(219b) Hierarchical Bayesian Estimation for Adsorption Isotherm Parameter Determination and Applications to CO2 capture

To slow down the current rise in the temperature of the earth and the abnormal changes of the climate and ease the impact of the greenhouse effect, researchers around the world are developing many separation techniques to recover greenhouse gases. Among the greenhouse gases, the impact of carbon dioxide (CO₂) is particularly significant, which has become one of the most active areas in separation research.

Among many separation techniques, adsorption has many advantages such as high energy utilization efficiency and reusability of the adsorbent. Because of these advantages, adsorption processes are promising and attract researchers to develop many novel adsorbents. Adsorption isotherms are measured as a way to evaluate conventional and novel adsorbents in adsorption processes. These large-scale experimental results are being collected in the database at the National Institute of Standards and Technology (NIST). The isotherm data on this database could be a crucial component in developing process models for separation, which can be utilized to develop and analyze the economics of the adsorption process.

However, a critical problem has been recently reported by Park et al. [1], where substantial mismatches of the adsorbed amount of have been reported by different researchers even for the same adsorbent, specifically for adsorbents called metal-organic frameworks (MOFs), at the similar ranges of temperature and pressure. These discrepancies could be caused by different measurement techniques and procedures, but more importantly by variations in the underlying material’s properties such as inconsistent surface areas and reaction yield due to different adsorbent synthesis procedures. In their study, a statistical technique was applied to find upper and lower bounds where the adsorbed amount is believed to be reliable. Nevertheless, the problem of determining an isotherm model and incorporating parametric uncertainty upon the consensus bounds have not been addressed yet.

In this study, we resolve the issue stated above by applying the hierarchical Bayesian estimation. In this method, statistical inference by Bayes' theorem is used to update the probability for hypothesis as more data or information becomes available. By hierarchical Bayesian estimation we can quantify the differences in the adsorption amount reported by different researchers, while obtaining a single set of the probability density distributions of isotherm parameters simultaneously. The application of hierarchical Bayesian estimation allows researchers to utilize the isotherm data on the NIST database to develop a reliable isotherm model, which can save the measurement cost and time substantially, which leads to efficient development and economic evaluation of adsorption processes. This method can be applied to a wide variety of applications of adsorption not only for capture.

Reference:

[1] J. Park, J. D. Howe, D. S. Sholl, How Reproducible Are Isotherm Measurements in Metal–Organic Frameworks?, Chem. Mater. 29 (2017) 10487-10495.