401 and kinetics [1–3,7]. Distribution-ratio formulations that depend on extractant concentration and pH, consistent with chelation stoichiometry and slope analysis, are widely used to characterize stagewise behavior [2,3]. Industrial design balances mass transfer, organic-to-aqueous ratios (O/A), and acid management across mixer–settler trains and stripping contacts, guided by McCabe–Thiele analysis and equilibrium isotherms [1,4,7]. Accurate representation of acidity via [H⁺], pH, and H₂SO₄ equivalents is central to prediction and control [5,6]. Against this backdrop, SX/EW players increasingly face declining ore grades, ageing equipment, and variability in PLS composition particularly elevated Fe which depresses copper extraction efficiency (~80–85%), degrade organic performance, and lower electrowinning current efficiency (~60–75%), resulting in throughput losses (≈5–10%), higher specific energy use, and more lowergrade cathodes. Assay latency and fragmented data integration exacerbate the response lag. To address these gaps, this paper investigates an operator-assistant approach that combines first principle-based modeling with data-driven inference, executes at the edge, and delivers interpretable, ranked recommendations under human-in-the-loop supervision. This paper articulates an architecture that ingests planning targets, laboratory assays, field sensors, and historian data into a unified Operator Assistant comprising a Digital Twin (hybrid, first principle -first with data-driven residuals) and an Optimizer for prescriptive guidance, connected via open industrial protocols (e.g., OPC UA, MQTT). The contributions of this work are: (i) a research-grade formulation of a first principle -based, stagewise SX model that captures Cu/Fe partitioning and acid balance with explicit dependence on [H⁺] and [HR]; (ii) the formulation of a hybrid Digital Twin that couples this first principle model with machine learning residuals and an embedded Optimizer for actionable decision support (iii) an edge-oriented integration of plant data streams and open protocols to support real-time state estimation, what-if analysis, and ranked recommendations, learning residuals and an embedded Optimizer for actionable decision support 2. ARCHITECTURE (CONTROL LAYERS) The architecture illustrated in Figure 1 represents a structured approach to integrating heterogeneous data streams and advanced computational modules for improved decision-making in solvent extraction operations. At the foundation of this architecture lies a multi-layered data acquisition system that consolidates information from four distinct sources. Planning systems provide high-level production targets, operational schedules, and constraint sets, which serve as boundary conditions for optimization. Laboratory Analysis contributes periodic assay data, such as copper concentrations in pregnant leach solution (PLS), raffinate, and electrolyte samples, which are critical for calibration and reconciliation of predictive models. Field Sensors deliver continuous real-time measurements, including flow rates, temperatures, pH, oxidationreduction potential (ORP), and phase ratios, enabling dynamic monitoring of process states. Complementing these streams, Historical Data offers long-term operational records that support trend analysis, parameter estimation, and anomaly detection. All these inputs converge within the Operator Assistant, which functions as the central intelligence layer. This component is subdivided into two key modules: the Digital Twin and the Optimizer. The Digital Twin acts as a virtual representation of the solvent extraction circuit, integrating first principle -based models with data-driven corrections to simulate process behavior under varying conditions. It assimilates real-time sensor data for current state estimation, laboratory assays for calibration, and historical trends for parameter tuning and uncertainty quantification. Predictions generated by the Digital Twin—such as copper extraction efficiency, phase continuity, and reagent consumption—are then passed to the Optimizer. The Optimizer applies mathematical optimization techniques to identify operating strategies that satisfy multiple objectives, such as maximizing copper recovery, minimizing acid consumption, and maintaining phase stability, while adhering to equipment and safety constraints. The data flow within the architecture is bidirectional, enabling continuous learning and adaptation. After recommendations are implemented, updated sensor readings and laboratory results are fed back into the Digital Twin for model refinement and performance evaluation. Connectivity across all layers is achieved through open industrial communication standards, including Modbus TCP IP, Ethernet, OPC UA, MQTT, and REST APIs etc., ensuring interoperability with existing plant infrastructure and facilitating integration with control systems and operator dashboards. The final output of this architecture is a set of actionable insights and ranked recommendations presented to operators, accompanied by confidence scores and
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