Simulation Of Gas Flow Research Articles

A multi-level parallel solver for rarefied gas flows in porous media

A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Bhatnagar–Gross–Krook model equation is solved by the discrete velocity method with an iterative scheme. The multi-level MPI/OpenMP parallelization is implemented with the aim to efficiently utilize the computational resources to allow direct simulation of rarefied gas flows in porous media based on digital rock images for the first time. The multi-level parallel approach is analyzed in detail confirming its better performance than the commonly-used MPI processing alone for an iterative scheme. With high communication efficiency and appropriate load balancing among CPU processes, parallel efficiency of 94% is achieved for 1536 cores in the 2D simulations, and 81% for 12288 cores in the 3D simulations. While decomposition in the spatial space does not affect the simulation results, one additional benefit of this approach is that the number of subdomains can be kept minimal to avoid deterioration of the convergence rate of the iteration process. This multi-level parallel approach can be readily extended to solve other Boltzmann model equations.

An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks

We present an explicit second order staggered finite difference (FD) discretization scheme for forward simulation of natural gas transport in pipeline networks. By construction, this discretization approach guarantees that the conservation of mass condition is satisfied exactly. The mathematical model is formulated in terms of density, pressure, and mass flux variables, and as a result permits the use of a general equation of state to define the relation between the gas density and pressure for a given temperature. In a single pipe, the model represents the dynamics of the density by propagation of a non-linear wave according to a variable wave speed. We derive compatibility conditions for linking domain boundary values to enable efficient, explicit simulation of gas flows propagating through a network with pressure changes created by gas compressors. We compare our staggered grid method with an explicit operator splitting method and a lumped element scheme, and perform numerical experiments to validate the convergence order of the new discretization approach. In addition, we perform several computations to investigate the influence of non-ideal equation of state models and temperature effects on pipeline simulations with boundary conditions on various time and space scales.

Error Analysis and Model Adaptivity for Flows in Gas Networks

Abstract In the simulation and optimization of natural gas flow in a pipeline network, a hierarchy of models is used that employs different formulations of the Euler equations. While the optimization is performed on piecewise linear models, the flow simulation is based on the one to three dimensional Euler equations including the temperature distributions. To decide which model class in the hierarchy is adequate to achieve a desired accuracy, this paper presents an error and perturbation analysis for a two level model hierarchy including the isothermal Euler equations in semilinear form and the stationary Euler equations in purely algebraic form. The focus of the work is on the effect of data uncertainty, discretization, and rounding errors in the numerical simulation of these models and their interaction. Two simple discretization schemes for the semilinear model are compared with respect to their conditioning and temporal stepsizes are determined for which a well-conditioned problem is obtained. The results are based on new componentwise relative condition numbers for the solution of nonlinear systems of equations. More- over, the model error between the semilinear and the algebraic model is computed, the maximum pipeline length is determined for which the algebraic model can be used safely, and a condition is derived for which the isothermal model is adequate.

Simulation of free-molecular and transition multicomponent gas flow through the system of filaments with different temperatures

This work studies plane transition flow (Kn = 0.1–10) of a mixture of noble gases in the system, consisting of several rows of stretched filaments having different temperatures. Problem statement studying equilibrium state in closed system is considered. Calculations were performed using method of event-driven molecular dynamics (EDMD). It is shown that temperature difference leads to gas separation effect, which can be thereafter enhanced by increasing the number stages (rows of filaments).

Experimental validation of theoretical calculation and numerical simulation for optimization of divers’s breathing apparatus

Abstract In order to optimize the breathing apparatus in the open circuit for divers, theoretical calculus and numerical simulation of resistances specific to the potential flow of gas through the studied circuit were made. Respiratory gas flow simulation through three constructive versions of the second stage pressure reducer intake mechanism was done after modeling the respiratory air circuit through the two main restrictors: the first variable (between the seat and the piston) and the second fixed (the hole in the cylindrical piston). The results regarding the theoretical calculation and numerical simulation have been validated by experimental testing of two of the studied models. Experimental measurements were made on a tester at the Diving Center of Constanta's Hyperbaric Laboratory. The volume flow rate of supplied respiratory gas was recorded, together with the inspire depression that opens the mechanism, until the maximum flow rate for each constructive version. After validating the results of the theoretical calculation and numerical simulation on the two models, the conclusion is the same: the resistance decreases if the geometry of the cylindrical hole in the piston (the second fixed restrictor) changes in a conical hole

Simultaneous Removal of SO2 and NO by Using Piperazine-urea-triethylene Diamine Ternary System

Performance of simultaneous removal of SO2 and NO from the simulated thermal power plants gas using piperazine-urea-triethylene diamine ternary system absorbent was investigated in this paper. Furthermore, the influences of the concentration of triethylene diamine, pH value, the absorption temperature and the total inlet flow rate of the simulated gas on simultaneous absorption behavior were discussed by means of the removal efficiency of SO2 and NO. A better simultaneous desulfurization and denitration behavior could be obtained under the absorption condition of triethylene diamine concentration of 0.3 mol/L, pH value of 6, inlet simulated gas flow rate of 500 ml/min, and the absorption temperature of 40 °C. Under the above absorption condition, the simultaneous NO removal efficiency of 70.28% and SO2 removal efficiency of 99.30% could be obtained.

A Fully Coupled Model for the Simulation of Gas Flow in Multiscale Shale Reservoirs Combining Multiple Effects

Gas flow mechanisms in shale reservoirs with multiscale pores and fractures are extremely complex. In this study, a dual fracture framework model was adopted to describe gas flow in multiscale shale reservoirs. Gas flow through a shale reservoir occurs through both the shale matrix and hydraulic fractures. This study considered bulk phase and adsorbed gas flow in the shale matrix. Next, a series of partial theories were combined to derive a fully coupled model simulating gas flow in multiscale shale reservoirs: (1) fractal theory was adopted to obtain the pore distribution within shale reservoirs; (2) mechanical equilibrium equations were used to investigate the stress-sensitivity of permeability and porosity; and (3) a Langmuir adsorption model was applied to describe the effects of gas adsorption/desorption. The proposed model was validated using traditional models as well as field data on gas production from Marcellus Shale, and was subsequently applied to study variations of mass flux in various flow regimes with respect to reservoir pressure. We found that mass flux in the slip flow regime decreased at first and then increased with decreasing reservoir pressure, while in the continuum regime, Knudsen diffusion and surface diffusion the mass flux decreased with decreasing reservoir pressure. Stress-sensitivity has a significant impact on bulk phase gas flow, while adsorption/desorption influence both the bulk phase gas flow and adsorbed gas flow. At high pressures, the impact of stress-sensitivity on total gas mass flux is greater than that of adsorption/desorption, while the reverse was true for low pressures. The proposed model shows promising applications for analyzing various gas flow regimes in multiscale pores/fractures, and accurately evaluating in situ apparent permeability.

Modified Patterson temperature jump condition considering viscous heat generation

Recently, new type of the Smoluchowski temperature jump condition has been proposed by considering viscous heat generation in rarefied gas flow simulations, and improved prediction of the surface gas temperature in comparing with DSMC data. Two forms of the Patterson jump condition have been revisited for rarefied gas flow simulations in the literature. In this paper, the modified Patterson temperature jump condition is proposed by considering viscous heat generation. We numerically investigate the effect of the slip velocity, the wall temperature and viscous heat generation on the surface gas temperature for external high-speed rarefied gas flow simulations by using various forms of the Patterson jump condition. Three configurations such as the sharp leading-edge flat plate, the sharp 25–55-deg biconic, and micro-airfoil NACA0012 are selected for simulations with Mach number from 2 to 15.6, and Knudsen number ranging from 0.04 to 0.26. The simulation results obtained show that the modified Patterson jump condition gives good agreement with the DSMC data, and predict temperatures better than those of new type of the Smoluchowski jump condition for all cases considered.

Permeability correlation with porosity and Knudsen number for rarefied gas flow in Sierpinski carpets

In recent years, application of porous media is highlighted among researchers due to their wide range of usability in micro-scale problems, such as gas reservoirs, micro-filtering, heat exchangers, etc. With this respect, the accurate description of flow behavior using governing equations based on the continuum assumption is not valid since the mean free path is comparable to the characteristics length of the problem. For this purpose, a simple methodology for diffusion reflection boundary condition is developed and validated for two valuable benchmarks, namely micro-channel flow and fractal porous media, where the results were in good agreement with literature. Then, pore-scale simulation of the rarefied gas flow inside the square- and circular-based Sierpinski carpets in the slip and transition flow regimes (based on the developed boundary condition) for different porosities are carried out, using lattice Boltzmann method (LBM). In each case, the effects of different key parameters such as pressure gradient in the x-direction (body force), porosity, and Knudsen number on the velocity contours, velocity profiles, flow structures, and permeability are investigated. It is found that the velocity magnitude is reduced as Knudsen number increases, where the reduction rate of velocity in the slip flow regime is greater than that of the transition one. Also, a correlation between the permeability with porosity and Knudsen number in the Darcy flow regime (Re<<1) is presented. For both geometries, it is observed that the permeability varies logarithmically with Knudsen number and exponentially with the porosity.

Simulation of gas separation effect in microchannel with moving walls

Numerical simulation of a free-molecular gas flow through plane microchannel with walls performing forced curving motion according to sine law is presented. It is shown that the probability of gas molecules to pass through the channel significantly depends on relation between wave speed of walls harmonic oscillations and characteristic thermal speed of gas molecules. It is then shown how this effect can be utilized for gas separation, and the comprehensive study of the influence of the main parameters (channel width and length, wave amplitude and length, etc.) on the magnitude of effect is performed.

Effects of the shape and height of artificial 2D roughness elements on deposition of nano and microparticles in the turbulent gas flow inside a horizontal channel

In this paper, deposition of the particles in turbulent incompressible gas flow inside a horizontal channel with different two-dimensional artificial roughness shapes and heights is studied. The Eulerian–Lagrangian method is used for numerical simulation of the particulate gas flow. The Reynolds stress model (RSM) with enhanced wall treatment is applied to simulate the anisotropic turbulence in the gas flow. The Lagrangian equation of the particles motion includes drag, gravity, Saffman lift, and Brownian forces. Discrete phase simulations are compared with the available correlations for a smooth channel to show the validation of the simulations. The results show that the rate of deposition for small particles is affected significantly by the flow pattern in the space between two roughness elements. For small particles (τ+<10), deposition of the particles depends on the v component of the gas velocity. Gravity force is assumed to be perpendicular to the main flow direction. For large particles (τ+>10), the gravity force is more effective on the deposition velocity.

Particle simulation of nonequilibrium gas flows based on ellipsoidal statistical Fokker–Planck model

In order to improve the efficiency of particle simulation method for gas flows spanning the rarefied and continuum regimes, one promising approach is to employ the Fokker–Planck-type gas kinetic model. The ellipsoidal statistical Fokker–Planck (ES-FP) model treats the evolution of individual molecular velocity as a continuous stochastic process, which can be equivalently described by the Langevin dynamics where the forces acting on each gas molecule are a linear drag force and an anisotropic fluctuating force. By utilizing the exact stochastic integral solution of the corresponding Langevin equation, the ES-FP model is numerically implemented in a particle Monte Carlo manner. In a validation of the particle scheme, excellent agreement is obtained between the simulation results and the analytical solution for the same initial-value problem of ES-FP equation. The ES-FP particle method is used to simulate the relaxation process in a nonequilibrium gas, and agrees well with the direct simulation Monte Carlo (DSMC) method in the predictions of viscous stress and heat flux. Furthermore, extensive ES-FP particle simulations are performed for Couette flows at different Knudsen numbers ranging from 0.001 to 10, as well as supersonic flat-plate flows at different Knudsen numbers ranging from 0.001 to 0.1. Both flow fields and surface quantities are investigated and compared with the DSMC or theoretical solutions. In the ES-FP simulations, the Prandtl number of gas can be corrected, and the physical behaviors in different flow regimes can be properly captured. With reasonable agreement between the ES-FP and DSMC results, the ES-FP simulation is found to be more efficient than DSMC and can significantly save memory cost and CPU time, especially for multi-dimensional flows in the low-Knudsen-number regime.

Modified Extended Finite Element Methods for Gas Flow in Fractured Reservoirs: A Pseudo-Pressure Approach

Fluid flow in fractured porous media has always been important in different engineering applications especially in hydrology and reservoir engineering. However, by the onset of the hydraulic fracturing revolution, massive fracturing jobs have been implemented in unconventional hydrocarbon resources such as tight gas and shale gas reservoirs that make understanding fluid flow in fractured media more significant. Considering ultralow permeability of these reservoirs, induced complex fracture networks play a significant role in economic production of these resources. Hence, having a robust and fast numerical technique to evaluate flow through complex fracture networks can play a crucial role in the progress of inversion methods to determine fracture geometries in the subsurface. Current methods for tight gas flow in fractured reservoirs, despite their advantages, still have several shortcomings that make their application for real field problems limited. For instance, the dual permeability theory assumes an ideal uniform orthogonal distribution of fractures, which is quite different from field observation; on the other hand, numerical methods like discrete fracture network (DFN) models can portray the irregular distribution of fractures, but requires massive mesh refinements to have the fractures aligned with the grid/element edges, which can greatly increase the computational cost and simulation time. This paper combines the extended finite element methods (XFEM) and the gas pseudo-pressure to simulate gas flow in fractured tight gas reservoirs by incorporating the strong-discontinuity enrichment scheme to capture the weak-discontinuity feature induced by highly permeable fractures. Utilizing pseudo-pressure formulations simplifies the governing equations and reduces the nonlinearity of the problem significantly. This technique can consider multiple fracture sets and their intersection to mimic real fracture networks on a plain structured mesh. Here, we utilize the unified Hagen–Poiseuille-type equation to compute the permeability of tight gas, and finally adopt Newton–Raphson iteration method to solve the highly nonlinear equations. Numerical results illustrate that XFEM is considerably effective in fast calculation of gas flow in fractured porous media.

A globally mass-conservative method for dual-continuum gas reservoir simulation

In this paper, we find that the numerical simulation of gas flow in dual-continuum porous media may generate unphysical or non-robust results using regular finite difference methods. The reason is the unphysical mass loss caused by the gas compressibility and the non-diagonal dominance of the discretized equations caused by the non-linear well term. The well term contains the product of density and pressure. For oil flow, density is independent of pressure so that the well term is linear. For gas flow, density is related to pressure by the gas law so that the well term is non-linear. To avoid these two problems, numerical methods are proposed using the mass balance relation and the local linearization of the non-linear source term to ensure the global mass conservation and the diagonal dominance of discretized equations in the computation. The proposed numerical methods are successfully applied to dual-continuum gas reservoir simulation. Mass conservation is satisfied while the computation becomes robust. Numerical results show that the location of the production well relative to the large-permeability region is very sensitive to the production efficiency. It decreases apparently when the production well is moved from the large-permeability region to the small-permeability region, even though the well is very close to the interface of the two regions. The production well is suggested to be placed inside the large-permeability region regardless of the specific position.

Lattice Boltzmann simulation of gas flow and permeability prediction in coal fracture networks

The cleat or natural fracture system is a dominant factor controlling the permeability of coal seams. Gas permeability and porosity of coal samples with artificially generated fractures are measured under varying effective stress. Based on the experimental results and the Walsh model, fracture width and roughness are estimated. Considering the fracture aperture and roughness, we present a 3D geometry model to reconstruct coal fracture networks on the basis of the Voronoi tessellations. The lattice Boltzmann method (LBM) is applied to simulate fracture flows and to predict the associated permeability. For comparison purposes, simulations in a single fracture are carried out initially. For a single smooth fracture, the results of LBM simulations show a good agreement with the cubic law. For a single rough fracture, the cubic law overestimates the permeability, and it is two to four orders of magnitude higher than the laboratory measurement. The predicted permeability by LBM simulation is in acceptable agreement with laboratory measurement. Furthermore, the flows through the fracture networks with smooth fracture surfaces are simulated. By comparison to the matchstick model, simulation errors are mostly within 30%. Finally, the effects of structure, surface roughness and aperture on flows in fracture networks with rough fracture surfaces are investigated. The present study provides a promising approach to predict the associated permeability and transport characteristics in coal fracture networks.

On the numerical simulation of rarefied gas flows in micro-channels

Classical continuum methods break down for rarefied gas flows in micro-channels. Two non-continuum hydrodynamic models are investigated here: compressible Korteweg fluid-like and Bi-Velocity (Volume Diffusion) hydrodynamic models. The pressure driven rarefied gas flow in a rectangular micro-channel in the whole range of Knudsen number is numerically considered. The Korteweg model shows improved results in comparison with standard Navier–Stokes up to Knudsen number of unity. The Bi-Velocity method is found to allow a match between experiments and numerical results over the full range of Knudsen number.

Automatic mesh refinement and parallel load balancing for Fokker–Planck-DSMC algorithm

Recently, a parallel Fokker–Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors.Fokker–Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker–Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

Discrete fracture modeling of shale gas flow considering rock deformation

Rock deformation is an important mechanism in shale reservoirs and occurs simultaneously with gas flow during the production period. It may not only result in production variation, but also have an impact on reservoir flow behaviors. Accurate simulation of gas flow in deformable reservoirs is challenging considering dual porosity structure of shale reservoirs. Besides, the complex fracture network topology and interactions further complicates the simulation of the fracture system.In this work, we implement a discrete fracture model (DFM), in which the reservoir is divided into the matrix and fracture system. The DFMs use flexible Delaunay triangulation to represent individual fractures, hence they could handle complex fracture network. Based on the comprehensive study of the deformation of matrix and fracture, a flow model that considers rock deformation is presented to predict well production and reservoir dynamics. Numerical simulations are conducted to investigate the influence of rock deformation on a reservoir with complex fracture network. Results under no deformation (ND) condition and integrated deformation (ID) condition show that rock deformation has an obvious impact on the gas production and the pressure distribution. The percentage of production loss increases with reservoir pressure, while decreases as matrix permeability or fracture conductivity increases. Comparisons of production loss caused by the individual deformation depict that the natural fracture deformation (NFD) is dominant, the hydraulic fracture deformation (HFD) is minor, while the matrix deformation (MD) is negligible. Less percentage of production loss caused by the ID is observed than the sum caused by the NFD, the HFD, and the MD.

Global existence and long time behavior of the ellipsoidal-Fokker–Planck equation

ABSTRACTThe ellipsoidal-Fokker–Planck (ES-FP) model is proposed recently to obtain the correct Prandtl number in the numerical simulation of rarefied gas flows, which also satisfies the same properties as the Boltzmann equation, such as the H-theorem and the conservation laws of the mass, momentum, and energy. In this paper, we consider the Cauchy problem for this ES-FP equation in , and prove the global existence of the unique solution and establish its algebraic time convergence rate to the equilibrium state.

Simulation of Gas Flow in an Anti-Surge Valve by the ANSYS CFX Software Complex

Computer simulation of gas flow in an anti-surge valve for two designs of the valve, one with single-stage separator and the other with two-stage separator with transitional cavity, is performed. Unevenness of the mass flow of gas through the series of separator passages is discovered. It is established that this unevenness is lower in a valve with two-stage separator, leading to the conclusion that such valves are efficient for gaspumping compressor systems.