Radial heat transfer studies in low tube to particle diameter ratio fixed bed reactors

Leising, Guillaume M.

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Radial heat transfer studies in low tube to particle diameter ratio fixed bed reactors

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Fixed bed reactors are used in many different chemical processes, and are a very important part of chemical industry. To model fixed beds we must have a good qualitative understanding of heat transfer in them. Fixed bed models have been developed for high tube-to-particle ratio (N) beds. Modeling of low tube-to-particle beds (3 Â¡Ãœ N Â¡Ãœ 8), that are used in extremely exo- and endothermic processes in tube-and-shell type reactors, is complicated, due to the presence of wall effects across the entire radius of the bed. Heat transfer is one of the most important aspects. To obtain accurate models of heat transfer we need to study the physical mechanisms involved especially in the wall vicinity using CFD as a non intrusive tool to collect numerical data. An extra heat transfer resistance is always present near the wall. This is caused by three mechanisms which happen in the wall vicinity. The change of porosity which leads to a change of bed conductivity, the damping of mixing due to the lateral displacement of fluid, the presence of a laminar (viscous) sublayer at the wall. Many authors have been working on how to model the extra resistance near the wall. The main previous approach was to introduce a lumped parameter hw (heat transfer coefficient) which idealizes these three contributions to the extra heat resistance to be at the wall. Our approach will be to keep the parameter hw which will now represent only the viscous boundary layer idealized at the wall, and we are going to incorporate velocity and porosity profiles in the energy equation. In this way we will able to get rid of artificial parameters using the true conductivity of the bed, and the real velocity profile. So we need to study separately each contribution of the different physical mechanisms to clearly understand what happens in the wall vicinity. For this CFD will be a very powerful tool. How CFD models flow near the wall must be understood before starting simulations. Two main approaches for wall bounded flows are available and will be studied: either solve all way down to the wall, or bridge numerical values from the core of the bed to the wall using semi-empirical formulas called wall functions. These methods will be studied and compared. Also with CFD it is possible to run simulations without conduction in the bed, and so, study radial fluid displacement only and obtain reduced velocity profiles. Using the meshing it is also possible to get a very accurate porosity profile. These profiles will be combined in a simplified fixed bed model which will be used to predict temperature profiles. These may then be compared to the full CFD energy solution and to experiment to test the model.

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