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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
3.
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
4.
Sorption is a well-known phenomenon that may cause the retardation effect of zinc in the subsurface environment. In this study, the governing process for zinc sorption during transport was investigated by conducting 2-D plume tests in a laboratory scale sand tank model using the time domain reflectometry (TDR) method. Tracer solutions of NaNO3 and ZnSO4 were applied at a constant flow rate as a pulse type to capture the plumes of both solutes based on TDR-measured resistance. It was revealed that the observed zinc sulfate plume showed no retardation relative to sodium nitrate with a retardation factor of R ≈ 1. Instead of retardation, a prominent reduction of zinc sulfate mass occurred during transport through the tank model due to the irreversible sorption as well as longitudinal dispersion. This indicates that the controlling factor for the sorption process of zinc sulfate in the sand tank model is kinetic rather than equilibrium. These hydrogeological parameters would provide valuable information on the prediction of the fate of zinc in sandy aquifer materials. 相似文献
5.
Sandra Freiboth Holger Class Rainer Helmig Tobias Graf Wolfgang Ehlers Viktoria Schwarz Christos Vrettos 《Computational Geosciences》2009,13(3):281-300
Multiphase flow processes in unsaturated cohesive soils are often affected by deformation due to swelling and shrinking as
a result of varying water contents. This paper presents a model concept which is denoted ‘phenomenological’ in terms of the
processes responsible for soil deformation, since the effects of deformation on flow and transport are only considered by
constitutive relations that allow an adaptation of the hydraulic properties. This new model is validated in a detailed intercomparison
study with two state-of-the-art models that are capable of explicitly describing the processes relevant for the deformation.
A ‘numerical experiment’ with a state-of-the-art reference model is used to produce ‘measurement data’ for an inverse-modelling-based
estimation of the model input parameters for the phenomenological concept. 相似文献
6.
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
7.
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
8.
Johannes Schoenherr Zsolt Schléder Janos L. Urai Ralf Littke Peter A. Kukla 《International Journal of Earth Sciences》2010,99(5):1007-1025
We compared microstructures of Late Pre-Cambrian to Early Cambrian Ara Salt diapirs from the deep subsurface (3.5–5 km) of
the South Oman Salt Basin and from surface-piercing salt domes of the Ghaba Salt Basin. Laterally, these basins are approximately
500 km apart but belong to the same tectono-sedimentary system. The excellent data situation from both wells and outcrops
allows a unique quantification of formation and deformation mechanisms, spanning from sedimentation to deep burial, and via
re-activated diapir rise to surface piercement. Microstructures of gamma-irradiated and etched thin sections indicate dislocation
creep and fluid-assisted grain boundary migration as the main deformation mechanisms operating in the deep subsurface. Microstructures
from the surface are characterised by large ‘old’ subgrain-rich crystals. These ‘old’ grains are partly replaced by ‘new’
subgrain-free and subgrain-poor crystals, which show gamma irradiation-decorated growth bands and fibrous microstructures,
indicative of pressure solution creep and static recrystallisation, most likely due to surface piercement and exposure. Using
subgrain size piezometry, the maximum differential stresses for the subsurface salt is 1.7 MPa and those for the surface-piercing
salt is 3.4 MPa, the latter value displaying the high stress conditions in the diapir ‘stem’ as the salt rises on its way
to the surface. 相似文献
9.
Yannick Caillabet Pierre Fabrie Didier Lasseux Michel Quintard 《Computational Geosciences》2001,5(2):121-150
In this work, we are interested in solute transport in fissured porous media. The medium is considered as a special case of a two-region system, and a two-equation model previously obtained from a volume averaging technique is used to derive large-scale dispersion coefficients. These coefficients are obtained as solutions of a set of closure problems and the main objective of this work is to present an efficient method to solve these closure problems. The method makes use of an unstructured grid and special techniques to take into account the fissure network. Results are compared with other existing methods on simple fissured media. Finally, the technique is applied to a complex structure. 相似文献
10.
This study was based on the discrete fracture model to investigate the influence of fracture parameters on the solute transport
in the fractured rocks of andesite in Lan-Yu island, Taiwan. In the simulation cases, the centers of fractures, fracture lengths
and apertures were assumed to have Poisson’s distribution, negative exponential distribution and lognormal distribution, respectively.
With the above assumptions, constructing the discrete fracture model became practicable. Using the mass-balance equation with
specified boundary conditions, the flow field in the rock was solved. Then particles were released under the flow field. Monte
Carlo method was used assuming that the amount of particles was proportional to the flow rates to get the particle accumulated
percentage breakthrough curve and to estimate the dispersion coefficient. On the basis of the discrete fracture model, it
was possible to evaluate the property of dispersion behavior of andesite in Lan-Yu Island with flow and transport mechanism.
Properties of the dispersion behavior such as the relation between distance and traveling-time (ln〈r
2〉 and ln 〈t〉), anisotropic behavior, and the overall dispersion coefficient in a fracture network were characterized: the slope value
of ln〈r
2〉 and ln〈t〉 was 1.64 an indication of non-Fickian dispersion, the particles dispersion along the flow (D11) was bigger than that perpendicular
to the flow (D22), and the dispersion coefficient by this study was 0.91 m comparing the value 1 m from Sauty’s method. 相似文献
11.
Three-phase numerical model of water migration in partially frozen geological media: model formulation,validation, and applications 总被引：3，自引：0，他引：3
Scott L. Painter 《Computational Geosciences》2011,15(1):69-85
Water in the subsurface of the Earth’s cold regions—and possibly the subsurface of Mars—resides in the liquid, vapor, and
ice phases. However, relatively few simulations addressing full three-phase, nonisothermal water dynamics in below-freezing
porous media have been undertaken. This paper presents a nonisothermal, three-phase approach to modeling water migration in
partially frozen porous media. Conservation equations for water (as ice, liquid, and vapor) and a single gas species (in the
gas phase and dissolved in water) are coupled to a heat transport equation and solved by a finite-volume method with fully
implicit time stepping. Particular attention is given to the method of spatial differencing when the pore space is partially
filled with ice. The numerical model is able to reproduce freezing-induced water redistribution observed in laboratory experiments.
Simulations of Earth permafrost dynamics and of the formation and evolution of a planetary-scale cryosphere on Mars demonstrate
the new capabilities. 相似文献
12.
Sameh A. Sakr 《Hydrogeology Journal》1999,7(2):155-160
The problem of seawater intrusion is considered for the case of a confined coastal aquifer in which there is steady seaward
flow of fresh water. Using the GWCH2O model, the problem is solved first for the case of no dispersion where a distinct interface
exists separating the fresh water from the salt water. The problem is solved next by taking into account dispersion and diffusion
of the salt-water component, along with the density effect. In this respect, a two-dimensional finite-element model, 2D-VDTRAN,
is developed to simulate density-dependent solute transport.
To investigate the limitation of the sharp-interface approach in coastal aquifers for conditions of both steady state and
unsteady state, the problem is solved twice using the two models with different parameter values. These parameters are combined
in dimensionless form, resulting in four named parameters: seepage factor (A); dispersion-to-advection ratio (B); geometry
ratio (C); and time-scale factor (T). Using the density-dependent model, the dimensionless width of the transition zone (W/L)
is determined for different values of A, B, C, and T. Steady-state simulations show that the sharp-interface approach is valid
only when the system is dominated by advection, i.e., when 0<B≤5% for all values of A and C, or when A≥65% for all values
of B and C. However, the unsteady-state analysis shows that the applicability of the sharp-interface approach is sufficiently
accurate at early times.
Received, October 1997 Revised, June 1998, October 1998 Accepted, November 1998 相似文献
13.
R. C. Dey 《Journal of the Geological Society of India》2009,74(1):131-137
The subsurface Nagaur Basin in northwest Haryana and southwest Punjab hosts evaporite sequence, conformably overlain by Nagaur
red beds and grey beds. A polymictic conglomerate intervenes the Nagaur sequence and the overlying Tertiary sequence. The
focus is on the new finds of (i) distinctive ‘grey beds’ overlying ubiquitous red beds, (ii) ‘Malout conglomerate and grit’
horizon (Palaeocene-Miocene) marking an unconformity over the Nagaur Group (early Cambrian) and (iii) ‘entrapped gas and dried-up
leaves/carbonaceous flakes’ in the conglomerate unit and succeeding Tertiary rocks. Palaeoenvironmental significance has been
discussed. The Nagaur ‘red beds’ has been likened to ‘continental red beds’ of Schreiber (1978) and ‘reworked red beds’ of
Krynine (1949). The ‘grey beds’ are channel fillings, fresh material having been derived from fresh cuttings by streams/rivers
following structural grains in the Aravalli landscape where the interfluves provided weathered (oxidised) materials for the
red beds. Association of continental red beds and grey beds is known in the Newark Series (Triassic) of the Eastern United
States and the Keweenawan ‘late Precambrian’ of the Lake Superior region. 相似文献
14.
15.
Peter C. Lichtner 《Geochimica et cosmochimica acta》1985,49(3):779-800
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. 相似文献
16.
Sheng Peng 《Frontiers of Earth Science》2009,3(2):208-213
Heap leaching is essentially a process in which metals are extracted from mine ores with lixiant. For a better understanding
and modeling of this process, solute transport parameters are required to characterize the solute transport system of the
leach heap. For porous media like leach ores, which contain substantial gravelly particles and have a broad range of particle
size distributions, traditional small-scale laboratory experimental apparatus is not appropriate. In this paper, a 2.44 m
long, 0.3 m inner diameter column was used for tracer test with boron as the tracer. Tracer tests were conducted for 2 bulk
densities (1.92 and 1.62 g/cm3) and 2 irrigation rates (2 and 5 L/ (m2·h−1)). Inverse modeling with two-region transport model using computer code CXTFIT was conducted based on the measured breakthrough
curves to estimate the transport parameters. Fitting was focused on three parameters: dispersion coefficient D, partition coefficient β, and mass transfer coefficient ω. The results turned out to fall within reasonable ranges. Sensitivity
analysis was conducted for the three parameters and showed that the order of sensitivity is β > ω > D. In addition, scaling of these parameters was discussed and applied to a real scale heap leach to predict the tracer breakthrough. 相似文献
17.
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
18.
A comparative analysis of several vulnerability concepts 总被引：2，自引：0，他引：2
A comparative analysis of six vulnerability models aims to identify differences and similarities between several approaches
towards understanding vulnerability. The analysis yields a set of characteristics for explaining the condition of vulnerability
(multiple contexts, multiple dimensions, temporal variability, multiple scales and scale-interdependency). In addition, ‘adaptation’
and ‘adaptive capacity’ are identified as key elements of vulnerability. The results of the analysis are put into a wider
context not only of vulnerability but also of resilience and risk research. It is demonstrated that ‘adaptation’ and ‘adaptive
capacity’ serve as hinges not only for conceptualising vulnerability but between ‘vulnerability’ and ‘resilience’ alike. Based
on the results of the comparative analysis, a model of vulnerability focussing on the household and community scale is developed,
which displays the key findings of this work. 相似文献
19.
A new model for unsaturated flow in porous media, including capillary hysteresis and dynamic capillary effects, is analyzed. Existence and uniqueness of solutions are established and qualitative and quantitative properties of (particular) solutions are analyzed. Some results of numerical computations are given. The model under consideration incorporates simple play-type hysteresis and a dynamic term (time-derivative with respect to water content) in the capillary relation. Given an initial water content distribution, the model determines which parts of the flow domain are in drainage and which parts are in imbibition. The governing equations can be recast into an elliptic problem for fluid pressure and an evolution equation for water content. Standard methods are used to obtain numerical results. A comparison is given between J.R. Philip's semi-explicit similarity solution for horizontal redistribution in an infinite one-dimensional domain and solutions of the new model. 相似文献
20.
The underground transport of pathogenic bacteria and viruses may be described by the general transport equation considering
dispersion, adsorption, and biological elimination. The survival time of bacteria and viruses in groundwater is different
for the specific species and for the specific groundwater environment.
Dispersion causes a distribution of pollutants in time and space, thus their concentration decreases over time and with transport
distance. Microorganisms are reversibly adsorbed on underground particles, which causes a retardation of their transport velocity
with respect to groundwater flow velocity. An additional approach is provided by the filter theory.
Presented at the International Symposium, International Association of Hydrogeologists, “Impact of Agricultural Activities
on Ground Water Quality and Quantity,” Prague, Czechoslovakia, September, 1982. 相似文献