Mesoscale and macroscale methods

The scheme for catalyst characterization in general is given in Figure 4.3.2 (for a more detailed description of methods, cf. [17-19]). In order to properly describe the catalysts on an atomic scale, a mesoscale, and a macroscale, a number of different and complementary methods need to be applied. The overall bulk composition... 

Many of the macroscale and mesoscale P2 approaches rely on a molecular-level understanding of chemical and physical process at the microscale. For example, the synthesis of new catalysts to achieve higher yields with less wastes relies on a fundamental understanding of surface chemistry. There are a large number of methods available for undertaking P2 at the microscale via the molecular-level redesign of chemical products and processes. In line with the emergence... 

As discussed above, the stabdity condition is expected to reach extremum in sufficiendy large space (e.g., cross section of a fluidized bed) instead of local cell. The energy to sustain mesoscale structures in a fluidized bed comes largely from the mean relative motion between gas and particles on the macroscale. Furthermore, the dynamic evolution of mesoscale structure and its energy transfer is subject to both macroscale operating conditions and the conservation laws in microscale computational cells. As a result, a two-step scheme was proposed to fulfill the coupHng between EMMS and hydrodynamic conservation equations, called EMMS/matrix (Lu et al, 2009 Wang and Li, 2007). At the macroscale (reactor), the bi-objective optimization method in terms of min was first used to resolve the mesoscale parameters, say, dc and gc. These mesoscale parameters were then incorporated... 

It is meaningful to examine the relation between microscale model, mesoscale model, and micromodel. For reaction kinetics, microscale and mesoscale models adopt the same kinetics that based on element reaction system. For diffusion, mesoscale model embodies two diffusion mechanisms (one for micropores and another for mesopores and macropores), and microscale model considers one diffusion mechanism since it only has micropores. No diffusion was considered within the macropores. It is obvious that the mesoscale model possesses the same theoretical foundation as the microscale model, but its application scope has been enlarged compared to the microscale model. Therefore, it could be reliably used as a tool to derive some parameters, such as effective chemical kinetics and effective diffusion parameters, for macroscale model. In the section following, we discuss the method on how to link the microscale kinetics to the lumped macroscale kinetics via the mesoscale modeling approach. 

These two different scales are related using the homogenization method in mesoscale computation. For example, effective values of charge flux, elasticity tensor, and conductivities in macroscale are derived using values defined at the microscale and porosity of the region under consideration. 

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