Thermo-Chemo-Poromechanical Modeling of the Anode Mixture during the Baking Process: Constitutive Laws and Governing Equations

Abstract

Aluminum is reduced from alumina by the Hall-Héroult electrolysis process in which the anode is utilized as the positive electrode. The quality of the prebaked anode plays a crucial rule in the efficiency of the aluminum electrolysis process. To produce high-quality anodes in the aluminum industry, the anode baking process calls for a deep understanding of mechanisms that govern the evolution of the anode mixture properties under the high-temperature condition. Therefore, the aim of this paper is to establish a thermo-chemo-poromechanical model for the baking anode by using the theory of reactive porous media based on the theory of mixtures within the thermodynamic framework. For this purpose, an internal state variable called "shrinking index" is defined to characterize the chemical progress of the pitch pyrolysis in the anode skeleton, and the Clausius-Duhem inequality is developed according to the Lagrangian formalism. By introducing a reduced Green-Lagrange strain tensor, a Lagrangian free energy is formulated to found a set of state equations. Then, the thermodynamic dissipation for this pyrolyzing solid-gas mixture is derived, and a constitutive model linking the chemical pyrolysis with the mechanical behavior is achieved. A dissipation potential is consistently defined to ensure the non-negativeness of the thermodynamic dissipation and to obtain the constitutive laws for viscous behaviors. Field equations governing the volatile diffusion and the heat transfer through the draining mixture body are derived from the entropy balance.