Exploring complex systems in chemical engineering-the multi-scale methodology

Challenges in quantitative design of chemical processes mainly reside in their complex structures, which are usually multi-scale in nature, and are difficult to analyze by the average approach as commonly used. The multi-scale methodology has thus received more and more attention in recent years. There are three kinds of multi-scale methodology: descriptive for distinguishing the phenomenological difference of structures at different scales; and correlative for formulating phenomena at higher scales by analyzing the mechanisms at lower scales; and variational for revealing the dominant mechanisms of the structure and the relationship between the scales. This paper presents an overview of multi-scale methodologies with emphasis on the variational methodology, and proposes the possibility of establishing a generalized multi-scale methodology, effective for analyzing single-phase turbulent flow in pipe, gas–solid two-phase fluidization, and gas–solid–liquid three-phase fluidization. The variational multi-scale methodology consists of the following steps: • Phenomenological resolution with respect to scales of structures. • Identification of dominant mechanisms. • Establishment of conservation conditions with respect to different scales and correlation between different scales. • Formulation of variational criterion to identify what dominates the stability of structure and what compromise exists between different dominant mechanisms. • Integration between conservation conditions with stability conditions.