On the Taylor dispersion of reactive solutes in a parallel-plate fracture-matrix system

We study the transport of a reactive solute in an individual fracture. In particular, we present mathematical models of reactive transport in a two-dimensional, parallel-plate, fracture-matrix system. The models include linear and nonlinear irreversible, instantaneous reversible, and kinetic reversible reactions at the fracture wall as well as diffusion into the matrix surrounding the fracture. Using a variety of analytical methods, we derive one-dimensional “effective” models that capture the long-time behavior of the average concentration over the fracture cross section. The validity of each effective model is determined by comparing the effective concentration to the average concentration obtained from a numerical solution of the two-dimensional model.; The primary contributions of this dissertation can be categorized as follows. First, we provide a comprehensive theory of Taylor dispersion for a solute that undergoes either a linear irreversible, instantaneous reversible, or kinetic reversible reaction at the fracture wall. We demonstrate the efficacy of the asymptotic spectral comparison method in deriving effective models for these three cases.; Second, we present what is believed to be the first study on the influence of nonlinear surface reactions on Taylor dispersion in fractures. A multiple-scales perturbation approach is used to derive a nonlinear effective model that applies to a large class of weak nonlinear irreversible reactions. In addition, we calculate numerical solutions of the two-dimensional model assuming that the solute undergoes Langmuir or Freundlich adsorption at the fracture wall.; Third, we examine the influence of matrix diffusion and linear equilibrium adsorption in the matrix on retardation and dispersion in the fracture-matrix system. We examine the influence of the model parameters on the effective parameters, study the preasymptotic behavior of the spatial moments, and identify the conditions under which the effective equation is a valid approximation to the long-time behavior of the average concentration. The effective parameters are determined by matching the long-time behavior of the spatial moments of the effective concentration to the long-time behavior of the spatial moments of the average concentration. (Abstract shortened by UMI.)...