Solute Transport Behavior Research Articles

Predictive model of solute transport with reversible adsorption in spatially periodic hierarchical porous media

Solute transport in hierarchical porous media with reversible adsorption is predicted by the volume averaging method. A transient macroscopic advection-diffusion equation is derived to describe the multiscale solute transport problem. The theoretical expression of the dispersion tensor is obtained which is the function of pore-scale velocity profile. Steady closure equations are derived to calculate the dispersion tensor. With the aid of pore-scale simulation in unit cells of the hierarchical porous media, the dispersion tensor can be calculated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns comprised of ordered, porous pillars. It is straightforward to use the model to predict the solute transport behavior in fixed beds packed with particles.

Effect of surfactant SDS on DMSO transport across water/hexane interface by molecular dynamics simulation

Solute transport behavior across liquid–liquid interfaces plays important roles in many chemical engineering processes and usually occurs in the presence of surfactants. In this work, we report a full all-atom molecular dynamics simulation study of dimethyl sulfoxide (DMSO) crossing a water/hexane interface in different concentrations of sodium dodecylsulfate (SDS). By analyzing various properties, ranging from the configuration and energetic behaviors to the dynamic characteristics, we conclude that the presence of SDS has multiple non-trivial effects: (1) the association of SDS at the interface drives the interfacial region wider and decreases the interfacial tension with an almost linear dependence on SDS concentration; (2) higher SDS concentrations result in both a lower self-diffusion coefficient for DMSO and a smaller resistance force to DMSO moving out of the interfacial region, causing the exchange of DMSO between the interface and bulk region to become more frequent; and (3) the transition of the orientation preference of DMSO molecules passing from the interface to the water-rich phase vanishes. Current simulation studies examining the molecular level provide helpful insights for understanding the influence of surfactants on solute transport.

Long-term changes in nitrate conditions over the 20th century in two Midwestern Corn Belt streams

Summary Long-term changes in nitrate concentration and flux between the middle of the 20th century and the first decade of the 21st century were estimated for the Des Moines River and the Middle Illinois River, two Midwestern Corn Belt streams, using a novel weighted regression approach that is able to detect subtle changes in solute transport behavior over time. The results show that the largest changes in flow-normalized concentration and flux occurred between 1960 and 1980 in both streams, with smaller or negligible changes between 1980 and 2004. Contrasting patterns were observed between (1) nitrate export linked to non-point sources, explicitly runoff of synthetic fertilizer or other surface sources and (2) nitrate export presumably associated with point sources such as urban wastewater or confined livestock feeding facilities, with each of these modes of transport important under different domains of streamflow. Surface runoff was estimated to be consistently most important under high-flow conditions during the spring in both rivers. Nitrate export may also have been considerable in the Des Moines River even under some conditions during the winter when flows are generally lower, suggesting the influence of point sources during this time. Similar results were shown for the Middle Illinois River, which is subject to significant influence of wastewater from the Chicago area, where elevated nitrate concentrations were associated with at the lowest flows during the winter and fall. By modeling concentration directly, this study highlights the complex relationship between concentration and streamflow that has evolved in these two basins over the last 50 years. This approach provides insights about changing conditions that only become observable when stationarity in the relationship between concentration and streamflow is not assumed.

Numerical modeling of reactive solute transport in a single fracture with matrix diffusion under complex boundary condition

A numerical model using finite volume QUICK scheme has been developed for simulating the transport behavior of solutes in a coupled fracture–matrix system for pulse-type boundary condition as against the conventional constant continuous source-type boundary condition, which essentially reflects the reality better, as it is practically not feasible for any source type to discharge it continuously with the same magnitude for a very long period. The sensitivity of fracture and rock matrix parameters, namely fracture aperture thickness, matrix porosity, and matrix diffusion coefficient have been analyzed under this complex boundary condition. In addition, the role of nonlinear sorption as well as decay has also been investigated. Numerical results suggest that the reduction in relative concentration within the fracture resulting from pulse-type boundary condition should always not be mistaken for matrix diffusion. It has been concluded from the present numerical study that segregating and quantifying the role on individual components, namely (a) source exhaustion (pulse-type boundary condition); (b) matrix diffusion; (c) sorption; and (d) decay in characterizing the resultant transport behavior of solutes in a single fracture with matrix diffusion under a pulse-type boundary condition remains challenging and needs further research.

Simulation of experimental breakthrough curves using multiprocess non-equilibrium model for reactive solute transport in stratified porous media

In this paper, we have studied the behaviour of reactive solute transport through stratified porous medium under the influence of multi-process non-equilibrium transport model. Various experiments were carried out in the laboratory and the experimental breakthrough curves were observed at spatially placed sampling points for stratified porous medium. Batch sorption studies were also performed to estimate the sorption parameters of the material used in stratified aquifer system. The effects of distance dependent dispersion and tailing are visible in the experimental breakthrough curves. The presence of physical and chemical non-equilibrium are observed from the pattern of breakthrough curves. Multi-process non-equilibrium model represents the combined effect of physical and chemical non-ideality in the stratified aquifer system. The results show that the incorporation of distance dependent dispersivity in multi-process non-equilibrium model provides best fit of observed data through stratified porous media. Also, the exponential distance dependent dispersivity is more suitable for large distances and at small distances, linear or constant dispersivity function can be considered for simulating reactive solute in stratified porous medium.

Fundamentals and Modeling of Electrokinetic Transport in Nanochannels

AbstractWhen the channel size approaches the thickness of the charged layer (typically, ∼10–100 nm), the resulting molecular and non‐equilibrium effects are markedly different from those observed in larger channels and have a significant effect on the transport behavior of solutes and solvents. As a result, the problem of modeling fluidic behavior at the nanoscale has attracted increasing interest in recent years. This review introduces the fundamental theories and principles associated with electrokinetic transport and molecular dynamics modeling, and discusses various applications of nanofluidic devices in the physics, mechanics, and chemistry fields.

One-dimensional solute transport for uniform and varying pulse type input point source through heterogeneous medium

An analytical solution is developed for conservative solute transport in a one-dimensional heterogeneous porous medium. The solute dispersion parameter is considered uniform, while the seepage flow velocity is considered spatially dependent. Retardation factor is considered inversely proportional to square of the flow velocity. The seepage velocity flow is considered inversely proportional to the spatially dependent function. The solution is derived for two cases: the former one is for uniform pulse type input point source and the latter one is for varying pulse type input point source. The second condition is considered at the far end of the medium. It is of the second type (flux type) of homogeneous nature. Laplace transform technique (LLT) is employed to get the analytical solutions to the present problem. In the process, a new space variable is introduced. The solutions are graphically illustrated. The effects of heterogeneity of the medium on the solute transport behaviour, in the presence and absence of the source pollutant, are also studied. Laplace transformation technique is used to solve the present problems analytically.

Local‐ and field‐scale stochastic‐advective vertical solute transport in horizontally heterogeneous unsaturated soils

AbstractDescription of field‐scale solute transport in unsaturated soils is essential for assessing the degree of contamination, estimating fluxes past a control plane and for designing remedial measures. The flow field is usually described by numerical solution of the Richards equation followed by numerical solution of the advection‐dispersion equation to describe contaminant movement. These numerical solutions are highly complex, and do not provide the insights that are possible from simpler analytical representations. In this study, analytical solutions at the local scale are developed to describe purely advective vertical transport of a conservative solute along the principle characteristic of the flow field. Local‐scale model development is simplified by using a sharp‐front approximation for water movement. These local solutions are then upscaled to field‐scale solute transport by adopting a lognormally distributed horizontal hydraulic conductivity field to represent the natural heterogeneity observed in field soils. Analytical expressions are developed for the mean behavior of solute transport at the field scale. Comparisons with experimental observations find that trends of field‐scale solute behavior are reasonably reproduced by the model. The accuracy of the proposed solution improves with increasing spatial variability in the hydraulic conductivity as revealed by further comparisons with numerical results of the Richards equation‐based field‐scale solute movement. In some cases, the sharp‐front approximation may lead to anomalous field‐scale behavior depending on the role of pre and postponded conditions in the field, and this limitation is discussed. The proposed method shows promise for describing field‐scale solute movement in loamy sand and sandy loam soils.

Critical differences in chromatographic properties of silica- and polymer-based monoliths

Chromatographic analytical columns containing porous monolithic beds based on cross-linked polymers and derivatized silica have now been commercially available for several years and, despite some apparent conceptual similarities, are marketed and utilized for quite different chromatographic applications. While this distinction is well-accepted by users, the fundamental differences in chromatographic behavior of these materials that lead to this clear distinction in their primary application areas have not yet been systematically studied. To this end, the present experimental study investigates differences in the apparent chromatographic characteristics when using small molecules with commercially available monolithic reversed-phase analytical columns based on poly(styrene-co-divinyl benzene) and C18-derivatized silica. Relevant practical information is obtained from measurements made by “arrested elution” of non-retained and retained solutes and chromatographic elution performance across a wide range of retention factors with a set of structurally similar small molecules. Observations of apparent diffusion probed with “arrested elution” experiments and mass transport inferred from the observed efficiency at increased flow velocity in the monolithic structures (both under retained and non-retained conditions) lead to the conclusion that fundamentally different solute transport behavior is operative. The silica-based monolithic materials are used to establish a “reference” for comparison to observations with cross-linked porous polymeric monolithic materials. Despite the differences in morphology, chromatographic properties have their origin in the underlying physical structure of pore space. The derivatized surfaces in silica-based materials have their counterpart in pore-fluid gel interfaces in polymeric monoliths. The pore-fluid gel interfaces have their origin in varying solvation of polymer by eluent components. Consequently, they allow varying permeation of small molecules into the solvated polymer via partition. The traversing of small molecules through the polymer monolith's complex nanoscale physical structure plays a key factor when rationalizing any chromatographic performance as seen in the slopes of plate height curves which vary dramatically with mobile phase composition and solute identity.

Morphological, hydrological, biogeochemical and ecological changes and challenges in river restoration – the Thur River case study

Abstract. River restoration can enhance river dynamics, environmental heterogeneity and biodiversity, but the underlying processes governing the dynamic changes need to be understood to ensure that restoration projects meet their goals, and adverse effects are prevented. In particular, we need to comprehend how hydromorphological variability quantitatively relates to ecosystem functioning and services, biodiversity as well as ground- and surface water quality in restored river corridors. This involves (i) physical processes and structural properties, determining erosion and sedimentation, as well as solute and heat transport behavior in surface water and within the subsurface; (ii) biogeochemical processes and characteristics, including the turnover of nutrients and natural water constituents; and (iii) ecological processes and indicators related to biodiversity and ecological functioning. All these aspects are interlinked, requiring an interdisciplinary investigation approach. Here, we present an overview of the recently completed RECORD (REstored CORridor Dynamics) project in which we combined physical, chemical, and biological observations with modeling at a restored river corridor of the perialpine Thur River in Switzerland. Our results show that river restoration, beyond inducing morphologic changes that reshape the river bed and banks, triggered complex spatial patterns of bank infiltration, and affected habitat type, biotic communities and biogeochemical processes. We adopted an interdisciplinary approach of monitoring the continuing changes due to restoration measures to address the following questions: How stable is the morphological variability established by restoration? Does morphological variability guarantee an improvement in biodiversity? How does morphological variability affect biogeochemical transformations in the river corridor? What are some potential adverse effects of river restoration? How is river restoration influenced by catchment-scale hydraulics and which feedbacks exist on the large scale? Beyond summarizing the major results of individual studies within the project, we show that these overarching questions could only be addressed in an interdisciplinary framework.

On the reliability of analytical models to predict solute transport in a fracture network

Abstract. In hydrogeology, the application of reliable tracer transport model approaches is a key issue to derive the hydrodynamic properties of aquifers. Laboratory- and field-scale tracer dispersion breakthrough curves (BTC) in fractured media are notorious for exhibiting early time arrivals and late time tailing that are not captured by the classical advection–dispersion equation (ADE). These "non-Fickian" features are proven to be better explained by a mobile–immobile (MIM) approach. In this conceptualization the fractured rock system is schematized as a continuous medium in which the liquid phase is separated into flowing and stagnant regions. The present study compares the performances and reliabilities of the classical MIM and the explicit network model (ENM), taking expressly into account the network geometry for describing tracer transport behavior in a fractured sample at bench scale. Though ENM shows better fitting results than MIM, the latter remains still valid as it proves to describe the observed curves quite well. The results show that the presence of nonlinear flow plays an important role in the behavior of solute transport. First, the distribution of solute according to different pathways is not constant, but it is related to the flow rate. Second, nonlinear flow influences advection in that it leads to a delay in solute transport respect to the linear flow assumption. However, nonlinear flow is not shown to be related with dispersion. The experimental results show that in the study case the geometrical dispersion dominates the Taylor dispersion. However, the interpretation with the ENM shows a weak transitional regime from geometrical dispersion to Taylor dispersion for high flow rates. Incorporating the description of the flow paths in the analytical modeling has proven to better fit the curves and to give a more robust interpretation of the solute transport.

Analytical solution of a two-dimensional model of liquid chromatography including moment analysis

This work presents an analysis of a two-dimensional model of a liquid chromatographic column. Constant flow rates and linear adsorption isotherms are assumed. Different sets of boundary conditions are considered, including injections through inner and outer regions of the column inlet cross section. The finite Hankel transform technique in combination with the Laplace transform method is applied to solve the model equations. The developed analytical solutions illustrate the influence and quantify the magnitude of the solute transport in the radial direction. Comparing Dirichlet and Danckwerts boundary conditions, the predicted elution profiles differ significantly for large axial dispersion coefficients. For further analysis of the solute transport behavior, the temporal moments up to the fourth order are derived from the Laplace-transformed solutions. The analytical solutions for the concentration profiles and the moments are in good agreement with the numerical solutions of a high resolution flux limiting finite volume scheme. Results of different case studies are presented and discussed covering a wide range of mass transfer characteristics. The derived analytical solutions provide useful tools to quantify jointly occurring longitudinal and radial dispersion effects.

A numerical study of capillary pressure–saturation relationship for supercritical carbon dioxide (CO2) injection in deep saline aquifer

Carbon capture and sequestration (CCS) is expected to play a major role in reducing greenhouse gas in the atmosphere. It is applied using different methods including geological, oceanic and mineral sequestration. Geological sequestration refers to storing of CO2 in underground geological formations including deep saline aquifers (DSAs). This process induces multiphase fluid flow and solute transport behaviour besides some geochemical reactions between the fluids and minerals in the geological formation. In this work, a series of numerical simulations are carried out to investigate the injection and transport behaviour of supercritical CO2 in DSAs as a two-phase flow in porous media in addition to studying the influence of different parameters such as time scale, temperature, pressure, permeability and geochemical condition on the supercritical CO2 injection in underground domains. In contrast to most works which are focussed on determining mass fraction of CO2, this paper focuses on determining CO2 gas saturation (i.e., volume fraction) at various time scales, temperatures and pressure conditions taking into consideration the effects of porosity/permeability, heterogeneity and capillarity for CO2–water system. A series of numerical simulations is carried out to illustrate how the saturation, capillary pressure and the amount of dissolved CO2 change with the change of injection process, hydrostatic pressure and geothermal gradient. For example, the obtained results are used to correlate how increase in the mean permeability of the geological formation allows greater injectivity and mobility of CO2 which should lead to increase in CO2 dissolution into the resident brine in the subsurface.

Analytical solutions and moment analysis of chromatographic models for rectangular pulse injections

This work focuses on the analysis of two standard liquid chromatographic models, namely the lumped kinetic model and the equilibrium dispersive model. Analytical solutions, obtained by means of Laplace transformation, are derived for rectangular single solute concentration pulses of finite length and breakthrough curves injected under linear conditions. In order to analyze the solute transport behavior by means of the two models, the temporal moments up to fourth order are calculated from the Laplace-transformed solutions. The limiting cases of continuous injection and negligible mass transfer limitations are evaluated. For validation, the analytical solutions are compared with the numerical solutions of models using the discontinuous Galerkin finite element method. Results of different case studies are discussed for linear and nonlinear adsorption isotherms. The discontinuous Galerkin method is employed to obtain moments for both linear and nonlinear models numerically. Analytically and numerically determined concentration profiles and moments were found to be in good agreement.

Experimental investigation of solute transport in stratified porous media

In this study, an attempt is made to investigate the behaviour of solute transport through stratified porous media using laboratory experiments. A physical model is constructed to represent stratified porous media consisting of an advective region sandwiched between two non-advective regions. Pulse of tracer was injected at the inlet of the sand layer situated in between the clay matrix of the experimental model, and samples of tracer were collected at the other end of the model. An implicit finite-difference numerical technique is used to solve advective dispersive transport equations, including equilibrium sorption and first-order degradation constant for reactive transport through stratified porous media. A numerical model is used to simulate the breakthrough curves of experimental data of chloride and fluoride. It is seen that the peak of breakthrough curves is higher for the non-reactive solute compared to that of the reactive solute. The observed breakthrough curves were also found to be skewed in shape for solutes in stratified porous media. The numerical model was also found to be more sensitive to the value of transverse diffusion during simulation of experimental breakthrough curves. Finally, the values of effective diffusion coefficient and retardation coefficient are estimated by simulation of experimental breakthrough curves.

Contaminant transport through fractured-porous media: An experimental study

In this paper, an experimental study has been carried out to investigate the behavior of solute transport through fractured-porous media. Experimental set-up consists of fractured-porous media which has been created with clay (matrix) and a single fracture is created in middle of the clay matrix in flow direction. During experiment, the clay matrix is saturated with fresh water and solute tracer is injected in the fracture at inlet and the samples are collected from out let for different times of interval. Concentration profiles of experimental data of chloride and fluoride are simulated with developed numerical model to estimate transport parameters. Results show that the value of matrix-diffusion coefficient depends on fracture velocity and residence time till to reach in equilibrium condition. It is also found that higher value of diffusion coefficient leads to reduce the magnitude of solute concentration in the fracture. The experimental results indicate that there is substantial diffusion and sorption in the fractured-porous matrix. The estimated parameters and numerical model can be used for design of waste disposal system in the fractured matrix system. Finally, numerical results of various temporal moments have been predicted to study the behavior of reactive solute in the fracture, and it was found that the behavior of solute mass recovers, mean arrival time and second time moment are nonlinear along the travel distance for solute in the fracture in the presence of matrix-diffusion and decay rate coefficient.

Evidence of non-Darcy flow and non-Fickian transport in fractured media at laboratory scale

Abstract. During a risk assessment procedure as well as when dealing with cleanup and monitoring strategies, accurate predictions of solute propagation in fractured rocks are of particular importance when assessing exposure pathways through which contaminants reach receptors. Experimental data obtained under controlled conditions such as in a laboratory allow to increase the understanding of the fundamental physics of fluid flow and solute transport in fractures. In this study, laboratory hydraulic and tracer tests have been carried out on an artificially created fractured rock sample. The tests regard the analysis of the hydraulic loss and the measurement of breakthrough curves for saline tracer pulse inside a rock sample of parallelepiped shape (0.60 × 0.40 × 0.08 m). The convolution theory has been applied in order to remove the effect of the acquisition apparatus on tracer experiments. The experimental results have shown evidence of a non-Darcy relationship between flow rate and hydraulic loss that is best described by Forchheimer's law. Furthermore, in the flow experiments both inertial and viscous flow terms are not negligible. The observed experimental breakthrough curves of solute transport have been modeled by the classical one-dimensional analytical solution for the advection–dispersion equation (ADE) and the single rate mobile–immobile model (MIM). The former model does not properly fit the first arrival and the tail while the latter, which recognizes the existence of mobile and immobile domains for transport, provides a very decent fit. The carried out experiments show that there exists a pronounced mobile–immobile zone interaction that cannot be neglected and that leads to a non-equilibrium behavior of solute transport. The existence of a non-Darcian flow regime has showed to influence the velocity field in that it gives rise to a delay in solute migration with respect to the predicted value assuming linear flow. Furthermore, the presence of inertial effects enhance non-equilibrium behavior. Instead, the presence of a transitional flow regime seems not to exert influence on the behavior of dispersion. The linear-type relationship found between velocity and dispersion demonstrates that for the range of imposed flow rates and for the selected path the geometrical dispersion dominates the mixing processes along the fracture network.

Solute transport as affected by surface land characteristics in gravely calcareous arid soils

Gravely calcareous soils cover approximately most of arid lands (in percent); however, the solute transport behavior in these soils remains a current issue. This research aimed at estimating and correlating the solute transport parameters in gravely calcareous soils as being affected by different land uses through the knowledge of the soil mor- phological, physical, and chemical properties. Four different land use sites were selected: irrigated trees and bare, range, and alluvial sediment lands. Solute transport parameters of soil pore water velocity (V), dispersion coefficient (D), and retardation factor (R) were estimated using bromide break- through curve tests for surface soil columns. In addition, field Brilliant Blue FCF dye tracing experiment was conducted to determine the maximum dimensional move- ments. Soil morphological analysis was able to explain the heterogeneity in the solute transport parameters. Conductive solute transport mechanism with V of 17.99 m/day was favored in a high continuous pore system observed under tree lands. Presence of high gravel and CaCO3 contents under range lands increased pore system tortuosity and thus increased D magnitude up to 1,339.88 cm 2 /day. Existence of thin surface crusts at both bare soils and alluvial sediments had considerably restricted V down to 1.46 m/day. Dye staining technique aided the explanation of the existing variations by providing visual evidence on the preferential flow paths and patterns governing the solute transport mech- anism at each site.

Regional-scale integration of multiresolution hydrological and geophysical data using a two-step Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale for the purpose of improving predictions of groundwater flow and solute transport. However, extending corresponding approaches to the regional scale still represents one of the major challenges in the domain of hydrogeophysics. To address this problem, we have developed a regional-scale data integration methodology based on a two-step Bayesian sequential simulation approach. Our objective is to generate high-resolution stochastic realizations of the regional-scale hydraulic conductivity field in the common case where there exist spatially exhaustive but poorly resolved measurements of a related geophysical parameter, as well as highly resolved but spatially sparse collocated measurements of this geophysical parameter and the hydraulic conductivity. To integrate this multi-scale, multi-parameter database, we first link the low- and high-resolution geophysical data via a stochastic downscaling procedure. This is followed by relating the downscaled geophysical data to the high-resolution hydraulic conductivity distribution. After outlining the general methodology of the approach, we demonstrate its application to a realistic synthetic example where we consider as data high-resolution measurements of the hydraulic and electrical conductivities at a small number of borehole locations, as well as spatially exhaustive, low-resolution estimates of the electrical conductivity obtained from surface-based electrical resistivity tomography. The different stochastic realizations of the hydraulic conductivity field obtained using our procedure are validated by comparing their solute transport behaviour with that of the underlying true hydraulic conductivity field. We find that, even in the presence of strong subsurface heterogeneity, our proposed procedure allows for the generation of faithful representations of the regional-scale hydraulic conductivity structure and reliable predictions of solute transport over long, regional-scale distances.

A simple model for the transport of soil-dissolved chemicals in runoff by raindrops

Abstract The development of a physically based model to simulate the transport of soil solutes in runoff has provided a better understanding of the mechanisms of transport and has assisted in the development of effective methods to control nutrient loss from soils and the pollution of waterways. A refined model has been applied to experimental data in which the presumed exchange layer was replaced by a mixing zone. Assuming that the exchange rate is controlled by raindrop splash, the effects of diffusion can be neglected and the exchange rate, km, can be replaced by the variable er, the raindrop-induced water transfer rate, removing the need to calibrate km. To calibrate our model, laboratory experiments were conducted on disturbed loessial soil with three initial soil-moisture contents (5%, 15%, and 20%, measured gravimetrically) under three rainfall intensities (60, 96, and 129 mm h− 1) and three slope gradients (5, 15, and 25°). The model's simulated data agreed well with the experimental data, demonstrating that the refined model captured the temporal behaviour of solute transport in the runoff. This study provides a new approach to the modelling of chemical transport by investigating the effects of raindrops on sediments from soil in surface runoff.