饱和多孔介质中颗粒迁移和沉积特性研究
摘要
饱和多孔介质中颗粒迁移特性的研究在地下污染物扩散、核废料处置、石油开采、地下水回灌和水工结构的内部侵蚀破坏等方面有很重要的研究意义。本文通过对经典的一维颗粒过滤模型进行修正,求得了不同的注入方式以及含有源汇项的解析解。其次,建立了考虑弥散作用和沉积颗粒再释放作用影响的颗粒迁移的三维模型,将颗粒迁移问题的研究从一维向三维空间进行拓展。求得的解析解可以预测多孔介质中颗粒浓度、验证更加复杂的数值模型以及确定试验参数等。另一方面,通过室内土柱试验研究了渗流速度、渗流方向、颗粒浓度以及颗粒粒径分布等对颗粒迁移和沉积特性的影响。其次,探究了渗流速度增量和颗粒粒径对沉积颗粒再释放特性的影响。主要的研究内容包括：
(1)将多孔介质视为饱和、均质和各向同性介质,通过在颗粒沉积动力方程中考虑弥散作用,建立了饱和多孔介质中颗粒迁移的一维模型,求得了三种不同的颗粒注入方式(短时注入、瞬时注入以及注入浓度衰减)和含有源汇项时的相应的解析解,并且对解析解中各种迁移参数进行了讨论。对不同情况的解析解的分析可知,随着时间、沉积系数、迁移距离或者线源宽度等参数中任意参数的增大,颗粒的浓度峰值逐渐减小。沉积动力方程中忽略弥散作用会对颗粒浓度有很大的影响,不同的情况下的影响规律大不相同。
(2)以求得的一维解析解为基础,建立三维空间的颗粒迁移模型,模型分别在沉积动力方程中考虑弥散作用和沉积颗粒再释放作用的影响,并通过Laplace变换和Fourier变换求得了相应解析解的通解形式。其次,利用推导出的解析解的通解形式求出了点源和面源形式下的瞬时注入和周期性注入的具体形式的解析解。最后,以点源瞬时注入情况下的解析解为例,对各种迁移参数进行了详细的讨论。对于考虑弥散作用的三维迁移模型的解析解来说,随着时间的增大,低浓度等高线的范围逐渐向四周扩大,高浓度等高线的范围逐渐缩小。随着沉积系数的增大,浓度等高线的范围逐渐缩小。对于考虑颗粒释放作用的三维迁移模型来说,释放系数越大,相应的浓度等高线的范围越大。
(3)通过土柱试验研究颗粒粒径、颗粒浓度和水动力对颗粒迁移和沉积特性的影响,开展了4种不同粒径和4种不同浓度的试验系列,每个系列中进行了3种不同的渗流速度的试验。结果表明：对于大小和形状一定的颗粒来说,通过测试颗粒浊度来反映其浓度的变化能取得较好的结果。其次,对于同一粒径的颗粒,渗流速度越大,流出液中颗粒的浓度峰值越大。在同一渗流速度条件下,颗粒粒径越大,流出液中其浓度峰值越小。另外,渗流速度一定时,颗粒的浓度存在一个和渗流速度相关的临界值,颗粒的临界浓度随着渗流速度增加也逐渐增大。
(4)通过试验的手段研究粒径和渗流速度对多孔介质中颗粒释放特性的影响。根据渗流速度增量的不同,试验分为两种不同的试验系列,在每一个试验系列中分别对两种不同粒径的颗粒进行试验。其次,研究了渗流速度增量和颗粒粒径对沉积颗粒释放规律的影响。最后,对试验完成后石英砂中沉积颗粒量随深度变化的特性进行了定量分析。一般来说,中位粒径小的颗粒的释放量要大于相应的中位粒径较大的颗粒。渗流速度的增量不同,沉积的颗粒的特征也大不相同。
(5)利用室内土柱试验探究了渗流速度、渗流方向以及颗粒分布对饱和多孔介质中颗粒迁移和沉积特性的影响机制。试验包括三种不同的渗流方向的试验系列(向下流,水平流和向上流)。同时,以修正后的对流弥散方程求得的解析解对试验曲线进行拟合,对3种不同粒径分布的颗粒的迁移参数进行对比分析,揭示了不同水力条件下颗粒的粒径分布对其迁移和沉积特性的影响机制。颗粒的弥散度和渗流方向有很大的关系,在渗流自上至下时弥散度的变化最明显。另外,随着渗流速度的增加,颗粒的沉积系数随之减小,相应的回收率随之增加,并且中位粒径或均一性指数对颗粒的沉积特性有一定的影响。
Particle transport and deposition in saturated porous media play an important role in pollutant purification, nuclear waste disposal, oil exploration and internal erosion of hydraulic structures. According to the correction of the classic one-dimensional particle filter model, this paper obtained analytical solutions for different injection methods and containing sources and sinks. Secondly, the three-dimensional models which have considered the dispersion effect and particle release effect were established, so the study of particle transport extends to three-dimensional space. The solutions may be used for predicting particle concentration, verification of more complicated numerical model and determination test parameters. On the other hand, according to the soil column test, the effect of seepage velocity, seepage direction, particle concentration and particle size distribution on particle transport and deposition have been studied. Besides, the effects of increment of seepage velocity and particle size on the release of deposition particle have been studied. The main contents include:
(1) In the present study, the porous media regarded as saturated, homogeneous and isotropic medium. Analytical solutions of corrected convection-dispersion models that takes into account dispersive flux on the deposition kinetic was obtained, including four types (short time injection, instantaneous injection, concentration decay injection and containing sources and sinks). The studies show that, the peak value of concentration decreases with increasing time, deposition rate, distance or the width of the source. Furthermore, these observations suggest that particle concentration affected by dispersive flux on the deposition kinetic equation, and the effect is strongly coupled to conditions.
(2) Based on the one dimensional model, three-dimensional models which have consider the dispersion effect and particle release effect was established. General solutions were derived with the help of Laplace and Fourier transforms. According to the general solutions, specific solutions (instantaneous injected and periodically injected) are presented for point and areal inflow regions. Finally, the analytical solution for point source under instantaneous injection was taken as example of specific solutions, and a detailed discussion of the various transport parameters was conducted. The range of low concentration contour increases with increasing time and high concentration contour decreases with increasing time. The concentration contours decrease with increasing deposition rate. The concentration contours increase with increasing release coefficient for the three-dimensional model which have consider particle release effect.
(3) Experiments were conducted to investigate the effects of particle size, particle concentration, hydrodynamic force on the transport and deposition of particle in saturated porous media. Four different size and four different concentration experimental series were performed, which series including three different seepage velocities experiment. The studies show that, particle turbidity can represent particle concentration of certain size and shape particle. The peak concentration of effluent increases with the increasing seepage velocity for the same particle size. Besides, there exists a critical concentration for particles under a constant flow velocity, the critical concentration of particles increases with the increasing seepage velocity.
(4) In order to study the effect of particle size and seepage velocity on the release of deposited particle,4different suspended particle concentrations have been studied under3flow velocities in columns of saturated porous media. Two different velocity increment series which including two different particle size were performed. Besides, the effects of flow velocity increment and particle size on the release of deposited particle have been studied. Finally, the relationship between the amount of deposited particle and the depth was quantitatively analyzed. Generally, the release amount of small median particle size particle is greater than larger median particle size particle. The characteristics of the deposited particle are larger dependent on flow velocity increment.
(5) Experiments were conducted to investigate the coupled effects of flow rate, flow direction, and particle size distribution on the transport and deposition of particle in saturated porous media. Three experimental series were performed, including downward flow, horizontal flow and upward flow. The breakthrough curves are well described by analytical solutions of a corrected convection-dispersion model. The flow direction is shown to be significant factors affecting the dispersivity of particle, especially in downward flow. Besides, the deposition rate decreases and the recovery rate increases with increasing flow rate. Furthermore, the particle deposition is affected by the median diameters or monodisperse index of particle.
(1)将多孔介质视为饱和、均质和各向同性介质,通过在颗粒沉积动力方程中考虑弥散作用,建立了饱和多孔介质中颗粒迁移的一维模型,求得了三种不同的颗粒注入方式(短时注入、瞬时注入以及注入浓度衰减)和含有源汇项时的相应的解析解,并且对解析解中各种迁移参数进行了讨论。对不同情况的解析解的分析可知,随着时间、沉积系数、迁移距离或者线源宽度等参数中任意参数的增大,颗粒的浓度峰值逐渐减小。沉积动力方程中忽略弥散作用会对颗粒浓度有很大的影响,不同的情况下的影响规律大不相同。
(2)以求得的一维解析解为基础,建立三维空间的颗粒迁移模型,模型分别在沉积动力方程中考虑弥散作用和沉积颗粒再释放作用的影响,并通过Laplace变换和Fourier变换求得了相应解析解的通解形式。其次,利用推导出的解析解的通解形式求出了点源和面源形式下的瞬时注入和周期性注入的具体形式的解析解。最后,以点源瞬时注入情况下的解析解为例,对各种迁移参数进行了详细的讨论。对于考虑弥散作用的三维迁移模型的解析解来说,随着时间的增大,低浓度等高线的范围逐渐向四周扩大,高浓度等高线的范围逐渐缩小。随着沉积系数的增大,浓度等高线的范围逐渐缩小。对于考虑颗粒释放作用的三维迁移模型来说,释放系数越大,相应的浓度等高线的范围越大。
(3)通过土柱试验研究颗粒粒径、颗粒浓度和水动力对颗粒迁移和沉积特性的影响,开展了4种不同粒径和4种不同浓度的试验系列,每个系列中进行了3种不同的渗流速度的试验。结果表明：对于大小和形状一定的颗粒来说,通过测试颗粒浊度来反映其浓度的变化能取得较好的结果。其次,对于同一粒径的颗粒,渗流速度越大,流出液中颗粒的浓度峰值越大。在同一渗流速度条件下,颗粒粒径越大,流出液中其浓度峰值越小。另外,渗流速度一定时,颗粒的浓度存在一个和渗流速度相关的临界值,颗粒的临界浓度随着渗流速度增加也逐渐增大。
(4)通过试验的手段研究粒径和渗流速度对多孔介质中颗粒释放特性的影响。根据渗流速度增量的不同,试验分为两种不同的试验系列,在每一个试验系列中分别对两种不同粒径的颗粒进行试验。其次,研究了渗流速度增量和颗粒粒径对沉积颗粒释放规律的影响。最后,对试验完成后石英砂中沉积颗粒量随深度变化的特性进行了定量分析。一般来说,中位粒径小的颗粒的释放量要大于相应的中位粒径较大的颗粒。渗流速度的增量不同,沉积的颗粒的特征也大不相同。
(5)利用室内土柱试验探究了渗流速度、渗流方向以及颗粒分布对饱和多孔介质中颗粒迁移和沉积特性的影响机制。试验包括三种不同的渗流方向的试验系列(向下流,水平流和向上流)。同时,以修正后的对流弥散方程求得的解析解对试验曲线进行拟合,对3种不同粒径分布的颗粒的迁移参数进行对比分析,揭示了不同水力条件下颗粒的粒径分布对其迁移和沉积特性的影响机制。颗粒的弥散度和渗流方向有很大的关系,在渗流自上至下时弥散度的变化最明显。另外,随着渗流速度的增加,颗粒的沉积系数随之减小,相应的回收率随之增加,并且中位粒径或均一性指数对颗粒的沉积特性有一定的影响。
Particle transport and deposition in saturated porous media play an important role in pollutant purification, nuclear waste disposal, oil exploration and internal erosion of hydraulic structures. According to the correction of the classic one-dimensional particle filter model, this paper obtained analytical solutions for different injection methods and containing sources and sinks. Secondly, the three-dimensional models which have considered the dispersion effect and particle release effect were established, so the study of particle transport extends to three-dimensional space. The solutions may be used for predicting particle concentration, verification of more complicated numerical model and determination test parameters. On the other hand, according to the soil column test, the effect of seepage velocity, seepage direction, particle concentration and particle size distribution on particle transport and deposition have been studied. Besides, the effects of increment of seepage velocity and particle size on the release of deposition particle have been studied. The main contents include:
(1) In the present study, the porous media regarded as saturated, homogeneous and isotropic medium. Analytical solutions of corrected convection-dispersion models that takes into account dispersive flux on the deposition kinetic was obtained, including four types (short time injection, instantaneous injection, concentration decay injection and containing sources and sinks). The studies show that, the peak value of concentration decreases with increasing time, deposition rate, distance or the width of the source. Furthermore, these observations suggest that particle concentration affected by dispersive flux on the deposition kinetic equation, and the effect is strongly coupled to conditions.
(2) Based on the one dimensional model, three-dimensional models which have consider the dispersion effect and particle release effect was established. General solutions were derived with the help of Laplace and Fourier transforms. According to the general solutions, specific solutions (instantaneous injected and periodically injected) are presented for point and areal inflow regions. Finally, the analytical solution for point source under instantaneous injection was taken as example of specific solutions, and a detailed discussion of the various transport parameters was conducted. The range of low concentration contour increases with increasing time and high concentration contour decreases with increasing time. The concentration contours decrease with increasing deposition rate. The concentration contours increase with increasing release coefficient for the three-dimensional model which have consider particle release effect.
(3) Experiments were conducted to investigate the effects of particle size, particle concentration, hydrodynamic force on the transport and deposition of particle in saturated porous media. Four different size and four different concentration experimental series were performed, which series including three different seepage velocities experiment. The studies show that, particle turbidity can represent particle concentration of certain size and shape particle. The peak concentration of effluent increases with the increasing seepage velocity for the same particle size. Besides, there exists a critical concentration for particles under a constant flow velocity, the critical concentration of particles increases with the increasing seepage velocity.
(4) In order to study the effect of particle size and seepage velocity on the release of deposited particle,4different suspended particle concentrations have been studied under3flow velocities in columns of saturated porous media. Two different velocity increment series which including two different particle size were performed. Besides, the effects of flow velocity increment and particle size on the release of deposited particle have been studied. Finally, the relationship between the amount of deposited particle and the depth was quantitatively analyzed. Generally, the release amount of small median particle size particle is greater than larger median particle size particle. The characteristics of the deposited particle are larger dependent on flow velocity increment.
(5) Experiments were conducted to investigate the coupled effects of flow rate, flow direction, and particle size distribution on the transport and deposition of particle in saturated porous media. Three experimental series were performed, including downward flow, horizontal flow and upward flow. The breakthrough curves are well described by analytical solutions of a corrected convection-dispersion model. The flow direction is shown to be significant factors affecting the dispersivity of particle, especially in downward flow. Besides, the deposition rate decreases and the recovery rate increases with increasing flow rate. Furthermore, the particle deposition is affected by the median diameters or monodisperse index of particle.
引文
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