Description Of Gas Flow Research Articles

A peridynamics approach modeling gas flow in porous media with damaged regions

The study of gas flow within porous media, particularly those characterized by complex pore-fracture networks, is critical for applications in fields such as shale gas engineering, gas extraction, and hydrogeology. This paper proposes a convenient and novel peridynamics approach to describe gas flow behavior in fracture regions and transition regions between fractured and intact regions in porous media, where the bonds naturally describe the interactions between material points in damaged areas. For implementation, we interpolate the permeability of the bonds in the transition region by using local damage values, and adopt a meshfree discretization approach that does not require additional mesh refinement for damaged or fractured regions. Numerical examples are provided and compared with the traditional finite element method to verify the accuracy and effectiveness of the proposed method.

Software for CO2 Storage in Natural Gas Reservoirs

The paper presents a simulation-based approach for optimizing CO2 injection into depleted gas reservoirs, with the goal of enhancing underground CO2 storage. The research employs a two-dimensional dynamic reservoir model, developed using Darcy’s law, to describe gas flow in a pressure-homogeneous porous medium, along with real gas equations. The model integrates the Du Fort–Frenkel and finite-difference methods to accurately simulate the behavior of CO2 during injection and storage. Real data from an operational gas storage facility were used to calibrate the model. CO2sim v1 software, specifically developed for this purpose, simulates CO2 injection cycles and quiescence phases, enabling the optimization of storage capacity and energy efficiency. The reservoir model, based on the engineering of the geological structure, is discretized into approximately 16,000 cells and solved using the finite-difference method, allowing for rapid simulation of CO2 injection and quiescence processes. The average computation time for a 150-day cycle is approximately 5 min. Simulation results indicate that increasing the number of injection wells and carefully controlling the injection rates significantly improves the distribution of CO2 within the reservoir, thereby enhancing storage efficiency. Additionally, appropriate well placement and prolonged quiescence periods lead to better CO2 dispersion, increasing the storage potential while reducing energy costs. The study concludes that further development of the software, along with comprehensive technical and economic assessments, is required to fully optimize CO2 storage on a commercial scale.

Three-Dimensional Model for Bioventing: Mathematical Solution, Calibration and Validation

Bioventing is an established technique extensively employed in the remediation of soil contaminated with petroleum hydrocarbons. In this study, the objective was to develop an improved foundational bioventing model that characterizes gas flow in vadose zones where aqueous and non-aqueous phase liquid (NAPL) are present and immobile, accounting for interphase mass transfer and first order biodegradation kinetics. By incorporating a correlation for the biodegradation rate constant, which is a function of soil properties including initial population of petroleum degrader microorganisms in soil, sand content, clay content, water content, and soil organic matter content, this model offers the ability to integrate a specific biodegradation rate constant tailored to the soil properties for each site. The governing equations were solved using the finite volume method in OpenFOAM employing the “porousMultiphaseFoam v2107” (PMF) toolbox. The equation describing gas flow in unsaturated soil was solved using a mixed pressure-saturation method, where calculated values were employed to solve the component transport equations. Calibration was done against a set of experimental data for a meso-scale reactor considering contaminant volatilization rate as the pre-calibration parameter and the mass transfer coefficient between aqueous and NAPL phase as the main calibration parameter. The calibrated model then was validated by simulating a large-scale reactor. The modelling results showed an error of 2.9% for calibrated case and 4.7% error for validation case which present the fitness to the experimental data, proving that the enhanced bioventing model holds the potential to improve predictions of bioventing and facilitate the development of efficient strategies to remediate soil contaminated with petroleum hydrocarbons.

Simulation of the Knudsen Pump by means of Quasi Gasdynamic Equation System

The use of miniature micropumps based on the effect of thermal gas sliding along the walls with an applied temperature gradient (Knudsen pump) is very relevant when creating modern miniature devices. Currently, algorithmically complex methods such as DSMC are usually used to simulate gas flows in such pumps. Progress in the development of algorithms based on a quasi-gasdynamic system of equations, pushed the authors to apply such algorithm to modeling the flow of a binary gas mixture gases in one variant of a micropump. The equations of the QGD system are conservation laws with additional dissipative terms. These terms contain a coefficient determined by the characteristic time between particles collisions. In this paper, the problem of flow in a rectangular Knudsen pump is solved based on this algorithm for a gas mixture in a single-fluid approximation. Different variants of the composition of the gas mixture are considered. The Knudsen numbers for which it is possible to describe gas flows by the QGD system correspond to flows of dense or moderately rarefied gases. Calculations for not too large Knudsen numbers demonstrated a good agreement with the results obtained by the DSMC method which is much more complex and expensive.

Conservative semi-Lagrangian method for continuity equation with various time steps in different parts of computational domain

The system of Navier Stokes differential equations describes gas flow near rocket nozzle. To find solution of this system in general case, scientists and engineers use numerical methods. Modern numerical methods do not allow engineers to model all features of gas flow. It happened because of sophisticated physical processes and limitations of computational hardware. So, at least where are two ways to improve it: to enlarge hardware or reduce computational complicacy. The global aim of many science investigations is to develop numerical approach with reduced computational complicacy and at the same time without loss of computational accuracy. In 1959, Aksel C. Wiin-Nielsen proposed a new and effective trajectories method for problem of numerical forecasting. In 1966, K. M. Magomedov developed similar approach (method of characteristics) for numerical modelling of space (three dimensional on space) gas flow. In 1982, O. Pironneau showed a new and effective approach for two dimensional approximation of the Navier Stokes problem. It was based on method of characteristics also. Nowadays, these methods are called semi-Lagrangian or Eulerian Lagrangian methods. They use Lagrangian nature of the transport process. To apply this advantage, scientists decompose each equation of Navier Stokes system into three parts: convective part (hyperbolic type), elliptic part and part of right-hand side. Scientists use semi-Lagrangian approach to approximate the convective parts of equations. To develop and test modern algorithms from family of semi-Lagrangian methods, we use continuity equation from the system of Navier Stokes equations. Conservative versions of semi-Lagrangian approach are based on Gauss Ostrogradsky (divergence) theorem. It allows scientists to get conservation low (balance equation) for numerical solution in norm of L1 space. Aim of our investigation is to use different time steps in different parts of computation domain. It enables us to obtain at the same time three advantages: convergence of numerical solution to exact solution, reduction of computational complicacy, implementation of conservation low (balance equation) without weight coefficients. For this purpose we decompose computational domain into two parts (subdomains) and use different time steps in them. Main complication is design algorithm in the boundaries of computational subdomains. We use one dimensional (on space) problem to demonstrate ability of developing numerical method with described advantages. Generalization of considered approach for two- or even three-dimensional cases allows engineers to model gas flow more accurately and without artificial viscosity. It is essentially important in the parts of computational domain with high level of solution gradient.

Molecular diameters of rarefied gases

Molecular diameters are an important property of gases for numerous scientific and technical disciplines. Different measurement techniques for these diameters exist, each delivering a characteristic value. Their reliability in describing the flow of rarefied gases, however, has not yet been discussed, especially the case for the transitional range between continuum and ballistic flow. Here, we present a method to describe gas flows in straight channels with arbitrary cross sections for the whole Knudsen range by using a superposition model based on molecular diameters. This model allows us to determine a transition diameter from flow measurement data that paves the way for generalized calculations of gas behaviour under rarefied conditions linking continuum and free molecular regime.

Boundary-value problem with an integral conjugation condition for a partial differential equation with the fractional Riemann-Liouville derivative that describes gas flows in a channel surrounded by a porous medium

Boundary-value problem with an integral conjugation condition for a partial differential equation with the fractional Riemann-Liouville derivative that describes gas flows in a channel surrounded by a porous medium

Numerical validation of the dusty-gas model for binary diffusion in low aspect ratio capillaries

The dusty-gas model is an empirical formulation commonly used to describe gas flows in porous media. While experiments have validated the model for pores with high aspect ratios, a validation for near-unity aspect ratios is lacking. We used direct simulation Monte Carlo to evaluate the accuracy of the dusty-gas model for binary diffusion in low aspect ratio capillaries. Our results suggest that the dusty-gas model deviates from the Monte Carlo simulations by less than 3% for aspect ratios ≥ 1, thus supporting its suitability as a phenomenological model for transport in nanoporous structures in various applications such as heat transfer, catalysis, and water purification.

Mathematical correlations in two-phase modeling of fluidized bed adsorbers

Choosing proper formulas for estimating different variables is imperative when modeling a fluidized bed using two–phase theory. In this study, a two–phase model was used to model the adsorption of volatile organic compounds (VOC) in a multistage fluidized bed adsorber. Two different approaches were used to describe gas flow and mixing in the emulsion phase, perfectly mixed (EGPM: Emulsion Gas – Perfectly Mixed) and plug flow (EGPF: Emulsion Gas – Plug flow). The impact of different formulas for estimating bubble size, bed porosity at minimum fluidization velocity, adsorption and interphase mass transfer coefficients, as well as tortuosity on the performance of the model was determined by comparing the model outcomes with experimental data. Finally, using a large dataset obtained from fluidized bed adsorption systems with different adsorbents, adsorbates, bed sizes, and operating conditions, a broadly-applicable set of formulas was suggested which could be used to describe the behavior of different countercurrent fluidized bed adsorbers. From the results, the two–phase model could successfully predict the experimental data, with EGPF showing better performance than EGPM. Proper use of formulas, especially those describing bed voidage and interphase mass transfer coefficient, could markedly improve the performance of the two-phase model. The two-phase model using the set of formulas proposed here was able to accurately replicate a large dataset of fluidized bed adsorption experiments over a wide range of operating conditions.

Modeling coupled gas flow and geomechanics process in stimulated coal seam by hydraulic flushing

Hydraulic flushing (HF) is an efficient technique for improving coal mine gas extraction. Although much research has been conducted in recent decades, many problems on its mechanism of enhancing permeability still exist. For example, how does coal strength affect the enhanced permeability by HF? Can a larger borehole generate a higher gas flowrate? Therefore, a coupled gas flow-geomechanics model was developed based on an equivalent fractured-coal model to solve these issues. Plastic volumetric strain was introduced in this model to quantify the coal structure, which can improve the numerical models for coal permeability, gas flow in fracture and diffusion in matrix, respectively. The model was used to describe gas flow in the virgin and disturbed coal seams. Results show that neglecting coal failure can cause erroneous stress and permeability distributions, and lead to an overestimation of gas pressure and an underestimation of gas extraction amount. Effects of coal strength and borehole diameter on the distributions of stress, plastic zone, permeability and gas pressure were systematically studied. It indicates that the stress relief, plastic and enhanced-permeability zones around the boreholes in soft coal are obviously larger than those in hard coal. The stress-concentration level and permeability reduction in soft coal are greater than those in hard coal. After 500 d extraction, gas pressure in soft coal has a higher decrease than that in hard coal, indicating that the enhanced permeability by HF of soft coal is larger than that of hard coal. Besides, the investigation on the effects of borehole diameter shows that there exists an optimal borehole diameter. Gas pressure between the boreholes decreases before the optimal diameter, and increases sharply after the optimal diameter due to the high stress concentration. For the Pingmei 8th mine, the optimal borehole diameter is about 1.0 m. Field tests indicate that the optimized HF can considerably eliminate the risk of coal and gas outburst.

SELF-SIMILAR SOLUTIONS OF THE PROBLEM OF POLYTROPIC GAS FLOW ALONG AN OBLIQUE WALL INTO VACUUM

Two-dimensional polytropic gas flows representable as endless series are constructed as solutions of the corresponding standard characteristic Cauchy problems in the space of self-similar variables. The convergence of the series is proved, and a procedure for constructing the coefficients of the series is described. It is found that in one particular case, the series terminates and coincides with the well-known analytical solution that was used by V. A. Suchkov to describe gas flow along an oblique wall into vacuum and by A. F. Sidorov to describe infinite compression of prismatic gas volumes. It is shown that in the case of compressive flow of the gas, its infinite compression by impermeable pistons moving according to different laws is possible, and the gas-dynamic parameters of the flow are studied. Highly nonuniform pressure distribution during compression of prismatic targets is obtained.

Transport Simulations on Scanning Transmission Electron Microscope Images of Nanoporous Shale

Digital rock physics is an often-mentioned approach to better understand and model transport processes occurring in tight nanoporous media including the organic and inorganic matrix of shale. Workflows integrating nanometer-scale image data and pore-scale simulations are relatively undeveloped, however. In this paper, a workflow is demonstrated progressing from sample acquisition and preparation, to image acquisition by Scanning Transmission Electron Microscopy (STEM) tomography, to volumetric reconstruction to pore-space discretization to numerical simulation of pore-scale transport. Key aspects of the workflow include (i) STEM tomography in high angle annular dark field (HAADF) mode to image three-dimensional pore networks in µm-sized samples with nanometer resolution and (ii) lattice Boltzmann method (LBM) simulations to describe gas flow in slip, transitional, and Knudsen diffusion regimes. It is shown that STEM tomography with nanoscale resolution yields excellent representation of the size and connectivity of organic nanopore networks. In turn, pore-scale simulation on such networks contributes to understanding of transport and storage properties of nanoporous shale. Interestingly, flow occurs primarily along pore networks with pore dimensions on the order of tens of nanometers. Smaller pores do not form percolating pathways in the sample volume imaged. Apparent gas permeability in the range of 10−19 to 10−16 m2 is computed.

Dust distribution study at the blast furnace top based on k–S –up model

The dust distribution law acting at the top of a blast furnace (BF) is of great significance for understanding gas flow distribution and mitigating the negative influence of dust particles on the accuracy and service life of detection equipment. The harsh environment inside a BF makes it difficult to describe the dust distribution. This paper addresses this problem by proposing a dust distribution k-Sε-u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> model based on interphase (gaspowder) coupling. The proposed model is coupled with a k-Sε model (which describes gas flow movement) and a model up (which depicts dust movement). First, the kinetic energy equation and turbulent dissipation rate equation in the k-Sε model are established based on the modeling theory and single-Green-function two-scale direct interaction approximation (SGF-TSDIA) theory. Second, a dust particle movement u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> model is built based up on a force analysis of the dust and Newton's laws of motion. Finally, a coupling factor that describes the interphase interaction is proposed, and the k-Sε-u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> model, with clear physical meaning, rigorous mathematical logic, and adequate generality, is developed. Simulation results and on-site verification show that the k-Sε-u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> model not only has high precision, but also reveals the aggregate distribution features of the dust, which are helpful in optimizing the installation position of the detection equipment and improving its accuracy and service life.

Gas flow through a bore-piston ring contact

This work reports on the derivation of simplified but accurate models to describe gas flow through a bore-piston ring contact in reciprocating machines like compressors or IC engines. On the basis of the aperture field of a contact deduced from real measurements carried out on an expanding ring in a bore, a scale analysis on the complete compressible flow model is performed, assuming ideal gas law. It is shown that the flow can be treated as stationary and three distinct flow regimes can be identified (namely incompressible, compressible creeping, and compressible inertial regimes). Three dimensionless parameters characterizing these regimes are identified. While for the two former regimes, classical analytical Poiseuille type of models are derived, an Oseen approximation is further employed for the latter, yielding a quasi-analytical solution. The models are successfully compared to direct numerical simulations (DNS) of the complete initial set of balance equations in their steady form performed on an aperture field of sinusoidal shape. These simplified models are of particular practical interest since they allow an accurate gas flow-rate estimate through a real contact using the aperture field as the geometrical input datum, together with the thermodynamic conditions (pressure and temperature). This represents an enormous advantage as DNS is still very challenging in practice due to the extremely small value of the contact aperture to contact length ratio.

A Review of Gas Flow and Its Mathematical Models in Shale Gas Reservoirs

The application of horizontal wells with multistage hydraulic fracturing technologies has made the development of shale gas reservoirs become a worldwide economical hotspot in recent years. The gas transport mechanisms in shale gas reservoirs are complicated, due to the multiple types of pores with complex pore structure and special process of gas accumulation and transport. Although there have been many attempts to come up with a suitable and practical mathematical model to characterize the shale gas flow process, no unified model has yet been accepted by academia. In this paper, a comprehensive literature review on the mathematical models developed in recent years for describing gas flow in shale gas reservoirs is summarized. Five models incorporating different transport mechanisms are reviewed, including gas viscous flow in natural fractures or macropores, gas ad-desorption on shale organic, gas slippage, diffusion (Knudsen diffusion, Fick diffusion, and surface diffusion), stress dependence, real gas effect, and adsorption layer effect in the nanoshale matrix system, which is quite different from conventional gas reservoir. This review is very helpful to understand the complex gas flow behaviors in shale gas reservoirs and guide the efficient development of shale gas. In addition to the model description, we depicted the type curves of fractured horizontal well with different seepage models. From the review, it can be found that there is some misunderstanding about the essence of Knudsen/Fick diffusion and slippage, which makes different scholars adopt different weighting methods to consider them. Besides, the contribution of each mechanism on the transport mechanisms is still controversial, which needs further in-depth study in the future.

A New Macro-Model of Gas Flow and Parameter Extraction for a CMOS-MEMS Vacuum Sensor

When using a MEMS sensor to measure the vacuum of a medium, the transition flow between the viscous flow and molar flow is usually used to describe the gas convection due to the physical principle, which is difficult to study through analysis and simulation. In this study, the description of gas flow under different pressures in a CMOS-MEMS vacuum sensors has been incorporated into a new behavioral ANSYS model. The proposed model was built and the characteristic parameters in the model were obtained based on a CMOS-MEMS thermopile patterned with circular symmetry and an embedded heater as a heat source. It contains a characteristic length to describe the effective distance of heat dissipation to the silicon substrate, and the corresponding transition pressure to describe the symmetrical phenomenon of gas heat conduction. The macro-model is based on the description of the physical characteristics of heat transfer and the characteristic parameters of the CMOS-MEMS vacuum sensor. The characteristic length of 49 μm and the corresponding transition pressure of 2396 mTorr for the thermoelectric-type vacuum sensor were extracted and verified successfully. The results show that the average error for the prediction of vacuum sensing by the macro-model we proposed is about 1.11%. This approach provides more applications for vacuum analysis. It can reduce the complexity of simulation and analysis and provide better simulation effects, including gas conduction mechanisms.

Pore-scale simulation of gas flow in microscopic permeable media with complex geometries

Lattice Boltzmann method (LBM) is an efficient tool to perform direct numerical simulation of gas flow in micro-size pores. Despite great advances in LBM and its use in describing gas flow in micro-size channels in slip and transitional flow regimes, exploring formulations that are able to capture flow behavior in domains with complex boundary geometries remains a challenging task. As a result, the impact of complexities in pore structures on gas flow may not be fully explored using LBM. In this study, we propose to use the combined bounce-back and Maxwellian diffusive reflection scheme to capture the slip velocity with a new set of slip coefficients. Optimal values of slip coefficients are determined using a gradient based method, where the results from the linearized Boltzmann equation is used as the reference solution. The proposed formulation is further validated against predictions from molecular dynamics simulation in the presence of complex geometries by introducing obstacles of different shapes in straight channels. LBM with the proposed boundary treatment is then used to investigate gas flow in a synthetic microscopic permeable medium. Results indicate that gas exhibits different flow configurations as Knudsen number varies, and apparent gas permeability appears to have up to a second-order dependency on the reciprocal mean pressure in slip and transitional flow regimes.

Gas Flow by Invasion Percolation Through the Hydrate Stability Zone

AbstractWe describe gas flow through the hydrate stability zone as a growing gas network with hydrate forming on its edges. The diffusion‐limited model successfully describes the dynamics of hydrate formation observed experimentally. We obtain an expression for the rate of hydrate growth in a region where gas and water coexist. Our modeled rate of hydrate formation is much lower than predicted with a kinetics‐based approach, and it more successfully simulates the hydrate formation rate observed in geologic systems. Current simulation approaches can readily incorporate our approach to describe hydrate formation in geological systems.

Multiscale gas transport behavior in heterogeneous shale matrix consisting of organic and inorganic nanopores

The complicated nanoporous structure and significant heterogeneity of shale matrix make it challenging to fully understand the gas transport behavior in shale. Towards this end, herein a multiscale approach was presented via coupling molecular dynamics (MD) simulations, analytical model and pore network model (PNM). Using MD simulations, we showed that gas transport in organic nanopores manifests a typical slippage feature whereas gas slippage breaks down in inorganic nanopores, which should be attributed to “rough” potential energy surface (PES) of inorganic walls. Based on the results of MD simulations, a unified gas transport model was derived to describe gas flow behaviors in organic and inorganic pores by integrating continuum flow theory and gas-surface dynamics theory. In particular, gas transport process in heterogeneous shale matrix was performed with the help of pore network model and the influence of multiple factors on the gas permeability of shale matrix were analysed and discussed.

The Impacts of Nano-Micrometer Pore Structure on the Gas Migration and Accumulation in Tight Sandstone Gas Reservoirs

The uncertainties between reservoir quality and gas migration and accumulation in tight sandstone gas reservoirs are intrinsically attributed to complex microscopic pore structures. Integrated analysis including the physical simulation experiment of gas migration and accumulation, X-ray computed tomography (X-CT), and casting thin section (CTS) were conducted on core plug samples collected from the Upper Paleozoic Permian Lower Shihezi and Shanxi tight sandstone of the Daniudi area in the Ordos Basin to investigate the impacts of pore structure on the gas migration and accumulation. Physical simulation suggested that the gas flows in migration in tight sandstone reservoirs were characterized by deviated-Darcy linear flow and non-linear flow regimes. Minimum and stable migration pressure square gradients determined by application of apparent permeability were employed as key parameters to describe gas flow. Pore structure characterization revealed that the tight sandstone reservoir was characterized by wide pore and throat size distributions and poor pore-throat connectivity. The pore–throat combinations could be divided into three types, including the macropore and coarse throat dominant reservoir, full-pore and full-throat form, and meso-small pore and fine throat dominant form. Comparative analyses indicated that pore and throat radii determined the gas flow regimes by controlling the minimum and stable migration pressure gradients. Gas accumulation capacity was dominated by the connected effective porosity, and the gas accumulation process was controlled by the cumulative effective porosity contribution from macropores to micropores. Variations in pore structures resulted in differences in gas migration and accumulation of tight sandstone reservoirs. The macropore and coarse throat-dominant and the full-pore and full-throat reservoirs exhibited greater gas migration and accumulation potentials than the small pore and fine throat dominate form.