Nonlocal reactive transport in physically, chemically and biologically heterogeneous media

Xiaolong Hu, Purdue University

Abstract

The complex heterogeneity of natural porous media and uncertainty in data preclude using traditional deterministic approaches to model solute transport. Therefore, stochastic approaches have been employed to effectively describe the heterogeneous environment in which groundwater movement and contaminant transport take place. Chapter 1 summarizes the evolution of stochastic theory over the last two decades. Stochastic theories have been successfully employed to study dispersion at the field scale with uncertainty in the conductivity. However, stochastic theories of reactive chemical transport remain immature. Many of the mechanisms that cause the macrodispersion of reactive chemicals are still unclear. New stochastic theories for reactive chemicals are required for the more complex problems. Since most solutes in groundwater do not move through chemically inert and biologically sterile media, we must consider chemical and biological processes during transport. In this study a series of eulerian stochastic models have been developed to simulate reactive transport processes in physically, chemically and biologically heterogeneous materials. Chapters 2, 3, and 4 provide models (with explicit solutions) of increasing complexity to handle successively, linear nonequilibrium adsorption with random $K\sb{d},$ linear nonequilibrium sorption with random reaction rates, and nonequilibrium sorption with microbiological degradation. The models are written explicitly in terms of measurable quantities and they can be used to predict plume development in heterogeneous media or to design novel experiments. Data for these models consists of various covariance functions, of which several have not been studied experimentally. This work thus suggests the need to design new field experiments. In the general model, the concentration or gradient of concentration is convoluted in time and space with various correlation functions. We call this form fully nonlocal. In chapter 5 we analyze the errors induced by various localizations of these models. Some of these latter approaches are currently widely used in practice and we examine the errors such simplifications induce. In chapter 6 we compare the eulerian method with Cvetkovic and Dagan's (J. Fluid Mech, 1994) and Dagan and Cvetkovic's (WRR, 1993) Lagrangian methods. Standardly, Dagan and coworkers neglect local dispersion. We examine the errors associated with this approximation.

Degree

Ph.D.

Advisors

Cushman, Purdue University.

Subject Area

Environmental science|Hydrology|Soil sciences

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