Dynamic Discrepancy Reduced Order Modeling for Fischer-Tropsch Synthesis Over Cobalt-based Catalyst

Advances in carbon capture techniques and demands in alternative fuel sources have increased over the past couple of decades. The Fischer-Tropsch Synthesis (FTS) provides a viable way to produce hydrocarbons from natural gas, coal, CO2, or biomass. However, current comprehensive models for FTS encompass large number of reacting species, readsorption and conversion of primary products, surface intermediates, and coverage-dependent reaction rates. To accurately predict the products obtained through the process a reduced order model has been developed. By reducing the number of parameters of an existing comprehensive model, uncertainty is introduced. The uncertainty can be quantified by using discrepancy functions within the chemical rate equations, there by representing the reduced order model as a set of stochastic differential equations. Representing the uncertainty as model discrepancy functions, a Bayesian approach is used to calibrate the reduced order model to data obtained from literature. Through a Bayesian Smoothing Splines (BSS-ANOVA) framework, the stochastic differential equations are decoupled into deterministic differential equations and stochastic coefficients. The parameters are solved for using a Sequential Monte Carlo approach with importance sampling. Through the use of these stochastic coefficients, fidelity is restored to the reduced order model. Thus, the model can be fully described by fewer parameters than initially needed, as well as a reduction in the computational complexity