A Predictive Model of Adsorption of Cryogenic Liquids in Aerogel-Based Materials

Propellants such as hydrogen, oxygen, or methane are generally stored as cryogenic liquids in highly insulated tanks. An advantage of this type of storage is that more mass can be stored per unit volume compared with storage as a gas. However, cryogenic tanks are often bulky and difficult to make into conformal geometries. Adsorption storage in porous and malleable materials, such as aerogel blankets, is a promising alternative method for storing these commodities. Previous studies have shown that when the commodity is adsorbed from the liquid cryogen, instead of from a gaseous state, the mass adsorbed per unit volume of aerogel blanket is higher than the mass for the same volume of cryogen at normal boiling point. However, while gaseous adsorption is well studied, studies on liquid cryogen adsorption have been limited, and therefore the mechanism is not as well understood. Currently, there are no models for predicting liquid cryogen adsorption, and those adapted from gaseous adsorption models have two main shortcomings. First, models such as the Brunauer- Emmett-Teller or deep-learning require extensive experimental data for validation, which are not currently available. Second, alternative solutions are based on computationally intensive methods, such as Monte-Carlo simulation. This work presents a new closed-form predictive model for liquid cryogen adsorption that does not require computationally expensive techniques. Based on the principle that physisorption involves the adhesion of molecules to a surface through van der Waals forces, the model uses the van der Waals diameters of the cryogens and iteratively calculates the mass of each layer of adsorbed molecules on the aerogel surface. Using existing datasets, the proposed predictive model is demonstrated to be versatile, and capable of predicting adsorption of cryogens in various porous materials, including pure silica aerogel and aerogel-based materials (e.g., aerogel blanket). The model achieves an accuracy between 96% to over 99%, depending on the type of adsorbent and cryogen. An important finding of this work is that, while the commodity inside the nanopores of the aerogel exists solely as adsorbed molecules, the density of the commodity inside the pores is equivalent to a solid close-packed crystal of that cryogen.