Gas Diffusion Model Research Articles

Modeling of Gas Diffusion in Ni/YSZ Electrodes in CO2 and Co‐electrolysis

AbstractCarbon formation may occur during CO2 and CO2/H2O electrolysis using solid oxide electrolyzer cells due to the Boudouard reaction (2CO → CO2 + C(s)). Formed carbon may disintegrate the cell structure and it is therefore of importance to be able to predict when carbon is formed, and take actions to prevent its formation.For prediction of carbon formation, the gas composition in the electrode must be known. In this work, the diffusion of gases in the electrode has been modeled with the dusty gas model in 1 and 2 dimensions, and the effect of tortuosity, porosity, temperature, electrode thickness, pore diameter, current density, pitch and rib width has been investigated. It is shown that diffusion limitations on reactant/product transport may lead to carbon formation.The parameters describing the microstructure and the dimensions of the cathode channels and interconnect ribs are found to have a large effect on the carbon formation propensity. Given a set of parameters, a simple correlation between the CO mole fraction in the channel and under the interconnect rib, and current density during CO2‐electrolysis can be derived. This correlation makes it possible to efficiently integrate the calculation of carbon formation risk in existing electrolyzer cell models.

A coupling model for gas diffusion and seepage in SRV section of shale gas reservoirs

A prerequisite to effective shale gas development is a complicated fracture network generated by extensive and massive fracturing, which is called SRV (stimulated reservoir volume) section. Accurate description of gas flow behaviors in such section is fundamental for productivity evaluation and production performance prediction of shale gas wells. The SRV section is composed of bedrocks with varying sizes and fracture networks, which exhibit different flow behaviors – gas diffusion in bedrocks and gas seepage in fractures. According to the porosity and permeability and the adsorption, diffusion and seepage features of bedrocks and fractures in a shale gas reservoir, the material balance equations were built for bedrocks and fractures respectively and the continuity equations of gas diffusion and seepage in the SRV section were derived. For easy calculation, the post-frac bedrock cube was simplified to be a sphere in line with the principle of volume consistency. Under the assumption of quasi-steady flow behavior at the cross section of the sphere, the gas channeling equation was derived based on the Fick's laws of diffusion and the density function of gas in bedrocks and fractures. The continuity equation was coupled with the channeling equation to effectively characterize the complicated gas flow behavior in the SRV section. The study results show that the gas diffusivity in bedrocks and the volume of bedrocks formed by volume fracturing (or the scale of fracturing) jointly determines the productivity and stable production period of a shale gas well. As per the actual calculation for the well field A in the Changning–Weiyuan Block in the Sichuan Basin, the matrix has low gas diffusivity – about 10−5 cm2/s and a large volume with an equivalent sphere radius of 6.2 m, hindering the gas channeling from bedrocks to fractures and thereby reducing the productivity of the shale gas well. It is concluded that larger scale of volume fracturing and higher fracture density in the SRV section are important guarantees for efficient development of shale gas reservoirs.

Research of Ammonia Concentration Distribution Simulation in Road Transportation Leakage Based on the Gaussian Model

The leakage of liquid ammonia during road transportation is chosen as the research object in this paper, and then the model of toxic gas diffusion after leakage accident is established; MATLAB is used to achieve the accident simulation and risk analysis of continuous leakage from moving and fixed point source. On the basis of different harm to human body of different concentrations of ammonia and the spread concentration curve of the ammonia, the dangerous area is divided into five zones: mild zone, moderate zone, severe zone, dead zone and instantaneous dead zone; according to the comparison between leakage diffusion processes from moving and fixed point source, following conclusions can be reached: during the leakage, area of dangerous zones increased and after the leakage, dangerous zone areas first increased and then decreased; the peak ammonia concentration from fixed source is higher than that from moving point source, whereas influence area of the former is smaller than the latter. This method can quickly simulate the scope and severity of leakage accident in road transportation and provide references for the emergency rescue after accidents.

Flue gas diffusion for integrated dry-cooling tower and stack system in power plants

For the integrated dry-cooling tower and stack, the flue gas diffusion characteristics are of great concerns for the pollutant control and tower anticorrosion. In this work, the computational models of flue gas diffusion for the integrated dry-cooling tower and stack system are developed and experimentally validated. By means of numerical simulations, the flue gas diffusions inside and outside the dry-cooling tower are investigated and the flue gas concentrations at different heights of the inner tower shell and on the ground level are obtained. The rising height of flue gas is studied and compared with the separate stack. The total mass flow rate of cooling air and heat rejection of air-cooled heat exchanger for both the dry cooling system with and without the stack inside the dry-cooling tower are also obtained. The results show that not only the thermo-flow performances of the natural draft dry cooling system with the integrated stack can be improved, but also the air pollution alleviation can be guaranteed. At high wind speeds, the inner tower shell faces corrosion risks due to the flue gas deposition, so the anticorrosion measures for the tower should be taken.

Experimental and Modeling Study on Reduction of Hematite Pellets by Hydrogen Gas

Gaseous reduction by hydrogen was performed for three types of hematite pellets, two from industry and one prepared in the laboratory. The reduction mechanisms of the pellets were studied based on the morphologies of the partially reduced samples. Two mechanisms were found, the mechanisms of the two types of industrial pellets being very similar. The degree of reduction was followed as a function of time for each type of pellets. On the basis of the reaction mechanism of the industrial pellets, a mathematical model was developed. As a pioneer effort, the model combined the computational fluid dynamics approach for the flow and mass transfer in the gas phase with model of gas diffusion in the solid phase as well as the description of the chemical reaction at the reaction sites. The calculation results agreed well with the experimentally obtained reduction curves. The present work also emphasized the importance of evaluation of the reduction mechanisms and the properties of different types of iron ore pellets prior to developing a process model. While the present approach has established a good foundation for the dynamic modeling of the shaft reactor, more efforts are required to accomplish a realistic process model.

分子拡散領域における細孔内での気体の非等モル相互拡散のモデル

分子拡散領域における細孔内での気体の非等モル相互拡散のモデル

Improving the accuracy of the gradient method for determining soil carbon dioxide efflux

AbstractSoil CO2 efflux (Fsoil) represents a significant source of ecosystem CO2 emissions that is rarely quantified with high‐temporal‐resolution data in carbon flux studies. Fsoil estimates can be obtained by the low‐cost gradient method (GM), but the utility of the method is hindered by uncertainties in the application of published models for the diffusion coefficient. Therefore, to address and resolve these uncertainties, we compared Fsoil measured by 2 soil CO2 efflux chambers and Fsoil estimated by 16 gas transport models using the GM across 1 year. We used 14 published empirical gas diffusion models and 2 in situ models: (1) a gas transfer model called “Chamber model” obtained using a calibration between the chamber and the gradient method and (2) a diffusion model called “SF6 model” obtained through an interwell conservative tracer experiment. Most of the published models using the GM underestimated cumulative annual Fsoil by 55% to 361%, while the Chamber model closely approximated cumulative Fsoil (0.6% error). Surprisingly, the SF6 model combined with the GM underestimated Fsoil by 32%. Differences between in situ models could stem from the Chamber model implicitly accounting for production of soil CO2, while the conservative tracer model does not. Therefore, we recommend using the GM only after calibration with chamber measurements to generate reliable long‐term ecosystem Fsoil measurements. Accurate estimates of Fsoil will improve our understanding of soil respiration's contribution to ecosystem fluxes.

Numerical Analysis of Sensitivity of SAW Structure to the Effect of Toxic Gases

AbstractThe paper presents the results of numerical analysis of the SAW gas sensor in the steady and non-steady states. The effect of SAW velocity changes vs surface electrical conductivity of the sensing layer is predicted. The conductivity of the porous sensing layer above the piezoelectric waveguide depends on the profile of the diffused gas molecule concentration inside the layer. The Knudsen’s model of gas diffusion was used.Numerical results for the effect of gas CH4on layers: WO3, TiO2, NiO, SnO2in the steady state and CH4in the non-steady state in recovery step in the WO3sensing layer have been shown. The main aim of the investigation was to study thin film interaction with target gases in the SAW sensor configuration based on simple reaction-diffusion equation.The results of the numerical analysis allow to select the sensor design conditions, including the morphology of the sensor layer, its thickness, operating temperature, and layer type. The numerical results basing on the code elaborated numerical system (written in Python language), were analysed. The theoretical results were verified and confirmed experimentally.

Prediction of biopore- and matrix-dominated flow from X-ray CT-derived macropore network characteristics

Abstract. Prediction and modeling of localized flow processes in macropores is of crucial importance for sustaining both soil and water quality. However, currently there are no reliable means to predict preferential flow due to its inherently large spatial variability. The aim of this study was to investigate the predictive performance of previously developed empirical models for both water and air flow and to explore the potential applicability of X-ray computed tomography (CT)-derived macropore network characteristics. For this purpose, 65 cylindrical soil columns (6 cm diameter and 3.5 cm height) were extracted from the topsoil (5 cm to 8.5 cm depth) in a 15 m × 15 m grid from an agricultural field located in Silstrup, Denmark. All soil columns were scanned with an industrial X-ray CT scanner (129 µm resolution) and later employed for measurement of saturated hydraulic conductivity, air permeability at −30 and −100 cm matric potential, and gas diffusivity at −30 and −100 cm matric potential. Distribution maps for saturated hydraulic conductivity, air permeability, and gas diffusivity reflected no autocorrelation irrespective of soil texture and organic matter content. Existing empirical predictive models for saturated hydraulic conductivity and air permeability showed poor performance, as they were not able to realistically capture macropore flow. The tested empirical model for gas diffusivity predicted measurements at −100 cm matric potential reasonably well, but failed at −30 cm matric potential, particularly for soil columns with biopore-dominated flow. X-ray CT-derived macroporosity matched the measured air-filled porosity at −30 cm matric potential well. Many of the CT-derived macropore network characteristics were strongly interrelated. Most of the macropore network characteristics were also significantly correlated with saturated hydraulic conductivity, air permeability, and gas diffusivity. The predictive Ahuja et al. (1984) model for saturated hydraulic conductivity, air permeability, and gas diffusivity performed reasonably well when parameterized with novel, X-ray CT-derived parameters such as effective percolating macroporosity for biopore-dominated flow and total macroporosity for matrix-dominated flow. The obtained results further indicate that it is crucially important to discern between matrix-dominated and biopore-dominated flow for accurate prediction of macropore flow from X-ray CT-derived macropore network characteristics.

Time-Dependent Methane Diffusion Behavior in Coal: Measurement and Modeling

In-depth understanding of how methane diffuses in porous media like coal is critical for enhanced coalbed methane recovery and coal seam methane drainage. However, the classic unipore gas diffusion model can only describe methane diffusion behavior in coal at the early time diffusion stage. Describing the whole methane diffusion behavior in coal has not been reasonably addressed in the coalbed methane field. Considering the large surface-to-volume ratio of coal, the authors proposed a time-dependent gas diffusion model to describe the whole diffusion process. This work first proposed a power–law relationship between diffusion coefficient and time according to previous studies of the time-dependent gas diffusion process in porous media. Then, both the analytical solution and its approximation solution for the time-dependent gas diffusion model were derived. Six methane diffusion tests in crushed coal were conducted to validate the proposed model under different pressures (0.5, 1.5, 2.5 MPa) and temperatures (20 and \(30\,{^{\circ }}\hbox {C}\)). Modeling results show that the time-dependent gas diffusion model is superior to the classic unipore gas diffusion model for describing the whole methane diffusion process in coal. Increasing temperature always accelerates methane diffusion in coal; the higher the temperature the larger the diffusion coefficient.

A DIFFUSIVITY MODEL FOR GAS DIFFUSION IN DRY POROUS MEDIA COMPOSED OF CONVERGING–DIVERGING CAPILLARIES

Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging–diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging–diverging effect included is in good agreement with reported experimental data.

A dynamic evacuation simulation framework based on geometric algebra

Integrating dynamic analysis models into geographic information system (GIS)-based evacuation simulations is important yet complex. Different models must be smoothly assembled according to the data processing flow to obtain a dynamic, data-forced evacuation simulation. However, because of the diversity of data types and dynamic data updating among different models, closely integrated evacuation simulations are complex and inefficient. In this study, geometric algebra (GA) is introduced to develop a dynamic evacuation simulation framework for a hazardous gas diffusion scheme. In the framework, geospatial data are first integrated into a unified virtual scene with different forms of multivector representation. The major simulation models of gas diffusion, risk assessment, and dynamic evacuation routing compose the major steps of the evacuation simulation. On the basis of the generalized multivector structure, dynamic exchange and updating geospatial data at different evacuation steps can be performed seamlessly with the multivector structure and GA operators. The framework is tested with a case study of a three-dimensional residential area, which shows that our framework can support the integration of dynamic evacuation processes and the model integration is direct and smooth. This framework may also provide a new solution for the integration and dynamic data updating in spatiotemporal GIS.

A new mathematical simulation model for gas injection enhanced coalbed methane recovery

The main purpose of this study is to improve the numerical evaluation of gas injection enhanced coalbed methane (ECBM) recovery by establishing a new mathematical coalbed methane (CBM) simulation model, in which the two-dimensional Peng–Robinson equation of state (2D PR EOS) model and the Maxwell-Stefan bidisperse pore diffusion (MS-BPD) model for multicomponent gas adsorption and diffusion are implemented. First, the extended Langmuir, ideal adsorbed solution and 2D PR-EOS models were investigated and compared with the experimental data of pure and mixed gas for modeling multicomponent gas adsorption behavior. Then, the MS-BPD model was developed based on the 2D PR-EOS model, bidisperse diffusion mechanisms, and Maxwell-Stefan diffusion theory, which provided an improved simulation of multicomponent gas diffusion behavior. On the basis of previous research, we developed a new CBM simulation model to analyze the effects of injection gas composition on the gas injection ECBM recovery process. The results indicate that mixed-gas injections are able to enhance methane recovery. The optimum composition of injected gas is 75% N2 and 25% CO2, which increases methane recovery by 25% over the pressure depletion production process. This CBM simulation model will provide an effective technical approach for research and development of CBM by gas injection.

Weighted Global Artificial Bee Colony Algorithm Makes Gas Sensor Deployment Efficient.

This paper proposes an improved artificial bee colony algorithm named Weighted Global ABC (WGABC) algorithm, which is designed to improve the convergence speed in the search stage of solution search equation. The new method not only considers the effect of global factors on the convergence speed in the search phase, but also provides the expression of global factor weights. Experiment on benchmark functions proved that the algorithm can improve the convergence speed greatly. We arrive at the gas diffusion concentration based on the theory of CFD and then simulate the gas diffusion model with the influence of buildings based on the algorithm. Simulation verified the effectiveness of the WGABC algorithm in improving the convergence speed in optimal deployment scheme of gas sensors. Finally, it is verified that the optimal deployment method based on WGABC algorithm can improve the monitoring efficiency of sensors greatly as compared with the conventional deployment methods.

Experimental and Numerical Study on Scale Effects of Gas Emission from Coal Particles

In order to study the scale effects and formation mechanism of gas emission from coal particles, we conducted gas desorption and diffusion experiments, investigated the variation of particle size and its effect on gas flow, analyzed and discussed the control mechanism and gas diffusion model of coal. Based on the above, we found that the bidisperse diffusion model was suitable to study the size effects of gas emission and further established a simplified numerical method of bidisperse diffusion model and compared it with the experiment results. The results showed that the accumulated gas emission volume and the initial gas emission speed have scale characteristics. The scale effects of gas emission from coal are determined by the multi-scale pore structure of coal. The diffusion coefficient and path of coal particle determined the gas flow process. Through the gas desorption and diffusion experiments, we can find a way to determine the critical diffusion parameters. On the basis of experiments and theoretical analyses performed, the processes of gas emission from coal particles are studied and their mathematical models are put forward. These models can describe the experimental phenomena fairly.

An analytical model for gas diffusion through fractal nanofibers in complex resources

Gas diffusion in porous nanofibers is of great interest in complex resources. In this work, a fractal analytical model is derived, to quantify gas diffusion across fibrous porous media composed of nanofibers in complex resources. The proposed model is expressed in terms of the porosity, the pore area fractal dimension, the tortuosity fractal dimensions, and the geometrical structures of porous nanofibers. It is found that the diffusion coefficient increases with the increase of pore area and porosity. However, it is shown that the diffusion coefficient increases with the decrease of the tortuosity fractal dimension in complex resources. Using the classical fractal theory, the analytical model of diffusion coefficient with clear physical importance reveals the important physical principles for gas diffusion through porous nanofibers in complex resources and is recommended. The normalized gas diffusivity predicted from the present model agrees well with the existing experimental data. The validity of the proposed analytical model can be thus verified. The present analytical model has revealed the important physical mechanisms for gas diffusion through porous nanofibers in complex resources.

A fully coupled multiscale shale deformation-gas transport model for the evaluation of shale gas extraction

Horizontal drilling and hydraulic fracturing are two enabling technologies to create a shale gas reservoir. For the created reservoir scale, we define shale blocks between hydraulic fractures as matrixes. In the matrix scale, flow processes are defined in the components of inorganic minerals and kerogens, respectively. Under this framework, a set of partial differential equations are derived to define various flow and deformation processes: (1) mechanical equilibrium equation that defines the shale deformation; (2) gas flow in the kerogen system of matrix; (3) gas flow in the inorganic system of matrix; and (4) gas flow in the hydraulic fracture system. For each of gas flow systems, a permeability or diffusivity model is derived to define its evolution. All systems are fully coupled through these permeability models and mass exchanges between different systems. The fully couple PDE system was solved by using COMSOL, a popular PDE solver. The model was verified against gas production data from the Marcellus Shale and the Barnett Shale, respectively. The verified model was applied to investigate the impact of adsorption parameters, flow regimes (Knudsen number), initial permeability of the inorganic matrix, and the effective stress variations on the gas production. Model results show that the Langmuir parameters affect both the cumulative gas production and the gas extraction processes; that the impact of flow regimes is closely related to the initial permeability of the inorganic matrix; and that the impact of effective stress variations on the permeability of hydraulic fractures is more significant than that on the matrix system.

Evaluation of gas diffusivity models for no-tilled and tilled volcanic ash soils

ABSTRACTAccurate quantification of soil gas diffusion is essential to understand the gas transport mechanism in soils, especially for soil greenhouse gas emissions. To date, the performance of soil gas diffusivity (Dp/D0, where Dp is the soil gas diffusion coefficient and D0 is the diffusion coefficient in free air) models has seldom been evaluated for no-tilled and tilled volcanic ash soils. In the present study, six commonly used models were evaluated for volcanic ash soils under two treatments by comparing the predicted and measured soil gas diffusivities at water potentials of pF 1.3–3. The Buckingham-Burdine-Campbell (BBC), soil-water-characteristic-dependent (SWC-dependent), and two-region extended Archie’s Law (2EAL) models showed better performance for both no-tilled and tilled volcanic ash soils, which is likely because porosity and pore size parameters of bimodal soils were taken into consideration in these models. Since the BBC model showed better accuracy than the SWC-dependent and 2EAL models and required fewer, more easily measurable parameters, this study recommends the BBC model for predicting soil gas diffusivity of volcanic ash soil under different tillage managements. In future studies, the BBC model should be further tested at water potentials of pF > 3, and may be improved by including the parameters of pore continuity and saturation.

A two-dimensional microscale model of gas exchange during photosynthesis in maize (Zea mays L.) leaves

CO2 exchange in leaves of maize (Zea mays L.) was examined using a microscale model of combined gas diffusion and C4 photosynthesis kinetics at the leaf tissue level. Based on a generalized scheme of photosynthesis in NADP-malic enzyme type C4 plants, the model accounted for CO2 diffusion in a leaf tissue, CO2 hydration and assimilation in mesophyll cells, CO2 release from decarboxylation of C4 acids, CO2 fixation in bundle sheath cells and CO2 retro-diffusion from bundle sheath cells. The transport equations were solved over a realistic 2-D geometry of the Kranz anatomy obtained from light microscopy images. The predicted responses of photosynthesis rate to changes in ambient CO2 and irradiance compared well with those obtained from gas exchange measurements. A sensitivity analysis showed that the CO2 permeability of the mesophyll-bundle sheath and airspace–mesophyll interfaces strongly affected the rate of photosynthesis and bundle sheath conductance. Carbonic anhydrase influenced the rate of photosynthesis, especially at low intercellular CO2 levels. In addition, the suberin layer at the exposed surface of the bundle sheath cells was found beneficial in reducing the retro-diffusion. The model may serve as a tool to investigate CO2 diffusion further in relation to the Kranz anatomy in C4 plants.

A Survey on Gas Leakage Source Detection and Boundary Tracking with Wireless Sensor Networks

Gas leakage source detection and boundary tracking of continuous objects have received a significant research attention in the academic as well as the industries due to the loss and damage caused by toxic gas leakage in large-scale petrochemical plants. With the advance and rapid adoption of wireless sensor networks (WSNs) in the last decades, source localization and boundary estimation have became the priority of research works. In addition, an accurate boundary estimation is a critical issue due to the fast movement, changing shape, and invisibility of the gas leakage compared with the other single object detections. We present various gas diffusion models used in the literature that offer the effective computational approaches to measure the gas concentrations in the large area. In this paper, we compare the continuous object localization and boundary detection schemes with respect to complexity, energy consumption, and estimation accuracy. Moreover, this paper presents the research directions for existing and future gas leakage source localization and boundary estimation schemes with WSNs.