Pore-scale Mixing Research Articles

Sufficient premixing enhances enzymatic hydrolysis efficiency of lignocellulose at high-solids loading

Low efficiency of the high-solids enzymatic hydrolysis process leads to a sharp increase in energy consumption and enzyme dosage, which hinders the development of lignocellulose biorefinery. Inhomogeneity of trace amounts of enzymes and bulk substrates mixing may be a main barrier to the efficiency. In this study, the mixing degree of enzyme and substrate at high-solids loadings were explored. The 30% solids loading group took 52.9 times longer to reach the same mixing degree as the 5% solids loading group. The mixing process is divided into two stages: reactor-scale mixing and pore-scale mixing, the latter being the rate-limiting step at high-solids loadings. Sufficient premixing improved pore-scale mass transfer, resulting in 194.25% enzymatic hydrolysis efficiency improvement at the enzyme dosage of 5 FPU/g dry matter, cellulase dosage decreased from 40 FPU/g dry matter to 5 FPU/g dry matter and earlier liquefaction at 20% solids loading. Periodic vibration as an efficient premixing method enhanced high-solids enzymatic hydrolysis efficiency. This study is a step forward to the industrial application of high-solids enzymatic hydrolysis.

Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media.

We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion, namely, the smoothing of intrapore velocity contrasts, the increase of the tortuosity of particle paths, and the setting of a maximum time for particle transitions. Based on these mechanisms, we derive a theory that predicts anomalous and normal hydrodynamic dispersion in terms of the characteristic pore length, Eulerian velocity distribution, and Péclet number.

Microfluidic pore model study of precipitates induced by the pore-scale mixing of an iron sulfate solution with simulated groundwater

Precipitates induced by the pore-scale mixing of iron sulfate solutions with simulated groundwater were investigated using a microfluidic pore model to assess the environmental impacts of the infiltration of acid mine drainage into a shallow aquifer. This model was employed to visualize the formation of precipitates in a porous network and to evaluate their physicochemical influences on pore flow. Four types of groundwater (Na–HCO3, Na–SO4, Na–Cl, and Ca–Cl) were evaluated, and precipitation rates were calculated by processing images of precipitates in the pores captured via microscopy. The results showed that all groundwater types formed a yellow-brownish precipitate at the interface of the iron solution and simulated groundwater flow. Microscopic X-ray analyses demonstrated that precipitate morphology varied with groundwater type. Faster precipitation was observed in the following order by groundwater type: Na–HCO3 > Na–Cl > Na–SO4 > Ca–Cl, which was attributed to the different stability constants of the major anions in each simulated groundwater with Fe ions. Chemical equilibrium models suggested that precipitates were Fe minerals, with FeOOH as the predominant form consistent with the results of X-ray photoelectron spectrometry. The presence of FeOOH implies that precipitates may serve as an effective sorption barrier against some nutrients and heavy metals for the underlying groundwater. However, dye-flow experiments suggested that the precipitates may clog aquifer pores, thereby altering hydrogeological properties in the aquifer.

Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction

We upscale reactive mixing using effective dispersion coefficients to capture the combined effect of pore-scale heterogeneity and molecular diffusion on the evolution of the mixing interface between two initially segregated dissolved species. Effective dispersion coefficients are defined in terms of the average spatial variance of the solute distribution evolving from a pointlike injection, that is, the transport Green function. We numerically investigate the temporal behavior of the longitudinal effective dispersion coefficients for two porous media of different pore-scale heterogeneity as measured by the statistics of the flow speed, and different Péclet numbers. We find that the effective dispersion coefficients evolve with time, or equivalently travel distance. As the solute samples the pore-scale flow heterogeneity due to advection and transverse diffusion, the effective dispersion coefficients evolve from the value of molecular diffusion to the corresponding hydrodynamic dispersion coefficients. Thus, at times smaller than the diffusion time over a characteristic pore length, the effective dispersion coefficients can be significantly smaller than the hydrodynamic dispersion coefficients. This difference can explain frequently observed mismatches between pore-scale reactive mixing data, and predictions using Darcy scale transport descriptions based on hydrodynamic dispersion coefficients that are constant in time. This suggests that the notion of incomplete mixing on the support scale can be quantified in terms of effective pore-scale dispersion coefficients. We use effective dispersion in order to approximate the transport Green function in terms of a Gaussian-shaped distribution that is characterized by the effective variance. This is approximation is termed dispersive lamella. Based on this representation, we study reactive mixing between two initially segregated solutes. The dispersive lamella approach accurately predicts the evolution of the product mass of an instantaneous bimolecular reaction obtained from direct numerical simulations. This demonstrates that effective dispersion is an accurate measure for width of the mixing interface between the two reacting species. These results shed some new light on pore-scale mixing, the notion of incomplete mixing, and its prediction and upscaling in terms of an effective mixing model.

Stretching and folding sustain microscale chemical gradients in porous media

Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles, and microorganisms across a wide spectrum of natural and industrial processes. Current macroscopic models that average pore-scale fluctuations into an effective dispersion coefficient have shown significant limitations in the prediction of many important chemical and biological processes. Yet, it is unclear how three-dimensional flow in porous structures govern the microscale chemical gradients controlling these processes. Here, we obtain high-resolution experimental images of microscale mixing patterns in three-dimensional porous media and uncover an unexpected and general mixing mechanism that strongly enhances concentration gradients at pore-scale. Our experiments reveal that systematic stretching and folding of fluid elements are produced in the pore space by grain contacts, through a mechanism that leads to efficient microscale chaotic mixing. These insights form the basis for a general kinematic model linking chaotic-mixing rates in the fluid phase to the generic structural properties of granular matter. The model successfully predicts the resulting enhancement of pore-scale chemical gradients, which appear to be orders of magnitude larger than predicted by dispersive approaches. These findings offer perspectives for predicting and controlling the vast diversity of reactive transport processes in natural and synthetic porous materials, beyond the current dispersion paradigm.

Potential impact of pore-scale incomplete mixing on biodegradation in aquifers: From batch experiment to field-scale modeling

Biogeochemical reactions take place when reactants are present at the same location and time, which occurs through pore-scale mixing. Although the degree of mixing should be variable in space and time, most conventional reactive transport models do not consider mixing-dependent reaction rates and often make predictions based on rates measured with batch experiments. We quantify the effect of pore-scale mixing on the biodegradation rate of dissolved organic carbon (DOC) with sediment batch experiments, and study its potential impact on the field-scale fate and transport of DOC with numerical simulations. We collected sediment samples from an aquifer storage transfer and recovery (ASTR) field site located in Busan, South Korea, and conducted batch experiments to measure mixing-dependent biodegradation rates. Complete mixing conditions were realized by continuously shaking the batch, and diffusion-limited mixing conditions were realized by keeping the batch under static conditions. The two mixing conditions are most widely used conditions in batch experiments and they also represent the maximum and minimum degree of mixing. The different mixing conditions led to significant differences in the biodegradation rates (a factor of 4.9 on average). We then performed reactive transport modeling using the measured biodegradation rates to study the potential impact of pore-scale incomplete mixing on the field-scale DOC biodegradation. The results show that pore-scale mixing can significantly affect the effectiveness of biodegradation at the ASTR site. We generalize this finding by performing a comprehensive nondimensional sensitivity analysis of the fate and transport of DOC to pore-scale mixing conditions over a wide range of Pe´clet and Damköhler numbers. We show that pore-scale incomplete mixing can be a major source of uncertainty in field-scale model predictions.

Chaotic mixing in three-dimensional porous media

Under steady flow conditions, the topological complexity inherent to all random three-dimensional (3D) porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a 3D fluid mechanical analogue of the baker’s map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence, pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW), which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that the chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with the longitudinal advection, whereas the topological constraints associated with two-dimensional porous media limit the mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.

Numerical Simulation and Experimental Study of Bimolecular Reactive Transport in Porous Media

The traditional advection–dispersion–reaction equation (ADRE) often meets difficulty in simulating diffusion-controlled reactive transport, because the grid-based ADRE with a laboratory-measured reaction rate overpredicts pore-scale mixing and the product concentration. In this study, we chose bimolecular reactive transport (A $$\,+\,$$ B $$\,\rightarrow \,$$ AB) in porous media as an example and developed a fully implicit Galerkin finite-element method with Picard’s linearization scheme for solving the ADRE considering incomplete mixing at pore scale (IM-ADRE) based on a continuum approximation by Sanchez-Vila et al. (Water Resour Res 46:W12510, 2010). Sensitivity analysis showed that the IM-ADRE model was most sensitive to the parameter “m,” which was the power index of time used to control the decline rate of the time-dependent kinetic reaction term considering effects of incomplete mixing at pore scale. We used the IM-ADRE model to interpret the column experiment reported by Raje and Kapoor (Environ Sci Technol 34(7):1234–1239, 2000), which studied bimolecular reactive transport of aniline (AN) +1,2-naphthoquinone-4-sulfonic acid (NQS) $$\rightarrow $$ 1,2-naphthoquinone-4-aminobenzene (NQAB) in porous media. Previous studies found that the discrepancy between the simulated and observed peak product concentrations was as large as 55 % by the traditional ADRE, while the discrepancy was reduced to 5 % by the IM-ADRE model. We further conducted new reactive transport column experiments with NQS and AN to systematically understand the nature of bimolecular reactive transport in porous media and further check the validity of the IM-ADRE model. Our experiments differed from previous ones in two aspects. First, we used two different realistic porous media with six different flow velocities while previous experiments mostly involved artificial media such as glass beads under two similar flow velocities. Second, our experiment used a column (with the length of 100 cm) relatively longer than that (18 cm) in Raje and Kapoor (2000), and thus, the boundary effect of the column was minimized, and the time dependence of the effective reaction term could be further checked rigorously. Our study reveals that the IM-ADRE is a feasible tool in quantifying reactive transport at a travel distance up to 100 cm, further validating the effective, time-dependent rate coefficient proposed empirically by Sanchez-Vila et al. (2010).

Predictions of dynamic changes in reaction rates as a consequence of incomplete mixing using pore scale reactive transport modeling on images of porous media

We present a pore scale model capable of simulating fluid/fluid reactive transport on images of porous media from first principles. We use a streamline-based particle tracking method for simulating flow and transport, while for reaction to occur, both reactants must be within a diffusive distance of each other during a time-step. We assign a probability of reaction (Pr), as a function of the reaction rate constant (kr) and the diffusion length. Firstly, we validate our model for reaction against analytical solutions for the bimolecular reaction (A+B→C) in a free fluid. Then, we simulate transport and reaction in a beadpack to validate the model through predicting the fluid/fluid reaction experimental results provided by Gramling et al. (2002). Our model accurately predicts the experimental data, as it takes into account the degree of incomplete mixing present at the sub-pore (image voxel) level, in contrast to advection–dispersion–reaction equation (ADRE) model that over-predicts pore scale mixing. Finally, we show how our model can predict dynamic changes in the reaction rate accurately accounting for the local geometry, topology and flow field at the pore scale. We demonstrate the substantial difference between the predicted early-time reaction rate in comparison to the ADRE model.

Homogenizability conditions for multicomponent reactive transport

We consider multicomponent reactive transport in porous media involving three reacting species, two of which undergo a nonlinear homogeneous reaction, while a third precipitates on the solid matrix through a heterogeneous nonlinear reaction. The process is fully reversible and can be described with a reaction of the kind A+B⇌C⇌S. The system’s behavior is fully controlled by Péclet (Pe) and three Damköhler (Daj,j={1,2,3}) numbers, which quantify the relative importance of the four key mechanisms involved in the transport process, i.e. advection, molecular diffusion, homogeneous and heterogeneous reactions. We use multiple-scale expansions to upscale the pore-scale system of equations to the macroscale, and establish sufficient conditions under which macroscopic local advection–dispersion–reaction equations (ADREs) provide an accurate representation of the pore-scale processes. These conditions reveal that (i) the heterogeneous reaction leads to more stringent constraints compared to the homogeneous reactions, and (ii) advection can favorably enhance pore-scale mixing in the presence of fast reactions and relatively low molecular diffusion. Such conditions are summarized by a phase diagram in the (Pe,Daj)-space, and verified through numerical simulations of multicomponent transport in a planar fracture with reacting walls. Our computations suggest that the constraints derived in our analysis are robust in identifying sufficient as well as necessary conditions for homogenizability.

Pore-Scale Mixing and Transverse Dispersivity of Randomly Packed Monodisperse Spheres

We show that transverse dispersion in flow through randomly packed monodisperse spheres (sphere diameter d) is a velocity-dependent superposition of three separable random processes-diffusion with coefficient D(r), intrinsic mechanical dispersion with dispersivity l(m)=d/33 caused by advection on streamlines, and a newly identified coupled mechanical dispersion with dispersivity l(c)=d/11, which arises by coupled advection and transverse diffusion at the pore scale. The velocity dependence of the transverse dispersivity is derived from first principles. Our analysis is insensitive to details of the pore geometry and is verified by pulsed field gradient NMR experiments which covered 4.5 orders of magnitude in reduced velocity.

AC Diffusion: Transport in Porous Networks Subjected to Zero-Time-Average Advective Flow

Diffusion is a slow transport mechanism and advective transport tends to dominate in large-size systems. An alternative transport mechanism is explored herein, whereby zero time-average cyclic fluid flow is compounded with pore-scale mixing to render effective transport. Two one-dimensional cyclic flow cases are analyzed: a rigid porous network with two open boundaries subjected to cyclic flow through, and a compressible porous network with only one open boundary subjected to cyclic compression. The corresponding analytical models predict diffusion-like macroscale response and provide explicit expressions for the effective diffusion coefficients in terms of the microstructure of the porous medium and flow conditions. A parallel experimental study is conducted to corroborate analytical predictions. Results confirm the relevance of pore-scale mixing in cyclic flow as a transport mechanism in porous networks.

NMR measurement of hydrodynamic dispersion in porous media subject to biofilm mediated precipitation reactions

Noninvasive measurements of hydrodynamic dispersion by nuclear magnetic resonance (NMR) are made in a model porous system before and after a biologically mediated precipitation reaction. Traditional magnetic resonance imaging (MRI) was unable to detect the small scale changes in pore structure visualized during light microscopy analysis after destructive sampling of the porous medium. However, pulse gradient spin echo nuclear magnetic resonance (PGSE NMR) measurements clearly indicated a change in hydrodynamics including increased pore scale mixing. These changes were detected through time-dependent measurement of the propagator by PGSE NMR. The dynamics indicate an increased pore scale mixing which alters the preasymptotic approach to asymptotic Gaussian dynamics governed by the advection diffusion equation. The methods described here can be used in the future to directly measure the transport of solutes in biomineral-affected porous media and contribute towards reactive transport models, which take into account the influence of pore scale changes in hydrodynamics.

Pore-scale modeling of competitive adsorption in porous media

In this paper we present a smoothed particle hydrodynamics (SPH) pore-scale multicomponent reactive transport model with competitive adsorption. SPH is a Lagrangian, particle based modeling method which uses the particles as interpolation points to discretize and solve flow and transport equations. The theory and details of the SPH pore-scale model are presented along with a novel method for handling surface reactions, the continuum surface reaction (CSR) model. The numerical accuracy of the CSR model is validated with analytical and finite difference solutions, and the effects of spatial and temporal resolution on the accuracy of the model are also discussed. The pore-scale model is used to study competitive adsorption for different Damköhler and Peclet numbers in a binary system where a plume of species B is introduced into a system which initially contains species A. The pore-scale model results are compared with a Darcy-scale model to investigate the accuracy of a Darcy-scale reactive transport model for a wide range of Damköhler and Peclet numbers. The comparison shows that the Darcy model over estimates the mass fraction of aqueous and adsorbed species B and underestimates the mass fractions of species A. The Darcy-scale model also predicts faster transport of species A and B through the system than the pore-scale model. The overestimation of the advective velocity and the extent of reactions by the Darcy-scale model are due to incomplete pore-scale mixing. As the degree of the solute mixing decreases with increasing Peclet and Damköhler numbers, so does the accuracy of the Darcy-scale model.

Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number

Relative (effective) lateral dispersion of a passive solute was examined at transitional Reynolds numbers within a two-dimensional array of randomly distributed circular cylinders of uniform diameter d. The present work focuses on dense arrays, for which previously developed theory [Y. Tanino and H. M. Nepf, J. Fluid Mech. 600, 339 (2008)] implies that the asymptotic (long-time/long-distance) dispersion coefficient, when normalized by the mean interstitial fluid velocity, ⟨u¯⟩, and d, will only exhibit a weak dependence on Reynolds number, Red≡⟨u¯⟩d/ν, where ν is the kinematic viscosity. However, the advective distance required to reach asymptotic dispersion is expected to be controlled by pore-scale mixing, which is strongly Red-dependent prior to the onset of full turbulence. Laser-induced fluorescence was used to measure the time-averaged lateral concentration profiles of solute released continuously from a point source in arrays of solid volume fraction ϕ=0.20 and 0.35 at Red=48–120. Results are compared to previous measurements at higher Red. Lateral dispersion reaches the same rate as asymptotic dispersion in fully turbulent flow at x≈154d at (ϕ,Red)=(0.20,110–120) and at x≈87d at (ϕ,Red)=(0.35,300–390). In contrast, dispersion does not reach the fully turbulent flow limit at Red<100 within the range of x considered. Also, concentration profiles deviate further from a Gaussian distribution at ϕ=0.35 than at 0.20 for similar Red and xϕ/d. From these observations, it can be inferred that the pre-asymptotic regime extends farther downstream, in terms of the number of cylinders spanned, at lower Red and at larger ϕ.

Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside two-dimensional model networks

A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels, using an optical technique allowing for simultaneous local and global concentration mappings. Two solutions of different polymer concentrations (500 and 1000ppm) have been used at different Péclet numbers. At the macroscopic scale, the displacement front displays a diffusive spreading: for Pe≤10, the dispersivity ld is constant with Pe and increases with the polymer concentration; for Pe>10, ld increases as Pe1.35 and is similar for the two concentrations. At the local scale, a time lag between the saturations of channels parallel and perpendicular to the mean flow has been observed and studied as a function of the flow rate. These local measurements suggest that the change of dispersion regime is related to variations of the degree of mixing at the junctions. For Pe≤10, complete mixing leads to pure geometrical dispersion enhanced for shear thinning fluids; for Pe>10, weaker mixing results in higher correlation lengths along flow paths parallel to the mean flow and in a combination of geometrical and Taylor dispersion.

Approaches for modeling longitudinal dispersion in pore-networks

The purpose of this study is to quantify the dispersivity in the longitudinal direction by upscaling pore scale mixing over a network domain and to verify the dispersivity with that obtained through the more rigorous upscaling technique, the Brownian particle tracking model (BPTM). We model a porous medium with a network of pore-units that are comprised of pore bodies and bonds of finite volume. Such a pore-unit is assumed to be a mixing cell with the steady state flow condition for a single fluid. Dispersivity can be obtained by solving the mixing cell model (MCM) for the concentration in each pore-unit and by averaging the concentrations for a large number of pore units (as a function of time and space). A minimal size of network that ascertains an asymptotic value of dispersivity was determined and verified with large size pore networks. This numerically computed dispersivity is compared with the results from the BPTM for the same porous medium and flow conditions. We show that the dispersivity obtained from the MCM is equally reliable for the heterogeneous pore-networks and can be estimated as a function of pore size heterogeneity. For homogeneous networks with the MCM, the iteration time step plays an important role. On the other hand, for networks with the BPTM, the assumption of intra-bond velocity profile affects the results.

The future of applied tracers in hydrogeology

Tracingtechniqueshave a broadapplicationinscience andhave demonstrated particular usefulness in hydrogeology.Applied tracers, which are defined as non-natural con-stituents that are intentionally introduced, are especiallypowerful investigative tools because the tracer application(or source term) is controlled and well characterized. Thispermits quantification of transport parameters and mea-surement of subsurface properties in a way often un-matched by standard physical methods. Furthermore,tracer tests directly measure properties in-situ and can beused to investigate very specific processes by selectingtracers with appropriate physicochemical properties. Inmany cases, tracer test methods offer the most accurate orpractical way to measure specific parameters, and in somecases, they are the only reliable investigative technique.Depending on the application, tracer tests can be used tocharacterize properties representative of large subsurfacevolumes or investigate small-scale transport phenomena.Applied tracers have been widely used for centuries tocharacterize flowpaths and estimate groundwater velocities.In fact, Kass (1998) notes that the Jewish historian FlaviusJosephus recorded in approximately 10 A.D. the use ofchaff as a tracer to link the spring source of the JordanRiver to a nearby pond. Quantitative tracer tests usingchloride, fluorescein, and bacteria were first conducted inthe large karst regions in Europe in the late 1800s and early1900s. After World War II, advances in chemical mea-surement technology permitted quantification of signifi-cantly lower tracer breakthrough concentrations and madehigh-frequency sampling economically feasible. Addition-ally, these technological advances lead to a significant in-crease in the diversity of constituents used as tracers.Historically, applied tracers in hydrogeology havebeen used mostly to characterize groundwater flow in kartregions. During the 1960s, benchmark studies exploitedapplied tracers to understand the controls on groundwaterrecharge (Horton and Hawkins 1965; Zimmerman et al.1966) and significantly advanced an understanding of theflowpaths of rainfall to the water table. During the past 30years, applied tracers have been used increasingly to un-derstand solute transport phenomena in porous media andfractured rock aquifers, motivated primarily by environ-mental concerns related to disposal of radioactive andother wastes. For example, the well-known large-scaletracer experiments conducted at the Borden, Cape Cod,and Macro Dispersion Experiment (MADE) sites in the1980s (Sudicky 1986; LeBlanc et al. 1991; Boggs et al.1992, respectively) were designed to compare observedfield-scale solute dispersion to macrodispersion predictedby stochastic analysis of independently-measured aquiferheterogeneity. These experiments have resulted in nu-merous important publications investigating the signifi-cance of local geologic heterogeneity, large-scale hy-draulic conductivity trends, sorption, and rate-limitedprocesses on solute transport. The results of these testshave also been used to evaluate the performance of nu-merical contaminant transport models.Tracing as a hydrogeologic investigative tool hasgrown significantly, and over the past decade, many newapplications of applied tracers have been developed toinvestigate advanced transport phenomena, includingmulti-species reactive transport, colloid-facilitated trans-port, pore-scale mixing, and fracture-matrix control. Thisincrease in tracer research is indicated by the increase inthe number of papers. The increase of papers published inHydrogeology Journal and other groundwater-relatedjournals over the past decade that incorporate either anapplied tracer technique as part of a broader hydrogeo-logical investigation or specifically develop a new use ofapplied tracers in hydrogeology. For example, Aggarwal

Measurement of Mixing-Controlled Reactive Transport in Homogeneous Porous Media and Its Prediction from Conservative Tracer Test Data

Numerical and theoretical studies have indicated that pore-scale mixing can be the limiting process for reactions among dissolved compounds in porous media. It has been claimed that multicomponent reactions in porous media could be accurately estimated using mixing coefficients obtained from point-like measurements of conservative tracer concentrations. In this study, we verify these concepts experimentally by tracer tests in a homogeneously packed saturated sand column. Fiber-optic fluorometry was applied to detect point-related concentrations of fluorescein, which was used as both the conservative and the reactive tracer. In the reactive tracer experiment, an acidic solution containing the tracer was displaced by an alkaline solution without tracer. Since the fluorescence of fluorescein is quenched at low pH, the fluorescence intensity measured in the reactive breakthrough curve indicated the mixing of the two solutions. The measured reactive breakthrough curves were compared to predictions based on the conservative breakthrough curves. Predictions and measurements agreed well. Our results imply that incomplete mixing on the pore scale is of minor significance for field-scale applications. On this scale, however, even weak sorption might influence mixing significantly.

Reactive transport in porous media: a comparison of model prediction with laboratory visualization.

Groundwater transport models that accurately describe spreading of nonreactive solutes in an aquifer can poorly predict concentrations of reactive solutes. The dispersive term in the advection-dispersion equation can overpredict pore-scale mixing, and thereby overpredict homogeneous chemical reaction. We quantified this experimentally by imaging instantaneous colorimetric reactions between solutions of aqueous CuSO4 and EDTA4- within a 30-cm long translucent chamber packed with cryolite sand that closely matched the optical index of refraction of water. A charge-coupled device camera was used to quantify concentrations of blue CuEDTA2- within the chamber as it was produced by mixing of the two reactants at different flow rates. We compared these experimental results with a new analytic solution for instantaneous bimolecular reaction coupled with advection and dispersion of the product and reactants. For all flow rates, the concentrations of CuEDTA2- recorded in the experiments were about 20% less than predicted by the analytic solution, thereby demonstrating that models assuming complete mixing at the pore scale can overpredict reaction during transport.