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Open Access Publications from the University of California

Theory and Simulation of Diffusion Processes in Porous Media


The subsurface is spatially heterogeneous in geologic material composition leading to non-uniform groundwater flow fields. Preferential flow in highly conductive materials and diffusion into less conductive materials such as silts and clays, commonly present in alluvial aquifer systems in substantial volume fractions as high as 20 to 80 percent, enhance the dispersion, sequestration, and dilution of contaminants. This dissertation elucidates processes affecting groundwater solute migration in highly heterogeneous porous media, concentrating on ( 1) the role of diffusion in the dilution and sequestration of contaminants in the subsurface, (2) the modeling methods needed to address this phenomenon, and (3) the implications for natural attenuation of contaminant plumes.

Simulations of contaminant migration and remediation in the alluvial-fan system of Lawrence Livermore National Laboratory confirm the importance of molecular diffusion in sequestering contaminants due to its role in promoting mass transfer in local- and field-scale low-permeability zones. Overall transport behavior and efficacy of pump-and-treat remediation show acute sensitivity to magnitude of effective diffusion coefficient, particularly within the range of uncertainty as inferred through laboratory studies of solute diffusion in clays. Simulations reveal an increase in the holdback of mass near source locations and a decrease in pump-and-treat efficiency with increase in effective diffusion coefficient. Results help to explain observations of scale-dependent-dispersion phenomena and confirm the well-founded limitations of pump and treat. Further, they emphasize the importance of characterizing the geologic structure of low-permeability lithologic units in assessing the viability of remedial technologies. In light of the need for scientific justification of natural attenuation phenomena recently endorsed as remedial technologies by the EPA, this research is particularly relevant to groundwater remediation problems confronting hydrologists and engineers.

Transport simulations are facilitated by new theory and numerical methods to simulate diffusion processes by random walks in composite porous media, i.e., porous media in which effective subsurface transport parameters may be discontinuous (step functions). Discontinuities in effective subsurface transport properties commonly arise (1) at abrupt contacts between geologic materials (i.e., composite porous media) and (2) in discrete velocity fields of numerical groundwater-flow solutions. However, standard random-walk methods for simulating transport and the theory on which they are based only apply when effective transport properties are sufficiently smooth. Limitations of standard theory have precluded development of random-walk methods that obey advec­tion dispersion equations in composite porous media. This problem is solved by general­izing stochastic differential equations (SDEs) to the case of discontinuous coefficients and developing random-walk methods to numerically integrate these equations. The new random-walk methods obey advection-dispersion equations, even in composite media. The techniques retain many of the computational advantages of standard random-walk methods, including the ability to efficiently simulate solute-mass distributions and arrival times while suppressing errors, such as numerical dispersion. The results apply to prob­lems found in many scientific disciplines and offer a unique contribution to diffusion the­ory and the theory of SDEs.

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