(266b) Dynamic Discrepancy Reduced Modeling: Overview and Applications

Dynamic discrepancy reduced modeling [1]-[2] is a "grey box" method of reduced order modeling, uncertainty quantification and propagation. The fundamental idea is a dynamic network reduction, which obtains a system of drastically reduced order using a projection of a high-dimensionality system onto a low-dimensionality space. The reduced models retain the first principles structure of the high-order system. Variability lost in the order reduction is replaced by application of Gaussian process (GP) stochastic functions within the reduced model form. The reduced models acquire information from the high-fidelity antecedent and/or experimental data through Bayesian calibration [3]-[4], a process which results in a stochastic version of the reduced model form that replicates the behavior of the high-fidelity / experimental system in the training set while providing an estimate of the uncertainty encountered due to model interpolation or extrapolation through a space of time-dependent functional inputs.

The method will be presented in general mathematical terms, to include a rigorous definition of extrapolation. Examples will then be discussed in steam reformation of methane along with a pair of examples in carbon capture. Emphasis will be placed on an application of the method to a solid sorbent carbon capture system, utilizing a sophisticated reaction-diffusion model of the sorbent [5]. A dynamic discrepancy version of the chemical adsorption model was implemented and calibrated to experimental data. The reduced model was then incorporated into a process-scale model of an adsorber.

[1] K.S. Bhat, D.S. Mebane, C.B. Storlie and P. Mahapatra, "Upscaling uncertainty with dynamic discrepancy for a multi-scale carbon capture system," arXiv:1411.2578, 2014.

[2] D.C. Miller, M. Syamlal, D.S. Mebane, C.B. Storlie, D. Bhattacharyya, N.V. Sahinidis, D. Agarwal, C. Tong, S.E. Zitney, A. Sarkar, S. Sundaresan, E. Ryan, D. Engel and C. Dale, "Carbon capture simulation initiative: A case study in multiscale modeling and new challenges," Ann. Rev. Chem. Biomol. Eng. 5 (2014) 301.

[3] D.S. Mebane, K.S. Bhat, J.D. Kress, D.J. Fauth, M.L. Gray, A. Lee and D.C. Miller, "Bayesian calibration of thermodynamic models for the uptake of CO2 in supported amine sorbents using ab initio priors," Phys. Chem. Chem. Phys. 15 (2013) 4355.

[4] J. Kalyanaraman, Y. Fan, Y. Labreche, R.P. Lively, Y. Kawajiri and M.J. Realff, "Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO2 adsorption on amine sorbents," Comput. Chem. Eng. 81 (2015) 376.

[5] D.S. Mebane, J.D. Kress, C.B. Storlie, D.J. Fauth, M.L. Gray and K. Li, "Transport, zwitterions and the role of water for CO2 adsorption in mesoporous silica-supported amine sorbents," J. Phys. Chem. C 117 (2013) 26617.