Three-dimensional model phases process

Because of the expanded scale and need to describe additional physical and chemical processes, the development of acid deposition and regional oxidant models has lagged behind that of urban-scale photochemical models. An additional step up in scale and complexity, the development of analytical models of pollutant dynamics in the stratosphere is also behind that of ground-level oxidant models, in part because of the central role of heterogeneous chemistry in the stratospheric ozone depletion problem. In general, atmospheric Hquid-phase chemistry and especially heterogeneous chemistry are less well understood than gas-phase reactions such as those that dorninate the formation of ozone in urban areas. Development of three-dimensional models that treat both the dynamics and chemistry of the stratosphere in detail is an ongoing research problem. 

Figure 4-13 shows an example from a three-dimensional model simulation of the global atmospheric sulfur balance (Feichter et al, 1996). The model had a grid resolution of about 500 km in the horizontal and on average 1 km in the vertical. The chemical scheme of the model included emissions of dimethyl sulfide (DMS) from the oceans and SO2 from industrial processes and volcanoes. Atmospheric DMS is oxidized by the hydroxyl radical to form SO2, which, in turn, is further oxidized to sulfuric acid and sulfates by reaction with either hydroxyl radical in the gas phase or with hydrogen peroxide or ozone in cloud droplets. Both SO2 and aerosol sulfate are removed from the atmosphere by dry and wet deposition processes. The reasonable agreement between the simulated and observed wet deposition of sulfate indicates that the most important processes affecting the atmospheric sulfur balance have been adequately treated in the model. 

Additive and impurity rejection at the growing crystal front leads to uneven distribution in a crystalline polymer. This redistribution process has been studied by UV and fluorescence microscopy and by an electron microscope with energy dispersive x-ray analysis. In polymer samples which are quenched after rapid crystallization, the additive distribution is kinetically determined and may be modeled in a computer as a three-dimensional zone-refining process. In annealed polymer samples, low molecular weight additives are uniformly concentrated in the amorphous phase. The additive distribution reflects that of crystalline material within the polymer. Antioxidant and uv stabilzer redistribution probably does not have a major effect on polymer stability, but the redistribution of partially oxidized, impure polymer may be important... 

The formalism of density functional theory (DFT) has received considerable attention as a way to describe the adsorption process at the fluid/solid interface. The older approach was to treat the adsorbate as a separate, two-dimensional phase existing in equilibrium with the bulk gas phase. This model works well in the monolayer region, but at higher surface concentrations the formation of multilayers requires the adoption of some sort of three-dimensional model to account for increasing adsorbate-adsorbate interaction and diminishing adsorption potential. 

Why is it important for a process engineer to be able to review a three-dimensional model (actual or virtual/electronic) of the plant prior to the construction phase of a project ... 

In addition to phase change and pyrolysis, mixing between fuel and oxidizer by turbulent motion and molecular diffusion is required to sustain continuous combustion. Turbulence and chemistry interaction is a key issue in virtually all practical combustion processes. The modeling and computational issues involved in these aspects have been covered well in the literature [15, 20-22]. An important factor in the selection of sub-models is computational tractability, which means that the differential or other equations needed to describe a submodel should not be so computationally intensive as to preclude their practical application in three-dimensional Navier-Stokes calculations. In virtually all practical flow field calculations, engineering approximations are required to make the computation tractable. 

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