Simulation Of Gas Transport Research Articles

A model for describing advective and diffusive gas transport through initially saturated bentonite with consideration of temperature

Understanding the gas migration mechanism in an initially saturated bentonite is of great importance for evaluation of the long-term performance of a deep geological repository for disposal of high-level radioactive wastes. Previous researches usually neglect the gas diffusion process, but adopted the advective gas flow theory (visco-capillary flow or dilatant gas flow) to describe the gas transport in the initially water-saturated bentonite clays. In this study, gas migration process was regarded as results of a combination of diffusive transport of dissolved gas through pore water and advective flow along the gas pathways formed in the bentonite matrix. Meanwhile, dilation of the gas flow pathways with variation of the external stress and gas pressure during the advective flow was also considered. Based on this concept, a new model was proposed to describe the advective and diffusive gas transports with consideration of temperature. Validation was conducted using the gas injection tests performed under different boundary conditions in literature. Comparisons show that the diffusion and advection-controlled process provided by the proposed model can effectively simulate gas transport in the compacted GMZ bentonite. For gas migration under lower injection pressures, the contributions of advective gas flow to the gas flux are comparable to that of diffusion. With the increase of the injection pressure, the advective gas fluxes would gradually dominate over the diffusive transport. Meanwhile, predicted degree of saturation of the compacted bentonite is maintained at above 99% during the whole gas migration process, indicating that advective movement of gas was highly discrete in initially saturated bentonite.

A lattice Boltzmann model for simulating gas transport in coal nanopores considering surface adsorption and diffusion effects

The gas flow in coal is extremely complicated as a combined results of multiple flow mechanisms and complex pore structures. Comprehensive understanding of gas flow behaviors in coal is of great importance for the prediction of coalbed methane (CBM) production and the elimination of gas-induced disasters in coal mines. Based on the lattice Boltzmann method (LBM), this study constructs a LB model considering surface adsorption and diffusion effects, which involves multiple mechanisms of gas flow, including viscous flow, enhanced gas slippage (gas slippage is enhanced by surface diffusion) and surface diffusion. The results show that in micropores (<2 nm) and mesopores (2–50 nm), under the effect of adsorbed gas, bulk gas flow velocity increases at a low pressure but decreases at a high pressure. Adsorbed gas surface diffusion permeability, enhanced gas slippage permeability and viscous flow permeability decrease with the rise of pore pressure. In nanopores in coal reservoirs, surface diffusion more significantly enhances gas slippage at a low pressure and in smaller pores. Besides, in the flow calculation, gas slippage without the considering effect of adsorbed gas and Knudsen diffusion can replace each other. According to the results from the LB model, the apparent diffusion coefficients of gas in coal particles decreases with the increase of pore pressure in smaller pores(<10 nm) but increases in larger pores(>10 nm). The study further investigates flow mechanisms controlling the CBM extraction yield in different extraction stages. In the early stage of extraction, the CBM extraction yield is controlled by Darcy seepage in fractures; in the middle stage, it is controlled by viscous flow in larger matrix pores; in the late stage, it is controlled by gas diffusion induced by the superposition of surface diffusion and enhanced gas slippage in matrix micropores and mesopores.

Mortar dynamic coupled model for calculating interface gas exchange between organic and inorganic matters of shale

Shale gas has revolutionized the world energy in recent years. In this work, a mortar dynamic coupled model (MDCM) is successfully built for simulating gas transport from molecular motion in nanopores to highly permeable fractures. Results show that the production duration of MDCM can reach about tenfold that of a single medium model, which affords a microscale explanation for the long tail production. We also propose a two-stage process in the variation of the mass-exchange-rate with the pressure difference of organic matter and inorganic matter: it is nonlinear in Stage Ⅰ, while shows a linear relationship in Stage Ⅱ. Combined with theoretical analyses, numerical simulations and dimensional analyses, an efficient and practical relation for calculating the interface gas exchange in tail production is obtained. The relation offers a valuable tool for the gas transport properties in fractured shale and is finally validated by a gas expansion experiment. Better performance can be obtained in terms of accuracy and precision than the current model. These results stress the need for a change of paradigm from statistic to dynamic trans-scale transport. The new insights into transport in the long-term shale gas production suggest new leads for the industry.

Simulation of gas transport in a landfill with layered new and old municipal solid waste

Average biodegradation rate of newly filled municipal solid waste (MSW) in landfills is relatively fast, and the landfill gas produced by the new MSW biodegradation can cause great variations in gas pressure. To predict the gas pressure distribution in the MSW layer, a one-dimensional gas transport model is established in this study. The following factors are considered in this model: (1) the variation of gas permeability with depth; (2) the anisotropy ratio of gas permeability; (3) the settlement caused by waste biodegradation. Furthermore, a single peak model for gas production is applied as the source term of gas production. The equation for settlement caused by waste biodegradation is presented, and the time of peak gas production rate is obtained by fitting the settlement of the newly filled layer. The stratification of the unsaturated and saturated regions is taken into account by distinguishing the difference in gas saturation. The layering of the new and old waste layers is considered by distinguishing the difference in the length of time that waste has been degraded to produce gas. Based on the method of numerical calculation, the gas pressure distribution in the landfill with layered new and old MSW is well simulated. The position where the maximum gas pressure occurs is found. The sensitivity analysis shows that the influence of the anisotropy ratio on gas pressure distribution is more significant.

Multiscale simulations of shale gas transport in micro/nano-porous shale matrix considering pore structure influence

Unravelling the transport characteristic of shale gas in actual extraction process is significantly important to improve the gas recovery efficiency and production. But the geological complexity of shale formations in particular makes it challenging to comprehensively cognize the transport mechanisms at multiscale. Traditional shale gas transport model based on circle nanopores system would be failed to capture the realistic transport process of shale gas in the matrix consisting of abundant micro/nano-pores with complex pore structures. Towards this end, herein multiscale simulations were performed to investigate the transport characteristic and mechanism of shale gas in micro/nano-porous shale matrix combining the molecular dynamics (MD) simulations, analytical model and pore network model. MD simulations of shale gas (methane) transport in nanopores demonstrated that the transport behavior is determined by the competition between gas-wall interaction (gas diffusion) and gas-gas intermolecular interaction (viscous flow). Considering different pore structures (e.g., circle, square, triangular, and slit), we proposed a multiscale analytical model with the coupling of continuum flow theory and diffusion effect (Knudsen diffusion and surface diffusion), which is well verified by results from MD simulations and exhibits the practicability of predicting shale gas transport from nanoscale to macroscale. Furthermore, with the aid of pore network model, micro/nano-porous structure was constructed to simulate gas transport in shale matrix. It was found that traditional simulations of shale gas transport in matrix based on circular nanopores would underestimate the transport capacity, for example, that of slit nanopore system is enhanced by as much as 126%. In particular, shale gas transport in shale matrix can be remarkably influenced by the reservoir pressure. At early stage of exploitation, the shale gas transport in matrix is mainly contributed by macropores (H > 100 nm) with the dominant transport characteristic of viscous flow. With the decrease of pressure in continuous exploitation, nanopores (H < 10 nm) will become the primary flow paths due to the enormously enhanced diffusion effect. The intrinsic tendency of our simulated multiscale transport may be useful for understanding the transport behavior and extraction of shale gas in porous shale formations.

REV-scale simulation of gas transport in shale matrix with lattice Boltzmann method

Shale gas reservoirs have obscured transport properties owing to the complex micro-porous structure and extremely low permeability. In this study, a lattice Boltzmann (LB) model at representative elementary volume (REV) scale has been proposed to simulate gas transport in a 2-dimensional (2D) micro-porous media reconstructed by optimized quartet structure generation set (QSGS) method. The velocity distributions and apparent permeability of gas transport inside the reconstructed porous media are demonstrated and analyzed, and the gas flow mechanisms such as slippage, gas adsorption and surface diffusion have been investigated. The simulation results indicate that gas displays considerable different flow behaviors due to the effects of gas slippage, and the apparent permeability is significantly related to the Knudsen number (Kn). Moreover, the increasing adsorbed gas concentration in the pore surface has great impact on the gas transport behaviors, which is accounting for the decreasing apparent permeability. Surface diffusion can strongly affect the apparent permeability, but the strength of this effect is subject to the adsorbed gas concentration. It is hoped that this study can provide some novel insights into the investigation of gas transport in shale gas reservoirs.

Stochastic algorithm for simulating gas transport coefficients

The aim of this paper is to create a molecular algorithm for modeling the transport processes in gases that will be more efficient than molecular dynamics method. To this end, the dynamics of molecules are modeled stochastically. In a rarefied gas, it is sufficient to consider the evolution of molecules only in the velocity space, whereas for a dense gas it is necessary to model the dynamics of molecules also in the physical space. Adequate integral characteristics of the studied system are obtained by averaging over a sufficiently large number of independent phase trajectories. The efficiency of the proposed algorithm was demonstrated by modeling the coefficients of self-diffusion and the viscosity of several gases. It was shown that the accuracy comparable to the experimental one can be obtained on a relatively small number of molecules. The modeling accuracy increases with the growth of used number of molecules and phase trajectories.

Modeling and simulation of gas transport in carbon-based organic nano-capillaries

Modeling of transport of fluids in organic nanopores of shale is associated with complexities due to existence of ultratight pores and strong fluid–solid interactions. In this study, adsorption and transport of three different gases (argon, methane, and neon) are investigated by performing molecular simulations of identical setups of nano-scale carbon capillaries made up of smooth graphite sheets. The simulations are performed for capillaries with 2, 4, 6, and 8nm diameters for a wide range of pressures and pressure gradients. The velocity, density, diffusion coefficients, and viscosities of the gases are computed and compared.Based on the molecular simulation results, as the pressure of the system increases, amount of the adsorbed gas molecules on the capillary walls increases to reach the saturation state. Computed velocity profiles show that for all gases in the capillaries, velocity profiles are plug-shaped. Computed gas velocities from molecular simulations are compared with the velocities predicted by regularized 13-moment model by adjusting the tangential momentum accommodation coefficients (TMAC). The calculated TMAC values are found to be between 0.03 to 0.18 for the pressure range tested. It is found that as the Knudsen number increases, the molecules reflect more specularly in the capillaries. We also investigated the effect of adsorption on TMAC values and found that the TMAC values can be predicted by including the effect of adsorption surface coverage into consideration. Furthermore, it is found that the Knudsen diffusion model underestimates the molecular fluxes in the capillaries by at least one order of magnitude. The corrected and transport diffusivity coefficients decrease as pressure increases and approach one another at low pressures.The viscosity of the gases are calculated for different fugacities and Knudsen numbers based on self-diffusivity coefficients for two capillary sizes of 2 and 4nm. The computed viscosities of all gases decrease as pressure increases. For all gases, the viscosity under confinement are lower than their nominal values. Viscosity values for argon and methane increase approximately linearly with fugacity for both capillaries. The viscosity values of neon for the capillaries are almost the same for fugacities less than 90atm. It is also shown that the viscosity models for gases under confinement are not good candidates to be used in organic nanopores due to adsorption of gases to pore surface.

Multiscale model reduction for shale gas transport in a coupled discrete fracture and dual-continuum porous media

Natural gas production from shale formations involves highly complex geological features consisting of fractures that are embedded spatially-distributed in a matrix made of organic and inorganic materials. In this paper, we develop a coupled multiscale and multi-continuum approach for simulating gas transport in the shale formation. The multiscale method allowed us to capture detailed interactions between the fractures and the background. For the fine-scale heterogeneities involving organic and inorganic materials distribution in the matrix, we use a dual-continuum approach. The matrix is coupled to the fractures by use of the Generalized Multiscale Finite Element Method (GMsFEM). In our previous work (Akkutlu et al., 2016), we used a single-continuum background coupled to the fracture network. This paper presents a significant extension and considers dual-continuum media as a background. GMsFEM systematically identifies the fracture networks by constructing corresponding multiscale basis functions. GMsFEM also accurately represents the fractures interacting with the background media. Moreover, GMsFEM can handle any spatial fracture distributions and thus, it avoids the limitations of the multi-continuum approaches. Results show that the proposed numerical approach can accurately capture the interactions between the fractures and the multi-continuum model using a few multiscale basis functions.

A Comprehensive Model for Simulation of Gas Transport in Shale Formation With Complex Hydraulic-Fracture Geometry

Summary A comprehensive model for simulating gas transport in shale formation with complex fracture geometry is still lacking in the petroleum industry. First, the current models are challenging to efficiently handle the complex nonplanar fractures with varying fracture width and fracture permeability along fracture length caused by very-complicated gridding issues, a high computational cost, and complexities in development of computational codes. Second, the conventional gas-diffusivity equation needs to be revised to include all important gas-transport mechanisms such as gas slippage, gas diffusion, and gas desorption. Hence, the goal of this study was to develop a new model to fill this gap. We present an efficient semianalytical model by dividing fractures into several fracture segments to represent the complex nonplanar-fracture geometry and present a revised diffusivity equation to consider all the important gas-transport mechanisms for shale-gas reservoirs. We verified this model against a numerical reservoir simulator and an analytical solution for a single planar fracture. Transient-flow behavior between planar fractures and nonplanar fractures with and without considering the natural fractures was compared. Furthermore, a well with actual production data from the Marcellus Shale was analyzed. First, we use a complex hydraulic-fracture-propagation model to generate nonplanar-fracture geometry. Then, we apply the fracture geometry in the semianalytical model to evaluate well performance. Contributions of each mechanism to gas recovery are examined. By use of history matching and production forecasting, the difference of cumulative gas production between the nonplanar fractures and the converted planar fractures with equal fracture length is approximately 12% at 30 years of production. In addition, the contribution of gas diffusion, gas slippage, and gas desorption to gas recovery at 30 years of production compared with that without considering them is approximately 11, 16, and 25%, respectively. In total, the contribution of these three important mechanisms is approximately 56%. Hence, modeling of gas production from the nonplanar fractures and modeling the important gas-transport mechanisms in shale-gas reservoirs are significant.

An Integrative Model To Simulate Gas Transport and Production Coupled With Gas Adsorption, Non-Darcy Flow, Surface Diffusion, and Stress Dependence in Organic-Shale Reservoirs

Summary Gas adsorption, stress dependence, non-Darcy flow, and surface diffusion of the adsorbed layer are significant mechanisms in shale-gas reservoirs. However, the volume occupied by the adsorbed layer is generally overlooked by current industry standards and numerical models. In addition, stress dependence of matrix pores does not draw as much attention as hydraulic fractures, and surface diffusion has not been included in commercial simulators. Moreover, all these effects significantly affect each other, which can lead to additional complexity of gas transport and production. Therefore, development of an integrative model with consideration of these complicated mechanisms is needed. In this paper, we develop such a fully coupled model for shale-gas-reservoir simulations. We present the derivation of models reflecting the time-dependence effects of gas adsorption/desorption upon original gas in place (OGIP) and petrophysical properties. In particular, both the Langmuir and Brunauer, Emmett, and Teller (BET) (Brunauer et al. 1938) isotherms are included by use of a unified formula. Surface diffusion of adsorbed layer is also added to this model on the basis of rigorous derivation. More features, such as non-Darcy flow and stress dependence in matrix, natural fractures, hydraulic fractures, and leakage effect between matrix and natural fractures, are incorporated. After that, we present an implicit numerical algorithm to solve the model. Numerical simulations were performed in both 1D and 3D cases and compared with two sets of experimental data and three sets of production data in Marcellus and Barnett shale-gas fields. The simulations indicated that the new simulator cannot only lead to consistent results with these data, but also gives an accurate estimation of OGIP, which traditional models failed to do. It is noted that the model parameters we used for the simulations were close to the values suggested by the literature, if available. By use of this validated simulator, we demonstrated applications with respect to real shale reservoirs, studied the effects of the model parameters upon the gas transport and production, and achieved a variety of new insights.

Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method

Abstract This work reports an investigation of the impact of microstructure on the performance of solid oxide fuel cells (SOFC) composed of nickel yttria-stabilized zirconia (Ni YSZ). X-ray nano computed tomography (nano-CT) was used to obtain three-dimensional (3D) models of Ni-YSZ composite anode samples subjected to different thermal cycles. Key parameters, such as triple phase boundary (TPB) density, were calculated using 3D reconstructions. The electrochemical reaction occurring at active-TPB was modeled by the Lattice Boltzmann Method for simulation of multi-component mass transfer in porous anodes. The effect of different electrode geometries on the mass transfer and the electrochemical reaction in anodes was studied by TPB distributions measured by nano CT for samples subjected to different thermal cycles. The concentration polarization and the activation polarization were estimated respectively. The results demonstrate that a combined approach involving nano-CT experiments in conjunction with simulations of gas transport and electrochemical reactions using the Lattice Boltzmann method can be used to better understand the relationship between electrode microstructure and performance of nickel yttria-stabilized zirconia anodes.

Hydrogen permeation through Pd-based composite membranes: Effects of porous substrate, diffusion barrier and sweep gas

Gas transport in the diffusion barrier and porous substrate layers is modeled in order to evaluate its impacts on the performance of palladium-based composite membranes for H2 separation. A pseudo-2-dimensional model is created for a cylindrical membrane module with counter-current flow. It is hypothesized that displacement of proton transport paths may occur in the bulk metal membrane due to a non-permeable solid phase in direct contact with it. A flux-weighted effective membrane thickness is proposed to account for this effect, which has not been considered in previous literature. Both the dusty gas model (DGM) and binary fraction model (BFM) are used to simulate gas transport in the porous media. Predictions show that under certain circumstances, a well-designed diffusion barrier may cause a slight increase in H2 flux, contrary to common belief. Two mechanisms are identified which enhance membrane performance by sweeping the permeate side. Though gases with small Schmidt number were found to be more likely to penetrate through the membrane substrate and build significant concentration at the membrane-substrate interface, the choice of sweep gas may depend on other practical considerations, especially gas separation downstream. Combinations of porosity and pore size are recommended for the membrane substrate and diffusion barrier based on modeling results.

A multi-flow regimes model for simulating gas transport in shale matrix

The gas transport in shale matrix is of great research interest for optimised shale gas recovery. Pores and pore-throats in the gas-bearing shale are nano-scale, and hence transport of gas is governed by the slippage effect and Knudsen diffusion rather than viscous flow. Hence a proper mathematical model is needed for full understanding of shale gas transport. In this paper, a mathematical model that considers multi-flow regimes is proposed based on gas molecular kinetics theory. The flow regimes transition from slip flow to Knudsen diffusion, and can be adequately described by introducing a corrected intermolecular collision frequency. The proposed mathematical model predictions are compared with experimental data and found to match very well. Furthermore, the gas mass flux contributed by different flow regimes with the variation of Knudsen number is analysed. The numerical simulation results indicate that with the increase in Knudsen number, viscous flow becomes weakened, and the slippage flow reaches a peak and then decreases gradually. The contribution to the gas mass flux due to Knudsen diffusion starts at the early stage of transition flow, and becomes dominant at the later stage of transition flow.

A multi-flow regimes model for simulating gas transport in shale matrix

A multi-flow regimes model for simulating gas transport in shale matrix

Simulation of Gas Transport in Tight/Shale Gas Reservoirs by a Multicomponent Model Based on PEBI Grid

The ultra-low permeability and nanosize pores of tight/shale gas reservoir would lead to non-Darcy flow including slip flow, transition flow, and free molecular flow, which cannot be described by traditional Darcy’s law. The organic content often adsorbs some gas content, while the adsorbed amount for different gas species is different. Based on these facts, we develop a new compositional model based on unstructured PEBI (perpendicular bisection) grid, which is able to characterize non-Darcy flow including slip flow, transition flow, and free molecular flow and the multicomponent adsorption in tight/shale gas reservoirs. With the proposed model, we study the effect of non-Darcy flow, length of the hydraulic fracture, and initial gas composition on gas production. The results show both non-Darcy flow and fracture length have significant influence on gas production. Ignoring non-Darcy flow would underestimate 67% cumulative gas production in lower permeable gas reservoirs. Gas production increases with fracture length. In lower permeable reservoirs, gas production increases almost linearly with the hydraulic fracture length. However, in higher permeable reservoirs, the increment of the former gradually decreases with the increase in the latter. The results also show that the presence of CO2in the formation would lower down gas production.

Comparison of Numerically Stable Methods for Implementation of a Double Porosity Model with First-Order Reaction Terms

The influence of barometric cycling on gas transport through complex media can be described using a double porosity model. Here vertical channels simulate the effect of cracks that pass through homogeneous regions of media. The cracks are coupled to the atmosphere and act as boundaries for the sections of homogeneous media. Convection–diffusion models are then used to simulate gas transport through the coupled system. This approach has been used to model soil aeration, subsurface movement of volatile compounds, and the migration of gases to the surface after below ground nuclear detonations. In the present work, we describe four stable numerical methods that can be used to implement the double porosity model when first-order reactions produce and consume the gaseous species of interest. We find that all four methods satisfy analytical crosschecks and agree to at least seven digits of precision. An iterative solver based on Newton’s method is found to be optimal as it is easily scalable to 3-D models and to multithreaded execution.

Stochastic Aspects of Mass Transport in Gas Diffusion Layers

The relationship between the 3D morphology of gas-diffusion layers (GDL) of HT-PEFCs and their functionality is analyzed. A stochastic model describing the microstructure of paper-type GDL is combined with the Lattice-Boltzmann method (LBM) to simulate gas transport within the GDL microstructure. Virtual 3D microstructures representing paper-type GDL are generated by a stochastic model, where the binder morphology is systematically modified. On these structures, single phase single component gas flow is computed by the LBM. Quality criteria evaluating the spatial homogeneity of gas supply are introduced and related to the binder morphology. The spatial homogeneity of the gas supply is analyzed by a parametrized stochastic model describing the gas flow at the exit of the GDL. This approach gives insight into the spatial structure of the gas flow at the GDL exit. The quality of gas supply is quantified by characterizing size and arrangement of regions with high gas supply. This stochastic gas flow model predicts the quality of gas supply for further binder morphologies. Analyzing the quality criteria and the stochastic evaluation of the spatial structure of the gas flow field at the GDL exit, it is found that the binder morphology has an essential influence on the gas supply.

Lattice-Boltzmann modeling of gas transport in Ni-Yttria-stabilized zirconia anodes during thermal cycling based on X-ray computed tomography

The thermal cycling treatment of Ni-Yttria-stabilized zirconia (Ni-YSZ) anodes strongly influences their three-dimensional (3D) microstructure, including their interior connectivity, phase size and three-phase boundary (TPB) density. In this paper, a nondestructive imaging technology based on X-ray computed tomography is used to obtain the 3D microstructure of Ni-YSZ anode samples after thermal cycling. The lattice Boltzmann method (LBM) is used to simulate gas transport in these 3D microstructures. The mole fraction distributions of gases through the 3D connected pore phase are obtained from the simulated results, enabling the concentration polarization to be calculated. Moreover, the active-TPB density is associated with an electrochemical reaction to simulate the mass diffusion. These results may elucidate the relationship between the microstructure and electrochemical properties.

Molecular Dynamics Simulation of Gas Transport in Polyisoprene Matrix

Molecular Dynamics (MD) simulation was employed to study the diffusivity of biogas in a PI matrix with the aim to verify simulations as a useful tool to predict PI membrane properties for biogas treatment. The simulation model of PI numerical was reliable and accurate in predicting both the material properties and the diffusivity of gases in PI matrix. The diffusion coefficients (D) of the major components in biogas, namely CH4, CO2, H2O, O2, and N2, were computed by simulating trajectories of each gas in PI matrix at 300 K. The simulations gave DCO2 that was 6 times larger than DCH4, and this agrees well with permeabilities reported in the literature. This suggests that PI membranes could be used to treat biogas by separating CO2 and CH4. However, the diffusivities of N2, H2O, and CH4 are closely similar, so PI membranes are not capable of separating these. The potential application of PI membrane to CO2/CH4 separation seems worth further exploration.