Gas Transport Model Research Articles

STUDY ON GAS ADSORPTION AND TRANSPORT BEHAVIOR IN SHALE ORGANIC NANOPORE

The characteristics of shale gas reservoir are expressed in terms of complex pore structure and multiple gas occurrence pattern. Adsorbed gas and bulk gas coexist in nano-scale organic pores. The influence of organic pore shape on confined gas adsorption and flow behavior is not clear, which consequently causes the inaccuracy to understand gas transport mechanisms in shale gas reservoir. To solve this problem, different shapes of organic pore (circular pore, slit pore, triangle pore, square pore) are constructed in this study and Grand canonical Monte Carlo method is first applied to simulate gas adsorption process in different shapes of organic pore across different pore pressure. We found that gas adsorption behavior in different shapes of pores conforms well with the Langmuir adsorption pattern. The absolute adsorption, excess adsorption and gas adsorption parameter change with pore size and pore pressure is analyzed and the influence of pore shape on gas adsorption is studied on this basis. The mathematical model of adsorbed gas surface diffusion and free gas slip flow in different shapes of organic pore is established based on the understanding of thermodynamic gas adsorption pattern in different shapes of organic pore. The respective contribution of adsorbed gas flow and free gas flow on total gas permeability is studied in organic pores with different pore shape and pore size combining molecular simulation results with established gas transport models. The results indicate that the slit pore exhibits the largest value of maximum gas concentration, Langmuir pressure and the weakest adsorbed gas surface diffusion capacity compared with the other three pore shapes. The adsorbed gas surface diffusion influence on gas permeability can be neglected at pore radius larger than 5 nm for different pore shapes. This study reveals the influencing mechanism of organic pore shape on gas adsorption and flow ability during practical shale gas reservoir production.

Nanoconfined Water in Shales and Its Impact on Real Gas Flow

The presence of water, i.e., connate or hydraulic fracturing water, along with the gaseous hydrocarbons in shale nanopores is largely overlooked by previous studies. In this work, a new unified real gas-transport model has been developed for both organic and inorganic porous media accounting for the nanoconfined water film flow. More specifically, a gas core flows in the center of the organic/inorganic pore surrounded by a water film which can be further divided into an interfacial region (near-wall water) and bulk region (bulk water). We differentiate the varying water viscosity between the two regions and consider disparate slip boundaries; that is, the near-wall water can slip along the hydrophobic organic pore surface while it is negligible in hydrophilic inorganic pores. Incorporating modified boundary conditions into the Navier-Stokes equations, gas transport model through single organic/inorganic pore is derived. The model is also comprehensively scaled up to the porous media scale considering the porosity, tortuosity, and total organic carbon (TOC) contents. Results indicate that the gas flow capacity decreases in moist conditions with mobile or nonmobile water film. A mobile water film, however, compensates its negative effect up to 50% by enhancing gas flow compared with static water molecules. The real gas flow is dominated by the gas slippage and water film mobility which are dependent upon pore-scale parameters such as pore sizes, topology, pressure, and surface wettability. Compared with inorganic pores, gas transport in organic pores is greatly enhanced by the water film flow due to the strong water slip. Moreover, the contribution of water film mobility is remarkable in small pores with large contact angles, especially at high pressures. At moist conditions, the real gas effect enhances gas flow by improving both gas slippage and water film mobility, which is more prominent in smaller pores at high pressures. The presented model and its results will further advance our understanding of the mechanisms responsible for the water and gas transport in nanoporous media, and consequently, the hydrocarbon exploration of shale reservoirs.

Multi-scale modelling of gas transport and production evaluation in shale reservoir considering crisscrossing fractures

Advancements in recent shale gas development technologies like creating hydraulic fracturing have greatly improved the production of unconventional shale gas reservoirs (USGR). However, the production of USGR is still low mainly due to the inefficient gas transport in tight shale formation. Towards this end, the investigations about the mechanism of gas transport through the fractures and the effects of both hydraulic and natural fractures on the overall gas production are urgently needed. In this study, a multi-scale modelling is established to analyze the gas transport and production performance in shale formation with crisscrossing natural fractures using finite element method (FEM). For the base case with fracture-scale model, the gas transport behavior and pressure distribution within the matrix and crisscrossing fractures are revealed, demonstrating that the crisscrossing fractures serve as the fast paths to enhance the gas transport from shale matrix to wells. Then, the field-scale model is developed by considering the complex fracture networks consisting of the hydraulically fractured horizontal wells and crisscrossing natural fractures, which is well verified against field data. On this basis, the comprehensive analysis for the influence of various parameters, including the properties of matrix, hydraulic fractures and natural fractures, on the production performance are conducted to optimize the exploitation strategy of shale gas reservoir. It is believed that the multi-scale simulation framework and the optimized exploitation strategies presented in this study are useful for the enhanced gas recovery (EGR) of shale reservoir.

Strategic natural gas storage coordination among EU member states in response to disruption in the trans Austria gas pipeline: A stochastic approach to solidarity

The 2019 EU energy security agenda has led to the concept of solidarity: a coordinated response of Member States to “high-impact, low-probability” events jeopardizing the EU energy supply. At the core of this paper is a modeling analysis of storage as a non-market-based solidarity measure (the so-called strategic storage) considering whether it could be economically desirable to secure gas supply in case of disruption to the EU network. A two-stage stochastic cost minimization gas transport model was developed to study the short-term resilience of the network to supply shocks, such as a natural gas pipeline rupture, and the cost effective system response, in terms of transmission of gas flows, capacity use, and storage utilization in an interconnected gas system, taken the EU as a reference. Relative to a base scenario with no strategic storage, results show that gas import loss up to 80% on multiple different pipelines could lead to a +76% in total costs when no coordinated strategic storage is in place, compared with a −30% in total cost and a −60% in liquefied natural gas cost, when in use, emphasizing the cost-effectiveness achieved with strategic storage in securing energy to the system in emergency.

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.

A non-empirical model for gas transfer through circular nanopores in unconventional gas reservoirs

It is difficult to predict the flow performance in the nanopore networks since traditional assumptions of Navier–Stokes equation break down. At present, lots of attempts have been employed to address the proposition. In this work, the advantages and disadvantages of previous analytical models are seriously analyzed. The first type is modifying a mature equation which is proposed for a specified flow regime and adapted to wider application scope. Thus, the first-type models inevitably require empirical coefficients. The second type is weight superposition based on two different flow mechanisms, which is considered as the reasonable establishment method for universal non-empirical gas-transport model. Subsequently, in terms of slip flow and Knudsen diffusion, the novel gas-transport model is established in this work. Notably, the weight factors of slip flow and Knudsen diffusion are determined through Wu’s model and Knudsen’s model respectively, with the capacity to capture key transport mechanism through nanopores. Capturing gas flow physics at nanoscale allows the proposed model free of any empirical coefficients, which is also the main distinction between our work and previous research. Reliability of proposed model is verified by published molecular simulation results as well. Furthermore, a novel permeability model for coal/shale matrix is developed based on the non-empirical gas-transport model. Results show that (a) nanoconfined gas-transport capacity will be strengthened with the decline of pressure and the decrease in the pressure is supportive for the increasing amplitude; (b) the greater pore size the nanopores is, the stronger the transport capacity the nanotube is; (c) after field application with an actual well in Fuling shale gas field, China, it is demonstrated that numerical simulation coupled with the proposed permeability model can achieve better historical match with the actual production performance. The investigation will contribute to the understanding of nanoconfined gas flow behavior and lay the theoretical foundation for next-generation numerical simulation of unconventional gas reservoirs.

Fast and Accurate Multiscale Reduced-Order Model for Prediction of Multibreath Washout Curves of Human Respiratory System

The curve of exhaled inert gas concentration against exhaled volume is called gas washout curve. The slope at the end part of gas washout curve (Sₙ) is a measure of structural abnormalities. Sₙ depends on the spatial concentration distribution and dynamic of gas washout, which depends on several mechanisms including asymmetry of airways, nonhomogeneous ventilation, sequential emptying, and gas exchange with blood. Due to a large number of airways in human lungs, using simplified models is inevitable. On the other hand, these simplified models cannot capture some of the mentioned mechanisms and subsequently were not able to predict experimental trend of change in Sₙ with breath number in multibreath washout. The present study proposes a novel, accurate, and fast model of gas transport in human lungs, which can accurately predict this trend for the first time. The model consists of a proxy model of conducting airways and a reduced-order model of respiratory airways. A correlation is proposed for the estimation of model parameters, which are all functions of inert gas properties, ventilation, and structure of lung acini. The performance of the proposed model is validated in the prediction of Sₙ’s of various inert gases and lung clearance index. The obtained results show that the proposed model outperforms the previous ones based on both accuracy and required computational time. The effects of gas properties, functional residual capacity, and tidal volume on Sₙ are also investigated. The proposed model is fast where simulation of one breath nitrogen washout takes ∼0.18 s. Furthermore, it is flexible and can range from fully symmetric to detailed asymmetric airways.

An adaptive binary friction model for multicomponent gas transport in tight porous media

A new multicomponent gas transport model called the adaptive binary friction model (ABFM) was developed. The merit of the ABFM lies in the rigorous treatment of viscous slip and diffusion slip. The ABFM uses the general slip boundary condition to characterize viscous slip and thus is applicable in multiple flow regimes. The ABFM uses the Kramers and Kistemaker model to describe diffusion slip and thus satisfies Graham's law in a natural way. The ABFM also eliminates the restrictive assumptions made in previous models, such as uniform flow. Published experimental data on multicomponent gas transport were used to test the ABFM. The agreement of the ABFM results with the experimental data is good. Moreover, the ABFM can predict the transport of different gas mixtures under various conditions based on the determined pore structure parameters. Considering its versatility, the ABFM is anticipated to be useful in heterogeneous catalysis, membrane transport, etc.

Stochastic Estimation of the Slip Factor in Apparent Permeability Model of Gas Transport in Porous Media

In this paper, we introduce an estimation of the random Klinkenberg slip coefficient in the apparent permeability model using a chaos decomposition technique. The apparent permeability expression (Klinkenberg model) is used to describe natural gas transport in low-permeability media. In this process, the Klinkenberg factor is considered as a random parameter that depends on two random variables. The mean and variance (or standard deviation) of the two random variables can be estimated from the empirical data available in the literature. Therefore, the variation in the pressure is related directly to the random variation in the Klinkenberg factor. The polynomial chaos expansion is used to decompose the governing equation into a set of coupled deterministic equations that are solved and then used to compute the mean and variance of the solution. The algorithm of how to solve the deterministic coupled system is also presented. For verification, the model and its solution have been compared with the analytical solution of the basic steady-state version of the model. The comparison shows a very good agreement. The effects of a number of important parameters have been presented in graphs and discussed. It was found that the stochastic model works very well with small values of the liquid equivalent permeability, which meets the characteristics of low-permeability reservoirs. Also, the stochastic model works very well with small values of gas viscosity. On the other hand, the porosity seems to be not engaged well with the low-permeability model. The sensitivity of selection of random parameters is also investigated as well as the transient effect.

A Thermodynamically Consistent Phase Field Model for Gas Transport in Saturated Bentonite Accounting for Initial Stress State

A thermodynamically consistent phase field model that accounts for initial stress state is proposed in this paper to simulate the gas migration process in saturated bentonite. The energy contribution due to the fracturing process is included in Coussy’s thermodynamic framework for unsaturated porous media. The possible effect of the interfaces between different phases on the driving force functional for phase field and the effective stress has been identified from the proposed thermodynamic framework. In addition, the initial stress state is innovatively accounted for in the phase field model by introducing a fictitious strain tensor that is calculated from its corresponding initial stress tensor. It is the sum of the fictitious strain tensor and the strain tensor due to elastic deformation that governs the evolution of the phase field. The simulated results showed that the effect of the swelling pressure (regarded as the initial effective stress for a high swelling clay) on the fracture initiation has been well described by the proposed method. Specifically, the effect of either isotropic or anisotropic stress state on the fracturing process can be well reflected by the phase field approach based on Rankine-type fracture criterion. In contrast, the phase field approach based on the Griffith fracture criterion is more appropriate for the isotropic stress state than the anisotropic stress state because of the Poisson’s effect. Moreover, the gas pressure required to trigger the fracturing process needs to exceed the sum of the porewater pressure and the initial stress. The effect of the boundary condition on the evolution of fluid pressure and total stress has been qualitatively captured. It is found that the boundary with higher stiffness leads to a higher gas pressure in the developed fracture and a higher water pressure and total stress in the surrounding porous matrix. In addition, some key experimental findings, such as the preferential gas flow, the build-up of porewater pressure, the almost fully saturated state and the localized consolidation, have been qualitatively captured by the developed phase field model.

Diffusion-Based Modeling of Gas Transport in Organic-Rich Ultratight Reservoirs

SummaryThe complex pore structure and storage mechanism of organic-rich ultratight reservoirs make the hydrocarbon transport within these reservoirs complicated and significantly different from conventional oil and gas reservoirs. A substantial fraction of pore volume in the ultratight matrix consists of nanopores in which the notion of viscous flow may become irrelevant. Instead, multiple transport and storage mechanisms should be considered to model fluid transport within the shale matrix, including molecular diffusion, Knudsen diffusion, surface diffusion, and sorption. This paper presents a diffusion-based semianalytical model for a single-component gas transport within an infinite-acting organic-rich ultratight matrix. The model treats free and sorbed gas as two phases coexisting in nanopores. The overall mass conservation equation for both phases is transformed into one governing equation solely on the basis of the concentration (density) of the free phase. As a result, the partial differential equation (PDE) governing the overall mass transport carries two newly defined nonlinear terms; namely, effective diffusion coefficient, De, and capacity factor, Φ. The De term accounts for the molecular, Knudsen, and surface diffusion coefficients, and the Φ term considers the mass exchange between free and sorbed phases under sorption equilibrium condition. Furthermore, the ratio of De/Φ is recognized as an apparent diffusion coefficient Da, which is a function of free phase concentration. The nonlinear PDE is solved by applying a piecewise-constant-coefficient technique that divides the domain under consideration into an arbitrary number of subdomains. Each subdomain is assigned with a constant Da. The diffusion-based model is validated against numerical simulation. The model is then used to investigate the impact of surface and Knudsen diffusion coefficients, porosity, and adsorption capacity on gas transport within the ultratight formation. Further, the model is used to study gas transport and production from the Barnett, Marcellus, and New Albany shales. The results show that surface diffusion significantly contributes to gas production in shales with large values of surface diffusion coefficient and adsorption capacity and small values of Knudsen diffusion coefficient and total porosity. Thus, neglecting surface diffusion in organic-rich shales may result in the underestimation of gas production.

Evaluation of pore properties in coal through compressibility correction based on mercury intrusion porosimetry: A practical approach

As a commonly used method to evaluate the pore structures of coal, uncorrected MIP data may cause the results to be highly overestimated. In this study, a series of experiments were carried out to characterize the accurate pore structure of coal including MIP, low pressure N2/CO2 adsorption, scanning electron microscopy (SEM) and X-ray computed microtomography (μCT). Base on the process of mercury penetrate the pore by driven-pressure, it is clear that the mercury intrusion under high pressure can induce the coal matrix compression. Meanwhile, the MIP error (from 36.1% to 130.9% of the pore volume) was derived from coal matrix compression at the high pressure, and the interparticle pore and pockmark effects under low pressure. Here, a new and more practical pore volume correction method was proposed by simplifying the coal matrix compressibility calculation. The new method was tested to be valid for the tested coals with comparison of reported corrected data. The relationship model between intrusion pressure of mercury and pore diameter was revised by the pore morphology. The interparticle pores and pockmark effects mainly occur in the pressure range less than 0.01 MPa. In order to minimize the interparticle pores effect and pockmark effect, a new sample preparation method is recommended for MIP test. This study provides a practical approach to characterize the coal pore structure accurately using the MIP technique and the findings are impactful for the future gas transport modeling in various coals.

Numerical Modeling of Water and Gas Transport in Compacted GMZ Bentonite under Constant Volume Condition

During deep geological disposal of high-level and long-lived radioactive waste, underground water erosion into buffer materials, such as bentonite, and gas production around the canister are unavoidable. Therefore, understanding water and gas migration into buffer materials is important when it comes to determining the sealing ability of engineered barriers in deep geological repositories. The main aim of our study is to provide insights into the water/gas transport in a compacted bentonite sample under constant volume conditions. The results of our study indicate that water saturation is obtained after 450 hours, which is similar to experimental results. Gas migration testing shows that the degree of water saturation in the samples is very sensitive to the gas pressure. As soon as 2 MPa or higher gas pressure was applied, the water saturation degree decreased quickly. Laboratory experiments indicate that gas breakthrough occurs at 4 MPa, with water being expelled from the downstream side. This indicates that gas pressure has a significant effect on the sealing ability of Gaomizozi (GMZ) bentonite.

A Poisson–Schrodinger and cellular automaton coupled approach for two-dimensional electron gas transport modeling of GaN-based high mobility electron transistors

We propose the modeling of electron transport in GaN-based high electron mobility transistors (HEMTs) by combining the Poisson–Schrodinger method and the cellular automaton method. In HEMT, it is necessary to consider the influence of two-dimensional electron gas, band nonparabolicity, and upper valley on drift velocity. A wide range of electron transport modeling environments from low to high electric fields is required. By using the cellular automaton method instead of the traditional Monte Carlo carrier transport modeling method, noise-free drift velocity analysis is realized even at low electric fields. This makes it possible to stably investigate the effects of the HEMT structure and the influence of various scattering mechanisms on the drift velocity.

Modeling of the Transport and Exchange of a Gas Species in Lungs With an Asymmetric Branching Pattern. Application to Nitric Oxide.

Over the years, various studies have been dedicated to the mathematical modeling of gas transport and exchange in the lungs. Indeed, the access to the distal region of the lungs with direct measurements is limited and, therefore, models are valuable tools to interpret clinical data and to give more insights into the phenomena taking place in the deepest part of the lungs. In this work, a new computational model of the transport and exchange of a gas species in the human lungs is proposed. It includes (i) a method to generate a lung geometry characterized by an asymmetric branching pattern, based on the values of several parameters that have to be given by the model user, and a method to possibly alter this geometry to mimic lung diseases, (ii) the calculation of the gas flow distribution in this geometry during inspiration or expiration (taking into account the increased resistance to the flow in airways where the flow is non-established), (iii) the evaluation of the exchange fluxes of the gaseous species of interest between the tissues composing the lungs and the lumen, and (iv) the computation of the concentration profile of the exchanged species in the lumen of the tracheobronchial tree. Even if the model is developed in a general framework, a particular attention is given to nitric oxide, as it is not only a gas species of clinical interest, but also a gas species that is both produced in the walls of the airways and consumed within the alveolar region of the lungs. First, the model is presented. Then, several features of the model, applied to lung geometry, gas flow and NO exchange and transport, are discussed, compared to existing works and notably used to give new insights into experimental data available in the literature, regarding diseases, such as asthma, cystic fibrosis, and chronic obstructive pulmonary disease.

Apparent Permeability Model for Gas Transport in Multiscale Shale Matrix Coupling Multiple Mechanisms

Apparent gas permeability (AGP) is a significantly important parameter for productivity prediction and reservoir simulation. However, the influence of multiscale effect and irreducible water distribution on gas transport is neglected in most of the existing AGP models, which will overestimate gas transport capacity. Therefore, an AGP model coupling multiple mechanisms is established to investigate gas transport in multiscale shale matrix. First, AGP models of organic matrix (ORM) and inorganic matrix (IOM) have been developed respectively, and the AGP model for shale matrix is derived by coupling AGP models for two types of matrix. Multiple effects such as real gas effect, multiscale effect, porous deformation, irreducible water saturation and gas ab-/de-sorption are considered in the proposed model. Second, sensitive analysis indicates that pore size, pressure, porous deformation and irreducible water have significant impact on AGP. Finally, effective pore size distribution (PSD) and AGP under different water saturation of Balic shale sample are obtained based on proposed AGP model. Under comprehensive impact of multiple mechanisms, AGP of shale matrix exhibits shape of approximate “V” as pressure decrease. The presence of irreducible water leads to decrease of AGP. At low water saturation, irreducible water occupies small inorganic pores preferentially, and AGP decreases with small amplitude. The proposed model considers the impact of multiple mechanisms comprehensively, which is more suitable to the actual shale reservoir.

Analysis of early-time production data from multi-fractured shale gas wells by considering multiple transport mechanisms through nanopores

Analysis of early-time production and flowback data from multi-fractured shale gas wells is of critical importance in the characterization of hydraulic fractures (HF). However, the accurate estimation of HF properties in the current models is challenged by the complexity in multiple transport mechanisms and two-phase flow of shale gas reservoir. This study presents a new semi-analytical method to estimate HF attributes for shale gas wells exhibiting two-phase flow based on straight line analysis. The proposed method considers two-phase infinite acting linear flow (IALF) and boundary dominated flow (BDF) for both HF and matrix domains. In addition, matrix flow considers desorption, diffusion, slip flow, continuum flow, stress dependence rock, and adsorbed water film in the nanopores. A modified material balance equation is proposed to calculate average pressure in the fracture and distance of investigation (DOI) in the matrix by considering gas desorption and diffusion in the matrix domain. The accuracy of the proposed method is tested against numerical results obtained from commercial software (IMEX-CMG). The validation results confirm that the developed method can closely estimate initial fracture volume, permeability, and permeability modulus from early-time production data exhibiting two-phase IALF and BDF regimes. Furthermore, the results indicate that the consideration of desorption, diffusion, and slip flow plays an important role in the modeling of gas transport in shale matrix. The impact of these transport mechanisms on production modeling as well as characterization of HF properties becomes significant when the matrix experiences substantial pressure drops. For the purpose of field application, the proposed method is used to analyze flowback data from a multi-fractured horizontal well. The field results reveal that the calculated fracture properties are consistent between the proposed method and the long-term production data analysis method.

Source term estimation of natural gas leakage in utility tunnel by combining CFD and Bayesian inference method

As an effective way to construct and maintain various life pipelines in urban areas and industrial parks, the underground utility tunnel has been developed rapidly in China in recent years. However, the natural gas pipeline leakage in a utility tunnel may cause fire, explosion or other coupling disastrous accidents that could result in fatal consequences. The effective source term estimation (STE) of natural gas leakage can provide technical supports for emergency response during natural gas leakage accidents in utility tunnels. In this paper, a STE model with the combination of gas transport model, Bayesian inference and slice sampling method is proposed to estimate the source parameters of natural gas leakage in underground utility tunnels. The observed data can be integrated into the gas transport model and realize the inversion of natural gas leakage location and release rates. The parameter sensitivity analysis is presented to evaluate the robustness of the proposed model with good practicability, and the gas sensor layouts in the utility tunnel are analyzed and optimized. The spatio-temporal distribution of the leaked gas could be well predicted based on the estimation source parameters by the proposed STE model. The results show that the proposed model is an alternative and effective tool to provide technical supports for loss prevention and mitigation for natural gas leakage accidents in urban utility tunnels.

Upscaled Model for Multicomponent Gas Transport in Porous Media Incorporating Slip Effect

A two-scale model for multicomponent gas transport in porous media is developed. At the pore-scale, Stefan–Maxwell formulation is used to describe the multi-gas transport together with the mass and momentum conservation equations, whereas on the solid/fluid interface, a slip velocity according to the Kramers–Kistemaker condition is taken into account. The pore-scale equations are then upscaled using a formal homogenization procedure. The macroscopic model shows that the total average velocity is modified by a slip velocity which depends mostly on the diffusive flux of the light gas in the mixture. Application to hydrogen transport in electrochemical devices such as fuel cell, electrochemical hydrogen purifier/compressor, in which considerable contrast of molar mass between the gases occurs, is carried out. As a result, the gas slip effect can modify considerably the gas transport behavior within the porous medium of the devices. This is an important result because the gas transport mechanisms play a crucial role in their efficiency.

Modeling of gas transport in porous medium: Stochastic simulation of the Knudsen gas and a kinetic model with homogeneous scatterer

Mass transport of the Knudsen gas in a porous medium is investigated on the basis of the kinetic theory of gases. First, the mass flow conductance is computed numerically for various porosities and solid grain sizes by stochastic particle simulations (SPS). Then, a kinetic model with a homogeneous scatterer is introduced, which contains the reference Knudsen number as the sole parameter that characterizes the collision frequency of gas molecules with the micro-structural solid surface. With the aid of the standard asymptotic analyses for small and large Knudsen numbers combined with the percolation theory, the effective reference Knudsen number is identified to reproduce the SPS results for a wide range of porosities.