共查询到20条相似文献，搜索用时 31 毫秒
1.
Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain 总被引：1，自引：0，他引：1
Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in a longitudinal
finite initially solute free domain, for two dispersion problems. In the first one, temporally dependent solute dispersion
along uniform flow in homogeneous domain is studied. In the second problem the velocity is considered spatially dependent
due to the inhomogeneity of the domain and the dispersion is considered proportional to the square of the velocity. The velocity
is linearly interpolated to represent small increase in it along the finite domain. This analytical solution is compared with
the numerical solution in case the dispersion is proportional to the same linearly interpolated velocity. The input condition
is considered continuous of uniform and of increasing nature both. The analytical solutions are obtained by using Laplace
transformation technique. In that process new independent space and time variables have been introduced. The effects of the
dependency of dispersion with time and the inhomogeneity of the domain on the solute transport are studied separately with
the help of graphs. 相似文献
2.
R. R. Yadav Dilip Kumar Jaiswal Hareesh Kumar Yadav Gulrana 《Environmental Earth Sciences》2012,65(3):849-859
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. 相似文献
3.
A number of models have been established to simulate the behaviour of solute transport due to chemical pollution, both in croplands and groundwater systems. An approximate polynomial solution to convection–dispersion equation (CDE) based on boundary layer theory has been verified for the use to describe solute transport in semi-infinite systems such as soil column. However, previous studies have only proposed low order polynomial solutions such as parabolic and cubic polynomials. This paper presents a general polynomial boundary layer solution to CDE. Comparison with exact solution suggests the prediction accuracy of the boundary layer solution varies with the order of polynomial expression and soil transport parameters. The results show that prediction accuracy increases with increasing order up to parabolic or cubic polynomial function and with no distinct relationship between accuracy and order for higher order polynomials (\(n\geqslant 3\)). Comparison of two critical solute transport parameters (i.e., dispersion coefficient and retardation factor), estimated by the boundary layer solution and obtained by CXTFIT curve-fitting, shows a good agreement. The study shows that the general solution can determine the appropriate orders of polynomials for approximate CDE solutions that best describe solute concentration profiles and optimal solute transport parameters. Furthermore, the general polynomial solution to CDE provides a simple approach to solute transport problems, a criterion for choosing the right orders of polynomials for soils with different transport parameters. It is also a potential approach for estimating solute transport parameters of soils in the field. 相似文献
4.
5.
We derive a simple approximation for the steady-state distribution of solute subject to an arbitrary, irreversible transformation in a soil profile under the condition of steady fluid flow. The approximation accounts for the effect of dispersion in both the surface boundary condition and the transport equation. The accuracy of the approximation is determined explicitly for the cases of zero- and first-order kinetics, where exact solutions are available. Data from a numerical scheme are used to check the approximation's accuracy for the widely used Michaelis–Menten kinetic rate. It is shown that existing approximations in which the effect of dispersion in the transport equation is ignored can affect significantly the value determined for the Michaelis–Menten saturation constant. Parameters found when the new method is applied to experimental data are found to agree closely with those estimated directly from a least-squares fitting. 相似文献
6.
7.
Solute transport experiments were conducted in a one-dimensional saturated column using dissolved methoxy-nonafluorobutane (HFE-7100), a Novec engineered fluid developed by the 3M Corporation, as the solute. Novec engineered fluids are considered dense non-aqueous phase liquids (DNAPLs) because they are immiscible with water and have a specific gravity greater than one. The HFE-7100 fluid is safer and environmentally friendlier than common DNAPL contaminants such as tetrachloroethylene (PCE) or trichloroethylene (TCE); thus, it is an ideal substitute DNAPL for laboratory groundwater contamination research. Three sets of solute transport experiments were conducted. The first set of experiments was conducted in a glass-bead-packed column using dissolved HFE-7100 as the solute. The second set of experiments was conducted in a sand-packed column using dissolved HFE-7100 as the solute. The third set of experiments was conducted in a sand-packed column using dissolved PCE as the solute. The dissolved HFE-7100 column breakthrough concentrations were compared with dissolved PCE breakthrough concentrations. Results show that the one-dimensional solute transport equation was successful in describing the transport behavior of dissolved HFE-7100. This study demonstrates that the HFE-7100 fluid can be used as a safer substitute DNAPL for groundwater contaminant dissolution and transport research. 相似文献
8.
盐渍土壤中的物理化学作用对溶质运移具有重要影响.吸附和离子交换作用是土壤中常见的反应.利用室内土柱出流实验对这两种作用下的单组分和多组分溶质运移进行了探讨,用CXTFIT软件模拟了只考虑对流-弥散的常规溶质运移;用水文地球化学模拟软件PHREEQC进行了耦合吸附和离子交换反应的模拟.结果表明,土壤质地对单组分溶质的运移具有重要影响,而在多组分溶质运移中,组分之间的相互作用对溶质运移具有更为重要的影响,并且耦合物理化学作用的模拟精度更高. 相似文献
9.
This paper presents a non-equilibrium sorption dispersion–advection transport model for the analysis of pollutant migration through soil. The formulation involves a convolution integral of the product of the rate of change of concentration and a time-dependent sorption coefficient, suggesting an integral transformation of the governing equations. This facilitates the primary purpose of this paper, to incorporate a time-dependent solute sorption process into a computationally efficient and accurate semi-analytic Laplace transform method. An application of the non-equilibrium sorption model for backfiguring dispersion–advection equation parameters from experimental data is presented, and the implications of non-equilibrium sorption on the design of landfill liners is explored by means of an illustrative example. 相似文献
10.
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy’s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection–diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid–cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid–gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid–gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. 相似文献
11.
12.
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。 相似文献
13.
14.
One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium 总被引：1，自引：0，他引：1
SANJAY K YADAV ATUL KUMAR DILIP K JAISWAL NAVEEN KUMAR 《Journal of Earth System Science》2011,120(2):205-213
The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The
solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion
occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space
variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered
to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation
are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form.
These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier
works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type. 相似文献
15.
Determination of groundwater solute transport parameters in finite element modelling using tracer injection and withdrawal testing data 总被引：1，自引：0，他引：1 
下载免费PDF全文
下载免费PDF全文 Nguyen Van Hoang 《地下水科学与工程》2021,9(4):292-303
The groundwater tracer injection and withdrawal tests are often carried out for the determination of aquifer solute transport parameters. However, the parameter analyses encounter a great difficulty due to the radial flow nature and the variability of the temporal boundary conditions. An adaptive methodology for the determination of groundwater solute transport parameters using tracer injection and withdrawal test data had been developed and illustrated through an actual case. The methodology includes the treatment of the tracer boundary condition at the tracer injection well, the normalization of tracer concentration, the groundwater solute transport finite element modelling and the method of least squares to optimize the parameters. An application of this methodology was carried out in a field test in the South of Hanoi city. The tested aquifer is Pleistocene aquifer, which is a main aquifer and has been providing domestic water supply to the city since the French time. Effective porosity of 0.31, longitudinal dispersivity of 2.2 m, and hydrodynamic dispersion coefficients from D = 220 m2/d right outside the pumping well screen to D =15.8 m2/d right outside the tracer injection well screen have been obtained for the aquifer at the test site. The minimal sum of squares of the differences between the observed and model normalized tracer concentration is 0.00119, which is corresponding to the average absolute difference between observed and model normalized concentrations of 0.035 5 (while 1 is the worst and 0 is the best fit). 相似文献
16.
The migration of contaminant through soil is usually modeled using the advection‐dispersion equation and assumes that the porous media is stationary without introducing a constitutive equation to represent soil structure. Consequently, time‐dependent deformation induced by soil consolidation or physical remediation is not considered, despite the need to consider these variables during planning for the remediation of contaminated ground, the prediction of contaminated groundwater movement, and the design of engineered landfills. This study focuses on the numerical modeling of solute transfer during consolidation as a first step to resolve some of these issues. We combine a coupling theory‐based mass conservation law for soil‐fluid‐solute phases with finite element modeling to simulate solute transfer during deformation and groundwater convection. We also assessed the sensitivity of solute transfer to the initial boundary conditions. The modeling shows the migration of solute toward the ground surface as a result of ground settlement and the dissipation of excess pore water pressure. The form of solute transport is dependent on the ground conditions, including factors such as the loading schedule, contamination depth, and water content. The results indicate that an understanding of the interaction between coupling phases is essential in predicting solute transfer in ground deformation and could provide an appropriate approach to ground management for soil remediation. 相似文献
17.
S. A. Junejo Qi You Zhou M. A. Talpur Dongqing Wang Jian-long Yang 《Geochemistry International》2014,52(9):794-804
Accurate prediction of solute transport processes in surface water and its underlying bed is an important task not only for proper management of the surface water but also for pollution control in these water bodies. Key issue in this task is an estimation of parameters as diffusion coefficient and velocity for solute transport both in water body and in the underlying bed. This estimation would greatly help us to understand the deposition and release mechanism of solute across the water-bed interface. In this study, a column experiment was conducted in laboratory to estimate the velocity and diffusion coefficient of sodium chloride (NaCl) in water body and underlying sand layer (bed). The column used with a diameter of 30 cm and a height of 100 cm, was filled with sand at the lower half part and water at the upper half part. Total 64 stainless steel electrodes were installed on its surface around. The sodium chloride solution was injected from the top of the column, and electrical resistance between electrodes was monitored for 71 h. Then the dimensionless resistance breakthrough curve was fitted with one dimensional analytic solution for solute transport and the related diffusion coefficient and velocity parameters were estimated. The results show that the NaCl transport velocity was high in the water body but extremely low in the underlying sand layer (bed). The diffusion coefficient estimated in sand layer coincides with those reported well. This indicates that the electrical resistance based solute transport parameter estimation method is not only effective but also has an advantage of multipoints monitoring. This is useful both in mapping solute transport parameter for solute transport process analysis and in providing parameter input for solute transport numerical modeling. 相似文献
18.
岩溶区地下水数值模拟研究进展 总被引：2，自引：2，他引：0
岩溶含水介质的不均一性导致岩溶地下水流动、溶质运移和热量迁移的数学模拟研究成为地下水模拟的难点。本文综述了岩溶区地下水流模拟的几种方法,重点阐述了等效多孔介质法、双重连续介质法和三重介质法的定义、发展过程和适用范围,并回顾了这几种方法的研究成果。从等效多孔介质法到三重介质法,模拟精度不断提高,适用范围也逐渐由大区域实际问题向小区域理论研究过渡。介绍了溶质运移模拟和热迁移模拟的研究方法及实例。溶质运移模拟以对流弥散方程为基础,其中尺度效应是溶质运移模拟的重点研究问题;热量迁移模拟应考虑地下热水密度变化对地下热水运动的影响。溶质运移模拟和热量迁移模拟往往是将迁移模型和已经调试成功的地下水流动模型相耦合,从而达到模拟溶质及热量迁移的目的。由于溶质运移和热量迁移的复杂性,现阶段水流模型多数处于等效多孔介质模型阶段。综合理论及实际应用,指出精确刻画裂隙及管道和注重基础数学算法是岩溶水数值模拟进步的关键。 相似文献
19.
通过将经典时间分数阶对流-弥散方程的等待时间分布函数的尾部修改为指数型,推导出了改进时间分数阶对流-弥散方程,并提出有效的时空算子分裂数值求解方法。对两个理想算例和一个实际算例进行计算,结果表明,改进的时间分数阶对流-弥散方程继承了时间分数阶对流-弥散方程能模拟穿透曲线幂率型拖尾分布的优点,还可模拟穿透曲线尾部由幂率型转换到指数型的过程;特征时间λ、分数阶指数γ和两相容量比例系数β共同决定了运移行为。改进的新模型可以区分非均质介质中流动相和非流动相中的溶质浓度, 更细微地模拟非Fick溶质运移行为。 相似文献
20.
Anis Younes 《Comptes Rendus Geoscience》2004,336(6):547-552
Modelling contaminant transfer with biological/chemical/radioactive processes needs appropriate numerical methods able to reproduce sharp concentration fronts. In this work, we develop a new Eulerian–Lagrangian Localized Adjoint Method (ELLAM) for solving the reactive transport equation with non-constant coefficients. To avoid interpolation (leading to errors), we use a moving grid to define the solution and test functions. The method is used to simulate first the infiltration of solute into a column of unsaturated porous medium and second the multispecies transport. The developed ELLAM gives accurate results without non-physical oscillations or numerical diffusion, even when using large time steps. To cite this article: A. Younes, C. R. Geoscience 336 (2004). 相似文献