共查询到20条相似文献，搜索用时 15 毫秒
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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. 相似文献
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Analytical solutions for advective–dispersive solute transport in double‐layered finite porous media
Peter John Cleall 《国际地质力学数值与分析法杂志》2011,35(4):438-460
Analytical solutions for advection and dispersion of a conservative solute in a one‐dimensional double‐layered finite porous media are presented. The solutions are applicable to five scenarios that have various combinations of fixed concentration, fixed flux and zero concentration gradient conditions at the inlet and outlet boundaries that provide a wide number of options. Arbitrary initial solute concentration distributions throughout the media can be considered via explicit formulations or numerical integration. The analytical solutions presented have been verified against numerical solutions from a finite‐element‐based approach and an existing closed‐form solution for double‐layered media with an excellent correlation being found in both cases. A practical application pertaining to advective transport induced by consolidation of underlying sediment layers on contaminant movement within a capped contaminated sediment system is presented. Comparison of the calculated concentrations and fluxes with alternative approaches clearly illustrates the need to consider advection processes. Consideration of the different features of contaminant transport due to varying pore‐water velocity fields in primary consolidation and secondary consolidation stages is achieved via the use of non‐uniform initial concentration distributions within the proposed analytical solutions. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Advances in pore-scale imaging (e.g., μ-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utilized for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.We implement a phase-field model for the direct pore-scale simulation of incompressible flow of two immiscible fluids. The model naturally lends itself to the transport of fluids with large density and viscosity ratios. In the phase-field approach, the fluid-phase interfaces are expressed in terms of thin transition regions, the so-called diffuse interfaces, for increased computational efficiency. The conservation law of mass for binary mixtures leads to the advective Cahn–Hilliard equation and the condition that the velocity field is divergence free. Momentum balance, on the other hand, leads to the Navier–Stokes equations for Newtonian fluids modified for two-phase flow and coupled to the advective Cahn–Hilliard equation. Unlike the volume of fluid (VoF) and level-set methods, which rely on regularization techniques to describe the phase interfaces, the phase-field method facilitates a thermodynamic treatment of the phase interfaces, rendering it more physically consistent for the direct simulations of two-phase pore-scale flow. A novel geometric wetting (wall) boundary condition is implemented as part of the phase-field method for the simulation of two-fluid flows with moving contact lines. The geometric boundary condition accurately replicates the prescribed equilibrium contact angle and is extended to account for dynamic (non-equilibrium) effects. The coupled advective Cahn–Hilliard and modified Navier–Stokes (phase-field) system is solved by using a robust and accurate semi-implicit finite volume method. An extension of the momentum balance equations is also implemented for Herschel–Bulkley (non-Newtonian) fluids. Non-equilibrium-induced two-phase flow problems and dynamic two-phase flows in simple two-dimensional (2-D) and three-dimensional (3-D) geometries are investigated to validate the model and its numerical implementation. Quantitative comparisons are made for cases with analytical solutions. Two-phase flow in an idealized 2-D pore-scale conduit is simulated to demonstrate the viability of the proposed direct numerical simulation approach. 相似文献
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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
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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
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A recursion formulation for the transverse spreading of a solute is developed, and under conditions of steady flow in a stratified aquifer, the transport of a linearly sorbing solute undergoing nonequilibrium sorption is studied. The effect of spatial variability in the velocity field and the sorption kinetics are modeled to see the combined effect of the two processes on the spreading of the solute injected at a point in the aquifer. The main result of this work is a transport model based on a discrete formulation that includes local dispersion and leads to nonasymptotic behavior in the spreading of the plume in a direction normal to the mean flow velocity. 相似文献
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Multi-phase flow in porous media in the presence of viscous, gravitational, and capillary forces is described by advection diffusion equations with nonlinear parameters of relative permeability and capillary pressures. The conventional numerical method employs a fully implicit finite volume formulation. The phase-potential-based upwind direction is commonly used in computing the transport terms between two adjacent cells. The numerical method, however, often experiences non-convergence in a nonlinear iterative solution due to the discontinuity of transmissibilities, especially in transition between co-current and counter-current flows. Recently, Lee et al. (Adv. Wat. Res. 82, 27–38, 2015) proposed a hybrid upwinding method for the two-phase transport equation that comprises viscous and gravitational fluxes. The viscous part is a co-current flow with a one-point upwinding based on the total velocity and the buoyancy part is modeled by a counter-current flow with zero total velocity. The hybrid scheme yields C1-continuous discretization for the transport equation and improves numerical convergence in the Newton nonlinear solver. Lee and Efendiev (Adv. Wat. Res. 96, 209–224, 2016) extended the hybrid upwind method to three-phase flow in the presence of gravity. In this paper, we present the hybrid-upwind formula in a generalized form that describes two- and three-phase flows with viscous, gravity, and capillary forces. In the derivation of the hybrid scheme for capillarity, we note that there is a strong similarity in mathematical formulation between gravity and capillarity. We thus greatly utilize the previous derivation of the hybrid upwind scheme for gravitational force in deriving that for capillary force. Furthermore, we also discuss some mathematical issues related to heterogeneous capillary domains and propose a simple discretization model by adapting multi-valued capillary pressures at the end points of capillary pressure curves. We demonstrate this new model always admits a consistent solution that is within the discretization error. This new generalized hybrid scheme yields a discretization method that improves numerical stability in reservoir simulation. 相似文献
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A dynamic theory of hydrocarbon migration 总被引：1，自引：0，他引：1
This paper presents a new analysis of secondary migration of hydrocarbon that does not require capillary forces for trapping, but instead uses the method of characteristics and wave theory. The waves change speed and either reflect or refract (or partially reflect and partially refract) as they contact with layers of different flow capacities. Reflection of a certain wave from a boundary starts hydrocarbon accumulation below that boundary. The method is easy to use and conforms readily to graphical solution. For the sake of simplicity there is only two-phase flow. The application of this method gives new insights into the physics of migration and entrapment of oil. The method gives realistic times for oil accumulation and points to oil generation rate as the most sensitive variable. Oil and water densities, viscosities, and permeability are also important. We find that at the very small generation rates usually assumed the time required to develop a given column thickness is insensitive to the distance from the source rock. In general, the method also predicts a non-uniform saturation in the oil column caused by an interaction between buoyancy and viscous forces. Being based on the dynamic interactions of viscous and buoyancy forces, our theory is considerably at odds with hydrostatic approaches. We assume no capillary pressure, one-dimensional flow, and no regional groundwater flow, conditions which are not realized in actual migration. The theory should be viewed therefore as an end member of a more general theory; nevertheless, the largely graphical solutions give fundamental insights that are difficult to obtain by other techniques. 相似文献
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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
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A. P. S. Selvadurai 《国际地质力学数值与分析法杂志》2004,28(2):191-208
This paper examines the problem of the advective transport of a contaminant from sources in the shape of either a penny-shaped crack or an elongated needle-shaped cavity located in a porous medium of infinite extent. The advective transport is induced by Darcy flow in the porous medium, where the internal boundary is maintained at a constant potential. The paper presents an approximate analytical solution to this problem, which is deduced from a formulation that models a cavity in the shape of either an oblate or a prolate spheroid. The results also represent one of the few spatially three-dimensional exact analytical solutions for the, albeit linear, hyperbolic problem governing the contaminant transport problem. The paper also presents a canonical proof of uniqueness for advective contaminant transport problems associated with media of infinite extent. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Numerical modeling of two-phase fluid flow and oil slick transport in estuarine water 总被引：6，自引：6，他引：0
M. Nagheeby M.Sc. M. Kolahdoozan Ph.D. 《International Journal of Environmental Science and Technology》2010,7(4):771-784
Oil spills is one of the most important hazards in the estuarine and coastal water. In recent decades, engineers try to predict the status of oil slick to manage the pollution spreading. The prediction of oil slick transport is carried out mainly by means of numerical models. In the current study, the development and application of a two-phase fluid flow model to simulate oil transport in the marine environment are presented. Different transport and fate processes are included in the developed model. The model consists of the Lagrangian method for the advection process, the Random Walk technique for horizontal diffusion process and the empirical equations for the fate processes. The major forces for driving oil particles are fluid current, wind speed and turbulent flow. Therefore, the multi-component hydrocarbon method has been included to the developed model in order to predict fate processes. As prediction of particle velocity components is of major importance for oil slick advection, therefore the binomial interpolation procedure has been chosen for the particle velocity components computations. In addition, shoreline boundary condition is included in the developed model to simulate shore response to oil slick transport near the beaches. The results of the model applications are compared with the analytical solutions, experimental measurements and other numerical models cited in literature. Comparisons of different sets of results represent the capability of developed model to predict the oil slick transport. In addition, the developed model is tested for two oil spill cases in the Persian Gulf. 相似文献
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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. 相似文献
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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
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Conventional modelling of transport problems for porous media usually assumes that the Darcy flow velocities are steady. In certain practical situations, the flow velocity can exhibit time‐dependency, either due to the transient character of the flow process or time dependency in the boundary conditions associated with potential flow. In this paper, we consider certain one‐ and three‐dimensional problems of the advective transport of a chemical species in a fluid‐saturated porous region. In particular, the advective flow velocity is governed by the piezo‐conduction equation that takes into account the compressibilities of the pore fluid and the porous skeleton. Time‐ and/or mesh‐refining adaptive schemes used in the computational modelling are developed on the basis of a Fourier analysis, which can lead to accurate and optimal solutions for the advective transport problem with time‐ and space‐dependent advective flow velocity distributions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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为研究江汉平原—大别山区过渡带黏性层状土中溶质迁移的规律,以保守性阴离子Br-为示踪剂,通过等温吸附试验、一维弥散试验、HYDRUS-1D软件模拟反演手段,研究了Br-在黏性层状土中的吸附参数、迁移规律,模拟反演其弥散参数。结果表明：（1）Freundlich模型和Langmuir模型均能较好的拟合吸附试验结果,随着土壤中黏粒比例的增大,土壤对Br-的饱和吸附量有所增加;（2）层状土中土壤质地与结构均会影响穿透曲线的形状,但一维饱和土柱中的弥散过程主要取决于含水介质系统中黏性颗粒的占比,黏粒的增加会对溶质运移产生阻碍作用;（3）通过HYDRUS-1D软件构建模型反演弥散参数,R2均大于0.991,拟合效果较好,分析发现层状土中无论土壤组成类型还是层厚及排序的影响,其本质都是改变了土壤的平均孔隙流速从而影响弥散作用,平均孔隙流速越小其弥散系数越小;（4）试验中粉质黏土弥散系数约为0.005～0.048 cm2/d,远远小于下部砂土弥散系数0.524～7.477 cm2/d,差值达到了至少两个数量级,表明研究区内厚层黏土为控制地层,会较大程度阻碍地下水中溶质运移,上部含水层中的污染物或有机... 相似文献
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The fate and movement of dissolved substances in soils and groundwater has generated considerable concern for the quality of the subsurface environment. Many analytical solutions for the partial differential equations that describe solute and pollutant movement exist. Numerical solutions are more general, and often more difficult to verify. In order to determine the model error, the examination of the ability of numerical methods compared to analytical methods is strongly recommended. The objective of the study is to make a comparison between numerical and analytical solution models for solute transport equation. In this study, the numerical solution calculated with the WAVE-model is compared with the analytical solution calculated with CXTFTT-model. The study scenarios considered variables such as compartment depth, applied flux at the top and soil dispersivity under steady-state conditions. The simulations depend on 27 solute infiltration scenarios. The solute concentrations were calculated with the WAVE-model and the CXTFIT-model for each scenario. The WAVE-model error was evaluated with three methods: absolute average maximum error, relative average maximum error and relative average area error. The study implied that the WAVE-model error increased with the increase of the compartment depth, decreasing soil dispersivity, and decrease in flux. The study leads to the recommendation to use compartment depth as thin as possible to minimise the WAVE-model error. Furthermore, it is more useful to use several numerical solution models, such as SWMS-2D model, to evaluate and examine the WAVE-model. 相似文献
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1 IntroductionIncorporation of potentially toxic metals ( e.g.Cd, Cu, Cr, Pb, Hg, As, Se, Zn, Ni) into soils ei-ther through sewage-sludge irrigation or some othersources of pollution (e.g. atmospheric deposition, ap-plication of agri-chemicals) has posed… 相似文献