Anomalous reactive transport in porous media: Experiments and modeling

Enhanced Reaction Kinetics in Stationary Two-Phase Flow through Porous Media

Understanding the interaction between multiphase flow and reactive transport in porous media is critical for many environmental and industrial applications. When a nonwetting immiscible phase is present within the pore space, it can remain immobile, which we call unsaturated flow, or move, resulting in multiphase flow. Previous studies under unsaturated flow conditions have shown that, for a given flow rate, the product of a mixing-driven reaction increases as wetting phase saturation decreases. Conversely, the opposite effect is observed for a given Péclet number (i.e., the flow rate is adapted depending on the wetting phase saturation). However, the impact of multiphase flow dynamics on mixing-driven reactions is poorly understood due to experimental and numerical challenges. To assess the impact of multiphase flow conditions on product formation, we use an optimized chemiluminescence reaction and an experimental setup that allows the separate injection of reactants along with a stationary two-phase flow. In our experiments, the mass of the reaction product under stationary two-phase flow conditions increases faster than Fickian beyond the diffusive time. The global kinetics initially increase before experiencing a monotonic decrease with significant fluctuations caused by the displacement of the nonwetting phase. For a given flow rate of the wetting phase, product formation depends on the flow rate of the nonwetting immiscible phase.

On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field

Monotonously stratified porous medium, where the layered medium changes its hydraulic conductivity with depth, is present in various systems like tilled soil and peat formation. In this study, the flow pattern within a monotonously stratified porous medium is explored by deriving a non-dimensional number, Fhp, from the macroscopic Darcian-based flow equation. The derived Fhp theoretically classifies the flow equation to be hyperbolic or parabolic, according to the hydraulic head gradient length scale, and the hydraulic conductivity slope and mean. This flow classification is explored numerically, while its effect on the transport is explored by Lagrangian particle tracking (LPT). The numerical simulations show the transition from hyperbolic to parabolic flow, which manifests in the LPT transition from advective to dispersive transport. This classification is also applied to an interpolation of tilled soil from the literature, showing that, indeed, there is a transition in the transport. These results indicate that in a monotonously stratified porous medium, very low conducting (impervious) formations may still allow unexpected contamination leakage, specifically for the parabolic case. This classification of the Fhp to the flow and transport pattern provides additional insight without solving the flow or transport equation only by knowing the hydraulic conductivity distribution.

The bimolecular reactive transport in heterogeneous porous media: Sub-diffusion in interpretation of laboratory experiment

This present work consists of investigating the effects of particle size heterogeneity and flow rates on transport-reaction kinetics of CuSO4 and Na2EDTA2- in porous media, via the combination of a bimolecular reaction experiment and model simulations. In the early stages of transport, a peak is observed in the concentration breakthrough curve of the reactant CuSO4, related to the delayed mixing and reaction of the reactants. The numerical results show that an increase in flow rate promotes the mixing processes between the reactants, resulting in a larger peak concentration and a slighter tail of breakthrough curves, while an increase in medium heterogeneity leads to a more significant heavy tail. The apparent anomalous diffusion and heavy-tailing behavior can be effectively quantified by a novel truncated fractional derivative bimolecular reaction model. The truncated fractional-order model, taking into account the incomplete mixing, offers a satisfactory reproduction of the experimental data.

Fractional Advection-Diffusion-Asymmetry Equation

Fractional kinetic equations employ noninteger calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems. Motivated by work on contaminant spreading in geological formations, we propose and investigate a fractional advection-diffusion equation describing the biased spreading packet. While usual transport is described by diffusion and drift, we find a third term describing symmetry breaking which is omnipresent for transport in disordered systems. Our work is based on continuous time random walks with a finite mean waiting time and a diverging variance, a case that on the one hand is very common and on the other was missing in the kaleidoscope literature of fractional equations. The fractional space derivatives stem from long trapping times, while previously they were interpreted as a consequence of spatial Lévy flights.

Experimental and modeling evidence of kilometer-scale anomalous tracer transport in an alpine karst aquifer

Karst aquifers are important drinking water resources, but highly vulnerable to contamination. Contaminants can be transported rapidly through a network of fractures and conduits, with only limited sorption or degradation, which usually leads to a fast and strong response at karst springs. During migration, contaminants can also enter less mobile zones, such as pools or water in intra-karstic sediments, or advance from conduits into the adjacent fractured rock matrix. As contaminant concentrations in the main flow path(s) decrease, contaminants may migrate back into the main flow path and reach the karst springs at low (but significant) concentrations over a long time span. This is the conventional interpretation for the oft-observed steep rising limb and the long-tailed falling limb of tracer breakthrough curves in karst systems. Here, field measurements are examined from an alpine karst system in Austria where a series of distinctive, long-tailed breakthrough curves (BTCs) of conservative tracers were observed over distances up to 7400 m. Recognizing that the conventional advection-dispersion equation (ADE) cannot usually quantify such behavior, two other modeling approaches are considered, namely the two-region non-equilibrium (2RNE) model, which explicitly includes mobile and immobile zones, and a continuous time random walk (CTRW) model, which is based on a physically-based, probabilistic approach that describes anomalous (or non-Fickian) transport behavior characteristic of heterogeneous systems such as karst. In most cases, the ADE and 2RNE models do not quantify the low concentrations at longer travel times. The CTRW, in contrast, accounts for the long-tailed breakthrough behavior found in this karst system.

Effect of colloids on non-Fickian transport of strontium in sediments elucidated by continuous-time random walk analysis

Understanding the influence of colloids on radionuclide migration is of significance to evaluate environmental risks for radioactive waste disposals. In order to formulate an appropriate modelling framework that can quantify and interpret the anomalous transport of Strontium (Sr) in the absence and presence of colloids, the continuous time random walk (CTRW) approach is implemented in this work using available experimental information. The results show that the transport of Sr and its recovery are enhanced in the presence of colloids. The causes can be largely attributed to the trap-release processes, e.g. electrostatic interactions of Sr, colloids and natural sediments, and differences in pore structures, which gave rise to the varying interstitial velocities of dissolved and, if any, colloid-associated Sr. Good agreement between the CTRW simulations and the column-scale observations is demonstrated. Regardless of the presence of colloids, the CTRW modelling captures the characteristics of non-Fickian anomalous transport (0 < β < 2) of Sr. In particular, a range of 0 < β < 1, corresponding to the cases with greater recoveries, reveal strongly non-Fickian transport with distinctive earlier arrivals and tailing effects, likely due to the physicochemical heterogeneities, i.e. the repulsive interactions and/or the macro-pores originating from local heterogeneities. The results imply that colloids can increase the Sr transport as a barrier of Sr sorption onto sediments herein, apart from often being carriers of sored radionuclides in aqueous phase. From a modelling perspective, the findings show that the established CTRW model is valid for quantifying the non-Fickian and promoted transport of Sr with colloids.

Asymptotic Behavior of the Solution of the Space Dependent Variable Order Fractional Diffusion Equation: Ultraslow Anomalous Aggregation

We find the asymptotic representation of the solution of the variable-order fractional diffusion equation, which remains unsolved since it was proposed by Chechkin, Gorenflo, and Sokolov [J. Phys. A, 38, L679 (2005)JPHAC50305-447010.1088/0305-4470/38/42/L03]. We identify a new advection term that causes ultraslow spatial aggregation of subdiffusive particles due to dominance over the standard advection and diffusion terms in the long-time limit. This uncovers the anomalous mechanism by which nonuniform distributions can occur. We perform Monte Carlo simulations of the underlying anomalous random walk and find excellent agreement with the asymptotic solution.

Experimental investigation of transverse mixing in porous media under helical flow conditions

Plume dilution and transverse mixing can be considerably enhanced by helical flow occurring in three-dimensional heterogeneous anisotropic porous media. In this study, we perform tracer experiments in a fully three-dimensional flow-through chamber to investigate the effects of helical flow on plume spiraling and deformation, as well as on its dilution. Porous media were packed in angled stripes of materials with different grain sizes to create blocks with macroscopically anisotropic hydraulic conductivity, which caused helical flows. Steady-state transport experiments were carried out by continuously injecting dye tracers at different inlet ports. High-resolution measurements of concentration and flow rates were performed at 49 outlet ports. These measurements allowed quantifying the spreading and dilution of the solute plumes at the outlet cross section. Direct evidence of plume spiraling and visual proof of helical flow was obtained by freezing and slicing the porous media at different cross sections and observing the dye-tracer distribution. We simulated flow and transport to interpret our experimental observations and investigate the effects of helical flow on mixing-controlled reactive transport. The simulation results were evaluated using metrics of reactive mixing such as the critical dilution index and the length of continuously injected steady-state plumes. The results show considerable reaction enhancement, quantified by the remarkable decrease of reactive plume lengths (up to four times) in helical flows compared to analogous scenarios in uniform flows.

Comparative assessment of continuum-scale models of bimolecular reactive transport in porous media under pre-asymptotic conditions

We compare the ability of various continuum-scale models to reproduce the key features of a transport setting associated with a bimolecular reaction taking place in the fluid phase and numerically simulated at the pore-scale level in a disordered porous medium. We start by considering a continuum-scale formulation which results from formal upscaling of this reactive transport process by means of volume averaging. The resulting (upscaled) continuum-scale system of equations includes nonlocal integro-differential terms and the effective parameters embedded in the model are quantified directly through computed pore-scale fluid velocity and pore space geometry attributes. The results obtained through this predictive model formulation are then compared against those provided by available effective continuum models which require calibration through parameter estimation. Our analysis considers two models recently proposed in the literature which are designed to embed incomplete mixing arising from the presence of fast reactions under advection-dominated transport conditions. We show that best estimates of the parameters of these two models heavily depend on the type of data employed for model calibration. Our upscaled nonlocal formulation enables us to reproduce most of the critical features observed through pore-scale simulation without any model calibration. As such, our results clearly show that embedding into a continuum-scale model the information content associated with pore-scale geometrical features and fluid velocity yields improved interpretation of typically available continuum-scale transport observations.