Despite the potential of Direct Air Capture (DAC) technology, its scalability is one of the major challenges for the scientific community. Research has focused on developing sorbent materials rather than achieving scaling up through detailed modeling and process-level analysis. Therefore, there is a need for more research at the device design, process modeling, and optimization levels. Since DAC through adsorption typically involves cyclic processes with periodic CO₂ adsorption and subsequent regeneration of the adsorbent, more detailed models are needed that can capture these dynamics. Further development of DAC technology, relies on developing reactive transport models for optimizing equipment and process designs as well as operational efficiency. This kind of modeling approach provides detailed insights into gas flow patterns, heat transfer, and chemical and physical interactions. Some prior modeling work has been conducted at a process level, focusing on reducing the energy footprint and operational costs. Nevertheless, a holistic approach is still missing, where mathematical optimization is applied with data from the detailed reactive transport simulations.
To address this gap, our study develops and implements a 1D model in COMSOL Multiphysics to solve the coupled multiphysics problem. The model is used to simulate the cyclic steady state of the adsorption-desorption process and is validated against experimental data from the literature. The optimization of this model is achieved through advanced trust-region methods integrated with Gaussian Processes. Key decision variables were optimized to minimize the capture cost. We optimized the capture cost while considering the trade-off between energy consumption and productivity. The resulting minimum capture cost was determined to be 265.6 $/t-CO₂, which aligns with expected values reported in the literature. Numerical results suggest the effectiveness of the optimization strategies applied and underscore the importance of simultaneously selecting decision variables in improving performance in DAC processes. In parallel to optimization, a sensitivity analysis illuminated further the complex interplay between the decision variables and their effect on the specific energy and cost of removing the CO₂.
The modeling approach was extended to a 2D axisymmetric model to better visualize CO₂ uptake and temperature profiles, revealing significant radial gradients during the regeneration step. The 2D model was significantly more computationally costly compared to the 1D model, highlighting the tradeoff between spatial resolution and the ability to rapidly iterate. To our knowledge, this is the first comprehensive computational framework that integrates a coupled reaction-diffusion model of a cyclic steady-state DAC system with trust-region optimization, leveraging Gaussian Processes for information transfer.
*This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and was supported by Laboratory Directed Research and Development funding under project 22-SI-006. LLNL Release Number: LLNL-JRNL-872157.
