Gradient-based nonlinear model predictive control enabling demand-side management for adsorption-based direct air carbon capture

Adsorption-based Direct Air Carbon Capture and Storage (DACCS) is a promising carbon dioxide removal technology, albeit with high electricity demand. Demand-side management (DSM), i.e., shifting electricity demand to times of low electricity prices, can reduce electricity costs. In Postweiler et al. (2025), we demonstrated the efficacy of DSM for DACCS by solving a dynamic optimization problem via the gradient-free optimization method particle-swarm optimization (PSO). However, PSO is computationally very demanding and thus not real-time capable, severely limiting the resolution of time-continuous controls like flow rates. Herein, we implement real-time capable economic nonlinear model predictive control (eNMPC). We first modify the process model to obtain nonsmooth differential–algebraic equations enabling direct single shooting using a smoothing approach. We demonstrate our method in an eNMPC case study, showing real-time applicability on a single core of a standard CPU. We study the impact of the resolution and the choice of the controls, the foresight in the eNMPC setup, and the optimality tolerance on the computational performance. We choose a trade-off to compare the optimal profit achieved with the literature. We conclude that gradient-based dynamic optimization enables real-time applicability as well as more profitable operation, paving the way for large-scale DACCS employment.