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Contaminant transport in structured soil systems is often characterised by early and asymmetric breakthrough curves. These phenomena are usually interpreted using the mobile/immobile region model, which is suitable for the simulation of nonequilibrium processes. The parameters involved in two-region models, viz. the rate parameter, α, and the fraction of mobile zone, β, are often obtained by fitting procedures since there is no independent method available to estimate them. For porous media with a well- defined structure, e.g., one containing aggregates, β is often related to the volume fraction of the aggregates. However, both α and β are less understood when the two- region model is applied to media that are non-structured, but may have randomly distributed hydraulic conductivities. Laboratory experiments with randomly packed artificial media and numerical experiments using randomly distributed hydraulic conductivities were conducted to study the behaviour of these parameters. The variation of these parameters with pore-water velocity and porous medium characteristics is explored in detail. The results indicate that the rate parameter, α, usually increases linearly with pore-water velocity. The parameter, β, is a characteristic of the medium that varies with the standard deviation of the log of hydraulic conductivity.