Solute Transport In Porous Media Research Articles

Determination and impact factor analysis of hydrodynamic dispersion coefficient within a gravel layer using an electrolyte tracer method

Hydrodynamic dispersion is a measure for describing the process of solute transport in porous media. Characterizing the dispersion of water flow within gravel is essential for the prediction of solute transport especially nonpoint source pollutants migration in alpine watersheds where the land surface is typically covered with gravel. In this study, an integrated model and experimental method using an electrolyte tracer is proposed for determination of the hydrodynamic dispersion coefficient. Two experimental scenarios were designed to measure electrolyte tracer transport processes in both free water flow and gravel layer flow under different slope gradients and transport distances. Subsequently, the measured data were used to simultaneously calculate both the hydrodynamic dispersion coefficient and flow velocity by fitting the experimental data with the mathematical model. Dispersivity, as a critical feature of hydrodynamic dispersion, was determined as well under the two specified scenarios. Finally, the impact mechanisms of the gravel layer and factors related to the dispersion processes were comprehensively analyzed. The results indicate that the presence of a gravel layer significantly reduces flow velocity and the hydrodynamic dispersion coefficient, but increases solute dispersivity. For the flow within gravel layers, with much lower velocity, the positive effect of the gravel layer on dispersivity may be neutralized or even surpassed by the negative effect of flow velocity. The results should be helpful in characterizing the dispersion processes of water flow within gravel layer and hence in predicting solute transport, especially in nonpoint source pollutants migration in alpine watersheds where the land surface is richly covered with gravel.

Global sensitivity analysis and Bayesian parameter inference for solute transport in porous media colonized by biofilms

The concept of dual flowing continuum is a promising approach for modeling solute transport in porous media that includes biofilm phases. The highly dispersed transit time distributions often generated by these media are taken into consideration by simply stipulating that advection–dispersion transport occurs through both the porous and the biofilm phases. Both phases are coupled but assigned with contrasting hydrodynamic properties. However, the dual flowing continuum suffers from intrinsic equifinality in the sense that the outlet solute concentration can be the result of several parameter sets of the two flowing phases. To assess the applicability of the dual flowing continuum, we investigate how the model behaves with respect to its parameters. For the purpose of this study, a Global Sensitivity Analysis (GSA) and a Statistical Calibration (SC) of model parameters are performed for two transport scenarios that differ by the strength of interaction between the flowing phases.The GSA is shown to be a valuable tool to understand how the complex system behaves. The results indicate that the rate of mass transfer between the two phases is a key parameter of the model behavior and influences the identifiability of the other parameters. For weak mass exchanges, the output concentration is mainly controlled by the velocity in the porous medium and by the porosity of both flowing phases. In the case of large mass exchanges, the kinetics of this exchange also controls the output concentration.The SC results show that transport with large mass exchange between the flowing phases is more likely affected by equifinality than transport with weak exchange. The SC also indicates that weakly sensitive parameters, such as the dispersion in each phase, can be accurately identified. Removing them from calibration procedures is not recommended because it might result in biased estimations of the highly sensitive parameters.

Ability of Single-Rate Models to Predict Solute Distribution Coefficients in Systems with Heterogeneous Sorption Kinetics

Several sorption nonequilibrium models have been developed to gain a better understanding of solute transport in porous media, among which are those that assume a single-rate behavior. In this study, two commonly used single-rate models were fitted to computer-simulated breakthrough data from hypothetical column experiments in which multirate sorption kinetics exist at the pore scale. The objective was to determine how the sorption distribution coefficient (K) predicted using these models depends on the conditions under which the data were obtained. Simulated cases covered a range of experimental conditions and involved compounds with different sorption characteristics and different degrees of sorption rate heterogeneity. Results revealed that, for a system with a multirate sorption behavior, the true K value is under-predicted if the parameter estimation is determined by curve fitting a single-rate model. The extent of deviation between the fitted and true K increases with the decrease in residence time and increase in sorption rate heterogeneity. Functional relationships were developed between the relative reduction in K and solute residence time. Analysis using the relationships developed suggests that a major potential cause of the previously reported discrepancy between batch- and column-determined K could be attributed to the use of single-rate models for parameter prediction.

A Non-Linear Model for Solute Transport, Accounting for Sub-diffusive Concentration Decline and Sorption Saturation

Solute transport in porous media is very often complicated by solute immobilization on a solid matrix of porous media. Usually, immobilization is accounted by the mobile/immobile media approach (MIM). However, solute immobilization is very complicated phenomena with a variety of specific features. Therefore, in the literature there have been a lot of specific MIM-type models. Usually each model is constructed for to account one specific feature. Examples are the power decline of concentration in the large time limit at small concentration and the limitation of the immobilization process at high concentrations. Both effects have been evidenced by experiments. The present paper develops a hybrid nonlinear fractional MIM model potentially able to describe the above two features. A step-by-step process of constructing the nonlinear fractional MIM model is presented, and the main properties of the new model are discussed. Two limiting cases describe power law decline and sorption saturation have predicted by the new model equations. Numerical simulations illustrate limiting cases and the capabilities of new nonlinear fractional model.

Systems of partial differential equations in porous medium

We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for the sum of the solute concentrations, we show existence of a unique weak solution to the coupled system and derive regularity estimates. We also prove that the system supports solutions propagating with finite speed thus giving rise to free boundaries and interaction of compactly supported initial concentrations of different species.

Practical finite analytic methods for simulation of advection-dominated solute transport

The practical finite-analytic (PFA) method was applied to the solution of the one-dimensional advection–dispersion equation (ADE) for solute transport in porous media under advection-dominated (high Peclet number, Pe) conditions. Several PFA spatial-temporal computational molecules were developed for Cauchy and pulse loading boundary conditions. The PFA solutions were compared with solutions from the upwind method and quadratic upwind differencing (QUICK) scheme. For all boundary conditions the trapezoidal explicit PFA (EPFA) computational molecule gave the most accurate results at very high Pe number as long as the Courant number (Cr) was close to one. Stability analysis shows that the PFA molecules are always stable for high Pe number.

Multimodel framework for characterization of transport in porous media

AbstractWe consider modeling approaches to characterize solute transport in porous media, integrating them into a unique theoretical and experimental framework for model evaluation and data interpretation. To date, development of (conservative and reactive chemical) transport models and formulation of model calibration methods grounded on sensitivity‐based collection of measurements have been pursued in parallel. Key questions that remain include: For a given set of measurements, which conceptual picture of the transport processes, as embodied in a mathematical model or models, is most appropriate? What are the most valuable space‐time locations for solute concentration measurements, depending on the model selected? How is model parameter uncertainty propagated to model output, and how does this propagation affect model calibration? We address these questions by merging parallel streams of research—model formulation, reduction, calibration, sensitivity analysis, and discrimination—offering our view on an emerging framework that guides (i) selection of an appropriate number and location of time‐dependent concentration measurements given a transport model and (ii) assessment (through discrimination criteria) of the relative benefit of applying any particular model from a set of several models. Our strategy is to employ metrics to quantify the relative contribution of each uncertain model parameter to the variability of the model output. We evaluate these metrics through construction of a surrogate (or “meta”) transport model that has the additional benefit of enabling sensitivity analysis and model calibration at a highly reduced computational cost. We demonstrate the applicability of this framework, focusing on transport of reactive chemicals in laboratory‐scale porous media.

A hybrid pore‐scale and continuum‐scale model for solute diffusion, reaction, and biofilm development in porous media

AbstractIt is a challenge to upscale solute transport in porous media for multispecies bio‐kinetic reactions because of incomplete mixing within the elementary volume and because biofilm growth can change porosity and affect pore‐scale flow and diffusion. To address this challenge, we present a hybrid model that couples pore‐scale subdomains to continuum‐scale subdomains. While the pore‐scale subdomains involving significant biofilm growth and reaction are simulated using pore‐scale equations, the other subdomains are simulated using continuum‐scale equations to save computational time. The pore‐scale and continuum‐scale subdomains are coupled using a mortar method to ensure continuity of solute concentration and flux at the interfaces. We present results for a simplified two‐dimensional system, neglect advection, and use dual Monod kinetics for solute utilization and biofilm growth. The results based on the hybrid model are consistent with the results based on a pore‐scale model for three test cases that cover a wide range of Damköhler (Da = reaction rate/diffusion rate) numbers for both homogeneous (spatially periodic) and heterogeneous pore structures. We compare results from the hybrid method with an upscaled continuum model and show that the latter is valid only for cases of small Damköhler numbers, consistent with other results reported in the literature.

Impact of space‐time mesh adaptation on solute transport modeling in porous media

AbstractWe implement a space‐time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of nonreactive transport experiments in laboratory‐scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space‐time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space‐time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery‐based error estimator which enables us to properly select the size, shape, and orientation of the mesh elements. Adaptation of the time step is performed through an ad hoc local reconstruction of the temporal derivative of the solution via a recovery‐based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a nonuniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space‐time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space‐time discretization.

Practical finite analytic methods for simulation of solute transport with scale-dependent dispersion under advection-dominated conditions

The practical finite analytic (PFA) method was applied to the solution of the one-dimensional advection equation with scale-dependent dispersion equation (ASDE) for solute transport in porous media under advection-dominated (high Peclet number) conditions. A triangular explicit PFA (EPFA) with three different approaches (EPFA 1, 2 and 3) and the Crank–Nicolson (CN) centered and upwind techniques were developed to solve the ASDE with a dispersivity with linear dependence on transport distance. In EPFA 1, to get more accurate results for the ASDE, the existing PFA method was developed and combined with the FD method. In EPFA 2 the original PFA method was employed to check its accuracy for modeling the ASDE without any modifications. Finally, in EPFA 3, based on the current PFA solution, new formulations are proposed to evaluate the accuracy of this approach. For all conditions, EPFA 3 has the best behavior in comparison with other numerical techniques for different linear functions for distance dependence of dispersivity.

Efficiency enhancement of optimized Latin hypercube sampling strategies: Application to Monte Carlo uncertainty analysis and meta-modeling

The majority of literature regarding optimized Latin hypercube sampling (OLHS) is devoted to increasing the efficiency of these sampling strategies through the development of new algorithms based on the combination of innovative space-filling criteria and specialized optimization schemes. However, little attention has been given to the impact of the initial design that is fed into the optimization algorithm, on the efficiency of OLHS strategies. Previous studies, as well as codes developed for OLHS, have relied on one of the following two approaches for the selection of the initial design in OLHS: (1) the use of random points in the hypercube intervals (random LHS), and (2) the use of midpoints in the hypercube intervals (midpoint LHS). Both approaches have been extensively used, but no attempt has been previously made to compare the efficiency and robustness of their resulting sample designs. In this study we compare the two approaches and show that the space-filling characteristics of OLHS designs are sensitive to the initial design that is fed into the optimization algorithm. It is also illustrated that the space-filling characteristics of OLHS designs based on midpoint LHS are significantly better those based on random LHS. The two approaches are compared by incorporating their resulting sample designs in Monte Carlo simulation (MCS) for uncertainty propagation analysis, and then, by employing the sample designs in the selection of the training set for constructing non-intrusive polynomial chaos expansion (NIPCE) meta-models which subsequently replace the original full model in MCSs. The analysis is based on two case studies involving numerical simulation of density dependent flow and solute transport in porous media within the context of seawater intrusion in coastal aquifers. We show that the use of midpoint LHS as the initial design increases the efficiency and robustness of the resulting MCSs and NIPCE meta-models. The study also illustrates that this relative improvement decreases with increasing number of sample points and input parameter dimensions. Since the computational time and efforts for generating the sample designs in the two approaches are identical, the use of midpoint LHS as the initial design in OLHS is thus recommended.

Impact of biofilm‐induced heterogeneities on solute transport in porous media

AbstractIn subsurface systems, biofilm may degrade organic or organometallic pollutants contributing to natural attenuation and soil bioremediation techniques. This increase of microbial activity leads to change the hydrodynamic properties of aquifers. The purpose of this work was to investigate the influence of biofilm‐induced heterogeneities on solute transport in porous media and more specifically on dispersivity. We pursued this goal by (i) monitoring both spatial concentration fields and solute breakthrough curves from conservative tracer experiments in a biofilm‐supporting porous medium, (ii) characterizing in situ the changes in biovolume and visualizing the dynamics of the biological material at the mesoscale. A series of experiments was carried out in a flow cell system (60 cm3) with a silica sand (Φ = 50–70 mesh) as solid carrier and Shewanella oneidensis MR‐1 as bacterial strain. Biofilm growth was monitored by image acquisition with a digital camera. The biofilm volume fraction was estimated through tracer experiments with the Blue Dextran macromolecule as in size‐exclusion chromatography, leading to a fair picture of the biocolonization within the flow cell. Biofilm growth was achieved in the whole flow cell in 29 days and up to 50% of void space volume was plugged. The influence of biofilm maturation on porous medium transport properties was evaluated from tracer experiments using Brilliant Blue FCF. An experimental correlation was found between effective (i.e., nonbiocolonized) porosity and biofilm‐affected dispersivity. Comparison with values given by the theoretical model of Taylor and Jaffé (1990b) yields a fair agreement.

Electric–hydraulic–chemical coupled modeling of solute transport through landfill clay liners

Pollutant migration in dense clay barriers appears to be strongly influenced by the electric double layer of colloidal surfaces. Osmosis that resulted from chemical potential or electric potential difference across the clay membrane has been successively described in a number of theoretical works. Streaming potential (SP) which is present in charged porous medium under hydraulic gradient has been recognized as a significant factor governing the mass migration in compacted clays. However, few studies have been carried out in geo-environmental area with regard to this physical phenomenon. A coupled model was proposed to account for the effects of electrical, chemical and fluidic fields on solute transport in porous medium in this study. The electrical field deals with both the streaming potential and the externally applied electrical potential. The coupled nonlinear partial differential equations are numerically simulated by finite element method. Both the steady state solution and the time-dependent solution were investigated with the consideration of a series of influential factors. The streaming potential coefficient and the electro-osmotic coefficient were found to control the solute transport process. The potential application of the materials with tendency of producing SP was discussed. With appropriate selection of materials and parameters, optimum barring effect could be obtained for soil barriers in waste containment applications.

Unsaturated water flow and tracer transport modeling with Alliances

Understanding water flow and solute transport in porous media is of central importance in predicting the radionuclide fate in the geological environment, a topic of interest for the performance and safety assessment studies for nuclear waste disposal. However, it is not easy to predict transport properties in real systems because they are geologically heterogeneous from the pore scale upwards.This paper addresses the simulation of water flow and solute transport in the unsaturated zone of the Saligny site, the potential location for the Romanian low and intermediate level waste (LILW) disposal. Computation was based on the current available experimental data for this zone and was performed within Alliances, a software platform initially jointly developed by French organizations CEA, ANDRA and EDF.The output of the model developed was compared with the measured values in terms of saturation profile of the soil for water movement, in both steady and transient state. Very good results were obtained for the saturation profile in steady state and a close fit of the simulation over experimental data for the water saturation profile at a depth of 3m in transient state.In order to obtain information regarding the solute migration in depth and the solute lateral dispersion, a tracer test was launched on site and dispersivity coefficients of the solute were fitted in order to match the experimental concentration determined on samples from different locations of the site. Results much close to the experiment were obtained for a longitudinal dispersivity coefficient of 4 and a transversal dispersivity coefficient of 4, indicating a high tendency of radial dispersion of the solute rather than migration in depth.

A dual-porosity theory for solute transport in biofilm-coated porous media

In this work, we derive a Darcy-scale model for solute transport in porous media colonized by biofilms. Biofilms refer to structured communities of microbial cells that grow attached to an aqueous interface, e.g., the pore walls of a water-saturated porous medium. First, we present the pore-scale description of mass transport within and between the phases (water phase and biofilm phase) including the biologically-mediated reactions. Then, a two-equation Darcy-scale mass balance model (classically referred to as dual-porosity model), suitable both for local equilibrium and non-equilibrium conditions, is obtained from the method of volume averaging. Application of this macroscopic model to complex pore geometry of a two-dimensional porous medium supporting biofilms is presented. Comparisons with direct numerical simulation results confirm the large range of validity of the model. Finally, an illustrative example based on a scenario of reactive transport experimental tests is used to point out conditions for when the use of the proposed model is required.

English

The convection-dispersion equation (CDE) is the classical approach for modeling solute transport in porous media. So, estimating parameters became a key problem in CDE. For statistical method, some problems such as parameter uniqueness are still unsolved because of more factors. Due to the advantage of clear physical concept and unique parameter values, the simple deterministic method became very useful alternatives. In this paper, a simple method was proposed to estimate both D and R, and the validity was verified by experiment, which can be applied in agriculture and environmental fields for predicting soil quality property.

A reservoir model of tracer transport for karstic flow systems

A reservoir approach to analyzing tracer transport in steady-state karstic groundwater systems is evaluated. Tracer transport is dictated by a central flow system made up of a series of reservoirs or pools. These reservoirs may also have a ‘side capacity’ that represents less integrated hydraulic features that act to delay tracer as it moves through the system. The composite system results in a relatively extended tracer signal following a rapid first arrival, a behavior often observed in tracer experiments performed in karst. The reservoir model is an alternative to the often-used advection-dispersion model augmented with a first-order exchange between mobile and immobile fractions of the flow system (the MIM model). A well-known field tracer test is revisited using both the reservoir and MIM approach. The reservoir model indicates that ‘immobile’ zones actually represent only a small delay in tracer transport, but these delays, in sum, lead to a significant tail on the breakthrough curve. It is suggested that a reservoir analysis of tracer breakthrough in karst systems may be more relevant to physical descriptions of karstic groundwater systems than models such as MIM, which are based upon solute transport in porous media.

Upscaling solute transport in porous media from the pore scale to dual‐ and multicontinuum formulations

Key Points Relationship between dual continuum and pore‐scale transport formulations Dependence of mass transfer coefficients of MRMT models on pore‐scale processes Analytical expressions for the coefficients of the upscaled two‐equation model

New solutions for solute transport in a finite column with distance-dependent dispersivities and time-dependent solute sources

Summary Dispersivity is widely accepted to be scale-dependent. Numerous studies have been published for solute transport in porous media with distance-dependent dispersivities in infinite or semi-infinite domains which set the effluent boundaries to be infinitely far away. However, discussion of finite domains is often overlooked. In this study, two new semi-analytical solutions for solute transport in a finite column are developed with linear-asymptotic (LAF solution) or exponential distance-dependent (EF solution) dispersivities and time-dependent sources. These two solutions are compared with the corresponding solutions for semi-infinite domains (LAI and EI solutions). Results show that breakthrough curves calculated by the LAF/EF solution change faster and possess higher peak values than those calculated by the LAI/EI solution, and the discrepancies increase with the growth rate of the dispersivity and the asymptotic dispersivity. At a specific time, the concentrations calculated by the LAF/EF and the LAI/EI solutions are the same close to the solute source. However, the concentrations calculated by the LAF/EF solution are higher than those calculated by the LAI/EI solution after a certain distance from the source. Such distances decrease with the growth rate of the dispersivity and the asymptotic dispersivity. The performances of the LAF, EF, LAI and EF solutions do not differ much when they are applied to interpret the laboratory column tests conducted in both homogeneous and heterogeneous soil columns.

Challenges in the Application of Fractional Derivative Models in Capturing Solute Transport in Porous Media: Darcy-Scale Fractional Dispersion and the Influence of Medium Properties

Heterogeneous media consisting of segregated flow regions are fractional-order systems, where the regional-scale anomalous diffusion can be described by the fractional derivative model (FDM). The standard FDM, however, first, cannot characterize the Darcy-scale dispersion through repacked sand columns, and second, the link between medium properties and model parameters remains unknown. To fill these two knowledge gaps, this study applies a tempered fractional derivative model (TFDM) to capture bromide transport through laboratory repacked sand. Column transport experiments are conducted first, where glass beads and silica sand with different diameters are repacked individually. Late-time tails are observed in the breakthrough curves (BTC) of bromide even in relatively homogeneous glass beads. The TFDM can capture the observed subdiffusion, especially the late-time BTC with a transient declining rate. Results also show that both the size distribution of repacked sand and the magnitude of fluid velocity can affect subdiffusion. In particular, a wider sand size distribution or a smaller flow rate can enhance the subdiffusion, leading to a smaller time index and a higher truncation parameter in the TFDM. Therefore, the Darcy-scale dispersion follows the tempered stable law, and the model parameters might be related to the soil size and flow conditions.