Multi-step and two-step experiments in heterogeneous porous media to evaluate the relevance of dynamic effects

The determination of hydraulic properties in non-stationary experiments is suspected to be affected by dynamic effects. This is based on thermodynamic considerations on the pore scale displacement of wetting and non-wetting phase. But also macroscopic heterogeneities at the continuum scale may influence the dynamics of water during drainage and wetting. In this paper we investigate both aspects. Firstly, we present the results of typical multi-step outflow experiments in heterogeneous sand columns which are compared with two-step outflow experiments covering the same pressure range. The discrepancies caused by pressure steps of different size reveal the impact of dynamic effects due to the non-stationarity of the experiments. Secondly, the influence of macroscopic heterogeneities is investigated based on two-dimensional heterogeneous parameter fields where we compare static hydraulic properties with those obtained from simulated dynamic experiments. These analyses are restricted to numerical experiments because the focus is on the effect of heterogeneities and not on the validity of the applied model (i.e. Richards equation). We found that dynamic effects are not critical neither during the non-stationary experiments nor for heterogeneous parameter fields. This is a positive message for the usage of multi-step outflow experiments to estimate hydraulic parameters. A prerequisite for this clear statement was the introduction of a highly flexible parametrization of the pressure-saturation relation ψ(θ) which has the only physical constraint to be monotone.