Heat transfer interparticle

From the above it follows that in most practical situations a model, that takes into account only an intraparticle mass and an interparticle heat transfer resistance will give good results. However, in experimental laboratory reactors, which usually operate at low gas flow rates, this may not be true. In the above criteria the heat and mass transfer coefficients for interparticle transport also have to be known. These were amply discussed in Section 4.2. 

Kobylecki R, Horio M. On the microscopic aspect of interparticle heat transfer. Xu D, Mori S, eds. Proc 7 China-Japan Symposium on Fluidization. Xi an Xi an Publishing House, China, 2000, pp 59-64. 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

While the multiple steady-state phenomena may be, at least qualitatively, explained in terms of a simple one-step kinetic mechanism and interactions of the intraphase and interparticle heat and mass transfer (thermokinetic model), there is no acceptable explanation for the periodic activity (12). Since the values of the Lewis number are at least by a factor of 10 lower than those necessary to produce undamped oscillations, there is no doubt that the instability cannot be viewed in terms of mutual... 

The importance of adsorbent non-isothermality during the measurement of sorption kinetics has been recognized in recent years. Several mathematical models to describe the non-isothermal sorption kinetics have been formulated [1-9]. Of particular interest are the models describing the uptake during a differential sorption test because they provide relatively simple analytical solutions for data analysis [6-9]. These models assume that mass transfer can be described by the Fickian diffusion model and heat transfer from the solid is controlled by a film resistance outside the adsorbent particle. Diffusion of adsorbed molecules inside the adsorbent and gas diffusion in the interparticle voids have been considered as the controlling mechanism for mass transfer. 

Therefore, from Fig. 4.2, the correction factor C is found to be 5. The collisional heat transfer coefficient by interparticle collisions is thus given by Eq. (4.34) as... 

C c Specific heat of particles Interparticle clearance hp Particle convective heat transfer coefficient... 

If the plug flow assumption holds and the reactor truly behaves in a differential manner, a plot of Xgg Vs. W/Fgg should be linear with the slope equal to the reaction rate. However, as is evident from Figure 1, slight curvature persists in each plot. Typical calculations revealed that intra and interparticle heat and mass transfer problems should not exist at the operating conditions. The reaction rates, therefore, were obtained by evaluating the slope of each curve at the origin and as such can be called initial rates of reaction, Rq. 

In fluid-solid systems the interparticle gradients - between the external surface of the particle and the adjacent bulk fluid phase - may be more serious, because the effective thermal conductivity of the fluid may be much lower than that of the particle. For the interparticle situation the heat transfer resistances, in general, are more serious than the interparticle mass transfer effects they may become important if reaction rates and reaction heats are high and flow rates are low. Hie usual experimental test for interparticle effects is to check the influence of the flow rate on the conversion while maintaining constant the space velocity or residence time in the reactor. This should be done over a wide range of flow rates and the conversion should be measured very accurately. 

The performance of a chemical reactor depends not only on the relevant intrinsic kinetics of the reaction processes, but also on the physical processes occurring in the reactor. The physical processes such as interphase, interparticle, and intraparticle mass and heat transfer occurring within a multiphase reactor depend very significantly upon the mixing characteristics of the various phases involved. 

TTIf the annular baskets are used, the interparticle heat- and mass-transfer resistances, as well as the imraparlide heat- and mass-lransfer effects, may be large unless the reactor is highly agitated. 

Three mechanisms of heat transfer are known as conduction, convection, and radiation. On the microscopic scale, all three mechanisms share the aspect of energy exchange via interparticle collisions. Yet the macroscopic behavior and analysis... 

Although this discussion has focused on mass transfer, heat transfer is also an important consideration, particularly for highly exothermic reactions. In such cases, significant intraparticle and interparticle... 

The rates of polymerization and particle growth, and the development of the MWD and CCD depend on the temperature and concentration of monomers and chains transfer agent inside the growing polymer particles. In order to do so, the rates of mass transfer from the continuous phase, through the boundary around the particle (interparticle) and then through the particle (intraparticle), and of heat transfer in the other direction need to be predicted simultaneously. Problems combining reaction kinetics, mass and heat transfer phenomena are classical ones in chemical engineering. 

Heat transfer in interparticle void volume of column ... 

Figure 2.2 Bed heat transfer paths. 1. Internal conduction. 2. Particle-to-particle conduction. 3. Particle-to-particle radiation. 4. Interparticle convection.

The concept of criteria for exclusion of interparticle mass and heat transfer effects is the following. Since during a reaction non-zero gradients of concentration and/or of temperature always exist in the fixed bed reactor (albeit sometimes they are very small), a somewhat arbitrary assumption has to be made about the maximum deviation up to which the reaction can be considered not to be influenced by axial and radial mass and heat transport phenomena. The maximum deviation commonly used is 5%, for example, of the reaction rate compared to the zero-gradient rate or of the reactor length compared to the length of an ideal PFR. 

During fluidization of PVC, electrostatic charges arise of such magnitude that they affect the hydrodynamics of the system. This is disadvantageous for transfer processes in the bed, e.g., for heat transfer between the heating surface and the bed. This is a difficult problem in a fluidized bed because of intensive movement of particles and frequent interparticle... 

For concentrated dispersions where interparticle interactions are dominant, several theoretically based, semiempirical and empirical equations have been reported in the hterature [55-57]. As for homogeneous polymerization systems, the viscosity of disperse phase polymerization changes hence, indirect information of particle number and size can be obtained by monitoring the viscosity. Furthermore, since the viscosity of the polymerization media affects the heat transfer coefficient, onhne monitored viscosity will be very useful for understanding process changes and safety during the polymerization. 

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