The present paper focuses on solute transport behaviour in a Model Heterogeneous Porous Medium (MHPM) under different flow rates. We report tracer experiments under stationary hydraulic conditions, with 7 different stationary flow rates spanning two orders of magnitude. Several replicates are carried out on several MHPMs, allowing for a sound statistical assessment of experimental imprecision. The experimental BreakThrough Curves (BTCs) exhibit a dual transport mode in agreement with previously-reported field scale experiments. This dual transport mode is shown to be flow-rate independent under a suitable variable change, with the BTCs superposing in the limit of experimental uncertainty. The experiment is modelled using a classical Multi-Region Advection-Dispersion (MRAD) model with only two mobile regions. We present a flow rate independent reformulation of the MRAD model that that allows both water and solute continuity to be preserved during the calibration process. Assuming a linear dependence of the dispersion and exchange coefficients on the flow rate is shown to yield satisfactory model behaviour. This confirms the linearity of the dispersion coefficient with respect to the flow rate, often suggested in the literature, over a wide range of flow conditions.