivity GCMC simulations are performed to determine the competitive adsorption of carbon dioxide and methane. For each simulation, the pressure of each gas is kept constant and the same as the pressure for the other gas. The simulations are performed for a pressure range of 100 to 200 atm at 350 K. In order to compare the tendency of different components to be adsorbed to the wall, selectivity of carbon dioxide over methane is determined, (6) where S is selectivity, x is the mole fraction of the gas in the adsorbed phase, and y represents the gas mole fraction in the bulk gas phase. The selectivity values are larger than one for all pressures tested, which means that the carbon dioxide have higher tendency to be adsorbed to the wall (Fig. 5). As pressure increases, the selectivity decreases and tends to reach one. In other words, as pressures increases, storage of carbon dioxide in carbon-based channels in presence of methane becomes less efficient. Figure 5 Selectivity of carbon dioxide over methane at different pressures. Displacement In order to study the storage of carbon dioxide in the molecular level, displacements of methane molecules with carbon dioxide are simulated by introducing carbon dioxide molecules at the channel entrance with and without pressure gradients. Displacements in the absence of pressure gradients. A schematic representation of the displacement of methane molecules with carbon dioxide in the absence of pressure gradients is shown in Fig. 6. Initially, no

7 7 gas is present in the channel and reservoirs. Carbon walls are placed at both ends of the channel to avoid connection between the channel and the reservoirs. GCMC simulation of carbon dioxide is then performed in the reservoirs at the pressure of interest. Simultaneously, GCMC simulations of methane are performed in the channel. Once the pressure of gases reached to the pressure of interest, the walls are removed to allow the carbon dioxide molecules flow into the channel. At this stage, GCMC insertions and deletions are stopped in the reservoirs and channel. Moreover, the methane molecules that leave the channel are deleted and counted as produced. Figure 6 System configurations for displacement of methane molecules with carbon dioxide in the absence of pressure gradients. Molar percentage of each gas is determined at each time step and plotted in Fig. 7 for pressure range of 100 to 200 atm. The channel is initially filled with methane (concentration of methane is 100%). Once the walls are removed (time zero in Fig. 7), the carbon dioxide molecules enter the channel due to chemical potential gradient. For all pressures, methane molecules are displaced by carbon dioxide molecules. The replacement process is initially very quick for all pressures; Approximately 50% of methane molecules are replaced by carbon dioxide in 104 fs after beginning the simulations. As the pressure increases, the displacement process becomes slower. This is due to the fact that the selectivity of the carbon dioxide over methane decreases as pressure increases. On the other hand, at lower pressures, the carbon dioxide molecules have more freedom to move in channel and therefore, the displacement is quicker. Figure 7 Simulations results for displacement of methane molecules with carbon dioxide in the absence of pressure gradients.

8 8 Displacements in the presence of pressure gradients. In order to mimic injection of carbon dioxide into the channel, a simulation setup similar to the displacements in the absence of pressure gradients is used. However, instead of carbon dioxide in right reservoir, GCMC simulations of methane are performed at the same pressure as within the channel (100 atm for all simulations). GCMC simulations of carbon dioxide molecules are carried out in left reservoir at pressures larger than 100 atm to create pressure gradients. Similar to the previous simulations, the walls are placed at two ends of channel initially and once the pressures of interest are reached, the walls are removed (Fig. 8). Simulations are performed for four different pressures at the high-pressure reservoir (H). The mole percentages of each gas in the channel are computed and plotted with time in Fig. 9. Values of ΔP in this figure are calculated by subtracting the pressures in the low-pressure reservoir form the ones in the high-pressure reservoir. Similar to the simulations with no pressure gradients, a sharp decline in mole percentage of methane molecules is observed. Approximately 50% of methane molecules are replaced by carbon dioxide in 104 fs after beginning the simulations Figure 8 System configurations for injection simulations. Figure 9 Simulations results for displacement of methane molecules with carbon dioxide in the presence of pressure gradients. As the injection pressure (pressure in the high-pressure reservoir) increases, the methane molecules are replaced faster by carbon dioxide molecules. Furthermore, higher injection pressures result in lower mole

9 9 percentage of methane at the end of simulation. Therefore, low injection pressure are not just slower, but also would results in higher concentration of methane in channel. A comparison of the results of the two displacements shows that the displacement in presence of the pressure gradient is faster than the one in the absence of it. Conclusions Molecular dynamics simulations are performed to investigate the displacement of methane molecules with carbon dioxide in carbon- based organic channels. A comparison of adsorptions of methane and carbon dioxide indicates that the carbon dioxide have higher affinity to organic walls than methane. For methane, formation of the third layer occurs at higher pressures and once it forms, the difference between the density of the third layer with that in the second layer is less significant compared to carbon dioxide. The selectivity values of carbon dioxide over methane are larger than one for all pressures tested, which means that the carbon dioxide has a higher tendency to be adsorbed to the wall than methane. For carbon dioxide, a behavior similar to BET adsorption is observed, while for methane, the adsorption isotherm is similar to Langmuir isotherm. It is found that carbon dioxide molecules replace adsorbed methane molecules due to their higher affinity to the channel walls. A fast breakthrough and sharp concentration front is observed in the displacement of methane molecules with carbon dioxide molecules. For the displacement with no pressure gradients, as pressures increases, rate of storage of carbon dioxide in the channel becomes slower. Furthermore, amount of carbon dioxide storage and methane production rate increase as carbon dioxide injection pressure increases. Acknowledgements Authors acknowledge use of Super Computing Systems (Spruce Knob and Mountaineer) at West Virginia University, which are funded in part by the National Science Foundation EPSCoR Research Infrastructure Improvement Cooperative Agreement # , the state of West Virginia (WVEPSCoR via the Higher Education Policy Commission) and West Virginia University. References Brunauer, S., P. H. Emmett, and E. Teller (1938). Adsorption of gases in multimolecular layers. Journal of the American chemical society 60 (2), Cygan, R. T., V. N. Romanov, and E. M. Myshakin (2012). Molecular simulation of carbon dioxide capture by montmorillonite using an accurate and flexible force field. The Journal of Physical Chemistry C 116 (24), Duren, T., L. Sarkisov, O. M. Yaghi, and R. Q. Snurr (2004). Design of new materials for methane storage. Langmuir 20 (7), Firouzi, M. and J. Wilcox (2012). Molecular modeling of carbon dioxide transport and storage in porous carbon-based materials. Microporous and Mesoporous Materials 158, Godec, M., G. Koperna, R. Petrusak, and A. Oudinot (2013). Potential for enhanced gas recovery and co 2 storage in the marcellus shale in the eastern united states. International Journal of Coal Geology 118, Gumma, S. and O. Talu (2010). Net adsorption: a thermodynamic framework for supercritical gas adsorption and storage in porous solids. Langmuir 26 (22), Heffelfinger, G. S. and F. van Swol (1994). Diffusion in lennard-jones fluids using dual control volume grand canonical molecular dynamics simulation (dcv-gcmd). The Journal of chemical physics 100 (10), Humphrey, W., A. Dalke, and K. Schulten (1996). Vmd: visual molecular dynamics. Journal of molecular graphics 14 (1), Jewett, A. I., Z. Zhuang, and J.-E. Shea (2013). Moltemplate a coarse-grained model assembly tool. Biophysical Journal 104 (2), 169a. Kurniawan, Y., S. K. Bhatia, and V. Rudolph (2006). Simulation of binary mixture adsorption of methane and co2 at supercritical conditions in carbons. AIChE journal 52 (3), Liu, Y. and J. Wilcox (2012). Molecular simulation studies of co2 adsorption by carbon model compounds for carbon capture and sequestration applications. Environmental science & technology 47 (1),

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