A numerical model has been developed to predict the local concentrations of chemical species throughout the anolyte compartment in a simplified chlor-alkali reactor with a flow channel defined by a pair of parallel-plate electrodes. Mass transport by diffusion, migration, and advection has been approximated by numerically solving the Nernst-Planck equation for each species, coupled with a set of nonlinear and linear algebraic equations describing the chemistry and electroneutrality. The predicted concentration profiles for protons, chloride ions, chlorine, and hypochlorous acid/hypochlorite ions exhibit large concentration changes in the membrane boundary layer. The sharp pH increase from a bulk value of 2 to ca. 6 at the membrane would allow the undesirable local decomposition of hypochlorite to chlorate ions, which are produced in industrial reactors.