Multi-Objective Bayesian Optimization Framework for CO₂ Injection Strategy Design: A Sleipner-Inspired Study

This study develops a three-objective Bayesian optimization framework for injection strategies for geological CO₂ storage. In a mixed categorical–continuous decision space, the candidate designs vary the well configuration, the per-well injection rate, and a three-stage allocation of injection among nine numerical reservoir intervals. The objectives are to maximize the time-integrated retained CO₂ volume, minimize the final-time unretained CO₂ volume, which is used as a global containment-loss proxy, and minimize a representative full-chain cost expressed in 2024 EUR per metric tonne of injected CO₂. A new numerical simulator is used as a deterministic Sleipner-inspired test environment to describe the migration of CO₂ over injection time; this simulator is not history matched, and it is not presented as a predictive field-scale model. A joint objective-state multinomial-logit (MNL) model supplies probabilistic objective samples, and four acquisition strategies are compared: Thompson sampling, scalarized upper confidence bound (SCAL-UCB), expected hypervolume improvement (EHVI), and expected preference improvement (EPI). The comparison uses ten paired random seeds. Within each seed, all methods share the same 20-point initial design and perform 80 sequential evaluations. SCAL-UCB obtained the highest numerical mean final hypervolume and the lowest numerical mean IGD+, but Friedman tests did not detect significant method effects for final hypervolume (𝑝 = 0.472) or IGD+ (𝑝 = 0.564). Statistically supported pairwise differences were confined to Pareto-set size, for which TS and SCAL-UCB produced larger sets than EPI. Held-out validation showed lower average prediction error for the mixed-kernel GP and random forest than for MNL; MNL is therefore interpreted as an exploratory joint-state probabilistic surrogate. Sensitivity experiments indicate that the main conclusions are stable across the tested SCAL-UCB exploration coefficients and EHVI sample counts.