Scales of Interest

There are, roughly speaking, three scales of interest here, namely, microscopic or pore scale, mesoscopic or matrix block scale, and macroscopic or scales larger than the measurement scale such as soil columns.

At microscopic scales, one can comfortably apply fundamental hydrodynamic principles to calculate mass flux and reaction rates along pore space or fracture channels. However, this is possible only if the geometry of pore spaces is available. In our case, the unsaturated zones of the Melton Branch Watershed at ORNL are mostly the C (saprolite) and B (silt, clay) horizon materials. Here, we are interested in saprolite, especially. This microscopic image of microfractures in the saprolite has an average fracture aperture of 2.7 mm. Our observations suggest that the size of the fracture could range from a few mm to a few hundred mm. Our goal here, however, is to integrate information of pore structure at the microscopic scale into a macroscale model, which will be discussed later.

At the next higher scale, mesoscale features such bedding plane fractures shown in this rendering of a saprolite chunk, or root channels found in the B horizon silty clay soils are usually very visible in the Melton Branch soils. We can see at least two orthogonal sets of fractures here: bedding plane fractures and extension fractures parallel and perpendicular to the strike, and one set of shear fractures oriented at a certain angle with the orthogonal sets. These openings, visible to the naked eyes and larger than the microfractures shown in the last slide, are one of the most prevailing features at the Melton Branch Watershed. They are very much responsible for the preferential flow at the Melton Branch. The matrix materials at this scale, however, is a bit different from their smaller siblings. Because we have zoomed out a little bit, or more appropriately, looking at a scale of mm comparing to a scale of mm in the last slide, we are bound to take, if not for granted, the matrix blocks at this scale as an "averaged, equivalent" porous medium. An advective component of the mass transfer process, in addition to the more conceivable diffusive component, in fact, may effect to some extent the mass transfer process in the soil matrix. So, a legitimate question here would be: at this scale, what is the effect of medium structure on the mass transfer process? Can the fracture spacing and block size as shown here help us with the mass transfer coefficients that are needed for mass transfer computation? Can we built this information, whether in a deterministic or stochastic sense, into our modeling methodology?

In a numerical model of watersheds, soils or rock types are usually represented in the size of meters to tens of meters, depending on the scope of the study, the information available, and the resolution a computational facility (both hardware and software) can accommodate. This slide shows a worker standing in a newly excavated pit facing a soil profile from top to bottom: the organic matter rich A horizon, to the silty, clayey B horizon that contains a lot of plant roots, and the clay-saprolite interbedded C horizon that has been the focus of our discussion so far. The soil behind the soil profile has been used to conduct experiments including reactive and nonreactive tracer injection, microsphere and microbial transport, using a two-meter by two-meter irrigation system to simulate uniform pulse input at the surface of the soil. How do we account for the micro- and mesoscale "heterogeneity" present in one single computational unit within a large-scale model has never been proved easy. I think it is sometime ironic these days that we have to choose between a small scale model that accounts for at least mesoscale structures and a large-scale model that these structures have to be "averaged out." Are there ways that we can have a large-scale model and, in the mean time, account for, to some extent, the structures of small scale features? I certainly hope so!

To a quantitative hydrogeologist, the challenge of these soils to his or her theoretical conceptualization is not only the multiscale structures of the soil but also the individual processes and reactions that may occur or be effected by the heterogeneity at each of the scales we have looked at. So, let’s see what we have in the bag of biohydrogeochemical processes.