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1.
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
2.
Fluid exchange across the sediment–water interface in a sandy open continental shelf setting was studied using heat as a tracer. Summertime tidal oscillation of cross-shelf thermal fronts on the South Atlantic Bight provided a sufficient signal at the sediment–water interface to trace the advective and conductive transport of heat into and out of the seabed, indicating rapid flushing of ocean water through the upper 10–40 cm of the sandy seafloor. A newly developed transport model was applied to the in situ temperature data set to estimate the extent to which heat was transported by advection rather than conduction. Heat transported by shallow 3-D porewater flow processes was accounted for in the model by using a dispersion term, the depth and intensity of which reflected the depth and intensity of shallow flushing. Similar to the results of past studies in shallower and more energetic nearshore settings, transport of heat was greater when higher near-bed velocities and shear stresses occurred over a rippled bed. However, boundary layer processes by themselves were insufficient to promote non-conductive heat transport. Advective heat transport only occurred when both larger boundary layer stresses and thermal instabilities within the porespace were present. The latter process is dependent on shelf-scale heating and cooling of bottom water associated with upwelling events that are not coupled to local-scale boundary layer processes. 相似文献
3.
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
4.
Stable-isotope profiles show that flat-lying marble units acted as impermeable barriers to upward fluid flow in transitional amphibolite-granulite grade rocks of the Kigluaik Mountains, Seward Peninsula, Alaska. The degree of permeability is related to the composition of the marble. The margin of a thick pure dolomite marble chemically reacted with underlying metasyenite (aH2O=0.2) to form a 2 cm boundary layer of calcite + forsterite by introduction of SiO2. No fluid penetrated past this reaction front, although the high temperature of metamorphism (800°C) allowed transport of carbon and oxygen isotopes for an additional 2 cm by diffusion through the solid dolomite. A second marble with a higher silica content underwent more decarbonation, which enhanced porosity and lead to a greater extent of isotope transport (2–3 m) in contact with quartzo-feld-spathic gneiss below. An estimate of total fluid flux across the bottom of this marble layer based on the shape of the isotope profile is 1 cm3/cm2 directed down, out of the marble. At two other marble-gneiss contacts steep isotopic gradients coincide with lithologic contacts, indicating very little cross-lithology fluid flow. The extent of diffusional transport of isotopes in the marbles is limited and interpreted as indicating the transient presence of a pore fluid, generated by thermally driven devolatilization reactions. No wholesale pervasive advection of C-O-H fluid occurred across the thick, continuous, marble units near the exposed base of the Kigluaik Group section during the entire regional metamorphic cycle. Activities of pore-fluid species were controlled by internal processes. Movement of volatiles and stable-isotopes between contrasting rock-types was dominantly diffusive. Channelized fluid pathways through the marble units developed during uplift and cooling but were not present during peak metamorphism. Heating of the section occurred by conduction, probably from an underlying magma source, and not by advection of a C-O-H fluid. 相似文献
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6.
分析了运移参数的变化对GCL中污染物运移的影响。从衬垫底部浓度比、对流和扩散通量、污染物累积运移量等方面,对污染物在GCL中的运移进行了计算。结果表明,减小渗透系数和扩散系数可以有效减缓衬垫底部浓度比的增加速度。渗透系数对对流通量的大小、扩散通量的变化速度的影响较大;扩散系数主要影响最大扩散通量。当渗透系数较大时,可以忽略扩散累积运移量,用对流累积运移量代替总累积运移量引起的误差很小。当渗透系数较小时,忽略扩散运移量可能产生较大的误差,尤其是在扩散系数也较大的情况下误差更加明显。 相似文献
7.
The importance of relict burrow structures and burrow irrigation in controlling sedimentary solute distributions 总被引：1，自引：0，他引：1
Robert C. Aller 《Geochimica et cosmochimica acta》1984,48(10):1929-1934
Some areas of the seafloor, particularly the deep sea, are characterized by large numbers of apparently uninhabited or relict burrow structures formed by macrobenthic organisms. Because of low sedimentation rates or lack of physical disturbance these structures are stable for long periods of time and could potentially influence solute diffusion patterns in surface sediments. A two-dimensional diffusionreaction model which allows for diffusive rather than advective transport within stagnant, water-filled burrows demonstrates that, in the absence of advective irrigation, relict burrow structures are unlikely in most cases to significantly alter average solute distributions from those predicted by one-dimensional vertical models. This conclusion assumes changes in diffusive transport properties alone and does not account for any effects of relict structures on reaction rates or physical ventilation of deposits by bottom currents. Significant changes (≥5%) in solute distributions are generally produced only when the ratio of the halfdistance between burrows to relict burrow radii is ≤10 and sedimentary diffusion coefficients are ≤60% that in free solution. Because solute distributions in stagnant burrow waters are nearly that in surrounding sediment, sediment-water solute fluxes are also essentially unaffected by relict burrows except at extremely high abundances or fairly large differential diffusion rates between sediment and free solution. In contrast, even at low abundance, biologically irrigated or physically ventilated burrows produce major changes in solute transport and build-up patterns. 相似文献
8.
A Lagrangian perturbation method is applied to develop a method of moments for reactive solute flux through a three-dimensional, nonstationary flow field. The flow nonstationarity may stem from medium nonstationarity, finite domain boundaries, and/or fluid pumping and injecting. The reactive solute flux is described as a space–time process where time refers to the solute flux breakthrough in a control plane at some distance downstream of the solute source and space refers to the transverse displacement distribution at the control plane. The analytically derived moments equations for solute transport in a nonstationary flow field are too complicated to solve analytically; therefore, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. The approach provides a tool to apply stochastic theory to reactive solute transport in complex subsurface environments. Several case studies have been conducted to investigate the influence of the physical and chemical heterogeneity of a medium on the reactive solute flux prediction in nonstationary flow field. It is found that both physical and chemical heterogeneity significantly affect solute transport behavior in a nonstationary flow field. The developed method is also applied to an environmental project for predicting solute flux in the saturated zone below the Yucca Mountain Project area, demonstrating the applicability of the method in practical environmental projects. 相似文献
9.
Alan E. Boudreau 《Contributions to Mineralogy and Petrology》2008,156(4):431-437
The Merensky pegmatoid (normal reef) in the western Bushveld Complex is commonly characterized as a pyroxene-rich pegmatoidal
unit with a base that is enriched in chromite and platinum-group element-bearing sulfides overlying a leuconorite footwall.
Models for its formation have ranged from those that view it as entirely a magmatic cumulate succession to those that have
suggested that it is a zone of volatile-induced remelting. The consequences of the latter interpretation are investigated
using the numerical modeling program IRIDIUM, which links diffusive and advective mass and heat transport with a phase equilibration
routine based on the MELTS program. The initial system consists of a simple stratigraphic succession of a partially molten
leuconorite overlain by a partially molten pyroxenite, both initially at 1,190°C and 2 kbar. 2 wt% of a volatile fluid composed
of 75 mol% H2O, 20 mol% CO2 and 5 mol% H2S is then added to the lower 20 cm of the pyroxenite. The system is then allowed to evolve under conditions of chemical diffusion
in the liquid. The addition of the volatile components results in a modest increase in the amount of melt in the pyroxenite.
However, chemical diffusion across the leuconorite–pyroxenite boundary leads to more extensive melting at and below the boundary
with preferential loss of opx from the underlying leuconorite, preferential re-precipitation of sulfide and chromite and concentration
of the PGE at this boundary. These results mimic actual mineral and compositional profiles across the Merensky pegmatoid and
illustrate that long-term diffusion process can effectively produce mineralogical and compositional layering not present in
the original assemblage. 相似文献
10.
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
11.
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
12.
Observations of tidal trapping in a channel connected to large volumes along its perimeter showed that the exchange between
them is driven by advection due to tidal flows. Therefore, quantifying the longitudinal dispersion of scalars in the channel
that results from tidal trapping was not possible using traditional frameworks, which assume that the exchange is a diffusive
process. This study uses the concentration moment method to solve analytically for the dispersion coefficient of a solute
in a tidal channel which exchanges advectively with volumes along its edges. This constitutes a new framework for analyzing
the longitudinal dispersion that results from tidal trapping in systems such as a branching tidal channel or the breached
salt ponds of San Francisco Bay. A comparison of dispersion coefficients from traditional, diffusion-driven frameworks for
tidal trapping, the new advective framework derived in the present study, and observations show that the new formulation is
best suited to this environment. 相似文献
13.
Ø. Hammer D.K. Dysthe H. Lund P. Meakin B. Jamtveit 《Geochimica et cosmochimica acta》2008,72(20):5009-5021
We present a 2D numerical model for the growth of calcite from supersaturated aqueous solutions under laminar, open-channel flow conditions. The model couples solution chemistry, precipitation at solution/calcite interfaces, hydrodynamics, diffusion and degassing. The model output is compared with experimental results obtained using an oversaturated calcite solution produced by mixing CaCl2 and Na2CO3. The precipitation rate is observed to increase when the supersaturated solution flows over an obstruction, leading to a growth instability that causes the formation of terraces. At relatively high flow rates, the most important mechanism for this behaviour seems to be hydrodynamic advection of dissolved species either towards or away from the calcite surface, depending on location relative to the obstruction, which deforms the concentration gradients. At lower flow rates, steepening of diffusion gradients around protrusions becomes important. Enhanced degassing over the obstruction due to shallowing and pressure drop is not important on small scales. Diffusion controlled transport close to the calcite surface can lead to a fingering-type growth instability, which generates porous textures. Our results are consistent with existing diffusive boundary layer theory, but for flow over non-smooth surfaces, simple calcite precipitation models that include empirical correlations between fluid flow rate and calcite precipitation rate are inaccurate. 相似文献
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15.
A time-splitting approach for advection–dispersion equations is considered. The dispersive and advective fluxes are split into two separate partial differential equations (PDEs), one containing the dispersive term and the other one the advective term. On triangular elements a triangle-based high resolution Finite Volume (FV) scheme for advection is combined with a Mixed Hybrid Finite Element (MHFE) technique to solve dispersion. This approach introduces an error proportional to the time step and the overall scheme is only first order accurate if special care is not taken in the definition of the numerical flux approximation for advection. By incorporating the diffusive effects into the definition of this numerical flux, near second order accuracy (up to a logh factor) can be proved theoretically and validated by numerical experiments in both one- and two-dimensional cases. 相似文献
16.
Abstract Garnet granulites from Sri Lanka preserve textural and chemical evidence for prograde equilibration at temperatures of at least 700–750°C and pressures in the vicinity of 6–8 kbar. Associated strain patterns suggest prograde metamorphism occurred during and immediately following an episode of crustal thickening, with the prograde P–T conditions probably reflecting a combination of the conductive and advective transport of heat at the mid-levels of tectonically thickened crust. The occurrence of prograde wollastonite provides evidence for internally buffered fluid compositions, or fluid absent conditions, during peak metamorphism and precludes pervasive advection of a CO2 -rich fluid. The advective heat component is therefore likely to have been provided by the transport of silicate melt. Intricate symplectitic textures record partial re-equilibration of the garnet granulites to lower pressures (˜ 4–6 kbar) at high temperatures (600–750°C), and testify either to the erosional denudation of the overthick crust prior to significant cooling (i.e. quasi-isothermal decompression) or to a subsequent static heating possibly of early Palaeozoic age (Pan-African). The metamorphic history of the Sri Lankan granulites is compared with high grade terrains in the neighbouring fragments of Gondwana, with the emphasis on similarities with Proterozoic granulites of the East Antarctic craton. 相似文献
17.
Hui-Hai Liu 《Hydrogeology Journal》2014,22(7):1525-1534
In clay or other low-permeability media, water flow becomes non-Darcian and characterized by the non-linear relationship between water flux and hydraulic gradient. This work is devoted to addressing a number of key issues related to geological disposal of high-level nuclear waste in clay/shale formations. It is demonstrated that water flow velocity in the damaged zone (often considered as a potential preferential advection paths in a repository) surrounding the tunnel is extremely small, as a result of non-Darcian flow behavior, such that solute transport is dominated by diffusion, rather than advection. The finding is also consistent with the often-observed existence of persistent abnormal pressures in shale formations. While relative permeability is the key parameter for modeling the unsaturated flow process, without incorporating non-Darcian flow behavior, significant errors can occur in the determination of relative permeability values from traditional measurement methods. An approach for dealing with temperature impact on non-Darcian flow and a formulation to calculate non-Darcian water flux in an anisotropic medium are presented, taking into consideration that a geological repository is subject to temperature evolution in the near field as a result of heat generated by nuclear waste, and that shale formations are generally anisotropic. 相似文献
18.
Astrid Holstad 《Computational Geosciences》2000,4(2):103-139
We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous
media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the time integration
are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming
two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable
sized rectangular grids we choose limited κ=
related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular
grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
A transition region may be defined as a region of rapid change in medium properties about the interface between two porous media or at the interface between a porous medium and a reservoir. Modelling the transition region between different porous media can assist in the selection of the most appropriate boundary conditions for the standard advection–dispersion equation (ADE). An advantage of modelling the transition region is that it removes the need for explicitly defining boundary conditions, though boundary conditions may be recovered as limiting cases. As the width of a transition region is reduced, the solution of the transition region model (TR model) becomes equivalent to the solution of the standard ADE model with correct boundary conditions. In this paper numerical simulations using the TR model are employed to select the most appropriate boundary conditions for the standard ADE under a variety of configurations and conditions. It is shown that at the inlet boundary between a reservoir and porous medium, continuity of solute mass flux should be used as the boundary condition. At the boundary interface between two porous media both continuity of solute concentration and solute mass flux should be used. Finally, in a finite porous medium where the solute is allowed to advect freely from the exit point, both continuity of solute concentration and solute mass flux should be used as the outlet boundary condition. The findings made here are discussed with reference to a detailed review of previous relevant theoretical and experimental observations. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
20.
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