Reactive Transport In Heterogeneous Media Research Articles

Upscaling non-linear reactive transport in correlated velocity fields

While commonly non-local transport models have been shown to reproduce breakthrough curves resulting from transport in heterogeneous aquifers successfully, open questions include the formal link between the upscaled governing equations and the sub-scale heterogeneity, and the ability to account for the effect of heterogeneity on effective chemical reaction rates in the presence of non-linear multi-component reactions. Time-domain random walk approaches based on velocity Markov models provide a framework to resolve these issues by incorporating the spatial correlation of velocity of a solute particle in consecutive locations along its trajectory. These approaches often rely on particle tracking approaches, which, however, can be computationally burdensome especially when non-linear reactions are sought to be modeled. In this paper, an integro-differential equation is proposed for upscaling multi-component reactive transport in heterogeneous media that relies on copulas for representing the velocity correlation structure. For this purpose, we express concentration or flux of solutes as a distribution over their velocity. We then derive the integro-differential equation that governs the evolution of concentration distribution over a quantity defined as velocity-rank. In this way, the spatial evolution of breakthrough curves away from the source is predicted based on ergodic cross-sectional velocity distributions and a parameterized copula function which expresses the correlation between velocity-ranks of a solute particle along its trajectory. We demonstrate the validity of the proposed model by comparing breakthrough curves for conservative and non-linearly reacting solutes based on realizations of hydraulic conductivity fields to the results of the upscaled model.

Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation

We present a cumulative density function (CDF) method for the probabilistic analysis of $d$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic appr...

Multi-component reactive transport in heterogeneous media and its decoupling solution

The multi-component reactive transport model is widely used in contaminant transport, water–rock interaction, and other earth science fields. Since its complexity lies in its solution, a decoupling approach is used to simplify the model to enhance computational efficiency. A decoupling approach is presented for heterogeneous media, and used to solve the model in this situation. The whole domain is divided into several sub-domains due to the different reactions which may occur and the corresponding component matrix was obtained. The boundary between sub-domains could be divided into two parts, inflow and outflow, which are defined as the Neumann condition and the Dirichlet one, and the concentration of the latter could be calculated by the component in the adjacent sub-domain. Then the models in each sub-domain can be connected and solved. Taking a heterogeneous porous media as an example in which permanganate is partially dissolved during the process, firstly the result obtained by this method without considering porosity variation is compared to that from PHAST: good agreement is achieved, then while considering the change of porosity caused by the dissolution of the permanganate, the flow field, species concentration and porosity of the whole domain and typical sections and points during the reaction are analysed. It is concluded that: the decoupling approach to heterogeneous media is appropriate, and the results from the model could reflect the variation of physical fields due to groundwater in heterogeneous media.

Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media

Fast chemical reactions are driven by mixing‐induced chemical disequilibrium. Mixing is poorly represented by the advection‐dispersion equation. Instead, effective dynamics models, such as multirate mass transfer (MRMT), have been successful in reproducing observed field‐scale transport, notably, breakthrough curves (BTCs) of conservative solutes. The objective of this work is to test whether such effective models, derived from conservative transport observations, can be used to describe effective multicomponent reactive transport in heterogeneous media. We use a localized formulation of the MRMT model that allows us to solve general reactive transport problems. We test this formulation on a simple three‐species mineral precipitation problem at equilibrium. We first simulate the spatial and temporal distribution of mineral precipitation rates in synthetic hydraulically heterogeneous aquifers. We then compare these reaction rates to those corresponding to an equivalent (i.e., same conservative BTC) homogenized medium with transport characterized by a nonlocal in time equation involving a memory function. We find an excellent agreement between the two models in terms of cumulative precipitated mass for a broad range of generally stationary heterogeneity structures. These results indicate that mass transfer models can be considered to represent quite accurately the large‐scale effective dynamics of mixing controlled reactive transport at least for the cases tested here, where individual transport paths sample the full range of heterogeneities represented by the BTC.

Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.

Comparison of streamtube and three-dimensional models of reactive transport in heterogeneous media

Field-scale transport of reactive solutes is influenced strongly by physical and geochemical heterogeneity over a wide range of spatial scales. Accurate numerical simulation requires fine spatial and temporal discretization to resolve the smallest scales of heterogeneity, in addition to coupling large numbers of chemical components participating in geochemical and microbiological reactions. Standard approaches based upon finite difference or finite element discretization of the governing set of advection-dispersion-reaction equations can lead to computational difficulties for large problems. To overcome these difficulties, several streamtube-based models have been presented in the literature. These models neglect transverse dispersion, and hence reactive transport occurs along independent one-dimensional streamtubes. Therefore, streamtube models are well-suited for applications where the objective is to calculate solute flux breakthrough across a control plane. We develop a reactive streamtube model by modification of the Finite Element Heat and Mass transfer code (FEHM), an existing flow and transport code. FEHM can simulate unsaturated zone conditions, heat flow, and multicomponent reactive transport, and has been used extensively by the Yucca Mountain Project. Because the same underlying numerical algorithms are used in both the FEHM and streamtube models, direct comparison of their relative performance is possible. We perform this comparison for a three-dimensional reactive transport example, to demonstrate the large potential computational advantages of the streamtube approach.

A Heuristic Model of Aerobic Biodegradation of Dissolved Hydrocarbons in Aquifers

AbstractIn this paper, we present a heuristic model of mixing and aerobic degradation based on a conceptual understanding of the mixing process in heterogeneous media, rather than on a rigorous derivation from the stochastic transport equations. The mean‐behavior, heuristic approach, with a uniform velocity field, was used to reproduce organic plume behavior from a previously published simulation for random pore water velocity fields. The heuristic model presented herein requires that the mixing coefficient be calibrated to explain field data; therefore, in that sense, the model is not predictive. The numerical model uses a modified form of a particle tracking model to account for multispecies transport. Transport simulation includes a random‐walk component, while biodegradation is simulated with Monod kinetics. Numerical simulations are presented for nonreactive transport in homogeneous media, and for reactive transport in heterogeneous media. A sensitivity analysis of the model is performed to determine the effect of the mixing coefficient in the model.