A novel platform to evaluate the dampening of water and solute transport in an experimental channel under unsteady flow conditions

This paper presents a novel platform to study the dampening of water and solute transport in an experimental channel under unsteady flow conditions, where literature data are scarce. We address the question about what could be the smallest size of experimental platform that is useful for research, project studies, and teaching activities and that allows to do rational experiments characterized by small space occupation, short experimental duration, high measurement precision, high quality and reproducible experimental curves, low water and energy consumption, and the possibility to test a large variety of hydrograph scenarios. Whereas large scale hydraulic laboratories have focused their studies on sediment transport, our platform deals with solute transport. The objectives of our study are (a) building a platform that allows to do rational experiments, (b) enriching the lack of experimental data concerning water and solute transport under unsteady state conditions, and (c) studying the dampening of water and solute transport. We studied solute transport in a channel with lateral gain and lateral loss under different experimental configurations, and we show how the same lateral loss flow event can lead to different lateral loss mass repartitions under different configurations. In order to characterize water and solute dampening between the input and the output of the channel, we calculate dampening ratios based on peak coordinates of time flow curves and time mass curves and that express the decrease of peak amplitude and the increase of peak occurrence time between the input and output curves. Finally, we use a solute transport model coupling the diffusive wave equation for water transfer and the advection–diffusion equation for solute transport in order to simulate the experimental data. The simulations are quite good with a Nash–Sutcliffe efficiency NSE > 0.98 for water transfer and 0.84 < NSE < 0.97 for solute transport. This platform could serve hydrological modellers because it offers a variety of measured parameters (flow, water height, and solute concentration), at a fine time step under unsteady flow conditions.     

A numerical Eulerian method of moment for solute transport in a nonstationary dual-porosity medium

An Eulerian perturbation approach was applied to develop a method of moment for solute transport in a nonstationary, fractured medium. The conceptualized fractured medium is described through a dual-porosity model. Stochastic governing equations for mean concentration and concentration covariance were analytically derived to the first-order accuracy of log-conductivity variance and solved with a numerical method––a finite difference method. The developed method is called a numerical Eulerian method of moment (NEMM). This method was compared with the stationary transport theory [Water Resour. Res. 36(7) (2000) 1665] for predicting mean concentration and its spatial moments. The comparison indicated that the two methods matched very well in predicting first and second spatial moments. NEMM solutions were also compared with Monte Carlo simulations for solute transport in stationary fractured media. The results of the two methods were consistent for calculating small log conductivity variance. The theory was then used to study effects of various parameters and nonstationarity of the medium on flow and transport processes. Results indicated that medium nonstationarity would significantly influence the solute transport process. The nonstationary transport theory relaxes many assumptions adopted in stationary theories and paves the way for applying the NEMM to many environmental projects, especially in analyzing uncertainty of solute transport.     

A test case for the simulation of three-dimensional variable-density flow and solute transport in discretely-fractured porous media

A test case has been developed for three-dimensional simulations of variable-density flow and solute transport in discretely-fractured porous media. The simulation domain is a low-permeability porous matrix cube containing a single non-planar fracture. The initial solute concentration is zero everywhere. A constant solute concentration is assigned to the top of the domain, which increases near-top fluid density and induces downward density-driven flow. The test case is therefore comparable to downwelling of a dense brine below a saline disposal basin or a waste repository. Numerous fingers and distinct convection cells develop early in the fracture but the fingers later coalesce and convection becomes less apparent. To help test other variable-density flow and transport models, results of the test case are presented both qualitatively (concentration contours and velocity fields) and quantitatively (penetration depth, mass flux, total mass stored, maximum fracture and matrix velocity).     

Grid resolution study of ground water flow and transport

Three-dimensional grids representing a heterogeneous, ground water system are generated at 10 different resolutions in support of a site-scale flow and transport modeling effort. These grids represent hydrostratigraphy near Yucca Mountain, Nevada, consisting of 18 stratigraphic units with contrasting fluid flow and transport properties. The grid generation method allows the stratigraphy to be modeled by numerical grids of different resolution so that comparison studies can be performed to test for grid quality and determine the resolution required to resolve geologic structure and physical processes such as fluid flow and solute transport. The process of generating numerical grids with appropriate property distributions from geologic conceptual models is automated, thus making the entire process easy to implement with fewer user-induced errors. The series of grids of various resolutions are used to assess the level at which increasing resolution no longer influences the flow and solute transport results. Grid resolution is found to be a critical issue for ground water flow and solute transport. The resolution required in a particular instance is a function of the feature size of the model, the intrinsic properties of materials, the specific physics of the problem, and boundary conditions. The asymptotic nature of results related to flow and transport indicate that for a hydrologic model of the heterogeneous hydrostratigraphy under Yucca Mountain, a horizontal grid spacing of 600 m and vertical grid spacing of 40 m resolve the hydrostratigraphic model with sufficient precision to accurately model the hypothetical flow and solute transport to within 5% of the value that would be obtained with much higher resolution.     

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.     

Particle tracking in the vicinity of Helgoland,North Sea: a model comparison

Station Helgoland Roads in the south-eastern North Sea (German Bight) hosts one of the richest long-term time series of marine observations. Hydrodynamic transport simulations can help understand variability in the local data brought about by intermittent changes of water masses. The objective of our study is to estimate to which extent the outcome of such transport simulations depends on the choice of a specific hydrodynamic model. Our basic experiment consists of 3,377 Lagrangian simulations in time-reversed mode initialized every 7 h within the period Feb 2002–Oct 2004. Fifty-day backward simulations were performed based on hourly current fields from four different hydrodynamic models that are all well established but differ with regard to spatial resolution, dimensionality (2D or 3D), the origin of atmospheric forcing data, treatment of boundary conditions, presence or absence of baroclinic terms, and the numerical scheme. The particle-tracking algorithm is 2D; fields from 3D models were averaged vertically. Drift simulations were evaluated quantitatively in terms of the fraction of released particles that crossed each cell of a network of receptor regions centred at the island of Helgoland. We found substantial systematic differences between drift simulations based on each of the four hydrodynamic models. Sensitivity studies with regard to spatial resolution and the effects of baroclinic processes suggest that differences in model output cannot unambiguously be assigned to certain model properties or restrictions. Therefore, multi-model simulations are needed for a proper identification of uncertainties in long-term Lagrangian drift simulations.     

Characterizing hyporheic transport processes — Interpretation of electrical geophysical data in coupled stream–hyporheic zone systems during solute tracer studies

Quantifying hyporheic solute dynamics has been limited by our ability to assess the magnitude and extent of stream interactions with multiple domains: mobile subsurface storage (MSS, e.g., freely flowing pore water) and immobile subsurface storage (ISS, e.g., poorly connected pore water). Stream-tracer experiments coupled with solute transport modeling are frequently used to characterize lumped MSS and ISS dynamics, but are limited by the ability to sample only “mobile” water and by window of detection issues. Here, we couple simulations of near-surface electrical resistivity (ER) methods with conservative solute transport to directly compare solute transport with ER interpretations, and to determine the ability of ER to predict spatial and temporal trends of solute distribution and transport in stream–hyporheic systems. Results show that temporal moments from both ER and solute transport data are well correlated for locations where advection is not the dominant solute transport process. Mean arrival time and variance are especially well-predicted by ER interpretation, providing the potential to estimate rate-limited mass transport (i.e. diffusive) parameters from these data in a distributed domain, substantially increasing our knowledge of the fate and transport of subsurface solutes.     

Experimental analysis of pore-scale flow and transport in porous media

A novel, non-intrusive fluorescence imaging technique has been used to quantitatively measure the pore geometry, fluid velocity, and solute concentration within a saturated, three-dimensional porous medium. Discrete numerical averages of these quantities have been made over a representative volume of the medium and used to estimate macroscopic quantities that appear in conventional continuum models of flow and transport. The approach is meant to illustrate how microscopic information can be measured, averaged, and used to characterize medium-scale processes that are typically approximated constitutively. The experimental system consisted of a clear, cylindrical column packed with clear spherical beads and a refractive index-matched fluid seeded with fluorescent tracer particles and solute dye. By illuminating the fluid within the column with a scanning planar laser beam, details of flow and concentration within the pore spaces can be quantitatively observed, allowing for three-dimensional, dimensional, time dependent information to be obtained at good resolution. In time dependent information to be obtained at good resolution. In the current experiment, volumetrically averaged velocities and void-to-volume ratios are first compared with bulk measurements of fluid flux and medium porosity. Microscopic measurements of concentration are then used to construct cross-sectionally averaged profiles, mean breakthrough curves, and direct measurements of the dispersive flux, velocity variance, and concentration variance. In turn, the dispersive flux measurements are compared with mean concentration gradients to provide a basis for confirming the Fickian dispersion model and estimating dispersion coefficients for the medium. Coefficients determined in this manner are compared with others based upon traditional length-scale arguments, mean breakthrough analyses, and curve fits with numerical simulations.     

Analytical solutions for the coefficient of variation of the volume-averaged solute concentration in heterogeneous aquifers

Under the assumption that local solute dispersion is negligible, a new general formula (in the form of a convolution integral) is found for the arbitrary k-point ensemble moment of the local concentration of a solute convected in arbitrary m spatial dimensions with general sure initial conditions. From this general formula new closed-form solutions in m=2 spatial dimensions are derived for 2-point ensemble moments of the local solute concentration for the impulse (Dirac delta) and Gaussian initial conditions. When integrated over an averaging window, these solutions lead to new closed-form expressions for the first two ensemble moments of thevolume-averaged solute concentration and to the corresponding concentration coefficients of variation (CV). Also, for the impulse (Dirac delta) solute concentration initial condition, the second ensemble moment of thesolute point concentration in two spatial dimensions and the corresponding CV are demonstrated to be unbound. For impulse initial conditions the CVs for volume-averaged concentrations axe compared with each other for a tracer from the Borden aquifer experiment. The point-concentration CV is unacceptably large in the whole domain, implying that the ensemble mean concentration is inappropriate for predicting the actual concentration values. The volume-averaged concentration CV decreases significantly with an increasing averaging volume. Since local dispersion is neglected, the new solutions should be interpreted as upper limits for the yet to be derived solutions that account for local dispersion; and so should the presented CVs for Borden tracers. The new analytical solutions may be used to test the accuracy of Monte Carlo simulations or other numerical algorithms that deal with the stochastic solute transport. They may also be used to determine the size of the averaging volume needed to make a quasi-sure statement about the solute mass contained in it.     

Transport of nonsorbing solutes in a streambed with periodic bedforms

Previous studies of hyporheic zone focused largely on the net mass transfer of solutes between stream and streambed. Solute transport within the bed has attracted less attention. In this study, we combined flume experiments and numerical simulations to examine solute transport processes in a streambed with periodic bedforms. Solute originating from the stream was subjected to advective transport driven by pore water circulation due to current–bedform interactions as well as hydrodynamic dispersion in the porous bed. The experimental and numerical results showed that advection played a dominant role at the early stage of solute transport, which took place in the hyporheic zone. Downward solute transfer to the deep ambient flow zone was controlled by transverse dispersion at the later stage when the elapsed time exceeded the advective transport characteristic time t_c (= L/u_c with L being the bedform length and u_c the characteristic pore water velocity). The advection-based pumping exchange model was found to predict reasonably well solute transfer between the overlying water and streambed at the early stage but its performance deteriorated at the later stage. With dispersion neglected, the pumping exchange model underestimated the long-term rate and total mass of solute transfer from the overlying water to the bed. Therefore both advective and dispersive transport components are essential for quantification of hyporheic exchange processes.     

Using PHREEQC to simulate solute transport in fractured bedrock

The geochemical computer model PHREEQC can simulate solute transport in fractured bedrock aquifers that can be conceptualized as dual-porosity flow systems subject to one-dimensional advective-dispersive transport in the bedrock fractures and diffusive transport in the bedrock matrix. This article demonstrates how the physical characteristics of such flow systems can be parameterized for use in PHREEQC, it provides a method for minimizing numerical dispersion in PHREEQC simulations, and it compares PHREEQC simulations with results of an analytical solution. The simulations assumed a dual-porosity conceptual model involving advective-reactive-dispersive transport in the mobile zone (bedrock fracture) and diffusive-reactive transport in the immobile zone (bedrock matrix). The results from the PHREEQC dual-porosity transport model that uses a finite-difference approach showed excellent agreement compared with an analytical solution.     

Groundwater transport of crater-lake brine at Poa´s Volcano, Costa Rica

Poa´s Volcano is an active stratovolcano in Costa Rica that has a lake in its active crater. The crater lake has high temperatures (50–90 °C), high acidity (pH ≈ 0.0), and a high dissolved-solids content (100 g/kg). The volcano has numerous freshwater springs on its flanks, but a few on the northwestern flank are highly acidic (pH = 1.6–2.5) and have high dissolved-solids concentrations (2–22 g/kg). This study analyzes the regional groundwater system at Poa´s and demonstrates the likelihood that the water discharging from the acidic springs in the Rio Agrio watershed originates at the acidic crater lake. Both heat and solute transport are analyzed on a regional scale through numerical simulations using the HST3D finite-difference model, which solves the coupled equations for fluid flow, heat transport, and solute transport. The code allows fluid viscosity and density to be functions of both temperature and solute concentration. The simulations use estimates for recharge to the mountain and a range of values and various distributions of permeability and porosity. Several sensitivity analyses are performed to test how the uncertainty in many of the model parameters affects the simulation results. These uncertainties yield an estimated range of travel times from the crater lake to the Rio Agrio springs of 1–30 years, which is in close agreement with the results of tritium analyses of the springs. Calculated groundwater fluxes into and out of the crater lake are both about several hundred kg/s. These fluxes must be accounted for in water budgets of the crater lake.     

On the numerical analysis of bed-load transport of saltating grains

The focus of this paper is on the analysis of the influence of particles’ velocity distribution and their concentration on the sediment transport rate in bed-load from the Lagrangian perspective.Such aims are addressed by use of the relevant Lagrangian model of spherical saltating particles in which turbulence plays a significant role.The Monte Carlo approach is employed in the simulations to obtain the velocity and concentration of the saltating particles.Numerical simulations using two saltating particle models:(1) with;and(2) without particle-particle collisions are carried out.Based on the numerical results,we address the hypothesis that instead of averaged characteristics,the distributions of particles’ velocity and sediment concentration should be taken into account in the calculation of sediment transport rate.Moreover,our results also show that the interaction between particles during their collisions is the key for better understanding of the physics of sediment transport.All results are compared with well-known experimental formulae i.e.Meyer-Peter and Muller and Fernandez Luque and van Beek.     

Continuous time random walks for non-local radial solute transport

This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile–immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection–dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer tests.     

Sensitivity analysis of conservative and reactive stream transient storage models applied to field data from multiple-reach experiments

The transient storage model (TSM) has been widely used in studies of stream solute transport and fate, with an increasing emphasis on reactive solute transport. In this study we perform sensitivity analyses of a conservative TSM and two different reactive solute transport models (RSTM), one that includes first-order decay in the stream and the storage zone, and a second that considers sorption of a reactive solute on streambed sediments. Two previously analyzed data sets are examined with a focus on the reliability of these RSTMs in characterizing stream and storage zone solute reactions. Sensitivities of simulations to parameters within and among reaches, parameter coefficients of variation, and correlation coefficients are computed and analyzed. Our results indicate that (1) simulated values have the greatest sensitivity to parameters within the same reach, (2) simulated values are also sensitive to parameters in reaches immediately upstream and downstream (inter-reach sensitivity), (3) simulated values have decreasing sensitivity to parameters in reaches farther downstream, and (4) in-stream reactive solute data provide adequate data to resolve effective storage zone reaction parameters, given the model formulations. Simulations of reactive solutes are shown to be equally sensitive to transport parameters and effective reaction parameters of the model, evidence of the control of physical transport on reactive solute dynamics. Similar to conservative transport analysis, reactive solute simulations appear to be most sensitive to data collected during the rising and falling limb of the concentration breakthrough curve.     

Automatic Generation of Locally Refined Composite Grids for Efficient Solute Transport Modeling

Widely used numerical models of solute transport processes in subsurface aquifers are limited to nonlocally refined rectangular, or logically rectangular, structured grids. This presents an unsuitable option to efficient numerical simulations maintaining an acceptable level of accuracy. Optimal selection of locally refined cells for efficient solute transport models is challenging to the current generation of numerical models. We present a novel and relatively simple to implement algorithm addressing these shortcomings. This method operates in four steps involving travel times simulations, a grid coarsening stage followed by a selective local grid refinement based on a cell-wise indicator, and a final postprocessing step. The refinement index is the sum of weighted logarithmic distributions of scaled forward and backward travel times. We calculate representative flow and transport properties at the two scales of the composite grid with a flow-based upscaling technique. We present two test problems to demonstrate the performances of this new gridding algorithm. We obtain the most important speedups for composite grids generated with the highest indicator thresholds. When hydrodynamic dispersion effects increase, we obtain less important speedups. An important outcome of this work is that grid design depends on nature and strength of the underlying flow and solute transport processes. Therefore, we suggest developing solute transport workflows integrating this grid generation algorithm as an integral component to build comprehensive and efficient groundwater models.     

Investigation of Small‐Scale Preferential Flow with a Forced‐Gradient Tracer Test

A new tracer experiment (referred to as MADE‐5) was conducted at the well‐known Macrodispersion Experiment (MADE) site to investigate the influence of small‐scale mass‐transfer and dispersion processes on well‐to‐well transport. The test was performed under dipole forced‐gradient flow conditions and concentrations were monitored in an extraction well and in two multilevel sampler (MLS) wells located at 6, 1.5, and 3.75 m from the source, respectively. The shape of the breakthrough curve (BTC) measured at the extraction well is strongly asymmetric showing a rapidly arriving peak and an extensive late‐time tail. The BTCs measured at seven different depths in the two MLSs are radically different from one another in terms of shape, arrival times, and magnitude of the concentration peaks. All of these characteristics indicate the presence of a complex network of preferential flow pathways controlling solute transport at the test site. Field‐experimental data were also used to evaluate two transport models: a stochastic advection‐dispersion model (ADM) based on conditional multivariate Gaussian realizations of the hydraulic conductivity field and a dual‐domain single‐rate (DDSR) mass‐transfer model based on a deterministic reconstruction of the aquifer heterogeneity. Unlike the stochastic ADM realizations, the DDSR accurately predicted the magnitude of the concentration peak and its arrival time (within a 1.5% error). For the multilevel BTCs between the injection and extraction wells, neither model reproduced the observed values, indicating that a high‐resolution characterization of the aquifer heterogeneity at the subdecimeter scale would be needed to fully capture 3D transport details.     

Using data assimilation method to calibrate a heterogeneous conductivity field and improve solute transport prediction with an unknown contamination source

Hydraulic conductivity distribution and plume initial source condition are two important factors affecting solute transport in heterogeneous media. Since hydraulic conductivity can only be measured at limited locations in a field, its spatial distribution in a complex heterogeneous medium is generally uncertain. In many groundwater contamination sites, transport initial conditions are generally unknown, as plume distributions are available only after the contaminations occurred. In this study, a data assimilation method is developed for calibrating a hydraulic conductivity field and improving solute transport prediction with unknown initial solute source condition. Ensemble Kalman filter (EnKF) is used to update the model parameter (i.e., hydraulic conductivity) and state variables (hydraulic head and solute concentration), when data are available. Two-dimensional numerical experiments are designed to assess the performance of the EnKF method on data assimilation for solute transport prediction. The study results indicate that the EnKF method can significantly improve the estimation of the hydraulic conductivity distribution and solute transport prediction by assimilating hydraulic head measurements with a known solute initial condition. When solute source is unknown, solute prediction by assimilating continuous measurements of solute concentration at a few points in the plume well captures the plume evolution downstream of the measurement points.