Mathematical modelling of industrial aluminium cells with prebaked anodes: Part I: Current distribution and anode shape

Abstract

In aluminium electrolysis cells with prebaked anodes the anode shape changes with time after a new anode has been set, reaching a steady state profile after several days. Mathematical modelling of the anode consumption, using current densities obtained by solving the Laplace equation in 2D space, showed that a constant shape is reached after 6–8.6 days, depending on the width of the gap to a neighbouring anode or to the sidewall of the cell and on the shape of the frozen sideledge. The calculated steady state shapes were similar to measured shapes of industrial anodes. The current density decreases along the side of the anode from the nominal value at the underside (0.75 A cm−2) to a minimum near the surface of the electrolyte (0.08–0.28 A cm−2) depending on the geometry. The fraction of the current passing through the sides of the anode is of the order of 15%. Two approaches to the calculation of the anode shape are discussed: one method of incremental time steps, and one method using the 'near steady-state shape’ condition.