A Model of the Cathode Dynamics in Electric Field-Enhanced Smelting and Refining of Steel

"Electric Field-Enhanced Smelting and Refining is a process for driving the reaction between carbon in hot metal and iron oxide in slag, for example, in a steelmaking reactor. This process involves inserting electrodes into the slag and metal phases, such that the overall reaction FeO + C -> Fe + CO is separated into two half-cell reactions: Fe2+ + 2e· -> Fe at the cathode in the slag, and C + O 2 • -> CO + 2e· at the anodic slag-metal interface. Without the electrodes, the reaction is very slow, but with electrodes, the additional surface area available to the ferrous ions for reduction accelerates the reaction even without any applied bias. When a bias is applied to the electrodes, the electric field across the slag further accelerates the overall reaction.With or without applied bias, the process is first-order in the ferrous ion concentration, and limited by ferrous ion transport to the cathode. To complicate matters, as the liquid iron is reduced at the cathode, the Mullins-Sekerka instability leads to formation of dendrite-like liquid iron fingers which grow into the slag. Because of this, the design of the cathode can have a significant effect on the overall process kinetics, and understanding of the dynamics of these fingers and of their effect on mass transfer is necessary for the intelligent design of the overall process and the cathode in particular.Toward this end, a detailed mesoscopic two-phase slag-metal model is presented here which describes multi component diffusion in the slag and fluid flow in both phases in the vicinity of the cathode. Diffusion in the slag is driven by chemical and electrical potentials. The phase boundary is modeled as a diffuse interface using a phase field approach. Because this electrochemical reaction occurs at high-temperature, the kinetics of charge transfer and adsorption through the double layer are fast relative to transport, permitting the use of simple linear reaction kinetics. This also eliminates the need to discretize the double layer, with the result that charge neutrality may be assumed everywhere in the domain. Introducing electric field dependence of the gradient potential and well height coefficients in the free energy function allows the model to capture electrocapillarity at the interface."