402 expected KPI improvements. This human-in-the-loop approach ensures that decision-making remains transparent, safe, and aligned with operational objectives. Figure 1 – Architecture of Operator Assistant for Improving SX Operational Performance 3. DIGITAL TWIN (FIRST PRINCIPLE -BASED AND HYBRID MODELING) 3.1. Digital Twin The digital twin for the solvent extraction (SX) circuit is implemented as a hybrid model that integrates a first principle-based core (Section 3.2) with a data-driven residual learner and a compensation layer. Two complementary workflows operationalize this hybrid twin. The Hybrid model enables interpretable, constraint-consistent, and plant-specific predictions that support operator decision-making. 3.2. First principle -based modelling for SX The SX model is grounded in first-principles chemistry and stagewise mass balances to capture mechanistic copper transfer and acidity evolution across extraction and stripping. The governing equilibrium for copper chelation is expressed as Eq. (1), where HR denotes the hydroxyoxime extractant species; the reaction dictates both metal partitioning and proton release—two H⁺ per mole of Cu—leading to progressive acidity increase and known impacts on selectivity and kinetics [1,2,7]. Iron (III) is modeled analogously with higher proton stoichiometry, influencing Fe co-loading under varying pH [2]. The distribution ratio D is computed using Eq. (2), with exponents (Cu: n=2, m=2; Fe: n=3, m=3) consistent with chelation stoichiometry and slope analysis [2,3].
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