From Observability to Intervention in Purification: A Critical Framework for Digital Twins, Chemometrics, and Control Across Membranes, Adsorption, and Chromatography

Purification systems in water treatment, gas upgrading, bioprocessing, pharmaceuticals, and resource recovery operate under disturbances that expose the limits of static design and end-point analytics. The central question is no longer whether a model can reproduce historical data, but whether the process can infer its internal state early enough to protect purity, recovery, productivity, and robustness. This critical review examines how purification is moving from monitoring toward self-optimizing operation through process analytical technology, operando sensing, chemometrics, soft sensors, digital shadows, digital twins, hybrid models, and control-oriented optimization. Distinct from recent platform-specific or method-specific reviews, it compares membranes, adsorption and cyclic gas separations, chromatography, and integrated purification trains through the operational chain that links measurement, state estimation, model updating, decision support, and closed-loop action. The review also provides a cross-platform maturity framework and minimum reporting expectations for operational claims. The strongest published operational evidence remains concentrated in continuous downstream bioprocessing, while membrane and adsorption systems contribute major advances in fouling inference, adaptive surrogates, and state estimation. The review concludes by defining the evidentiary conditions required for trustworthy self-optimizing purification.