The effect of non divergence-free velocity fields on field scale ground water solute transport

Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field.     

An exact solution of solute transport by one-dimensional random velocity fields

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.     

An exact solution of solute transport by one-dimensional random velocity fields

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.     

Catchment‐scale conceptual modelling of water and solute transport in the dual flow system of the karst critical zone

Hydrological and hydrochemical processes in the critical zone of karst environments are controlled by the fracture‐conduit network. Modelling hydrological and hydrochemical dynamics in such heterogeneous hydrogeological settings remains a research challenge. In this study, water and solute transport in the dual flow system of the karst critical zone were investigated in a 73.5‐km² catchment in southwest China. We developed a dual reservoir conceptual run‐off model combined with an autoregressive and moving average model with algorithms to assess dissolution rates in the “fast flow” and “slow flow” systems. This model was applied to 3 catchments with typical karst critical zone architectures, to show how flow exchange between fracture and conduit networks changes in relation to catchment storage dynamics. The flux of bidirectional water and solute exchange between the fissure and conduit system increases from the headwaters to the outfall due to the large area of the developed conduits and low hydraulic gradient in the lower catchment. Rainfall amounts have a significant influence on partitioning the relative proportions of flow and solutes derived from different sources reaching the underground outlet. The effect of rainfall on catchment function is modulated by the structure of the karst critical zone (e.g., epikarst and sinkholes). Thin epikarst and well‐developed sinkholes in the headwaters divert more surface water (younger water) into the underground channel network, leading to a higher fraction of rainfall recharge into the fast flow system and total outflow. Also, the contribution of carbonate weathering to mass export is also higher in the headwaters due to the infiltration of younger water with low solute concentrations through sinkholes.     

Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

On the effects of preferential or barrier flow features on solute plumes in permeable porous media

Despite that discrete flow features (DFFs, e.g. fractures and faults) are common features in the subsurface, few studies have explored the influence of DFFs on solute plumes in otherwise permeable rocks (e.g. sandstone, limestone), compared to low-permeability rock settings (e.g. granite and basalt). DFFs can provide preferential flow pathways (i.e. ‘preferential flow features’; PFFs), or can act to impede flow (i.e. ‘barrier flow features’; BFFs). This research uses a simple analytical expression and numerical modelling to explore how a single DFF influences the steady-state distributions of solute plumes in permeable aquifers. The analysis quantifies the displacement and widening (or narrowing) of a steady-state solute plume as it crosses a DFF in idealised, 1 × 1 m moderately permeable rock aquifers. Previous research is extended by accounting for DFFs as 2D flow features, and including BFF situations. A range of matrix-DFF permeability ratios (0.01 to 100) and DFF apertures (0.25 mm to 2 cm), typical of sedimentary aquifers containing medium-to-large fractures, are considered. The results indicate that for the conceptual models considered here, PFFs typically have a more significant influence on plume distributions than BFFs, and the impact of DFFs on solute plumes generally increases with increasing aperture. For example, displacement of peak solute concentration caused by DFFs exceeds 20 cm in some PFF cases, compared to a maximum of 0.64 cm in BFF cases. PFFs widen plumes up to 9.7 times, compared to a maximum plume widening of 2.0 times in BFF cases. Plumes crossing a PFF are less symmetrical, and peak solute concentrations beneath PFFs are up to two orders of magnitude lower than plumes in BFF cases. This study extends current knowledge of the attenuating influence of DFFs in otherwise permeable rocks on solute plume characteristics, through evaluation of 2D flow effects in DFFs for a variety of DFF apertures, and by considering BFF situations.     

Hillslope soil water flowpaths and the dynamics of roadside soil cation pools influenced by road deicers

Over the past 60 years, road deicers (i.e. road salt) have been applied to roadways in high latitudes to improve road conditions in winter weather. However, the dissolution of road deicers in highway runoff creates waters with high concentrations of sodium, which can mobilize soil metals via soil cation‐exchange reactions. While several studies have detailed the interactions of road salt‐rich solutions and surface and ground waters, less attention has been given to how local hydrologic flowpaths can impact the delivery of these solutions to near‐road soils. Between 2013 and 2014, soil water samples were collected from a roadside transect of lysimeter nests in Pittsburgh, Pennsylvania (USA). Soil water samples were analysed for metal concentrations and resulting data used to examine cation dynamics. While patterns in soil water calcium and magnesium concentrations follow patterns in soil water sodium concentrations, additional processes influence patterns in soil water potassium concentrations. Specifically, we observe the highest calcium and magnesium concentrations in the deepest lysimeters, suggesting divalent cations are mobilized to, and potentially accumulate in, deeper soil horizons. In contrast, soil water potassium concentrations do not follow this pattern. Additionally, in all examined elements (Ca, Mg, K, Na, and Cl), the timing of concentration peaks appears be influenced by a combination of both distance from the roadside and sampling depth. These relationships not only suggest that multiple soil water flowpaths interact with our study transect but also confirm that road salt plumes persist and migrate following the road salting season. Characterizing the interactions of sodium‐rich solutions and roadside soil cation pools clarifies our understanding of metal dynamics in the roadside environment. A deeper understanding of these processes is necessary to effectively restore and manage watersheds as high total dissolved solid solutions (e.g. road deicing melt, unconventional natural gas brines, and marginal irrigation water) continue to influence hydrological systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of snow structure on water flow and solute transport

Water flow through a melting snow pack modifies its structure and stability and affects the release of water and nutrients into soils and surface waters. Field and laboratory observations indicate a large spatial variability on various scales of the liquid water content and flow, a dominant system feature currently not included in numerical models. We investigated experimentally water and dye tracer movement through microstructurally different snow pack horizons and the persistence of preferential flow paths. Naturally rounded snow of varying grain size was artificially packed to obtain well known conditions by sieving it into rectangular bins. Surface melt was induced with infrared lamps. The flow paths were visualized with tracers and liquid water content was monitored with time domain reflectometry probes. Vertical cuts through the snow pack were imaged. The dye tracer patterns allowed the two flow regimes ‘matrix flow’ and ‘preferential flow’ to be distinguished. Matrix flow is apparently dominated by film and capillary flow in the unsaturated snow matrix. The capillary barrier effect at a boundary between a fine over a coarse textured layer on matrix flow in snow was confirmed. In contrast, preferential flow appears as well‐defined flow fingers that advance from 0·1 to 1 cm s^?1. During a melt phase, the advancing flow fingers enlarge and are only partially time invariant. It remains to be shown whether the continuum concept, including the Darcy–Buckingham law is apt to describe the extremely non‐linear nature of water flow and the travel time of solutes in snow under conditions of melt water percolation. Probably, snow packs that include faceted crystals and large variations in bulk density, feature more pronounced capillary barriers and preferential flow triggering, but also stronger impeding of fingers by lateral dispersion. Further, triggering and persistence of preferential flow is complicated by the usually transient infiltration rate. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of solute transport in a divergent flow tracer test with scale‐dependent dispersion

It has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale‐dependent dispersion. In this study, Laplace‐transformed analytical solutions to advection‐dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale‐dependent dispersivity. Breakthrough curves obtained using the scale‐dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale‐dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale‐dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale‐dependent dispersivity model is 1·3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale‐dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1·3 for the scale‐dependent dispersion model if the dispersion process is more accurately characterized by scale‐dependent dispersion. Copyright © 2007 John Wiley & Sons, Ltd.     

Intercomparison of 3D pore-scale flow and solute transport simulation methods

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.     

Water flow and solute transport model of potentially toxic elements through unsaturated zone at regional wellfield Kosnica

The objective of this work was to build a prognostic water flow model and potentially toxic elements (lead, cadmium, zinc) transport model in the unsaturated zone. Research was conducted in the catchment area of Kosnica regional wellfield, where the unsaturated zone is characterised by Fluvisol. Lower sorption capacities were determined in the first horizons for all three potentially toxic elements. Correlation coefficient of the measured and simulated values of tracer concentration is 0.58 for the AC horizon and 0.84 for the 2C/C1 horizon. Based on calibrated water flow and transport parameters, a prognostic water flow model and potentially toxic elements (lead, cadmium, zinc) transport model in the unsaturated zone was built. In case of an accidental spill of potentially toxic elements with concentrations of 1000 mg/l, the risk of contamination of the aquifer is present. Copyright © 2016 John Wiley & Sons, Ltd.     

Variable-density groundwater flow and solute transport in irregular 2D fracture networks

Numerical simulations of variable-density flow and solute transport have been conducted to investigate dense plume migration for various configurations of 2D fracture networks. For orthogonal fractures, simulations demonstrate that dispersive mixing in fractures with small aperture does not stabilize vertical plume migration in fractures with large aperture. Simulations in non-orthogonal 2D fracture networks indicate that convection cells form and that they overlap both the porous matrix and fractures. Thus, transport rates in convection cells depend on matrix and fracture flow properties. A series of simulations in statistically equivalent networks of fractures with irregular orientation show that the migration of a dense plume is highly sensitive to the geometry of the network. If fractures in a random network are connected equidistantly to the solute source, few equidistantly distributed fractures favor density-driven transport. On the other hand, numerous fractures have a stabilizing effect, especially if diffusive transport rates are high. A sensitivity analysis for a network with few equidistantly distributed fractures shows that low fracture aperture, low matrix permeability and high matrix porosity impede density-driven transport because these parameters reduce groundwater flow velocities in both the matrix and the fractures. Enhanced molecular diffusion slows down density-driven transport because it favors solute diffusion from the fractures into the low-permeability porous matrix where groundwater velocities are smaller. For the configurations tested, variable-density flow and solute transport are most sensitive to the permeability and porosity of the matrix, which are properties that can be determined more accurately than the geometry and hydraulic properties of the fracture network, which have a smaller impact on density-driven transport.     

Reactive transport in stratified flow fields with idealized heterogeneity

A two-dimensional equation governing the steady state spatial concentration distribution of a reactive constituent within a heterogeneous advective–dispersive flow field is solved analytically. The solution which is developed for the case of a single point source can be generalized to represent analogous situations with any number of separate point sources. A limiting case of special interest has a line source of constant concentration spanning the domain’s upstream boundary. The work has relevance for improving understanding of reactive transport within various kinds of advection-dominated natural or engineered environments including rivers and streams, and bioreactors such as treatment wetlands. Simulations are used to examine quantitatively the impact that transverse dispersion (deviations from purely stochastic-convective flow) can have on mean concentration decline in the direction of flow. Results support the contention that transverse mixing serves to enhance the overall rate of reaction in such systems.     

Large-scale numerical simulation of groundwater flow and solute transport in discretely-fractured crystalline bedrock

A large-scale fluid flow and solute transport model was developed for the crystalline bedrock at Olkiluoto Island, Finland, which is considered as potential deep geological repository for spent nuclear fuel. Site characterization showed that the main flow pathways in the low-permeability crystalline bedrock on the island are 13 subhorizontal fracture zones. Compared to other sites investigated in the context of deep disposal of spent nuclear fuel, most deep boreholes drilled at Olkiluoto are not packed-off but are instead left open. These open boreholes intersect the main fracture zones and create hydraulic connections between them, thus modifying groundwater flow. The combined impact of fracture zones and open boreholes on groundwater flow is simulated at the scale of the island. The modeling approach couples a geomodel that represents the fracture zones and boreholes with a numerical model that simulates fluid flow and solute transport. The geometry of the fracture zones that are intersected by boreholes is complex, and the 3D geomodel was therefore constructed with a tetrahedral mesh. The geomodel was imported into the numerical model to simulate a pumping test conducted on Olkiluoto Island. The pumping test simulation demonstrates that fracture-borehole intersections must be accurately discretized, because they strongly control groundwater flow. The tetrahedral mesh provides an accurate representation of these intersections. The calibrated flow model was then used for illustrative scenarios of radionuclide migration to show the impact of fracture zones on solute transport once the boreholes were backfilled. These mass transport simulations constitute base cases for future predictive analyses and sensitivity studies, since they represent key processes to take into consideration for repository performance assessment.     

Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures

Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes.     

Test of scale modelling of sediment transport in steady unidirectional flow

In two steady uniform flows at different physical scales in a small open channel, with variables characterizing flow, sediment, and fluid adjusted for dynamic similitude by means of four dimensionless modelling parameters (a Reynolds number, a Froude number, a density ratio, and a length ratio), measured frequency distributions of height, spacing, and migration rate of current ripples were almost identical when scaled, thus verifying that exact Reynolds-Froude modelling of loose-sediment transport is valid and workable. Modelling should be valid as well for a wide range of other transport conditions in the same kind of flow, because no additional kinds of forces or effects would be present in transport of loose grains in modes other than as ripples. In scaled-down modelling, a scale ratio of 2.5 is attainable without recourse to exotic fluids by use of water at 85°C to model natural flows at 10°C.     

Microtopographical and hydrophysical controls on subsurface flow and solute transport: A continuous solute release experiment in a subarctic bog

Resource extraction and transportation activities in subarctic Canada can result in the unintentional release of contaminants into the surrounding peatlands. In the event of a release, a thorough understanding of solute transport within the saturated zone is necessary to predict plume fate and the potential impacts on peatland ecosystems. To better characterize contaminant transport in these systems, approximately 13,000 L/day of sodium chloride tracer (200 mg/L) was released into a bog in the James Bay Lowland. The tracer was pumped into a fully penetrating well (1.5 m) between July 5 and August 18, 2015. Horizontal and vertical plume development was measured via in situ specific conductance and water table depth from an adaptive monitoring network. Over the spill period, the bulk of the plume travelled a lateral distance of 100 m in the direction of the slight regional groundwater and topographical slope. The plume shape was irregular and followed the hollows, indicating preferential flow paths due to the site microtopography. Saturated transport of the tracer occurred primarily at ~25 cm below ground surface (bgs), and at a discontinuous high hydraulic conductivity layer ~125 cm bgs due to a complex and heterogeneous vertical hydraulic conductivity profile. Plume measurement was confounded by a large amount of precipitation (233 mm over the study period) that temporarily diluted the tracer in the highly conductive upper peat layer. Longitudinal solute advection can be approximated using local water table information (i.e., depth and gradient); microtopography; and meteorological conditions. Vertical distribution of solute within the peat profile is far more complex due to the heterogeneous subsurface; characterization would be aided by a detailed understanding of the site‐specific peat profile; the degree of decomposition; and the type of contaminant (e.g., reactive/nonreactive). The results of this research highlight the difficulty of tracking a contaminant spill in bogs and provide a benchmark for the characterization of the short‐term fate of a plume in these complex systems.     

Analysis of solute transport with a hyperbolic scale-dependent dispersion model

An empirical hyperbolic scale-dependent dispersion model, which predicts a linear growth of dispersivity close to the origin and the attainment of an asymptotic dispersivity at large distances, is presented for deterministic modelling of field-scale solute transport and the analysis of solute transport experiments. A simple relationship is derived between local dispersivity, which is used in numerical simulations of solute transport, and effective dispersivity, which is estimated from the analysis of tracer breakthrough curves. The scale-dependent dispersion model is used to interpret a field tracer experiment by nonlinear least-squares inversion of a numerical solution for unsaturated transport. Simultaneous inversion of concentration-time data from several sampling locations indicates a linear growth of the dispersion process over the scale of the experiment. These findings are consistent with the results of an earlier analysis based on the use of a constant dispersion coefficient model at each of the sampling depths.