Numerical modeling of formation of a gas hydrate in a finite-length porous bed purged by a gas

The process of formation of a gas hydrate in a finite-length porous medium partially saturated with water, which is purged by a cold gas, is studied. The influence of the initial parameters of the porous medium and purging conditions on the evolution of hydrate saturation and temperature is examined.     

局部多孔质气体静压轴向轴承静态特性的数值求解

运用数值方法分析局部多孔质节流气体静压轴向轴承的静态性能,分别建立局部多孔质圆柱塞内的压力分布方程和气体薄膜内的压力分布方程,利用坐标变换将局部多孔质圆柱塞的圆柱坐标与气体薄膜的圆柱坐标转换到同一笛卡儿坐标系,为有限元离散奠定基础.经过有限元推导,求得局部多孔质气体静压轴向轴承的承载能力与静态刚度,并对局部多孔质节流进行试验以验证理论模型的正确性.另外,对局部多孔质节流气体静压轴向轴承和小孔节流气体静压轴向轴承进行对比试验.结果表明:局部多孔质节流和小孔节流静压轴承的承载能力随着气膜厚度的减小而增加;静态刚度随着气膜厚度的增加先增加后减小;局部多孔质节流比小孔节流具有较高的承载能力和静态刚度.     

组合型多孔材料对容器管道系统内甲烷/空气的抑爆效果

为研究多孔材料对可燃气体的抑爆效果,选取了3类6种多孔材料分别组合后进行实验研究。以甲烷/空气预混气体作为研究对象,利用自制薄型铁环将多孔材料固定在密闭容器管道系统内,对比分析了薄型铁环、单层型多孔材料、双层组合型多孔材料和三层组合型多孔材料的抑爆效果。结果表明:薄型铁环增强了气体爆炸强度,铁环后爆炸压力最大;多孔材料抑爆效果明显,双层组合型多孔材料抑爆效果相比单层型多孔材料和三层组合型多孔材料稳定;抑爆效果最佳的组合型多孔材料为Al₂O₃ 10 mm/30 PPI+SiC 20 mm/20 PPI,爆炸压力抑制效果最佳的组合型多孔材料为Al₂O₃ 10 mm/30 PPI+Fe-Ni 10 mm/90 PPI+SiC 20 mm/10 PPI。     

On the stability of Taylor bubbles inside a confined highly porous medium

This work focuses on the local hydrodynamics of a multiphase gas–liquid flow forced into an innovative medium of high porosity (96%): an open cell solid foam. The gas (nitrogen) and liquid (ethanol) phases are injected at constant flow-rates in a millichannel to form a well-controlled Taylor flow which enters the porous medium. Based on a fluorescence technique, the apparent liquid holdup in the porous medium is quantified, and its evolution in time and along the porous medium extracted from spatiotemporal diagrams. The analysis of the main frequency, when varying the gas–liquid flow-rate ratio, leads to the identification of two hydrodynamic regimes. A model based on a scaling analysis is proposed to quantify the dimensionless numbers describing the transition between both regimes. It points out that the bubble length fixed by the Taylor flow is the control parameter. The model prediction of the critical bubble length at which the transition occurs is in good agreement with the experimental observations.     

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

A two-dimensional problem of the flow of a gas containing an impurity through a porous medium is considered. At the initial time, the gas containing a uniformly distributed impurity is at a high pressure in a spherical cavity in a porous medium at a certain distance from a flat surface. It is assumed that for t > the motion of the carrier gas is described by the system of equations for flow in a porous medium and the dispersion of the impurity is described by the equations of convective diffusion and nonequilibrium adsorption. A numerical method for solving the problem is discussed. Some results of calculations are given. The influence of the flat surface on the flow of the gas and the dispersion of the impurity is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1982.We thank V. N. Nikolaevskii for comments which permitted a significant improvement in the paper.     

Quasiequilibrium Knudsen boundary layer on a nonisothermal porous body

The state of a gas near a permeable nonisothermal body with ultrathin pores, that is, pores in which the motion of molecules is not accompanied by intermolecular collisions, is studied. A boundary layer of a new type, namely, the quasiequilibrium Knudsen boundary layer on the porous body surface, is investigated. It is formed on condition that within the body there is a heat flux, even when the body is in an equilibrium gas. The statistical methods for solving the Boltzmann equation are used to determine the temperature and pressure jumps across the Knudsen layer near thin perforated and porous membranes.     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Knudsen’s Permeability Correction for Tight Porous Media

Various flow regimes including Knudsen, transition, slip and viscous flows (Darcy’s law), as applied to flow of natural gas through porous conventional rocks, tight formations and shale systems, are investigated. Data from the Mesaverde formation in the United States are used to demonstrate that the permeability correction factors range generally between 1 and 10. However, there are instances where the corrections can be between 10 and 100 for gas flow with high Knudsen number in the transition flow regime, and especially in the Knudsen’s flow regime. The results are of practical interest as gas permeability in porous media can be more complex than that of liquid. The gas permeability is influenced by slippage of gas, which is a pressure-dependent parameter, commonly referred to as Klinkenberg’s effect. This phenomenon plays a substantial role in gas flow through porous media, especially in unconventional reservoirs with low permeability, such as tight sands, coal seams, and shale formations. A higher-order permeability correlation for gas flow called Knudsen’s permeability is studied. As opposed to Klinkenberg’s correlation, which is a first-order equation, Knudsen’s correlation is a second-order approximation. Even higher-order equations can be derived based on the concept used in developing this model. A plot of permeability correction factor versus Knudsen number gives a typecurve. This typecurve can be used to generalize the permeability correction in tight porous media. We conclude that Knudsen’s permeability correlation is more accurate than Klinkenberg’s model especially for extremely tight porous media with transition and free molecular flow regimes. The results from this study indicate that Klinkenberg’s model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high Knudsen number.     

Analytical Solutions to Gas Flow Problems in Low Permeability Porous Media

In most of conventional porous media the flow of gas is basically controlled by the permeability and the contribution of gas flow due to gas diffusion is ignored. The diffusion effect may have significant impact on gas flow behavior, especially in low permeability porous media. In this study, a dual mechanism based on Darcy flow as well as diffusion is presented for the gas flow in homogeneous porous media. Then, a novel form of pseudo pressure function was defined. This study presents a set of novel analytical solutions developed for analyzing steady-state and transient gas flow through porous media including effective diffusion. The analytical solutions are obtained using the real gas pseudo pressure function that incorporates the effective diffusion. Furthermore, the conventional assumption was used for linearizing the gas flow equation. As application examples, the new analytical solutions have been used to design new laboratory and field testing method to determine the porous media parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs. Then, permeability (k) and effective diffusion coefficient (D _e) was determined; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.     

Recovery of Methane From Gas Hydrates in a Porous Medium by Injection of Carbon Dioxide

This paper presents a mathematical model for methane hydrate–carbon dioxide replacement by injection of carbon dioxide gas into a porous medium rich in methane and its gas hydrate. Numerical solutions describing the pressure and temperature variation in a reservoir of finite length are obtained. It is shown that the replacement process is accompanied by a decrease in pressure and an increase in temperature of the porous medium. It is established that during the time of complete replacement of methane from a reservoir decreases with increasing permeability of the porous medium and the pressure of the injected gas.     

Contributions to numerical developments in shock waves attenuation in porous filters

The paper deals with the numerical method of the compressible gas flow through a porous filter emphasizing the treatment of the interface between a pure gaseous phase and a solid phase. An incident shock wave is initiated in the gaseous phase interacting with a porous filter inducing a transmitted and a reflected wave. To take into account the discontinuity jump in the porosity between the gaseous phase and the porous filter, an approximate Riemann solver is used to compute homogeneous non-conservative Euler equations in porous media using ideal gas state law. The discretization of this problem is based on a finite volume method where the fluxes are evaluated by a “volumes finis Roe” (VFRoe) scheme. A stationary solution is determined with a continuous variable porosity in order to test the numerical scheme. Numerical results are compared with the two-phase shock tube experiments and simulations of a shock wave attenuation and gas filtration in porous filters are presented.      

Gas Injection in a Liquid Saturated Porous Medium. Influence of Gas Pressurization and Liquid Films

We study numerically and experimentally the displacement of a liquid by a gas in a two-dimensional model porous medium. In contrast with previous pore network studies on drainage in porous media, the gas pressurization is fully taken into account. The influence of the gas injection rate on the displacement pattern, breakthrough time and the evolution of the pressure in the gas phase due in part to gas compressibility are investigated. A good agreement is found between the simulations and the experiments as regards the invasion patterns. The agreement is also good on the drainage kinetics when the dynamic liquid films are taken into account.     

ON FLOW IN POROUS MEDIA

渗流是流体在多孔介质中的流动,渗流现象广泛地存在于自然界、工程材料、动物、植物中。多孔介质种类繁多,包括岩石(含各类矿藏)、土壤、生物材料和人工多孔介质材料等。渗流理论已经成为人类开发地下水、地热、石油、天然气、煤炭与煤层气等诸多地下资源的重要理论基础。本文从渗流的基本概念、渗流的分类、渗流的影响因素、渗流的特征以及渗流的研究意义等方面进行了阐述。     

A lattice model of foam flow in porous media: A percolation approach

Because fluid flow in porous media is opaque to most observational techniques simulations of the processes occurring in porous media have become important. Typical reservoir simulations treat the flow as taking place in some averaged (Darcy-scale) medium but simulations can also be carried out at the level of the network of pores and throats of the porous medium. We report the results of a pore-scale investigation of mechanisms for the alteration of mobility by foam lamella blockage in a network of these spaces and channels of porous media. Saturation and relative permeability curves are obtained using well-known power-law expressions of percolation theory and a rescaling of the percolation parameter readily permits a number of lamella-blocking mechanisms to be treated. An explanation of the shift in breakthrough gas saturation and the deformation of the shape of permeabilityvs saturation curves upon introduction of foam is provided for a variety of blocking mechanisms. The qualitatively different features seen in experimental studies of modification of gas mobility by foam can be rationalized using only two parameters which characterize the throat-size at which blockage commences and the degree of blockage.     

复杂微通道气体流动的格子Boltzmann模拟

构建了一个模拟复杂微通道内气体流动的多松弛格子Boltzmann模型。该模型采用动力学曲面滑移边界,考虑了微尺度效应和努森层影响。此外,为了更准确地描述微通道内气体的滑移速度,在模型中引入孔隙局部Kn数来代替平均Kn数。之后采用Poiseuille流对模型进行验证,模拟结果与用直接模拟蒙特卡洛方法和分子模拟结果吻合较好,证明了该模型模拟微通道内处于滑移区和过渡区气体流动的有效性。最后,采用该模型模拟多孔介质内气体渗流过程。结果表明,随着孔隙平均Kn数的增加,多孔介质内的高渗区域增加,且优先从小孔隙中开始增加,这是由于小孔隙中微尺度效应更加明显,相对大孔隙流动阻力更小所致。     

前进式U形通风采空区风流与自燃的数值模拟

基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型 通风采空区自然发火模型. 通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟 计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-Ohttp://d.wanfangdata.com.cn/Periodical_lxysj200804005.aspx前进式开采U型通风;采空区;风流规律;自燃温度场;有限元; 基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型 通风采空区自然发火模型. 通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟 计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-Ohttp://d.wanfangdata.com.cn/Periodical_lxysj200804005.aspx前进式开采U型通风;采空区;风流规律;自燃温度场;有限元; 基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型 通风采空区自然发火模型. 通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟 计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-Ohttp://d.wanfangdata.com.cn/Periodical_lxysj200804005.aspx前进式开采U型通风;采空区;风流规律;自燃温度场;有限元;基于渗流方程、多组分气体渗流-扩散方程和多孔介质渗流传热方程,建立前进式开采U型通风采空区自然发火模型.通过迭代方法计算沿空巷道的侧漏风量,以此边界条件数值模拟计算出前进式开采U型通风采空区的漏风规律;根据瓦斯-O2-CO浓度和温度分布状态及其变化来描述自燃过程.在计算中,采空区非均质性按自然冒落考虑,兼顾瓦斯涌出对自燃的耦合作用;模拟得到,在前进式开采特有的3面漏风边界条件下,采空区自燃位置(最高温点)在开切眼冒落区进风一侧,自燃产生的有害气体和瓦斯随漏风流从回风边界渗出.在前进开采U型通风形式下,通风量在到达工作面时衰减很大,因此,前进开采布置一次推进距离不易过大;解决好沿空留巷的封堵材料和正确的堵漏措施,是保证前进式开采顺利进行的技术关键.     

Formation of a gas hydrate due to injection of a cold gas into a porous reservoir partly saturated by water

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008.     

Kinetic Models for a Gas Filled Porous Matrix. WAVE PROPAGATION

The propagation of small perturbation in a gas filled porous matrix is investigated. The skeleton is supposed rigid and governed by the energy balance equation, where the heat exchanged between the two phases is taken into account. The Boltzmann equation is written for the gas where the integrals of the collisions between gas and solid particles are evaluated as those for the particles of a mixture. Different choices of the time and space scales lead to models equations which hold for different rarefaction regimes. The wave propagation characteristics are then dealt with in various situations.     

Gas Flow in Porous Media With Klinkenberg Effects

Gas flow in porous media differs from liquid flow because of the large gas compressibility and pressure-dependent effective permeability. The latter effect, named after Klinkenberg, may have significant impact on gas flow behavior, especially in low permeability media, but it has been ignored in most of the previous studies because of the mathematical difficulty in handling the additional nonlinear term in the gas flow governing equation. This paper presents a set of new analytical solutions developed for analyzing steady-state and transient gas flow through porous media including Klinkenberg effects. The analytical solutions are obtained using a new form of gas flow governing equation that incorporates the Klinkenberg effect. Additional analytical solutions for one-, two- and three-dimensional gas flow in porous media could be readily derived by the following solution procedures in this paper. Furthermore, the validity of the conventional assumption used for linearizing the gas flow equation has been examined. A generally applicable procedure has been developed for accurate evaluation of the analytical solutions which use a linearized diffusivity for transient gas flow. As application examples, the new analytical solutions have been used to verify numerical solutions, and to design new laboratory and field testing techniques to determine the Klinkenberg parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs from The Geysers geothermal field. We show that this new approach and the traditional method of Klinkenberg yield similar results of Klinkenberg constants for the laboratory tests; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.