A finite element computational fluid dynamics sensitivity analysis for the conceptual design of a carbothermic aluminium reactor

The inherent complexity of numerous industrial processes in the metallurgical industry poses formidable technical challenges for modeling, design and simulation: consequently, it is exceptionally difficult not only to optimize the operation of traditional plants without extensive experimentation, but also to model and analyze the feasibility and profitability of various novel designs proposed. Most metallurgical unit operations encompass a wide spectrum of phenomena (convection, diffusion, reaction, external field effects) that often occur simultaneously in multiphase configurations. Accurate modeling of complex distributed chemical processes entails the use of partial differential equation (PDE) descriptions which can now be routinely handled using commercial solvers; an attractive feature of the latter is a potential to handle combinations of diverse physical phenomena that occur in complex processes and yield highly coupled nonlinear PDE mathematical models. Thus, detailed steady state simulations of metallurgical processes can be obtained via advanced interactive software environments. A steady state sensitivity analysis of state variable distributions (namely, potential, absolute temperature and molten slag velocity) with respect to a key design variable (imposed electrode voltage) is performed for a conceptual carbothermic reduction reactor proposed by Johansen et al. (2000) for production of aluminium. Simultaneous solution of charge, heat and momentum balances on a suitably simplified two-dimensional computational domain representing a section of this reactor is used to achieve the goal of this work, which is to study trends important in efficient design. The major conclusion of the present CFD sensitivity study is that the voltage imposed on the horizontal heating electrode pairs affects the interplay between heat conduction and convection, thus the topography and uniformity of the temperature distribution. The electrode voltage has been qualitatively proved to govern the location and size of high-temperature regions in the reactor, thus affecting the advance of the quite endothermic carbothermic reduction reaction as well as the per volume reactor productivity. Therefore, electrode voltage is a crucial reactor design parameter that can also be used very conveniently as a manipulation variable for the efficient operation and control of a carbothermic reactor.