Visual Representation of Carbon Dioxide Adsorption in a Low-Volatile

Energy Fuels 2009, 23, 5236–5246 Published on Web 09/23/2009

: DOI:10.1021/ef900314j

Visual Representation of Carbon Dioxide Adsorption in a Low-Volatile Bituminous Coal Molecular Model Marielle R. Narkiewicz and Jonathan P. Mathews* Department of Energy and Mineral Engineering, and The Earth and Mineral Sciences Energy Institute, The Pennsylvania State University, University Park, Pennsylvania 16802 Received April 8, 2009. Revised Manuscript Received August 21, 2009

Carbon dioxide can be sequestered in unmineable coal seams to aid in mitigating global climate change, while concurrently CH4 can be desorbed from the coal seam and used as a domestic energy source. In this work, a previously constructed molecular representation was used to simulate several processes that occur during sequestration, such as sorption capacities of CO2 and CH4, CO2-induced swelling, contraction because of CH4 and water loss, and the pore-blocking role of moisture. This is carried out by calculating the energy minima of the molecular model with different amounts of CO2, CH4, and H2O. The model used is large (>22 000 atoms) and contains a molecular-weight distribution, so that it has the flexibility to be used by other researchers and for other purposes in the future. In the low-level molecular modeling presented here, it was anticipated that CO2 would be adsorbed more readily than CH4, that swelling would be anisotropic, greater perpendicular to the bedding plane because of the rank of this coal, and finally, that, with the addition of moisture, CO2 capacity in the coal would be reduced. As expected with this high-rank coal, there was swelling when CO2 perturbed the structure of approximately 5%. It was found that, on the basis of the interconnected pore structure and molecular sizes, CO2 was able to access 12.4% more of the pore volume (as defined by helium) than CH4, in the rigid molecular representation. With water as stationary molecules, mostly hydrogen bound to the coal oxygen functionality, pore access decreased by 5.1% of the pore volume for CO2 accessibility and 4.7% of the pore volume for CH4 accessibility.

average chemical properties,3 carboxylation-oxidation data,4 molecular-weight distribution determined by laser desorption mass spectrometry (LDMS), and physical characteristics, such as density and porosity. The model contains a molecular-weight distribution, including small to large condensed, aromatic clusters that are methylated and connected through biaryl and heterocyclic linkages.4 This representation has 215 separate molecular entities, ranging between 78 and 3286 amu, creating a molecular-weight distribution, which is an improvement to the structural modeling of coal and is necessary for application of multiple processes. A preferred orientation, expected for this rank, was imposed via an applied external stress. The inclusion of these improvements better enabled the model to be used in behavioral observations and simulations. Creating all of this lead to the veracity of the complexity of the model. Another part of the complex nature of coal, which must be defined for sequestration studies, lies in its porosity, which is commonly simplified as a dual porosity system.5 The dual porosity model for coal suggests that gas transport occurs in two stages: (1) initially, gas moves through macropores/cleats by diffusion dominated by molecule-molecule collision or viscous flow, and (2) then gas moves through micropores by Knudsen and surface diffusions.6 A molecule with a smaller

Introduction Coal is a complex, strained, heterogeneous solid. Therefore, it is often difficult for a molecular model to describe the coal structure in entirety; however, a large, more diverse structure can be constructed and used to visualize many coal behavioral observations. A molecular representation of Pocahontas No. 3 bituminous coal was generated1 and is used in this paper to visualize adsorption of carbon dioxide for sequestration studies. Pocahontas No. 3, a low-volatile bituminous coal from Buchanan County in Virginia, was the coal of choice to model for several reasons. Pocahontas No. 3, an Argonne Premium coal, has copious data available. Most coal beds in the northeastern United States are bituminous, making this model an appropriate initial study for sequestration and coal bed methane simulations. Pocahontas No. 3 contains 89% vitrinite, 10% inertinite, and 1% liptinite.2 As a high-rank coal, there is less maceral structural diversity as coals become increasingly aromatic. The previously constructed model1 was generated through the union of several analytical criteria, including aromatic raft evaluation through lattice fringe analysis of high-resolution transmission electron microscopy (HRTEM) images, the *To whom correspondence should be addressed: 126 Hosler Building, University Park, PA 16802. Telephone: 814-863-6213. Fax: 814-8653248. E-mail: [email protected]. (1) Narkiewicz, M. R.; Mathews, J. P. Improved low-volatile bituminous coal representation: Incorporating the molecular-weight distribution. Energy Fuels 2008, 22 (5), 3104–3111. (2) Argonne Premium Coal Sample, Argonne Premium Coal Sample Analytical Data. (3) Stock, L. M.; Muntean, J. V. Chemical constitution of Pocahontas No. 3 coal. Energy Fuels 1993, 7 (6), 704–709. r 2009 American Chemical Society

(4) Stock, L. M.; Obeng, M. Oxidation and decarboxylation. A reaction sequence for the study of aromatic structural elements in Pocahontas No. 3 coal. Energy Fuels 1997, 11 (5), 987–997. (5) King, G. R.; Ertekin, T.; Schwerer, F. C. Numerical simulation of the transient behavior of coal-seam degasification wells. SPE Form. Eval. 1986, 165–183. (6) Cui, X.; Bustin, R. M.; Dipple, G. Selective transport of CO2, CH4, and N2 in coals: Insights from modeling of experimental gas adsorption data. Fuel 2004, 83 (3), 293–303.

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kinetic diameter and/or a larger adsorption energy will have access to more porosity.6 For this reason, CO2 will be preferentially adsorbed over CH4. Generally, there are roughly 2 CO2 molecules for every 1 CH4 molecule, for sorption capacity in bituminous coals.7 To identify energetically favorable adsorption sites, a simulation study was completed to test the molecular exchange of CH4 by CO2.8 From this study, it was concluded that preferential adsorption of CO2 over CH4 in some coals was explained by adsorption in pores on atomic scales.8 The rate and quantity of CO2 sorption will depend upon the pore size, shape, interconnectivity, and the ability of the coal to swell and possibly rearrange. Coal beds are potential sites for CO2 sequestration. The Regional Carbon Sequestration Partnership Projects estimate a potential of 156-183 billion metric tons of CO2 in unmineable coal beds.9 The CO2 that would otherwise be emitted to the atmosphere can be captured and injected (i.e., sequestered) into geologic formations, such as coal beds. As CO2 is sequestered, CH4 can simultaneously desorb, be captured, and subsequently used as a domestic energy source. It has also been shown that methane production from coal beds can be enhanced by CO2 injection.10 As CO2 interacts with the coal, it causes swelling, while shrinkage occurs because of desorption of CH4 and removal of H2O.11 The transport of CO2, CH4, and water is dependent upon the size, distribution, connectivity, and shape of the pores and the sorption or diffusion processes that occur; therefore, modeling is the best tool that can illustrate the transport phenomena that occurs during sequestration. Coal behavior however makes this challenging. For example, additional sorption sites may also be made available with the onset of CO2-induced swelling. The examination of the above will aid in quantifying the interactions between the molecules present in the molecular modeling. This paper demonstrates and describes the sorptive capacity of a low-volatile bituminous molecular model for both CO2 and CH4 through molecular modeling approaches, to better understand what is occurring during sequestration.

the micropore volume distribution. Both software programs were chosen because they have an array of use in modeling organics. Materials Studio is a versatile program run on a PC, is very user-friendly, and has been used for similar uses in the past. The simulations completed in this work range from energy minimizations and sorption experiments. Essentially, the local minimum energy is the enthalpy of the system at absolute zero.14 The forcefields used were the Universal, polymer consortium forcefield (pcff), and Dreiding forcefields, which are described as all-purpose forcefields, because they relate to most organic systems. The energetics of these forefields with a geometry optimization can be found in the Appendix. Sorption generates random configurations by translating, rotating, and possibly creating and destroying sorbate molecules in the model framework.14 These configurations are allowed on the basis of the interaction energy. That energy is calculated on the basis of the interaction between the sorbate molecules to the structure, as well as the sorbate molecules to each other. A sorbate is rejected (or destroyed) from the model if the energy between it and the structure is too high (termed a bad contact), specifically, if any sorbate and framework atoms are closer to each other than half of their van der Waals radii.14 The translation or rotation for a given sorbate is limited by the maximum step size (with default values of 1 A˚ for translation and 50° for rotation).14 The “locate” task was the particular ensemble used in our simulations, in which a defined number of sorbate molecules were added to a sorbent structure. The sorbent framework is probed to identify the preferential (i.e., lowest energy) sites for a sorbate molecule. A Monte Carlo search of the configurational area is performed as the temperature decreases, allowing sorbate molecules to be rotated and translated until the appropriate loading is achieved. The POR program calculates a simulated helium density, porosity, closed porosity, atomic surface, and micropore surface of a given molecular model.13 This program calculates the atomic occupied space of a grid consisting of 1 A˚3 cells in which the model is immersed.15 For the molecular representation, the minimum adsorbate size was defined as 5.08 A˚, the kinetic diameter of helium.16 Helium is the reference size because it is used to approximate the true density of coal and is the smallest molecule. The maximum adsorbate entrance size was defined as 20.0 A˚, the maximum size of a micropore. Inclusion of physical evaluations increased confidence in the accuracy of the representation.

Methodology Results and Discussion

Computer System and Software. The modeling was completed with a Silicon Graphics computer with two 300 MHz processors and a Dell Optiplex 755 with an Intel Core 2Duo at 2.33 GHz. Materials Studio v4.2.0 software12 was used for visualization and sorption simulations, and the POR program13 was used for

Micropore Volume. The model used in this study is shown in Figure 1, where the colored spheres are there to aid visualization, so that the heteroatoms can be seen. It is the largest coal structure generated and includes 215 fragments that allow, for the first time, a molecular-weight distribution. The molecular model was generated by combining several criteria: (1) aromatic raft evaluation through lattice fringe analysis of HRTEM images, (2) the average molecular properties of Stock and Muntean3 and the carboxylation-oxidation molecular-weight distribution data of Stock and Obeng,4 (3) molecular-weight distribution through LDMS, and (4) physical characteristics, such as helium density, porosity, and pore size distribution. The pore volume distribution was determined using several micropore entrance sizes in the

(7) Busch, A.; Gensterblum, Y.; Krooss, B. M. Methane and CO2 sorption and desorption measurements on dry Argonne Premium coals: Pure components and mixtures. Int. J. Coal Geol. 2003, 55 (2-4), 205– 224. (8) Tambach, T. J.; Mathews, J. P.; van Bergen, F. Molecular exchange of CH4 and CO2 in coal: Enhance coalbed methane on a nonscale. Energy Fuels 2009, DOI: 10.1021/ef900274q. (9) Department of Energy (DOE). Carbon Sequestration FAQ Information Portal. http://www.netl.doe.gov/technologies/carbon_seq/ FAQs/project-status.html (accessed in 2008). (10) White, C. M.; Smith, D. M.; Jones, K. L.; Goodman, A. L.; Jikich, S. A.; LaCount, R. B.; DuBose, S. B.; Ozdemir, E.; Morsi, B. I.; Schroeder, K. Sequestration of carbon dioxide in coal with enhanced coalbed methane recovery;A review. Energy Fuels 2004, 19 (3), 659– 724. (11) Department of Energy (DOE). U.S. Department of Energy Office of Science Office of Fossil Energy: Carbon Sequestration, State of the Science, 1999. (12) Accelrys. Molecular Simulation Documentation, Cerius2 4.0, Materials Studio 4.2; Molecular Simulations: San Diego, CA, 1999. (13) Faulon, J. L. Program “POR” Version 5.0 (Short Manual), 5.0, Albuquerque, NM, 1997.

(14) Accelrys. Materials Studio Help Topic Release Notes; Accelrys Software, Inc.: San Diego, CA, 2006. (15) Faulon, J. L.; Mathews, J. P.; Carlson, G. A.; Hatcher, P. G. Correlation between microporosity and fractal dimension of bituminous coal based on computer-generated models. Energy Fuels 1994, 8 (2), 408– 414. (16) Rao, M. B. Diffusion through carbon micropores;4 years later. Carbon 1991, 29 (6), 813–815.

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Figure 1. Molecular representation of Pocahontas No. 3 with heteroatoms shown as colored spheres to aid in visualization.

Figure 2. Micropore volume (A˚3) versus micropore entrance size (A˚) of the structure of Pocahontas No. 3.

POR program. The micropore volume can be seen in Figure 2. This plot illustrates that molecules of smaller size can access more of the pore volume. Adsorption of Gases. The pore volume accessibility allows for a quantitative expression of the capacity of CO2 and CH4 in a rigid coal structure. There is an expected 2:1 molar ratio of CO2/CH4 sorption capacity in bituminous coals.7 To show the 2:1 ratio in this coal model, the average value of coal bed methane found in the Pocahontas No. 3 seam obtained from the Bureau of Mines was converted to a molecular basis and is shown in Figure 3 as a visual of the average amount of methane that may initially be present. With the average coal bed methane content being 470 Scf/ton (daf), the molecular representation shown would hold 120 CH4 molecules. It was noted that few CH4 molecules were located in the center of the model. As previously described, these structures were created using the locate ensemble, where the number of molecules to add was defined, and those molecules will go

through translations, rotations, and rejections until they are accepted on the basis of their interaction energies (see the Methodology for more details). It appears that most of these CH4 molecules prefer the edge of the coal structure. A similar visualization was obtained for CO2 (240 molecules), with double the number of original CH4 molecules, to illustrate the 2:1 ratio (see Figure 4). This 2:1 ratio is applicable in bituminous coals and is a function of the relative gas (injection) pressure, as well as the shape and size of the molecules and pores. As shown in Figure 4, the CO2 molecules are more equally distributed throughout the model. Perhaps this is due to the higher number of CO2 molecules in this simulation, or it may be due to the higher affinity and smaller kinetic diameter that the CO2 molecule has over CH4. Alternatively, the orientation of the model (which is expected of a coal of this high rank) may have resulted in a more organized model and, thus, a more organized central region of the model (i.e., stacking of aromatic sheets). This would then impart enhanced molecular sieving in this region. 5238

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Figure 3. Visualization of the coal model containing 120 methane molecules (false colored in blue to aid in visualization).

Figure 4. Visualization of 240 CO2 molecules inside the Pocahontas No. 3 structure.

To compare the loading level of CO2 and CH4 within the molecular representation, the same number of molecules (25) was added to the structure to visualize where in the structure the molecules would reside (Figures 5 and 7). Again, the methane molecules were false-colored yellow to aid in visualization. The Monte Carlo steps of this experiment have also been included (see Table 1). The interior of the structure, shown with an expanded view of the adsorption sites of the coal, is shown in Figures 6 and 8. This low-level molecular mechanics simulation shows both CO2 and CH4 in the interior of the structure, but higher level modeling should be completed in the future to show preferential adsorption. There is slightly more clustering of methane molecules toward the center of the structure (Figure 5), but there are more molecules of carbon dioxide found closer to the center of the structure in Figure 7. The simulation with carbon dioxide molecules was also at a lower energy value than the simulation with methane molecules. The number of attempted methane molecules is slightly higher than carbon dioxide because more attempts had to be made to acquire the amount of molecules in the structure (25) because of the bulkier shape of the methane molecule compared to the linear shape of the carbon dioxide molecule.

Table 1. Monte Carlo Analysis Showing the Number of Rotations and Translations for Both CO2 and CH4 before the Molecules Are Accepted into the Structure CO2 CH4

sorbate

rotation

translation

accepted attempted accepted attempted

22965 27456 26224 27511

14142 27566 14684 27683

To further analyze the pore accessibility of CO2 versus CH4 (in a simplistic approach), V-shaped pores of different pore length were constructed from graphite sheets. At 273 K and 10 bar, CH4 or CO2 molecules were sorbed into the V-shaped pore structure and the two simulations were compared. Figure 9 illustrates that CO2 can access smaller pore entrances than CH4, however, minimally. This may be due to the shape of the molecules alone, because CO2 is a linear molecule and has access to places that the more spherical CH4 molecule cannot access. The porosity in the coal model is slit-shaped and not well-interconnected. The basis for slit-shaped pores is based on the data7 replicated in this study, in which it was concluded that, with the presence of little to no hysteresis between adsorption and desorption experiments, the pores are slitlike in appearance. Sorption experiments conducted 5239

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Figure 5. Visualization of the low loading level of 25 methane molecules (colored yellow) in the structure.

Figure 6. Interior view of adsorption sites with methane molecules.

Figure 7. Visualization of the low loading level of 25 carbon dioxide molecules in the structure.

simulating capacity at high gas pressures resulted in only half of the anticipated CO2 capacity. The work of Walker et al.17 indicates that 50% of the swelling (and thus capacity) is achieved through CO2 imbibition into the coal structure.

Swelling Studies. Coal is a glassy material that is capable of swelling in the presence of carbon dioxide by expanding the coal structure. Walker et al.17 stated that swelling can occur in two manners: (1) adsorption of a liquid-like layer on the pore surfaces and (2) imbibition of the fluid into the structure. If a sorbate reports a higher density than the helium density, swelling is noted.17 Several simulations were completed to show induced swelling from CO2 sorption.

(17) Walker, P. L.; Verma, S. K.; Rivera-Utrilla, J.; Khan, M. R. A direct measurement of expansion in coals and macerals induced by carbon dioxide and methanol. Fuel 1988, 67, 719–725.

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Figure 8. Interior view of adsorption sites with carbon dioxide molecules.

Data were taken from the adsorption isotherm of Krooss et al.18 to determine the relative number of molecules at specific gas pressures. Coals of higher rank contain larger aromatic sheets, which tend to orient parallel to the bedding plane, causing the coals to become anisotropically strained and swelling to be anisotropic and greater perpendicular to the bedding plane.19,20 Kelemen and Kwiatek reported a swelling of 3.56% because of CO2 adsorption in as-received Pocahontas No. 3.21 Carbon dioxide molecules were exposed to the structure, and the model was allowed to relax and swell. The swelling data is shown in Figure 10. The initial swelling was substantial (approximately 3.5%) but soon reached a plateau (between 4.3 and 6.4%). The figure also shows that swelling occurred in all directions. Although the structure did exemplify net swelling of approximately 5%, the simulation tool used was simplistic. The B direction was predominant and agreed with expectations that swelling should be greater perpendicular to the bedding plane than parallel to it. Many of the molecules resided at the edge of the structure because of energetic constraints. These would become proportionally less as the model increases in scale. Similar placements occurred in the simulations of Tambach et al.8 As stated previously, with the work of Walker et al.,17 it should be expected that more CO2 would be imbibed in the coal structure and not only within the pore structure. In this simulation, the swelling extent was not constrained. In actual sequestration sites, the coal is expected to be deep and

confining stresses may limit gas capacity and the extent of swelling.22-25 The simulation does not address structural rearrangement observed with CO2 exposure.26,27 Upon CO2 removal and then a second exposure, the uptake occurs more rapidly, indicating that a rearrangement had occurred.26 Molecular modeling however may yield insight into these issues along with careful coupled experimental approaches. Pair distribution function simulations obtained from highenergy small-angle X-ray scattering and model simulation on an earlier version of this model are one such example.28 Role of Moisture in Coal. When water is present within narrow pores, the roughness of the surface can either encourage or discourage hydrogen-bonded molecules.29 Moisture in coal is suggested to decrease the capacity of CO2 adsorption in coal.30 Pocahontas No. 3 has a moisture content of 0.68% on an ash-free basis.2 This is a high-rank coal and, therefore, typically has little moisture. Two forms of water can generally be found in coal: bulk water and bound water.31,32 Bulk water is moisture that is associated with other water molecules, often found in cleats or macropores. Bound water is a single water molecule that is tightly (25) Jikich, S. A.; McLendon, R.; Seshadri, K.; Irdi, G. A.; Smith, D. H. In carbon dioxide transport and sorption behavior in confined coal cores for enhanced coalbed methane and CO2 sequestration. In SPE Annual Technical Conference and Exhibition, Anaheim, CA, 2007; pp 1-17. (26) Goodman, A. L.; Favors, R. N.; Larsen, J. W. Argonne coal structure rearrangement caused by sorption of CO2. Energy Fuels 2006, 20 (6), 2537–2543. (27) Goodman, A. L.; Favors, R. N.; Hill, M. M.; Larsen, J. W. Structure changes in Pittsburgh No. 8 coal caused by sorption of CO2 gas. Energy Fuels 2005, 19 (4), 1759–1760. (28) Winans, R. E.; Chapman, K. W.; Chupas, P. J.; Seifert, S.; Clemens, A. H.; Calo, J. M.; Bain, E.; Mathews, J. P.; Narkiewicz, M. R. In situ studies of coal pressurized with CO2 by small angle and high energy, wide angle X-ray scattering. Prepr. Symp.-Am. Chem. Soc., Div. Fuel Chem. 2008, 53 (1), 283–285. (29) Striolo, A.; Chialvo, A. A.; Cummings, P. T.; Gubbins, K. E. Water adsorption in carbon-slit nanopores. Langmuir 2003, 19 (20), 8583–8591. (30) Goodman, A. L.; Busch, A.; Duffy, G. J.; Fitzgerald, J. E.; Gasem, K. A. M.; Gensterblum, Y.; Krooss, B. M.; Levy, J.; Ozdemir, E.; Pan, Z.; Robinson, R. L., Jr.; Schroeder, K.; Sudibandriyo, M.; White, C. M. An inter-laboratory comparison of CO2 isotherms measured on Argonne Premium coal samples. Energy Fuels 2004, 18 (4), 1175–1182. (31) Mraw, S. C.; O’Rourke, D. F. Water in coal pores: The enthalpy of fusion reflects pore size distribution. J. Colloid Interface Sci. 1982, 89 (1), 268–271. (32) Suuberg, E. M.; Otake, Y.; Yun, Y.; Deevi, S. C. Role of moisture in coal structure and the effects of drying upon the accessibility of coal structure. Energy Fuels 1993, 7 (3), 384–392.

(18) Krooss, B. M.; van Bergen, F.; Gensterblum, Y.; Siemons, N.; Pagnier, H. J. M.; David, P. High-pressure methane and carbon dioxide adsorption on dry and moisture-equilibrated Pennsylvania coals. Int. J. Coal Geol. 2002, 51 (2), 69–92. (19) Larsen, J. W.; Flowers, R. A., II; Hall, P. J.; Carlson, G. Structural rearrangement of strained coals. Energy Fuels 1997, 11 (5), 998–1002. (20) Cody, G. J.; Larsen, J. W.; Siskin, M. Anisotropic solvent swelling of coals. Energy Fuels 1988, 2 (3), 340–344. (21) Kelemen, S. R.; Kwiatek, L. M. Physical properties of selected block Argonne Premium bituminous coal related to CO2, CH4, and N2 adsorption. Int. J. Coal Geol. 2009, 77 (1-2), 2–9. (22) Hile, M. CO2 sorption by Pittsburgh-seam coal subjected to confining pressure. Pennsylvania State University, University Park, PA, 2006. (23) Pone, J. D. N.; Halleck, P. M.; Mathews, J. P. Sorption capacity and sorption kinetic measurement of CO2 and CH4 in confined and unconfined bituminous coal. Energy Fuels 2009, DOI: 10.1021/ ef9003158. (24) Smith, D. H.; Jikich, S. A.; Seshadri, K. Carbon dioxide sorption isotherms and matrix transport rates for non-powdered coal. In 2007 International Coalbed Methane Symposium, Tuscaloosa, AL, 2007; Vol. 0721, p 15.

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Figure 9. Sorption simulation of both (a) CO2 and (b) CH4 in V-shaped pores, to determine the critical pore size that CO2 can access and CH4 cannot access.

Figure 10. Adsorption of CO2 as a function of volume change, which represents any swelling that occurs when CO2 is adsorbed in the coal structure.

bound to the coal structure. Only the latter is shown in this molecular representation, because with the scale of this structure, no macropores are present and, thus, no bulk water. The amount of water molecules was calculated from the moisture content and the molecular weight of this structure. A total of 66 molecules were placed approximately 1.88 A˚ away from neighboring oxygen atoms that comprise some of the fragments in the structure. A total of 58% of the oxygen atoms in the coal are therefore associated with a water molecule, as seen in Figure 11.

To test the suggestion that water inhibits CO2 capacity, the micropore volume was analyzed before and after the water was added. There is speculation that water competes with CO2 for adsorption sites, thus reducing the CO2 capacity.33 The addition of 66 water molecules resulted in a 5.1% decrease of the available pore volume. It is important to note that this pore volume reduction is due to a static water molecule physically blocking pore entry. The chemical influence of the water molecule will extend beyond the van der Waals radii. Thus, the presence of water influences the transport of CO2 into the pore system. Pore Size Distribution. The amount of CO2 that sorbs to the coal structure depends upon the pore size, shape, and interconnectivity of the pores. Commonly, the Lennard-Jones

(33) Bustin, R. M.; Clarkson, C. R. Geological controls on coalbed methane reservoir capacity and gas content. Int. J. Coal Geol. 1998, 38 (1-2), 3–26.

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Figure 11. Molecular representation illustrating the 66 bound water molecules added near oxygen atoms.

Figure 12. Plot depicting the micropore volume that is accessible to helium, CO2, and CH4.

Lennard-Jones molecule.36 Using the critical pore sizes as calculated in Heuchel et al.36 and assuming the size of helium is the smallest pore entrance size, the pore size distribution was calculated and plotted (see Figure 12). As shown in Figure 8, it is noted that the helium or assumed true density equals 100% of the micropore volume. The critical pore sizes as defined by Heuchel et al.36 are 5.7 A˚ for CO2 and 6.1 A˚ for CH4. Carbon dioxide can access 80.8% of the micropore volume, while methane can only access 67.8% of the micropore volume. Thus, in a rigid representation, CO2 can access 13% more of the micropore volume than CH4, or if sorbate density within the pore is assumed to be the same, this is a 1.2:1 ratio of

potential is used to describe the kinetic diameter of the sorbate, and while this approach is considered accurate for slit-shaped carbon pores16,34,35 and spherical molecules, it is not accurate for linear molecules, where shape influences energetic interactions. Transport of non-spherical molecules through relatively narrow pores involves the loss of rotational freedom and thus cannot accurately be described solely through the kinetic diameter;16 therefore, they should be described by parameters that define the species. In a previous study, CO2 was treated as a two-center Lennard-Jones expression, including the quadrupole point, while CH4 was treated as a one-center (34) Walker, P. L.; Mahajan, O. P. Pore structure in coals. Energy Fuels 1993, 7, 559–560. (35) Rao, M. B. Molecular dimensions and kinetic diameters for diffusion for various species. Carbon 1987, 25 (3), 445–446.

(36) Heuchel, M.; Davies, G. M.; Buss, E.; Seaton, N. A. Adsorption of carbon dioxide and methane and their mixtures on an activated carbon: Simulation and experiment. Langmuir 1999, 15, 8695–8705.

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spline width = 1 A˚ buffer width = 0.5 A˚ van der Waals terms summation method = atom based truncation method = cubic spline cutoff distance = 9.5 A˚ spline width = 1 A˚ buffer width = 0.5 A˚ hydrogen bond terms summation method = atom based truncation method = cubic spline cutoff distance = 4.5 A˚ spline width = 0.5 A˚ buffer width = 0.5 A˚

CO2/CH4. The lower than expected ratio can be attributed to the lack of inclusion of CO2 imbibition into the structure. Conclusions The molecular diversity of a large coal representation was used in several simulations addressing sequestration issues within coal, such as sorption of CO2 and CH4, swelling of the structure caused by CO2, the role of moisture in sequestration, and micropore accessibility. Specifically, the following were concluded. Swelling. The structure swelled in all directions when CO2 was added to the structure. The direction perpendicular to the bedding plane was predominant and agreed with expectations that anisotropic swelling greater perpendicular to the bedding plane occurs. Water Impact. Stationary bound water molecules did not significantly block access of CO2 to the pores but did physically block 5.1% of the micropore volume from access to CO2. The placement of water molecules near oxygen functional groups served as a visualization of where water molecules would preferentially be found in the structure. Pore Access. A pore size distribution was created to determine the accessibility to pores that CO2 had over CH4. It was concluded that CO2 molecules could access 13% more of the micropore volume than CH4 molecules in a rigid coal molecule. The difference in accessibility is related to the critical dimension of the size of the molecules, where CO2 is smaller (5.7 A˚ compared to 6.1 A˚ for CH4). This result was lower than expected, most likely because of the inability of the sorption approach used to model the imbibition of CO2 into the coal structure. The results of this study are heuristic in that they elucidate certain conversion processes as related to molecular modeling of CO2 sequestration. Future work will include higher level modeling of the above to accurately represent the behavioral processes associated with sequestration and molecular modeling.

Initial Structure total enthalpy = 51 994 819 014.387 352 kcal/mol external pressure term = 0.000 000 kcal/mol total energy = 51 994 819 014.387 352 kcal/mol contributions to total energy (kcal/mol) valence energy (diagonal terms) = 98 599.336 bond = 51 715.811 angle = 16 630.505 torsion = 21 972.461 inversion = 8280.559 valence energy (cross terms) = 0.000 stretch-stretch = 0.000 stretch-bend-stretch = 0.000 stretch-torsion-stretch = 0.000 separated-stretch-stretch = 0.000 torsion-stretch = 0.000 bend-bend = 0.000 torsion-bend-bend = 0.000 bend-torsion-bend = 0.000 nonbond energy = 51 994 720 415.051 hydrogen bond = -1.328 van der Waals = 51 994 719 745.808 electrostatic = 670.571 rms force = 1.238  10010 kcal mol-1 A˚-1 max force = 1.673  10012 kcal mol-1 A˚-1

Acknowledgment. We thank the U.S. Department of Energy, who funded this research under Grant DE-FG26-02-NT41556. We also thank the reviewers who helped refine this paper.

Final Structure Appendix: Energy Parameters for Forcefields

total enthalpy = 104 613.930 154 kcal/mol external pressure term = 0.000 000 kcal/mol total energy = 104 613.930 154 kcal/mol contributions to total energy (kcal/mol) valence energy (diagonal terms) = 64 219.485 bond = 19 207.515 angle = 16 328.343 torsion = 20 852.318 inversion = 7831.308 valence energy (cross terms) = 0.000 stretch-stretch = 0.000 stretch-bend-stretch = 0.000 stretch-torsion-stretch = 0.000 separated-stretch-stretch = 0.000 torsion-stretch = 0.000 bend-bend = 0.000 torsion-bend-bend = 0.000 bend-torsion-bend = 0.000 nonbond energy = 40 394.445 hydrogen bond = -1.597 van der Waals = 40 255.728 electrostatic = 140.314

Forcite task = geometry optimization version = 4.3 Geometry Optimization Parameters algorithm = smart convergence tolerance energy = 0.002 kcal/mol maximum number of iterations = 10 000 external pressure = 0 GPa motion groups rigid = NO optimize cell = NO Energy Parameters forcefield = Dreiding Electrostatic terms summation method = atom based truncation method = cubic spline cutoff distance = 9.5 A˚ 5244

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rms force = 3.096  10 kcal mol A˚ max force = 9.244  10002 kcal mol-1 A˚-1 001

contributions to total energy (kcal/mol) valence energy (diagonal terms) = 18 257.817 bond = 64 651.382 angle = 15 528.878 torsion = 13 927.261 inversion = 1532.319 valence energy (cross terms) = 0.000 stretch-stretch = 0.000 stretch-bend-stretch = 0.000 stretch-torsion-stretch = 0.000 separated-stretch-stretch = 0.000 torsion-stretch = 0.000 bend-bend = 0.000 torsion-bend-bend = 0.000 bend-torsion-bend = 0.000 nonbond energy = -34.649 hydrogen bond = 0.000 van der Waals = 0.000 electrostatic = -34.649 rms force = 2.091  10000 kcal mol-1 A˚-1 max force = 1.807  10002 kcal mol-1 A˚-1

Forcite task = geometry optimization version = 4.3 Geometry Optimization Parameters algorithm = smart convergence tolerance energy = 0.002 kcal/mol maximum number of iterations = 10 000 external pressure = 0 GPa motion groups rigid = NO optimize cell = NO Energy Parameters forcefield = pcff electrostatic terms summation method = atom based truncation method = cubic spline cutoff distance = 9.5 A˚ spline width = 1 A˚ buffer width = 0.5 A˚ van der Waals terms summation method = atom based truncation method = cubic spline cutoff distance = 9.5 A˚ spline width = 1 A˚ buffer width = 0.5 A˚

Forcite task = geometry optimization version = 4.3 Geometry Optimization Parameters algorithm = smart convergence tolerance energy = 0.002 kcal/mol maximum number of iterations = 10 000 external pressure = 0 GPa motion groups rigid = NO optimize cell = NO

Initial Structure total enthalpy = 10 577 308.199 648 kcal/mol

Energy Parameters

external pressure term = 0.000 000 kcal/mol total energy = 10 577 308.199 648 kcal/mol contributions to total energy (kcal/mol) valence energy (diagonal terms) = 334 232.480 bond = 19 152.834 angle = 17 377.496 torsion = 294 600.477 inversion = 3101.673 valence energy (cross terms) = -1364.857 stretch-stretch = 1128.927 stretch-bend-stretch = 356.170 stretch-torsion-stretch = -6249.306 separated-stretch-stretch = 1210.524 torsion-stretch = -2096.675 bend-bend = -0.750 torsion-bend-bend = -176.506 bend-torsion-bend = 4462.759 nonbond energy = 10 244 440.577 hydrogen bond = 0.000 van der Waals = 10 242 369.584 electrostatic = 2070.993 rms force = 1.037  10005 kcal mol-1 A˚-1 max force = 8.258  10006 kcal mol-1 A˚-1

forcefield = Universal electrostatic terms summation method = atom based truncation method = cubic spline cutoff distance = 9.5 A˚ spline width = 1 A˚ buffer width = 0.5 A˚ van der Waals terms summation method = atom based truncation method = cubic spline cutoff distance = 9.5 A˚ spline width = 1 A˚ buffer width = 0.5 A˚ Initial Structure total enthalpy = 44 409 556 665.376 396 kcal/mol external pressure term = 0.000 000 kcal/mol total energy = 44 409 556 665.376 396 kcal/mol contributions to total energy (kcal/mol) valence energy (diagonal terms) = 86 511.361 bond = 29 988.112 angle = 31 561.111 torsion = 23 719.063 inversion = 1243.075 valence energy (cross terms) = 0.000 stretch-stretch = 0.000 stretch-bend-stretch = 0.000

Final Structure total enthalpy = 113 932.306 786 kcal/mol external pressure term = 0.000 000 kcal/mol total energy = 113 932.306 786 kcal/mol 5245

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stretch-torsion-stretch = 0.000 separated-stretch-stretch = 0.000 torsion-stretch = 0.000 bend-bend = 0.000 torsion-bend-bend = 0.000 bend-torsion-bend = 0.000 nonbond energy = 44 409 470 154.015 hydrogen bond = 0.000 van der Waals = 44 409 469 968.347 electrostatic = 185.668 rms force = 1.057  10010 kcal mol-1 A˚-1 max force = 1.429  10012 kcal mol-1 A˚-1

bond = 18 523.918 angle = 26 618.707 torsion = 23 099.692 inversion = 1260.164 valence energy (cross terms) = 0.000 stretch-stretch = 0.000 stretch-bend-stretch = 0.000 stretch-torsion-stretch = 0.000 separated-stretch-stretch = 0.000 torsion-stretch = 0.000 bend-bend = 0.000 torsion-bend-bend = 0.000 bend-torsion-bend = 0.000 nonbond energy = 30 993.130 hydrogen bond = 0.000 van der Waals = 31 010.943 electrostatic = -17.813 rms force = 1.882  10001 kcal mol-1 A˚-1 max force = 5.258  10002 kcal mol-1 A˚-1

Final Structure total enthalpy = 100 495.610 744 kcal/mol external pressure term = 0.000 000 kcal/mol total energy = 100 495.610 744 kcal/mol contributions to total energy (kcal/mol) valence energy (diagonal terms) = 69 502.481

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