H32D-01
Mixing-Controlled Reactive Transport: Where do we Stand?
Over the past years it has been widely recognized that insufficient solute mixing may cause severe limitations of chemical transformations in groundwater. In particular, natural attenuation of compounds that are continuously emitted may depend on transverse mixing, which is a very slow process. For homogeneous systems, it can be shown that the length of steady-state plumes is inversely proportional to the transverse dispersivity. Transverse pore-scale dispersion also controls the transfer from longitudinal spreading to longitudinal mixing. Thus, accurate estimation of transverse dispersion coefficients is of primary importance in mixing studies. Recently, several groups have developed techniques of mapping conservative-transport results to reactive systems. If the relationship between the concentrations of reactive compounds is algebraic, these concentrations can directly be computed from the mixing ratio. Such techniques are extremely helpful in uncertainty estimation, either via error propagation or by applying Monte Carlo techniques. Past studies on conservative solute transport in heterogeneous systems have led to conceptual confusions. Typically, these studies addressed the spatial distribution of ensemble-averaged concentrations. By averaging over an ensemble of possible realizations, the uncertainty of the plume position is transferred to intermediate concentration values. The single plume, however, may be much less smoothed at its boundaries. A particular approach of transferring the transport of conservative compounds to mixing-controlled reactive transport considers the expected width in breakthrough curves of point-like observations and the uncertainty in mean travel time. Other approaches require mean mixing ratios and their variance. The presentation gives an overview about timely issues of mixing-controlled reactive transport in heterogeneous media.
H32D-02 INVITED
Hybrid Pore- and Darcy-Scale Models of Coupled Reactive Transport.
Pore-scale simulations of flow, transport, and reactions in porous media (in which the geometry of solid grains and pore spaces is explicitly quantified) are being used to demonstrate links between microscopic and macroscopic phenomena. A diverse set of simulation methods have been developed including pore network models, Lattice-Boltzmann models, finite-volume PDE solvers, and Smoothed Particle Hydrodynamics (SPH). Typically, pore-scale models are used to develop understanding of fundamental processes that can then be incorporated into larger-scale models (e.g., darcy-scale) that treat porous media as effective continua. Rigorous upscaling requires that specific conditions or assumptions be met that are often, but not always, valid. In particular, where conditions that govern macroscopic processes are highly localized (such as strong concentration gradients at the scale of individual pores), valid means of upscaling pore-scale processes may not exist. An alternative to upscaling in such situations is hybrid multiscale modeling, in which multiple models defined at fundamentally different length and time scales are combined within the same overall spatial and temporal domain. Hybrid multiscale simulations are motivated by problems in which large-scale phenomena of interest (e.g., flow and contaminant transport) are strongly influenced by processes occurring at much smaller scales (e.g., diffusive mixing and reactions) that are not well represented by effective or averaged processes or properties. Executing an exhaustive simulation of processes at the smallest scales for a domain of engineering significance is currently impractical, and likely to remain so for a very long time. However, the hybrid multiscale approach, in which a small-scale model with high resolution is utilized in a fraction of the overall domain and is linked to a large-scale model with coarse resolution over the remainder of the overall domain, can provide necessary efficiency of characterization and computation that will render solution of these problems practical. We will present a number of specific pore-scale simulations based on the SPH method and a high-resolution finite volume method. We will then review hybrid multiscale modeling techniques and illustrate the hybrid approach using two different hybrid approaches to a diffusion-reaction problem. http://subsurface.pnl.gov
H32D-03
Biogeochemical Reaction Kinetics Associated With Uranium Bioremediation at Multiple Scales
Effective bioremediation requires understanding and quantification of biogeochemical reaction kinetics in natural porous media. Although the intrinsic rates of biogeochemical reactions have been measured in well-mixed laboratory systems, extrapolation of those rates to natural porous media remains challenging, partly due to the fact that natural systems are rarely well-mixed. In this work, we examine the reaction kinetics of iron and sulfate reductions involved in a bioremediation field experiment at the Old Rifle UMTRA site in Western Colorado where acetate as an electron donor was injected into the subsurface to reduce mobile U(VI) to relatively immobile U(IV). We examine at multiple spatial scales how the biogeochemical reaction rates are affected by the extent of mixing and how this in turn affects the efficiency of bioremediation and the evolution of physical and chemical properties of bioremediation sites over the long term. The rates of iron and sulfate reduction were examined at the pore scale and the field scale. At the pore scale (tens to thousands of microns), numerical experiments show that transport processes are fast enough to homogenize the concentration and that the intrinsic rate measured under well-mixed conditions can be directly used. However, at the field scale (tens of meters), dispersion/diffusion processes are not fast enough to homogenize the concentration and the local reaction rates depend on local, spatially variable concentrations. As such, the overall reaction rates at the field scale depend largely on the extent of mixing, which is controlled in large part by the physical and chemical heterogeneities present in the subsurface. Focusing on dissimilatory Fe reduction and assuming the same average flow velocity and the same average total solid iron content, we compare three different cases: 1) a homogeneous permeability distribution with a homogeneous Fe distribution; 2) a heterogeneous permeability distribution, determined from the inverse modeling of field-scale tracer breakthrough data, with a homogeneous Fe distribution; and 3) the same heterogeneous permeability distribution as in the second case, but with a heterogeneous Fe distribution based on an assumed negative correlation between permeability and iron content. Reactive transport modeling results were compared to field data to determine the overall volume-averaged reaction rates. The first case represents the largest extent of mixing and therefore leads to the largest overall Fe reduction rates, while the second and third cases, respectively, represent progressively lower extents of mixing and therefore lead to slower reduction rates. Differences in the overall Fe reduction rates result in different amounts and spatial patterns of precipitated secondary minerals. In the homogeneous case, secondary minerals precipitate evenly across the transverse distance, while in the heterogeneous cases, secondary minerals precipitate primarily where the contact between the electron donor acetate and solid iron is greatest. As such, both physical and chemical heterogeneity may dramatically affect reductions in permeability over the long term.
H32D-04 INVITED
Lab-Scale Experiments and Numerical Modeling of Mixing and Degradation of Pollutants in Aquifers
Prediction of natural attenuation rates in groundwater requires process based modeling of the biogeochemical reactions involved and field effective parameters on mixing rates. For the validation of the models we measured high resolution concentration profiles and mixing rates in a sequence of lab-experiments performed in quasi two- dimensional flow-through systems. Transport of conservative and reactive tracers, undergoing both abiotic and microbially-mediated degradation reactions, was investigated. Transversal mixing and reactions under changing flow fields and in heterogeneous porous media were directly compared with analogous physical and numerical experiments carried out with steady state flow and in homogeneous sediments. The results show that flow focusing in heterogeneous porous media significantly enhances mixing and reaction rates. Changing flow fields, however, are of minor importance. Moreover, the comparison between measured and simulated concentrations clearly indicates that when transverse dispersion/mixing coefficients of dissolved reactants and reaction parameters are known, forward numerical modeling can accurately predict the transport of pollutants in groundwater systems.
H32D-05
How Can We Account for Micro-scale Biodegradation Processes in Macro-scale Models of Contaminant Transport and Degradation?
Mathematical models for contaminant fate and transport in groundwater are generally defined at the macro-scale, i.e., at spatial scales larger than a single pore or grain of aquifer material. In such models, it is convenient and practical to incorporate mathematical descriptions of chemical reactions that depend upon concentrations defined at similar scales. The problem with this approach is that, for contaminants that undergo biologically- mediated degradation, the actual reaction process depends upon diffusion and reaction in micro-scale (pore- scale or smaller) biofilms or bacterial colonies. Thus, it is not inherently clear how we should account for biodegradation in macroscopic models of contaminant transport. Two approaches may be viable: (1) the microscropic processes may be "upscaled" to a macro-scale mathematical representation that is appropriate for the application of interest, or (2) the microscopic processes may be described explicitly at the appropriate scale, then linked to the macro-scale equations for contaminant transport. In this presentation, we report on our work toward both approaches. Under certain circumstances, micro-scale biodegradation processes may be upscaled to a "lumped" macro-scale reaction rate constant that accounts for several microscopic processes. When this is not feasible, micro-scale equations for diffusion and reaction can be coupled to macro-scale equations for transport by advection and dispersion. Solving these coupled equations can be computationally expensive, especially when the biofilm reaction kinetics are considered to be non-linear. We report on numerical methods that may be employed to solve the coupled system efficiently.
H32D-06 INVITED
Precipitation/dissolution calculations in complex multicomponent reactive transport problems based on mixing ratios
Mixing of waters in perfect chemical equilibrium with a given mineral leads indefectibly to local disequilibrium. A reaction takes place then in order to re-equilibrate the system. This reaction can be either precipitation or dissolution (in this latter case limited by mineral availability. Both reactions can lead eventually to changes in porosity and permeability at the local scale. The fate of solutes in natural systems, such as rivers and aquifers, are thus controlled by mixing, which in groundwater is a consequence of local diffusion/dispersion. The presentation will discuss a new methodology for computing exactly reaction rates on complex multicomponent reactive transport problems involving precipitation-dissolution of minerals. We start from the simple problem of the evaluation of reaction rates at the local scale when reactions are in equilibrium. Then we move to the problem of kinetic reactions on one hand, and to upscaling reaction rates on the other. All the solutions are exemplified by means of relatively simple flow set-ups, which allow obtaining analytical solutions even for quite complex geochemical set-ups. These solutions provide some insight to multispecies reactive problems, and more, can be used for benchmarking.
H32D-07
A Moving Boundary Analysis of Two-Species Reaction-Diffusion with Applications to Chemical Oxidation of DNAPLs in Fractured Rock
This study was motivated by a problem arising in the context of chemical oxidation of dissolved DNAPL in a rock matrix by delivering oxidants such as permanganate through fractures. Under continuous flushing/recirculation, the concentrations of permanganate are maintained at a relatively constant level, while it diffuses into the rock matrix and reacts with the DNAPL. The permanganate-DNAPL reaction is typically described as a bimolecular reaction, based on experimental kinetic data. Due to the relatively rapid rate of the oxidation reaction, an appropriately defined Damkohler number is large. Under these conditions, a thin reaction front develops and propagates into the rock matrix at a rate controlled by diffusion. A mathematical analysis of the dynamics of this reaction front is presented. The reaction front can be described as a moving boundary by analogy with the classical Stefan problem in heat transfer with phase change. The propagation of the reaction front can be quantified using a reaction front diffusivity, which can be calculated explicitly. The reaction front diffusivity is shown to depend on the initial concentrations of DNAPL and oxidant, and their effective diffusivities. Scaling arguments are proposed to quantify the temporal dynamics of the DNAPL consumption rate and the width of the reaction zone. The results of the analysis for (i) reaction front propagation, (ii) DNAPL/oxidant consumption rate and (iii) reaction zone width, are all confirmed by numerical simulations.
H32D-08
Upscaling Reactive Transport in Porous Media: Laboratory Visualizations and Stochastic Models
We present a field-scale model of reactive transport that describes the segregation and mixing of reactants at the small-scale by their joint distribution, thereby avoiding the nearly impossible task of explicitly resolving centimeter- scale patterns of reactant concentrations in field-scale models. We tested this model by collecting detailed quantitative images of colorimetric reactions during transport through translucent porous media. These novel experimental results reveal that: (1) The distributions of local solute concentrations are accurately parameterized by beta distributions; (2) The evolution of these distributions is predicted by coupling transport equations for the variance and covariance of local reactant concentrations with conventional transport and chemical reaction equations; and (3) The rate of concentration variance destruction, that drives chemical reaction, quickly equilibrates with the rate of variance production. We demonstrate this reactive-transport model for both our experimental results and through numerical simulation of double-Monod kinetic oxidation of hydrocarbons subject to linear adsorption. http://web.mit.edu/harvey-lab/Reactive%20Transport.html