Hydraulic Functions: The Good, the Bad and the Challenges.

Defining functions to describe hydraulic properties of soils and other types porous media has had a long history in Soil Physics and related fields. Hydraulic functions, and in particular parameters in hydraulic functions, enable us to characterize media and allow simulations of flow of water and transport of dissolved or suspended constituents to be conducted. Hydraulic functions have the benefit of allowing us to consider flow and transport in the continuum scale, i.e. they provide volume averages of transport phenomena that essentially occur at the pore-scale. Some hydraulic functions, however, make - largely untested- assumptions about pore-scale structure and processes. This is especially true for pore-size-distribution models that link water retention and unsaturated hydraulic conductivity but some recent work at the sample and pore-scales have indicated some problems with existing pore-size distribution models. Other reasons for renewed attention to upscaling between pore-scale and sample/field scales are new or dramatically improved pore-scale observational and computational methods (e.g. X-ray tomography, pore-scale fluid dynamics models). In addition, certain processes have a unique pore-scale nature that cannot easily be averaged to a continuum scale. One example is fluid retention hysteresis which often is considered to be a nuisance as it complicates measuring, modeling and understanding transport in porous media. However, a better understanding of trapping of fluid and or gases as a function of pressure will, for example, allow us to gage the viability of CO₂ sequestration in deep underground aquifers. This talk will deal with some continuum-scale improvements made to hydraulic functions and discuss some work being done by the author and others to better understand processes at the pore-scale with the ultimate goal to arrive at a better models for flow and transport in porous media.