Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

The article provides a short review on catalyst-based processes for the production of hydrogen starting from methane, both of fossil origin and from sustainable processes. The three main paths of steam- and dry-reforming, partial oxidation and thermo-catalytic decomposition are briefly introduced and compared, above all with reference to the latest publications available and to new catalysts which obey the criteria of lower environmental impact and minimize the content of critical raw materials. The novel strategies based on chemical looping with CO₂ utilization, membrane separation, electrical-assisted (plasma and microwave) processes, multistage reactors and catalyst patterning are also illustrated as the most promising perspective for CH₄ reforming, especially on small and medium scale. Although these strategies should only be considered at a limited level of technological readiness, research on these topics, including catalyst development and process optimization, represents the crucial challenge for the scientific community.