Weakly-supported electrolyses are frequently encountered in organic electrosynthesis in small scale flow reactors. Sometimes "self-supported" electrolyses are reported where no supporting electrolyte is deliberately added at all. To interpret the steady-state and transient behavior of these electrochemical micro- and millireactors, an orthogonal collocation method based on Chebyshev polynomials was developed for calculating the concentration and current distributions in parallel plate and annular geometries. This method takes into account diffusion, migration, and convection in unidirectional flow for an arbitrary number of dilute ionic species. In particular, the method is flexible with regard to the electrode and homogenous reactions so that intricate reaction schemes are conveniently simulated. As a case study, the effect of the supporting electrolyte concentration and the stability of the generated reactive intermediate ions on a generic paired electrosynthesis is investigated. The numerically calculated concentration profiles and current responses are then compared with asymptotic approximations. This reveals that fundamentally different operating regimes exist for a self-supported paired electrolysis compared to more conventional electrolyses where an excess of supporting electrolyte is added. The Matlab code and a detailed user guide is freely available via the Supplementary Information. (C) 2018 Elsevier Ltd. All rights reserved.