二维分数阶对流-弥散方程的数值解

对二维时间分数阶对流-弥散方程和二维空间分数阶对流-弥散方程分别建立了差分格式,实现了对其的数值求解。针对理想算例进行计算求解,分析了时间和空间分数阶阶数取不同值时的扩散变化规律,验证了各自所描述的时间相关性与空间相关性。同时与传统的二维整数阶对流-弥散方程的求解结果作了对比。当时间和空间分数阶阶数α与γ分别取整数时,二维时间分数阶对流-弥散方程和二维空间分数阶对流-弥散方程都与传统二维整数阶对流-弥散方程的计算结果相同,说明提出的对二维分数阶对流-弥散方程的数值求解方法是可行的。其结果对地下水溶质运移的进一步研究提供了有效的手段。     

注入时间和静水压力对孔隙热储层中Cl-运移影响

迄今为止,注入时间和静水压力对溶质在深层承压地热水中的运移规律影响研究少有报道。通过模拟35℃的低温地热环境,开展了注入时间1,2,3,4,5 h以及静水压力0,6,9 MPa条件下Cl^-的运移柱模拟试验。采用CXTFIT 2.1软件进行数值模拟,探讨了孔隙型热储砂土中Cl^-的运移规律和影响因素。结果表明：在模拟的低温孔隙型热储层中,不同注入时间和静水压力下,Cl^-的运移曲线均呈正态对称分布,一维对流弥散(CDE)模型也可较好地表征其穿透曲线,因此溶质扩散过程符合菲克定律。注入时间的不同,会引起Cl^-的穿透曲线、运移参数发生变化,这与不同注入时间条件下溶质注入总量、柱内溶质浓度差以及分子扩散能力不同有关。在不同静水压力条件下,弥散系数从0 MPa的25.22 cm²/h增加到9MPa的36.13 cm²/h,分子扩散系数、机械弥散系数以及弥散度也随之增大,因此溶质的弥散作用随静水压力的增大而增强。研究结果对于丰富地下水的溶质运移理论具有重要意义。     

岩溶管道与裂隙介质间溶质暂态存储机制

溶质暂态存储是岩溶地下水溶质运移过程中的普遍现象。为揭示岩溶管道与裂隙介质间溶质暂态存储机制,本文构建室内管道-裂隙物理模型,开展集中补给条件下的定量示踪试验,运用双区对流弥散模型实现溶质运移过程模拟。研究表明：随着集中补给水动力条件的增强,裂隙暂态存储水量呈线性增加趋势,溶质穿透曲线由单峰型向双峰型转变;管道和裂隙中的平均流速呈负相关关系,溶质在管道和裂隙中的滞留时间差决定了穿透曲线的形态;溶质暂态存储引发了穿透曲线的拖尾效应和双峰现象,对岩溶地下水溶质运移过程具有重要的控制作用。     

水箱-管道系统溶质运移实验研究及其岩溶水文地质意义

为了研究岩溶管道中溶潭对溶质运移的影响,在实验室内构建水箱-管道系统,在不同管道结构和水流条件下进行定量示踪实验并得到相应的穿透曲线(BTCs);采用Qtracer2软件分析溶质运移参数,采用滞后系数R分析实验结果与一维经典对流弥散方程解析解之间的差别。实验结果显示:随着水箱数量的增加,示踪剂(NaCl)峰值质量浓度逐渐降低,弥散系数和弥散度逐渐增加,穿透曲线拖尾逐渐增长,表明水箱的瞬态存储使溶质运移滞后;与不对称水箱相比,对称水箱BTC拖尾较长;峰现时间随着不对称水箱数量的增多明显滞后;出口流量增加时,弥散度减小,BTC拖尾变短。一维经典对流弥散方程解析解仅对单管道最大流量条件下的BTC拟合较好,对流量较小的单管道和水箱-管道系统的BTC拟合较差,需研究适用的模型解释其拖尾现象。     

连续时间随机游动理论模拟多孔介质中溶质运移的研究进展

近年来,基于连续时间随机游动(Continuous Time Random Walk, CTRW)理论所建立的模拟非均质多孔介质中溶质运移的方法已在大量的数值实验、室内实验、野外实验中得到了广泛的验证,为非均质多孔介质中的溶质运移行为提供了一种有效的模拟方法。简述了提出和发展CTRW的研究背景、基础理论以及与经典的对流-弥散方程等其他模拟方法的关系,综述了该理论在模拟溶质运移中的发展和应用,分析了实际应用中的关键问题,并展望了将其进一步发展应用于模拟反应性溶质运移的前景。     

非均质土柱中溶质迁移的连续时间随机游走模拟

非均质介质中溶质迁移往往出现非费克现象,传统的对流弥散方程(ADE)则难以较好地描述这种现象.采用连续时间的随机游走理论(CTRW)研究1250cm长一维非均质土柱中溶质运移问题,探讨CTRW模型中参数及非费克迁移的变化特征.研究结果表明,β值的大小与介质的非均质特征有关,非均质性越强,β值越小,但β值具有相对的稳定性,然而ADE的弥散系数则具有随尺度增大而增大的现象.对于介质非均质性较强和非费克现象较明显的溶质穿透曲线,尤其是在拖尾部分,与ADE相比,CTRW具有较高的模拟精度.     

城市小型河流水动力弥散和潜流交换过程

为研究城市小型河流中污染物的物理迁移过程规律,分析基流条件下流动水体与暂态存储区之间的滞留交互作用,采用溴化锂(LiBr)作为保守性示踪剂进行野外现场示踪试验,结合一维溶质运移存储模型(One-dimensional Transport with Inflow and Storage model, OTIS)定量解析潜流交换特性,估算纵向弥散系数(D)、潜流交换面积(A_s)、主河道断面面积(A)和潜流交换系数(α).模型度量指标D_aI值和均方根误差值结果表征参数模拟结果可靠性高,拟合效果理想.由泵入点O至下游1 300 m设置的A、B、C、D 4处监测点的模拟结果表明,水文参数D、A_s、A和α均随水文条件而变,OB河段(0~600 m)潜流交换能力较弱,主要以对流弥散过程为主;BD河段(600~1 300 m)具有较强的暂态存储能力,对溶质的滞留时间长;BC(600~1 000 m)和CD(1 000~1 300 m)河段交换系数分别为(3.42×10-6±0.65×10-6)s-1和(2.87×10-6±0.81×10-6 )s-1;河段BC存在2.2×10-5m3/(s·m)的侧向补给流量.4个河段对比发现,城市河流渠道化、河床沉积物贫瘠等特征导致潜流交换能力弱化.     

土石混合介质中非反应性阴离子运移试验研究

为探讨化学物质在土石混合介质中的运移过程和机理,采用饱和稳态流下的Cl-1混合置换试验,测定水流和溶质运移过程,分析土石混合介质的溶质穿透曲线特征及碎石组成和含量对运移过程的影响。选用CXTFIT2.1的平衡和物理非平衡对流弥散模型,对参数弥散系数D和滞留因子R进行反求。结果显示:不同土石比的D变异较大:0.258~22.31 cm2/h。R的波动范围为0.6~1.54;碎石含量影响土石介质的溶质运移过程表现为平均孔隙流速、弥散系数、弥散度均与土石比成负指数的幂函数关系。对碎石粒径与溶质运移参数进行相关分析发现,小粒径的碎石含量增加,则孔隙流速和弥散系数有减少的趋势,而大于10 mm的碎石有利于溶质的运移。通过土石介质的非反应性阴离子的混合置换试验研究,可以为非均一介质中化学物质运移提供参考。     

弯曲岩溶管道溶质运移的尺度效应研究

岩溶管道溶质运移的尺度效应研究对穿透曲线的正确解译非常重要,但目前针对单一弯曲管道中溶质运移尺度效应的研究仍比较缺乏。文章将岩溶管道和溶潭分别概化为透明软管和水箱,基于前期建立的水箱-管道系统(简称“管道系统”),在水箱下游设置不同长度的弯曲管道,通过示踪试验研究管道运移尺度对穿透曲线的影响,并采用暂时存储模型模拟试验曲线。结果表明：(1)随着水箱下游管道长度的增加,峰值质量浓度逐渐缓慢降低,穿透曲线上升段斜率无明显变化,穿透曲线拖尾逐渐缩短,表明运移管道长度增加对溶质运移的影响大于下游管道弯曲;(2)穿透曲线偏度系数、后段溶质羽穿透时间和溶质羽穿透时间与管道系统长度呈良好的负线性相关关系(R²>0.96);(3)当对称和不对称水箱管道系统长度分别增加至154.5 m和164.3 m时,偏度系数接近0,穿透曲线分布接近对称;(4)弥散系数、存储区截面积和交换系数与管道系统长度呈良好的负线性相关关系,当对称和不对称水箱管道系统长度分别增加至159.9 m和178.1 m时,存储区截面积接近0,水箱导致的溶质运移滞后效应基本消失。研究结果对野外岩溶管道穿透曲线的...     

基于CFP的岩溶管道流溶质运移数值模拟研究

多重岩溶含水介质的复杂性导致岩溶地下水流动及溶质运移的数学模拟成为地下水研究难点之一。为了探讨岩溶多重含水介质中地下水流溶质运移特征,文章构建了管道流CFP水流模型和MT3DMS溶质运移三维耦合数值模型。在阐述管道流CFP和MT3DMS基本原理的基础上,通过建立水文地质概念模型算例（1个落水洞、4个直管道）,探讨岩溶管道水流及溶质运移规律,分析讨论不同水文地质参数对浓度穿透曲线的影响。研究结果表明:管道流CFP模型能够刻画岩溶管道与基岩裂隙水流交换特征,MT3DMS模型能够模拟穿透曲线的拖尾现象,符合实际岩溶区特征。随着水力梯度、管道直径及管道渗透系数增大,孔隙度减小,浓度曲线峰值越大,峰值到达时间越快,浓度穿透曲线越对称。得出结论:耦合CFP水流模型和MT3DMS溶质运移模型能够刻画岩溶管道流溶质运移规律,为研究岩溶复杂介质污染物运移特征提供一种思路和途径。     

井内混合效应与尺度效应对注入井附近溶质径向弥散过程的影响

径向弥散是指溶质在径向流场下的迁移规律,被广泛用于描述含水层修复领域中污染物的迁移过程.然而,在现有描述径向弥散的模型中,往往忽略了井内混合效应对溶质径向弥散的影响.建立新的注入井附近溶质径向运移动力学模型,同时考虑井内混合效应与弥散度的尺度效应.采用Laplace变换推导该模型的半解析解,利用Stehfest数值逆变换获取溶质在实数空间的解.通过与不考虑混合效应的模型对比研究混合效应对溶质径向弥散的影响,并利用室内渗流槽中的溶质径向弥散实验数据验证模型的合理性与适用性.结果表明:混合效应和尺度效应对注水井附近溶质径向弥散有显著影响.具体地讲,井内的混合效应越显著,在井壁处及含水层中的穿透曲线越低,溶质浓度达到峰值所需时间越长,与不考虑混合效应模型的差异越明显;随尺度效应的增强,溶质提前穿透且扩散范围变大,溶质浓度达到峰值所需时间越长;与前人的模型相比,本研究模型能更好地模拟注水井附近的溶质径向弥散问题.      

Simulation of chloride transport in an aggregated soil using three conceptual models

Breakthrough curves (BTCs) of chloride displaced through columns of loessial soil aggregates of different sizes were measured under saturated steady flow conditions. The data were simulated using three conceptual models. Model I (CDE) assumed that all soil water was mobile and physical equilibrium existed in the system. Model II (two-region model) partitioned the soil water into mobile and immobile regions, and convective diffusive solute transport was limited to the mobile water region. Model III (two-flow region model) also divided the soil water into two regions based on their flow velocities, but both of the regions had a non-zero flow rate. Transfer of the chloride solute between the two soil water regions was assumed to occur at a rate proportional to the difference in solute concentration. The two unknown parameters in model I, three in model II, and four in model III were estimated by fitting the experimental data. The three models could well describe all the BTCs measured for columns packed with all the aggregate sizes at the low pore water velocity (0.68 cm/h); however, the values of the fitted parameters varied greatly. The Peclet numbers derived from both the two-region (model II) and two-flow region (model III) models behaved similarly and increased with increases in aggregate size. But the Peclet numbers derived from the convection dispersion equation (model I) were about two orders of magnitude greater than those derived from the other two models. The mobile water fraction obtained for the two-flow region model decreased with increases of aggregate size. The mass transfer coefficient decreased with an increase in pore water velocity due to the shorter residence time of the chloride solute in the soil columns.     

Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems

A time-space continuum model for transport of hydrothermal fluids in porous media is presented which provides for simultaneous, reversible and irreversible chemical reactions involving liquids, gases and minerals. Homogeneous and heterogeneous reactions are incorporated in the model in a similar fashion through source/sink terms added to the continuity equation. The model provides for moving reaction fronts through surfaces of discontinuity across which occur jump discontinuities in the various field variables satisfying generalized Rankine-Hugoniot relations. Reversible reactions including aqueous complexing, oxidation-reduction reactions, mineral precipitation and dissolution reactions and adsorption are explicitly accounted for by imposing chemical equilibrium constraints in the form of mass action equations on the transport equations. This is facilitated by partitioning the reacting species into primary and secondary species corresponding to a particular representation of the stoichiometric reaction matrix referred to as the canonical representation. The transport equations for the primary species combined with homogeneous and heterogeneous equilibria result in a system of coupled, nonlinear algebraic/partial differential equations which completely describe the evolution of the system in time. Spatially separated phase assemblages are accommodated in the model by altering the set of independent variables across surfaces of discontinuity. Constitutive relations for the fluid flux corresponding to primary species are obtained describing transport of both neutral and charged species by advection, dispersion and diffusion. Numerical implementation of the transport equations is considered and both explicit and implicit finite difference algorithms are discussed. Analytical expressions for the change in porosity and permeability with time are obtained for an assemblage of minerals reacting reversibly with a hydrothermal fluid under quasi-steady state conditions. Fluid flow is described by Darcy's law employing a phenomenological expression relating permeability and porosity. Finally an expression for the local retardation factor of solute species is derived for the case of advective transport in a single spatial dimension which accounts for the effects of homogeneous and heterogeneous equilibria including adsorption on the rate of advance of a reaction front. The condition for the formation of shock waves is given.     

溶质入渗土工合成衬垫的化学-渗透特性研究

溶质在土工合成衬垫（GCL）长期入渗过程中具有明显的化学-渗透特性。室内渗透试验表明：阳离子之间的置换效应对GCL衬垫渗透系数影响较大,10 mM的CaCl2溶液使渗透系数上升至2.5×10-11 m/s,而30 mM的CaCl2溶液使渗透系数上升至5.6×10-11 m/s。渗透液体浓度的增加缩短了溶质穿透GCL的时间,且预饱和处理试剂对GCL渗透系数的变化影响较大,采用蒸馏水作为预饱和试剂处理GCL衬垫对其渗透系数的影响明显小于CaCl2溶液;建立了考虑膜效应和离子交换效应条件下溶质运移耦合动力学模型,并对GCL穿透试验过程中溶质浓度的变化进行了预测,仿真计算结果表明,10 mM和30 mM两种CaCl2溶液渗透条件下,Ca2+浓度变化的试验结果和计算结果均相吻合,验证了耦合动力学模型的可靠性;从Ca2+浓度及流量穿透曲线分布可知,化学-渗透效应可有效地延缓溶质的迁移速度。随着溶质浓度的降低,阻滞作用更显著。因此,在分析GCL衬垫中溶质入渗特征时,必须考虑化学-渗透效应的影响。     

Three-dimensional temporally dependent dispersion through porous media: analytical solution

A three-dimensional model for non-reactive solute transport in physically homogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considered temporally dependent dispersion. The model also account for a uniform flow field, first-order decay which is inversely proportional to the dispersion coefficient and retardation factor. Porous media with semi-infinite domain is considered. Initially, the space domain is not solute free. Analytical solutions are obtained for uniform and varying pulse-type input source conditions. The governing solute transport equation is solved analytically by employing Laplace transformation technique (LTT). The solutions are illustrated and the behavior of solute transport may be observed for different values of retardation factor, for which simpler models that account for solute adsorption through a retardation factor may yield a misleading assessment of solute transport in ‘‘hydrologically sensitive’’ subsurface environments.     

水力传导度空间变异性的分形模拟研究进展

水力传导度是描述孔隙介质物理特性的重要参数,水力传导度的空间变异性直接影响到水分与溶质在介质中的运移状况。由于基于随机理论的方法难于描述具有多重变异尺度的水力传导度的空间变异性,使得基于分形理论的方法得到了较快发展和应用。详细介绍并评述了分形理论和方法的基本特征及研究进展,水力传导度的空间变异分形与弥散尺度效应的关系及其对溶质运移的影响。     

The transport of heat and matter by fluids during metamorphism

Non-dimensional solutions to the equations for the combined advective and diffusive one-dimensional transport of heat and solute in a layer are derived for fixed temperature/concentration on the boundaries and initial conditions of a linear gradient across the layer or a step function at the lower boundary. The solutions allow distinction of regimes in which advective or diffusive transport of either heat or solute predominate as a function of fluid flux, time and a length scale. The much lower diffusive coefficients for solute than heat results in a significant range of length scales and fluid flux rates characterised by advection of matter and diffusion of heat. The advective velocity of a component is a function of its fluid:rock partition coefficient. The most rapidly transported tracers which partition largely into the fluid phase, such as He, will travel orders of magnitude faster than heat or compatible solutes such as oxygen. Geochemical profiles in boundary layer regions where both advective and diffusive transport are significant are shown to be particularly informative as to properties of the rocks related to fluid flow such as porosity, permeability, time scales and fluid flux rates. The importance of advection can be directly estimated from the asymmetry of the geochemical profiles across individual layers.     

Panel 3: Chemical models of sea water systems

We have identified many problems in the chemistry of sea water and geochemical brines that can be elucidated by the application of classical as well as new methods of solution chemistry. Examples of the latter range from new methods of analysis for trace constituents to emerging theoretical developments which bring ab initio calculations of solute stabilities and rates within the range of possibility. Thus the sparse data from classical studies of speciation, thermodynamics, transport and chemical kinetics in sea water compel us to point out many instances in which the obvious need is for more (and better) data of the same kind. At the same time, however, the promise of new experimental and theoretical techniques requires emphasis.     

西宁市贵德县河滨公园林场第四系含水层弥散试验研究

地下水污染问题日益严重,研究溶质运移的弥散理论开始应用于实际问题。建立地下水溶质运移模型,对地下水中污染物的运移及发展趋势进行准确预测,是对地下水进行保护、对地下水污染进行控制的基础。而弥散参数的确定则是地下水溶质运移模型建立的关键环节之一,直接影响着模型预测结果的精度和准确性。 对西宁市贵德县地下水污染的水质运移规律进行分析,在贵德县河滨公园林场采用径向收敛流水动力弥散理论方法进行了第四系含水层现场弥散试验,计算了试验场地潜水含水层的弥散度,获得纵向弥散度(a_L)为0.843~0.998 cm,横向弥散度(a_T)经验推断值为0.17~0.20 cm,为进一步建立该地区的地下水溶质运移模型、预测地下水污染的发展趋势和评价该地区地下水环境质量提供了数据参考。