Hydrodynamic dispersion during absorption in a fine sand: 1. The constant concentration case

Abstract

The quasianalytical approach to hydrodynamic dispersion during horizontal absorption under constant concentration conditions is discussed, and an integral solution presented for the case of a constant dispersion coefficient. Experimental results for Bungendore fine sand, obtained during constant concentration absorption, are compared with concentration profiles calculated using the integral solution. The comparison is good when a constant dispersion coefficient of 10−8 m2 s−1 is used. An explicit computer‐based numerical analysis is then described briefly and checked against the integral result with excellent correspondence being achieved. The numerical analysis is used to determine concentration profiles for the case when the dispersion coefficient is velocity dependent. These profiles are compared with the experimental data, and it is observed that the bandwidth of the scatter of the data is greater than the spread of the concentration profiles. It is concluded that a definitive statement on the existence and magnitude of a velocity‐dependent effect cannot be made solely on the basis of the experimental data. However, the Péclet numbers appropriate to the system are greater than unity, suggesting that the dispersion coefficient is velocity dependent and that the parameters used in the numerical analysis to express this dependence are satisfactory for Bungendore fine sand under constant concentration absorption.