We believe the unsaturated and heterogeneous nature of landfills leads to the emergence of preferential pathways of water and dissolved compounds through the waste body. In this research we explore the origin of preferential flow in a porous media with a deterministic numerical model. In this model water flow is modeled with the Richards’ equation and non-sorbing, single component, solute transport with the advection dispersion equation. We compare results from systematic heterogeneous soils with known hydraulic properties driven by a range of different infiltration patterns with a homogeneous soil driven by the same infiltration pattern. The occurrence of of channeled flow in the heterogeneous soils and diffusion from non-flowing water towards flowing water leads to an emergence of non-equilibrium behavior in the macroscopic breakthrough curves. Results from laboratory experiments which were set-up in a similar way as the numerical experiments were resembling to the ones simulated giving confidence to our model. This research helps to understand modeling approach that needs to be used for analyzing data from full scale landfills in order to quantify leachate emissions and emission potential.