# Dependence of the formation factor on the unsaturated hydraulic properties of porous media

1995

## Authors

Lorentz, Simon A., author
Ward, Robert C., committee member
Durnford, Deanna, committee member
Warner, James W., committee member

## Abstract

Mathematical models of the hydraulic conductivity are used extensively to predict the movement of liquids in porous media. Included in these models is a description of the physics of flow as well as the nature of the conduits in which the liquids move through the medium. Since these flow channels comprise a complex network of pathways and have significantly varying geometries, the mathematical models developed assume a simplified arrangement and geometry of the flow channels which is termed the formation factor. The simplifications are derived from experimentally determined behavior of the porous media. These simplifications are generalized and used to describe the hydraulic conductivity of all porous media. The pore size distribution information is used to estimate the effective hydraulic radius of the medium. The effects of channel network and geometry are modelled by generalized relationships derived from experimentally determined formation factors or from unsaturated hydraulic conductivity observations. The dependence of the formation factor on the properties of porous media has not been studied. It is hypothesized that the effects of the channel network and geometry are a function of the pore size distribution or other properties of the porous medium and are thus material specific. It is proposed that a better understanding of the behavior of the hydraulics in porous media can be gained by determining the relationship between the channel geometry and the pore size distribution or other properties. Therefore, the specific purpose of this study is to: -Derive a simple mathematical model that describes both the unsaturated hydraulic conductivity as well as the formation factor that represents the channel geometry; -Determine the pore size distribution and other porous media properties, the formation factors and hydraulic conductivities at various saturations by laboratory experiments on two soils with significantly different pore size distributions; -Test the modelâ€™s capability to predict both the formation factor and hydraulic conductivity of the soils so that conclusions can be made about the dependency of the channel geometry or formation factor on the pores size properties of the media; and -Develop a generalized relationship for the formation factor using porous media properties. The results of the study indicate that the formation factor increases with increasing pore size distribution index. It also is apparent, however, that the pore formation factor is not uniquely dependant on the pore size distribution index and that the relative size of the pores also may contribute to the dependency of the formation factor on the unsaturated properties of the porous media. In addition, it has been determined that the dynamic flow process is influenced by the formation factor to a greater degree than is the static ion diffusion process.

## Subject

Fluid dynamics -- Mathematical modelsPorosity
Soil permeability -- Mathematical models