Mathematical modeling of a three-compartment electro-reactor process with ion-exchange membranes for recycling and resource recovery of desulfurization residuals

• A model of an electro-reactor for recycling and resource recovery was developed.
• The model accounts for geometrical factors, bubble formation, and mass transport.
• The analytical solutions were agreed well with the numerical solutions.
• The developed model is helpful to gain a deeper understanding of the process.

A mathematical model of a three-compartment electro-reactor process with ion-exchange membranes for recycling and resource recovery of desulfurization residuals was developed. This model describes the electrochemical separation process in the bulk solution and the diffusion boundary layer close to the membrane surfaces with a multiphysics-based approach. This approach considered the following mechanisms: diffusion and migration in different control volumes, the effect of bubbles, the effect of the geometry of the reactor, and the electrochemical reactions of the gases. The analytical solution to the developed model was obtained using a Laplace transformation, and the numerical solution was solved in Wolfram Mathematica and COMSOL Multiphysics. All analytical solutions exhibit a good agreement with the numerical solutions. The analysis of the model revealed that the following parameters may have a positive effect on the performance of the electro-reactor: (1) a high concentration gradient across the membrane enhances mass transport; (2) the current density is the key controlling parameter for both mass transport and bubble formation; (3) a small gap in the cell spacer may improve the performance of the reactor; (4) appropriate effective areas of the membrane for mass transfer guarantees high performance.