(328c) Data-Driven Model Building of Zeolite Adsorption Processes with Uncertainty Quantification and Propagation to Dynamic Simulations of CO2 Adsorption

The prediction and propagation of uncertainty in complex mathematical model simulations is a research subject attracting increasing attention in recent years [1,2]. Computer models, while a great tool to predict the behavior of a variety of specific applications, are full of unknown parameters whose values are inherently uncertain. Additionally, the model itself may not be a perfect description of the modeled process, resulting in unreliable predictions even with the best-fitting parameter values [3]. Therefore, advanced calibration tools are required to incorporate uncertainty into parameter estimation to enhance the performance of the model. Bayesian calibration is an invaluable calibration technique that can be used to address model uncertainty. It consists of making inferences about the unknown parameters and model form uncertainty based on experimental data, which results in posterior distributions of the parameters. By using models calibrated in this manner, numerical simulations produce predictive distributions of key process variables, enabling decision makers to appreciate the incertitude and spend less time and resources during scale-up by designing fewer and more effective incremental steps [4].

Post-combustion CO₂ capture is a technology for which the interest in up-scaling for commercial applications has gained significant momentum of late [5]. In this study, a rigorous complete dynamic mathematical model of a fixed bed adsorber for CO₂ adsorption onto NaX zeolite (also known as zeolite 13X) is developed and implemented in gPROMS®. The small-scale adsorption model that governs the dynamic phase equilibrium between the gas and the solid phase is constructed from adsorption isotherm and calorimetry data using a model form based on the Langmuir isotherm equipped with Gaussian process stochastic functions. The Bayesian approach to model construction and calibration quantifies uncertainty in the adsorption model. The physical adsorption model is then implemented into the process-scale fixed bed adsorber model, thus propagating uncertainty to the dynamic, non-isothermal fixed bed adsorber model.

To save computational time, two simplified mathematical models of the fixed bed adsorber are formulated. From a deterministic perspective, the simplified models are shown to be in close agreement with the complete model. In order to evaluate whether the simplified models can be used as substitutes of the complete model for uncertainty propagation, an ANOVA analysis is conducted at a significance level of 0.05, followed by linear contrast analysis to test specific hypothesis related to the output distributions of the three models.

A number of case studies are performed and for each case, the uncertainty is quantified in output variables of interest – namely, CO₂ breakthrough times and concentration and temperature profiles. The case studies show that the uncertainty inherent to the physical adsorption model scales up differently depending on the operating conditions. Some operating conditions give rise to increased process-scale uncertainty, while others to decreased uncertainty. An additional case study demonstrates that accounting for model form discrepancy at the small scale (in contrast with accounting for parameter uncertainty only) significantly reduces the uncertainty in the process-scale variables.

References

1. Bhat K. S., Mebane D. S., Storlie C. B., and P. Mahapatra, “Upscaling Uncertainty with Dynamic Discrepancy for a Multi-scale Carbon Capture System”. Journal of the American Statistical Association, 2017.
2. Kalyanaraman J., Kawajiri Y., Lively R. P., and M. J. Realff. “Uncertainty Quantification via Bayesian Inference Using Sequential Monte Carlo Methods for CO2 Adsorption Process”. AIChE Journal, 2016, 62 (9) pp. 3352-3368.
3. Kennedy M. C., and A. O’Hagan, “Bayesian calibration of computer models”, Journal of the Royal Statistical Society Series B, 2001, 63 (3) pp. 425-464. 
4. Miller D. C., Syamlal M., Mebane D. S., Storlie C., Bhattacharyya D., Sahinidis N. V., Agarwal D., Tong C., Zitney S. E., Sarkar A., Sun X., Sundaresan S., Ryan E., Engel D., and C. Dale (), “Carbon Capture Simulation Initiative: A Case Study in Multiscale Modeling and New Challenges”, Annual Review of Chemical and Biomolecular Engineering, 2014, 5 pp. 301-23.
5. Miller D. C., Agarwal D. A., and C. Tong, “CCSI and the role of advanced computing in accelerating the commercial deployment of carbon capture systems”, SciDAC Conference, June 2011.