Toward Sustainable CO2 Utilization: A Resource-Efficient, Model-Based Design-of-Experiments Framework for Optimizing Photocatalytic Conversion to Formic Acid and Ethanol

Converting waste carbon dioxide (CO2) into value-added chemicals is a central strategy for the circular carbon economy and for decoupling industrial activity from fossil carbon, directly supporting Sustainable Development Goal (SDG) 7 (Affordable and Clean Energy), SDG 9 (Industry, Innovation and Infrastructure), SDG 12 (Responsible Consumption and Production), and SDG 13 (Climate Action). The photocatalytic conversion of CO2 to formic acid (HCOOH) represents a promising dual-purpose route within this strategy: it simultaneously valorises atmospheric or industrial CO2 and enables safe, liquid-phase chemical hydrogen storage for the renewable energy transition. The RK-X technology, employing a homogeneous, biocompatible, silver-containing fulvic acid-based catalyst under visible light irradiation at ambient temperature and moderate CO2 pressure, has previously demonstrated the production of formic acid from CO2 and water. Building on this established reaction, 22 preliminary photocatalytic experiments were performed across a range of process conditions, with formic acid concentration determined by permanganometric (redox) titration (strictly, permanganate-oxidisable species expressed as formic acid equivalents). These measurements were used to identify physically grounded factor–response models, based on Henry’s Law, saturation kinetics, a power-law irradiance dependence, and Michaelis–Menten-type catalyst saturation, describing how pressure, reaction time, light output, and catalyst concentration govern formic acid yield. A Python-based computational framework (version: Python 3.9.6) then used these calibrated models to construct complete, balanced full factorial Design of Experiments (DoE) matrices, enabling the structure of the factorial design space to be explored beyond the scope of the original measurement set with the aim of limiting further physical experimentation, reagent consumption, and energy expenditure (a saving that is not quantified in this work). It is emphasised throughout that these matrices are model-generated rather than measured: the framework is an experiment-planning and screening tool, not a substitute for experimental measurement, and the analysis presented here does not constitute empirical validation of the RK-X reaction mechanism. A 24 DoE was first constructed with the four process factors, pressure [bar], reaction time [h], light output [kW], and catalyst concentration [mg/L], each at two levels, augmented with five center points. After statistical evaluation in TIBCO® STATISTICA (version 13.3), all main effects and two-factor interactions were found significant, and a significant curvature effect indicated the need for a three-level design. A subsequent 34 DoE was analysed, in which a quadratic-by-linear reaction time × catalyst concentration term reached significance in the analysed realisation but proved weak and scale-dependent in a sensitivity analysis across noise levels and random seeds, and is therefore not interpreted as a process finding. The transferability of the workflow was then assessed by re-parameterising the same framework for a related RK-X reaction producing ethanol; this is an assessment of methodological portability, not an independent experimental validation, although the physically executed pilot-scale ethanol measurements underlying this assessment are validated by a companion, independently peer-reviewed study. Because the analysed responses are generated by the calibrated models themselves, the reported p-values, curvature tests and pure-error estimates quantify the resolving power of the design under an assumed variance structure rather than providing independent evidence about the physical system; every conclusion is conditional on the calibrated models. A direct factorial analysis of the measured preliminary runs, which form a 24 design with five genuine replicates, shows strong curvature and, on a logarithmic scale, a single pressure × reaction time interaction that the separable model lacks; a revised model, propagation of parameter uncertainty, a simulated comparison of alternative designs and a two-stage follow-up plan are reported, and all code and datasets are provided. Interpreted on this basis, the work offers a transferable methodology, intended to be resource-efficient, for prioritising and sequencing the physical experiments required to develop and scale emerging CO2 utilization and renewable hydrogen storage technologies.