Molecular Dynamics Study of Transport and Storage of Methane in Kerogen

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1 Molecular Dynamics Study of Transport and Storage of Methane in Kerogen Mohammad Kazemi, Hossein Maleki, and Ali Takbiri-Borujeni, West Virginia University Copyright 2016, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Eastern Regional Meeting held in Canton, Ohio, USA, 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 Studying kerogen structure and its interactions with fluids is important for understanding the mechanisms involved in storage and production of hydrocarbons from shale. In this study, adsorption and transport of methane in a three dimensional type II kerogen model are studied using molecular dynamics simulations. Grand Canonical Monte Carlo (GCMC) simulations are used to simulate the adsorption of methane and NonEquilibrium Molecular Dynamics (NEMD) simulations are employed to simulate transport of methane in the kerogen model. The kerogen model prepared by Ungerer et al. (2014) is used in this study. In order to build a representative solid state model of kerogen, eight kerogen molecules are placed in a periodic cubic cell. Once the initial configuration of kerogen molecules is prepared, constant-temperature constant-volume (NVT) simulations and then constant-temperature constant-pressure (NPT) simulations are performed to obtain the final structure. For the final structure, density values are calculated and compared with the reported density range for kerogen density. Adsorption isotherm, self and transport diffusion coefficients of methane in the final kerogen structure are also calculated. Simulation results for the adsorption isotherm are fairly close to experimental results reported for a Haynesville shale sample. Computed values for self and transport diffusivities decrease as pressure increases and transport diffusion coefficients approach the self-diffusion coefficients. Introduction Kerogen is the source of hydrocarbons and the main constituents of the organic matter in sedimentary rocks (Rullkotter and Michaelis, 1990; Nomura et al., 1998). The quantity and composition of the hydrocarbons accumulated during the kerogen evolution depend on its chemical composition and structural features. Kerogen is a mixture of organic chemicals and its chemical formula and properties vary depending on the geographical location (Tissot et al., 1974). This makes the modeling of kerogen challenging. Studying kerogen structure and its interactions with fluids is important for understanding the mechanisms involved in storage and production of hydrocarbons from shale. Most of the current studies on the transport of fluids in organic-rich shale are mainly focused on fluid flow in simplified carbon-based conduits. The objective for this work is to determine the storage and transport properties of methane in a kerogen structure using molecular dynamics simulations. Three types of kerogens with different extents of maturation can be found in organic matter (Behar and Van- denbroucke, 1987; Ungerer et al., 2014). These types differ from each other by the chemical

2 2 content (carbon, oxygen, nitrogen, and sulfur content). Kerogen types are mainly defined by the percentage of elemental hydrogen present in them. Hydrogen content of immature kerogen decreases with thermal maturation (Vandenbroucke, 2003). Therefore, it can be used as a criteria to evaluate relative thermal maturity of kerogen (Ungerer et al., 2014). After burial of kerogen in sedimentary rocks, it loses its hydrogen and oxygen content and becomes more concentrated in carbon content. Type I kerogen has a highly aliphatic structure with a high H/C ratio and a relatively low O/C ratio. It is mainly originated from algal-lacustrine and algal-marine sources. Type II kerogen has a relatively high H/C ratio with a low O/C ratio. It is mainly originated from a mixture of sources from Type I and Type III. Type III kerogen has features similar to Vitrinites. It has a high O/C ratio with a relatively low H/C ratio (Behar and Vandenbroucke, 1987; Ungerer et al., 2014). It is dominantly originated from higher plants accumulated in non-marine environments. Due to high complexity of kerogen samples, it is never possible to propose a general kerogen model. Analytical data are now available for different types of kerogens originated from different source rocks and many two dimensional (2D) models for kerogens are generated (Behar and Vandenbroucke, 1987; Scouten et al., 1989; Kidena et al., 2008). For validation of kerogen structures, experimental and theoretical results, such as mechanical properties, should be compared. However, only using 3D structures, these properties can be calculated. In practice, the 2D structures can be converted to three dimensional (3D) structures using quantum mechanics and molecular dynamics methods (Ru et al., 2012; Orendt et al., 2013; Collell et al., 2014). The proposed 3D structures using computational techniques can provide wealth of information for comparisons of kerogens from different source rocks. Furthermore, they are helpful in predicting the mechanism in which the kerogen interacts with the bitumen and the mineral matter (Jeong and Kobylinski, 1983). These 3D models also provide the functional groups of kerogen exposed to surface and interior functional groups hidden inside the kerogen (Vandegrift et al., 1980). Availability of a validated 3D model allows further computational study in order to predict the type of interaction between the kerogen and the mineral matrix, which is essential for oil production. Two approaches have been used to create 3D models from 2D models. First approach considers quantum mechanics calculations, such Gaussian optimization, for finding the most stable conformation (global maxima) (Guan et al., 2015). This approach is not realistic for large systems (more than 500 atoms) (Dupuis et al., 1989; Heller, 2006). In the second approach, the most stable conformations is found using molecular dynamics simulations (Ungerer et al., 2014). Transport of fluids in nano-scale conduits has been extensively studied using three different MD simulation methods: Equilibrium Molecular Dynamics (EMD), external field Non-Equilibrium Molecular Dynamics (NEMD), and boundary driven non-equilibrium molecular dynamics (dual control volume grand canonical molecular dynamics or DCV-GCMD) (Arya et al., 2001). DCV-GCMD simulations have been used to investigate the sensitivity of transport properties of methane, carbon dioxide, and nitrogen to pore size, porosity, and pressure gradient (Firouzi and Wilcox, 2012). DCVGCMD simulations of flow of methane in carbon nanotubes have demonstrated that the adsorbed phase is mobile in high and low pressures and Knudsen diffusion and Hagen-Poiseuille equations can underestimate the methane flow by one order of magnitude Jin and Firoozabadi (2015). A comparison study of transport of four different gases with different adsorption affinity, methane and argon with high adsorption affinity and helium and neon with low adsorption affinity have been performed by Kazemi and Takbiri-Borujeni (2016c, d). They showed that as the average channel pressure increases, the contribution of the adsorbed phase to the total mass flux decreases. Their DCV-GCMD simulations have also shown that the Knudsen diffusion model underestimates the molecular flux (Kazemi and Takbiri-Borujeni, 2016b). NEMD simulations are easy to implement and computationally efficient for simulating the transport phenomena; however, the equivalence of external forcing function that drives diffusion and the actual chemical potential gradient has not been formally demonstrated (Arya et al., 2001). NEMD simulations have been applied to investigate the slippage of a non-adsorbing gas (Helium) in microporous media (Firouzi et al., 2014). The results indicated that the experimental measured permeability values are two orders of

3 3 magnitude larger than NEMD results. Kazemi and Takbiri-Borujeni (2016a,d) employed NEMD simulations to investigate the transport of two adsorbing gases, argon and methane, at different channel heights for different Knudsen numbers. They concluded that the contribution of the adsorbed molecules can be more than 50% of the total mass flux of the channel. There have been some studies on the adsorption and transport of multi-component hydrocarbon mixtures in shale organic matter. Ma and Jamili (2016) used Simplified Local-Density theory coupled with Modified Peng- Robinson equation of state to predict the density of pure and mixture hydrocarbons in confined pores. They found that the compositions of the fluid mixtures are not uniformly distributed across the pore. Heavier components (n- butane) tend to accumulate near the wall while lighter components (methane) tend to stay in the center region of the pore. Collell et al. (2015) used EMD and boundary driven non-equilibrium molecular dynamics (BD-NEMD) simulations to study the transport of fluid mixtures for different chemical compositions through a molecular model of kerogen type II. They computed Onsagers coefficients for pure and multi-component mixture of fluids. The results suggested that the flow inside kerogen is of diffusive nature. In this work, Grand Canonical Monte Carlo (GCMC) and NEMD simulations are used to simulate the adsorption behavior and transport of methane in kerogen. A type II kerogen model prepared by Ungerer et al. (2014) is used in this study. In order to build a representative solid state model of kerogen, eight kerogen molecules are placed in a periodic cubic cell. Once the initial configuration of kerogen molecules is prepared, constant- temperature constant-volume (NVT) simulations and then constant-temperature constant-pressure (NPT) simulations are performed to obtain the final structure. For the final structure, density values are calculated and compared with the reported density range for kerogen density. Adsorption isotherm, self and transport diffusion coefficients of methane in the final kerogen structure are also calculated. Model and Method Kerogen Molecular Model In this study, a model unit prepared by Ungerer et al. (2014) is employed to build a crystal structure of type II kerogen. The structure of the unit cell kerogen is shown in Fig. 1. The unit consists of 481 atoms with a formula of C242H219O13N5S2 with a molecular weight of gr/mol. In order to build a representative solid state model of kerogen, eight kerogen molecules are placed in a periodic cubic cell with 10 nm dimension using Moltemplate software (Jewett et al., 2013). The COMPASS (Condensed-Phase Optimized Molecular Potentials for Atomistic Simulation Studies) class2 force field is used to describe the interactions between atoms, bonds, and angles (Sun, 1998). Once the initial configuration of kerogen molecules is prepared, constant-temperature constant-volume (NVT) simulations are performed at 1000 K for 3 ns. Density of the system remains at gr/cm3 for whole NVT simulation time. Several conformations are sampled from NVT simulations. Each sampled conformation goes under successive constant-temperature constantpressure (NPT) simulations for a temperature range of 900 to 300 K at 100 atm pressure. All simulations are performed with 1 fs timestep using LAMMPS software (Plimpton, 1995). Each NPT simulation is performed for 500 ps. The final structure has a density of 1.03 gr/cm3 (Fig. 2), which agrees with the reported range for the kerogen density (0.95 to 1.45 gr/cm3).

4 4 Figure 1 Molecular structure of type II kerogen. Cyan color represents carbon atoms. Figure 2 Final structure of the eight kerogen units (a) 2D and (b) 3D representations. Each cell in the 2D representation is of 10 A size. Porosity Characterization In order to determine the porosity of the kerogen structure, Another Void Program (AVP) is employed (Cuff and Martin, 2004). In this method, two probes are used, one for identifying the accessible volume to external fluids and one for finding all the void spaces. The probe size radius for finding fluid accessible voids has a radius of 1.4 A. AVP is run on the final kerogen structure and total void volume and the largest void volume are determined. A probe size equal to diameter of a methane molecule is used for calculaton of the accessible void volume for the gas; a probe size of 0.5 A is used for isolated voids. Almost half of the void volume (343 A3) belongs to the isolated pores. The gas accessible pore volume is calculated to be 334 A3. The total volume of kerogen solid state is A3 and therefore, the kerogen porosity (available void volume to methane) is 0.7%.

5 5 Diffusion Coefficients Diffusion of gases in nanoporous materials have been extensively studied (Sholl, 2006; Dubbeldam and Snurr, 2007; Smit and Maesen, 2008; Kazemi and Takbiri-Borujeni, 2016d). EMD simulations are usually carried out to the determine the self-diffusivity coefficients. Self-diffusion, Ds, is defined as the mean square displacement of molecules over time and is defined as, (1) where N is the number molecules and i(t) is the displacement vector for the i-th molecule at time t. The angular bracket represents the ensemble average quantity. Another method to determine the selfdiffusivity is using the autocorrelation of the fluctuating streaming velocity values via Green-Kubo relation (Kanellopoulos, 2000), (2) where uz(t) = Σdxi/dt. Both methods essentially give the same results. In this work, the mean square displacement method is used. Another important type of diffusion is transport diffusivity or Fickian diffusion. Fickian constitutive relation describes the transport of single-component fluids as, (3) where Dt is the transport diffusivity, c is the spatial concentration gradient, and J is the molecular diffusive flux. This equation can be written in the terms of pressure gradient as (Roy et al., 2003), (4) where M is the molar mass, T is temperature, and R is the universal gas constant. In NEMD simulations, the transport coefficients can be calculated from the measured molecular flux as (Bhatia and Nicholson, 2003), (5) where kb is the Boltzmann constant, is the average gas density, and F is the applied external force. Molecular Dynamics Methods The kerogen molecules are placed in a simulation box with 20 nm x 3.5 nm x 3.5 nm dimension (Fig. 3). Grand Canonical Monte Carlo (GCMC) simulations are performed at different pressures to determine the adsorption isotherms for methane. In GCMC simulations, the pressure inside the control volume is kept constant by insertion and deletion of molecules. The probability of inserting a molecule is determined as, (6)

6 6 Figure 3 Simulation setup for EMD and NEMD simulations. where is the absolute activity at temperature T, Λ is the de Broglie wavelength, and μ is the chemical potential. Changes in the potential energy resulting from the insertion and deletion of molecules are represented by ΔU, volume of control volume is VCV, and number of molecules in control volume is NCV. Inserted molecules are assigned a velocity using Maxwell-Boltzmann distribution. The probability of deleting a molecule is, (7) Temperature of the inserted molecules is determined based on the specified reservoir temperature, i.e., 300 K. EMD and NEMD simulations are performed to find the self and transport diffusivity coefficients, respectively. COMPASS force field is used for all simulations. The like atom pairs interaction are modeled using LJ-9-6 potential. For unlike atom pairs, the sixth-order combination rule is used. Methane is treated as a LJ fluid and its interactions are modeled using LJ-12-6 potential. A cut off distance of 10 A is used for all simulations. NEMD simulations are performed at six different pressures. For each pressure, four external forces of 0.01, 0.05, 0.1, and are applied to the inlet region. Simulations are performed for 5 ns with a timestep of 1 fs. The NEMD simulations are performed within NVT ensemble. An initial Gaussian velocity distribution with a temperature of 300 K is considered for methane molecules. The exerted force to the molecules is proportional to pressure drop as described by (Zhu et al., 2002; Carr et al., 2011), (8) where A is the area perpendicular to the applied force. Determining the actual pressure gradient in NEMD simulations is not straightforward. Therefore, to compare the molecular fluxes and velocities in different pressure gradients, the term NF/AL, which is proportional to pressure gradient, is used. The number of molecules at the inlet region is calculated at each time step and averaged over the total simulation time. Results and Discussion Adsorption Isotherms In order to differentiate between the bulk and adsorbed molecules, excess loading values are calculated. Excess adsorption is the subtraction of total gas quantity in pore spaces and the unconfined gas quantity (bulk state) in the same volume.

7 7 The excess quantities are calculated for a pressure range of 10 to 130 aim. Excess adsorption values increase from 1.72 to 4.11 mmol/gr as pressure increases from 10 to 130 aim (Fig. 4). Excess loading values tend to reach a plateau at pressures above 80 aim. Typically, the excess adsorption values decrease at high pressures when the gas adsorption reaches its maximum value (saturated state) while the gas density keeps increasing. We expect to see a reduction in excess adsorption values at pressures higher than 130 aim. Figure 4 Excess adsorption isotherm calculated from MD simulations along with the experimental results of Gasparik et al. (2014). The experiments were run on a sample of Haynesville shale with Vitrinite Reflectance of 2.1% and total organic content (TOC) of 3.3%. The excess adsorption results are compared with the experimental results of Gasparik et al. (2014) for a Hay- nesville shale sample with Vitrinite Reflectance (VR) of 2.1% and total organic content (TOC) of 3.3% (Fig. 4). This VR value indicates that the shale sample is in the dry gas zone. The molecular simulation results are fairly close to experimental results. One possible reason that they are not matched is that the experiments were performed at a temperature of 338 K, while the simulations are performed at 300 K. However, as the temperature increases, the excess adsorption amount reduces at the same pressure (Mosher et al., 2011). Hence, lower values of excess amount is expected for simulations with higher temperatures. Diffusion Coefficients Self-diffusion coefficients are calculated from EMD simulations using Eq. 1. Selfdiffusion coefficients steeply decrease as pressure increases at low pressures (Fig. 5a). They do not decrease significantly at pressures higher than 50 aim. As the loading of methane inside kerogen pores increases from 1.72 to 3.11 mmol/gr for a pressure range of 10 to 50 aim, the self diffusion coefficients decrease from to m2/s.

8 8 Figure 5 Diffusion coefficients vs. pressure. (a) Self diffusion coefficients of methane in kerogen (b) Transport diffusion coefficients. Transport diffusion coefficients are computed for a pressure range of 10 to 100 atm. Similar to selfdiffusion coefficients, as the pressure increases, the transport diffusion coefficients decrease from to m2/s (Fig. 5b). As pressure increases, transport diffusion coefficients approach the selfdiffusion coefficients. The transport diffusion coefficients are higher than self-diffusivity coefficients for pressures less than 100 atm. For self and transport diffusion coefficients, there is a steep decrease in the values at low pressures (lower than 40 atm), while at higher pressures the values do not significantly decrease with pressure (they reach a plateau). Conclusions In this study, adsorption and transport of methane in a three dimensional type II kerogen model are studied using molecular dynamics simulations. The kerogen model prepared by Ungerer et al. (2014) is used in this study. Grand Canonical Monte Carlo (GCMC) simulations are used to simulate the adsorption of methane and Non-Equilibrium Molecular Dynamics (NEMD) simulations are employed to simulate transport of methane in the kerogen model. Simulation results for the adsorption isotherm are fairly close to experimental results reported for the Haynesville shale sample. As pressure increases, transport diffusion coefficients approach the self-diffusion coefficients. For self and transport diffusion coefficients, there is a steep decrease in the values at low pressures (lower than 40 atm), while at higher pressures the values do not significantly decrease with pressure. 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. Nomenclature Displacement vector A Area perpendicular to the applied force c Concentration

9 9 Ds Dt F J kb M N p+ P R T U V Z Self-diffusion Transport diffusivity External force Molecular diffusive flux Boltzmann constant Molar mass Number molecules Probability of inserting a molecule Probability of deleting a molecule Universal gas constant Temperature Potential energy Volume Absolute activity Greek Symbols Average gas density Λ de Broglie wavelength μ Chemical potential Subscripts References CV Control volume i i-th molecule Arya, G., H. C. Chang, and E. J. Maginn (2001). A critical comparison of equilibrium, non-equilibrium and boundarydriven molecular dynamics techniques for studying transport in microporous materials. Journal of Chemical Physics 115(17), Behar, F. and M. Vandenbroucke (1987). Chemical modelling of kerogens. Organic Geochemisiry 11(1), Bhatia, S. K. and D. Nicholson (2003). Hydrodynamic origin of diffusion in nanopores. Physical review leiiers 90(1), Boosari, S. S. H., U. Aybar, and M. O. Eshkalak (2016). Unconventional resource's production under desorption- induced effects. Peiroleum. Carr, R., J. Comer, M. D. Ginsberg, and A. Aksimentiev (2011). Modeling pressure-driven transport of proteins through a nanochannel. Nanoiechnology, IEEE Transactions on 10(1), Collell, J., G. Galliero, R. Vermorel, P. Ungerer, M. Yiannourakou, F. Montel, and M. Pujol (2015). Transport of Multicomponent Hydrocarbon Mixtures in Shale Organic Matter by Molecular Simulations. Journal of Physical Chemisiry C 119(39), Collell, J., P. Ungerer, G. Galliero, M. Yiannourakou, F. Montel, and M. Pujol (2014). Molecular simulation of bulk organic matter in type ii shales in the middle of the oil formation window. Energy & Fuels 28(12), Cuff, A. L. and A. C. Martin (2004). Analysis of void volumes in proteins and application to stability of the p53 tumour suppressor protein. Journal of molecular biology 344(5), Dabirian, R., R. Mohan, O. Shoham, and G. Kouba (2016). Critical sand deposition velocity for gas-liquid stratified flow in horizontal pipes. Journal of Natural Gas Science and Engineering 33, Dabirian, R., R. S. Mohan, O. Shoham, G. Kouba, et al. (2015). Sand transport in stratified flow in a horizontal pipeline. In SPE Annual Technical Conference and Exhibiiion. Society of Petroleum Engineers. Dubbeldam, D. and R. Snurr (2007). Recent developments in the molecular modeling of diffusion in nanoporous materials. Molecular Simulaiion 33(4-5), Dupuis, M., J. Watts, H. Villar, and G. Hurst (1989). The general atomic and molecular electronic structure system hondo: version 7.0. Compuierphysics communicaiions 52(3),

10 10 Eshkalak, M. O., U. Aybar, et al. (2015). The effect of desorption-induced porosity-permeability changes and geomechanics on production from us shale gas formations. In 49th US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association. Firouzi, M., K. Alnoaimi, A. Kovscek, and J. Wilcox (2014). Klinkenberg effect on predicting and measuring helium permeability in gas shales. International Journal of Coal Geology 123, Firouzi, M. and J. Wilcox (2012). Molecular modeling of carbon dioxide transport and storage in porous carbon- based materials. Microporous and Mesoporous Materials 158, Gasparik, M., P. Bertier, Y. Gensterblum, A. Ghanizadeh, B. M. Krooss, and R. Littke (2014). Geological controls on the methane storage capacity in organic-rich shales. International Journal of Coal Geology 123, Guan, X.-H., Y. Liu, D. Wang, Q. Wang, M.-S. Chi, S. Liu, and C.-G. Liu (2015). Three-dimensional structure of a huadian oil shale kerogen model: An experimental and theoretical study. Energy & Fuels 29(7), Heller, E. (2006). Guided gaussian wave packets. Accounts of chemical research 39(2), Jeong, K. and T. Kobylinski (1983). Organic-mineral matter interactions in green river oil shale. Prepr. Pap.-Am. Chem. Soc., Div. Fuel Chem.;(United States) 28(C0NF ). Jewett, A. I., Z. Zhuang, and J.-E. Shea (2013). Moltemplate a coarse-grained model assembly tool. Biophysical Journal 104(2), 169a. Jin, Z. and A. Firoozabadi (2015). Flow of methane in shale nanopores at low and high pressure by molecular dynamics simulations. The Journal of chemical physics 143(10), Kanellopoulos, N. K. (2000). Recent advances in gas separation by microporous ceramic membranes, Volume 6. Elsevier. Kazemi, M. and A. Takbiri-Borujeni (2016a). Effect of adsorption in flow of gases in organic nanopores: A molecular dynamics study. In Unconventional Resources Technology Conference, San Antonio, Texas. Kazemi, M. and A. Takbiri-Borujeni (2016b). Flow of gases in nanocapillary organic nanopores of shale: A boundarydriven molecular simulation study. In SPE Western Regional Meeting. Society of Petroleum Engineers. Kazemi, M. and A. Takbiri-Borujeni (2016c). Flow of gases in slit shaped organic nanopores of shale: A boundary-driven molecular simulation study. In SPE Low Perm Symposium. Soeciety of Petroleum Engineers. Kazemi, M. and A. Takbiri-Borujeni (2016d). Non-equilibrium molecular dynamics simulation of gas flow in organic nanochannels. Journal of Natural Gas Science and Engineering. Kidena, K., S. Murata, and M. Nomura (2008). A newly proposed view on coal molecular structure integrating two concepts: Two phase and uniphase models. Fuel Processing Technology 89(4), Ma, Y. and A. Jamili (2016). Modeling the density profiles and adsorption of pure and mixture hydrocarbons in shales. Journal of Unconventional Oil and Gas Resources 14, Mosher, K., Y. Liu, and J. Wilcox (2011). The Impaci of Pore Size On Meihane and CO2 Adsorpiion In Carbon. Ph. D. thesis, Stanford University. Nomura, M., L. Artok, S. Murata, A. Yamamoto, H. Hama, H. Gao, and K. Kidena (1998). Structural evaluation of zao zhuang coal. Energy & fuels 12(3), Orendt, A. M., I. S. Pimienta, S. R. Badu, M. S. Solum, R. J. Pugmire, J. C. Facelli, D. R. Locke, K. W. Chapman, P. J. Chupas, and R. E. Winans (2013). Three-dimensional structure of the siskin green river oil shale kerogen model: a comparison between calculated and observed properties. Energy & Fuels 27(2), Plimpton, S. (1995). Fast parallel algorithms for short-range molecular dynamics. Journal of compuiaiional physics 117(1), Roy, S., R. Raju, H. F. Chuang, B. A. Cruden, and M. Meyyappan (2003). Modeling gas ow through microchannels and nanopores. Journal of applied physics 93(8). Ru, X., Z. Cheng, L. Song, H. Wang, and J. Li (2012). Experimental and computational studies on the average molecular structure of chinese huadian oil shale kerogen. Journal of Molecular Siruciure 1030, Rullkotter, J. and W. Michaelis (1990). The structure of kerogen and related materials. a review of recent progress and future trends. Organic Geochemisiry 16(4), Scouten, C., M. Siskin, K. Rose, T. Aczel, S. Colgrove, and R. PabstJr (1989). Detailed structural characterization of the organic material in rundle ramsay crossing oil shale. American Chemical Socieiy, Division of Peiroleum Chemisiry, Preprinis;(USA) 34(CONF ). Sholl, D. S. (2006). Understanding macroscopic diffusion of adsorbed molecules in crystalline nanoporous materials via atomistic simulations. Accounis of Chemical Research 39(6), Smit, B. and T. L. Maesen (2008). Molecular simulations of zeolites: adsorption, diffusion, and shape selectivity. Chemical reviews 108(10), Sun, H. (1998). Compass: an ab initio force-field optimized for condensed-phase applications overview with details on alkane and benzene compounds. The Journal of Physical Chemisiry B 102(38), Tissot, B., B. Durand, J. Espitalie, and A. Combaz (1974). Influence of nature and diagenesis of organic matter in formation of petroleum. AAPG Bulleiin 58(3),

11 11 Ungerer, P., J. Collell, and M. Yiannourakou (2014). Molecular modeling of the volumetric and thermodynamic properties of kerogen: Influence of organic type and maturity. Energy & Fuels 29(1), Vandegrift, G. F., R. E. Winans, R. G. Scott, and E. P. Horwitz (1980). Quantitative study of the carboxylic acids in green river oil shale bitumen. Fuel 59(9), Vandenbroucke, M. (2003). Kerogen: from types to models of chemical structure. Oil & gas science and technology 58(2), Zhu, F., E. Tajkhorshid, and K. Schulten (2002). Pressure-induced water transport in membrane channels studied by molecular dynamics. Biophysical journal 83(1),