Predictive Equilibrium–Flux Framework for Zn(II) Extraction and Stripping with Cyanex 272

Abstract The design and scale-up of hydrometallurgical solvent extraction circuits require quantitative understanding of both equilibrium partitioning and intrinsic stripping kinetics. Although Zn(II) extraction by Cyanex 272 (bis(2,4,4-trimethylpentyl)phosphinic acid) is well documented, hydrodynamics-independent kinetic descriptions of stripping remain unavailable. This work addresses this gap by developing a predictive equilibrium–flux framework for the Zn(II)/Cyanex 272/kerosene/H 2 SO 4 system. Equilibrium studies confirm a cation-exchange mechanism (Zn²⁺ + 2HA ⇌ ZnA 2 + 2H⁺) with second-order pH dependence and exothermic thermodynamics (ΔH = −6.9 to −21.4 kJ mol⁻¹). Sulfuric acid achieves >95% stripping efficiency at ≥0.50 M. The core contribution is the first quantitative flux-based kinetic analysis using the single-drop technique, yielding first-order dependence on [H⁺] and [Zn] org , positive sulfate order (0.4), and negative half-order inhibition by free extractant ([H₂A₂]⁻⁰·⁵). The apparent activation energy Eₐ = 41.1 kJ mol⁻¹ and activation entropy ΔS‡ = −85 J mol⁻¹ K⁻¹ (first report) confirm reaction-influenced interfacial control with an associative mechanism. The integrated design equation F b = k.[Zn]¹·⁰ org .[H⁺]¹·⁰.[SO₄²⁻]⁰·⁴.[H₂A₂]⁻⁰·⁵.e (−Eₐ/RT) , with k = 3.34 × 10⁻⁷ kmol m⁻² s⁻¹ and R² = 0.986 (n = 32). The model is validated by leave-one-out cross-validation (R² = 0.978, error = 7.2%) and independent literature data (error = 8.3%). Dimensionless analysis yields D a = 0.42 and H a = 0.68, confirming a mixed reaction–diffusion regime. Sobol sensitivity analysis identifies [H⁺] as dominant (S i = 0.42), while Monte Carlo simulation quantifies prediction uncertainty at ±10.8%. A proof-of-concept Random Forest model achieved a testing R² of 0.981 and MAPE of 5.8%, with feature importance confirming [H⁺] dominance (0.86). Techno-economic analysis for a 50,000 t/year plant yields an IRR of 28.5% and a payback period of 2.3 years, with 15–20% lower H 2 SO 4 consumption. Life cycle assessment demonstrates a 42% reduction in global warming potential. The validated framework enables direct scale-up to industrial circuits, delivering $0.5–1.5 million annual savings.