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1.
Preliminary risk assessment for prioritisation of site investigations requires efficient screening to reveal type and level of contamination. The screening methods, tree coring and soil gas sampling were applied and compared at two forested sites contaminated with tetrachloroethylene (PCE) or trichloroethylene (TCE) to evaluate their ability to locate source zones and contaminant hot spots. One test site represented a relatively homogeneous sandy soil and aquifer, and the second a more heterogeneous geology with both sandy and less permeable clay till layers overlying a chalk aquifer. Tree cores from different tree species were sampled and analysed, and compared to soil gas measurements and existing soil gas data. Both methods were found useful as screening tools to locate hot spots of PCE and TCE in the shallow subsurface. Tree coring was found to be particularly beneficial as a complement to soil gas sampling at sites with low permeable soils, and where contamination was located in the capillary rise or shallow groundwater. The shorter time required for tree coring reduced the costs compared to soil gas sampling, but the sensitivity and precision of tree coring were lower. However, this did not affect the feasibility of using tree coring to locate the hot spots. Moreover, a combination of the two methods can help to focus any subsequent investigations like soil or groundwater sampling. The use of tree coring to complement soil gas sampling for pre‐screening is expected to result in higher certainty for revealing hot spots and source zones at contaminated sites.  相似文献   

2.
Field investigations were carried out to determine the occurrence of tetrachloroethene (PCE) dense nonaqueous phase liquid (DNAPL), the source zone architecture and the aquitard integrity at a 30‐ to 50‐year old DNAPL release site. The DNAPL source zone is located in the clay till unit overlying a limestone aquifer. The DNAPL source zone architecture was investigated through a multiple‐lines‐of‐evidence approach using various characterization tools; the most favorable combination of tools for the DNAPL characterization was geophysical investigations, membrane interface probe, core subsampling with quantification of chlorinated solvents, hydrophobic dye test with Sudan IV, and Flexible Liner Underground Technologies (FLUTe) NAPL liners with activated carbon felt (FACT). While the occurrence of DNAPL was best determined by quantification of chlorinated solvents in soil samples supported by the hydrophobic dye tests (Sudan IV and NAPL FLUTe), the conceptual understanding of source zone architecture was greatly assisted by the indirect continuous characterization tools. Although mobile or high residual DNAPL (S t > 1%) only occurred in 11% of the source zone samples (intact cores), they comprised 86% of the total PCE mass. The dataset, and associated data analysis, supported vertical migration of DNAPL through fractures in the upper part of the clay till, horizontal migration along high permeability features around the redox boundary in the clay till, and to some extent vertical migration through the fractures in the reduced part of the clay till aquitard to the underlying limestone aquifer. The aquitard integrity to DNAPL migration was found to be compromised at a thickness of reduced clay till of less than 2 m.  相似文献   

3.
Transport and Biological Fate of Toluene in Low-Permeability Soils   总被引:1,自引:0,他引:1  
The effect of simultaneous sorption, diffusion, and biodegradation on the fate and transport of toluene in low-permeability soil formations was examined. A transport model accounting for vapor and liquid sorption, vapor diffusions, and first-order biodegradation was developed to describe the movement of volatile solute in unsaturated soils. Modeling studies were followed with laboratory batch and column studies on fine-grained soil samples obtained from a gasoline-contaminated site. Batch experiments yielded the sorption and diffusion coefficients for generating theoretical solute transport profiles. Column studies were conducted to examine toluene sorption, diffusion, and biodegradation under aerobic and denitrifying conditions. Results from the column studies indicated that vapor sorption onto the soil was minimal due to the high moisture content of the soil. Comparison of model predictions with experimental results indicated that the SASK model, which is based on the resistivity theory, provided a more accurate prediction of the vapor phase tortuosity than the frequently used Millington-Quirk equation. Laboratory results of toluene concentration profiles matched well with the model predictions and yielded degradation rates comparable to those obtained in the field. Column studies, examining toluene biodegradation under aerobic and denitrifying conditions in low-permeability soils, indicated that the presence of excess nitrate in aerobic environments yielded higher solute degradation rates than those observed under exclusively aerobic systems.  相似文献   

4.
Excessive groundwater withdrawal has caused severe land subsidence worldwide. The pore water pressure and the deformation of pumped hydrostratigraphic units are complex. A fully coupled three-dimensional numerical simulation was carried out for different pumping plans in this paper. When groundwater is pumped from a confined aquifer, the great compaction occurs in the pumped aquifer and its upper and lower adjacent aquitard units. Land subsidence is smaller and the area affected by land subsidence is greater when groundwater is pumped from the deeper confined aquifer. The pore water pressure in the pumped confined aquifer changes immediately with pumpage. In the adjacent aquitard units, however, the pore water pressure increases in the early pumping time and decreases in the early recharging time. The decrease in the pore water pressure vertically spreads from the interface between aquitard and pumped aquifer to the other surface of the aquitard. The pumped aquifer compacts and rebounds immediately with pumping and non-pumping or recharging actions, while the compaction and rebounding of the aquitard units clearly lag behind. The compaction of the adjacent aquitard unit first occurs near the interface between aquitard and pumped aquifer units, and the compaction zone spreads outward as the pumping goes on. The aquitards may expand vertically within some zones. Due to the inelastic deformation of soil skeleton, different pumping plans result in different land subsidence. For the same net pumpage, maximal land subsidence and horizontal displacement are the smallest for constant discharge and the greatest for recharge-discharge cycle.  相似文献   

5.
Porous aquifer materials are often characterized by layered heterogeneities that influence groundwater flow and present complexities in contaminant transport modeling. Such flow variations also have the potential to impact the dissolution flux from dense nonaqueous phase liquid (DNAPL) pools. This study examined how these heterogeneous flow conditions affected the dissolution of a tetrachloroethene (PCE) pool in a two-dimensional intermediate-scale flow cell containing coarse sand. A steady-state mass-balance approach was used to calculate the PCE dissolution rate at three different flow rates. As expected, aqueous PCE concentrations increased along the length of the PCE pool and higher flow rates decreased the aqueous PCE concentration in the effluent. Nonreactive tracer studies at two flow rates confirmed the presence of a vertical flow gradient, with the most rapid velocity located at the bottom of the tank. These results suggest that flow focusing occurred near the DNAPL pool. Effluent PCE concentrations and pool dissolution flux rates were compared to model predictions assuming local equilibrium (LE) conditions at the DNAPL pool/aqueous phase interface and a uniform distribution of flow. The LE model did not describe the data well, even over a wide range of PCE solubility and macroscopic transverse dispersivity values. Model predictions assuming nonequilibrium mass-transfer-limited conditions and accounting for vertical flow gradients, however, resulted in a better fit to the data. These results have important implications for evaluating DNAPL pool dissolution in the field where subsurface heterogeneities are likely to be present.  相似文献   

6.
Degradation of dissolved chlorinated solvents using granular iron is an established in situ technology. This paper reports on investigations into mixing iron and bentonite with contaminated soil for in situ containment and degradation of dense nonaqueous phase liquid source zones. In the laboratory, hypovials containing soil, water, bentonite, iron, and free-phase trichloroethene (TCE) were assembled. Periodic measurement of TCE, chloride, and degradation products showed progressive degradation of TCE to nondetectable levels. Subsequently, a demonstration was conducted at Canadian Forces Base Borden near Alliston, Ontario, Canada, where, in 1991, a portion of the surficial aquifer was isolated and free-phase tetrachloroethene (PCE) was introduced. Using a drill rig equipped with large-diameter mixing blades, three mixed zones were prepared containing 0%, 5%, and 10% granular iron by volume. The bentonite was added to serve as a lubricant to facilitate injection of the iron and to isolate the contaminated zone. Analysis of core samples showed reasonably uniform distributions of iron through the mixed zones. Monitoring over a 13-month period following installation showed, relative to the control, a decline in PCE concentrations to virtually nondetectable values. Reaction rates in the laboratory tests were similar to those reported in the literature, while the rate in the field test was substantially lower. The lower rate may be a consequence of mass transfer limitations under the static conditions of the field test. Results indicate that mixing iron and bentonite into source zones may be an effective means of source-zone remediation, with the particular advantage of being relatively immune to effects of geologic heterogeneity.  相似文献   

7.
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   

8.
Aquifer vulnerability to pesticide migration through till aquitards   总被引:1,自引:0,他引:1  
This study investigates the influence of key factors-mainly recharge rate and degradation half-life--on downward migration of the widely used pesticide mecoprop (MCPP) through a typical clayey till aquitard. The study uses the numerical model FRAC3Dvs, which is a three-dimensional discrete fracture/matrix diffusion (DFMD) numerical transport model. The model was calibrated with laboratory and field data from a site near Havdrup, Denmark, but the overall findings are expected to be relevant to many other sites in similar settings. Fracture flow and MCPP transport parameters for the model were obtained through calibration using well-characterized laboratory experiments with large (0.5 m diameter by 0.5 m high) undisturbed columns of the fractured till and a field experiment. A second level of upscaling and sensitivity analysis was then carried out using data on hydraulic head, fracture spacing, and water budget from the field site. The simulations of downward migration of MCPP show that MCPP concentration and mass flux into the underlying aquifer, and hence the aquifer vulnerability to this pesticide compound, is mainly dependent on the degradation rate of the pesticide, the overall aquitard water budget, and the ground water recharge rate into the aquifer. The influence of flow rate, matrix diffusion, and degradation rate are intertwined. This results in one to four orders of magnitude higher MCPP flux into the aquifer from aquifer recharge rates of 20 and 120 mm/yr, respectively, for no degradation and MCPP half-life of 0.5 yr. From a sensitivity analysis it was found that the range of MCPP flux into the aquifer varied less than one order of magnitude due to (1) changing fracture spacing from 1 to 10 m, or (2) preferential flow along inclined thin sand layers, which represent common conditions for the current and other settings of clayey till in Denmark and other glaciated areas in Europe and North America. The results indicate that for aquifers overlain by fractured clayey tills, the vulnerability to contamination with pesticides (pesticide flux into the aquifer) and other widespread agricultural contaminants is going to vary strongly in the watershed as a function of the distribution of aquitard water budget (flow rate) and aquitard redox environment (controlling contaminant degradation rates), even if the thickness of the till is relatively constant. DFMD modeling of cause-effect relationships within such systems has great potential to support decisions in planning, regulation, and contaminant remediation.  相似文献   

9.
Cone penctrometer test (CPT) based Raman spectroscopy was used to identify separate phase tetrachloroethylene (PCE) and trichlorocthylene (TCE) contamination in the subsurface at two locations during field tests conducted at the U.S. Department of Energy's (DOE) Savannah River site. Clear characteristic Raman spectral peaks for PCE and TCE were observed at two sites and several depths during CPT deployment. Because of the uniqueness of a Raman spectrum for a given compound, these data are compelling evidence of the presence of the two compounds. The Raman spectral results correlated with high PCE and TCE concentrations in soil samples collected from the same subsurface zones, confirming that the method is a viable dense nonaqueous phase liquid (DNAPL) characterization technique. The Raman spectroscopic identification of PCE and TCE in these tests represents the first time that DNAPLs have been unequivocally located in the subsurface by an in situ technique.
The detection limit of the Raman spectroscopy is related to the probability of contaminant droplets appearing on the optical window in the path of the probe light. Based on data from this fieldwork the Raman technique may require a threshold quantity of DNAPL to provide an adequate optical cross section for spectroscopic response. The low aqueous solubility of PCE and TCE and relatively weak optical intensity of the Raman signal precludes the detection of aqueous phase contaminants by this method, making it selective for DNAPL contaminants only.  相似文献   

10.
Pumping test evaluation of stream depletion parameters   总被引:1,自引:0,他引:1  
Lough HK  Hunt B 《Ground water》2006,44(4):540-546
  相似文献   

11.
Microbiological degradation of perchloroethylene (PCE) under anaerobic conditions follows a series of chain reactions, in which, sequentially, trichloroethylene (TCE), cis‐dichloroethylene (c‐DCE), vinylchloride (VC) and ethene are generated. First‐order degradation rate constants, partitioning coefficients and mass exchange rates for PCE, TCE, c‐DCE and VC were compiled from the literature. The parameters were used in a case study of pump‐and‐treat remediation of a PCE‐contaminated site near Tilburg, The Netherlands. Transport, non‐equilibrium sorption and biodegradation chain processes at the site were simulated using the CHAIN_2D code without further calibration. The modelled PCE compared reasonably well with observed PCE concentrations in the pumped water. We also performed a scenario analysis by applying several increased reductive dechlorination rates, reflecting different degradation conditions (e.g. addition of yeast extract and citrate). The scenario analysis predicted considerably higher concentrations of the degradation products as a result of enhanced reductive dechlorination of PCE. The predicted levels of the very toxic compound VC were now an order of magnitude above the maximum permissible concentration levels. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

12.
Sedimentation may have a significant effect on the transport of solutes and environmental isotopes in sediment. The depth profiles of the Cl?, δ2H and δ18O in a borehole in the aquifer–aquitard system in the Pearl River Delta (PRD), China, were obtained by centrifuging the core sediment samples. A one‐dimensional model based on the sedimentation and sea level changes of the PRD during the Holocene was built to investigate numerically the transport mechanisms of Cl?, δ2H and δ18O. The sedimentation process was modelled as a moving boundary problem with the moving rate equal to the sedimentation rate. The model was calibrated and the parameters were obtained by comparing simulated and measured data. Very good agreement between all the three observed profiles and the simulated ones demonstrates the reliability of the model and the parameters. Simulation results show that the shapes of the curves are controlled by the combination of sedimentation and upper boundary conditions. Diffusion solely is adequate to reconstruct the observed profiles, which indicates that diffusion is the dominant vertical transport mechanism. The effective diffusion coefficients of the aquitard and the aquifer equal to 5.0 × 10?11 and 2.0 × 10?10 m2/s, respectively. The results of this study will help in understanding the transport mechanisms of solutes and environmental tracers in deltas with geology and hydrogeology similar to the PRD. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

13.
The objective of this study was to experimentally determine the influence of pore structure on the transport and dissolution of trichloroethylene (TCE) in clay-rich saprolite. In order to simulate a "spill," pure-phase TCE containing a water-insoluble fluorescent dye was injected into two heterogeneous 24-cm-diameter by 37-cm-long undisturbed columns of water-saturated saprolite. TCE entry occurred at capillary pressures of 2.7 and 4.0 kPa. Ten or 28 d after injection, the column was sliced horizontally into three sections and visually examined. The distribution of fluorescent dye indicated that pure-phase TCE migrated mainly through fractures in the shale saprolite and through fine root holes or other macropores in the limestone saprolite residuum. Analysis of saprolite subsamples indicated that TCE was present throughout much of the saprolite column but usually at concentrations less than the solubility of TCE. This spreading was caused by diffusion, which also contributed to the rapid dissolution of TCE in the fractures and macropores. Modeling was carried out using previously published dissolution and diffusion equations. The calculations confirm that rapid disappearance of immiscible TCE can occur in this type of material because of the small size of fracture or macropore openings and the high porosity of the fine-grained material. This study indicates that industrial solvents can readily enter fractures and macropores in otherwise very fine-grained subsoils and then rapidly dissolve and diffuse into the fine-pore structure, from which they may be very difficult to remove.  相似文献   

14.
A series of numerical simulations using a fully coupled poroelastic numerical model is performed to analyze the so-called Rhade effect. A three-layer aquifer system composed of two aquifers separated by an aquitard, and a corresponding single-layer aquifer system composed of an equivalent lumped material are simulated for the purpose of comparison. In the numerical simulation of the layered aquifer system, the Rhade effect is observed in the aquitard and upper aquifer immediately after the stop of groundwater pumping from the lower aquifer. In contrast, the numerical simulation results of the lumped aquifer system do not show such Rhade effect throughout the entire domain during the groundwater pumping shutoff period. These numerical simulation results strongly suggest that hydraulically less permeable and mechanically more deformable aquitards that generally exist in layered aquifer systems particularly play an important role in causing the Rhade effect at the end of groundwater pumping. The Rhade effect is caused by two mechanisms: a slower hydraulic propagation (head recovery) of the unpumping stress than its mechanical propagation (extension) from the pumped aquifer into the adjacent aquitard and unpumped aquifer due to the relatively lower hydraulic conductivity of the aquitard, and an amplification of the faster mechanical propagation (excessive extension) in the lower part of the aquitard due to its relatively higher deformability. However, the unpumping stress is evenly distributed throughout the entire domain of the lumped aquifer system over time without such hydrogeomechanical mechanisms since it does not have an aquitard and hence is hydraulically and mechanically homogeneous.  相似文献   

15.
A mathematical model that describes the drawdown due to constant pumpage from a finite radius well in a two‐zone leaky confined aquifer system is presented. The aquifer system is overlain by an aquitard and underlain by an impermeable formation. A skin zone of constant thickness exists around the wellbore. A general solution to a two‐zone leaky confined aquifer system in Laplace domain is developed and inverted numerically to the time‐domain solution using the modified Crump (1976) algorithm. The results show that the drawdown distribution is significantly influenced by the properties and thickness of the skin zone and aquitard. The sensitivity analyses of parameters of the aquifer and aquitard are performed to illustrate their effects on drawdowns in a two‐zone leaky confined aquifer system. For the negative‐skin case, the drawdown is very sensitive to the relative change in the formation transmissivity. For the positive‐skin case, the drawdown is also sensitive to the relative changes in the skin thickness, and both the skin and formation transmissivities over the entire pumping period and the well radius and formation storage coefficient at early pumping time. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

16.
Reductive dechlorination of perchloroethylene (PCE) and trichloroethylene (TCE) by vitamin B12 is an analogue of the microbial reductive dechlorination reaction and is presently being applied as a remediation technique. Stable carbon isotopic analysis, an effective and powerful tool for the investigation and monitoring of contaminant remediation, was used to characterize the isotopic effects of reductive dechlorination of PCE and TCE by vitamin B12 in laboratory microcosms. In laboratory experiments, 10 mg/L vitamin B12 degraded >90% of the initial 20 mg/L PCE with TCE, the primary product of PCE degradation, accounting for between 64% and 72% of the PCE degraded. In experiments with TCE, 147 mg/L vitamin B12 degraded >90% of the initial 20 mg/L TCE with cis -dichloroethene ( c DCE), the primary product of degradation accounting for between 30% and 35% of the TCE degraded. Degradation of both PCE and TCE exhibited first-order kinetics. Strong isotopic fractionation of the reactant PCE and of the reactant TCE was observed over the course of degradation. This fractionation could be described with a Rayleigh model using enrichment factors of −16.5%o and −15.8%o for PCE, and −17.2%o and −16.6%o for TCE. Fractionation was similar in all experiments, with a mean enrichment factor of −16.5%o ± 0.6%o. The occurrence of such large enrichment factors indicates that isotopic analysis can be used to monitor the dechlorination of PCE and TCE by vitamin B12 and remediation of ground water plumes. Evidence indicates that isotopic fractionation is taking place during complexation of the chlorinated ethenes to vitamin B12, as has been suggested for reductive dechlorination by zero valent iron. The differences between e values for this reaction and those observed for anaerobic biodegradation of the chlorinated ethenes suggest that there may be differences in the rate-determining step for these two processes.  相似文献   

17.
Closed‐form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint‐Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed‐form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values.  相似文献   

18.
1D resistivity sounding and 2D resistivity imaging surveys were integrated with geological and hydrochemical data to assess the aquifer vulnerability and saltwater intrusion in the north of Nile Delta, Egypt. In the present study, the El-Gharbyia main drain was considered as a case study to map the sand bodies within the upper silt and clay aquitard. Twenty Schlumberger soundings and six 2D dipole-dipole profiles were executed along one profile close to the western side of the main drain. In addition, 14 groundwater samples and 4 surface water samples from the main drain were chemically analyzed to obtain the major and trace elements concentrations.The results from the resistivity and hydrochemical data were used to assess the protection of the groundwater aquifer and the potential risk of groundwater pollution. The inverted resistivities and thicknesses of the layers above the aquifer layer were used to estimate the integrated electrical conductivity (IEC) that can be used for quantification of aquifer vulnerability. According to the aquifer vulnerability assessment of an underlying sand aquifer, the southern part of the area is characterized by high vulnerability zone with slightly fresh to brackish groundwater and resistivity values of 11-23 Ω.m below the clay cap. The resistivity sections exhibit some sand bodies within the clay cap that lead to increase the recharging of surface waste water (650 mg/l salinity) and flushing the upper part of underlying saltwater aquifer. The region in the north has saltwater with resistivity less than 6 Ω.m and local vulnerable zones within the clay cap. The inverted 2D dipole-dipole profiles in the vulnerable zones, in combination with drilling information have allowed the identification of subsoil structure around the main drain that is highly affected by waste water.  相似文献   

19.
The effects of wellbore‐wall compression from rough excavation on monitored groundwater levels and qualities under natural hydraulic gradient conditions were investigated in a shallow clayey Andisol aquifer. Nine wellbores reaching the underlying aquitard at about 2.6‐m depth were constructed by dynamic cone penetrometry to mimic rough wellbore construction. Five of these were constructed under wet aquifer soil conditions and the remaining four under dry conditions. A 15‐month period monitoring showed that the groundwater levels in the wellbores constructed under wet conditions responded significantly in retard of, and in narrower ranges than, those constructed under dry conditions. The wellbore‐wall hydraulic conductivities at the former wellbores were calculated to be more than one to two orders of magnitude lower than those at the latter ones. Furthermore, remarkable nitrate removal attributable to the occurrence of a heterotrophic denitrification was observed in one of the former wellbores. In contrast, the groundwater levels and qualities in the latter wellbores appeared to be generally similar to those monitored in the conventional soil coring and augering‐derived wellbores. Our results suggest that the wellbore‐wall compression induced by rough excavation under wet and soft aquifer soil conditions leads to a substantial decrease in the wellbore‐wall hydraulic conductivity, which in turn can lead to unreliable groundwater levels and qualities. This problem can occur in clayey Andisols whenever the aquifer soil is wet; however, the problem can be largely avoided by constructing the wellbore under dry and hard aquifer soil conditions.  相似文献   

20.
Radial reactive transport is investigated in an aquifer–aquitard system considering the important processes such as advection, radial and vertical dispersions for the aquifer, vertical advection and dispersion for the aquitards, and first-order biodegradation or radioactive decay. We solved the coupled governing equations of transport in the aquifer and the aquitards by honoring the continuity of concentration and mass flux across the aquifer–aquitard interfaces and recognizing the concentration variation along the aquifer thickness. This effort improved the averaged-approximation (AA) model, which dealt with radial dispersion in an aquifer–aquitard system by excluding the aquitard advection. To compare with our new solution, we expanded the AA model by including the aquitard advection. The expanded AA model considerably overestimated the mass in the upper aquitard when an upward advection existed there. The rates of mass change in the upper aquitard from the new solution and the AA model solution increased with time following sub-linear fashions. The times corresponding to the peak values of the residence time distributions for the AA model, the expanded AA model, and the new model were almost the same. The residence time distributions seemed to follow the Maxwell–Boltzmann distribution closely when plotting the time in logarithmic scale. In addition, we developed a finite-element COMSOL Multiphysics simulation of the problem, and found that the COMSOL solution agreed with the new solution well.  相似文献   

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