Ali Takbiri-Borujeni

Predicting Gas Apparent Permeability of Shale Samples: A Novel Analytical Approach

Natural gas production of the United States from shale resources increased from 4 percent of total gas production in 2005 to 40 percent in 2012. These resources are different from conventional hydrocarbon resources due to the presence of extremely tight organic pores and low permeabilities. Presence of the nanopores may cause rarefaction effects, especially in laboratory conditions, which increases the effects of temperature and pressure on the apparent permeability of shale samples. In order to determine the permeability of these resources, laboratory measured apparent permeabilities, if conducted in low pressure and temperature, need to be extrapolated to reservoir conditions. In addition, gas flow in low pressures has important applications in predicting the gas production rates from unconventional reservoirs. Analytical methods for estimating gas apparent permeability (AP) of shale have been already proposed, e.g. Navier-Stokes and Advective -Diffusive Models (ADM); however, they are valid for a limited range of Knudsen numbers (Kn 0.5) and they have oversimplifying assumptions that overestimate the mass flux (or permeability) of nanopores. In addition, their results do not show the effect of temperature and gas molecular weight on AP. The presented work aims to develop an analytical model for gas apparent permeability of nanopores which is valid for Knudsen number up to unity. Solutions to the Regularized 13 (R13)-moment equations (extension of Grad’s 13-moments equations) provide a reliable tool to derive an analytical model for gas AP in nanotubes. The novelty of this work is that we provide an analytical model for gas AP which is valid for higher range of Knudsen numbers (by comparing with the kinetic data) in contrast to the previously developed analytical models. The new model is used to predict the impact of controlling parameters such as temperature, pressure, molecular weight, pore size, and Tangential Momentum Accommodation Coefficient (TMAC) on gas AP. It is shown that the gas molecular weight and temperature have significant effect on gas apparent permeability at low pressures. The effect of adsorption on AP of nanotubes is studied by employing the experimental Langmuir isotherms of different shale samples. The bundle of tubes method is used to compare R13 AP model with the experimental data of a Marcellus shale core plug. The model’s AP results for Nitrogen and Carbon Dioxide agree with the experimental measurements.

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

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.

Effects of Stress-Dependent Hydraulic Properties of Proppant Packs on the Productivity Indices of the Hydraulically Fractured Gas Reservoirs

Hydraulic fracturing stimulates wells and has enabled exploitation of the vast unconventional hydrocarbon resources in the US and globally. Proppants, which are granular materials that prevent fractures from closing, must provide high fracture conductivities and withstand closure stresses without getting crushed. Advances in imaging technologies and high-performance computing enable calculation of transport and mechanical properties of pore-scale images. Imagebased mechanical and flow simulations can rapidly and accurately estimate the transport properties of proppant packs in fractures at different closure stresses, providing a credible alternative to difficult and expensive physical experiments. This study examines transport properties of a ceramic proppant pack with confining stresses from zero to 20,000 psi. The images of this packing show rearrangement of the packing structure, embedding of the grains at the rock wall, and crushing of individual proppant particles. Lattice Boltzmann (LB) simulation results of this proppant pack indicate that the permeability and inertial flow parameter are sensitive to stress at high stresses (which crush the proppant particles) compared to lower stresses. Predicted stress-dependent permeability and non-Darcy factors corresponding to the effective stress fields around the hydraulic fractured completions are included in a two-dimensional gas reservoir simulator to calculate the productivity indices. Productivity indices with permeability and non-Darcy factors kept constant at initial effective stress (6000 psi) are ca. 0.03 percent higher than those with stress-dependent permeability and non-Darcy factors for a gas rate of 20 MMscf/D.Hydraulic fracturing stimulates wells and has enabled exploitation of the vast unconventional hydrocarbon resources in the US and globally. Proppants, which are granular materials that prevent fractures from closing, must provide high fracture conductivities and withstand closure stresses without getting crushed. Advances in imaging technologies and high-performance computing enable calculation of transport and mechanical properties of pore-scale images. Imagebased mechanical and flow simulations can rapidly and accurately estimate the transport properties of proppant packs in fractures at different closure stresses, providing a credible alternative to difficult and expensive physical experiments. This study examines transport properties of a ceramic proppant pack with confining stresses from zero to 20,000 psi. The images of this packing show rearrangement of the packing structure, embedding of the grains at the rock wall, and crushing of individual proppant particles. Lattice Boltzmann (LB) simulation results of this proppant pack indicate that the permeability and inertial flow parameter are sensitive to stress at high stresses (which crush the proppant particles) compared to lower stresses. Predicted stress-dependent permeability and non-Darcy factors corresponding to the effective stress fields around the hydraulic fractured completions are included in a two-dimensional gas reservoir simulator to calculate the productivity indices. Productivity indices with permeability and non-Darcy factors kept constant at initial effective stress (6000 psi) are ca. 0.03 percent higher than those with stress-dependent permeability and non-Darcy factors for a gas rate of 20 MMscf/D.

Flow of Multicomponent Gases in Carbon-Based Organic Nanopores

In the study of transport of gases in shale reservoirs, a special attention should be paid to gas transport in organic nanopores due to their nano-scale pore sizes and adsorption phenomena at the pore surfaces. Most of current studies are focused on the transport of single component fluids, mainly methane. The objective for this work is to investigate transport of multicomponent gases in carbon-based organic pores. In this study, adsorption and transport of multicomponent gas systems in identical setups of graphite channels with rough surfaces are investigated using non-equilibrium molecular dynamics simulations (NEMD). Simulations are performed for two gas samples with different compositions for channel heights of 2 and 4 nm. For each simulation, the velocity, density, and mass flux profiles are computed. Moreover, the selectivity values of heaviest molecule (hexane) over other gas components are determined. Finally, diffusion coefficients of each gas component are computed and compared. Based on MD simulation results, most of heavier gas components are adsorbed to the wall. Hexane, which is the heaviest gas component, has a higher tendency to be adsorbed to the channel walls compared to lighter gas components. Therefore, in real systems, most of the heavier components may stay in reservoir in adsorbed state. Furthermore, in contrary to previous studies in which plug-shaped flow profile were observed, parabolic-shaped velocity profile are observed due to presence of rough channel surfaces and heavier gas components. Based on the simulation results, heavier gas components have lower diffusion coefficients compared to lighter components. This work is one of the few in-depth investigations of the transport of natural gas systems in organic pores. The results in this study can potentially modify the multiscale formalism of fluid flow in shale resources.

Effect of Kerogen Type and Maturity on Performance of Carbon Dioxide Storage in Shale

Potential for sequestration of carbon dioxide in organic rich shale is investigated in this work. Adsorption isotherms and Onsager diffusion coefficients are determined using molecular dynamics simulations for atomistic kerogen models. The kerogen unit models prepared by (Ungerer et al., 2014) are used in this study. To build representative solid state models for kerogen, eight kerogen molecules are placed in a periodic cubic cell. Once the initial configuration of kerogen molecules is prepared, constant-temperature constantvolume simulations and then constant-temperature constant-pressure simulations are performed to obtain the final structures. For the final structure, computed density and adsorption isotherms are within the reported experimental values. Grand Canonical Monte Carlo (GCMC) simulations are performed for CH4-CO2 mixtures to investigate binary adsorption isotherms in kerogen models with different maturities. Equilibrium molecular dynamics (EMD) simulations are used to determine Onsager diffusion coefficients. As pressure for each species in the binary mixtures increases, its adsorbed amount increases and adsorbed amount of the other species decreases. Adsorbed amount of CO2 is higher than that of CH4 for all kerogen types at all pressures tested due to the strong permanent quadrapole moment of CO2. Due to higher adsorption affinity of CO2 to kerogen pore surfaces compared to CH4, its Onsager diffusion coefficients are smaller than those for CH4 for all kerogen types. Introduction Shale gas is expected to account for 30% of world natural gas production by 2040 (U.S. Energy Information Administration, 2014). Large scale production of gas from shale resources can lead to large capacities for storage of CO2 in these resources. Furthermore, due to the higher affinity of the organic matter to CO2 compared to CH4, injection of CO2 can replace the adsorbed CH4 and therefore, enhances the recovery of natural gas (Kazemi and Takbiri-Borujeni, 2016c). Modeling transport and storage of CO2 in organic pores of shale is complex due to small sizes of the pores and also differences in magnitude of intermolecular forces between fluid molecules and solid molecules at the pore walls (Kazemi and Takbiri-Borujeni, 2015; Kazemi

Molecular Dynamics Study of Transport and Storage of Methane in Kerogen

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.