Discussion of "On the use of the Kozeny–Carman equation to predict the hydraulic conductivity of soils"

Abstract

Hansen 993 It is well known that independent estimates of hydraulic conductivity (i.e., sine mensura experiri) are not, in general, very reliable. From clay to cobbles, the value of k increases over many orders of magnitude. As the authors have indicated, the independent estimation of this fundamental hydrogeologic parameter is also quite an old problem. Other early attempts within civil engineering, from the perspective of water filtration, are those of Hazen (1894, 1911) and Fair and Hatch (1933). In subsequent decades it became known that even difficult to measure differences in the matrix and (or) of the particles making it up can have a large effect on experimentally determined values of hydraulic conductivity, even when the particles are hard and cohesionless (e.g., Wahyudi et al. 2003). Nonetheless, contributions such as that presented by the authors are always welcomed by the engineering and earth sciences communities, who never have sufficient field data and must deal with clients who may be reluctant to pay for experimental work. “Carman” (ca. 1937) and Blake (ca. 1922) were both chemical engineers. On the other hand, a rough translation of the Kozeny citation indicates a different perspective: “Kozeny, J. 1927. About capillaries conducting water in the earth. Committee Report of the Viennese Academy, 136(2a): 271–306.” The Kozeny–Carman (KC) equation (also known as the Blake–Kozeny equation) is considered by the chemical engineering community to be applicable to a subset of the cases covered by the Ergun (1952) equation and such modern derivatives as the Ergun–Reichelt equation (Reichelt 1972), also of chemical engineering origin. These are applicable to a much wider range of Reynolds numbers (Re), including Carman’s low-Re data set, and some compensate for the higher porosity near the wall in an explicit manner (Fand and Thinakaran 1990). The chemical engineering connection has some significance in that the manufacturers of such artificial particles as pall rings and berl saddles, used in flowthrough packed-column unit operations, will publish the surface area per unit bulk volume of such packings (see, for example, Table 20-3 in Sissom and Pitts 1972). The fundamental idea behind the KC equation is the hydraulic mean radius, m. Most statements of the KC equation, however, do not show m. The fundamental definition of the hydraulic mean radius is