Chem. Eng. Sci.

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 aid 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. (C) 2003 Elsevier Science Ltd. All rights reserved.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 aid 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