Heterogeneous Hydraulic Conductivity Research Articles

Influence of pumping operational schedule on solute concentrations at a well in randomly heterogeneous aquifers

We investigate the way diverse groundwater extraction strategies affect the history of solute concentration recovered at a pumping well while taking into account random spatial variability of the system hydraulic conductivity. Considering the joint effects of spatially heterogeneous hydraulic conductivity and temporally varying well pumping rates leads to a realistic evaluation of groundwater contamination risk at the pumping well location. We juxtapose the results obtained when the pumping well extracts a given amount of water operating (a) at a uniform pumping rate and (b) under a transient regime. The analysis is performed within a numerical Monte Carlo framework. Our results show that contaminant concentration breakthrough curves (BTCs) at the well are markedly affected by the transient pumping strategy according to which the well is operated. Our results document the occurrence in time of multiple peaks in the mean and variance of flux-averaged concentrations at the extraction well operating at a transient rate. Our findings suggest that lowest and largest values of mean and variance of flux-averaged concentration at the well tend to occur at the same time. We show that uncertainty associated with detected BTCs at the well increases for pumping regimes displaying a high degree of temporal variability. As such, the choice of the type of engineering control to the temporal sequence of pumping rates could represent a key factor to drive quantification of uncertainty of the contaminant concentration detected at the well. It is documented that pumping rate fluctuations induce a temporally oscillating risk pattern at the well, thus suggesting that the selection of a dynamic pumping regime has a clear influence on the temporal evolution of risk at the well.

Conservative transport upscaling based on information of connectivity

AbstractConnected structures in highly heterogeneous hydraulic conductivity fields lead to channels and preferential pathways for the main fluid flux and fastest solute particles. Their spatial complement is zones of slow advection, where solutes are delayed, causing tailing of solute breakthrough curves. These delays depend on the inclusion's size and the hydraulic conductivity contrast between inclusion and channel. The interplay between channels and small‐scale low conductivity inclusions leads to anomalous transport at larger scales. We test whether a simple separation of transport processes between channels and inclusions could be used to parameterize an effective transport model accounting for anomalous transport. Effective transport is represented by a multirate mass transfer model (MRMT): fast channel transport is controlled by parameters of the mobile zone, while slow advective delays are controlled by parameters of the mobile‐immobile exchange. We delineate the connected channels and analyze their connectivity followed by characterizing the low conductivity inclusions. We parameterize a MRMT model using connectivity and the statistics of the low permeable inclusions. Finally, we compare the parameterized MRMT with detailed numerical simulations in heterogeneous hydraulic conductivity fields with a clear separation between connected channel network and inclusions. In intermediately connected hydraulic conductivity fields only the cut‐off time of the tails is represented while early and intermediate time behavior is not reproduced. We suggest that an effective model for the latter case should account for additional processes like variability in advective velocity.

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 (Kv) and vertical head gradient (VHG) using in-situ permeameter tests. On exposed stream banks, both horizontal hydraulic conductivity (Kh) and Kv were measured by on-site permeameter tests. In the submerged streambed, Kv 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 Kv values were higher in the streambed. From stream stage to the topmost layer of tested sediment, through increasing elevation, the Kh 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.

Spatial distribution of hydraulic conductivity in soils of secondary tropical montane cloud forests and shade coffee agroecosystems

Disturbance of the tropical montane cloud forest (TMCF) produces secondary forests and coffee agroecosystems that conserve part of the arboreal-shrub vegetation of the native forests. However, it remains unknown whether the contribution of these two land use types to the conservation of the soil hydraulic properties is comparable to that of the original forest. Given the heterogeneous nature of both the land use within the landscape and the vegetation within the plots, the spatial distribution of these properties also remains unclear. We used variography and linear models to study the mean variation and spatial heterogeneity of field-saturated hydraulic conductivity (Kfs) at two different scales (plot and landscape) and examined its relationship with soil properties that are sensitive to land use change. The results suggest that secondary forests and coffee agroecosystems have a high capacity for water conduction, although this capacity is significantly lower in the latter. No structure was apparent in the spatial distribution of Kfs within the plots; however, a north–south gradient was detected at landscape level. In addition to a similar gradient, the soil properties that control Kfs (i.e., organic matter content, initial water content and bulk density) presented nested patches of average diameter 119–150m. The average values of Kfs and its distribution in a gradient across the landscape were explained statistically by land use type, initial soil moisture and clay content. This suggests that there is an interaction between land use and the soil properties that determine Kfs and its spatial distribution at landscape level.

Scalable subsurface inverse modeling of huge data sets with an application to tracer concentration breakthrough data from magnetic resonance imaging

AbstractCharacterizing subsurface properties is crucial for reliable and cost‐effective groundwater supply management and contaminant remediation. With recent advances in sensor technology, large volumes of hydrogeophysical and geochemical data can be obtained to achieve high‐resolution images of subsurface properties. However, characterization with such a large amount of information requires prohibitive computational costs associated with “big data” processing and numerous large‐scale numerical simulations. To tackle such difficulties, the principal component geostatistical approach (PCGA) has been proposed as a “Jacobian‐free” inversion method that requires much smaller forward simulation runs for each iteration than the number of unknown parameters and measurements needed in the traditional inversion methods. PCGA can be conveniently linked to any multiphysics simulation software with independent parallel executions. In this paper, we extend PCGA to handle a large number of measurements (e.g., 106 or more) by constructing a fast preconditioner whose computational cost scales linearly with the data size. For illustration, we characterize the heterogeneous hydraulic conductivity (K) distribution in a laboratory‐scale 3‐D sand box using about 6 million transient tracer concentration measurements obtained using magnetic resonance imaging. Since each individual observation has little information on the K distribution, the data were compressed by the zeroth temporal moment of breakthrough curves, which is equivalent to the mean travel time under the experimental setting. Only about 2000 forward simulations in total were required to obtain the best estimate with corresponding estimation uncertainty, and the estimated K field captured key patterns of the original packing design, showing the efficiency and effectiveness of the proposed method.

Free thermal convection in heterogeneous porous media

This study investigates free thermal convection in heterogeneous porous media and its dependency on grid discretization. Heterogeneous hydraulic conductivity fields are described with a geostatistical approach. Numerical experiments are carried out with the heterogeneous thermal Elder problem. Results are evaluated qualitatively and quantitatively. Key results show that (1) grid convergence for thermal variable-density flow simulations in heterogeneous porous media can be achieved, (2) the degree and structure of a heterogeneous hydraulic conductivity field significantly affect thermal convective flow patterns, (3) steady-state heat distribution depends on the hydraulic conductivity field rather than on thermal conductivity, (4) more variant log hydraulic conductivity fields result in an increase of the heat flux, of the heat stored, and of the upwelling length of thermal plume fingers, (5) an increase in the horizontal correlation length of the log hydraulic conductivity field leads to an increase of the heat stored and the upwelling length, but it does not affect the heat flux, and (6) an increase in the mean of the log hydraulic conductivity field leads to an increase of the heat flux, of the heat stored, and of the upwelling length.

Horizontal trench system effects on leachate recirculation in bioreactor landfills

ABSTRACTHorizontal trenches (HTs) are constructed during the waste filling for leachate recirculation in bioreactor landfills. Leachate distribution depends on HT configuration (i.e., spacing between successive HTs), leachate injection rate, modes of injection, and hydraulic properties and MSW heterogeneity. Presently, the effects of these variables on the moisture distribution have not been studied systematically. This study provides a systematic evaluation of the effect of the HTs variables on the moisture distribution and pore fluid pressures. A two-phase flow model is used to model a bioreactor landfill having an HT leachate injection system. It quantifies the effects of the unsaturated hydraulic properties and MSW heterogeneity, trench configuration, leachate injection flux, and mode of injection on hydraulic behaviour. The results show that unsaturated hydraulic conductivity and MSW heterogeneity significantly shape the zone of influence and excess pore pressures. Under heterogeneous-anisotropic conditions, the leachate migrates more laterally and the developed pore-pressures are lower than for homogeneous MSW. A closely-spaced, multi-level, staggered HT system is found to provide uniform and adequate moisture distribution in MSW. An intermittent mode of injection that alternates between the shallow and deep trenches with a higher leachate injection flow rate is found to be effective to control the excess pore pressures.

A hybrid simulation–optimization approach for solving the areal groundwater pollution source identification problems

Summary In this study, a new simulation–optimization approach is proposed for solving the areal groundwater pollution source identification problems which is an ill-posed inverse problem. In the simulation part of the proposed approach, groundwater flow and pollution transport processes are simulated by modeling the given aquifer system on MODFLOW and MT3DMS models. The developed simulation model is then integrated to a newly proposed hybrid optimization model where a binary genetic algorithm and a generalized reduced gradient method are mutually used. This is a novel approach and it is employed for the first time in the areal pollution source identification problems. The objective of the proposed hybrid optimization approach is to simultaneously identify the spatial distributions and input concentrations of the unknown areal groundwater pollution sources by using the limited number of pollution concentration time series at the monitoring well locations. The applicability of the proposed simulation–optimization approach is evaluated on a hypothetical aquifer model for different pollution source distributions. Furthermore, model performance is evaluated for measurement error conditions, different genetic algorithm parameter combinations, different numbers and locations of the monitoring wells, and different heterogeneous hydraulic conductivity fields. Identified results indicated that the proposed simulation–optimization approach may be an effective way to solve the areal groundwater pollution source identification problems.

Impact of the spatial structure of the hydraulic conductivity field on vorticity in three-dimensional flows.

A material fluid element within a porous medium experiences deformations due to the disordered spatial distribution of the Darcy scale velocity field, caused by the heterogeneity of hydraulic conductivity. A physical consequence of this heterogeneity is the presence of localized kinematical features such as straining, shearing and vorticity in the fluid element. These kinematical features will influence the shape of solute clouds and their fate. Studies on the deformation of material surfaces highlighted the importance of stretching and shearing, whereas vorticity received so far less attention, though it determines folding, a deformation associated with the local rotation of the velocity field. We study vorticity in a three-dimensional porous formation exploring how its fluctuations are influenced by the spatial structure of the porous media, obtained by immersing spheroidal inclusions into a matrix of constant hydraulic conductivity. By comparing porous formations with the same spatial statistics, we analyse how vorticity is affected by the different shape and arrangement of inclusions, defined as the medium 'microstructure'. We conclude that, as microstructure has a significant impact on vorticity fluctuations, the usual second-order statistical description of the conductivity field is unable to capture local deformations of the plume.

A field proof-of-concept of tomographic slug tests in an anisotropic littoral aquifer

Hydraulic tomography is increasingly recognized as a characterization approach that can image pathways or barriers to flow as well as their connectivity. In this study, we assess the performance of a transient analysis of tomographic slug test head data in estimating heterogeneity in horizontal hydraulic conductivity (Kh), hydraulic conductivity anisotropy (the ratio between vertical and horizontal hydraulic conductivity – Kv/Kh) and specific storage (Ss) under actual field conditions. The tomographic experiment was carried out between two wells in a moderately heterogeneous and highly anisotropic silt and sand littoral aquifer. In this field proof-of-concept, the inversion of the two-dimensional (2D) head dataset was computed with a 2D radial flow algorithm that considers Kh, Kv/Kh, Ss and wellbore storage effects. This study demonstrated that a transient analysis of tomographic slug tests is able to capture the key features of the littoral environment of the test: the vertical profiles of Kh and Kv are indeed in agreement with those from other field and laboratory tests, and Ss values exhibit physically plausible profiles. Furthermore, the simulation of independent inter-well hydraulic tests (slug and pumping tests screened over the entire aquifer) using resolved Kh, Kv/Kh and Ss tomograms produce responses very close to field observations. This study demonstrates that the effects of fine scale heterogeneity that induces K-anisotropy at larger scales can be captured through a transient analysis of tomographic slug tests, which are very difficult to quantify otherwise with conventional hydraulic tests, thus allowing a better representation of properties controlling flow and transport in aquifer systems.

Specific storage and hydraulic conductivity tomography through the joint inversion of hydraulic heads and self-potential data

Transient hydraulic tomography is used to image the heterogeneous hydraulic conductivity and specific storage fields of shallow aquifers using time series of hydraulic head data. Such ill-posed and non-unique inverse problem can be regularized using some spatial geostatistical characteristic of the two fields. In addition to hydraulic heads changes, the flow of water, during pumping tests, generates an electrical field of electrokinetic nature. These electrical field fluctuations can be passively recorded at the ground surface using a network of non-polarizing electrodes connected to a high impedance (> 10MOhm) and sensitive (0.1mV) voltmeter, a method known in geophysics as the self-potential method. We perform a joint inversion of the self-potential and hydraulic head data to image the hydraulic conductivity and specific storage fields. We work on a 3D synthetic confined aquifer and we use the adjoint state method to compute the sensitivities of the hydraulic parameters to the hydraulic head and self-potential data in both steady-state and transient conditions. The inverse problem is solved using the geostatistical quasi-linear algorithm framework of Kitanidis. When the number of piezometers is small, the record of the transient self-potential signals provides useful information to characterize the hydraulic conductivity and specific storage fields. These results show that the self-potential method reveals the heterogeneities of some areas of the aquifer, which could not been captured by the tomography based on the hydraulic heads alone. In our analysis, the improvement on the hydraulic conductivity and specific storage estimations were based on perfect knowledge of electrical resistivity field. This implies that electrical resistivity will need to be jointly inverted with the hydraulic parameters in future studies and the impact of its uncertainty assessed with respect to the final tomograms of the hydraulic parameters.

Dual state-parameter simultaneous estimation using localised ensemble Kalman filter and application in environmental model

Parameters in a hydrological model play a pivotal role for prediction. Good estimates of the parameters and state variables enable the model to generate accurate forecasts. In this paper, a dual state-parameter estimation approach is realised based on the localised ensemble Kalman filter (EnKF) for estimation of both parameters and state variables of a groundwater flow model. The hydraulic head field (state variable) and the distribution of heterogeneous hydraulic conductivity (parameter) are simultaneously estimated through limited groundwater level observations and the localisation method. The localisation method is used to map updated weights and correlation distances from measured grid point to the grid point to be updated. The horizontal de-correlation length is determined by geostatistical method with a value L = 25 m. The analysed results indicate that the distribution of hydraulic conductivity estimated by the localised EnKF approach could well match the real field only after five data assimilation steps with few 25 observation wells. Meanwhile, the simulation of hydraulic conductivity is significantly improved by the localised EnKF approach.

Application of 1D paleo‐fluvial process modelling at a basin scale to augment sparse borehole data: example of a Permian formation in the Galilee Basin, Australia

AbstractThe heterogeneous hydraulic conductivity (K) in water‐bearing formations controls subsurface flow and solute transport processes. Geostatistical techniques are often employed to characterize the K distribution in space based on the correlation between K measurements. However, at the basin scale, there are often insufficient measurements for inferring the spatial correlation. This is a widespread problem that we address in this study using the example of the Betts Creek Beds (BCB) in the Galilee Basin, Australia. To address the lack of data, we use a 1D stochastic fluvial process‐based model (SFPM) to quantify the total sediment thickness, Z(x), and the sandstone proportion over the total thickness, Ps(x), in the BCB. The semivariograms of Z(x) and Ps(x) are then extracted and used in sequential Gaussian simulation to construct the 2D spatial distribution of Z(x) and Ps(x). Ps(x) can be converted to a K distribution based on classical averaging methods. The results demonstrate that the combination of SFPM and geostatistical simulation allows for the evaluation of upscaled K distribution with a limited number of K measurements. Copyright © 2015 John Wiley & Sons, Ltd.

Connectivity metrics based on the path of smallest resistance

Connectivity is an intrinsic feature of heterogeneous hydraulic conductivity fields which governs the paths of smallest resistance, along which water and solute fluxes concentrate. It is often organized as a network of channels which shows the fastest Darcy velocities and provides pathways for particles contributing to early time solute breakthrough. In subsurface hydrology the topological or static connectivity metrics are poorly defined, thus connectivity is usually characterized by dynamic connectivity indicators, derived from effective flow and transport behavior. We obtain a connected channel network using information about hydraulic conductivity only and define static connectivity metrics based on resistance of the individual channels as well as the channel width. Then we compare the static connectivity metrics with connectivity indicators derived from flow and transport simulations to check whether these connectivity metrics are able to predict effective flow and transport. We find a good agreement for flow and an acceptable one for transport for a large range of 2-D hydraulic conductivity fields with different connectivity structures. We conclude that our method provides a good estimate of effective hydraulic conductivity and early time solute breakthrough using our connectivity metrics based on information of the resistance and geometry of the connected channel network.

Nonlinear effects of locally heterogeneous hydraulic conductivity fields on regional stream–aquifer exchanges

Abstract. Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream–aquifer exchanges, and (H3) the biases result from slow paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream–aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW (Modular Three-dimensional Finite-difference Groundwater Flow Model) simulation environment, and the PEST (parameter estimation) tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop lognormally distributed conductivity (K) fields on local grid scales. Stream–aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce coherent slow paths in groundwater fluxes that in turn reduce aquifer–stream exchanges. Since surface water–groundwater exchanges are critical hydrologic processes in basin-scale water budgets, these results also have implications for water resources management.

Multiscale hyporheic exchange through strongly heterogeneous sediments

AbstractHeterogeneity in hydraulic conductivity (K) and channel morphology both control surface water‐groundwater exchange (hyporheic exchange), which influences stream ecosystem processes and biogeochemical cycles. Here we show that heterogeneity in K is the dominant control on exchange rates, residence times, and patterns in hyporheic zones with abrupt lithologic contrasts. We simulated hyporheic exchange in a representative low‐gradient stream with 300 different bimodal K fields composed of sand and silt. Simulations span five sets of sand‐silt ratios and two sets of low and high K contrasts (1 and 3 orders of magnitude). Heterogeneity can increase interfacial flux by an order of magnitude relative to homogeneous cases, drastically changes the shape of residence time distributions, and tends to decrease median residence times. The positioning of highly permeable sand bodies controls patterns of interfacial flux and flow paths. These results are remarkably different from previous studies of smooth, continuous K fields that indicate only moderate effects on hyporheic exchange. Our results also show that hyporheic residence times are least predictable when sand body connectivity is low. As sand body connectivity increases, the expected residence time distribution (ensemble average for a given sand‐silt ratio) remains approximately constant, but the uncertainty around the expectation decreases. Including strong heterogeneity in hyporheic models is imperative for understanding hyporheic fluxes and solute transport. In streams with strongly heterogeneous sediments, characterizing lithologic structure is more critical for predicting hyporheic exchange metrics than characterizing channel morphology.

Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections.

We investigate transport on regular fracture networks that are characterized by heterogeneity in hydraulic conductivity. We discuss the impact of conductivity heterogeneity and mixing within fracture intersections on particle spreading. We show the emergence of non-Fickian transport due to the interplay between the network conductivity heterogeneity and the degree of mixing at nodes. Specifically, lack of mixing at fracture intersections leads to subdiffusive scaling of transverse spreading but has negligible impact on longitudinal spreading. An increase in network conductivity heterogeneity enhances both longitudinal and transverse spreading and leads to non-Fickian transport in longitudinal direction. Based on the observed Lagrangian velocity statistics, we develop an effective stochastic model that incorporates the interplay between Lagrangian velocity correlation and velocity distribution. The model is parameterized with a few physical parameters and is able to capture the full particle transition dynamics.

Prediction of solute transport in a heterogeneous aquifer utilizing hydraulic conductivity and specific storage tomograms

AbstractA sequential procedure of hydraulic tomographical inversion is applied to characterize at high resolution the spatial heterogeneity of hydraulic conductivity and specific storage at the field test site Stegemühle, Germany. The shallow aquifer at this site is examined by five short‐term multilevel pumping tests with 30 pumping‐observation pairs between two wells. Utilizing travel time diagnostics of the recorded pressure response curves, fast eikonal‐based inversion is shown to deliver insight into the sedimentary structures. Thus, the structural information from the generated travel time tomogram is exploited to constrain full calibration of the pressure response curves. Based on lateral extrapolation from the measured inter‐well profile, a three‐dimensional reconstruction of the aquifer is obtained. It is demonstrated that calibration of spatially variable specific storage in addition to hydraulic conductivity can improve the fitting of the model while the structural features are only slightly changed. At the field site, two tracer tests with uranine and sodium‐naphthionate were also performed and their concentrations were monitored for 2 months. The measured tracer breakthrough curves are employed for independent validation of the hydraulic tomographical reconstruction. It is demonstrated that major features of the observed solute transport can be reproduced, and structures relevant for macrodispersive tracer spreading could be resolved. However, for the mildly heterogeneous aquifer, the tracer breakthrough curves can also be approximated by a simplified homogeneous model with higher dispersivity. Therefore, improved validation results that capture specific characteristics of the breakthrough curves would require additional hydraulic measurements.

Delineation of connectivity structures in 2‐D heterogeneous hydraulic conductivity fields

AbstractConnectivity is a critical aquifer property controlling anomalous transport behavior at large scales. But connectivity cannot be easily defined in a continuous field based on information of the hydraulic conductivity alone. We conceptualize it as a connecting structure—a connected subset of a continuous hydraulic conductivity field that consists of paths of least hydraulic resistance. We develop a simple and robust numerical method to delineate the connectivity structure using information of the hydraulic conductivity field only. First, the topology of the connectivity structure is determined by finding the path(s) of least resistance between two opposite boundaries. And second, a series of connectivity structures are created by inflating and shrinking the individual channels. Finally, we apply this methodology to different heterogeneous fields. We show that our method captures the main flow channels as well as the pathways of early time solute arrivals. We find our method informative to study connectivity in 2‐D heterogeneous hydraulic conductivity fields.

Stochastic analysis of the hydraulic conductivity estimated for a heterogeneous aquifer via numerical modelling

Abstract. The paper aims to evaluate the impacts of the average hydraulic conductivity of the heterogeneous aquifer on the estimated hydraulic conductivity using the observations from pumping tests. The results of aquifer tests conducted at a karst aquifer are first introduced. A MODFLOW groundwater flow model was developed to perform numerical pumping tests, and the heterogeneous hydraulic conductivity (K) field was generated using the Monte Carlo method. The K was estimated by the Theis solution for an unconfined aquifer. The effective hydraulic conductivity (Ke) was calculated to represent the hydraulic conductivity of a heterogeneous aquifer. The results of numerical simulations demonstrate that Ke increase with the mean of hydraulic conductivity (EK), and decrease with the coefficient of variation of the hydraulic conductivity (Cv). The impact of spatial variability of K on the estimated Ke at two observation wells with smaller EK is less significant compared to the cases with larger EK.