Articles | Volume 20, issue 5
Research article
03 May 2016
Research article |  | 03 May 2016

The referential grain size and effective porosity in the Kozeny–Carman model

Kosta Urumović and Kosta Urumović Sr.

Abstract. In this paper, the results of permeability and specific surface area analyses as functions of granulometric composition of various sediments (from silty clays to very well graded gravels) are presented. The effective porosity and the referential grain size are presented as fundamental granulometric parameters expressing an effect of the forces operating on fluid movement through the saturated porous media. This paper suggests procedures for calculating referential grain size and determining effective (flow) porosity, which result in parameters that reliably determine the specific surface area and permeability. These procedures ensure the successful application of the Kozeny–Carman model up to the limits of validity of Darcy's law. The value of effective porosity in the referential mean grain size function was calibrated within the range of 1.5 µm to 6.0 mm. The reliability of the parameters applied in the KC model was confirmed by a very high correlation between the predicted and tested hydraulic conductivity values (R2 =  0.99 for sandy and gravelly materials; R2 =  0.70 for clayey-silty materials). The group representation of hydraulic conductivity (ranging from 10−12 m s−1 up to 10−2 m s−1) presents a coefficient of correlation of R2 =  0.97 for a total of 175 samples of various deposits. These results present new developments in the research of the effective porosity, the permeability and the specific surface area distributions of porous materials. This is important because these three parameters are critical conditions for successful groundwater flow modeling and contaminant transport. Additionally, from a practical viewpoint, it is very important to identify these parameters swiftly and very accurately.

Short summary
Calculation of hydraulic conductivity of porous materials is crucial for further use in hydrogeological modeling. The Kozeny–Carman model is theoretically impeccable but has not been properly used in recent scientific and expert literature. In this paper, proper use of the Kozeny-Carman formula is given through presentation of geometric mean grain size in the drilled-core sample as the referential mean grain size. Also, procedures for identification of real effective porosity of porous media are presented.