Experimental and modeling evidence of kilometer-scale anomalous tracer transport in an alpine karst aquifer

Microplastic accumulation in groundwater: Data-scaled insights and future research

Given that microplastics (MPs) in groundwater have been concerned for risks to humans and ecosystems with increased publications, a Contrasting Analysis of Scales (CAS) approach is developed by this study to synthesize all existing data into a hierarchical understanding of MP accumulation in groundwater. Within the full data of 386 compiled samples, the median abundance of MPs in Open Groundwater (OG) and Closed Groundwater (CG) were 4.4 and 2.5 items/L respectively, with OG exhibiting a greater diversity of MP colors and larger particle sizes. The different pathways of MP entry (i.e., surface runoff and rock interstices) into OG and CG led to this difference. At the regional scale, median MP abundance in nature reserves and landfills were 17.5 and 13.4 items/L, respectively, all the sampling points showed high pollution load risk. MPs in agricultural areas exhibited a high coefficient of variation (716.7%), and a median abundance of 1.0 items/L. Anthropogenic activities at the regional scale are the drivers behind the differentiation in the morphological characteristics of MPs, where groundwater in residential areas with highly toxic polymers (e.g., polyvinylchloride) deserves prolonged attention. At the local scale, the transport of MPs is controlled by groundwater flow paths, with a higher abundance of MP particles downstream than upstream, and MPs with regular surfaces and lower resistance (e.g., pellets) are more likely to be transported over long distances. From the data-scaled insight this study provides on the accumulation of MPs, future research should be directed towards network-based observation for groundwater-rich regions covered with landfills, residences, and agricultural land.

A Fractional-order dual-continuum model to capture non-Fickian solute transport in a regional-scale fractured aquifer

Contaminant transport in fractured media exhibits complex dynamics, including multiple peaks in breakthrough curves (BTCs) and non-Fickian diffusion, thereby posing significant challenges to the application of traditional transport models. Here we undertook a detailed study of a natural-gradient tracer test conducted in a regional-scale fractured carbonate aquifer situated in southwestern Germany, where the observed BTCs contained both dual peaks and positive skewness. These BTCs were used to optimize parameters and interpret their physical meanings for several transport models, including the dual-continuum model (DCM) and the fractional derivative equation (FDE) model. Tracer concentration distributions were simulated in both single- and dual-continuum media employing the DCM and FDE models. Our results demonstrated that while the DCM model could reasonably replicate the bimodal BTC, the FDE (which accounts for solute retention) outperformed in capturing the heavy-tailed BTC. This was attributed to the limitations of grid-based numerical models that assume Fickian diffusion and fail to map small-scale medium heterogeneity exhaustively. In contrast, a parsimonious model like the FDE, with upscaled parameters, was found to be more effective in capturing regional-scale non-Fickian transport. To further characterize the multiple BTC peaks the standard FDE missed, we proposed a fractional derivative dual-continuum model (fDCM). This model was found to be adept at capturing both the multi-peak and late-time heavy tail in the BTC. Our study thus opens an alternate pathway for modeling solute transport in regional-scale fractured to partially karstified aquifers.

Tracking contaminants in groundwater flowing across a river bottom within a complex karst system: Clues from hydrochemistry, stable isotopes, and tracer tests

Tracking contaminants in karst aquifers is challenging because of the high heterogeneity encountered in carbonate rocks. Multi-tracer tests, combined with chemical and isotopic analyses, were conducted to solve a groundwater contamination incident within a complex karst aquifer in Southwest China. Results showed that: (1) the wastewater from a paper mill, public sewers, and septic tanks were the three main potential contaminant sources identified by chemical and isotopic methods; (2) a direct effect of the paper mill wastewater with high Na⁺ (up to 2230.5 mg/L) and chemical oxygen demand (COD) concentrations on spring water quality was confirmed by multi-tracer tests, which changed the water type from Ca-HCO₃ in the 1970s to Ca-Na-HCO₃ in the present study and resulted in a depleted carbon isotope value (-16.5‰); and (3) the studied aquifer is a highly complex karst system, due to two conduits crossed each other without mixing, contaminants traveled a long distance (up to 14 km) within the lower conduit, paper mill-contaminated groundwater flowed across a river bottom and discharged to the opposite bank, and an active subsurface divide occurred. After several months of operation, the groundwater restoration measure based on karst hydrogeologic conditions proved that cutting off contaminant sources for karst aquifer self-restore was effective in practice, which contributed to the decline in NH₄⁺ (from 7.81 mg/L to 0.04 mg/L), Na⁺ (from 50.12 mg/L to 4.78 mg/L), and COD (from 16.42 mg/L to 0.9 mg/L) concentrations coupled with an increase in δ¹³C-DIC value (from -16.5‰ to -8.4‰) in the earlier contaminated karst spring. This study's integrated method is expected to screen and confirm contaminant sources within complex karst systems rapidly and effectively, thereby contributing to karst groundwater environmental management.

Upscaling dispersivity for conservative solute transport in naturally fractured media

Physical heterogeneities are prevalent features of fracture systems and significantly impact transport processes in aquifers across different spatiotemporal scales. Upscaling solute transport parameter is an effective way of quantifying parameter variability in heterogeneous aquifers including fractured media. This paper develops conceptual models for upscaling conservative transport parameters in fracture media. The focus is on upscaling dispersivity. Lagrangian-based transport model (LBTM) for dispersivity upscaling are derived for the solute transport in two-dimensional fractures surrounded by an impermeable matrix. The LBTM is validated against the random walk particle tracking (RWPT) model, which enables highly efficient and accurate predictions of conservative solute transport. The results show that the derived scale-dependent analytical expressions are in excellent agreement with RWPT model results. In addition, LBTM results are also compared to experimental results from the observed breakthrough curve of a conservative solute transport through a single natural fracture within a granite core. Comparing results from the LBTM and transport experiment shows that LBTM based estimated dispersivity is 10.55% higher than the measured value. Errors introduced by the experiments, the conceptual assumptions in deriving models, and the heterogeneities of fracture apertures not fully sampled by measuring instruments are main factor for such discrepancy. The sensitivity analysis indicates that the longitudinal and transverse dispersivities are positively related to the integral scale and the variance of the log-fracture aperture. The longitudinal dispersivity is strongly contolled by the variance of the log-fracture aperture. The LBTM may be useful for directly predicting solute transports, requiring only the acquisition of fractured geostatistical data. This work provides a better understanding of transport processes in fractured media which ultimately control water quality across scales.

A novel method to measure air-immobile regions of the composting pile by inverse calculation combined with gas tracer test

Air-immobile regions in composting piles obstruct O₂ mass transport and exacerbate the formation and emission of harmful off-gases. However, effective methods for measuring the parameters of these air-immobile regions are lacking. With quartz sand piles, this study first adjusted the circumstances of a gas tracer test (gas tracer, its injection volume, and chamber type) using the two-region model (TRM). The effects of β (proportional coefficient of gas in the air-mobile region) and ω (mass exchange coefficient) on the breakthrough curves (BTCs) of the gases were then explored. Finally, an inverse calculation method was used to measure the feature parameters of air-immobile regions in two composting piles (temperature-increasing and thermophilic phases) and estimate the O₂ concentrations in different composting piles (50, 100, 200 cm whole height; layers of 50, 100, 200 cm height in a 200-cm high pile). The results showed that the optimal conditions were achieved when 100 mL helium (He) as the gas tracer and a cylinder with a height/diameter ratio of 3 as the chamber were used. With the simulating composting piles, increasing β or ω slowed breakthrough and decreased peak concentration in BTCs of a gas tracer. Tracer-inverse calculation protocol can be used to efficiently estimate the volume ratios of air-immobile regions (φ) and first-order mass transfer coefficient (α), with the values of 39%/46% and 0.001/0.006 min^-1 in the composting piles during temperature-increasing /thermophilic phase. The TRM also predicted the O₂ concentration in the off-gas or air-mobile/immobile regions of the temperature-increasing-phase composting piles.

Assessment of Mobilization Potential of Per- and Polyfluoroalkyl Substances for Soil Remediation

This study investigated the mobilization of a wide range of per- and polyfluoroalkyl substances (PFASs) present in aqueous film-forming foams (AFFFs) in water-saturated soils through one-dimensional (1-D) column experiments with a view to assessing the feasibility of their remediation by soil desorption and washing. Results indicated that sorption/desorption of most of the shorter-carbon-chain PFASs (C ≤ 6) in soil reached greater than 99% rapidly─after approximately two pore volumes (PVs) and were well predicted by an equilibrium transport model, indicating that they will be readily removed by soil washing technologies. In contrast, the equilibrium model failed to predict the mobilization of longer-chain PFASs (C ≥ 7), indicating the presence of nonequilibrium sorption/desorption (confirmed by a flow interruption experiment). The actual time taken to attain 99% sorption/desorption was up to 5 times longer than predicted by the equilibrium model (e.g., ∼62 PVs versus ∼12 PVs predicted for perfluorooctane sulfonate (PFOS) in loamy sand). The increasing contribution of hydrophobic interactions over the electrostatic interactions is suggested as the main driving factor of the nonequilibrium processes. The inverse linear relationship (R² = 0.6, p < 0.0001) between the nonequilibrium mass transfer rate coefficient and the Freundlich sorption coefficient could potentially be a useful means for preliminary evaluation of potential nonequilibrium sorption/desorption of PFASs in soils.

Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.

Transport-based source tracking of contaminants in a karst aquifer: Model implementation, proof of concept, and application to event-based field data

Identification and location of contamination sources is crucial for water resource protection - especially in karst aquifers which provide 25% of the world´s population with water but are highly vulnerable to contamination. Transport-based source tracking is proposed and verified here as a complementary approach to microbial and chemical source tracking in karst aquifers for identifying and locating such sources of contamination and for avoiding ambiguities that might arise from using one method alone. The transport distance is inversely modelled from contaminant breakthrough curves (BTC), based on analytical solutions of the 1D two-region non-equilibrium advection dispersion equation using GNU Octave. Besides the BTC, the model requires reliable estimates of transport velocity and input time. The model is shown to be robust, allows scripted based, automated 2D sensitivity analyses (interplay of two parameters), and can be favourable when distributed numerical models are inappropriate due to insufficient data. Sensitivity analyses illustrate that the model is highly sensitive to the input time, the flow velocity, and the fraction of the mobile fluid region. A conclusive verification approach was performed by applying the method to synthetic data, tracer tests, and event-based field data. Transport distances were correctly modelled for a set of artificial tracer tests using a discharge-velocity relationship that could be established for the respective karst catchment. For the first time such an approach was shown to be applicable to estimate the maximum distance to the contamination source for coliform bacteria in karst spring water combined with microbial source tracking. However, prediction intervals for the transport distance can be large even in well-studied karst catchments mainly related to uncertainties in the flow velocity and the input time. Using a maximum transport distance is proposed to account for less permeable, "slower" pathways. In general, transport-based source tracking might be used wherever transport can be described by the 1D two-region non-equilibrium model, e.g. rivers and fractured or porous aquifers.

Generalized Skewed Model for Spatial-Fractional Advective–Dispersive Phenomena

The conventional mathematical model expressed by the advection–dispersion equation has been widely used to describe contaminant transport in porous media. However, studies have shown that it fails to simulate early arrival of contaminant, long tailing breakthrough curves and presents a physical scale-dependency of the dispersion coefficient. Recently, advances in fractional calculus allowed the introduction of fractional order derivatives to model several engineering and physical phenomena, including the anomalous dispersion of solute particles. This approach gives birth to the fractional advection–dispersion equation. This work presents new solutions to the fractional transport equation that satisfies the initial condition of constant solute injection in a semi-infinite medium. The new solution is derived based on a similarity approach. Moreover, laboratory column tests were performed in a Brazilian lateritic soil to validate the new solution with experimental data and compare its accuracy with the conventional model and other fractional solutions. The new solution outperforms the existing ones and reveals an interesting fractal-like scaling rule for the diffusivity coefficients.

Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions

We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random-walk models for multirate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover, we find the associated breakthrough curves, the tracer density at a fixed point in space as a function of time, and the mobile and immobile concentration profiles and the respective moments of the transport. Specifically, we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities, transient anomalous transport is observed. Our results have direct applications in geophysical contexts, but also in biological, soft matter, and solid state systems.

Flow Path Resistance in Heterogeneous Porous Media Recast into a Graph-Theory Problem

Abstract

This work aims to describe the spatial distribution of flow from characteristics of the underlying pore structure in heterogeneous porous media. Thousands of two-dimensional samples of polydispersed granular media are used to (1) obtain the velocity field via direct numerical simulations, and (2) conceptualize the pore network as a graph in each sample. Analysis of the flow field allows us to distinguish preferential from stagnant flow regions and to quantify how channelized the flow is. Then, the graph’s edges are weighted by geometric attributes of their corresponding pores to find the path of minimum resistance of each sample. Overlap between the preferential flow paths and the predicted minimum resistance path determines the accuracy in individual samples. An evolutionary algorithm is employed to determine the “fittest” weighting scheme (here, the channel’s arc length to pore throat ratio) that maximizes accuracy across the entire dataset while minimizing over-parameterization. Finally, the structural similarity of neighboring edges is analyzed to explain the spatial arrangement of preferential flow within the pore network. We find that connected edges within the preferential flow subnetwork are highly similar, while those within the stagnant flow subnetwork are dissimilar. The contrast in similarity between these regions increases with flow channelization, explaining the structural constraints to local flow. The proposed framework may be used for fast characterization of porous media heterogeneity relative to computationally expensive direct numerical simulations.

Article Highlights

Step-like rising and falling of a breakthrough curve observed at a karst spring

Spring breakthrough curves induced by conventional advection and dispersion often present a gentle (smooth) change of concentration with time. We investigated an electrical-conductivity breakthrough curve which originated from a chemical release into the aquifer matrix and was measured in June 2007 at Qinglondong Spring, southwest China. The curve presented abrupt rising and falling limbs. Modeling efforts were focused on the migration of the contaminants from the conduit wall to the spring. The conduit production segment was defined to be the conduit section where the chemical plume entered the conduit from aquifer fractures. The first model assumed that the time variance of the plume front reaching the conduit wall was much shorter than transport time over the conduit production segment. The model yielded a decrease of spring discharge which was inconsistent with the observed increase with time. In the second model, the above assumption was relaxed, and wall contaminant flux was inverted as function of downstream distance and time. The observed abrupt rising and falling in the breakthrough curve were interpreted as: (1) Taylor dispersion was too small to identify for a short conduit; (2) seepage from the fractures to the conduit was monodirectional and diluting.

Lévy walk dynamics in an external harmonic potential

Lévy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, robots, and viruses. We here investigate a key feature of LWs-their response to an external harmonic potential. In this generic setting for confined motion we demonstrate that LWs equilibrate exponentially and may assume a bimodal stationary distribution. We also show that the stationary distribution has a horizontal slope next to a reflecting boundary placed at the origin, in contrast to correlated superdiffusive processes. Our results generalize LWs to confining forces and settle some longstanding puzzles around LWs.