A particle tracking transport method for the simulation of resident and flux-averaged concentration of solute plumes in groundwater models

A new numerical technique called the convolution-based particle tracking (CBPT) method is developed to simulate resident or flux-averaged solute concentrations in groundwater models. The method is valid for steady-state flow and linear transport processes such as sorption with a linear sorption isotherm and first-order decay. The CBPT method uses particle tracking to take advantage of the ability of particle-based approaches to maintain sharp fronts for advection-dominated transport problems common in groundwater modeling and because of the flexibility of the random walk method to simulate a wide range of possible forms of the dispersion tensor. Furthermore, the algorithm for carrying out the convolution and superposition calculation from particle tracking results is very efficient. We show that from a single particle tracking run, source term variability, sorption, and decay can all be simulated rapidly without rerunning the underlying transport model unless the flow field or dispersion parameters are changed. A series of verification simulations are presented to demonstrate the accuracy and efficiency of the CBPT method compared to more conventional particle tracking approaches.     

Using global node-based velocity in random walk particle tracking in variably saturated porous media: application to contaminant leaching from road constructions

Precise and efficient numerical simulation of transport processes in subsurface systems is a prerequisite for many site investigation or remediation studies. Random walk particle tracking (RWPT) methods have been introduced in the past to overcome numerical difficulties when simulating propagation processes in porous media such as advection-dominated mass transport. Crucial for the precision of RWPT methods is the accuracy of the numerically calculated ground water velocity field. In this paper, a global node-based method for velocity calculation is used, which was originally proposed by Yeh (Water Resour Res 7:1216–1225, 1981). This method is improved in three ways: (1) extension to unstructured grids, (2) significant enhancement of computational efficiency, and (3) extension to saturated (groundwater) as well as unsaturated systems (soil water). The novel RWPT method is tested with numerical benchmark examples from the literature and used in two field scale applications of contaminant transport in saturated and unsaturated ground water. To evaluate advective transport of the model, the accuracy of the velocity field is demonstrated by comparing several published results of particle pathlines or streamlines. Given the chosen test problem, the global node-based velocity estimation is found to be as accurate as the CK method (Cordes and Kinzelbach in Water Resour Res 28(11):2903–2911, 1992) but less accurate than the mixed or mixed-hybrid finite element methods for flow in highly heterogeneous media. To evaluate advective–diffusive transport, a transport problem studied by Hassan and Mohamed (J Hydrol 275(3–4):242–260, 2003) is investigated here and evaluated using different numbers of particles. The results indicate that the number of particles required for the given problem is decreased using the proposed method by about two orders of magnitude without losing accuracy of the concentration contours as compared to the published numbers.     

Uncertainty in simulated groundwater-quality trends in transient flow

In numerical modeling of groundwater flow, the result of a given solution method is affected by the way in which transient flow conditions and geologic heterogeneity are simulated. An algorithm is demonstrated that simulates breakthrough curves at a pumping well by convolution-based particle tracking in a transient flow field for several synthetic basin-scale aquifers. In comparison to grid-based (Eulerian) methods, the particle (Lagrangian) method is better able to capture multimodal breakthrough caused by changes in pumping at the well, although the particle method may be apparently nonlinear because of the discrete nature of particle arrival times. Trial-and-error choice of number of particles and release times can perhaps overcome the apparent nonlinearity. Heterogeneous aquifer properties tend to smooth the effects of transient pumping, making it difficult to separate their effects in parameter estimation. Porosity, a new parameter added for advective transport, can be accurately estimated using both grid-based and particle-based methods, but predictions can be highly uncertain, even in the simple, nonreactive case.     

激光测速粒子对复杂流动的响应研究——Ⅰ颗粒非恒定运动数学模型及其数值方法

流体激光测速的精度与示踪粒子的跟随特性即流体中异质粒子的非恒定运动特性密切相关。首先对粒子非恒定运动方程进行了探讨,着重考虑了在高颗粒雷诺数时该方程的修正问题,简要分析了该方程的数学属性,并构造了这类方程的数值计算方法。分析表明,高颗粒雷诺数下的粒子非恒定运动方程为非线性奇异积分方程,而当颗粒雷诺数小于1时,则线性化为第二类渥尔特拉(Volterra)积分方程。以几种均匀流中球形小颗粒的非恒定运动为算例,计算结果与其解析解及有关实验数据的比较表明,数值方法具有良好的计算精度。     

Three-Dimensional Modeling of Mass Transfer in Porous Media Using the Mixed Hybrid Finite Elements and the Random-Walk Methods

A three-dimensional (3D) mass transport numerical model is presented. The code is based on a particle tracking technique: the random-walk method, which is based on the analogy between the advection–dispersion equation and the Fokker–Planck equation. The velocity field is calculated by the mixed hybrid finite element formulation of the flow equation. A new efficient method is developed to handle the dissimilarity between Fokker–Planck equation and advection–dispersion equation to avoid accumulation of particles in low dispersive regions. A comparison made on a layered aquifer example between this method and other algorithms commonly used, shows the efficiency of the new method. The code is validated by a simulation of a 3D tracer transport experiment performed on a laboratory model. It represents a heterogeneous aquifer of about 6-m length, 1-m width, and 1-m depth. The porous medium is made of three different sorts of sand. Sodium chloride is used as a tracer. Comparisons between simulated and measured values, with and without the presented method, also proves the accuracy of the new algorithm.     

The influence of the void fraction on the particle migration: A coupled computational fluid dynamics–discrete element method study about drag force correlations

Granular soils subjected to flow through their soil skeleton can show a behaviour in which fine particles migrate through the pore space between coarser particles. This process is called internal instability or suffusion. This contribution deals with the numerical analysis of the migration of fine particles in a soil column subjected to fluid flow with unresolved coupled computational fluid dynamics–discrete element method (CFD–DEM) with special regards to the used drag force correlation. The contribution investigates the influence of the Schiller–Naumann model and its extension with a voidage term on the migration behaviour of fine particles. The voidage term is further varied with a parameter, which controls the impact of the change of the void fraction on the drag force. It could be observed that the Schiller–Naumann model does not yield in a suffusive behaviour while the extended models show significant particle migration. Thereby, increasing the impact of the void fraction on the drag force results in stronger particle migration. These results reveal the need for good validation techniques. They indicate how the drag force correlation can be adapted to depict the correct particle migration behaviour.     

Pore‐scale modeling of surface erosion in a particle bed

A fully coupled transient two‐dimensional model was employed to study fundamentals of flood‐induced surface erosion in a particle bed. The interaction of the liquid and solid phases is the key mechanism related to surface erosion. The solid phase was idealized at a particle scale by using the discrete element method. The fluid phase was modeled at a mesoscale level and solved using the lattice Boltzmann method. The fluid forces applied on the particles were calculated on the basis of the momentum the fluid exchanges with the particle. The proposed approach was used to model both single particles and particle beds subjected to Couette flow conditions. The behavior of both the single particle and the particle bed depended on particle diameter and surface shear fluid velocity. The conducted simulations show that the fluid flow profile penetrates the bed for a small distance. This penetration initiates sheet‐flow and surface erosion as the fluid interacts with particles. The effect of suppressing particle rotation on the fluid‐induced forces on the particle was also examined. Suppressing particle spinning may lead to underestimated erosion rate. Results of fluid and particle velocities were compared against experimental results and appeared to agree with the observed trends.Copyright © 2013 John Wiley & Sons, Ltd.     

An experimental and theoretical study of the seepage migration of suspended particles with different sizes

This study experimentally investigates the effect of particle size, particle concentration and flow velocity on the migration of suspended particles of size 1.02–47 μm in porous media. The results show that at the same flow velocity, the peak values of the breakthrough curves decrease and corresponding pore volumes increase slightly with increasing particles size. The migration velocity of smaller suspended particles is even greater than water flow velocity, which is attributed to the size exclusion effect. With increase of the injected particle concentration, the deposition coefficients of small single particles increase at first and then tend to a steady state or even decrease slightly, explained by the maximum retention concentration. The dispersivity of small particles decreases with increasing velocity. However, at a high flow velocity, the hydrodynamic dispersivity becomes increasingly dominant with the increase of particle size. The deposition coefficients for large-sized particles are higher than those for small-sized particles, which is attributed to considerable mass removal due to straining. An analytical solution, considering the release effect of sorbed particles, is developed to account for the one-dimensional flow and dispersive effect using a source function method, and then three transport parameters—dispersivity, deposition coefficient and release coefficient—are fitted using the experimental results. Finally, suspended-particle migration is predicted by the proposed model for short-time constant-concentration injection and repeated three-pulse injection. Overall, particle size has a significant effect on the seepage migration parameters of suspended particles in porous media such as the particle velocity, dispersivity and deposition coefficient.     

Effects on groundwater flow of abandoned engineered structures for the safety assessment of the proposed high-level nuclear waste repository site at Forsmark,Sweden

Effects on groundwater flow of abandoned engineered structures in relation to a potential geological repository for spent high-level nuclear fuel in fractured crystalline rock at the Forsmark site, Sweden, are studied by means of numerical modeling. The effects are analyzed by means of particle tracking, and transport-related performance measures are calculated. The impacts of abandoned, partially open repository tunnels are studied for two situations with different climate conditions: a “temperate” climate case with present-day boundary conditions, and a generic future “glacial” climate case with an ice sheet covering the repository. Then, the impact of abandoned open boreholes drilled through the repository is studied for present-day climate conditions. It is found that open repository tunnels and open boreholes can act as easy pathways from repository level to the ground surface; hence, they can attract a considerable proportion of particles released in the model at deposition hole positions within the repository. The changed flow field and flow paths cause some changes in the studied performance measures, i.e., increased flux at the deposition holes and decreased transport lengths and flow-related transport resistances. However, these effects are small and the transport resistance values are still high.     

Particle transport within water-saturated porous media: Effect of pore size on retention kinetics and size selection

The transport and filtration behaviour of fine particles (silt) in columns packed with sand was investigated under saturated conditions by using step-input injections. Three samples of different particle size distributions (coarse medium, fine medium and a mixture of both) were used in order to highlight the influence of the pore size distribution on particle retention and size selection of recovered particles. The main parameters of particle transport and deposition were derived from the adjustment of the experimental breakthrough curves by an analytical model. The higher particle retention occurs in the mixture medium, owing to its large pore size distribution, and the filtration coefficient decreases with increasing flow velocity. Particle size distribution of recovered particles shows a thorough size selection: (i) the first recovered particles are the coarser ones; (ii) the size of the recovered particles increases with increasing flow velocity and enlarger pore distribution of the medium.     

激光测速粒子对复杂流动的响应研究——Ⅱ典型流场中粒子跟随性的数值分析

以修正后适用于高颗粒雷诺数的粒子非恒定运动方程为基础,将该方程无量纲化,定义了一般流场中粒子跟随性的概念,给出了粒子跟随性的数学表述。据此对典型流场中粒子的运动进行了数值计算,并定量分析了粒径、密度等参数对不同流动中示踪粒子跟随特性的影响。     

Implication of surface modified NZVI particle retention in the porous media: Assessment with the help of 1-D transport model

Retention of surface-modified nanoscale zero-valent iron (NZVI) particles in the porous media near the point of injection has been reported in the recent studies. Retention of excess particles in porous media can alter the media properties. The main objectives of this study are, therefore, to evaluate the effect of particle retention on the porous media properties and its implication on further NZVI particle transport under different flow conditions. To achieve the objectives, a one-dimensional transport model is developed by considering particle deposition, detachment, and straining mechanisms along with the effect of changes in porosity resulting from retention of NZVI particles. Two different flow conditions are considered for simulations. The first is a constant Darcy’s flow rate condition, which assumes a change in porosity, causes a change in pore water velocity and the second, is a constant head condition, which assumes the change in porosity, influence the permeability and hydraulic conductivity (thus Darcy’s flow rate). Overall a rapid decrease in porosity was observed as a result of high particle retention near the injection points resulting in a spatial distribution of deposition rate coefficient. In the case of constant head condition, the spatial distribution of Darcy’s velocities is predicted due to variation in porosity and hydraulic conductivity. The simulation results are compared with the data reported from the field studies; which suggests straining is likely to happen in the real field condition.     

基于水下摄影的床面泥沙运动特性试验研究

为提高推移质试验的观测精度与效率,基于水下摄影和粒子跟踪（UP/PTV）技术,实现明槽流床面泥沙运动状态的精细试验观测。通过剔除床面颗粒震颤干扰、设置颗粒临界运动阈值和多重滤波筛选程序,提高采集样本数据的有效性。利用多组低强度推移质试验,提取床面颗粒运动轨迹、速度、单步时长等数据,并进行粒子运动的Lagrange过程分析和概率密度分布（PDF）研究。研究表明:粒间碰撞和近底紊流扫荡的影响使粒子速度在单步步长内呈现先急剧增加再缓慢衰减的变化特征;速度PDF曲线显示细尾Gamma函数特性,同时受粒子震颤效应影响,加速度PDF曲线则具有拉普拉斯分布特征;粒子速度与摩阻流速之间关系密切,保持3.4~3.5的比值;粒子单步时长与步长的联合分布呈幂函数变化规律,拟合曲线指数一般为1.25~1.3。幂律指数大小受推移质输沙强度与床面粒子异质性的影响。     

Upscaling polydispersed particle transport in porous media using pore network model

Understanding particle transport in porous media is critical in the sustainability of many geotechnical and geoenvironmental infrastructure. To date, the determination of the first-order rate coefficients in the advection–dispersion equation for simulating attachment and detachment of particles in saturated porous media typically has been relied on the result of laboratory-scale experiments. However, to determine attachment and detachment coefficients under varied hydraulic and geochemical variables, this method requires a large experimental matrix because each test provides only one set of attachment and detachment coefficients. The work performed in this study developed a framework to upscale the results obtained in pore-scale modeling to the continuum scale through the use of a pore network model. The developed pore network model incorporated variables of mean particle size, the standard deviation of particle size distribution, and interparticle forces between particles and sand grains. The obtained retention profiles using the pore network model were converted into attachment coefficients in the advection–dispersion equation for long-term and large-scale simulation. Additionally, by tracking individual particles during and after the simulation, the pore network model introduced in this study can also be employed for modeling the clogging phenomenon, as well as fundamental investigation of the impact of particle size distribution on particle retention in the sand medium.

     

对MPS法在溃坝模拟中数值压力振荡问题的改进

为探索模拟大变形自由面流体运动的高精度数值计算方法,以溃坝水流运动为例,基于MPS法(Moving Particle Semi-implicit method,移动粒子半隐式法)建立了一个垂向二维改良MPS法数值计算模型。首先,为了改善传统MPS法中存在的自由表面粒子误判以及数值能量耗散问题,提出新的自由表面粒子识别方法和高精度的压力梯度模型。在此基础上,以Lobovsky'等的溃坝物理模型实验为例,探讨不同形式压力泊松方程源项对溃坝冲击压计算精度的影响,提出一个新的源项形式。数值结果分析表明,新自由表面粒子识别方法和高精度压力梯度模型可以有效地减少自由面粒子的误判概率,抑制水流运动计算中的数值能量耗散。而压力计算结果与实验结果的对比表明,所提出的压力泊松方程源项可以有效地减少数值压力震荡的幅度。     

三峡建库前后下荆江有效流量研究

有效流量是天然河流某一时段内悬移质输沙量最大所对应的流量,可反映中、短期造床作用。根据监利水文站1991—2016年逐月流量、输沙量及悬移质级配,分析三峡建库前后流量频率及不同粒径组悬移质泥沙输移特性;运用理论分析法与分组频率法计算下荆江分组悬移质输沙量对应有效流量的大小、重现期、历时。研究成果表明:受来水来沙、水流挟沙能力以及床沙补给等因素影响,有效流量随泥沙粒径增大而减小。建库后,因河床冲刷各粒径组间有效流量偏差增大,0. 062 mm0. 125 mm粒径组泥沙有效流量重现期减小;细颗粒泥沙含沙量严重不饱和河道输送粗颗粒泥沙的能力相对较大,悬移质级配粗化;累积50%的泥沙输移需43%～82%的累积流量以及62%～90%的累积历时,且累积流量和累积历时随着泥沙粒径的增大而减小和缩短。研究三峡建库前后有效流量变化对分析冲刷条件下下荆江河段河床演变具有重要意义。     

Mineral ballast and particle settling rates in the coastal upwelling system off NW Africa and the South Atlantic

The ocean off NW Africa is the second most important coastal upwelling system with a total annual primary production of 0.33 Gt of carbon per year (Carr in Deep Sea Res II 49:59–80, 2002). Deep ocean organic carbon fluxes measured by sediment traps are also fairly high despite low biogenic opal fluxes. Due to a low supply of dissolved silicate from subsurface waters, the ocean off NW Africa is characterized by predominantly carbonate-secreting primary producers, i.e. coccolithophorids. These algae which are key primary producers since millions of years are found in organic- and chlorophyll-rich zooplankton fecal pellets, which sink rapidly through the water column within a few days. Particle flux studies in the Mauretanian upwelling area (Cape Blanc) confirm the hypothesis of Armstrong et al. (Deep Sea Res II 49:219–236, 2002) who proposed that ballast availability, e.g. of carbonate particles, is essential to predict deep ocean organic carbon fluxes. The role of dust as ballast mineral for organic carbon, however, must be also taken into consideration in the coastal settings off NW Africa. There, high settling rates of larger particles approach 400 m day⁻¹, which may be due to a particular composition of mineral ballast. An assessment of particle settling rates from opal-production systems in the Southern Ocean of the Atlantic Sector, in contrast, provides lower values, consistent with the assumptions of Francois et al. (Global Biogeochem Cycles 16(4):1087, 2002). Satellite chlorophyll distributions, particle distributions and fluxes in the water column off NW Africa as well as modelling studies suggest a significant lateral flux component and export of particles from coastal shelf waters into the open ocean. These transport processes have implications for paleo-reconstructions from sediment cores retrieved at continental margin settings.     

双峰型非均匀沙推移运动特性及输移规律

采用图像识别与推移质动态监测技术,开展基于双峰型非均匀推移质的系列水槽试验.通过引入反映床面粗糙度、粘性底层特性与颗粒非均匀度η(粗细比)的综合水流强度函数Ψ_b、特征弗劳德数Fr_b,系统研究了不同水流强度与床沙组成条件下的推移质输移特性以及颗粒非均匀度对输沙率的影响.通过对关键因子的辨识与量纲分析,提出了双峰型非均匀推移质输移模式,建立了基于近壁特征因子的水流强度Ψ_b与非均匀推移质输移强度Φ'的函数关系.对双峰型底沙输移机理的分析表明,非均匀沙的组成特征使得η成为影响Φ'的重要参量;正是细粒对粗粒的解怙作用对粗沙运动产生重要影响,使推移质输移率与颗粒非均匀度间呈现驼峰关系,峰值对应的粗细比η_c约为3∶7.     

Discrete-Element Computation of Averaged Tensorial Fields in Sand Piles Consisting of Polygonal Particles

This work is a contribution to the understanding of the mechanical properties of non-cohesive granular materials in the presence of friction and a continuation of our previous work (Roul et al. 2010) on numerical investigation of the macroscopic mechanical properties of sand piles. Besides previous numerical results obtained for sand piles that were poured from a localized source (“point source”), we here consider sand piles that were built by adopting a “line source” or “raining procedure”. Simulations were carried out in two-dimensional systems with soft convex polygonal particles, using the discrete element method (DEM). First, we focus on computing the macroscopic continuum quantities of the resulting symmetric sand piles. We then show how the construction history of the sand piles affects their mechanical properties including strain, fabric, volume fraction, and stress distributions; we also show how the latter are affected by the shape of the particles. Finally, stress tensors are studied for asymmetric sand piles, where the particles are dropped from either a point source or a line source. We find that the behaviour of stress distribution at the bottom of an asymmetric sand pile is qualitatively the same as that obtained from an analytical solution by Didwania and co-workers (Proc R Soc Lond A 456:2569–2588, 2000).     

悬浮颗粒的浓度对其在饱和多孔介质中迁移和沉积特性的影响

多孔介质中悬浮颗粒迁移和沉积特性的研究对地下污染物净化、石油开采、核废料处置、水土保持等有很重要的意义。对4种不同浓度的悬浮颗粒在3种不同的渗流速度下进行室内试验,研究悬浮颗粒的浓度对其迁移和沉积特性的影响。结果表明,在一定的悬浮颗粒浓度下,随着渗流速度的增加,穿透曲线中的悬浮颗粒的相对浓度也增大。同时,渗流速度一定时,悬浮颗粒的浓度存在一个临界值,小于该临界值,穿透曲线中的相对浓度随悬浮颗粒的浓度增大而增大;大于该临界值时,相对浓度随悬浮颗粒的浓度增大而减小。另外,悬浮颗粒的临界浓度是与渗流速度相关的,随着渗流速度增加,悬浮颗粒的临界浓度也逐渐增大