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1.
— A new non-contact and non-destructive optical scanning instrument provided a large number of high-precision measurements of thermal conductivity tensor components in samples of sedimentary and impact rocks, as well as new insights into interrelations between thermal conductivity and other physical properties. More than 800 core samples (dry and fluid-saturated) of sedimentary rocks from different Russian oil-gas deposits and impact rocks from the well “Nördlingen 1973” drilled in the Ries impact structure (Germany) were studied using optical scanning technology. It was established that the thermal conductivity parallel to the stratification is more informative for petrophysical investigations than the thermal conductivity perpendicular to the layering. Different approaches were developed to estimate porosity, permeability, pore space geometry, and matrix thermal conductivity with a combination of thermal conductivity measurements in dry and fluid-saturated samples and mathematical modelling. These approaches allow prediction of the rock porosity and permeability and their spatial distribution along a well using thermal conductivity measurements performed with the optical scanning instrument directly applied to cores. Conditions and constraints for using Lichtenecker-Asaad's theoretical model for the estimation of porosity and thermal conductivity of sedimentary rocks were determined. A correlation between thermal conductivity and acoustic velocity, porosity, density, and electric resistivity of impact rocks was found for different rock types. New relationships between permeability, electrical and thermal conductivity found for sedimentary rocks are described.  相似文献   

2.
Considering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less‐mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore‐fluid sampling and geoelectrical measurements can be used to quantify less‐mobile porosity exchange dynamics using the time‐varying relation between fluid and bulk electrical conductivity. For this study, we use macro‐scale (10 s of cm) advection–dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less‐mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations, a lag between fluid and bulk electrical conductivity, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less‐mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types, effective less‐mobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow‐dependent effects directly impact local less‐mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here, less‐mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low‐to‐moderate rate (approximately 3–40 cm/day) hyporheic fluid fluxes. Overall, our model‐based results show that less‐mobile porosity may be expected in a range of natural hyporheic sediments and that changes in flowpath orientation and magnitude will impact less‐mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales.  相似文献   

3.
Measurement uncertainty is a key hindrance to the quantification of water fluxes at all scales of investigation. Predictions of soil‐water flux rely on accurate or representative measurements of hydraulic gradients and field‐state hydraulic conductivity. We quantified the potential magnitude of errors associated with the parameters and variables used directly and indirectly within the Darcy – Buckingham soil‐water‐flux equation. These potential errors were applied to a field hydrometric data set collected from a forested hillslope in central Singapore, and their effect on flow pathway predictions was assessed. Potential errors in the hydraulic gradient calculations were small, approximately one order of magnitude less than the absolute magnitude of the hydraulic gradients. However, errors associated with field‐state hydraulic conductivity derivation were very large. Borehole (Guelph permeameter) and core‐based (Talsma ring permeameter) techniques were used to measure field‐saturated hydraulic conductivity. Measurements using these two approaches differed by up to 3\9 orders of magnitude, with the difference becoming increasingly marked within the B horizon. The sensitivity of the shape of the predicted unsaturated hydraulic conductivity curve to ±5% moisture content error on the moisture release curve was also assessed. Applied moisture release curve error resulted in hydraulic conductivity predictions of less than ±0\2 orders of magnitude deviation from the apparent conductivity. The flow pathways derived from the borehole saturated hydraulic conductivity approach suggested a dominant near‐surface flow pathway, whereas pathways calculated from the core‐based measurements indicated vertical percolation to depth. Direct tracer evidence supported the latter flow pathway, although tracer velocities were approximately two orders of magnitude smaller than the Darcy predictions. We conclude that saturated hydraulic conductivity is the critical hillslope hydrological parameter, and there is an urgent need to address the issues regarding its measurement further. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

4.
Currently, monitoring tools can be deployed in observation boreholes to better assess groundwater flow, flux of dissolved contaminants and their mass discharge in an aquifer. The relationship between horizontal water velocity in observation boreholes and Darcy fluxes in the surrounding aquifer has been studied for natural flow conditions (i.e., no pumping). Interpretation of measurements taken with dilution tests, the colloidal borescope, the Heat Pulse Flowmeter, and other techniques require the conversion of observed borehole velocity u to aquifer Darcy flux q . This conversion is typically done through a proportionality factor α = u/q . In experimental studies as well as in theoretical developments, reported values of α vary almost three orders of magnitude (from 0.5 to 10). This large variability in reported values of α could be explained by: (1) unclear distinction between Darcy flux and water seepage velocity, (2) unclear definition of water velocity in the borehole, (3) effects of well screen and the presence of the measurement device itself on the observable velocities, and (4) hydraulic conditions in the borehole annulus. We address (1), (2) from a conceptual/theoretical perspective, and (3) by means of numerical simulations. We show that issue (1) in low porosity aquifers can yield to order-of-magnitude discrepancies in estimates of q ; (2) may result in discrepancies of up to 50%, and (3) can cause differences up to 20% of water velocity in the borehole void space compared to the theoretical case of an open borehole.  相似文献   

5.
Small‐scale point velocity probe (PVP)‐derived velocities were compared to conventional large‐scale velocity estimates from Darcy calculations and tracer tests, and the possibility of upscaling PVP data to match the other velocity estimates was evaluated. Hydraulic conductivity was estimated from grain‐size data derived from cores, and single‐well response testing or slug tests of onsite wells. Horizontal hydraulic gradients were calculated using 3‐point estimators from all of the wells within an extensive monitoring network, as well as by representing the water table as a single best fit plane through the entire network. Velocities determined from PVP testing were generally consistent in magnitude with those from depth specific data collected from multilevel monitoring locations in the tracer test, and similar in horizontal flow direction to the average hydraulic gradient. However, scaling up velocity estimates based on PVP measurements for comparison with site‐wide Darcy‐based velocities revealed issues that challenge the use of Darcy calculations as a generally applicable standard for comparison. The Darcy calculations were shown to underestimate the groundwater velocities determined both by the PVPs and large‐scale tracer testing, in a depth‐specific sense and as a site‐wide average. Some of this discrepancy is attributable to the selective placement of the PVPs in the aquifer. Nevertheless, this result has important implications for the design of in situ treatment systems. It is concluded that Darcy estimations of velocity should be supplemented with independent assessments for these kinds of applications.  相似文献   

6.
Reclamation of peat bogs for agriculture changes the physical and chemical characteristics of the peat matrix, for example, drainage and tillage accelerate decomposition, altering peat porosity, pore size distribution, and hydraulic properties. This study investigated changes in near-saturated hydraulic conductivity over time after drainage of peat soil for agricultural use by conducting tension infiltrometer measurements in a mire that has been gradually drained and reclaimed for agriculture during the past 80 years (with fields drained 2, 12, 40, and 80 years before the measurements). At pore water pressure closest to saturation (pressure head −1 cm), hydraulic conductivity in the newest field was approximately nine times larger than that in the oldest field, and a decreasing trend with field age was observed. A similar (but weaker) trend was observed with −3 cm pressure head (approximately four times larger in the newest field in comparison to the oldest), but at −6 cm head, there were no significant differences. These results indicate that peat degradation reduces the amount of millimetre-sized pores in particular. They also indicate that changes in peat macroporosity continue for several decades before a new steady state is reached.  相似文献   

7.
Since October 2001, four soil CO2 flux stations were installed in the island of São Miguel (Azores archipelago), at Fogo and Furnas quiescent central volcanoes. These stations perform measurements by the accumulation chamber method and, as the gas flux may be influenced by external variables, the stations are equipped with several meteorological sensors. Multivariate regression analysis applied to the large datasets obtained allowed observing that the meteorological variables may influence the soil CO2 flux oscillations from 18% to 50.5% at the different monitoring sites. Additionally, it was observed that meteorological variables (mainly soil water content, barometric pressure, wind speed and rainfall) play a different role in the control of the gas flux, depending on the selected monitoring site and may cause significant short-term (spike-like) fluctuations. These divergences may be potentially explained by the porosity and hydraulic conductivity of the soils, topographic effects, drainage area and different exposure of the monitoring sites to the weather conditions. Seasonal effects are responsible for long-term oscillations on the gas flux.  相似文献   

8.
Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (ECbulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.  相似文献   

9.
The processes of water movement through the Coombe Deposit in a chalk dry valley near Eastbourne in Southeast England were investigated using simple methods based on regular weekly measurements of rainfall, soil water content, and soil water potential. The drainage flux (recharge) through the soil was determined using the water balance method during the winter and the zero flux plane (ZFP) method after the appearance of the ZFP in the spring. The unsaturated hydraulic conductivity was derived applying Darcy's Law in a novel way using the measured potential gradients and weekly drainage fluxes. The derived conductivity characteristics were adequate to identify the flow mechanisms, to illustrate the difference in behaviour between the horizons of the soil profile, and to give some indication of pore water velocities. The mean daily drainage flux at 2.85 m depth during the recharge period from 10 October 1980 to 29 May 1981 was 1.6 mm d?1. Weekly mean rates of up to 3.7 mm d?1 were observed, but peak short term rates must have considerably exceeded this figure. It was shown that, in the lower part of the Coombe Deposit, when drainage fluxes are large, much of the flux passes through a very small proportion of the wetted cross-sectional area of the soil. This gives rise to pore water velocities of at least 3 m d?1 at a depth of 2.85 m and 0.5 m d?1 between 0.5 m and 2.5 m depth. These results show that pollutants may be moved very rapidly through the profile in this, and similar, material. The core sampling techniques normally used to monitor pollutant movement in the chalk are unlikely to succeed in detecting this movement, not only because it is transient but also because it occupies only a very small proportion of the water filled pores.  相似文献   

10.
Velocities of compressional and shear waves in limestones   总被引:2,自引:1,他引:2  
Carbonate rocks are important hydrocarbon reservoir rocks with complex textures and petrophysical properties (porosity and permeability) mainly resulting from various diagenetic processes (compaction, dissolution, precipitation, cementation, etc.). These complexities make prediction of reservoir characteristics (e.g. porosity and permeability) from their seismic properties very difficult. To explore the relationship between the seismic, petrophysical and geological properties, ultrasonic compressional‐ and shear‐wave velocity measurements were made under a simulated in situ condition of pressure (50 MPa hydrostatic effective pressure) at frequencies of approximately 0.85 MHz and 0.7 MHz, respectively, using a pulse‐echo method. The measurements were made both in vacuum‐dry and fully saturated conditions in oolitic limestones of the Great Oolite Formation of southern England. Some of the rocks were fully saturated with oil. The acoustic measurements were supplemented by porosity and permeability measurements, petrological and pore geometry studies of resin‐impregnated polished thin sections, X‐ray diffraction analyses and scanning electron microscope studies to investigate submicroscopic textures and micropores. It is shown that the compressional‐ and shear‐wave velocities (Vp and Vs, respectively) decrease with increasing porosity and that Vp decreases approximately twice as fast as Vs. The systematic differences in pore structures (e.g. the aspect ratio) of the limestones produce large residuals in the velocity versus porosity relationship. It is demonstrated that the velocity versus porosity relationship can be improved by removing the pore‐structure‐dependent variations from the residuals. The introduction of water into the pore space decreases the shear moduli of the rocks by about 2 GPa, suggesting that there exists a fluid/matrix interaction at grain contacts, which reduces the rigidity. The predicted Biot–Gassmann velocity values are greater than the measured velocity values due to the rock–fluid interaction. This is not accounted for in the Biot–Gassmann velocity models and velocity dispersion due to a local flow mechanism. The velocities predicted by the Raymer and time‐average relationships overestimated the measured velocities even more than the Biot model.  相似文献   

11.
For many scientific and practical tasks, it is important to estimate the soil–water percolation fluxes. This paper builds on measurements with large horizontal time‐domain reflectometry water content sensors in a loamy Mollisol. The sensors were installed into pre‐drilled holes and the gaps between them, and the soil was filled with a slurry of local soil with water. This gave rise to envelopes around them that contained artificial macropores. The sensors reacted to intensive rains by a rapid increase of their readings, often above the native soil's porosity, followed by an almost equally rapid decrease. The paper explores the feasibility of quantifying the rapid percolation, based on these anomalous water content peaks, and demonstrates that this is possible in principle, if the processes are simulated by a suitable model. A two‐dimensional dual porosity non‐equilibrium (mobile‐immobile) model was tried. The envelope around the sensor was modelled as an annulus with higher porosity and hydraulic conductivity, which attracts preferential flow and amplifies the percolation signal. With the model at hand, the flux hydrographs can be derived from model simulations and measured precipitation. For contrast, the Durner equilibrium dual porosity model was tried but was found little suitable. However, even the mobile‐immobile model did not perform perfectly. Simulated water contents were similar to the measured ones at some depths but not in the others, and the percolation fluxes were overestimated, compared to cumulative soil–water balance. Efforts to improve model performance were not successful. Hence, the model structure needs to be improved. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

12.
A novel, non-intrusive fluorescence imaging technique has been used to quantitatively measure the pore geometry, fluid velocity, and solute concentration within a saturated, three-dimensional porous medium. Discrete numerical averages of these quantities have been made over a representative volume of the medium and used to estimate macroscopic quantities that appear in conventional continuum models of flow and transport. The approach is meant to illustrate how microscopic information can be measured, averaged, and used to characterize medium-scale processes that are typically approximated constitutively. The experimental system consisted of a clear, cylindrical column packed with clear spherical beads and a refractive index-matched fluid seeded with fluorescent tracer particles and solute dye. By illuminating the fluid within the column with a scanning planar laser beam, details of flow and concentration within the pore spaces can be quantitatively observed, allowing for three-dimensional, dimensional, time dependent information to be obtained at good resolution. In time dependent information to be obtained at good resolution. In the current experiment, volumetrically averaged velocities and void-to-volume ratios are first compared with bulk measurements of fluid flux and medium porosity. Microscopic measurements of concentration are then used to construct cross-sectionally averaged profiles, mean breakthrough curves, and direct measurements of the dispersive flux, velocity variance, and concentration variance. In turn, the dispersive flux measurements are compared with mean concentration gradients to provide a basis for confirming the Fickian dispersion model and estimating dispersion coefficients for the medium. Coefficients determined in this manner are compared with others based upon traditional length-scale arguments, mean breakthrough analyses, and curve fits with numerical simulations.  相似文献   

13.
在实验室对5块储层砂岩进行了模拟地层压力条件下的超声波速度测试。砂岩样品采自WXS凹陷的W地层,覆盖了从低到高的孔隙度和渗透率范围。实验选用了卤水和4种不同密度油作为孔隙流体,结合温度变化,实现了对流体粘度引致的速度频散研究。对实验结果的分析表明:(1)对于高孔隙度和渗透率的样品,无论是哪种流体饱和,观察到的超声波速度测试值和零频率Gassmann预测值的差异较小(约2-3%),基本上可以用Biot模型解释;对于中等孔隙度和渗透率的样品,低粘度流体(<约3mP?S)的频散效应也可以用Biot模型得到合理解释;(2)对于低、中孔隙度和渗透率样品,当流体粘度增加时,喷射流机制起主导作用,导致严重的速度频散(可达8%)。对储层砂岩的微裂隙纵横比进行了估计并用于喷射流特征频率的计算,当高于该特征频率时,Gassmann理论的假设条件受到破坏,实验室测得的高频速度不能直接用于地震低频条件下的W地层砂岩的Gassmann流体替换研究。  相似文献   

14.
The vertical transport of contaminants from source areas is employed in many risk assessment models and screening tools in order to estimate the contaminant mass discharge (CMD) into underlying aquifers. The key parameters for estimating CMD are the contaminant source area and concentration, and the vertical water flux, the latter of which depends on the vertical hydraulic conductivity and the vertical hydraulic gradient in the subsurface. This study focuses on advancing the use of the combined membrane interface probe hydraulic profiling tool (MiHPT) to investigate the vertical hydraulic gradient across a clay till overlying a sandy aquifer at a contaminated site in Denmark. Only the HPT is necessary for the estimate of vertical hydraulic gradient. The hydraulic head, clay till thickness, and resulting vertical hydraulic gradients found using the MiHPT compared well with observations from nearby nested wells. The parameter with the largest discrepancy was the thickness of the clay till. The advantage of the MiHPT is its relatively quick depth discrete access to information regarding subsurface permeability, vertical hydraulic gradients and contaminant distribution across a site. In this case study, performance of additional dissipationtests during the HPT log to acquire determination of the vertical hydraulic gradient increased the cost by 3% compared to standard HPT logs.  相似文献   

15.
Modeling unsaturated flow in porous media requires constitutive relations that describe the soil water retention and soil hydraulic conductivity as a function of either potential or water content. Often, the hydraulic parameters that describe these relations are directly measured on small soil cores, and many cores are needed to upscale to the entire heterogeneous flow field. An alternative to the forward upscaling method using small samples are inverse upscaling methods that incorporate soft data from geophysical measurements observed directly on the larger flow field. In this paper, we demonstrate that the hydraulic parameters can be obtained from cross borehole ground penetrating radar by measuring the first arrival travel time of electromagnetic waves (represented by raypaths) from stationary antennae during a constant flux infiltration experiment. The formulation and coupling of the hydrological and geophysical models rely on a constant velocity wetting front that causes critical refraction at the edge of the front as it passes by the antennae. During this critical refraction period, the slope of the first arrival data can be used to calculate (1) the wetting velocity and (2) the hydraulic conductivity of the wet (or saturated) soil. If the soil is undersaturated during infiltration, then an estimate of the saturated water content is needed before calculating the saturated hydraulic conductivity. The hydraulic conductivity value is then used in a nonlinear global optimization scheme to estimate the remaining two parameters of a Broadbridge and White soil.  相似文献   

16.
When the purpose of aquifer testing is to yield data for modeling aqueous mass transport, pumping tests and gradient measurement can only partially satisfy characterization requirements. Effective porosity, ground water flow velocity, and the vertical distribution of hydraulic conductivity within the aquifer are left as unknowns. Single well tracer methods, when added to the testing program, can be used to estimate these parameters. A drift, and pumpback test yields porosity and velocity, and point-dilution testing yields depth-discrete hydraulic information, A single emplacement of tracer into a test well is sufficient to conduct both tests. The tracer tests are facilitated by a simple method for injecting and evenly distributing the tracer solution into a wellbore, and by new ion-selective electrode instrumentation, specifically designed for submersible service, for monitoring the concentration of tracers such as bromide.  相似文献   

17.
海底冷泉形成的一种可能机制是海平面下降引起天然气水合物的分解.本文基于对冷泉渗漏特征的分析,建立了二维轴对称模型,利用有限元方法定量分析了南海区域海平面下降对冷泉形成的影响.结果表明,末次冰盛期(26.5~19.0ka BP)海平面下降引起的冷泉活动可以持续到现在,但是从水合物停止分解至今,超孔隙压力的极值在持续减小,而流体向海底的渗漏达西速度先快速减小、然后缓慢减小.同时发现,流体向海底的渗漏达西速度与管状通道的渗透率、通道周围介质的渗透率以及通道的半径等有关,估计目前的冷泉活动还可以持续10000年以上.海平面下降引起的天然气水合物分解,可能是影响全球气候变化的一个重要因素.  相似文献   

18.
This work deals with the evaluation of the dynamic pressures and the associated forces on a pair of rigid vertical cantilever walls retaining a uniform, fully saturated poroelastic layer of soil. Hysteretic damping in the soil skeleton may also be present. Wall pressures and forces are induced by horizontal ground shaking harmonically varying with time and spatially invariant. The problem is solved analytically under conditions of plane strain. The governing partial differential equations of motion, after separation of variables and the simplifying assumptions of zero vertical normal stresses and zero horizontal variation of vertical displacements, reduce to a system of two ordinary differential equations for the amplitudes of the solid skeleton horizontal displacement and the pore water pressure, which are easily solved. The parameters examined include the ratio of the distance between walls to the height of the retained soil material and the soil material properties such as porosity, permeability and damping. The comprehensive numerical data presented indicate that the displacements, wall pressures and resultant forces are highly dependent on the distance between the walls for any values of porosity and permeability.  相似文献   

19.
Water exchange between surface water and groundwater can modulate or generate ecologically important fluxes of solutes across the sediment‐water interface. Seepage meters can directly measure fluid flux, but mechanical resistance and surface water dynamics may lead to inaccurate measurements. Tank experiments were conducted to determine effects of mechanical resistance on measurement efficiency and occurrence of directional asymmetry that could lead to erroneous net flux measurements. Seepage meter efficiency was high (average of 93%) and consistent for inflow and outflow under steady flow conditions. Wave effects on seepage meter measurements were investigated in a wave flume. Seepage meter net flux measurements averaged 0.08 cm/h—greater than the expected net‐zero flux, but significantly less than theoretical wave‐driven unidirectional discharge or recharge. Calculations of unidirectional flux from pressure measurements (Darcy flux) and theory matched well for a ratio of wave length to water depth less than 5, but not when this ratio was greater. Both were higher than seepage meter measurements of unidirectional flux made with one‐way valves. Discharge averaged 23% greater than recharge in both seepage meter measurements and Darcy calculations of unidirectional flux. Removal of the collection bag reduced this net discharge. The presence of a seepage meter reduced the amplitude of pressure signals at the bed and resulted in a nearly uniform pressure distribution beneath the seepage meter. These results show that seepage meters may provide accurate measurements of both discharge and recharge under steady flow conditions and illustrate the potential measurement errors associated with dynamic wave environments.  相似文献   

20.
A direct-drive high-resolution passive profiler (HRPP) was developed to quantify and delineate concentrations of chlorinated volatile organic compounds (CVOCs), geochemical indicators and CVOC-degrading microorganisms/genes, as well as to perform compound-specific stable isotope analysis (CSIA) of CVOCs and estimate interstitial velocity at <30-cm resolution. The profilers can be coupled together to provide a continuous sample interval and advanced to depths up to approximately 9 m below-ground surface (bgs) within saturated media where direct-push techniques are feasible. The HRPP was field tested in a previous dense nonaqueous phase liquid (DNAPL) source zone at the former Naval Air Station in Alameda, CA. HRPP data sets were compared to the following traditional groundwater data sets: CVOC and anion concentrations in standard and multilevel monitoring well water samples, CVOC concentrations in soil core samples, qualitative contaminant profiles delineated with a membrane interface probe (MIP), microbial community and CSIA profiles from Bio-Traps® deployed in wells, groundwater velocity from passive flux meters (PFMs), lithologic profiles correlated with MIP electrical conductivity (EC), and velocity estimates based on permeability profiles measured with a Geoprobe hydraulic profiling tool (HPT). In some cases, the HRPP data were equivalent to traditional techniques and, in other cases, the HRPP data were more representative of local variability rather than bulk aquifer conditions. Overall the results support the use of the HRPP to provide high-resolution data on concentrations, velocity, and microbial activity in temporary direct-push deployments without well installation, providing a new tool to better assess source zones and contaminated groundwater plumes, even in low permeability media, and to increase the fidelity of site transport models.  相似文献   

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