Multiscale analysis chapter

For the rest of the chapter, we present a more specific survey treatment of tools, technologies, and best practices for undertaking P2 by adopting a multiscale analysis of categorizing these tools into macro-, meso-, and microscale. ... 

This chapter presented a general methodology for multiscale analysis modeling, and optimization. Specific application of this general method wa<... 

In this chapter, the multiscale analysis of FTS process is illustrated, and the effects of every scale are discussed on the product distribution of FTS reaction. Flowever, constraint will be exploded in mesoscales viewpoint because there are many combined factors to influence FTS reaction, such as complex reaction mechanism, mass transfer of reactants and products, and flow type of reactor. Therefore, the ASF distribution is always improper in the FTS system. On the other hand, the flow model of the reactor has been investigated, but how the reactor influence the reaction performance of catalyst is still not clear. Therefore, if we want to know the product distribution of different reactors, a lot of experiment should be taken place. Based on these points, the mesoscale phenomena and effects for products of FTS reaction should be investigated in detail. 

Kinetics of multiscale systems studied in this chapter and developed theory of dynamic limitation demonstrates that in multiscale limit lumping analysis can work (almost) exactly. Lumped concentrations are sums in groups, but these groups can intersect and usually there exist several intersections. 

The three chapters in this volume deal with various aspects of singular perturbations and their numerical solution. The first chapter is concerned with the analysis of some singular perturbation problems that arise in chemical kinetics. In it the matching method is applied to find asymptotic solutions of some dynamical systems of ordinary differential equations whose solutions have multiscale time dependence. The second chapter contains a comprehensive overview of the theory and application of asymptotic approximations for many different kinds of problems in chemical physics, with boundary and interior layers governed by either ordinary or partial differential equations. In the final chapter the numerical difficulties arising in the solution of the problems described in the previous chapters are discussed. In addition, rigorous criteria are proposed for... 

Fischer-Tropsch synthesis (FTS), directly converting a mixture of carbon monoxide and hydrogen (syngas) into sulfur-free hydrocarbons, has attracted much attention from academic and industrial community. However, the development of FTS mainly depends on experience, resulting in the inefficient development of catalysts and industrialization design. Recently, a new analysis method, mesoscale analysis, has attracted more attention due to researching on between different scales or crossing several scales, which would contribute to efficient R D process of FTS. This chapter will summarize the multiscale effects on FTS products distribution such as ASF distribution, kinetic model. 

---