We analyze measurements, conceptual pictures, and mathematical models of flow and transport phenomena in fractured rock systems. Fractures and fracture networks are key conduits for migration of ...hydrothermal fluids, water and contaminants in groundwater systems, and oil and gas in petroleum reservoirs. Fractures are also the principal pathways, through otherwise impermeable or low permeability rocks, for radioactive and toxic industrial wastes which may escape from underground storage repositories. We consider issues relating to (i) geometrical characterization of fractures and fracture networks, (ii) water flow, (iii) transport of conservative and reactive solutes, and (iv) two-phase flow and transport. We examine the underlying physical factors that control flow and transport behaviors, and discuss the currently inadequate integration of conceptual pictures, models and data. We also emphasize the intrinsic uncertainty associated with measurements, which are often interpreted non-uniquely by models. Throughout the review, we point out key, unresolved problems, and formalize them as open questions for future research.
We investigate the effects of high fluid velocities on flow and tracer transport in heterogeneous porous media. We simulate fluid flow and advective transport through two-dimensional pore-scale ...matrices with varying structural complexity. As the Reynolds number increases, the flow regime transitions from linear to nonlinear; this behavior is controlled by the medium structure, where higher complexity amplifies inertial effects. The result is, nonintuitively, increased homogenization of the flow field, which leads in the context of conservative chemical transport to less anomalous behavior. We quantify the transport patterns via a continuous time random walk, using the spatial distribution of the kinetic energy within the fluid as a characteristic measure.
Anomalous (or “non‐Fickian”) transport is ubiquitous in the context of tracer migration in geological formations. We quantitatively identify the origin of anomalous transport in a representative ...model of a heterogeneous porous medium under uniform (in the mean) flow conditions; we focus on anomalous transport which arises in the complex flow patterns of lognormally distributed hydraulic conductivity (K) fields, with several decades of K values. Transport in the domains is determined by a particle tracking technique and characterized by breakthrough curves (BTCs). The BTC averaged over multiple realizations demonstrates anomalous transport in all cases, which is accounted for entirely by a power law distribution
∼t−1−β of local transition times. The latter is contained in the probability density function ψ(t) of transition times, embedded in the framework of a continuous time random walk (CTRW). A unique feature of our analysis is the derivation of ψ(t) as a function of parameters quantifying the heterogeneity of the domain. In this context, we first establish the dominance of preferential pathways across each domain, and characterize the statistics of these pathways by forming a particle‐visitation weighted histogram,
Hw(K), of the hydraulic conductivity. By converting the ln(K) dependence of
Hw(K) into time, we demonstrate the equivalence of
Hw(K) and ψ(t), and delineate the region of
Hw(K) that forms the power law of ψ(t). This thus defines the origin of anomalous transport. Analysis of the preferential pathways clearly demonstrates the limitations of critical path analysis and percolation theory as a basis for determining the origin of anomalous transport. Furthermore, we derive an expression defining the power law exponent β in terms of the
Hw(K) parameters. The equivalence between
Hw(K) and ψ(t) is a remarkable result, particularly given the nature of the K heterogeneity, the complexity of the flow field within each realization, and the statistics of the particle transitions.
Key Points
Quantitative connection between CTRW parameters and conductivities is determined
Dynamic controls are critical factors to determine key transport features
Transport is not explained only by structural knowledge of the disordered medium
Abstract
For an effectively one-dimensional, semi-infinite disordered system connected to a reservoir of tracer particles kept at constant concentration, we provide the dynamics of the concentration ...profile. Technically, we start with the Montroll–Weiss equation of a continuous time random walk with a scale-free waiting time density. From this we pass to a formulation in terms of the fractional diffusion equation for the concentration profile
C
(
x
,
t
)
in a semi-infinite space for the boundary condition
C
(
0
,
t
)
=
C
0
, using a subordination approach. From this we deduce the tracer flux and the so-called breakthrough curve (BTC) at a given distance from the tracer source. In particular, BTCs are routinely measured in geophysical contexts but are also of interest in single-particle tracking experiments. For the ‘residual’ BTCs, given by
1
−
P
(
x
,
t
)
, we demonstrate a long-time power-law behaviour that can be compared conveniently to experimental measurements. For completeness we also derive expressions for the moments in this constant-concentration boundary condition.
Non‐Fickian (or anomalous) transport of contaminants has been observed at field and laboratory scales in a wide variety of porous and fractured geological formations. Over many years a basic ...challenge to the hydrology community has been to develop a theoretical framework that quantitatively accounts for this widespread phenomenon. Recently, continuous time random walk (CTRW) formulations have been demonstrated to provide general and effective means to quantify non‐Fickian transport. We introduce and develop the CTRW framework from its conceptual picture of transport through its mathematical development to applications relevant to laboratory‐ and field‐scale systems. The CTRW approach contrasts with ones used extensively on the basis of the advection‐dispersion equation and use of upscaling, volume averaging, and homogenization. We examine the underlying assumptions, scope, and differences of these approaches, as well as stochastic formulations, relative to CTRW. We argue why these methods have not been successful in fitting actual measurements. The CTRW has now been developed within the framework of partial differential equations and has been generalized to apply to nonstationary domains and interactions with immobile states (matrix effects). We survey models based on multirate mass transfer (mobile‐immobile) and fractional derivatives and show their connection as subsets within the CTRW framework.
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► AgNPs are mobile in natural soil. ► AgNP transport is enhanced in soil with larger aggregates. ► Humic acid in solution increases mobility of AgNPs. ► Chloride-AgNP chemistry has a ...significant role in AgNP retention in soil.
The effect of soil properties on the transport of silver nanoparticles (AgNPs) was studied in a set of laboratory column experiments, using different combinations of size fractions of a Mediterranean sandy clay soil. The AgNPs with average size of ∼30nm yielded a stable suspension in water with zeta potential of −39mV. Early breakthrough of AgNPs in soil was observed in column transport experiments. AgNPs were found to have high mobility in soil with outlet relative concentrations ranging from 30% to 70%, depending on experimental conditions. AgNP mobility through the column decreased when the fraction of smaller soil aggregates was larger. The early breakthrough pattern was not observed for AgNPs in pure quartz columns nor for bromide tracer in soil columns, suggesting that early breakthrough is related to the nature of AgNP transport in natural soils. Micro-CT and image analysis used to investigate structural features of the soil, suggest that soil aggregate size strongly affects AgNP transport in natural soil. The retention of AgNPs in the soil column was reduced when humic acid was added to the leaching solution, while a lower flow rate (Darcy velocity of 0.17cm/min versus 0.66cm/min) resulted in higher retention of AgNPs in the soil. When soil residual chloride was exchanged by nitrate prior to column experiments, significantly improved mobility of AgNPs was observed in the soil column. These findings point to the importance of AgNP–soil chemical interactions as a retention mechanism, and demonstrate the need to employ natural soils rather than glass beads or quartz in representative experimental investigations.
Increased availability of nanoparticle-based products will, inevitably, expose the environment to these materials. Engineered nanoparticles (ENPs) may thus find their way into the soil environment ...via wastewater, dumpsters and other anthropogenic sources; metallic oxide nanoparticles comprise one group of ENPs that could potentially be hazardous for the environment. Because the soil bacterial community is a major service provider for the ecosystem and humankind, it is critical to study the effects of ENP exposure on soil bacteria. These effects were evaluated by measuring bacterial community activity, composition and size following exposure to copper oxide (CuO) and magnetite (Fe3O4) nanosized (<50 nm) particles. Two different soil types were examined: a sandy loam (Bet-Dagan) and a sandy clay loam (Yatir), under two ENP concentrations (1%, 0.1%). Results indicate that the bacterial community in Bet-Dagan soil was more susceptible to change due to exposure to these ENPs, relative to Yatir soil. More specifically, CuO had a strong effect on bacterial hydrolytic activity, oxidative potential, community composition and size in Bet-Dagan soil. Few effects were noted in the Yatir soil, although 1% CuO exposure did cause a significant decreased oxidative potential and changes to community composition. Fe3O4 changed the hydrolytic activity and bacterial community composition in Bet-Dagan soil but did not affect the Yatir soil bacterial community. Furthermore, in Bet-Dagan soil, abundance of bacteria annotated to OTUs from the Bacilli class decreased after addition of 0.1% CuO but increased with 1% CuO, while in Yatir soil their abundance was reduced with 1% CuO. Other important soil bacterial groups, including Rhizobiales and Sphingobacteriaceae, were negatively affected by CuO addition to soil. These results indicate that both ENPs are potentially harmful to soil environments. Furthermore, it is suggested that the clay fraction and organic matter in different soils interact with the ENPs and reduce their toxicity.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Temporal variations in the subsurface velocity field are often (if not always) present in the real world to at least some degree. However, an accounting of their effects on chemical transport has ...been largely neglected. Here we demonstrate experimentally the effects of a time‐varying velocity field on conservative chemical tracer transport in porous media, as compared to constant velocity conditions. We find that velocity‐field fluctuations increase chemical tracer spreading and residence time, which intensify the anomalous nature of the transport. This behavior is modeled by a continuous time random walk particle tracking method formulated to account for time‐dependent velocity fields. The model matches the experimental results with a parsimonious and consistent set of parameters. The model is then applied to study the effects of different magnitudes in velocity‐field fluctuations, as well as different degrees of porous media heterogeneity, on 1‐D and 2‐D spatiotemporal propagation of an injected, point‐source, chemical plume. Increased intensity of velocity‐field fluctuations, and increased porous medium heterogeneity, each serve to increase the extent of chemical spreading and anomalous behavior.
Key Points
Effects of time‐dependent velocity‐field fluctuations on chemical transport in porous media are studied via experiments and simulation
Velocity‐field fluctuations strongly affect the anomalous nature of chemical transport and are quantifiable within a CTRW framework
Effects of a time‐dependent velocity field on chemical transport are increasingly significant in more heterogeneous porous media
We investigate the occurrence of anomalous (non‐Fickian) transport in an hydrological catchment system at kilometer scales and over a 36‐year period. Using spectral analysis, we examine the ...fluctuation scaling of long‐term time series measurements of a natural passive tracer (chloride), for rainfall and runoff. The scaling behavior can be described by a continuous time random walk (CTRW) based on a power‐law distribution of transition times, which indicates two distinct power‐law regimes in the distribution of overall travel times in the catchment. The CTRW provides a framework for assessing anomalous transport in catchments and its implications for water quality fluctuations.
Plain Language Summary
Rain falling on an hydrological catchment, and chemicals dissolved in the rain, can follow circuitous pathways below the ground surface until they reach a stream outlet that drains the catchment. Dissolved chemicals can diffuse into lower conductivity regions within the subsurface, and chemicals can also be transported in relatively fast pathways. We investigate a unique data set that monitors chemical transport over kilometer scales, and over a long, 36‐year duration. We develop a mathematical framework to describe the transport and retention of chemical tracers in a catchment, and their arrival times to a draining outlet. Solutions of the equations exhibit characteristic features of tracer concentration variations, and offer a means to characterize and quantity catchment response to chemical inputs.
Key Points
An hydrological catchment system at kilometer scales is shown to exhibit anomalous (non‐Fickian) transport over a 36‐year period
A continuous time random walk suggests two distinct power‐law regimes in the distribution of overall catchment travel times
In the catchments considered here, preferential flow appears to occur at all length and time scales
In parallel to technological advances and ever-increasing use of nanoparticles in industry, agriculture and consumer products, the potential ecotoxicity of nanoparticles and their potential ...accumulation in ecosystems is of increasing concern. Because scientific reports raise a concern regarding nanoparticle toxicity to plants, understanding of their bioaccumulation has become critical and demands more research. Here, the synthesis of isotopically-labeled nanoparticles of silver, copper and zinc oxide is reported; it is demonstrated that while maintaining the basic properties of the same unlabeled (“regular”) nanoparticles, labeled nanoparticles enable more sensitive tracing of nanoparticles within plants that have background elemental levels. This technique is particularly useful for working with elements that are present in high abundance in natural environments. As a benchmark, labeled and unlabeled metal nanoparticles (Ag-NP, Cu-NP, ZnO-NP) were synthesized and compared, and then exposed in a series of growth experiments to Arabidopsis thaliana; the NPs were traced in different parts of the plant. All of the synthesized nanoparticles were characterized by TEM, EDS, DLS, ζ-potential and single particle ICP-MS, which provided essential information regarding size, composition, morphology and surface charge of nanoparticles, as well as their stability in suspensions. Tracing studies with A. thaliana showed uptake/retention of nanoparticles that is more significant in roots than in shoots. Single particle ICP-MS, and scanning electron micrographs and EDS of plant roots showed presence of Ag-NPs in particular, localized areas, whereas copper and zinc were found to be distributed over the root tissues, but not as nanoparticles. Thus, nanoparticles in any natural matrix can be replaced easily by their labeled counterparts to trace the accumulation or retention of NPs. Isotopically-labeled nanoparticles enable acquisition of specific results, even if there are some concentrations of the same elements that originate from other (natural or anthropogenic) sources.
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•Isotopically labeled nanoparticles (Ag-NP, Cu-NP, ZnO-NP) were synthesized.•NPs were characterized by TEM, EDS, DLS, ζ-potential and single particle ICP-MS.•Uptake/retention of NPs is more significant in roots than in shoots of A. thaliana.•sp-ICP-MS, SEM and EDS of plant roots showed presence of Ag-NPs, Cu and Zn.
Isotopically labeled nanoparticles (Ag-NP, Cu-NP, ZnO-NP) for potentially better tracing the uptake/retention of NPs in plants.
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