The development of robust mathematical models could provide the necessary tools for a more rapid, efficient, and reliable spouted bed technology development. Computer simulations can be very useful to aid this design and scale-up process: firstly, they can contribute to obtain a fundamental insight into their complex dynamic behavior by understanding the elementary physical principles such as drag, friction, dissipation etc.; secondly, the simulations can be used as a design tool where the ultimate goal is to have a numerical model with predictive capabilities for gas-particle flows at engineering scale. Clearly, one single simulation method will not be able to achieve this goal, but a hierarchy of methods modelling phenomena on different length and time scales can achieve this. The most fruitful approach will be when they are simultaneously followed, so that they can mutually benefit from each other. In this sense, this paper presents a review of the current state of the art of modelling on spouted and spout-fluid beds through an analysis of recent literature following a multiscale approach (molecular and particle, lab, plant and industrial scale). The main features of the different scales together with their current limits are discussed and specific topics are highlighted as paths that still need to be explored. In summary, the paper aims to define the theoretical setline and the basis of improvement that would lead to a robust multiscale model with solid links between micro and macroscopic phenomena. If done with the correct balance between accuracy and computational costs it will gear SB towards their reliable and successful implementation.

Hydrothermal carbonization (HTC) is a proven cost-effective and energy-efficient method for waste management and value-added product recovery. There are, however, several issues that require further improvement or research. Identifying the strengths and weaknesses of HTC in comparison to traditional pyrolysis is crucial for scientists to choose between them or use both (complementary) to achieve specific product properties. Additionally, sharing information on diverse modeling approaches and scales is crucial to enhance the robustness and universality of HTC process models. In addition, the study on the applicability of hydrochars on target applications such as soil amendment is crucial to give back nutrients to soils and face the dependence on finite specific feedstocks in this field. Also, proper management of the process by-products, especially process water, must be addressed to improve the carbon and hydric footprint of the process. Reviewing the suitability of HTC to treat specific challenging wastes, whose strength is not related to their calorific value but to their nutrient composition (i.e., manures), is also an appealing topic for HTC research. This paper aims to tackle the above-mentioned issues through an updated review and discussion of research gaps that require further investigation.