Multiscale approaches

In this chapter, we have discussed three levels of modeling for dense gas-solid flows, with the emphasis on the technical details of each of the models, which have not been published elsewhere. Up till now, the models have mainly been used to obtain qualitative information, that is, to acquire insight into the mechanisms underlying the gas-solid flow structures. However, the ultimate objective of the multiscale approach is to obtain quantitative... 

As a matter of fact, one may think of a multiscale approach coupling a macroscale simulation (preferably, a LES) of the whole vessel to meso or microscale simulations (DNS) of local processes. A rather simple, off-line way of doing this is to incorporate the effect of microscale phenomena into the full-scale simulation of the vessel by means of phenomenological coefficients derived from microscale simulations. Kandhai et al. (2003) demonstrated the power of this approach by deriving the functional dependence of the singleparticle drag force in a swarm of particles on volume fraction by means of DNS of the fluid flow through disordered arrays of spheres in a periodic box this functional dependence now can be used in full-scale simulations of any flow device. 

The important impact of these experimental insights for molecular modeling is that the development of structure versus property relations of PEMs does not require multiscale approaches going all the way to the macroscopic scale. Rather, the main job is done if one arrives at the scale of several 10s of nanometers. Notably, operation at low hydration emphasizes even more the importance of (sub)nanoscale phenomena controlled by explicit interactions in the polymer-water-proton system. 

Schreier H, Brown S (2004) Multiscale approaches to water management land-use impacts on nutrient and sediment dynamics. Scales in Hydrology and Water Management, Intern. Assoc. Hydrol. Sci, lAHS Publ, 287 61-75... 

Lerou J, Ng K. Chemical reaction engineering a multiscale approach to a multiobjective task. Chem. Eng. Sci. 1996 51 1595-1614. 

The main goal of simulation methods is to obtain information on the spatial and temporal behavior of a complex system (a material), that is, on its structure and evolution. Simulation methods are subdivided into atomistic and phenomenological methods. Atomistic methods directly consider the evolution of the system of interest at the atomic level with regard to the microscopic structure of the substance. These methods include classical and quantum MD and various modifications of the MC technique. Phenomenological methods are based on macroscopic equations in which the atomistic nature of the material is not directly taken into account. Within the multiscale approach, both groups of methods mutually complement each other, which permits the physicochemical system under study to be described most comprehensively. 

G. Lu et al From electrons to finite elements a concurrent multiscale approach for metals. Physl. Rev. B Cond. Matt. Matls. Phys. 73, 024108 (2006)... 

To achieve these new developments the approach cover a large domain of technical disciplines and also a multiscale approach in time and length. This new complexity require to increase the relative weight of modeling and scientific calculation in the process development. For exemple, CFD calculation is currently used for the development of reactor technologies and reactor internal, but most of the time it is difficult to couple hydrodynamic modelisation and reaction modelisation. A lot of improvement are expected by coupling these two approaches. 

The modeling tools have to be used in all the steps of process development taking into account a multiscale approach and without forgetting the measurement technologies needed for model validation. 

It is significant to notice that the concepts and principles to vary and manipulate any aspects of the phenomena will generate the corresponding partial solutions, from which the ultimate intensified process and equipment will be synthesized. Herein, the multiscale approach for variations and manipulations of the phenomena is emphasized. It means that the concepts and principles should be explored at all possible scales for the... 

If the values of local mean bubble diameter and local gas flux are available, a fluid dynamic model can estimate the required influence of mass transfer and reactions on the fluid dynamics of bubble columns. Fortunately, for most reactions, conversion and selectivity do not depend on details of the inherently unsteady fluid dynamics of bubble column reactors. Despite the complex, unsteady fluid dynamics, conversion and selectivity attain sufficiently constant steady state values in most industrial operations of bubble column reactors. Accurate knowledge of fluid dynamics, which controls the local as well as global mixing, is however, essential to predict reactor performance with a sufficient degree of accuracy. Based on this, Bauer and Eigenberger (1999) proposed a multiscale approach, which is shown schematically in Fig. 9.13. 

Figure 5 Multiscale approach to understand rate of CO2 diffusion into and CH4 diffusion out of a structure I hydrate, (left) Molecular simulation for individual hopping rates, (middle) Mesoscale kinetic Monte Carlo simulation of hopping on the hydrate lattice to determine dependence of diffusion constants on vacancy, CO2 and CH4 concentrations, (right) Macroscopic coupled non-linear diffusion equations to describe rate of CO2 infusion and methane displacement. Graph from Stockie. ...

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