Mixed Integer Nonlinear Programming (MINLP) theory and applications have pervaded the field of computer-aided design and optimization of many traditional, well-studied chemical processes. Exemplary processes studied include many common petrochemical unit operations, such as multicomponent, azeotropic, reactive and isotope distillation, heat and mass exchanger networks, reactor networks, solvent and supercritical fluid extraction, and membrane separation systems. Petrochemical industries have certainly benefited a lot from MINLP problem formulations. Metallurgical industries, however, are historically characterized by a high degree of complexity (high-temperature reactions, multiphase flow) resulting in lack of accurate and detailed models. Advances can provide design recommendations for cost savings and profitability improvements.

Carbothermic reduction of alumina for the production of pure aluminium is a high-yield, economically favorable and environmentally benign process with identified industrial potential. This method is identified as a feasible alternative to the prevalent electrochemical reduction by feasibility studies, but its complexity poses remarkable technical obstacles to implementation. The conceptual multistage electrothermic reactor recently proposed (Johansen, Aune et al., 2000) is a quite attractive idea for achieving reactor scaleup but entails significant design challenges. The most interesting one is the distributed nature of this process, since the electrothermic heating necessary for this endothermic reaction is achieved by using independent AC electrode pairs. Both placement as well as electrode voltage tuning are nontrivial problems given the complexity: optimal design should maximize productivity, minimize superheating and avoid short-circuiting.

The paper elaborates on a previous coarse MINLP model for carbothermic aluminium production we presented in the last ESCAPE-13 at Lappeenranta, Finland (Gerogiorgis and Ydstie, 2003). The present study employs a suitably simplified finite volume model of the carbothermic reactor: a detailed two-dimensional structured discretization of the domain is considered and a steady state CSTR reactor model is used at each of the resulting rectangular finite volumes to probe accurately mass, heat and component balances using temperature-dependent physical properties. The CSTR connectivity is decided by analyzing the slag flow calculated by a 2D CFD model. The presence of electrode pairs (inert DC current conductors) is modeled using binary variables, with piecewise constant voltage and field intensity profiles considered along the horizontal axis. Detailed thermodynamic equilibrium calculations are performed as part of the MINLP model in order to reliably elucidate chemical species' concentrations within each of the finite volumes. The goal is to (a) perform electrode placing and voltage optimization under balance constraints in order to achieve maximization of liquid Al product and minimization of inevitable gas losses, (b) conduct sensitivity analyses illustrating the effect of possible designs on reactor productivity.