Multi-scale Asymptotic Analysis of Gas Transport in Shale Matrix (original) (raw)
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A multi-scale approach to the physical adsorption in slit pores
Chemical Engineering Science, 2011
Adsorption isotherms are the foundation of gas storage and separation operations. The isotherm models are classified into three scale levels with empiricisms in macroscopic level, requirements of long computing time and idealized conditions in microscopic level, as well as gaps in knowledge between these two levels. A multi-scale modeling methodology is developed in this paper in order to reduce the identified limitations. Microscopic molecular simulations (MS) based on the grand canonical Monte Carlo (GCMC) method are carried out followed by the development of the localized adsorption isotherms defined as the intermediate level models. They are represented by the Boltzmann factor and the local Langmuir equations. The macroscopic models are then formulated through the integration of small scale models. The following three contributions are achieved in the paper. First of all, guidelines for the validity of the Boltzmann factor are established, showing its practical significance, and the local Langmuir isotherm is justified as a good approximation to the results from microscopic simulations. Secondly, it is demonstrated that the pore size distributions can be determined using GCMC simulations coupled with the measured adsorption isotherms as exemplified by a case study on a coal specimen. Finally, using the measurement data reported by Bae and Bhatia (2006) for carbon dioxide adsorption on coal, we show that the overall adsorption isotherms can be determined from the multi-scale approach through the integration of smaller scale models with pore size distributions without the empiricism, indicating the success of the methodology. Further work is needed to improve the prediction accuracy for methane adsorption on coal specimens.
Energy Reports
Gas transport in ultra-tight rock is non-Darcian. In addition to continuum flow, there are multiple other flow mechanisms such as slip flow and pore and surface diffusion. Various multi-physics models have been put forth in the literature to forecast the apparent permeability of gas in shales and ultratight formations. However, a means of accurately describing the relative contributions of physics in multiscale pore systems remains a challenge. Moreover, it is important to explain pore size, pressure dependency, and the relationships among adsorption, diffusion, and permeability in porous media. For these reasons, a semi-analytical model is proposed to predict gas permeability according to the viscous flux, pore diffusion and surface diffusion and establish control of the adsorbed gas layer. The reliability of the equations developed was checked by validation using experimental and molecular simulation data obtained from macropore-and micropore-sized nanotubes systems respectively. Furthermore, the equations' performance for micropores was compared to existing theoretical shale permeability models. The subsequent sensitivity analysis showed that permeability is sensitive to the nanoscale geometry factor and adsorption mechanisms. Moreover, the relevance of the surface diffusion was found to increase as the pore size decreased. For instance, surface diffusion constituted over 50% of the apparent permeability below the 10 MPa and 5.0 MPa conditions in micro-and mesopore systems, respectively, while the Darcy scale phenomenon controlled the transport of gas in macropores. Across all diffusion regimes, the microstructure geometry and sorption dynamics significantly influenced the total diffusion of methane, particularly at low pressures and decreased pore sizes. The decline in reservoir pressure during production shifted the relative importance of the adsorption and diffusion mechanisms, consequently altering the apparent gas permeability. Therefore, reservoir management teams should take into account the dynamics of gas permeability at different pressures and representative pore sizes throughout the life cycle of the asset.
Pore-scale modeling of competitive adsorption in porous media
Journal of Contaminant Hydrology, 2011
In this paper we present a smoothed particle hydrodynamics (SPH) pore-scale multicomponent reactive transport model with competitive adsorption. SPH is a Lagrangian, particle based modeling method which uses the particles as interpolation points to discretize and solve flow and transport equations. The theory and details of the SPH pore-scale model are presented along with a novel method for handling surface reactions, the continuum surface reaction (CSR) model. The numerical accuracy of the CSR model is validated with analytical and finite difference solutions, and the effects of spatial and temporal resolution on the accuracy of the model are also discussed. The pore-scale model is used to study competitive adsorption for different Damköhler and Peclet numbers in a binary system where a plume of species B is introduced into a system which initially contains species A. The pore-scale model results are compared with a Darcy-scale model to investigate the accuracy of a Darcy-scale reactive transport model for a wide range of Damköhler and Peclet numbers. The comparison shows that the Darcy model over estimates the mass fraction of aqueous and adsorbed species B and underestimates the mass fractions of species A. The Darcyscale model also predicts faster transport of species A and B through the system than the porescale model. The overestimation of the advective velocity and the extent of reactions by the Darcyscale model are due to incomplete pore-scale mixing. As the degree of the solute mixing decreases with increasing Peclet and Damköhler numbers, so does the accuracy of the Darcy-scale model.
Raoof, A. and S.M. Hassanizadeh, Upscaling Transport of Adsorbing Solutes in Porous Media
Adsorption of solutes in porous media is commonly modeled as an equilibrium process. Indeed, one may safely assume that within the pore space, the concentration of adsorbed solute at a point on the grain surface is algebraically related to the concentration in the fluid next to the grain. The same, however, cannot be said about average concentrations. In fact, during solute transport, concentration gradients develop within the pore space, and these could potentially give rise to a scale-dependent adsorption process. The main objective of this research is to develop relationship between porescale adsorption coefficient and corresponding upscaled adsorption parameters. Two approaches are used: Theoretical averaging and numerical upscaling. In the averaging approach, equilibrium adsorption is assumed at the pore-scale and solute transport equations are averaged over REV. This leads to explicit expressions for macro-scale adsorption rate constants as a function of micro-scale parameters. In the numerical approach, first we simulate solute transport within a single tube undergoing equilibrium adsorption at the pore wall, and then flux averaged concentration breakthrough curves are obtained. These are used to determine the upscaled adsorption rate constants as functions of pore-scale hydraulic and adsorption parameters. Results of the two approaches agree very well.
Impact of mass balance calculations on adsorption capacities in microporous shale gas reservoirs
Fuel, 2007
Determination of the adsorbed reservoir capacity of gas shales by adsorption analyses as done routinely by mass balance maybe in significant error if the effects of pore-size dependent void volume (porosity) is not considered. It is shown here that with increasing pressure, helium, which is invariably used to measure void volume, can access pores that are not available for adsorption to gases with larger kinetic diameters as highlighted by experiments with zeolites of known pore-size distribution. Helium can diffuse and/or adsorb in restricted pores of the microporous samples, as indicated by a larger void volume with pressure. The error in adsorption calculations due to helium void volume calibrations for high pressure methane isotherms is most significant with low organic-carbon content, moisture-equilibrated shales and mudrocks in which the overall adsorptive capacity is low. In such samples negative adsorption can be calculated due to the void volume of helium used in the mass balance calculations exceeding the void volume to methane-a reflection of greater pore-space accessibility of the smaller helium molecule than methane. The amount of the error introduced by using helium void volume in mass balance calculations is pore-size and pore-size distribution dependent. Organic-rich shales and mudrocks or coals which do not show negative methane adsorption also maybe in error but the error is masked by their larger adsorbed gas capacities. Such findings underline the importance of analysis gas-type as kinetic diameter size will influence the penetrability/diffusion of the gas through the sample and hence the calculated adsorbed gas capacities.
Effect of the reservoir size on gas adsorption in inhomogeneous porous media
Journal of Physics: Condensed Matter, 2009
We study the influence of the relative size of the reservoir on the adsorption isotherms of a fluid in disordered or inhomogeneous mesoporous solids. We consider both an atomistic model of a fluid in a simple, yet structured pore, whose adsorption isotherms are computed by molecular simulation, and a coarse-grained model for adsorption in a disordered mesoporous material, studied by a density functional approach in a local mean-field approximation. In both cases, the fluid inside the porous solid exchanges matter with a reservoir of gas that is at the same temperature and chemical potential and whose relative size can be varied, and the control parameter is the total number of molecules present in the porous sample and in the reservoir. Varying the relative sizes of the reservoir and the sample may change the shape of the hysteretic isotherms, leading to a "reentrant" behavior compared to the grand-canonical isotherm when the latter displays a jump in density. We relate these phenomena to the organization of the metastable states that are accessible for the adsorbed fluid at a given chemical potential or density.
2017
Gas production from shale gas reservoirs plays a significant role in satisfying increasing energy demands. Comparedwith conventional sandstone and carbonate reservoirs, shale gas reservoirs are characterized by extremely low porosity, ultra-low permeability and high clay content. Slip flow, diffusion, adsorption and desorption are the primary gas transport processes in shale matrix, while Darcy flow is restricted to fractures. Understanding methane diffusion and adsorption, and gas flow and equilibrium in the low-permeability matrix of shale is crucial for shale formation evaluation and for predicting gas production. Modeling of diffusion in low-permeability shale rocks requires use of the Dusty gas model (DGM) rather than Fick’s law. The DGM is incorporated in the TOUGH2 module EOS7C-ECBM, a modified version of EOS7C that simulates multicomponent gas mixture transport in porous media. Also included in EOS7C-ECBM is the extended Langmuir model for adsorption and desorption of gases....
Molecular simulation of shale gas adsorption and diffusion in inorganic nanopores
Molecular Simulation, 2014
We studied the structural and dynamical properties of methane and ethane in montmorillonite (MMT) slit pore of sizes 10, 20 and 30 Å using grand canonical Monte Carlo and classical molecular dynamics (MD) simulations. The isotherm, at 298.15 K, is generated for pressures up to 60 bar. The molecules preferentially adsorb at the surface as indicated by the density profile. In case of methane, we observe only a single layer, at the pore wall, whose density increases with increasing pressure. However, ethane also displays a second layer, though of low density in case of pore widths 20 and 30 Å . In-plane self-diffusion coefficient, D k , of methane and ethane is of the order of 10 26 m 2 /s. At low pressure, D k increases significantly with the pore size. However, D k decreases rapidly with increasing pressure. Furthermore, the effect of pore size on D k diminishes at high pressure. Ideal adsorbed solution theory is used to understand the adsorption behaviour of the binary mixture of methane (80%) and ethane (20%) at 298.15 K. Furthermore, we calculate the selectivity of the gases at various pressures of the mixture, and found high selectivity for ethane in MMT pores. However, selectivity of ethane decreases with increase in pressure or pore size.