Acidic Mine Waters (AMWs) are characterised by high acidity (pH < 3) as H2SO4 and elevated contents of metals (Al, Fe, Cu, Zn), including rare earth elements (REEs). Due to the exhaustion of minable REE containing-minerals, AMWs are increasingly regarded as an alternative source of REEs. Among the different alternatives for the pre-concentration of AMWs required to make the REE extraction possible, nanofiltration (NF) membranes emerge as a promising technology because they not only successfully reject multivalent ions (metals), allowing its concentration in the retentate stream, but also permit the transport of monovalent ones, such as H+ and HSO4−, allowing the recovery of sulphuric acid in the permeate. Despite this potential of NF, there is still a lack of modelling tools for predicting the performance of NF membranes because of its dependence on solution composition, membrane properties and interaction between both. In this study, a prediction tool based on the Solution-Electro-Diffusion model (including the effect of solution composition) was developed and experimentally validated for the application of two polyamide-based NF membranes (NF270 and Desal DL) for the recovery of REEs and H2SO4 from three different synthetic solutions mimicking AMWs (pH 1.0, 60 mg/L REEs and, 25–600 mg/L Al, Cu, Ca and Zn) differing in their Fe concentration (0–2125 mg/L). Metals were effectively rejected (>98%), whereas H2SO4 was transported across the membrane (H+ rejections <30%). The mathematical model was able to predict the performance of both membranes as well as the potential scaling events associated with Fe and Al hydroxides and hydroxy-sulphates. Display omitted •Acidic mine waters as a potential source for chemicals recovery•Nanofiltration membranes for acid recovery and metal concentration•A numerical algorithm as a design tool for NF based separation processes•Use of Solution–Electro–Diffusion model to predict nanofiltration performance•Dependence of membrane permeances to species on solution composition