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1.
Matrix diffusion can attenuate the rate of plume migration in fractured bedrock relative to the rate of ground water flow for both conservative and nonconservative solutes of interest. In a system of parallel, equally spaced constant aperture fractures subject to steady-state ground water flow and an infinite source width, the degree of plume attenuation increases with time and travel distance, eventually reaching an asymptotic level. The asymptotic degree of plume attenuation in the absence of degradation can be predicted by a plume attenuation factor, beta, which is readily estimated as R' (phi(m)/phi(f)), where R' is the retardation factor in the matrix, phi(m) is the matrix porosity, and phi(f) is the fracture porosity. This dual-porosity relationship can also be thought of as the ratio of primary to secondary porosity. Beta represents the rate of ground water flow in fractures relative to the rate of plume advance. For the conditions examined in this study, beta increases with greater matrix porosity, greater matrix fraction organic carbon, larger fracture spacing, and smaller fracture aperture. These concepts are illustrated using a case study where dense nonaqueous phase liquid in fractured sandstone produced a dissolved-phase trichloroethylene (TCE) plume approximately 300 m in length. Transport parameters such as matrix porosity, fracture porosity, hydraulic gradient, and the matrix retardation factor were characterized at the site through field investigations. In the fractured sandstone bedrock examined in this study, the asymptotic plume attenuation factors (beta values) for conservative and nonconservative solutes (i.e., chloride and TCE) were predicted to be approximately 800 and 12,210, respectively. Quantitative analyses demonstrate that a porous media (single-porosity) solute transport model is not appropriate for simulating contaminant transport in fractured sandstone where matrix diffusion occurs. Rather, simulations need to be conducted with either a discrete fracture model that explicitly incorporates matrix diffusion, or a dual-continuum model that accounts for mass transfer between mobile and immobile zones. Simulations also demonstrate that back diffusion from the matrix to fractures will likely be the time-limiting factor in reaching ground water cleanup goals in some fractured bedrock environments.  相似文献   

2.
In general, the accuracy of numerical simulations is determined by spatial and temporal discretization levels. In fractured porous media, the time step size is a key factor in controlling the solution accuracy for a given spatial discretization. If the time step size is restricted by the relatively rapid responses in the fracture domain to maintain an acceptable level of accuracy in the entire simulation domain, the matrix tends to be temporally over-discretized. Implicit sub-time stepping applies smaller sub-time steps only to the sub-domain where the accuracy requirements are less tolerant and is most suitable for problems where the response is high in only a small portion of the domain, such as within and near the fractures in fractured porous media. It is demonstrated with illustrative examples that implicit sub-time stepping can significantly improve the simulation efficiency with minimal loss in accuracy when simulating flow and transport in fractured porous media. The methodology is successfully applied to density-dependent flow and transport simulations in a Canadian Shield environment, where the flow and transport is dominated by discrete, highly conductive fracture zones.  相似文献   

3.
《Advances in water resources》2004,27(11):1045-1059
Transient and steady-state analytical solutions are derived to investigate solute transport in a fractured porous medium consisting of evenly spaced, parallel discrete fractures. The solutions incorporate a finite width strip source, longitudinal and transverse dispersion in the fractures, source decay, aqueous phase decay, one-dimensional diffusion into the matrix, sorption to fracture walls, and sorption within the matrix. The solutions are derived using Laplace and Fourier transforms, and inverted by interchanging the order of integration and utilizing a numerical Laplace inversion algorithm. The solutions are verified for simplified cases by comparison to solutions derived by Batu [Batu V. A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type condition at the source. Wat Resour Res 1989;25(6):1125] and Sudicky and Frind [Sudicky EA, Frind EO. Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures. Wat Resour Res 1982;18(6):1634]. The application of the solutions to a fractured sandstone demonstrates that narrower source widths and larger values of transverse dispersivity both lead to lower downstream concentrations in the fractures and shorter steady-state plumes. The incorporation of aqueous phase decay and source concentration decay both lead to lower concentrations and shorter plumes, with even moderate amounts of decay significantly shortening the persistence of contamination.  相似文献   

4.
An equivalent medium model for wave simulation in fractured porous rocks   总被引：3，自引：0，他引：3  
Seismic wave propagation in reservoir rocks is often strongly affected by fractures and micropores. Elastic properties of fractured reservoirs are studied using a fractured porous rock model, in which fractures are considered to be embedded in a homogeneous porous background. The paper presents an equivalent media model for fractured porous rocks. Fractures are described in a stress‐strain relationship in terms of fracture‐induced anisotropy. The equations of poroelasticity are used to describe the background porous matrix and the contents of the fractures are inserted into a matrix. Based on the fractured equivalent‐medium theory and Biot's equations of poroelasticity, two sets of porosity are considered in a constitutive equation. The porous matrix permeability and fracture permeability are analysed by using the continuum media seepage theory in equations of motion. We then design a fractured porous equivalent medium and derive the modified effective constants for low‐frequency elastic constants due to the presence of fractures. The expressions of elastic constants are concise and are directly related to the properties of the main porous matrix, the inserted fractures and the pore fluid. The phase velocity and attenuation of the fractured porous equivalent media are investigated based on this model. Numerical simulations are performed. We show that the fractures and pores strongly influence wave propagation, induce anisotropy and cause poroelastic behaviour in the wavefields. We observe that the presence of fractures gives rise to changes in phase velocity and attenuation, especially for the slow P‐wave in the direction parallel to the fracture plane.  相似文献   

5.
Water levels and water quality of open borehole wells in fractured bedrock are flow-weighted averages that are a function of the hydraulic heads and transmissivities of water contributing fractures, properties that are rarely known. Without such knowledge using water levels and water quality data from fractured bedrock wells to assess groundwater flow and contaminant conditions can be highly misleading. This study demonstrates a cost-effective single packer method to determine the hydraulic heads and transmissivities of water contributing fracture zones in crystalline bedrock wells. The method entails inflating a pipe plug to isolate sections of an open borehole at different depths and monitoring changes in the water level with time. At each depth, the change in water level with time was used to determine the sum of fracture transmissivities above the packer and then to solve for individual fracture transmissivity. Steady-state wellbore heads along with the transmissivities were used to determine individual fracture heads using the weighted average head equation. The method was tested in five wells in crystalline bedrock located at the University of Connecticut in Storrs. The single packer head and transmissivity results were found to agree closely with those determined using conventional logging methods and the dissolved oxygen alteration method. The method appears to be a simple and cost-effective alternative in obtaining important information on flow conditions in fractured crystalline bedrock wells.  相似文献   

6.
Boreholes drilled through contaminated zones in fractured rock create the potential for vertical movement of contaminated ground water between fractures. The usual assumption is that purging eliminates cross contamination; however, the results of a field study conducted in a trichloroethylene (TCE) plume in fractured sandstone with a mean matrix porosity of 13% demonstrates that matrix-diffusion effects can be strong and persistent. A deep borehole was drilled to 110 m below ground surface (mbgs) near a shallow bedrock well containing high TCE concentrations. The borehole was cored continuously to collect closely spaced samples of rock for analysis of TCE concentrations. Geophysical logging and flowmetering were conducted in the open borehole, and a removable multilevel monitoring system was installed to provide hydraulic-head and ground water samples from discrete fracture zones. The borehole was later reamed to complete a well screened from 89 to 100 mbgs; persistent TCE concentrations at this depth ranged from 2100 to 33,000 microg/L. Rock-core analyses, combined with the other types of borehole information, show that nearly all of this deep contamination was due to the lingering effects of the downward flow of dissolved TCE from shallower depths during the few days of open-hole conditions that existed prior to installation of the multilevel system. This study demonstrates that transfer of contaminant mass to the matrix by diffusion can cause severe cross contamination effects in sedimentary rocks, but these effects generally are not identified from information normally obtained in fractured-rock investigations, resulting in potential misinterpretation of site conditions.  相似文献   

7.
A comprehensive understanding of seasonal hydrological dynamics is required to describe the influence of pore‐water pressure on the stability of landslides in snowy regions. This study reports on the results of continuous meteorological and hydrological observations over 2 years on a landslide body comprising Neogene sedimentary rocks in northern Japan, where a thick (3–5 m) seasonal snowpack covers the land surface. Monitoring of the volumetric water content in shallow unsaturated zones (<0.8 m depth) and pore‐water pressure in saturated bedrock at depths of 2.0 and 5.2 m revealed clear seasonality in hydrological responses to rainfall and meltwater supply. During snow‐free periods, both the shallow soil moisture and deep pore‐water pressure responded rapidly to intense rainwater infiltration. In contrast, during snowmelt, the deep pore pressure fluctuated in accordance with the daily cycle of meltwater input, without notable changes in shallow moisture conditions. During occasional foehn events that cause intense snow melting in midwinter, meltwater flows preferentially through the layered snowpack, converging to produce a localized water supply at the ground surface. This episodically triggers a significant rise in pore‐water pressure. The seasonal differences in hydrological responses were characterized by a set of newly proposed indices for the magnitude and quickness of increases in the pressure head near the sliding surface. Under snow‐covered conditions, the magnitude of the pressure increase tends to be suppressed, probably owing to a reduction in infiltration caused by a seasonal decrease in the permeability of surface soils, and effective pore‐water drainage through the highly conductive colluvial layer. Deep groundwater flow within bedrock remained in a steady upwelling state, enhanced by increasing moisture in shallow soils under snow cover, reflecting the convergence of subsurface water from surrounding hillslopes.  相似文献   

8.
Contaminated groundwater in fractured bedrock can expose ecosystems to undesired levels of risk for extended periods due to prolonged back-diffusion from rock matrix to permeable fractures. Therefore, it is key to characterize the diffusive mass loading (intrusion) of contaminants into the rock matrix for successful management of contaminated bedrock sites. Even the most detailed site characterization techniques often fail to delineate contamination in rock matrix. This study presents a set of analytical solutions to estimate diffusive mass intrusion into matrix blocks, it is recovered by pumping and concentration rebound when pumping ceases. The analytical models were validated by comparing the results with (1) numerical model results using the same model parameters and (2) observed chloride mass recovery, rebound concentration, and concentration in pumped groundwater at a highly fractured bedrock site in Alberta, Canada. It is also demonstrated that the analytical solutions can be used to estimate the total mass stored in the fractured bedrock prior to any remediation thereby providing insights into site contamination history. The predictive results of the analytical models clearly show that successful remediation by pumping depends largely on diffusive intrusion period. The results of initial mass from the analytical model was used to successfully calibrate a three-dimensional discrete fracture network numerical model further highlighting the utility of the simple analytical solutions in supplementing the more detailed site numerical modeling. Overall, the study shows the utility of simple analytical methods to support long-term management of a contaminated fractured bedrock site including site investigations and complex numerical modeling.  相似文献   

9.
Evaluating contaminants impacting wells in fractured crystalline rock requires knowledge of the individual fractures contributing water. This typically involves using a sequence of tools including downhole geophysics, flow meters, and straddle packers. In conjunction with each other these methods are expensive, time consuming, and can be logistically difficult to implement. This study demonstrates an unsteady state tracer method as a cost‐effective alternative for gathering fracture information in wells. The method entails introducing tracer dye throughout the well, inducing fracture flow into the well by conducting a slug test and then profiling the tracer concentration in the well to locate water contributing fractures where the dye has been diluted. By monitoring the development of the dilution zones within the wellbore with time, the transmissivity and the hydraulic head of the water contributing fractures can be determined. Ambient flow conditions and the contaminant concentration within the fractures can also be determined from the tracer dilution. This method was tested on a large physical model well and a bedrock well. The model well was used to test the theory underlying the method and to refine method logistics. The approach located the fracture and generated transmissivity values that were in excellent agreement with those calculated by slug testing. For the bedrock well tested, two major active fractures were located. Fracture location and ambient well conditions matched results from conventional methods. Estimates of transmissivity values by the tracer method were within an order of magnitude of those calculated using heat‐pulse flow meter data.  相似文献   

10.
Understanding the effects of in situ fluid content and fracture parameters on seismic characteristics is important for the subsurface exploration and production of fractured porous rocks. The ratio of normal-to-shear fracture compliance is typically utilized as a fluid indicator to evaluate anisotropy and identify fluids filling the fractures, but it represents an underdetermined problem because this fluid indicator varies as a function of both fracture geometry and fluid content. On the bases of anisotropic Gassmann's equation and linear-slip model, we suggest an anisotropic poroelasticity model for fractured porous reservoirs. By combining a perturbed stiffness matrix and asymptotic ray theory, we then construct a direct relationship between the PP-wave reflection coefficients and characteristic parameters of fluids(P-and S-wave moduli) and fractures(fracture quasi-weaknesses), thereby decoupling the effects of fluid and fracture properties on seismic reflection characterization.By incorporating fracture quasi-weakness parameters, we propose a novel parameterization method for elastic impedance variation with offset and azimuth(EIVOA). By incorporating wide-azimuth observable seismic reflection data with regularization constraints, we utilize Bayesian seismic inversion to estimate the fluid content and fracture parameters of fractured porous rocks. Tests on synthetic and real data demonstrate that fluid and fracture properties can be reasonably estimated directly from azimuthal seismic data and the proposed approach provides a reliable method for fluid identification and fracture characterization in a gas-saturated fractured porous reservoir.  相似文献   

11.
A vertically fractured transversely isotropic (VFTI) elastic medium is one in which any number of sets of vertical aligned fractures (each set has its normal lying in the horizontal x1, x2‐plane) pervade the medium and the sets of aligned fractures are the only features of the medium disturbing the axi‐symmetry about the x3‐axis implying that in the absence of fractures, the background medium is transversely isotropic (TI). Under the assumptions of long wavelength equivalent medium theory, the compliance matrix of a fractured medium is the sum of the background medium's compliance matrix and a fracture compliance matrix. For sets of parallel rotationally symmetric fractures (on average), the fracture compliance matrix is dependent on 3 parameters − its normal and tangential compliance and its strike direction. When one fracture set is present, the medium is orthorhombic and the analysis is straightforward. When two (non‐orthogonal) or more sets are present, the overall medium is in general elastically monoclinic; its compliance tensor components are subject to two equalities yielding an 11 parameter monoclinic medium. Constructing a monoclinic VFTI medium with n embedded vertical fracture sets, requires 5 TI parameters plus 3×n fracture set parameters. A deconstruction of such an 11 parameter monoclinic medium involves using its compliance tensor to find a background transversely isotropic medium and several sets of vertical fractures which, in the long wavelength limit, will behave exactly as the original 11 parameter monoclinic medium. A minimal deconstruction, would be to determine, from the 11 independent components, the transversely isotropic background (5 parameters) and two fracture sets (specified by 2 × 3 = 6 parameters). Two of the background TI medium's compliance matrix components are known immediately by inspection, leaving nine monoclinic components to be used in the minimal deconstruction of the VFTI medium. The use of the properties of a TI medium, which are linear relations on its compliance components, allows the deconstruction to be reduced to solving a pair of non‐linear equations on the orientations of two fracture sets. A single root yielding a physically meaningful minimum deconstruction yields a unique minimal representation of the monoclinic medium as a VFTI medium. When no such root exists, deconstruction requires an additional fracture set and uniqueness is lost. The boundary between those monoclinic media that have a unique minimal representation and those that do not is yet to be determined.  相似文献   

12.
We explore the contribution of fractures (joints) in controlling the rate of weathering advance for a low‐porosity rock by using methods of homogenization to create averaged weathering equations. The rate of advance of the weathering front can be expressed as the same rate observed in non‐fractured media (or in an individual block) divided by the volume fraction of non‐fractured blocks in the fractured parent material. In the model, the parent has fractures that are filled with a more porous material that contains only inert or completely weathered material. The low‐porosity rock weathers by reaction‐transport processes. As observed in field systems, the model shows that the weathering advance rate is greater for the fractured as compared to the analogous non‐fractured system because the volume fraction of blocks is < 1. The increase in advance rate is attributed both to the increase in weathered material that accompanies higher fracture density, and to the increase in exposure of surface of low‐porosity rock to reaction‐transport. For constant fracture aperture, the weathering advance rate increases when the fracture spacing decreases. Equations describing weathering advance rate are summarized in the ‘List of selected equations’. If erosion is imposed at a constant rate, the weathering systems with fracture‐bounded bedrock blocks attain a steady state. In the erosional transport‐limited regime, bedrock blocks no longer emerge at the air‐regolith boundary because they weather away. In the weathering‐limited (or kinetic) regime, blocks of various size become exhumed at the surface and the average size of these exposed blocks increases with the erosion rate. For convex hillslopes, the block size exposed at the surface increases downslope. This model can explain observations of exhumed rocks weathering in the Luquillo mountains of Puerto Rico. Published 2017. This article is a U.S. Government work and is in the public domain in the USA  相似文献   

13.
Optical sensors are promising for collecting high resolution in‐well groundwater nitrate monitoring data. Traditional well purging methods are labor intensive, can disturb ambient conditions and yield an unknown blend of groundwater in the samples collected, and obtain samples at a limited temporal resolution (i.e., monthly or seasonally). This study evaluated the Submersible Ultraviolet Nitrate Analyzer (SUNA) for in‐well nitrate monitoring through new applications in shallow overburden and fractured bedrock environments. Results indicated that SUNA nitrate‐N concentration measurements during flow cell testing were strongly correlated (R 2 = 0.99) to purged sample concentrations. Vertical profiling of the water column identified distinct zones having different nitrate‐N concentrations in conventional long‐screened overburden wells and open bedrock boreholes. Real‐time remote monitoring revealed dynamic responses in nitrate‐N concentrations following recharge events. The monitoring platform significantly reduced labor requirements for the large amount of data produced. Practitioners should consider using optical sensors for real‐time monitoring if nitrate concentrations are expected to change rapidly, or if a site's physical constraints make traditional sampling programs challenging. This study demonstrates the feasibility of applying the SUNA in shallow overburden and fractured bedrock environments to obtain reliable data, identifies operational challenges encountered, and discusses the range of insights available to groundwater professionals so they will seek to gather high resolution in‐well monitoring data wherever possible.  相似文献   

14.
A new approach to locate transmissive fractures and decipher vertical borehole flow conditions in fractured crystalline bedrock wells is presented, which uses dissolved oxygen (DO) as a benign tracer. The method was tested in two fractured crystalline bedrock wells previously characterized by televiewer and flow meter logging under both ambient and stressed (slug test) conditions. The method entailed elevating wellbore DO concentrations by circulating water through showerheads or injection of compressed air. The DO dilution was used to locate inflowing fractures. Changes in the DO concentration with time were used to ascertain flow within the borehole and to locate outflowing fractures and stagnant zones. Flow rates were also estimated. Fractures detected by the method corresponded to those observed by televiewer logging and for the most part were comparable to flow meter results. Given the effectiveness, time‐efficiency and low cost, the method is a promising alternative to other methods currently in use to characterize transmissive fractures in wells.  相似文献   

15.
Nonpoint sources of nitrogen (N) and other nutrients are a major source of water pollution within the Chesapeake Bay watershed and other basins around the world. Human activities associated with agricultural practices can account for a large percentage of N loadings delivered to streams and rivers. This work aims to improve understanding of N transport from groundwater to surface waters, quantifying the principal hydrological processes driving water and N fluxes into and out of a headwater agricultural stream reach. The study site is a 175-m stream reach in a heavily cultivated 40-ha watershed in east-central Pennsylvania. This subwatershed is underlain by fractured shale bedrock, and receives most of its baseflow from groundwater, either by diffuse matrix discharge through the streambed or by localized discharge through riparian seeps. Samples of stream, seep, and shallow groundwater were collected approximately monthly under steady hydrologic conditions in 2017. Calculated matrix flow from hydraulic head and conductivity measurements paired with differential stream gauging was used to solve for the riparian seep flux using a mass balance approach. Riparian seep fluxes ranged from 45 to 217 m3/d, transporting 0.6–4.2 kg N d−1 of nitrate-N from the fractured bedrock aquifer to the stream. Hydrochemical data suggest that the stream is mainly disconnected from the underlying aquifer and that seeps supply essentially all water and N to the system. Seeps are likely sourced with N in nearby agricultural fields and accelerated through the system with shorter residence times than shallow groundwater. Water isotope data reinforced this notion. This study underscores the importance of agriculture as a source of N to ground and surface waters. Identifying source areas that are causing groundwater enrichment of N and seep areas where N discharges to streams is beneficial for developing N pollution mitigation strategies and implementing management practices that aim to reduce nutrient loads to the Chesapeake Bay.  相似文献   

16.
We present laboratory ultrasonic measurements of shear‐wave splitting from two synthetic silica cemented sandstones. The manufacturing process, which enabled silica cementation of quartz sand grains, was found to produce realistic sandstones of average porosity 29.7 ± 0.5% and average permeability 29.4 ± 11.3 mD. One sample was made with a regular distribution of aligned, penny‐shaped voids to simulate meso‐scale fractures in reservoir rocks, while the other was left blank. Ultrasonic shear waves were measured with a propagation direction of 90° to the coincident bedding plane and fracture normal. In the water saturated blank sample, shear‐wave splitting, the percentage velocity difference between the fast and slow shear waves, of <0.5% was measured due to the bedding planes (or layering) introduced during sample preparation. In the fractured sample, shear‐wave splitting (corrected for layering anisotropy) of 2.72 ± 0.58% for water, 2.80 ± 0.58% for air and 3.21 ± 0.58% for glycerin saturation at a net pressure of 40 MPa was measured. Analysis of X‐ray CT scan images was used to determine a fracture density of 0.0298 ± 0.077 in the fractured sample. This supports theoretical predictions that shear‐wave splitting (SWS) can be used as a good estimate for fracture density in porous rocks (i.e., SWS = 100εf, where εf is fracture density) regardless of pore fluid type, for wave propagation at 90° to the fracture normal.  相似文献   

17.
The purpose of this study is to compare the reliability of various methods of estimating normal rock fracture compliance from elastic wave measurements. We compare ultrasonic through‐transmission laboratory measurements for a smooth fracture in a Westerly granite specimen with numerical simulations and analytical solutions. The focus is on deriving compliance from time delays. The influence of specimen and source transducer width was constrained using numerical wave simulations. We find that measured ultrasonic phase delays are better suited to estimate the fracture compliance than group delays. Using the frequency domain instead of the time domain increases the accuracy of the fracture compliance estimates. We further show that for cases where precise phase delay measurements are unavailable, employing first break times in conjunction with numerical simulations can be considered as an alternative.  相似文献   

18.
Starting in 2008, a 4‐year tracer study was conducted to evaluate ambient changes in groundwater concentrations of a 1,3,6‐naphthalene trisulfonate tracer that was added to drill water. Samples were collected under open borehole conditions and after installing a multilevel groundwater monitoring system completed with 11 discrete monitoring zones within dense and fractured basalt and sediment layers in the eastern Snake River aquifer. The study was done in cooperation with the U.S. Department of Energy to test whether ambient fracture flow conditions were sufficient to remove the effects of injected drill water prior to sample collection. Results from thief samples indicated that the tracer was present in minor concentrations 28 days after coring, but was not present 6 months after coring or 7 days after reaming the borehole. Results from sampling the multilevel monitoring system indicated that small concentrations of the tracer remained in 5 of 10 zones during some period after installation. All concentrations were several orders of magnitude lower than the initial concentrations in the drill water. The ports that had remnant concentrations of the tracer were either located near sediment layers or were located in dense basalt, which suggests limited groundwater flow near these ports. The ports completed in well‐fractured and vesicular basalt had no detectable concentrations.  相似文献   

19.
A conceptual model for describing effective saturation in fractured hard rock is presented. The fracture network and the rock matrix are considered as an equivalent continuum medium where each fracture is conceptualized as a porous medium of granular structure and the rock matrix is assumed to be impermeable. The proposed model is based on the representation of a rough‐walled fracture by an equivalent porous medium, which is described using classical constitutive models. A simple closed‐form equation for the effective saturation is obtained when the van Genuchten model is used to describe saturation inside fractures and fractal laws are assumed for both aperture and number of fractures. The relative hydraulic conductivity for the fractured rock is predicted from a simple relation derived by Liu and Bodvarsson. The proposed constitutive model contains three independent parameters, which may be obtained by fitting the proposed effective saturation curve to experimental data. Two of the model parameters have physical meaning and can be identified with the reciprocal of the air entry pressure values in the fractures of minimum and maximum apertures. Effective saturation and relative hydraulic conductivity curves match fairly well the simulated constitutive relations obtained by Liu and Bodvarsson. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

20.
Many studies indicate that small‐scale heterogeneity and/or mobile–immobile mass exchange produce transient non‐Fickian plume behavior that is not well captured by the use of the standard, deterministic advection‐dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non‐Fickian transport coupled with simultaneous sequential first‐order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed‐form, steady‐state, multi‐species analytical solutions are also derived for non‐Fickian transport in highly heterogeneous aquifers with linear sorption–desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi‐species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over‐estimate cleanup rates and under‐predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.  相似文献   

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