Modelling inter- and intra-particle mass transfer in direct lithium extraction process using packed beds filled with porous adsorbents

This study investigates the use of a pore volume diffusion model, and the mechanisms of mass transfer involved in direct lithium extraction (DLE) from low-concentration brines using packed beds filled with porous adsorbents. It aims to demonstrate the importance of optimizing adsorbent properties and operational conditions to enhance the efficiency of DLE. Unlike typical packed-bed models that neglect pore diffusion and assume simplified linear driving force kinetics, this work incorporates mass transfer and fluid flow governed by Brinkman and continuity equations, surface reactions via the Langmuir isotherm, and pore-scale diffusion modelled by Fick’s law. The model enhances the prediction of the adsorption process and is used to investigate the effects of adsorbent properties and operational parameters such as pellet porosity, particle diameter, initial (feed) concentration, flow rate, and column dimensions. It was concluded that pellet porosity can significantly improve the DLE efficiency, for example, in tested scenarios, around 10 % increase in the effective diffusion coefficient of the pellet (from 7.81 ×10 −10 m 2 /s to 8.52 ×10 −10 m 2 /s) was estimated when pellet porosity increased from 0.74 to 0.79, which also led to a 35 % increase in adsorption capacity (from 10.0 mg/g to 13.5 mg/g). On the other hand, it was found that particle size and flow rate primarily affect saturation time and pressure drop, without a notable effect on the adsorption capacity. Also, it was confirmed that the higher the feed concentration the higher the adsorption capacity. Optimization through response surface methodology (RSM) identified the optimal conditions for the tested adsorbents and operational conditions, suggesting the use of adsorbents with the highest porosity (79 %) in an adsorption column with a length-to-diameter ratio of 10 (i.e., a 25 cm column length and a 25 mm inner diameter). It was found that in this case, employing the highest initial concentration of 400 mg/L, with a flow rate of 4 mL/min and pellets diameter of 2 mm led to an adsorption capacity of 15.7 mg/g in 362 min. Evaluation of effective diffusion coefficients and film transfer rates for different cases confirmed the significance of minimizing mass transfer resistances in the tested cases. These findings emphasize the importance of balancing maximum adsorption capacity with operational efficiency for effective lithium extraction. Therefore, the proposed modelling approach and optimization technique could provide a tool for designing DLE and optimizing the performance of different adsorbent materials under various operational conditions. • A 5 % higher intraparticle porosity led to a 35 % increase in Li + adsorption capacity. • The pore volume diffusion model helped explore the desirable adsorbent properties. • Porosity of adsorbents is key for higher adsorption capacity and diffusion rate. • Optimal DLE design depends on adsorbent properties and operational conditions.