Pore‐network modeling of particle retention in porous media

Transport and filtration of micron and submicron particles in porous media is important in applications such as water purification, contaminants dispersion, and drilling mud invasion. Existing macroscopic models often fail to be predictive without empirical adjustments and a more fundamental approach may be required. We develop a physically‐representative, 3D pore network model based on a particle tracking method to simulate particle retention and permeability impairment in polydisperse particle systems. The model includes the effect of hydraulic drag, gravity, electrostatic and van der Waals forces, as well as Brownian motion. A converging‐diverging pore throat geometry is used to capture the mechanism of interception. With the analytical solution of fluid velocity within a pore throat, the trajectory of each particle is calculated explicitly. We also incorporate surface roughness and particle–surface interaction to determine particle attachment and detachment. Pore throat structure and conductivity are updated dynamically to account for the effect of deposited particles. Predictions of effluent concentration and macroscopic filtration coefficient are in good agreement with published experimental data. We find that the filtration coefficient is dependent on the relative angle between fluid flow and gravity. Particle deposition by interception is significant for large particle/grain size ratios. Brownian diffusion is the primary cause of retention at low Peclet numbers, especially for small gravity numbers. Particle size distribution is found to be a cause of hyperexponential deposition often observed in experiments. Permeability reduction was small for strong repulsive forces because particles only deposited in paths of slow velocity. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3118–3131, 2017     

Flow of nanodispersed catalyst particles through porous media: Effect of permeability and temperature

The proposed in situ catalytic upgrading of heavy oil to achieve an environmentally sustainable method for heavy oil recovery requires the placement of nanodispersed catalyst particles deep into the formation where it can accelerate the high‐temperature upgrading reactions. In continuation of the previous work [Zamani et al., Energy Fuels 24, 4980‐4988 (2010)], this paper presents results of several new experiments carried out to examine the effects of other parameters, including the connate brine salinity, absolute permeability, sand‐bed temperature and particle concentration on the propagation of nanoparticles in porous media. The results show that lower permeability, increased operating temperature and higher particle concentration did not significantly affect the propagation of nanodispersed catalyst suspension through the sand‐bed. Virtually the same filtration behaviour, displaying a rapid increase of effluent concentration at 1 pore volume injected to a steady concentration close to the inlet concentration was seen in all experiments. A classical phenomenological approach was used to model the macroscopic propagation behaviour of suspended particles in the porous medium. The model was successful in history matching the effluent composition profile observed in the experiments and the deposition profile obtained from post‐test analysis of the sand‐bed. © 2011 Canadian Society for Chemical Engineering     

多孔介质内颗粒流动特性的格子Boltzmann模拟

地下岩石孔隙中小颗粒的运移和沉积会使得储层渗透性能降低,影响石油开发。为了探究悬浮颗粒在多孔介质中的流动过程,采用格子Boltzmann方法对三维多孔介质内流体和颗粒的运动过程进行了数值模拟,采用有限体积颗粒法构建多孔介质中骨架颗粒和悬浮颗粒。通过Half-Way反弹格式实现流体与颗粒间的相互作用,考虑孔隙结构、入口流速、孔隙率和颗粒直径对颗粒流动特性的影响,探究颗粒的运移和沉积规律。结果表明,入口速度对不同孔隙结构下颗粒的运动作用显著。随着入口速度增大,颗粒与颗粒、孔隙壁面以及流体之间的动量和能量交换作用增强,缩短了颗粒的运移路径,颗粒沉积率逐渐变小,颗粒拟温度增大。孔隙率的下降强化了颗粒间的碰撞,孔隙率由0.581降低至0.400,使得颗粒拟温度提升至9倍。颗粒拟温度随颗粒直径的增加而增加。但随着孔隙率增加,颗粒轴向速度增加,颗粒最高轴向速度可达入口流速的11倍,而颗粒接触力降低。     

考虑颗粒旋转的流化床流动和气化反应模拟

摒弃传统颗粒动力学模型中颗粒绝对光滑的假设,以粗糙颗粒为研究对象,同时考虑颗粒碰撞过程中的对心和切向分力建立了粗糙颗粒动力学模型,采用近似求解给出了相关本构关系式。结合粉煤气化反应模型模拟研究了鼓泡流化床内粉煤颗粒的流动-反应过程,获得了床内粗糙颗粒时均速度和浓度的径向分布。与光滑颗粒的计算结果相比,粗糙颗粒的脉动能量增大,床内不均匀特性进一步增强。同时得到的各气体组分的浓度分布与他人的实验结果相吻合。     

多孔介质燃烧-换热器的二维数值研究

通过二维数值模型研究了多孔介质燃烧-换热器。在宽广的工况范围内,研究多孔介质燃烧-换热器内的温度、速度分布和压力损失,研究主要工作参数过量空气系数和功率对换热管总的热效率的影响。结果表明,过量空气系数和功率对总的热效率有显著的影响,随二者的增大,总的热效率降低。实验验证了数值计算结果的有效性。     

纳米粒子在多孔介质中迁移模型的优化

当前,纳米粒子在土壤等多孔介质中的传输多采用单集去除率（η）进行定量描述。然而,单集去除率仅考虑单个介质颗粒对纳米粒子的作用,并未考虑介质颗粒之间的孔隙对纳米粒子的拦截效应,如T-E模型。鉴于此,采用持水度（f_r）来定量反映多孔介质的孔隙特征,并对现有的T-E模型进行了修正。实验表明,纳米粒子通过具有相同孔隙度（f）砂柱的穿透率并不相同,且与持水度（f_r）呈反比关系。在此基础上,将截留机制产生的碰撞效率（η_I）调整为与孔隙度（f）和持水度（f_r）同时相关的表达式来实现对原有模型的优化。此外,通过砂柱对纳米二氧化硅（nSiO₂）的传输实验和纳米二氧化钛（nTiO₂）在不同粒径石英砂中的传输实验证明,优化模型适用于不同粒径的多孔介质并可以更准确地预测纳米粒子在多孔介质中的迁移。     

Experimental study of CO2 hydrate formation in porous media with different particle sizes

To investigate the effect of the particle size of porous media on CO₂ hydrate formation, the formation experiments of CO₂ hydrate in porous media with three particle sizes were performed. Three kinds of porous media with mean particle diameters of 2.30 μm (clay level), 5.54 μm (silty sand level), and 229.90 μm (fine sand level) were used in the experiments. In the experiments, the formation temperature range was 277.15–281.15 K and the initial formation pressure range was 3.4–4.8 MPa. The final gas consumption increases with the increase in the initial pressure and the decrease in the formation temperature. The hydrate formation at the initial formation pressure of 4.8 MPa in 229.90 μm porous media is much slower than that at the lower formation pressure and displays multistage. In the experiments with different formation temperatures, the gas consumption rate at the temperature of 279.15 K is the lowest. In 2.30 and 5.54 μm porous media, the hydrate formation rates are similar and faster than those in 229.90 μm porous media. The particle size of the porous media does not affect the final gas consumption. The gas consumption rate per mol of water and the final water conversion increase with the decrease in the water content. The induction time in 5.54 μm porous media is longer than that in 2.30 and 229.90 μm porous media, and the presence of NaCl significantly increases the induction time and decreases the final conversion of water to hydrate.     

Transport in deformable hygroscopic porous media during microwave puffing

Microwave puffing is a process used to obtain low‐fat healthy foods by rapid heating of food products to develop high internal pressures in the material that cause significant structural changes. Two‐way coupling of complex multiphase transport and large deformations in the material, which is critical to simulate the puffing process accurately, was implemented. A porous media model that includes different phases, solid, liquid water, and gas, and incorporates pressure driven flow and evaporation was used to describe the transport processes in the material. Large deformations were included to model structural changes, with the material treated as hyperelastic. Arbitrary Lagrangian–Eulerian (ALE) framework was used. The model was validated using experimental temperature, moisture, and volume measurement and used to comprehensively understand the puffing process. Uncertainty analysis was carried out to estimate uncertainty in model prediction due to the choice of critical input parameters such as bulk modulus and permeabilities. © 2012 American Institute of Chemical Engineers AIChE J, 59: 33–45, 2013     

逾渗多孔介质对固体颗粒吸附过程的影响

研究了悬浮液中的颗粒在通过逾渗多孔介质时的被吸附特性。采用数值计算的方法;通过求解描述低速流体流动的Stokes方程以及简化的颗粒运动方程;初步得到颗粒在逾渗多孔介质中的运动轨迹;并在此基础上;求得颗粒与多孔介质内表面的碰撞概率;进而研究颗粒的被吸附特性。数值结果表明均匀多孔介质和分形多孔介质对颗粒的吸附存在本质差异。颗粒流出概率（实际中常表示为出口悬浮液中的颗粒浓度）与多孔床深度间的指数关系仅对均匀多孔介质成立;而对分形多孔介质并不成立。     

Optimization of flow in additively manufactured porous columns with graded permeability

Chemical engineering systems often involve a functional porous medium, such as in catalyzed reactive flows, fluid purifiers, and chromatographic separations. Ideally, the flow rates throughout the porous medium are uniform, and all portions of the medium contribute efficiently to its function. The permeability is a property of a porous medium that depends on pore geometry and relates flow rate to pressure drop. Additive manufacturing techniques raise the possibilities that permeability can be arbitrarily specified in three dimensions, and that a broader range of permeabilities can be achieved than by traditional manufacturing methods. Using numerical optimization methods, we show that designs with spatially varying permeability can achieve greater flow uniformity than designs with uniform permeability. We consider geometries involving hemispherical regions that distribute flow, as in many glass chromatography columns. By several measures, significant improvements in flow uniformity can be obtained by modifying permeability only near the inlet and outlet.     

多孔介质内气泡熟化特性孔隙尺度研究

多孔介质内的气泡熟化行为广泛存在于CO₂封存等领域,为探究多孔介质内气泡的熟化特性,本文采用空气作为模拟气体,通过可视化实验和数值计算,对双孔隙和四孔隙气泡熟化过程进行了研究,阐释了多孔介质非均质性对熟化过程的影响规律。结果表明：在双孔隙气体饱和度较小情况下,虽然也发生正向熟化,但是孔隙结构的存在使熟化速率明显低于自由流体情况;四孔隙研究显示多孔介质非均质性对气泡熟化过程影响显著,由于孔隙的几何限制,气泡在某些情况下会发生逆Ostwald熟化,即生长的气泡在充满当前孔隙空间后会停止生长并反向熟化导致尺寸缩小;在非均质多孔介质中,由于熟化作用,气泡有传质到大孔隙区域趋势,导致大孔隙区域富集大气泡,存在泄漏风险,从而影响封存。     

地下水人工补给过程中流速对多孔介质胶体堵塞的影响机理

通过一系列室内砂柱模拟实验,研究了流速对胶体在饱和多孔介质中滞留-迁移行为的影响;运用COMSOL软件模拟,拟合实验数据后得到表征胶体沉积的关键参数。结果表明：流速增大缩短了胶体在多孔介质中的滞留时间,并增强水动力拖拽力,导致介质对胶体的吸附量减少,有利于胶体的迁移;回灌时间的延续造成的多孔介质渗透系数降低,可通过瞬间增大流速使渗透系数在较短时间内恢复,然而随后形成新的吸附渗透性仍会降低。水源离子强度、介质粗糙度等因素会影响胶体迁移的流速效应。在相同条件下,吸附系数随着离子强度的增大而增加,随着流速的增大而增加。综合来看,离子强度的增加可抵消一部分水动力拖拽力的影响,提高胶体在多孔介质中滞留的概率;介质表面粗糙度的增加,可削弱水动力拖拽力作用,同时增加胶体与介质的吸附、沉积点位和接触面积,导致胶体易于在多孔介质中发生滞留并可能进一步导致介质堵塞。     

基于逾渗理论的多孔过滤介质孔径分布估计方法

结合逾渗理论和网格模型,建立了过滤系数与过滤介质孔径分布的联系方程。利用此方程结合过滤实验数据获得过滤介质孔径分布的统计参数,同时与其他方法获得孔径分布参数以及其他文献中的数据进行比较,并利用计算机模拟过滤过程验证了获得的孔径分布参数,结果表明基于逾渗理论的过滤模型用于孔径分布参数的估计是比较准确和有效的。     

离子组成对氧化石墨烯在饱和多孔介质中迁移行为的影响

采用室内饱和石英砂柱一维渗流模拟实验,研究离子强度相同、离子组成(钠吸附比)不同的电解质溶液对氧化石墨烯(GO)在地下环境中迁移行为的影响。通过测定GO穿透过程的沉积动力学曲线,结合数学模型与界面化学理论,对其迁移沉积机理进行分析。结果显示,当钠吸附比从0增加到∞时,砂柱出流最大浓度升高,GO回收率增加,穿透实验沉积速率、去除效率和吸附效率分别从0.356 min^-1、1.04×10^-2、0.054减小到0.039 min^-1、1.1×10^-3、0.003。研究认为布朗扩散是造成GO颗粒与石英砂粒相互接触的主要机制,Ca²⁺浓度变化是造成不同钠吸附比环境下GO不同迁移行为的主要因素,其机理在于Ca²⁺与GO发生电中和与桥接作用,改变了颗粒间的静电斥力与引力平衡,进而影响了GO颗粒粒度与形态,并最终强化了砂柱对GO的截留效应。     

Filtration combustion of hydrogen-air, propane-air, and methane-air mixtures in inert porous media

The filtration combustion characteristics of hydrogen-air, propane-air, and methane-air mixtures in inert porous media have been studied experimentally. It is shown that the dependences of the combustion wave velocity on the fuel-air equivalence ratio are V-shaped. For hydrogen-air mixtures, the velocity minimum is shifted to the rich region, and for propane-air and methane-air mixtures, it is shifted to the lean region. For lean hydrogen-air and rich propane-air mixtures, the measured maximum temperatures in the combustion wave are found to be reduced relative to those calculated theoretically. For methane-air mixtures, a reduction in the measured temperatures is observed over the entire range of the mixture composition. The results are interpreted within the framework of the hypothesis of selective diffusion of gas mixture components. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 4, pp. 8–20, July–August, 2006.     

The flow and displacement in porous media of fluids with yield stress

We study the mobilization and subsequent flow in a porous medium of a fluid with a yield stress, modeled as a Bingham plastic. We use single-capillary expressions for the mobilization and flow in a pore-throat, and a pore-network model that accounts for distributed yield-stress thresholds. First, we extend the statistical physics method of invasion percolation with memory, which models lattice problems with thresholds, to incorporate dynamic effects due to the viscous friction following the onset of mobilization. Macroscopic relations between the applied pressure gradient and the flow rate for single-phase flow are proposed as a function of the pore-network microstructure and the configuration of the flowing phase. Then, the algorithm is applied to model the displacement of a Bingham plastic by a Newtonian fluid in a porous medium. The results find application to a number of industrial processes including the recovery of oil from oil reservoirs and the flow of foam in porous media.     

低场核磁法测定凝胶过滤介质的孔径分布

凝胶过滤介质在蛋白质、多糖等生物大分子的分离纯化过程中具有非常重要的作用,其中介质的孔径分布是决定分离纯化效果的关键因素。由于绝大部分凝胶过滤介质是软凝胶,因此很难用常规的方法如压汞法、低温氮吸附法等测定其孔径分布。本文探索了利用低场核磁共振测定凝胶过滤介质的孔径分布的方法。首先通过抽滤、自制琼脂糖凝胶块等实验确定了峰的归属,明确了介质孔内水、介质间隙水和自由水在核磁共振横向弛豫时间(T₂)图谱上的分布范围;随后与逆体积排阻层析法(ISEC)测定的结果相对比,得出层析介质孔径和介质孔内水弛豫时间的关系;最后通过高斯正态拟合得到了介质的孔径分布。实验结果证实了低场核磁共振法测定凝胶过滤介质孔径分布的可行性。该法操作简单、测定迅速,并可以为其他层析介质孔径分布的测定提供参考。