Effect of Reactive Surface Areas Associated with Different Particle Shapes on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Rocks

In this article, the effect of reactive surface areas associated with different particle shapes on the reactive infiltration instability in a fluid-saturated porous medium is investigated through analytically deriving the dimensionless pore-fluid pressure-gradient of a coupled system between porosity, pore-fluid flow and reactive chemical-species transport within two idealized porous media consisting of spherical and cubic grains respectively. Compared with the critical dimensionless pore-fluid pressure-gradient of the coupled system, the derived dimensionless pore-fluid pressure-gradient can be used to assess the instability of a chemical dissolution front within the fluid-saturated porous medium. The related theoretical analysis has demonstrated that (1) since the shape coefficient of spherical grains is greater than that of cubic grains, the chemical system consisting of spherical grains is more unstable than that consisting of cubic grains, and (2) the instability likelihood of a natural porous medium, which is comprised of irregular grains, is smaller than that of an idealized porous medium, which is comprised of regular spherical grains. To simulate the complicated morphological evolution of a chemical dissolution front in the case of the chemical dissolution system becoming supercritical, a numerical procedure is proposed for solving this kind of problem. The related numerical results have demonstrated that the reactive surface area associated with different particle shapes can have a significant influence on the morphological evolution of an unstable chemical-dissolution front within fluid-saturated porous rocks.     

含液颗粒材料液固耦合分析的离散颗粒模型及特征线SPH法

对含液颗粒材料流固耦合分析建议了一个基于离散颗粒模型与特征线SPH法的显式拉格朗日-欧拉无网格方案。在已有的用以模拟固体颗粒集合体的离散颗粒模型[1]基础上,将颗粒间间隙内的流体模型化为连续介质,对其提出并推导了基于特征线的SPH法。数值例题显示了所建议方案在模拟颗粒材料与间隙流相互作用的能力和性能以及间隙流体对颗粒结构承载能力及变形的影响。     

Experimental Investigation and Modelling of Colloidal Release in Porous Media

Gas production from underground storage reservoirs is sometimes associated with solid particles eroded from the rock matrix. This phenomenon often called sand production can cause damage to the storage equipments, leading the operator to choke the wells and prevent them from producing at full capacity. Colloid release is often associated as a precursor of larger solid production. Indeed, in sandstone storage sites, clay release induced by the presence of condensed water associated with the gas production in the near-wellbore region can be a forecast of intergranular cement erosion. The objective of this work is twofold: firstly to experimentally investigate colloidal particle detachment through ionic strength reduction (absence of salinity of the condensed water) in porous media and secondly to determine its evolution with time and to model it. Laboratory experiments with model systems are developed to reproduce the particle generation and their transport in porous media. The model porous medium is a packed column of two powders: silicon carbide particles of 50 μm and silica particles of 0.5 μm (3% by weight) initially mixed together. Brine flows at different concentrations are imposed through the porous sample and, at very low salt concentration, colloid silica particles are massively released from the medium. Experimental evolutions of the particle concentration with time are compared to solutions of the advection–dispersion equation including first-order source terms for colloid release. The dispersion coefficients of the porous medium have been determined with tracer tests. The experimental results exhibit a different behaviour at short- and long-time intervals and a model has been built to predict the colloid production evolution with the introduction of two different time scales for the eroded rate. The model can be used in a core test to evaluate the amount of detachable fines and the rate of erosion.     

Smoothed Particle Hydrodynamics Model of Non-Aqueous Phase Liquid Flow and Dissolution

A smoothed particle hydrodynamics model was developed to simulate the flow of mixtures of aqueous and non-aqueous phase liquids in porous media and the dissolution of the non-aqueous phase in the aqueous phase. The model was used to study the effects of pore-scale heterogeneity and anisotropy on the steady state dense non-aqueous phase liquid (DNAPL) saturation when gravity driven DNAPL displaces water from initially water saturated porous media. Pore-scale anisotropy was created by using co-oriented non-overlapping elliptically shaped grains to represent the porous media. After a steady state DNAPL saturation was reached, water was injected until a new steady state DNAPL saturation was reached. The amount of trapped DNAPL was found to be greater when DNAPL is displaced in the direction of the major axes of the soil grains than when it is displaced in the direction of the minor axes of the soil grains. The amount of trapped DNAPL was also found to increase with decreasing initial saturation of the continuous DNAPL phase. For the conditions used in our simulations, the saturation of the trapped DNAPL with a smaller initial DNAPL saturation was more than 3 times larger than the amount of trapped DNAPL with a larger initial saturation. These simulations were carried out assuming that the DNAPL did not dissolve in water. Simulations including the effect of dissolution of DNAPL in the aqueous phase were also performed, and effective (macroscopic) mass transfer coefficients were determined. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Permeability anisotropy due to consolidation of compressible porous media

The characterisation of flow through porous media is important for all solid–liquid separation and fluid transport realms. The permeability of porous media can be anisotropic and furthermore, the extent of anisotropy can be increased as a result of an applied compressive force. However, the understanding of how anisotropy develops is incomplete. An overview of research on permeability anisotropy is given and an expression for predicting anisotropy as a function of void ratio is offered. The two underlying assumptions of the proposed model are: flow in different directions occurs within the same network of pores and deformation is primarily due to the compression of the particles in the direction of the applied force rather than due to particle rearrangement. The assumption of network connectivity allows permeability anisotropy to be described as a function of flow path tortuosity only. Results are presented for hydraulic anisotropy measured in lignite that has been upgraded by a compression dewatering method known as mechanical thermal expression. The lignite permeability is shown to be up to eight times greater in the direction perpendicular to compression, suggesting that the rate of dewatering could be significantly increased by choosing the drainage to also be perpendicular to the direction of the applied compressive force. It is illustrated that the proposed anisotropy model can be used to accurately predict the experimentally determined permeability anisotropy ratios for lignite, as well as for other materials including sand, clay and kaolin.     

A Two-Dimensional Network Model to Simulate Permeability Decrease Under Hydrodynamic Effect of Particle Release and Capture

A model was developed to simulate permeability decrease induced by hydrodynamic effects when injecting a fluid in a reservoir with respect to particle release and capture mechanisms and the parameters of the fluid–rock system. The kinetics of particle release and capture were integrated after computing the initial permeability of the porous medium with a square lattice of a two–dimensional network model. The rate of particle release is related to the difference between a microscopic velocity of the fluid and a critical velocity. The permeability decrease shows a direct link to the reduction of pore throat radii by three mechanisms of particle capture: straining and particle accumulation through direct interception or diffusion. Comparison between the simulations and the experimental results shows that the model reproduces the physics of the permeability decrease phenomenon, although the values are overestimated. The difference between the two sets of results can be explained by the fact that the simulations are realized at constant pressure whereas the experiments are realized at constant flow rate, and that re–entrainment of the trapped particles was not taken into account in the model.     

A 2D granular medium with rotating particles

A two-dimensional (2D) model of a granular medium is represented as a square lattice consisting of elastically interacting round particles possessing one rotational and two translational degrees of freedom. The differential equations describing propagation and interaction of waves of various types in such a medium have been derived in the long-wavelength approximation. Accounting for microrotations of the particles and moment interactions between them leads to the consideration of so-called microrotation waves (spin waves). In the absence of microrotations, the governing equations degenerate into 2D Lamé equations for anisotropic media. A one-to-one correspondence has been established between the microstructure parameters and effective elasticity constants of the second-order. Dependence of elasticity constants on the size of grains has been analyzed. The proposed model is compared in the continuous approximation to the equations of the 2D Cosserat continuum possessing macroscopic anisotropy.     

基于介观结构的饱和与非饱和多孔介质有效应力

基于描述含液颗粒材料介观结构的Voronoi 胞元模型和离散颗粒集合体与多孔连续体间的介-宏观均匀化过程, 定义饱和与非饱和多孔介质有效应力. 导出了计及孔隙液压引起之颗粒体积变形的饱和多孔介质广义有效应力. 用以定义广义有效应力的Biot 系数不仅依赖于颗粒材料的多孔连续体固体骨架及单个固体颗粒的体积模量(材料参数),同时与固体骨架当前平均广义有效应力及单个固体颗粒的体积应变(状态量) 有关. 提出了描述非饱和多孔介质中非混和固体颗粒、孔隙液体和气体等三相相互作用的具介观结构的Voronoi 胞元模型.具体考虑在低饱和度下双联(binary bond) 模式的摆动(pendular) 液桥系统介观结构. 导出了基于介观水力-力学模型的非饱和多孔介质的各向异性有效应力张量与有效压力张量. 考虑非饱和多孔介质Voronoi 胞元模型介观结构的各向同性情况,得到了与非饱和多孔连续体理论中唯象地假定的标量有效压力相同的有效压力形式.但本文定义的与确定非饱和多孔介质有效应力和有效压力相关联的Bishop 参数由基于三相介观水力-力学模型, 作为饱和度、孔隙度和介观结构参数的函数导出,而非唯象假定.      

CFD–DEM simulation of particle deposition characteristics of pleated air filter media based on porous media model

In this study, the three-dimensional physical model of pleated air filtration media was simplified to porous media model, and the calculation parameters of porous media were obtained based on experimental data. The model of V-shaped pleated air filter media is constructed, the height of the media pleat is 50 mm and the pleat thickness is 4 mm, the pleat angle is 3.7°. The Hertz-Mindlin contact model was modified by Johnson Kendall Roberts (JKR) adhesion contact model. The deposition process of particles in media was simulated based on computational fluid dynamics (CFD) theory and discrete element method (DEM). Results show that the CFD–DEM coupling method can be effectively applied to the macro research of pleated air filter media. The particles will form dust layer and dendrite structure on the fiber surface, and the dust layer will affect the subsequent air flow organization, and the dendrite structure will eventually form a “particle wall”. The formation of the “particle wall” will prevent the particles from moving further in the fluid domain, which makes area of pleated angle become the “low efficiency” part about the particle deposition. Compared with area of pleated angle, the particles are concentrated in the opening area and the middle area of the pleated to agglomerate and deposit.     

A stochastic model for filtration of particulate suspensions with incomplete pore plugging

A population balance model for particulate suspension transport with capture of particles by porous medium accounting for complete and incomplete plugging of pores by retained particles is derived. The model accounts for pore space accessibility, due to restriction on finite size particle movement through the overall pore space, and for particle flux reduction, due to transport of particles by the fraction of the overall flux. The novel feature of the model is the residual pore conductivity after the particle retention in the pore and the possibility of one pore to capture several particles. A closed system of governing stochastic equations determines the evolution of size distributions for suspended particles and pores. Its averaging results in the closed system of hydrodynamic equations accounting for permeability and porosity reduction due to plugging. The problem of deep bed filtration of a single particle size suspension through a single pore size medium where a pore can be completely plugged by two particles allows for an exact analytical solution. The phenomenological deep bed filtration model follows from the analytical solution.     

Porous Medium Flow and an Overlying Parallel Flow: PIV Interrogation Area and Overlaps, Interfacial Location, and Depth Ratio Effects

This paper presents an experimental work aimed at studying the effects of particle image velocimetry (PIV) interrogation area and overlaps, location of the interface, as well as depth ratios on the flow at the interface between a model porous medium and an overlying free flow. The porous media were modeled using square arrays of circular rods of diameter and porosity 0.88, filling fraction ranging from 0.47 to 0.75, and depth-to-porous medium pore ratio ranging from 5.75 to 13.69. Using a pressure-driven refractive-index matched viscous fluid, the bulk Reynolds number was kept approximately constant at a regime in which inertia was not a factor. PIV measurements were made across various streamwise-transverse planes of the test section. For the present tests, it was observed that PIV interrogation area (IA) and overlap effects on the interfacial velocities are negligible when the IA sizes in dimensionless units ranged from 0.017 to 0.145 in flow parameters and 0.036 to 0.300 in porous media parameters. Other dimensionless slip parameters are however significantly affected. Interfacial slip parameters of porous media models were found to change by as much as 120 % with change in the interfacial location. The interfacial location sensitivity was also found to be dependent on the direction of deviation, the type of porous medium, and depth ratios. Volume averaged results showed that for flows over models of porous media, the depth-to-porous medium pore ratio effects are more prominent compared with the filling fraction effects, for both two- and three-dimensional porous media.     

Reliability study of super-ellipsoid DEM in representing the packing structure of blast furnace

In industrial blast furnaces (BFs), the investigations involving the flow behaviors of particles and the resultant burden structure are essential to optimize its operation stability and energy consumption. With the advance of computing capability and mathematical model, the discrete element method (DEM) specialized in characterizing particle behavior has manifested its power in the investigation of BFs. In the framework of DEM, many particle models have been developed, but which model is more suitable for simulating the particle behaviors of BFs remains a question because real particles in BFs have large shape and size dispersity. Among these particle models, the super-ellipsoid model possesses the ability to change shape flexibly. Therefore, the focus of this study is to investigate whether the super-ellipsoid model can meet the requirement of authenticity and accuracy in simulating the behaviors of particles with large shape and size dispersity. To answer this question, a simplified BF charging system composed of a hopper and a storage bin is established. The charging process and the final packing structure are analyzed and compared between experiments and simulations with different shape indexes. The results show that super-ellipsoid particles have prominent advantages over spherical particles in terms of representing the real BF particles, and it can more reasonably reproduce the flow behaviors and packing structure of experimental particles. The computation cost of super-ellipsoid particles is also acceptable for engineering applications. Finally, the micro-scale characteristics of packing structure is analyzed and the single-ring charging process in industry-scale BF using super-ellipsoid particles is conducted.     

Modeling gas dynamic particle interaction in rarefied gas flows

In the case of slow, so-called creeping viscous flow a considerable amount of information on the interaction between individual particles or groups of particles has been obtained theoretically by means of the Stokes equations [1]. Regimes in which it is necessary to take inertia, compressibility and the rarefaction of the medium into account (see, for example, [2]) have received much less attention, especially from the experimental standpoint. As a rule, previous experiments have involved freely falling particles in a viscous fluid, but the experimental possibilities of determining the forces and moments exerted on a particle by a liquid or gas at small Reynolds numbers can be considerably expanded by investigating subsonic, flows of rarefied gas obtained with the aid of porous media. The results of such studies of the flow past a spherical particle and its interaction with another particle are presented in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–157, January–February, 1987.     

A Novel Workflow to Model Permeability Impairment through Particle Movement and Deposition in Porous Media

This article presents a practical transfer function type solution to a complex problem in which variations in a number of parameters can be taken into account. A new mathematical model, which is based on mass balance transfer function of particles movement/retention in porous media, has been derived. It is used to predict permeability reduction as a function of time. The linear forms as well as the radial forms of the model are described. Although the differential equations derived are similar to the general form of diffusion–convection equations, the marked difference is the suitability of the model, for being applied for variation of parameters, such as particle concentration in the fluid, injection rate, density of solid particles, against the depth and time of invasion. This transfer function has been solved, and the results of the simulation run agree reasonably well with the experimental damage data obtained in laboratory. Owing to its simplicity, this model is more practical to describe permeability reduction for the flow of suspended particles in porous media.     

DEM investigation on conveying of non-spherical particles in a screw conveyor

Screw conveyors are extensively used in modern industry such as metallurgy, architecture and pharmaceutical due to their high-efficiency in the transportation of granular materials. And substantial efforts have been devoted to the study of the screw conveyors. Numerical method is an effective way to study screw conveyor. However, previous studies have mainly focused in the regime of spherical particles while the in-depth investigations for non-spherical particles that should be the most encountered in practical applications are still limited. In view of the above situations, discrete element method (DEM), which has been widely accepted in simulating the discrete systems, is utilized to investigate the conveying process of non-spherical particles in a horizontal screw conveyor, with particles being modeled by super-ellipsoids. In addition, a wear model called SIEM (Shear Impact Energy Model) is incorporated into DEM to predict the wear of screw conveyor. The DEM simulation results demonstrate that the particle shape is influential for the flow behaviors of particles and the wear of conveyor. The conveying performance evaluated quantitatively of both mass flow rate and power consumption is subsequently obtained to investigate the effect of sphericity of particle with different operation parameters. Moreover, particle collision frequency and collision energy consumption are acquired to investigate the possible particle breakage between particles and screw blade. The comparisons between particle–particle collision and particle–wall collision reveal that particles with large shape index have more possibility to be damaged in particle–wall impingement.     

A Stochastic Model for Particulate Suspension Flow in Porous Media

A population balance model for a particulate suspension transport with size exclusion capture of particles by porous rock is derived. The model accounts for particle flux reduction and pore space accessibility due to restriction for large particles to move through smaller pores – a particle is captured by a smaller pore and passes through a larger pore. Analytical solutions are obtained for a uniform pore size medium, and also for a medium with small pore size variation. For both cases, the equations for averaged concentrations significantly differ from the classical deep bed filtration model.     

Modelling of Power-law Fluid Flow Through Porous Media Using Smoothed Particle Hydrodynamics

The flow of non-Newtonian fluids through two-dimensional porous media is analyzed at the pore scale using the smoothed particle hydrodynamics (SPH) method. A fully explicit projection method is used to simulate incompressible flow. This study focuses on a shear-thinning power-law model (n < 1), though the method is sufficiently general to include other stress-shear rate relationships. The capabilities of the proposed method are demonstrated by analyzing a Poiseuille problem at low Reynolds numbers. Two test cases are also solved to evaluate validity of Darcy’s law for power-law fluids and to investigate the effect of anisotropy at the pore scale. Results show that the proposed algorithm can accurately simulate non-Newtonian fluid flows in porous media.     

Sediment–Water Interface Flow with the Multiparticle Collision Dynamics

This paper presents an experimental study of particle transport in porous medium using a self-developed sand layer transportation–deposition testing system, aiming at delineating the detachment characteristics of deposited particles in porous medium. Two experimental modes, increase flow velocity and change flow direction, were adopted in this study. The tests were conducted using quartz powder as the particles and quartz sand as the porous media to study the response of detachment characteristics to changes in particle diameter (\(d_{s}\), with median diameter 18 and 41 \(\upmu \)m) and grain diameter (\(d_{p}\), with median diameter 0.36 and 1.25 mm). Breakthrough curves after the second peak were well described by a double exponential model with parameters of weight coefficient and detachment coefficient. This study shows that both modes can change the detach rate of deposited particles observably, and detach rate is affected by the value of flow velocity greatly.     

No‐slip consistent immersed boundary particle tracking to simulate impaction filtration in porous media

In this paper, we present a new method for simulating the motion of a disperse particle phase in a carrier gas through porous media. We assume a sufficiently dilute particle‐laden flow and compute, independently of the disperse phase, the steady laminar fluid velocity using the immersed boundary method. Given the velocity of the carrier gas, the equations of motion for the particles experiencing the Stokes drag force are solved to determine their trajectories. The ‘no‐slip consistent’ particle tracking algorithm avoids possible numerical filtration of very small particles due to the nonzero velocity field at the solid–fluid interface introduced by the immersed boundary method. This physically consistent tracking allows a reliable estimation of the filtration efficiency of porous filters due to inertial impaction. We illustrate and test our new approach for model porous media consisting of a structured array of aligned rectangular fibers, arranged in line and staggered. In the staggered geometry, the effect of the residual velocity at the solid–fluid interface is significant for particles with low inertia. Without adopting the developed no‐slip consistent numerical method, an artificial numerical filtration is observed, which becomes dominant for small enough particles. For both the in line and the staggered geometries, the filtration rate depends quite strongly and non monotonically on the particle inertia. This is expressed most clearly in the staggered arrangement in which a very strong increase in the filtration efficiency is observed at a well‐defined critical droplet size, corresponding to a qualitative change in the dominant particle paths in the porous medium. Copyright © 2013 John Wiley & Sons, Ltd.