 The assumption of electrochemical equilibrium at membrane–electrolyte interfaces is frequently accepted in a mathematical simulation of multiple ion transport (MIT) across a single-layer perfluorinated sulfonated cation-selective membrane (CM). This assumption is obviously inaccurate at high electric current loads typical of industrial applications, e.g. brine electrolysis. An assessment of this problem is one of the main objectives of this contribution. For this purpose, a one-dimensional stationary Poisson–Nernst–Planck (PNP) model was employed to describe MIT across a CM. The model input parameters used correspond closely to industrial chlor-alkali electrolysis. The model results are compared with those of an equivalent model published earlier that considered the classical Nernst–Planck equation and Donnan equilibrium at the CM–electrolyte interfaces (denoted as the DNP model). Both the DNP and the PNP models provide identical results at low current loads. However, a comparison at high current loads close to ‘industrial scale’ was impossible due to convergence problems of the DNP model. The ion transport numbers and membrane permselectivity were estimated by means of the PNP model. This model predicts conditions at the membrane interfaces close to thermodynamic equilibrium even in a current density range up to 10,000 A m−2. Additionally, the PNP model takes into account the kinetics of water autoprotolysis. It was shown that a high flux of OH− ions across a CM effectively alkalizes the catholyte diffusion layer, ensuring a precipitation of alkaline earth cations outside the CM and thus minimizing internal CM blockage.