(350e) Computational Model of the Mark-IV Electrorefiner- 2D Potential and Current Distributions

An electrochemical process has been developed by Argonne National Laboratory (ANL) to treat sodium-bonded spent fuel from the Experimental Breeder Reactor-II (EBR-II) located at Idaho National Laboratory (INL). At the heart of this innovative process lies the Mark-IV (Mk-IV) electrorefiner (ER). The spent driver fuel from EBR-II is chopped into 1/4 inch segments and loaded into steel fuel dissolution baskets which act as the anode. Uranium and other active metals in the spent fuel are electrochemically dissolved while essentially pure uranium is transferred through a LiCl/KCl eutectic electrolyte and simultaneously deposited on a stainless steel cathode mandrel.

In order to better understand the processes occurring within the Mk-IV ER, a computational model has been developed based on fundamental electrochemical, thermodynamic, and kinetic theories using the Matlab computer software. Both the potential and current distributions throughout the ER can convey important information in better understanding the entire electrochemical process.

The potential distribution can be found using the Laplace equation: ∂²Φ/∂x² + ∂²Φ/∂y² = 0, where Φ is potential. The model determines the potentials at the anode and cathode throughout the electrorefining process. These values constitute Dirichlet boundary conditions at these locations, while at the ER outer wall, ∂Φ/∂x + ∂Φ/∂y = 0, or a Neumann boundary condition is used. Matlab has a partial differential equation (PDE) solver, which uses the finite element method, that has been combined with the model and used to solve this two-dimensional PDE.

The current distribution is then calculated from the resulting potential distribution. Assuming the bulk electrolyte is well mixed and there are no concentration gradients the current distribution can be described by: i=-F²*(∂Φ/∂x + ∂Φ/∂y)*Σ(z_i²*u_i*c_i), where i is current density (A/m²), F is Faraday's constant (96,485 C/eq), z_i is the ionic charge of species i (eq/mol), u_i is species i's ionic mobility through the electrolyte (m²?mol)/(J?s), and c_i is the concentration of species i (mol/m³).

Preliminary results show steep potential gradients ranging from 1-3 V/m in the regions directly between the anodes and cathode, while areas further from the electrodes have much less variable potential. The results reveal that the majority of the current, and therefore most of the uranium, travels through the area of highest potential gradient, or directly from the anodes to the cathode. Based on these preliminary results, the conductivity of the solution at average concentrations of ions, throughout the electrochemical process is approximately 193 mho/m. The two-dimensional potential and current distributions within the Mark-IV ER will be presented and analyzed for three different species: U³⁺, Pu³⁺, and Zr⁴⁺ along with the total distributions. The results will also be shown for different times as the electrorefining process progresses.