Harry Vereecken

Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models

Abstract We assess the usefulness of electrical resistivity tomography (ERT) in imaging and characterising subsurface solute transport in heterogeneous unconfined aquifers. A field tracer experiment was conducted at the Krauthausen test site, Germany. The spatial and temporal evolution of the injected NaBr solute plume was monitored in a 2D ERT image plane located downstream of the injection well for 90 days. Since ERT maps changes in bulk electrical conductivity, the reconstructed images at selected time intervals are first converted to solute concentration maps by postulating a linear relation. The concentration maps are then analysed using an equivalent convection–dispersion model (CDM), which conceptualises the aquifer as a homogeneous medium with a uniform mean flow velocity. As demonstrated by associated synthetic model studies, ERT resolution in terms of recovered equivalent dispersivities is limited due to spatial smoothing inherent to the imaging algorithm. Since for heterogeneous media, local concentrations within the plume deviate from those predicted by the equivalent CDM, we also interpret the ERT-derived pixel breakthrough curves in terms of an equivalent stream-tube model (STM). The STM represents transport in the aquifer by a set of 1D convection–dispersion processes, allowing the degree of mixing and the heterogeneity of transport within the plume to be quantified. We believe that the observed tracer plume is satisfactorily described by the equivalent CDM, probably because the tracer plume was small relative to the heterogeneity scale of the aquifer. Even though application of the STM revealed some deviation from the ideal homogeneous case, the equivalent dispersivity in the STM matches the longitudinal dispersivity of the CDM closely, consistent with predominantly homogeneous mixing. However, the STM analysis illustrates how ERT results can be used to quantify the variability of parameters relevant to flow and transport in heterogeneous aquifers.

Seasonal and event dynamics of spatial soil moisture patterns at the small catchment scale

[1] Our understanding of short- and long-term dynamics of spatial soil moisture patterns is limited due to measurement constraints. Using new highly detailed data, this research aims to examine seasonal and event-scale spatial soil moisture dynamics in the topsoil and subsoil of the small spruce-covered Wustebach catchment, Germany. To accomplish this, univariate and geo-statistical analyses were performed for a 1 year long 4-D data set obtained with the wireless sensor network SoilNet. We found large variations in spatial soil moisture patterns in the topsoil, mostly related to meteorological forcing. In the subsoil, temporal dynamics were diminished due to soil water redistribution processes and root water uptake. Topsoil range generally increased with decreasing soil moisture. The relationship between the spatial standard deviation of the topsoil soil moisture (SD� ) and mean water content (� ) showed a convex shape, as has often been found in humid temperate climate conditions. Observed scatter in topsoil SD� (� ) was explained by seasonal and event-scale SD� (� ) dynamics, possibly involving hysteresis at both time scales. Clockwise hysteretic SD� (� ) dynamics at the event scale were generated under moderate soil moisture conditions only for intense precipitation that rapidly wetted the topsoil and increased soil moisture variability controlled by spruce throughfall patterns. This hysteretic effect increased with increasing precipitation, reduced root water uptake, and high groundwater

Analysis of air-launched ground-penetrating radar techniques to measure the soil surface water content

We analyze the common surface reflection and full-wave inversion methods to retrieve the soil surface dielectric permittivity and correlated water content from air-launched ground-penetrating radar (GPR) measurements. In the full-wave approach, antenna effects are filtered out from the raw radar data in the frequency domain, and full-wave inversion is performed in the time domain, on a time window focused on the surface reflection. Synthetic experiments are performed to investigate the most critical hypotheses on which both techniques rely, namely, the negligible effects of the soil electric conductivity (?) and layering. In the frequency range 1–2 GHz we show that for ? > 0.1 Sm?1, significant errors are made on the estimated parameters, e.g., an absolute error of 0.10 in water content may be observed for ? = 1 Sm?1. This threshold is more stringent with decreasing frequency. Contrasting surface layering may proportionally lead to significant errors when the thickness of the surface layer is close to one fourth the wavelength in the medium, which corresponds to the depth resolution. Absolute errors may be >0.10 in water content for large contrasts. Yet we show that full-wave inversion presents valuable advantages compared to the common surface reflection method. First, filtering antenna effects may prevent absolute errors >0.04 in water content, depending of the antenna height. Second, the critical reference measurements above a perfect electric conductor (PEC) are not required, and the height of the antenna does not need to be known a priori. This averts absolute errors of 0.02–0.09 in water content when antenna height differences of 1–5 cm occur between the soil and the PEC. A laboratory experiment is finally presented to analyze the stability of the estimates with respect to actual measurement and modeling errors. While the conditions were particularly well suited for applying the common reflection method, better results were obtained using full-wave inversion.

Temporal Stability of Soil Water Contents: A Review of Data and Analyses

Temporal stability (TS) of soil water content (SWC) has been observed throughout a wide range of spatial and temporal scales. Yet, the evidence with respect to the controlling factors on TS SWC remains contradictory or nonexistent. The objective of this work was to develop the first comprehensive review of methodologies to evaluate TS SWC and to present and analyze an inventory of published data. Statistical analysis of mean relative difference (MRD) data and associated standard deviations (SDRD) from 157 graphs in 37 publications showed a trend for the standard deviation of MRD (SDMRD) to increase with scale, as expected. The MRD followed generally the Gaussian distribution with R 2 ranging from 0.841 to 0.998. No relationship between SDMRD and R 2 was observed. The smallest R 2 values were mostly found for negatively skewed and platykurtic MRD distributions. A new statistical model for temporally stable SWC fields was proposed. The analysis of the published data on seven measurement-, terrain-, and climate-related potentially controlling factors of TS SWC suggested intertwined effects of controlling factors rather than single dominant factors. This calls for a focused research effort on the interactions and effects of measurement design, topography, soil, vegetation and climate on TS SWC. Research avenues are proposed which will lead to a better understanding of the TS phenomenon and ultimately to the identification of the underlying mechanisms.

Sensitivity of the transport and retention of stabilized silver nanoparticles to physicochemical factors

Saturated sand-packed column experiments were conducted to investigate the influence of physicochemical factors on the transport and retention of surfactant stabilized silver nanoparticles (AgNPs). The normalized concentration in breakthrough curves (BTCs) of AgNPs increased with a decrease in solution ionic strength (IS), and an increase in water velocity, sand grain size, and input concentration (Co). In contrast to conventional filtration theory, retention profiles (RPs) for AgNPs exhibited uniform, nonmonotonic, or hyperexponential shapes that were sensitive to physicochemical conditions. The experimental BTCs and RPs with uniform or hyperexponential shape were well described using a numerical model that considers time- and depth-dependent retention. The simulated maximum retained concentration on the solid phase (Smax) and the retention rate coefficient (k1) increased with IS and as the grain size and/or Co decreased. The RPs were more hyperexponential in finer textured sand and at lower Co because of their higher values of Smax. Conversely, RPs were nonmonotonic or uniform at higher Co and in coarser sand that had lower values of Smax, and tended to exhibit higher peak concentrations in the RPs at lower velocities and at higher solution IS. These observations indicate that uniform and nonmonotonic RPs occurred under conditions when Smax was approaching filled conditions. Nonmonotonic RPs had peak concentrations at greater distances in the presence of excess amounts of surfactant, suggesting that competition between AgNPs and surfactant diminished Smax close to the column inlet. The sensitivity of the nonmonotonic RPs to IS and velocity in coarser textured sand indicates that AgNPs were partially interacting in a secondary minimum. However, elimination of the secondary minimum only produced recovery of a small portion (<10%) of the retained AgNPs. These results imply that AgNPs were largely irreversibly interacting in a primary minimum associated with microscopic heterogeneity.

Transport and retention of multi-walled carbon nanotubes in saturated porous media: Effects of input concentration and grain size

Water-saturated column experiments were conducted to investigate the effect of input concentration (C₀) and sand grain size on the transport and retention of low concentrations (1, 0.01, and 0.005 mg L⁻¹) of functionalized ¹⁴C-labeled multi-walled carbon nanotubes (MWCNT) under repulsive electrostatic conditions that were unfavorable for attachment. The breakthrough curves (BTCs) for MWCNT typically did not reach a plateau, but had an asymmetric shape that slowly increased during breakthrough. The retention profiles (RPs) were not exponential with distance, but rather exhibited a hyper-exponential shape with greater retention near the column inlet. The collected BTCs and RPs were simulated using a numerical model that accounted for both time- and depth-dependent blocking functions on the retention coefficient. For a given C₀, the depth-dependent retention coefficient and the maximum solid phase concentration of MWCNT were both found to increase with decreasing grain size. These trends reflect greater MWCNT retention rates and a greater number of retention locations in the finer textured sand. The fraction of the injected MWCNT mass that was recovered in the effluent increased and the RPs became less hyper-exponential in shape with higher C₀ due to enhanced blocking/filling of retention locations. This concentration dependency of MWCNT transport increased with smaller grain size because of the effect of pore structure and MWCNT shape on MWCNT retention. In particular, MWCNT have a high aspect ratio and we hypothesize that solid phase MWCNT may create a porous network with enhanced ability to retain particles in smaller grain sized sand, especially at higher C₀. Results demonstrate that model simulations of MWCNT transport and fate need to accurately account for observed behavior of both BTCs and RPs.

Analysis of solute transport in a heterogeneous aquifer: the Krauthausen field experiment

Abstract A field-scale natural gradient tracer experiment with bromide, uranin and lithium was conducted in a heterogeneous aquifer at Krauthausen, Germany. The temporal and spatial evolution of the solute plumes was monitored over 398 days for bromide and 449 days for uranin and lithium. The spatial variability of basic aquifer parameters, hydraulic conductivity, and sorption parameters of the aquifer material was investigated in detail. Local Darcian velocities were measured using NH 4 Br 82 as a radioactive tracer in 33 observation wells. Vertical and horizontal correlation lengths of hydraulic properties were determined using variogram analysis. The magnitude of the local Darcian velocities was found to be lognormally distributed. In addition, the groundwater flow direction showed a clear trend in the vertical direction. The horizontal correlation length of the magnitude of Darcian velocity agreed with the correlation length of K estimated from grain size data. Batch experiments on aquifer sediments showed that sorption of uranin and lithium could be described by a Freundlich isotherm. The Freundlich n parameter of uranin sorption showed little variation with depth. The time evolution of the bromide plume was quantified in terms of spatial moments. The longitudinal effective dispersivity estimated from spatial moment analysis was within the range of calculated effective dispersivities, taking into account the uncertainty of estimates of the ln K statistics.

Three-Dimensional Geostatistical Inversion of Flowmeter and Pumping Test Data

We jointly invert field data of flowmeter and multiple pumping tests in fully screened wells to estimate hydraulic conductivity using a geostatistical method. We use the steady-state drawdowns of pumping tests and the discharge profiles of flowmeter tests as our data in the inference. The discharge profiles need not be converted to absolute hydraulic conductivities. Consequently, we do not need measurements of depth-averaged hydraulic conductivity at well locations. The flowmeter profiles contain information about relative vertical distributions of hydraulic conductivity, while drawdown measurements of pumping tests provide information about horizontal fluctuation of the depth-averaged hydraulic conductivity. We apply the method to data obtained at the Krauthausen test site of the Forschungszentrum Jülich, Germany. The resulting estimate of our joint three-dimensional (3D) geostatistical inversion shows an improved 3D structure in comparison to the inversion of pumping test data only.

Retention and Remobilization of Stabilized Silver Nanoparticles in an Undisturbed Loamy Sand Soil

Column experiments were conducted with undisturbed loamy sand soil under unsaturated conditions (around 90% saturation degree) to investigate the retention of surfactant stabilized silver nanoparticles (AgNPs) with various input concentration (Co), flow velocity, and ionic strength (IS), and the remobilization of AgNPs by changing the cation type and IS. The mobility of AgNPs in soil was enhanced with decreasing solution IS, increasing flow rate and input concentration. Significant retardation of AgNP breakthrough and hyperexponential retention profiles (RPs) were observed in almost all the transport experiments. The retention of AgNPs was successfully analyzed using a numerical model that accounted for time- and depth-dependent retention. The simulated retention rate coefficient (k1) and maximum retained concentration on the solid phase (Smax) increased with increasing IS and decreasing Co. The high k1 resulted in retarded breakthrough curves (BTCs) until Smax was filled and then high effluent concentrations were obtained. Hyperexponential RPs were likely caused by the hydrodynamics at the column inlet which produced a concentrated AgNP flux to the solid surface. Higher IS and lower Co produced more hyperexponential RPs because of larger values of Smax. Retention of AgNPs was much more pronounced in the presence of Ca(2+) than K(+) at the same IS, and the amount of AgNP released with a reduction in IS was larger for K(+) than Ca(2+) systems. These stronger AgNP interactions in the presence of Ca(2+) were attributed to cation bridging. Further release of AgNPs and clay from the soil was induced by cation exchange (K(+) for Ca(2+)) that reduced the bridging interaction and IS reduction that expanded the electrical double layer. Transmission electron microscopy, energy-dispersive X-ray spectroscopy, and correlations between released soil colloids and AgNPs indicated that some of the released AgNPs were associated with the released clay fraction.

Estimating the unsaturated hydraulic conductivity from theoretical models using simple soil properties

Abstract The knowledge of the unsaturated hydraulic conductivity is one of the prerequisites to describe water flow and solute transport in soils. In this paper we examined the quality of 11 different theoretical models to predict the unsaturated hydraulic conductivity for a wide variety of soils. The hydraulic conductivity models were fitted to 44 measured curves using a quasi Newton parameter estimation method minimizing an ordinary least squared objective function. The optimized parameter set for the best model having the lowest overal mean squared error was related to basic soil properties such as texture, organic carbon, bulk density and the measured saturated hydraulic conductivity. The model evaluation showed that theoretical models can only describe the measured data succesfully when the tortuosity and the pore size interaction term are allowed to vary across different soils. Models with completely fixed parameters obtained from literature were not able to describe the measured data. The generalized theoretical models as described by Mualem and Dagan were equally flexible. The Mualem model was choosen to derive estimation or pedotransfer functions between the tortuosity ( b ), the pore size interaction term ( x ) and soil properties. Different regression equations have been derived depending upon the available information. Soil texture alone is not sufficient to provide reasonable estimates, resulting in a coefficient of determination of 30% for x and 11% for b . The best estimates where obtained when using information from the moisture retention characteristic and the measured saturated hydraulic conductivity ( K sat ). Introducing K sat in the regression equation improved the coefficient of determination with 7% for x and 56% for b .