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 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.

[1]  J. Krumhansl,et al.  Multiscale Science: Materials in the 21st Century , 2000 .

[2]  Stanislaw Sieniutycz,et al.  Nonequilibrium theory and extremum principles , 1990 .

[3]  Jean-Claude Charpentier,et al.  Process engineering and problems encountered by chemical and related industries in the near future. Revolution or continuity , 1998 .

[4]  Brian E. Mapes,et al.  Multiscale variability of deep convection in relation to large-scale circulation in TOGA COARE , 1996 .

[5]  Feng Qiu,et al.  Multi-Scale Model for Binary Mixtures Containing Nanoscopic Particles , 2000 .

[6]  Kiran Alapaty,et al.  Simulation of carbon monoxide transport during April 1994 , 1999 .

[7]  Jinghai Li,et al.  Compromise and resolution - Exploring the multi-scale nature of gas-solid fluidization , 2000 .

[8]  H. de Lasa,et al.  Kinematic waves and flow patterns in bubble columns and three-phase fluidized beds , 1992 .

[9]  Jinghai Li,et al.  Application of the energy-minimization multi-scale method to gas–liquid–solid fluidized beds , 2001 .

[10]  Matthias K. Gobbert,et al.  A Multiscale Simulator for Low Pressure Chemical Vapor Deposition , 1997 .

[11]  John M. Gauch,et al.  Image segmentation and analysis via multiscale gradient watershed hierarchies , 1999, IEEE Trans. Image Process..

[12]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[13]  Thomas Y. Hou,et al.  A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media , 1997 .

[14]  J. Rivet,et al.  Hydrodynamic behavior of Brownian particles in a position-dependent constant force field , 1999 .

[15]  Ilya Prigogine,et al.  Introduction to Thermodynamics of Irreversible Processes , 1967 .

[16]  Dan M. Frangopol,et al.  MULTISCALE MODELING OF INTERACTIVE DIFFUSION PROCESSES IN CONCRETE , 2000 .

[17]  Guo,et al.  The multi-scale attribute of transport and reaction systems , 2001 .

[18]  R. L. Cumming,et al.  Predation on reef-building corals: multiscale variation in the density of three corallivorous gastropods, Drupella spp. , 1999, Coral Reefs.

[19]  B. Bakshi.  Multiscale PCA with application to multivariate statistical process monitoring , 1998 .

[20]  Ted Belytschko,et al.  Multi-scale methods , 2000 .

[21]  F. Gestermann,et al.  Inbetriebnahme und erste Betriebsergebnisse des Dampferzeugers mit zirkulierender Wirbelschichtfeuerung bei Bayer AG, Leverkusen , 1989 .

[22]  S. Lee,et al.  Experimental investigation of the shear strength of a unidirectional carbon/aluminum composite under dynamic torsional loading , 1998 .

[23]  Jinghai Li,et al.  Physical mapping of fluidization regimes—the EMMS approach , 2002 .

[24]  E. Rank,et al.  A multiscale finite-element method , 1997 .

[25]  John H. Cushman,et al.  Multiscale, hybrid mixture theory for swelling systems—II: constitutive theory , 1996 .

[26]  Jinghai Li,et al.  Analytical solution of the energy-minimization multi-scale model for gas-solid two-phase flow , 1998 .

[27]  Jinghai Li,et al.  Multiscale nature of complex fluid-particle systems , 2001 .

[28]  Jinghai Li,et al.  The EMMS model - its application, development and updated concepts , 1999 .

[29]  Kathryn E. Freemark,et al.  Effects of landscape structure on nest predation in roadsides of a midwestern agroecosystem: a multiscale analysis , 2000, Landscape Ecology.

[30]  Godin,et al.  A multiscale model of plant topological structures , 1998, Journal of theoretical biology.

[31]  James Wei.  Multiscale Structure of Uniformity in Mixtures , 1999 .

[32]  Wei Ge,et al.  Dissipative structure in concurrent-up gas–solid flow , 1998 .

[33]  Wei Ge,et al.  A simple variational criterion for turbulent flow in pipe , 1999 .

[34]  V. M. Kiiko,et al.  A Study of Structure Formation and Failure of Short Fibre Composites with Metal and Ceramic Matrices , 1998 .

[35]  Franck Plouraboué,et al.  Multi-scale roughness transfer in cold metal rolling , 1999 .

[36]  Jinghai Li,et al.  METHOD OF ENERGY MINIMIZATION IN MULTI-SCALE MODELING OF PARTICLE-FLUID TWO-PHASE FLOW , 1988 .

[37]  Matthias Bauer,et al.  A concept for multi-scale modeling of bubble columns and loop reactors , 1999 .

[38]  K. Stasiewicz,et al.  Multiscale current structures observed by Freja , 1998 .

[39]  J. Leon,et al.  Multiscale analysis of discrete nonlinear evolution equations , 1999, solv-int/9902005.

[40]  H. Rafii-Tabar,et al.  Multiscale numerical modelling of cracK propagation in tvvo-dimensional metal plate , 1998 .

[41]  Wenbin Zhang,et al.  Numerical study of pattern formation in weakly damped parametric surface waves , 1998 .

[42]  Jan J. Lerou,et al.  Chemical reaction engineering : A multiscale approach to a multiobjective task , 1996 .

[43]  O. Levenspiel.  Chemical Reaction Engineering , 1972 .

[44]  Nicolas Pérez de la Blanca,et al.  Boundary simplification using a multiscale dominant-point detection algorithm , 1998, Pattern Recognit..

[45]  D. Vlachos.  Multiscale integration hybrid algorithms for homogeneous–heterogeneous reactors , 1997 .

[46]  John R. Grace,et al.  Use of dimensional similitude for scale-up of hydrodynamics in three-phase fluidized beds , 1999 .

[47]  William R. Cotton,et al.  Multiscale Evolution of a Derecho-Producing Mesoscale Convective System , 1998 .

[48]  John Horgan,et al.  From Complexity to Perplexity , 1995 .

[49]  Lisa Chong,et al.  Whole-istic Biology , 2002, Science.

[50]  Jinghai Li,et al.  Energy Transport and Regime Transition in Particle-Fluid Two-Phase Flow , 1988 .

[51]  Hernan G. Arango,et al.  Circulation and Dynamics of the Western North Atlantic. Part I: Multiscale Feature Models , 1997 .