Acidic mine waters (AMWs) contains moderate concentrations of sulphuric acid, relatively high concentrations of metals (Al, Fe, Cu and Zn) and minor amounts or rare earth elements (REE). The established management routes for AMW treatment include a neutralization-precipitation step, which implies a high cost due to the reagents consumption. Nanofiltration (NF) membranes are emerging as an alternative to conventional methods to treat AMW due to a good passage of mono-charged ions (e.g. hydrogen sulphate, proton) for further recovery of sulphuric acid and high rejection of multi-charged ions, such as transition metals and REE. The behavior of one typical NF membrane (NF270, poly(piperazinamide)) was tested in a cross-flow experimental set-up with model solutions at pH 1.0. Moreover, experimental results were modelled according to Solution-Electro-Diffusion Model coupled with reactive transport to characterize the transport of species across the membrane, by means of the membrane permeances. Finally, the performance of NF270 working at batch mode was predicted with the obtained membrane permeances.