Updated: Nov. 28, 2001.
Copyright © 2000 by Walt W McNab, Concord, CA, U.S.A.. 
All Rights Reserved.

Computer-Mediated Distance Learning

Course on

INSTRUCTOR:

WALT W. McNAB

 Introduction

The latter---namely, transport in the presence of chemical reactions-- is often referred to as reactive transport. Reactive transport plays a key role in a variety of problems that may face the hydrologist (and/or environmental scientist or engineer), who deals with subsurface contamination. Such problems include, among others, the fate of petroleum hydrocarbon and chlorinated hydrocarbon plumes under different biogeochemical regimes, as well as the immobilization of trace metal contaminants in response to adsorption and precipitation reactions. Moreover, aside from practical interests in aquifer contamination, reactive transport concepts are central to the understanding of natural processes the subsurface. These processes may include:

 Some examples

Modeling the reactive transport (i.e., transport accompanied by chemical reactions)  involved in the acid mine drainage problem outlined above, requires:

Fuel Hydrocarbon Biodegradation. As a second example, consider the release of a petroleum hydrocarbon, such as gasoline, from a leaking underground fuel tank into an underlying aquifer (Figure 2). 

Relatively soluble components of the gasoline mixture, such as toluene (C₇H₈), will dissolve into groundwater underneath the tank location. This substance, the  toluene, will then serve as an energy source for microorganisms that are always present in the subsurface. Such organisms require an oxidizing agent to convert hydrocarbons into CO₂ energy. The most favorable oxidizing agent from a thermodynamic viewpoint is dissolved oxygen (O₂). Once all the dissolved O₂ is depleted, other oxidizing agents  (alternatively called electron acceptors) may be used by the microorganisms. As illustrated on the Figure 2, these may include ferric iron (contained in the solid phase, such as iron oxyhydroxides), sulfate, and even CO₂ itself via the process of methanogenesis. These reactions may lead to biogeochemical zonation within the aquifer, where different aqueous species are found in different areas and local-scale mineral precipitation and dissolution reactions occur in response to changes in aquifer chemistry.

Although the oxidation-reduction (redox) reactions presented in this example are, in reality, entirely mediated by microorganisms (i.e., biotransformation reactions), the use of reactive transport models, based on equilibrium thermodynamics, for modeling aqueous speciation may yield important insights into the behavior of such systems. Moreover, kinetic (i.e., reaction rate) constraints may be imposed on the reactions to capture some of the effects of the actions of microorganisms on a macro-scale, so that simulations may closely match field observations in many instances.

In particular, it is possible to capture the two-way coupling between aquifer chemistry and the rates of the oxidation reactions. This statement is based on the observation that, often, rates of biotransformation reactions slow down as the system becomes more chemically reducing, perhaps reflecting in part the decrease in energy yield.

 

 Some basic concepts

The core of any model that describes phenomena of flow, transport, and transformation of any extensive quantity in a porous medium domain is the balance equation of that quantity (The mass balance equation for a specified chemical species is referred to as transport equation, or advection-dispersion equation). Obviously, the balance equation constitutes only part of the model that describes the transport of the considered extensive quantity. . The complete model includes also flux equations (for the considered extensive quantity), constitutive relations, various definitions, and initial and boundary conditions. If you are not familiar with the methodology of constructing models of flow and transport in porous medium domain, go to the appropriate literature, or take an appropriate course. Take a look at the course on MODELING GROUND WATER FLOW AND CONTAMINANT TRANSPORT. This is also a self-study computer mediated distance learning course offered by CMDL E&T. In what follows Iíll assume that you are familiar with balance equations, their structure and how to construct them for flow and transport problems of interest.

model of the considered problem.

The mass balance equation of species i in an aqueous phase (a liquid in which the dominant chemical species is water, H₂O) of (approximately) constant density, takes the form:

in which c_i denotes the concentration (mass per unit volume of solution) of the i-th species. The source term, G_i, represents the strength of the source of the i-th species (i.e., the rate of increase of mass of the i-th species per unit volume of solution, with a negative source representing a sink), V denotes the velocity of the solution (here, the aqueous phase), D denotes the sum of the coefficients of dispersion and of molecular diffusion in porous medium, and f denotes the porosity.

reactions, and radioactive decay. All these are processes that occur within the aqueous phase.

 Heterogeneous reactions, or processes that involve interactions between components in the aqueous phase and constituents of the solid phase, or transfer across interphase boundaries within the void space. Examples include equilibration reactions between aqueous species and mineral phases (involving precipitation or dissolution), adsorption and desorption phenomena, and  ion exchange.

 

Reactions of either type that contribute to the overall source term G _i may be described by using equilibrium or kinetic models. In equilibrium models the concentrations of the multiple species are simultaneously adjusted within the aqueous phase in accordance with equilibrium relationships and mass balance constraints. Such models are appropriate when the rates of reactions are relatively rapid (in comparison with other transport and transformation mechanisms). For example, equilibrium models are appropriate for the description of complexation or ion exchange reactions. In other situations, when reaction rates are relatively slow, kinetic models (i.e., models which consider reaction progress as a function of time) may be more appropriate. For example, kinetic models provide better descriptions of mineral precipitation and dissolution reactions, as well as of many redox reactions. Assumptions involving the use of equilibrium models or kinetic models for different problems may exert profound influences on the behavior of simulated systems and will be explored in detail later in the course.

 the fully-coupled models and those based on the

 two-step approach.

 Issues to consider

 For the transport model alone, many of the classical numerical modeling issues, that are familiar to solute transport modeling, such as the adequacy of time and space discretization to assure a reasonably accurate solution.

 For the chemical speciation model, assumptions concerning the selection of species in the modeled system (i.e., are all of the relevant species being considered), reaction kinetics, and the accuracy of the thermodynamic database.

 Information concerning the solid phase. For example, are the compositions and distributions of important mineral phases in the modeled system accurately known?