A Multiscale Model for Conceptual Design and Simulation of a Carbothermic Reduction Process for Aluminium Production

Multiscale modeling is a tool aimed at combining mathematical descriptions of different process scales into a single, properly tailored scale integration hierarchy allowing for reliable modeling and simulation. This concept has already been successfully applied in deriving accurate state variable distributions for processes that exhibit full spatiotemporal variation and thus do not allow for the standard simplifications. This paper discusses the fundamental considerations required for the development of a multiscale model and presents the main implementation challenges for a conceptual high-temperature multiphase reactor. The objective is to simultaneously solve the electric charge, heat, momentum, mass and molar balances for the carbothermic reduction of alumina, a complex electrochemical process for aluminium production. This multiscale model relies on a decomposition of the PDE (mass, heat and momentum) balances into two levels: the first modeling level consists of a series of CSTR reactors resembling a conceptual reactor, and the second modeling level uses a Computational Fluid Dynamics model for each of those sections. The main contribution of our study is that it proposes a framework for solving complex process problems of the metallurgical industry, where the spatially distributed state variables are of particular importance.