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1.
A generalized, efficient, and practical approach based on the travel‐time modeling framework is developed to estimate in situ reaction rate coefficients for groundwater remediation in heterogeneous aquifers. The required information for this approach can be obtained by conducting tracer tests with injection of a mixture of conservative and reactive tracers and measurements of both breakthrough curves (BTCs). The conservative BTC is used to infer the travel‐time distribution from the injection point to the observation point. For advection‐dominant reactive transport with well‐mixed reactive species and a constant travel‐time distribution, the reactive BTC is obtained by integrating the solutions to advective‐reactive transport over the entire travel‐time distribution, and then is used in optimization to determine the in situ reaction rate coefficients. By directly working on the conservative and reactive BTCs, this approach avoids costly aquifer characterization and improves the estimation for transport in heterogeneous aquifers which may not be sufficiently described by traditional mechanistic transport models with constant transport parameters. Simplified schemes are proposed for reactive transport with zero‐, first‐, nth‐order, and Michaelis‐Menten reactions. The proposed approach is validated by a reactive transport case in a two‐dimensional synthetic heterogeneous aquifer and a field‐scale bioremediation experiment conducted at Oak Ridge, Tennessee. The field application indicates that ethanol degradation for U(VI)‐bioremediation is better approximated by zero‐order reaction kinetics than first‐order reaction kinetics.  相似文献   

2.
This pore-scale modeling study in saturated porous media shows that compound-specific effects are important not only at steady-state and for the lateral displacement of solutes with different diffusivities but also for transient transport and solute breakthrough. We performed flow and transport simulations in two-dimensional pore-scale domains with different arrangement of the solid grains leading to distinct characteristics of flow variability and connectivity, representing mildly and highly heterogeneous porous media, respectively. The results obtained for a range of average velocities representative of groundwater flow (0.1–10 m/day), show significant effects of aqueous diffusion on solute breakthrough curves. However, the magnitude of such effects can be masked by the flux-averaging approach used to measure solute breakthrough and can hinder the correct interpretation of the true dilution of different solutes. We propose, as a metric of mixing, a transient flux-related dilution index that allows quantifying the evolution of solute dilution at a given position along the main flow direction. For the different solute transport scenarios we obtained dilution breakthrough curves that complement and add important information to traditional solute breakthrough curves. Such dilution breakthrough curves allow capturing the compound-specific mixing of the different solutes and provide useful insights on the interplay between advective and diffusive processes, mass transfer limitations, and incomplete mixing in the heterogeneous pore-scale domains. The quantification of dilution for conservative solutes is in good agreement with the outcomes of mixing-controlled reactive transport simulations, in which the mass and concentration breakthrough curves of the product of an instantaneous transformation of two initially segregated reactants were used as measures of reactive mixing.  相似文献   

3.
This paper presents a formulation accounting for the effect of delayed drainage phenomenon (DDP) on the breakthrough of contaminant flux in an aquitard, by considering the movement of soil particles, porosity variation, hydraulic head variation, and transient flow during the consolidation. The water flow equation in an aquitard was based on the Terzaghi's consolidation theory, and the contaminant transport equation was derived on the basis of the mass balance law. Two cases were used to illustrate the effect of DDP on the contaminant transport in an aquitard of small deformation. It is found that the breakthrough time of contaminant in an aquitard is very long, which is mainly ascribed to the low permeability of aquitard and sorption of soil particles. It is also found that the increase of depletion, which is in general induced by the increase of thickness and specific storativity and the decrease of hydraulic conductivity, enhances the impact of DDP on the contaminant transport in an aquitard. A larger delay index (τ0) of DDP gives a greater delay breakthrough time (DBT) of solute transport in an aquitard, which controls the difference of the breakthrough time of contaminant transport in aquitards with and without the occurrence of DDP. For the cases where advection plays a dominant role during the process of solute transport, τ0 is almost linearly correlated with DBT, and the ratio of DBT over the breakthrough time without consideration of DDP also approximately shows a linear relationship with the ratio of specific storativity to porosity, given a fixed drawdown in the adjacent aquifer with the sorption being ignored.  相似文献   

4.
The breakthrough curve obtained from a single-well push-pull test can be adjusted to account for dilution of the injection fluid in the aquifer fluid. The dilution-adjusted breakthrough curve can be analyzed to estimate the reaction rate of a solute. The conventional dilution-adjusted method assumes that the ratios of the concentrations of the nonreactive and reactive solutes in the injection fluid vs. the aquifer fluid are equal. If this assumption is invalid, the conventional method will generate inaccurate breakthrough curves and may lead to erroneous conclusions regarding the reactivity of a solute. In this study, a new method that generates a dilution-adjusted breakthrough curve was theoretically developed to account for any possible combination of nonreactive and reactive solute concentrations in the injection and aquifer fluids. The newly developed method was applied to a field-based data set and was shown to generate more accurate dilution-adjusted breakthrough curves. The improved dilution-adjusted method presented here is simple, makes no assumptions regarding the concentrations of the nonreactive and reactive solutes in the injection and aquifer fluids, and easily allows for estimating reaction rates during push-pull tests.  相似文献   

5.
A solution conduit has a permeable wall allowing for water exchange and solute transfer between the conduit and its surrounding aquifer matrix. In this paper, we use Laplace Transform to solve a one‐dimensional equation constructed using the Euler approach to describe advective transport of solute in a conduit, a production‐value problem. Both nonuniform cross‐section of the conduit and nonuniform seepage at the conduit wall are considered in the solution. Physical analysis using the Lagrangian approach and a lumping method is performed to verify the solution. Two‐way transfer between conduit water and matrix water is also investigated by using the solution for the production‐value problem as a first‐order approximation. The approximate solution agrees well with the exact solution if dimensionless travel time in the conduit is an order of magnitude smaller than unity. Our analytical solution is based on the assumption that the spatial and/or temporal heterogeneity in the wall solute flux is the dominant factor in the spreading of spring‐breakthrough curves, and conduit dispersion is only a secondary mechanism. Such an approach can lead to the better understanding of water exchange and solute transfer between conduits and aquifer matrix. Highlights:
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6.
We consider a one-dimensional model biodegradation system consisting of two reaction–advection equations for nutrient and pollutant concentrations and a rate equation for biomass. The hydrodynamic dispersion is ignored. Under an explicit condition on the decay and growth rates of biomass, the system can be approximated by two component models by setting biomass kinetics to equilibrium. We derive closed form solutions for constant speed traveling fronts for the reduced two component models and compare their profiles in homogeneous media. For a spatially random velocity field, we introduce travel time and study statistics of degradation fronts via representations in terms of the travel time probability density function (pdf) and the traveling front profiles. The travel time pdf does not vary with the nutrient and pollutant concentrations and only depends on the random water velocity. The traveling front profiles are expressed analytically or semi-analytically as functions of the travel time. The problem of nonlinear transport by a random velocity reduces to two subproblems: one being nonlinear transport by a known (unit) velocity, and the other being linear (advective) transport by a random velocity. The approach is illustrated through some examples where the randomness in velocity stems from the spatial variability of porosity.  相似文献   

7.
We investigate the importance of selecting two different methodologies for the determination of hydraulic conductivity from available grain-size distributions on the stochastic modeling of the depth-averaged breakthrough curve observed during a forced-gradient tracer test experiment. The latter was performed in the Lauswiesen alluvial aquifer, located near the city of Tübingen, Germany, by injecting NaBr into a well at a distance of about 50 m from a pumping well. We also examine the joint effect of the choice of the transport model adopted to describe solute transport at the site and the way the spatial distribution of porosity is assessed. In the absence of direct measurements of porosity, we consider: (a) the model used by Riva et al. (J Contam Hydrol 88:92–118, 2006; J Contam Hydrol 101:1–13, 2008), which relates the natural logarithms of effective porosity and conductivity through an empirical, experimentally-based, linear relationship derived for a nearby experimental site; and (b) a model based on a commonly used relationship linking the total porosity to the coefficient of uniformity of grain size distributions. Transport is described in terms of a purely advective process and/or by including mass exchange processes between mobile and immobile regions. Modeling of flow and transport is performed within a Monte Carlo framework, upon conceptualizing the aquifer as a random composite medium. Our results indicate that the model adopted to describe the correlation between conductivity and porosity and the way grain-sieve information are incorporated to depict the heterogeneous distribution of hydraulic conductivity can have relevant effects in the interpretation of the data at the site. All the conceptual models employed to describe the structural heterogeneity of the system and transport features can reasonably reproduce the global characteristics of the experimental depth-averaged breakthrough curve. Specific details, such as the peak concentration and the time of first arrival, can be better reproduced by a double porosity transport model when a correlation between conductivity and porosity based on grain size information at the site is considered. The best prediction of the late-time behavior of the measured breakthrough curves, in terms of the observed heavy tailing, is offered by directly linking porosity distribution to the spatial variability of particle size information.  相似文献   

8.
The importance of transience in the management of hydrogeologic systems is often uncertain. We propose a clear framework for determining the likely importance of transient behavior in groundwater systems in a management context. The framework incorporates information about aquifer hydraulics, hydrological drivers, and time scale of management. It is widely recognized that aquifers respond on different timescales to hydrological change and that hydrological drivers themselves, such as climate, are not stationary in time. We propose that in order to assess whether transient behavior is likely to be of practical importance, three factors need to be examined simultaneously: (1) aquifer response time, which can be expressed in terms of the response to a step hydrological change (τstep) or periodic change (τcycle); (2) temporal variation of the dominant hydrological drivers, such as dominant climatic systems in a region; (3) the management timescale and spatial scale of interest. Graphical tools have been developed to examine these factors in conjunction, and assess how important transient behavior is likely to be in response to particular hydrological drivers, and thus which drivers are most likely to induce transience in a specified management timeframe. The method is demonstrated using two case studies; a local system that responds rapidly and is managed on yearly to decadal timeframes and a regional system that exhibits highly delayed responses and was until recently being assessed as a high level nuclear waste repository site. Any practical groundwater resource problem can easily be examined using the proposed framework.  相似文献   

9.
Fractured rocks have presented formidable challenges for accurately predicting groundwater flow and contaminant transport. This is mainly due to our difficulty in mapping the fracture‐rock matrix system, their hydraulic properties and connectivity at resolutions that are meaningful for groundwater modeling. Over the last several decades, considerable effort has gone into creating maps of subsurface heterogeneity in hydraulic conductivity (K) and specific storage (Ss) of fractured rocks. Developed methods include kriging, stochastic simulation, stochastic inverse modeling, and hydraulic tomography. In this article, I review the evolution of various heterogeneity mapping approaches and contend that hydraulic tomography, a recently developed aquifer characterization technique for unconsolidated deposits, is also a promising approach in yielding robust maps (or tomograms) of K and Ss heterogeneity for fractured rocks. While hydraulic tomography has recently been shown to be a robust technique, the resolution of the K and Ss tomograms mainly depends on the density of pumping and monitoring locations and the quality of data. The resolution will be improved through the development of new devices for higher density monitoring of pressure responses at discrete intervals in boreholes and potentially through the integration of other data from single‐hole tests, borehole flowmeter profiling, and tracer tests. Other data from temperature and geophysical surveys as well as geological investigations may improve the accuracy of the maps, but more research is needed. Technological advances will undoubtedly lead to more accurate maps. However, more effort should go into evaluating these maps so that one can gain more confidence in their reliability.  相似文献   

10.
Abstract

The dependence of the recession of the ground water levels and the ground water discharge upon the initial state of the aquifer is examined for deep unconfined aquifers. It is shown that only in the early stages of the recession does the initial state exert a limited influence on the recession. An estimate of the upper limit of the time t 0 for which for t > t 0 the recession becomes effectively independent of the initial state of the aquifer, valid for physically realistic initial states can be gained from inequalities (11) and (12a) and equation (16). t 0 depends essentially on the parameters of the aquifer and it is estimated that for useful aquifers t 0 can not be expected to exceed one month in relatively adverse cases. This explains why empirical recessions often are found to be consistent, of an exponential form.  相似文献   

11.
A river at equilibrium is described by a statistically-stationary mean bed elevation profile that arises in response to steady supplies of relief, water and sediment. Outside of the profile shape, how is the equilibrium state of a river most reliably identified and rigorously defined? Motivated by a proposed link between equilibrium and physical processes, we use scaling theory to develop the dimensionless channel response number ξ=KUb/Up. ξ is a metric for the local disequilibrium state of gravel-bed mountain streams, which reflects a balance between the rate of topographic adjustment Ub, and the rate of bed sediment texture adjustment Up. The coefficient K can take one of two forms depending on choice of length scale for topographic adjustment. We hypothesize that equilibrium occurs where and when ξ≈O(1), and consequently, disequilibrium is the more general state captured by conditions of ξ≉O(1). The rates Ub and Up are controlled by the mechanics of sediment deposition and entrainment at the local scale of the channel width. The extent to which either process regulates disequilibrium depends on the bed strength, which is set by the time-varying grain size distribution and packing. We use flume experiments to understand ξ and find that in the limit ξ>>1, the time-varying response of an experimental channel depends sensitively on the spatially-averaged bed shear stress ratio τ/τref. When τ/τref≈1.5, Ub was the dominant control on disequilibrium. However, when τ/τref≈2.0, Up contributed more significantly to disequilibrium. These results suggest that after an upstream supply perturbation, the equilibrium timescale is governed by Up, which we show is consistent with expectations from linear damping theory. Our experimental test of ξ is promising, but inconclusive with respect to our hypothesis. This uncertainty can be readily addressed with numerical or additional physical experiments. © 2019 John Wiley & Sons, Ltd.  相似文献   

12.
Abstract

Abstract Characterization of heterogeneity at the field scale generally requires detailed aquifer properties such as transmissivity and hydraulic head. An accurate delineation of these properties is expensive and time consuming, and for many if not most groundwater systems, is not practical. As an alternative approach, stochastic representation of random fields is used and presented in this paper. Specifically, an iterative stochastic conditional simulation approach was applied to a hypothetical and highly heterogeneous pre-designed aquifer system. The approach is similar to the classical co-kriging technique; it uses a linear estimator that depends on the covariance functions of transmissivity (T), and hydraulic head (h), as well as their cross-covariances. A linearized flow equation along with a conditional random field generator constitutes the iterative process of the conditional simulation. One hundred equally likely realizations of transmissivity fields with pre-specified geostatistical parameters were generated, and conditioned to both limited transmissivity and head data. The successful implementation of the approach resulted in conditioned flow paths and travel-time distribution under different degrees of aquifer heterogeneity. This approach worked well for fields exhibiting small variances. However, for random fields exhibiting large variances (greater than 1.0), an iterative procedure was used. The results show that, as the variance of the ln[T] increases, the flow paths tend to diverge, resulting in a wide spectrum of flow conditions, with no direct discernable relationship between the degree of heterogeneity and travel time. The applied approach indicates that high errors may result when estimation of particle travel times in a heterogeneous medium is approximated by an equivalent homogeneous medium.  相似文献   

13.
An analytical solution for calculating the contaminant discharge rate in an aquifer following an instantaneous release of reactive contaminant mass to groundwater is used to derive relationships for the time and magnitude of peak concentration in a river receiving the transported material. Relationships are developed for the time of peak concentration relative to the time of travel for the contaminant, and the magnitude of peak concentration relative to the concentration calculated at the time of travel. Both quantities are found to be a function of two dimensionless parameters characterizing advective‐dispersive‐reactive transport—the Peclet number and the Damkohler number. It is shown that the time to peak concentration may occur before the time of travel, considering advection and retardation only, depending on the magnitudes of the Peclet and Damkohler numbers. Similarly, the magnitude of peak concentration may exceed the concentration calculated assuming that the time of peak concentration coincides with time of travel for the contaminant. For large Damkohler numbers, equating the time of peak concentration with the time of travel for the contaminant can significantly underestimate peak concentrations.  相似文献   

14.
Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (Ss) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and Ss of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.  相似文献   

15.
Abstract

A method has recently been proposed for finding the radius rc of the electrically-conducting fluid core of a planet of outer radius rs from observations of the magnetic field B in the accessible region near or well above the surface of the planet (Hide, 1978). The method is based on the supposition that when the magnetic field is produced by hydromagnetic dynamo action in the core, implying that the magnetic Reynolds number R there is large, (a) fluctuations in B can occur everywhere on the comparatively short advective time-scale τ A associated with fluid motions in the core and so can fluctuations in the quantity N, defined for any closed surface S as the total number of intersection of magnetic lines of force with S, provided that S lies well outside the core, but (b) at the surface of the core, where lines of magnetic force emerge from their region of origin, concomitant fluctuations in N are negligibly small, of the order of τ A/τO where τ O (= RτA ) is the Ohmic decay time of the core.

A proof of this supposition follows directly from the general expression derived in the present paper showing that when S is a material surface the time rate of change of N is equal to minus twice the line integral of the current density divided by the electrical conductivity around all the lines on S where the magnetic field is tangential to S. This expression (which Palmer in an accompanying paper rederives and extends to the relativistic case using the mathematical formalism of Cartan’s exterior calculus) also provides a direct demonstration of the well-known result that although high electrical conductivity, sufficient to make R ? 1, is a necessary condition for hydromagnetic dynamo action, such action is impossible in a perfect conductor, when R→ ∞.  相似文献   

16.
The problem of permeable reactive barrier (PRB) capture and release behavior is investigated by means of an approximate analytical approach exploring the invariance of steady-state solutions of the advection–dispersion equation to conformal mapping. PRB configurations considered are doubly-symmetric funnel-and-gate as well as less frequent drain-and-gate systems. The effect of aquifer heterogeneity on contaminant plume spreading is hereby incorporated through an effective transverse macro-dispersion coefficient, which has to be known. Results are normalized and graphically represented in terms of a relative capture efficiency M of contaminant mass or groundwater passing a control plane (transect) at a sufficient distance up-stream of a PRB as to comply with underlying assumptions. Factors of safety FS are given as the ratios of required capture width under advective–dispersive and purely advective transport for achieving equal capture efficiency M. It is found that M also applies to the release behavior down-stream of a PRB, i.e., it describes the spreading and dilution of PRB treated groundwater possibly containing incompletely remediated contamination and/or remediation reaction products. Hypothetical examples are given to demonstrate results.  相似文献   

17.
We look at the large-scale dynamo properties of spatially periodic, time dependent, helical 2D flows of the form u(x, t)?=?(? y ?ψ?(x, y, t), ?? x ?ψ?(x, y, t), ?ψ (x, y, t). These flows act as kinematic fast dynamos and are able to generate a mean magnetic field uniform and constant in the xy-plane but whose direction varies periodically along z with wavenumber k. Using Mean Field Electrodynamics, the generation mechanism can be understood in terms of a k-dependent α-effect, which depends on the magnetic Reynolds number, R m . We calculate this effect for different motions and investigate how its limit as k?→?0 depends on R m and on the properties of the flows such as their spatial structure or correlation time. This work generalises earlier studies based on 2D steady flows to motions with time dependence.  相似文献   

18.
Abstract

In this paper we analyse the stationary mean energy density tensor Tij = BiBj for the x 2-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for Tij is found analytically. Only Trr , T θθ and T φφ are unequal to zero, and we present their dependence on the radial distance r.

The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient β≈?u2?τc/3 and the vorticity coefficient γ ≈ ?|?×u|2?τc/3 where u(r, t) is the turbulent velocity and c its correlation time. But the solution is independent of the dynamo coefficient α≈??u·?×u?τc/3 although α does occur in the equation for Tij . This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which Tij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos.  相似文献   

19.
Heat as a tracer in fractured porous aquifers is more sensitive to fracture-matrix processes than a solute tracer. Temperature evolution as a function of time can be used to differentiate fracture and matrix characteristics. Experimental hot (50 °C) and cold (10 °C) water injections were performed in a weathered and fractured granite aquifer where the natural background temperature is 30 °C. The tailing of the hot and cold breakthrough curves, observed under different hydraulic conditions, was characterized in a log–log plot of time vs. normalized temperature difference, also converted to a residence time distribution (normalized). Dimensionless tail slopes close to 1.5 were observed for hot and cold breakthrough curves, compared to solute tracer tests showing slopes between 2 and 3. This stronger thermal diffusive behavior is explained by heat conduction. Using a process-based numerical model, the impact of heat conduction toward and from the porous rock matrix on groundwater heat transport was explored. Fracture aperture was adjusted depending on the actual hydraulic conditions. Water density and viscosity were considered temperature dependent. The model simulated the increase or reduction of the energy level in the fracture-matrix system and satisfactorily reproduced breakthrough curves tail slopes. This study shows the feasibility and utility of cold water tracer tests in hot fractured aquifers to boost and characterize the thermal matrix diffusion from the matrix toward the flowing groundwater in the fractures. This can be used as complementary information to solute tracer tests that are largely influenced by strong advection in the fractures.  相似文献   

20.
Traditional characterization of hyporheic processes relies upon modelling observed in‐stream and subsurface breakthrough curves to estimate hyporheic zone size and infer exchange rates. Solute data integrate upstream behaviour and lack spatial coverage, limiting our ability to accurately quantify spatially heterogeneous exchange dynamics. Here, we demonstrate the application of near‐surface electrical resistivity imaging (ERI) methods, coupled with experiments using an electrically conductive stream tracer (dissolved NaCl), to provide in situ imaging of spatial and temporal dynamics of hyporheic exchange. Tracer‐labelled water in the stream enters the hyporheic zone, reducing electrical resistivity in the subsurface (to which subsurface ERI is sensitive). Comparison of background measurements with those recording tracer presence provides distributed characterization of hyporheic area (in this application, ∼0·5 m2). Results demonstrate the first application of ERI for two‐dimensional imaging of stream‐aquifer exchange and hyporheic extent. Future application of this technique will greatly enhance our ability to quantify processes controlling solute transport and fate in hyporheic zones, and provide data necessary to inform more complete numerical models. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

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