The features of electroconvection in a smooth rectangular desalting channel of an electrodialysis apparatus with heterogeneous ion-exchange membranes have been theoretically investigated. A 2D model of electroconvection for a binary electrolyte has been constructed for overlimiting current regimes in the form of the Nernst-Planck-Poisson and Navier-Stokes equations. The influence of surface morphology of the heterogeneous ion-exchange membranes on vortex structures and on mass transfer of salt ions has been studied. The current-voltage characteristic has been calculated for the heterogeneous ion-exchange membranes. It has been shown that mass transfer in the membrane channel can be enhanced by improving the surface morphology of the heterogeneous ion-exchange membranes. The strong-base homogeneous membrane AMX and the modified heterogeneous membrane AMH-M have been studied using the rotating membrane disk technique.