Evaluation of hydraulic conductivity in shallow groundwater formations: a comparative study of the Csókás’ and Kozeny–Carman model

The Kozeny–Carman equation has achieved widespread use as a standard model for estimating hydraulic conductivity of aquifers. An empirically modified form applicable in shallow formations called Csókás’ formula is discussed, which is based on the relation between the effective grain-size and formation factor of freshwater-bearing unconsolidated sediments. The method gives a continuous estimate of hydraulic conductivity along a borehole by using electric and nuclear logging measurements without the need of grain-size data. In the first step, synthetic well-logging data sets of different noise levels are generated from an exactly known petrophysical model to test the noise sensitivity of the Csókás’ method and to assess the degree of correlation between the results of Csókás’ and Kozeny–Carman model. In the next step, borehole logs acquired from Hungarian sites are processed to make a comparison between the Csókás’ formula and the Kozeny–Carman equation including grain-size data measured on rock samples. The hydraulic conductivity logs derived separately from the Csókás’ and Kozeny–Carman formulae show reliable interpretation results, which are also validated by the Hazen’s formula and statistical factor analysis. The fundamental goal of Professor Csókás’ research was to derive some useful hydraulic parameters solely from well-logging observations. This idea may be of importance today since the input parameters can be determined more accurately by advanced measurement techniques. Hence, the Csókás’ formula may inspire the hydrogeophysicists to make further developments for a more efficient exploration of groundwater resources