(560a) A Bayesian Method for Finding the Tolerances Around a Bi-Objective Pareto Front: Application to Electrochemical Carbon Capture Solution Chemistries
AIChE Annual Meeting
Thursday, November 11, 2021 - 8:00am to 8:19am
Current optimization methods work well for continuous input variables or well defined discrete input variables, but not for chemical compound searches and solution chemistry optimization. Due to their construction from individual atoms, chemical compounds form a discrete set, but the flexibility of viable functional group substitutions makes the set intractably large. The simplest approach of approximating chemical properties as continuous variables often leads to calculated optima that might not exist because there is no compound that has the appropriate combination of properties. Restricting the search space to databases has been successful for materials design, but for emerging technologies like electrochemical carbon capture, the number of well-characterized compounds is too small to be confident that the calculated optima derived from the database describe the best possible performance. Quantitative structure-property relationships can bridge this gap by estimating properties of feasible yet untested compounds, but QSPR methods are often too inaccurate for properties like equilibrium constants, leading to highly inaccurate performance estimates. This problem becomes substantially more complicated if there are multiple objectives that seek to describe an entire Pareto frontier. New computational methods are necessary to apply optimization techniques to electrochemical carbon capture and guide the selection of the optimal molecule and solution composition.
We have developed a Bayesian inference-based method that is flexible to bi-objective, multi-constraint optimization problems to guide the search for realizable optimal solution compositions. Gaussian processes (GP) are used to create surrogate functions for each objective and constraint, which can then be applied to a set of acceptance criteria that define allowable suboptimal performance. Each possibility in the search space can then be described by the probability that it meets all acceptance criteria. By iteratively sampling the regions with ambiguous outcomes (i.e. probabilities close to 0.5), determining their outcomes explicitly, and updating the GP with the new information, the set of potential solutions can be refined to give the set of acceptable results. By broadening the results from only the Pareto frontier to a set of near-optimal results, the likelihood that a realizable solution composition exists within this space increases. This near-optimal set can be further described with feature importance rankings by applying GP to constrained models in which only some of the input variables are known. The conditional probabilities derived from these models can be used to rank the input variables from most to least important, as well as define each variables' tolerances conditioned on specific information. These rankings and tolerances provide a systematic approach for finding real compounds that can satisfy acceptably optimal performance by indicating which properties should be prioritized and how large of a trade-off is acceptable.
We demonstrate this method with a simple optimization test function to showcase its flexibility to various optimization constraints, then apply it to optimize the solution composition of electrochemical carbon capture using proton coupled electron transfers (PCET) in order to minimize the energy demand and maximize the CO2 capture rate. In this process, PCET at the electrode change the solution pH, which drives absorption and desorption of CO2 in alkaline and acidic solution, respectively. Using trends in the properties of quinones, the most common type of molecule used in PCET-based carbon capture, we identified that the two pKa's of the reduced form hydroquinone are the most important variables for overall carbon capture performance. Additionally, there is an optimal second pKa for a given feed gas CO2 partial pressure and desired balance between minimizing the energy demand and maximizing the capture rate. This is counter to initial assumptions in the literature, which suggest that higher pKa values are always more favorable. Ultimately, this case study shows the flexibility and utility of our computational method in helping accelerate the optimization of solution chemistries for process design.