Gas Transport Model Research Articles

Effect of Soil Volumetric Water Content on the CO2 Diffusion Coefficient

Purpose: The soil air diffusion coefficient (Ds) is particularly important for the study of soil gas diffusion movement, and there are still many uncertainties in the widely used methods; as such, a method was designed to in situ measure the soil gas diffusion coefficient. Methods: Four different soil media were selected and studied by means of a designed in situ measurement of soil gas diffusion coefficients, and these were compared and analyzed with the predictions of several commonly used prediction models. In addition, they were combined with gas transport models to validate the results of the empirical models that were obtained by the in situ measurements. Results: The results of the data indicate that increasing the volumetric soil moisture content decreases the soil gas diffusion coefficient, with changes in the soil gas diffusion coefficient for the small-grained quartz sand medium being similar to those predicted by the Buckingham model. The soil gas diffusion coefficients for the large-grained quartz sand were similar to the Millington and Quirk model predictions at low humidity; for increased humidity, it was instead similar to the Buckingham model predictions. The soil gas diffusion coefficients of the two active media were closer to those of the SWLR model with high Cm. In addition, the R2 of the measured data was verified, by empirical modeling, to be greater than 0.54, and inversion experiments were conducted to verify that the results were consistent with those of the SWLR model. Conclusion: When measuring relative diffusion coefficients in the field, we recommend the in situ measurement method, which is more reflective of the actual situation in natural environments and provides more accurate data support for soil carbon flux studies.

Fundamental study of gas species transport in the oxygen electrode of solid oxide fuel and electrolysis cells

A fundamental analysis of multicomponent gas transport models was performed in application to the oxygen electrodes of solid oxide cells. It is common practice to neglect the effect of pressure gradients within oxygen electrodes, even though a net molar flux at the electrolyte surface implies that a pressure gradient must exist. The influence of both Darcy velocity and Knudsen flux are considered in the context of ordinary (Fickian) diffusion, the dusty gas model, and the binary friction model. Comparisons between the models and different sets of assumptions are made via parametric studies on operating load, oxygen partial pressure, microstructural properties, and electrode thickness. Results show that the pressure gradient will have a significant impact on the oxygen concentration distribution and therefore the concentration overpotential. In electrolysis mode, pressure increases up to 1 atm are predicted, indicating that pressure at the electrode/electrolyte interface could contribute to electrode delamination. Additionally, it is found that Darcy's law is insufficient for calculating the pressure distribution without accounting for the flux due to Knudsen diffusion. Additionally, it is found that for the range of properties typical of oxygen electrodes, there is a negligibly small difference between the dusty gas model and binary friction model from a practical standpoint.

A micro-macro coupled permeability model for gas transport in coalbed methane reservoirs

It is of great scientific and engineering significances to reveal the coupling mechanism of microscale and macroscale permeabilities in coalbed methane (CBM) reservoirs. In this paper, firstly, the characteristics of the pore-fracture system of coal matrix, such as gas content, permeability, connectivity, geometric size difference, and direction of micro-fracture development, are revealed. Secondly, a coupled permeability model is established, and the coal rank control mechanism on the transformation of microscale and macrosclae permeabilities is clarified. Thirdly, based on the microscale gravitational field model, the coal rank-pressure coupling influence mechanism on slippage/diffusion/jump of adsorbed gas in the surface control field is clarified. Results show that: (a) under a certain temperature, the microscale permeability and macroscale permeability of coal matrix have a statistical correlation, and the degree of coal metamorphism is the only variable controlling the transformation of micro-macro permeabilities. (b) With the increase of coal rank from 0.5% to 3.5%, the conversion coefficient of bulk gas permeability decreases by 15 orders of magnitude. (c) With the increase of coal metamorphism, the porosity and the density of oxygen-containing functional groups decrease, leading to the proportion of the area of adsorbed water film decreases at first and then increases.

A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities

We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate them and that we know their global Lipschitz constants. The algorithm is a successive linear relaxation method in which we alternate between solving a master problem, which is a mixed-integer linear relaxation of the original problem, and a subproblem, which is designed to tighten the linear relaxation of the next master problem by using the Lipschitz information about the respective functions. By doing so, we follow the ideas of Schmidt, Sirvent, and Wollner (Math Program 178(1):449–483 (2019) and Optim Lett 16(5):1355-1372 (2022)) and improve the tackling of multivariate constraints. Although multivariate nonlinearities obviously increase modeling capabilities, their incorporation also significantly increases the computational burden of the proposed algorithm. We prove the correctness of our method and also derive a worst-case iteration bound. Finally, we show the generality of the addressed problem class and the proposed method by illustrating that both bilevel optimization problems with nonconvex and quadratic lower levels as well as nonlinear and mixed-integer models of gas transport can be tackled by our method. We provide the necessary theory for both applications and briefly illustrate the outcomes of the new method when applied to these two problems.

Permeability coupling model of multiple migration mechanisms in rough micro-fractures of shales

To study the gas transmission characteristics in organic pores of rough shale reservoirs, firstly, considering the effect of roughness, adsorption layer, and stress sensitivity on fracture width variation, the effective fracture width model was established. On this basis, the real gas transport models of the adsorbed gas and bulk gas in rough reservoirs have been studied respectively, and the apparent permeability coupling model of rough microfracture of shale are proposed according to the difference of actual flow area. The validity of the proposed models was verified by comparing them with the simulation data, and the contribution of each migration mechanism to the total flow under different roughness and fracture width variation factors was analyzed. It is found that the formation pressure is proportional to the influence of roughness on permeability. When the initial crack width increases, the corresponding pore pressure decreases when the roughness has a greater influence on the proportion of slip flow. The influence of roughness on the Knudsen diffusion ratio and surface diffusion ratio will be greater when the initial crack width is smaller. In addition, if the initial crack width and pore pressure are constant, the greater the relative roughness, the greater the Knudsen diffusion ratio and surface diffusion ratio, and the smaller the slippage flow proportion.

Spatiotemporal simulation of gas-liquid transport in the production process of continuous undulating pipelines

Large sections of gas accumulation easily form in continuously undulating liquid pipelines to impede the commissioning process affecting the safe operation of the pipeline. To solve the gas resistance and overpressure during the commissioning of continuously undulating pipeline in complex terrain, a whole process commissioning simulation model is proposed to quantitatively calculate the location and volume of gas accumulation and to monitor the pressure drop across the line in the real time. Based on a single V-shaped pipe compression process model, the proposed model considers the influence of back pressure, gas-liquid migration and integrates different process such as high point exhausting, pigging process and pump-pipe coordination. Multiple operating conditions of two real pipelines are simulated, and the results show that the proposed model has an accuracy of within ±15% for predicting the pressure along the pipeline and tracking the pigging device, indicating that the gas transport model of the continuous undulating pipeline production process has acceptable accuracy. In addition, the applicability of the proposed model under different operating condition is also verified. Specifically, the gas accumulation ratio and safety pressure of the entire pipeline are calculated by considering multiple sets of different exhaust Schemes for different flow rates, high points, and the use of pigging devices on two different real pipelines, demonstrating that the model has good generality and feasibility. Secondly, the model can calculate the pressure drop at different positions along the entire pipeline, monitor the position of the pigging device in real time, and simulate comprehensive production exhaust Schemes, demonstrating that the model has comprehensive functionality and some generality. In summary, the proposed model can provide validation and guidance for the subsequent production of related continuous undulating liquid pipelines.

The study on modeling and simulation of shale multi-scale matrix-fracture system

Shale is a complex porous medium with multi-scale pores and well-developed fracture networks. This paper aims to use modeling and numerical simulation methods to study the transport of shale gas in a complex multi-scale matrix-fracture system. In this study, mathematical modeling and programming was used to establish digital models of shale gas multi-scale matrix and 3D discrete fracture network. Based on the transport mechanisms of shale gas, this study derives the mathematical models of shale gas transport in different transport media, and uses the finite element method to solve and analysis the transport of shale gas in the multi-scale matrix-fracture system. The model is verified by real shale gas field data. The results show that the fractal dimension of organic pores have great effects on shale gas transport. When the fractal dimension is greater than 1.4, the increase on gas production is particularly obvious. Compared with organic pores, the effect of fractal dimension of inorganic pores is smaller. The existence of the fracture network has an effect of up to 25% on gas production, and the optimal fracture density is 200.

Bayesian calibration with summary statistics for the prediction of xenon diffusion in UO2 nuclear fuel

The evolution and release of fission gas impacts the performance of UO2 nuclear fuel. We have created a Bayesian framework to calibrate a novel model for fission gas transport that predicts diffusion rates of uranium and xenon in UO2 under both thermal equilibrium and irradiation conditions. Data sets are taken from historical diffusion, gas release, and thermodynamic experiments. These data sets consist invariably of summary statistics, including a measurement value with an associated uncertainty. Our calibration strategy uses synthetic data sets in order to estimate the parameters in the model, such that the resulting model predictions agree with the reported summary statistics. In doing so, the reported uncertainties are effectively reflected in the inferred uncertain parameters. Furthermore, to keep our approach computationally tractable, we replace the fission gas evolution model by a polynomial surrogate model with a reduced number of parameters, which are identified using global sensitivity analysis. We discuss the efficacy of our calibration strategy, and investigate how the contribution of the different data sets, taken from multiple sources in the literature, can be weighted in the likelihood function constructed as part of our Bayesian calibration setup, in order to account for the different number of data points in each set of data summaries. Our results indicate a good match between the calibrated diffusivity and non-stoichiometry predictions and the given data summaries. We demonstrate a good agreement between the calibrated xenon diffusivity and the established fit from Turnbull et al. (1982), indicating that the dominant uranium vacancy diffusion mechanism in the model is able to capture the trends in the data.

Shale gas transport model considering gas adsorption and desorption

The gas migration mechanism and apparent permeability in shale reservoirs are significantly different from those in conventional gas reservoirs, which is mainly caused by nanoscale phenomena and organic matter as gas storage and supply media. However, in shale reservoirs, gas flow behavior plays an important role in well performance, so it is necessary to develop a new apparent permeability model considering gas transport mechanism. Therefore, in order to study the change of matrix permeability under different pressures in the development process of shale adsorption layer, combined with previous studies, considering the seepage mechanism of stress sensitivity, real gas effect and adsorption, a new model of apparent permeability is created by combining multiple gas transmission mechanisms. The sensitivity analysis of the new model is carried out by changing the corresponding parameters, and the corresponding conclusions are drawn. In this work, the established model can accurately calculate the apparent permeability of viscous flow, Knudsen diffusion and desorption, which makes us have a more accurate understanding of the transmission mechanism of shale gas and contributes to the efficient and sustainable development of shale gas.

Pore-scale hydro-mechanical modeling of gas transport in coal matrix

We present a 3D model coupling a discrete element model and a pore network model specifically developed to describe the different diffusion mechanisms at stake in coal matrix as well as the associated adsorption induced deformations. The material is assumed to be saturated with gas and diffusion occurs through the combination of Knudsen diffusion within the pore space, surface diffusion at the solid surface, and adsorption–desorption at the pore-solid interface. The model is hydro-mechanically coupled in the sense that changes in pore pressure produce hydrostatic forces that deform the solid skeleton, while deformation of the pore space induces pore pressure changes that promote interpore flow. Sorption induced deformations are taken into account by considering an additional pressure term related to the concentration of gas within the medium (the so-called solvation pressure). The implemented transport models are verified against analytical solutions describing diffusion in porous media with and without sorption–desorption, and a comparison is made with a swelling experiment performed on a coal specimen to illustrate the relevance of the proposed approach for describing adsorption induced deformation. As a result, this new pore-scale model offers a precise way to assess coal matrix sorption induced deformation and contributes to the knowledge of CBM storage and transport processes.

Modeling of dual-permeability gas and solute reactive transport in macroporous agricultural soils with a focus on GHG cycling and emissions

Agricultural soil is the domain where biogeochemical C-N turnover is affected by atmospheric and hydrologic processes, playing a vital role in anthropogenic greenhouse gas (GHG) emissions and thus affecting global climate change. GHG cycling and emissions are further complicated by the characteristics of soil structure, in particular macropores (i.e., preferential flow pathway). In this study, the processes of non-equilibrium gas diffusion and gas exchange were implemented into an existing dual-permeability flow and reactive solute transport model. The model was then used in a sensitivity analysis to evaluate the suitability of the modeling approach to account for development of anaerobic hotspots, with an emphasis on assessing N2O production and emissions. The sensitivity analysis combined with characteristic time scale analysis suggests that the development of anaerobic hotspots is controlled by a combination of both physical and geochemical parameters. Time scale analysis of O2 supply and consumption indicates that the occurrence of anaerobic hotspots is determined by the balance between characteristic times of O2 diffusion through the soil profile or exchange between macropores and the soil matrix, and the characteristic time of O2 consumption. Motivated by these findings, the present model was applied to simulate GHG cycling at a field site in Ontario, Canada, featuring macroporous agricultural soil. The model generally reproduced observed spatiotemporal variations in pore gas O2 and GHG concentrations and fluxes. Simulation results suggest that at this site, gas exchange processes between regions of preferential flow and the soil matrix play an important role in controlling the spatial variation of O2 in the soil. The simulations illustrate how the release of GHGs from the soil matrix into the macropores can lead to GHG emissions to the atmosphere. The modeling approach presented here, including dual domain flow and solute transport, as well as dual domain gas transport, shows promise for future studies with the aim to develop a more complete understanding of how soil structure affects complex GHG cycling in agricultural soils.

An analytical model for multi-component shale gas transport through micro-scale fractures in shale gas reservoirs

An analytical model for multi-component shale gas transport through micro-scale fractures in shale gas reservoirs

A predictive procedure to model gas transport and intrinsic properties of rubbery polymeric membranes using equilibrium thermodynamics and free volume theory

A predictive procedure to model gas transport and intrinsic properties of rubbery polymeric membranes using equilibrium thermodynamics and free volume theory

Gas transport in organic-rich nanoporous media with nonequilibrium sorption kinetics

We present a mathematical model for one-dimensional gas transport in organic-rich nanoporous media subject to nonequilibrium sorption. The model is developed from two governing equations to simulate Knudsen diffusion and viscous flow in the free phase, and surface diffusion in the sorbed phase. The pore space is shared between the free and sorbed phases by defining concentration-dependent free- and sorbed-phase volume fractions. The governing equations are coupled through a source/sink term described by a kinetic sorption model. The impact of the reduced effective pore space and sorption on free-phase mass transfer is characterized by defining effective diffusion coefficients. The governing equations are numerically solved based on the finite element method. The model is utilized to analyze the temporal and spatial concentration data obtained using X-ray micro-CT scans from two experiments, including Krypton transport into a coal sample and Xenon uptake into a shale sample. The proposed model closely reproduces total concentration profiles in both experiments, and captures the concentration peak in Xe-shale system due to the significant nonequilibrium sorption and slower process of reaching equilibrium. The modeling results show that surface diffusion dominates the total mass transport in Xe-shale system with higher adsorption affinity. In Kr-coal system with lower adsorption affinity, the sorbed phase contributes significantly to the total mass transport mainly at high pressures. In addition, the sorbed phase can occupy up to 30% of pore space, which reduces the free-phase diffusion coefficient by 40% in Xe-shale and 80% in Kr-coal. Accordingly, neglecting the sorbed-phase volume in nanoporous media may overestimate the effective free-phase diffusion coefficient. This study shows the significance of the nonequilibrium adsorption for gas transport in nanoporous media.

Modeling of anomalous gas transport in heterogeneous unconventional reservoirs using a nonlinear generalized diffusivity equation

Exploitation of unconventional reservoirs is enabled by multi-fractured horizontal wells. Hydraulic fractures are created with the purpose of enhancing fluid conductivity in such low permeability formation. These hydraulic fractures, along with the intricate structure of the reservoir, such as the presence of natural fractures, result in a highly heterogeneous system and introduces significant challenges with respect to obtaining a proper description of fluid movement. This paper proposes the use of anomalous transport concept based on fractional-time derivative to model gas flow through highly heterogeneous unconventional reservoirs. A modified Darcy’s law that accounts for non-local temporal effects, i.e. history, is adopted to account for the complex flow mechanisms encountered in such disordered media with a wide range of heterogeneity scales. Studies previously developed on this topic solely focused on slightly-compressible fluid transport without further consideration of the nonlinear dependency of fluid properties to pressure. In this regard, the development of predictive models simultaneously considering reservoir heterogeneity and the nonlinear nature of gas transport is yet to be accomplished. In this work, transient pressure diffusion is modeled by the so-called nonlinear Generalized Diffusivity Equation (nGDE), and an integral solution is derived based on Green’s function method. It is observed that for the cases of higher heterogeneity level, higher pressure drawdown is required to maintain a given specified (constant) rate, significantly increasing the deviation of the system response from its linear (slightly-compressible) behavior. This finding corroborates the importance of properly accounting for the nonlinear behavior of gas properties and highlights that available analytical solutions suffer drawbacks when extrapolated to compressible flow scenarios.

Polymers of intrinsic microporosity containing aryl-phthalimide moieties: synthesis, modeling, and membrane gas transport properties

High-performance polymers for membrane gas separation require the careful design of the structure-porous relationship.

Experimental study on the law of transitional gas flow in porous media

There are many nanoscale pores in deep low permeability coal seams. The flow of coalbed methane (gas) in nanoscale pores belongs to the gas flow in porous media with medium and high Knudsen numbers. Its flow mechanism is one of the key unsolved scientific problems. In order to explore the gas transport law in nanopores of coal, a gas transport model based on microscopic boundary restriction was adopted to describe the gas flow law, and its rationality was verified by experimental data. The Field Emission Scanning Electron Microscope was used to scan the nanopores of customized anodized aluminum membrane. Then, the Maximally Stable Extremal Regions (MSER) algorithm of MATLAB and binarization algorithm were employed to quantify the pore structure parameters (equivalent pore size and porosity) of the membrane nanoscale pores. Finally, PMI micro-flow permeability tester was used to carry out different rarefied degree gas penetration experiments through anodized aluminum membranes, and the adopted gas transport model was verified. The results show that the binarization method is more accurate to characterize sample whose theoretical pore sizes are 20–35 nm, while MSER characterizes samples whose theoretical pore sizes are 110–150 nm and 200–300 nm more accurately. In other words, binarization method is more accurate for characterizing mesopores, while MSER algorithm is more accurate for macropores. The results have important reference value for more accurate extraction of nanopore parameters of porous media. Compared with traditional gas transport model, the adopted model considering the microscopic boundary restriction in this paper is closer to the experimental results. Moreover, it is suitable for describing the gas flow law in multiscale nanopores. The study provided important guiding significance for ascertaining the gas migration law in low permeability coal seam, improving the prediction accuracy of gas extraction and taking effective measures to increase production. The research results can further enrich the theoretical system of gas transport in coal, which is conducive to the efficient gas extraction, and is of great significance to promote the realization of carbon peak and carbon neutrality.

Estimating the Geological Structure and Transport Properties of Denied and Limited Access Sites

AbstractOnsite measurements are the standard for establishing geological conditions and related transport properties. However, making direct measurements is not always possible, either because a location is too remote, too vast, or access is outright denied. The latter is typically the case at nuclear test sites, or military installations. Here we describe a systematic method to characterize geology and estimate fracture width, spacing, tortuosity, permeability, and porosity at locations where direct measurements cannot be made. Fractures are treated as fractals with their respective fractal dimensions determined using surface images. Tortuosity in the geological matrix (i.e., bulk media) is determined using rock class with the latter also being used to determine distributions for permeability and porosity. The approach is tested using areal images and rock class for the Nevada Test Site and validated by comparison to field and core measurements. Past work has shown that testing a nuclear weapon underground can affect not only the migration time for gases to the surface but also their isotopic ratios. Accurately modeling gas transport and isotopic fractionation requires knowledge of the geology. However, suspected tests are typically conducted at sites to which the international community has no access.

A two-dimensional semi-analytical model for tracer gas injection and transport in a landfill system

Identifying the location of a leakage is the very first basic step for preventing the escape of landfill gas and leachate from defects. A two-dimensional semi-analytical model is presented for the transport of tracer gas injection in landfills. Tracer gas transport in the landfill cover, liner and waste body is considered. Constant concentration and flux boundary conditions for the injection well are adopted. The proposed approach can be used for leakage detection of the barrier systems in landfills. It is shown that the air-filled porosities of the waste body and the upper cover have a great influence on the tracer gas emission flux on the cover system while the effect of air-filled porosity of the bottom liner can be neglected. The transport mechanism of the tracer gas in the waste body can have a significant impact on the behaviour of the tracer gas in the upper cover and the bottom liner. SF6 emission flux increases with decreasing of the thickness of the upper cover and increasing thickness of the waste body. It is proposed that a constant flux injection boundary should be adopted in the field for leakage detection. The analytical model presented here is a relatively simplified model, which can be used for the validation and guidance of field tracer test.

Study on Apparent Permeability Model for Gas Transport in Shale Inorganic Nanopores

Inorganic nanopores occurring in the shale matrix have strong hydrophilicity and irreducible water (IW) film can be formed on the inner surface of the pores making gas flow mechanisms in the pores more complex. In this paper, the existence of irreducible water (IW) in inorganic pores is considered, and, based on the Knudsen number (Kn) correction in shale pores, a shale gas apparent permeability model of inorganic nano-pores is established. The effect of the Kn correction on the apparent permeability, the ratio of flow with pore radius and the effect of IW on the apparent permeability are assessed. The main conclusions are as follows: (1) at low pressure (less than 10 MPa) and for medium pore size (pore radius range of 10 nm–60 nm), the effect of the Kn correction should be considered; (2) considering the effect of the Kn correction, bulk phase transport replaces surface diffusion more slowly; considering the existence of IW, bulk phase transport replaces surface diffusion more slowly; (3) with increase in pressure, the IW effect on gas apparent permeability decreases. Under low pressure, the IW, where pore size is small, promotes fluid flow, while the IW in the large pores hinders fluid flow. In conditions of ultra-high pressure, the IW promotes gas flow.