Abstract
Critical metals are indispensable in renewable, low-carbon, and hydrogen technologies due to their unique catalytic and electrochemical properties. They are primarily sourced through mining, which is associated with significant environmental impacts and geopolitical risks due to the uneven global distribution of ore deposits. As a result, efficient recovery of these metals from secondary sources such as electronic waste has become increasingly important. In this context, liquid-liquid extraction (LLE) has emerged as a promising separation technique due to its high selectivity and scalability. The development of intensified, continuous-flow LLE in small channels offers further advantages in terms of mass transfer efficiency, solvent utilization, and process sustainability, making it an attractive approach for the recovery of critical metals. A flow pattern known as segmented flow further enhances mass transfer in LLE in small channels. This work presents a hybrid modelling approach for developing a predictive model of a segmented flow LLE process, intended for digital twin implementation in critical metals recovery. Within the hybrid modelling framework, mass transfer is modelled using a lumped approach, which allows to treat mass transfer independently from flow hydrodynamics. Further, hydrodynamic and mass transfer models are developed in parallel using Gaussian process (GP)-based active learning (AL) and model-based design of experiments (MBDoE), respectively. Prior knowledge of flow regimes is used in developing the hydrodynamic model. The method was tested in an in silico case study and shown to efficiently develop reliable models for segmented flow extraction in small channels.