1-, 2-, and 3-dimensional effective conductivity of aquifers

Starting with a stochastic differential equation with random coefficients describing steady-state flow, the effective hydraulic conductivity of 1-, 2-, and 3-dimensional aquifers is derived. The natural logarithm of hydraulic conductivity (lnK) is assumed to be heterogeneous, with a spatial trend, and isotropic. The effective conductivity relates the mean specific discharge in an aquifer to the mean hydraulic gradient, thus its importance in predicting Darcian discharge when field data represent mean or average values of conductivity or hydraulic head. Effective conductivity results are presented in exact form in terms of elementary functions after the introduction of special sets of coordinate transformations in two and three dimensions. It was determined that in one, two, and three dimensions, for the type of aquifer heterogeneity considered, the effective hydraulic conductivity depends on: (i) the angle between the gradient of the trend of lnK and the mean hydraulic gradient (which is zero in the one-dimensional situation); (2) (inversely) on the product of the magnitude of the trend gradient of lnK, b, and the correlation scale of lnK, and (3) (proportionally) on the variance of lnK, _f ² . The productb plays a central role in the stability of the results for effective hydraulic conductivity.     

Conceptual model of leachate migration in a granular aquifer derived from the integration of multi-source characterization data (St-Lambert,Canada)

Numerical models encompassing source zones and receptors, based on representative conceptual models and accounting for aquifer heterogeneity, are needed to understand contaminant migration and fate; however, aquifer characterization seldom provides the necessary data. This study aimed to develop a workflow for field characterization and data integration, which could: (1) be adapted to the definition of subwatershed-scale aquifer heterogeneity (over 10 km²) and (2) adequately support mass transport model development. The study involved the field investigation of a shallow granular aquifer in a 12-km² subwatershed in Saint-Lambert-de-Lauzon, Canada, in which a decommissioned landfill is emitting a leachate plume managed by natural attenuation. Using proven field methods, the characterization sequence was designed to optimize each method in terms of location, scale of acquisition, density and quality. The emphasis was on the acquisition of detailed indirect geophysical data that were integrated with direct hydraulic and geochemical data. This report focuses on the first qualitative and geostatistical data integration steps of the workflow leading to the development of a hydrogeological conceptual model. This is a prerequisite for further integration steps: prediction of hydrofacies and hydraulic conductivity (K), geostatistical simulations of K, studies of geochemical processes and numerical modeling.     

Estimating regional-scale fractured bedrock hydraulic conductivity using discrete fracture network (DFN) modeling

Estimating bedrock hydraulic conductivity of regional fractured aquifers is challenging due to a lack of aquifer testing data and the presence of small and large-scale heterogeneity. This study provides a novel approach for estimating the bedrock hydraulic conductivity of a regional-scale fractured bedrock aquifer using discrete fracture network (DFN) modeling. The methodology is tested in the mountainous Okanagan Basin, British Columbia, Canada. Discrete fractures were mapped in outcrops, and larger-scale fracture zones (corresponding to lineaments) were mapped from orthophotos and LANDSAT imagery. Outcrop fracture data were used to generate DFN models for estimating hydraulic conductivity for the fractured matrix (K _m). The mountain block hydraulic conductivity (K _mb) was estimated using larger-scale DFN models. Lineament properties were estimated by best fit parameters for a simulated pumping test influenced by a fracture zone. Unknown dip angles and directions for lineaments were estimated from the small-scale fracture sets. Simulated K _m and K _mb values range from 10^–8 to 10^–7?m/s and are greatest in a N–S direction, coinciding with the main strike direction of Okanagan Valley Fault Zone. K _mb values also decrease away from the fault, consistent with the decrease in lineament density. Simulated hydraulic conductivity values compare well with those estimated from pumping tests.     

Variation in time-to-compliance for pump-and-treat remediation of mass transfer-limited aquifers with hydraulic conductivity heterogeneity

In this study, the impact of correlation length (λ) of hydraulic conductivity (K) heterogeneity on pump-and-treat (P&T) remediation period (time-to-compliance) for a mass transfer-limited aquifer is evaluated. Additionally, impacts of variance (σ ²), different distributions of high and low K zones and different initial contaminant masses are explored. Two different P&T policies including different number of wells pumping at different rates are employed for the investigation. Simulation–optimization approach in which a genetic algorithm (GA) is linked with a groundwater flow and contaminant transport model is used. Results show that K heterogeneity, in terms of λ _ln K , s_ln K² \sigma_{\ln \,K}^{2} and respective locations of low and high K zones, significantly impacts the time-to-compliance. Contaminant presence at low K zones can increase the time required to clean up the aquifer. Lower variation is observed in time-to-compliance for the remediation design utilizing higher number of wells pumping at slower rates compared to the design with a single well pumping at a higher rate. Higher number of wells increases the robustness of P&T remediation system when aquifer is heterogeneous in K.     

The effect of aquifer heterogeneity on natural attenuation rate of BTEX

Monitored natural attenuation can be a viable option for remediation of groundwater contamination by BTEX compounds. Under the field conditions, the rate of contaminant mass attenuation through natural processes, such as biodegradation, to a large extent affected by the groundwater flow regime, which is primarily controlled by the aquifer heterogeneity. Numerical simulation techniques were used to describe quantitatively the relationship between biodegradation rate of BTEX and aquifer heterogeneity. Different levels of aquifer heterogeneity were described by random hydraulic conductivity fields (K) having different statistical parameters, the coefficient of variation (CV) and the correlation length (h). The Turning Bands Algorithm was used to generate such K fields. Visual MODFLOW/RT3D was used to simulate the fate and transport of dissolved BTEX plume within heterogeneous aquifers. The multispecies reactive transport approach described BTEX degradation using multiple terminal electron-accepting processes. First-order biodegradation rate constants were calculated from simulated BTEX plumes in heterogeneous flow fields. The results showed that aquifer heterogeneity significantly affected biodegradation rate; it decreased with increasing CV when h was in the range of up to 12 m, whereas it increased with increasing CV when h was greater than about 12 m. For well characterized aquifers, this finding could be of great value in assessing the effectiveness of natural attenuation during feasibility studies at BTEX contaminated sites.     

Field characterization and data integration to define the hydraulic heterogeneity of a shallow granular aquifer at a sub-watershed scale

Providing a sound basis for aquifer management or remediation requires that hydrogeological investigations carried out to understand groundwater flow and contaminant transport be based on representative data that capture the heterogeneous spatial distribution of aquifer hydraulic properties. This paper describes a general workflow allowing the characterization of the heterogeneity of the hydraulic properties of granular aquifers at an intermediate scale of a few km². The workflow involves characterization and data integration steps that were applied on a 12-km² study area encompassing a decommissioned landfill emitting a leachate plume and its main surface water receptors. The sediments composing the aquifer were deposited in a littoral–sublittoral environment and show evidence of small-scale transitional heterogeneities. Cone penetrometer tests (CPT) combined with soil moisture and electrical resistivity (SMR) measurements were thus used to identify and characterize spatial heterogeneities in hydraulic properties over the study area. Site-specific statistical relationships were needed to infer hydrofacies units and to estimate hydraulic properties from high-resolution CPT/SMR soundings distributed all over the study area. A learning machine approach was used due to the complex statistical relationships between colocated hydraulic and CPT/SMR data covering the full range of aquifer materials. Application of this workflow allowed the identification of hydrofacies units and the estimation of horizontal hydraulic conductivity, vertical hydraulic conductivity and porosity over the study area. The paper describes and discusses data acquisition and integration methodologies that can be adapted to different field situations, while making the aquifer characterization process more time-efficient and less labor-intensive.     

Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)

Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport.     

基于不同地质统计方法的渗透系数场对污染物运移的影响

渗透系数场的空间变异性是影响污染物运移结果的决定因素,而地质统计方法是解决渗透系数空间变异性的主要技术手段。本文利用野外场地实测数据,采用普通克里格法和指示克里格法、顺序高斯模拟法和顺序指示模拟法四种地质统计方法,插值估测和模拟再现随机渗透系数场,进而对比研究四种渗透系数场对大尺度污染物运移的影响。研究结果表明,污染羽的质心位置（一阶矩）主要由渗透系数的平均值来决定;污染羽在空间上的展布范围（二阶矩）主要受渗透系数空间变异方差的影响;条件模拟克服了估计法的平滑效果,较好地再现真实曲线的波动性,渗透系数（ lnK）估计方差与污染羽空间二阶矩随着条件模拟次数的增加而减小,并且顺序指示模拟程度更加明显。     

渗透系数的空间变异性对污染物运移的影响研究

随机水文地质学方法,较传统的确定性方法而言,是解决非均质含水层中水流和溶质运移问题的一种更为合理的手段。据以往研究,假设渗透系数场遵循对数正态分布,利用直接傅立叶变换方法来生成渗透系数随机场。应用基于随机理论的蒙特卡罗方法,来研究渗透系数的空间变异性对污染物运移结果的影响。实例研究表明,污染物在含水层中运移过程中污染羽的展布范围(二阶矩)随着渗透系数空间变异方差的增大而扩大,而污染羽在空间上的质心位置(一阶矩)基本不受方差的影响,仅取决于渗透系数随机场的均值大小。另外还分析了污染羽在各点的浓度变化方差和变异系数分别随渗透系数变异方差的变化状况。     

High-resolution aquifer analog of fluvial–aeolian sediments of the Guarani aquifer system

The Guarani aquifer system (GAS) represents one of the biggest aquifers in the world and is the most relevant groundwater resource in South America. For the first time, by combining field and laboratory measurements, a high-resolution aquifer analog model of fluvial–aeolian sediments of the GAS in São Paulo State (Brazil) is constructed. Three parallel sections of frontal outcrops, 28 m × 5.8 m, and two parallel sections of lateral outcrops, 7 m × 5.8 m, are recorded during open-pit mining of sandy sediments and describe in detail the three-dimensional distribution of the local lithofacies and hydrofacies. Variations of hydraulic conductivity, K, and porosity, n, are resolved on the centimeter scale, and the most permeable units of the fluvial–aeolian facies association are identified. The constructed aquifer analog model shows moderate hydraulic heterogeneity and a mean K value of 1.36 × 10^?4 m/s, which is greater than the reported range of K values for the entire GAS in São Paulo State. The results suggest that the examined sedimentary unit constitutes a relevant portion of the GAS in São Paulo State in the context of groundwater extraction and pollution. Moreover, the constructed aquifer analog is considered an ideal basis for future numerical model experiments, aiming at in-depth understanding of the groundwater flow and contaminant transport patterns at this GAS portion or at comparable fluvial–aeolian facies associations.     

Estimation of Hydraulic Conductivity and Its Uncertainty from Grain-Size Data Using GLUE and Artificial Neural Networks

Various approaches exist to relate saturated hydraulic conductivity (K _s) to grain-size data. Most methods use a single grain-size parameter and hence omit the information encompassed by the entire grain-size distribution. This study compares two data-driven modelling methods??multiple linear regression and artificial neural networks??that use the entire grain-size distribution data as input for K _s prediction. Besides the predictive capacity of the methods, the uncertainty associated with the model predictions is also evaluated, since such information is important for stochastic groundwater flow and contaminant transport modelling. Artificial neural networks (ANNs) are combined with a generalised likelihood uncertainty estimation (GLUE) approach to predict K _s from grain-size data. The resulting GLUE-ANN hydraulic conductivity predictions and associated uncertainty estimates are compared with those obtained from the multiple linear regression models by a leave-one-out cross-validation. The GLUE-ANN ensemble prediction proved to be slightly better than multiple linear regression. The prediction uncertainty, however, was reduced by half an order of magnitude on average, and decreased at most by an order of magnitude. This demonstrates that the proposed method outperforms classical data-driven modelling techniques. Moreover, a comparison with methods from the literature demonstrates the importance of site-specific calibration. The data set used for this purpose originates mainly from unconsolidated sandy sediments of the Neogene aquifer, northern Belgium. The proposed predictive models are developed for 173 grain-size K _s-pairs. Finally, an application with the optimised models is presented for a borehole lacking K _s data.     

Heterogeneity of hydraulic conductivity and Darcian flux in the submerged streambed and adjacent exposed stream bank of the Beiluo River,northwest China

Recognizing the heterogeneity of hydraulic conductivity and hyporheic flow is critical for understanding contaminant transfer and biogeochemical and hydrological processes involving streams and aquifers. In this study, the heterogeneity of hydraulic conductivity and Darcian flux in a submerged streambed and its adjacent exposed stream banks were investigated in the Beiluo River, northwest China. In the submerged streambed, Darcian flux was estimated by measurement of vertical hydraulic conductivity (K _v) and vertical head gradient (VHG) using in-situ permeameter tests. On exposed stream banks, both horizontal hydraulic conductivity (K _h) and K _v were measured by on-site permeameter tests. In the submerged streambed, K _v values gradually decreased with depth and the higher values were concentrated in the center and close to the erosional bank. Compared to the exposed stream banks, the K _v values were higher in the streambed. From stream stage to the topmost layer of tested sediment, through increasing elevation, the K _h values increased on the erosional bank, while they decreased on the depositional bank. The values of VHG along the thalweg illustrate that downwelling flux occurred in the deepest area while upwelling flux appeared in the other areas, which might result from the change of streambed elevation. The higher value of the Darcian flux in the submerged streambed existed near the erosional bank.     

Delineating subsurface heterogeneity at a loop of River Steinlach using geophysical and hydrogeological methods

Stratigraphic heterogeneity is a key controlling factor for flow and transport in groundwater systems. In this case study, we have combined two- and three-dimensional images of electric resistivity with hydrogeological data to delineate such stratigraphic heterogeneity at a loop of River Steinlach close to Tübingen, Germany, where we estimated spatially varying aquifer parameters using established evaluation techniques. We developed a three-layer stratigraphic model consisting of heterogeneous sandy gravel overlain by a fine alluvium including top soil, and underlain by sandstone weathered at its top. The sandy gravel makes up the aquifer unit while we interpret the sandstone as aquitard. We classified the area into two stratigraphic segments based on resistivity data. The Southern segment consists of a thicker alluvium where the aquifer material contains more clay than in the Northern segment. Two different stratigraphic structures were also delineated at the Southern and Northern segments, respectively. These structures are visible in inversion results as low-resistivity features trending in the SE–NW in the Southern segment and NE–NW in the Northern segment. Both structures may be previous flow paths of River Steinlach, and the low permeability material overlying them may impair flow exchange in the area. We performed slug and pumping tests to estimate the hydraulic conductivity (K) of the aquifer. The K distributions show slight variation with higher values obtained at wells within the Northern segment and close to the river bank. A qualitative comparison of measured hydraulic conductivities with the resistivity distribution shows good agreement of the spatial patterns. The stratigraphic and hydraulic heterogeneities delineated in this work are important for experimental and modeling studies of flow, transport, and hyporheic exchange at the site.     

Short Note: Effective Hydraulic Conductivity and Transmissivity for Heterogeneous Aquifers

Regional scale models of groundwater flow and transport often employ domain discretizations with grid blocks larger than typical scales of field data. For heterogeneous formations, this difference in scales is often handled by using effective (upscaled) parameters. We investigate the problem of upscaling hydraulic conductivity and transmissivity from a small scale of measurement to a larger scale of grid blocks. Transmissivity statistics is expressed in terms of statistics of hydraulic conductivity, and expressions for the effective (upscaled) hydraulic conductivity K _eff and transmissivity T _eff for steady state flow in confined heterogeneous aquifers are derived by means of stochastic averaging and perturbation analysis. These expressions reveal that the commonly used relation T _eff = BK _eff, where B is the confined aquifer thickness, is not generally valid.     

水力层析法与克立金法估算非均质含水层渗透系数场比较

含水层非均质性空间分布特征的识别,是准确模拟地下水流和污染物运移的前提.基于室内非均质含水层砂箱实验,分别利用水力层析法和克立金插值法刻画了非均质含水层渗透系数场.研究结果表明:(1) 水力层析法与克立金法相比,不仅可以更好地刻画非均质含水层渗透系数场,还可以更高精度地预测地下水流过程;(2) 水力层析抽水实验中,通过增加抽水实验组数可以有效地提高水力层析参数反演的精度,但是抽水实验组数增加到一定程度以后,再增加抽水组数不会显著提升参数反演的效果.后续需要进一步研究水力层析抽水实验合适的组数,进一步对抽水井进行优化布设.      

High-resolution saturated hydraulic conductivity logging of borehole cores using air permeability measurements

Saturated hydraulic conductivity (K _s) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. The hand-held air permeameter technique was investigated for high-resolution hydraulic conductivity determination on borehole cores using a spatial resolution of ～0.05 m. The suitability of such air permeameter measurements on friable to poorly indurated sediments was tested to improve the spatial prediction of classical laboratory-based K _s measurements obtained at a much lower spatial resolution (～2 m). In total, 368 K _s measurements were made on ～350 m of borehole cores originating from the Campine basin, northern Belgium, while ～5,230 air permeability measurements were performed on the same cores, resulting in a K _s range of seven orders of magnitude. Cross-validation demonstrated that, using air permeameter data as the secondary variable for laboratory based K _s measurements, the performance increased from R ²?=?0.35 for ordinary kriging (laboratory K _s only) to R ²?=?0.61 for co-kriging. The separate treatment of horizontal and vertical hydraulic conductivity revealed considerable anisotropy in certain lithostratigraphical units, while others were clearly isotropic at the sample scale. Air permeameter measurements on borehole cores provide a cost-effective way to improve spatial predictions of traditional laboratory based K _s.     

Effect of hypersaline cooling canals on aquifer salinization

The combined effect of salinity and temperature on density-driven convection was evaluated in this study for a large (28 km²) cooling canal system (CCS) at a thermoelectric power plant in south Florida, USA. A two-dimensional cross-section model was used to evaluate the effects of hydraulic heterogeneities, cooling canal salinity, heat transport, and cooling canal geometry on aquifer salinization and movement of the freshwater/saltwater interface. Four different hydraulic conductivity configurations, with values ranging over several orders of magnitude, were evaluated with the model. For all of the conditions evaluated, aquifer salinization was initiated by the formation of dense, hypersaline fingers that descended downward to the bottom of the 30-m thick aquifer. Saline fingers reached the aquifer bottom in times ranging from a few days to approximately 5 years for the lowest hydraulic conductivity case. Aquifer salinization continued after saline fingers reached the aquifer bottom and coalesced by lateral movement away from the site. Model results showed that aquifer salinization was most sensitive to aquifer heterogeneity, but was also sensitive to CCS salinity, temperature, and configuration.     

Probability of plume interception using conditional simulation of hydraulic head and inverse modeling

A procedure to estimate the probability of intercepting a contaminant groundwater plume for monitoring network design has been developed and demonstrated. The objective of the procedure is to use all available information in a method that accounts for the heterogeneity of the aquifer and the paucity of data. The major components of the procedure are geostatistical conditional simulation and parameter estimation that are used sequentially to generate flow paths from a suspected contaminant source location to a designated monitoring transect. From the flow paths, a histogram is constructed that represents the spatial probability distribution of plume centerlines. With an independent estimate of the plume width, a relationship between the total cost and the probability of detecting a plume can be made. The method uses geostatistical information from hydraulic head measurements and is conditioned by the data and the physics of groundwater flow. This procedure was developed specifically for the design of monitoring systems at sites where very few, if any, hydraulic conductivity data are available.     

Nonaqueous liquid pool dissolution in three-dimensional heterogeneous subsurface formations

A three-dimensional numerical flow and contaminant transport model is developed to investigate the effect of variable hydraulic conductivity on average mass transfer coefficients associated with the dissolution of dense nonaqueous phase liquid (DNAPL) pools in heterogeneous, water-saturated subsurface formations. Randomly generated, three-dimensional hydraulic conductivity fields are used to represent a heterogeneous confined aquifer. Model simulations indicate that the average mass transfer coefficient is inversely proportional to the variance of the log-transformed hydraulic conductivity. A power law correlation relating the Sherwood number to the variance of the log-transformed hydraulic conductivity and appropriate Peclet numbers is developed. A reasonable fit between predicted and numerically determined mass transfer coefficients is observed.     

Complementary use of tracer and pumping tests to characterize a heterogeneous channelized aquifer system in New Zealand

The combined use of pumping and tracer test data enabled the derivation of equivalent average hydraulic conductivities (K_avg) for each test in a heterogeneous channelized alluvial aquifer, whereas K values of the preferential flow paths were two orders of magnitude higher. Greater and earlier drawdown was generally observed along preferential flow lines in a pumping test, within an array of 21 wells. The study aim was to characterize hydraulic properties of a channelized aquifer system in New Zealand by combining tracer and pumping test data. Estimates were able to be made of the percentage of highly permeable channels within the profile (～1.2%), effective porosity that reflected the maximum fraction of highly permeable channels within the aquifer (?_eff–pc ～0.0038), and flows through highly permeable channels (～98%) and the sandy gravel matrix material (～2%). Using ?_eff–pc, a tracer test K_avg value (～93 m/day) was estimated that was equivalent to pumping test values (～100 m/day), but two orders of magnitude smaller than K calculated solely from transport through permeable channels (K_pc ～8,400 m/day). Derived K values of permeable and matrix material were similar to values derived from grain size distribution using the Kozeny-Carman equation.