Particle intraparticle heat transfer

The properties of wood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is briefly presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. 

The isothermal effectiyeness factor When the heat effects are negligible or the external and intraparticle heat transfer coefficients are very large, the particle is isothermal and hence > =1.0 and therefore the two equations reduce to one which in this case is linear ... 

The importance of the intraparticle heat transfer resistance is evident for particles with relatively short contact time in the bed or for particles with large Biot numbers. Thus, for a shallow spouted bed, the overall heat transfer rate and thermal efficiency are controlled by the intraparticle temperature gradient. This gradient effect is most likely to be important when particles enter the lowest part of the spout and come in contact with the gas at high temperature, while it is negligible when the particles are slowly flowing through the annulus. Thus, in the annulus, unlike the spout, thermal equilibrium between gas and particles can usually be achieved even in a shallow bed, where the particle contact time is relatively short. 

During sterilization by heat there are two steps in the heat transfer process -heat transfer to the particle surface and intraparticle heat transfer. Due to the poor mixing characteristics of solid beds and the fact that intraparticle heat transfer is limited to conduction, it is more problematic to ensure sterility of a solid substrate than it is to ensure sterility of a liquid medium. In unmixed beds it is highly likely that the effectiveness of the sterilization process will vary with position. 

Catalyst particles in three-phase fixed-bed reactors are usually completely filled with liquid. Then intraparticle temperature gradients are negligible due to the low effective diffusivities in the liquid phase, as pointed out by Satterfield [13] and Baldi [92]. However, if the limiting reactant and the solvent are volatile, vapor-phase reaction may occur in the gas-filled pores, causing significant intraparticle temperature gradients [109, 110]. In these conditions, intraparticle heat transfer resistance is necessary to describe the heat transfer. 

Since the critical values of y(3 and Lw are y/3 = 4 and, Lw > 1 respectively, then referring to the results reported in Table II, it seems highly unrealistic to expect multiple steady states and periodic activity for a single catalyst particle resulting from intraparticle heat and mass transfer alone. 

The form of equation (21) is interesting. It shows that the uptake curve for a system controlled by heat transfer within the adsorbent mass has an equivalent mathematical form to that of the isothermal uptake by the Fickian diffusion model for mass transfer [26]. The isothermal model hag mass diffusivity (D/R ) instead of thermal diffusivity (a/R ) in the exponential terms of equation (21). According to equation (21), uptake will be proportional to at the early stages of the process which is usually accepted as evidence of intraparticle diffusion [27]. This study shows that such behavior may also be caused by heat transfer resistance inside the adsorbent mass. Equation (22) shows that the surface temperature of the adsorbent particle will remain at T at all t and the maximum temperature rise of the adsorbent is T at the center of the particle at t = 0. The magnitude of T depends on (n -n ), q, c and (3, and can be very small in a differential test. 

The true intrinsic kinetic measurements require (1) negligible heat and mass transfer resistances by the fluids external to the catalyst (2) negligible intraparticle heat and mass transfer resistances and (3) that all catalyst surface be exposed to the reacting species. The choice of the reactor among the ones described in this section depends upon the nature of the reaction system and the type of the required kinetic data. Generally, the best way to determine the conditions where the reaction is controlled by the intrinsic kinetics is to obtain rate per unit catalyst surface area as a function of the stirrer speed. When the reaction is kinetically controlled, the rate will be independent of the stirrer speed. The intraparticle diffusional effects and flow uniformity (item 3, above) are determined by measuring the rates for various particle sizes and the catalyst volume, respectively. If the reaction rate per unit surface area is independent of stirrer speed, particle size, and catalyst volume, the measurements can be considered to be controlled by intrinsic kinetics. It is possible... 

The classic Thiele-Damkohler theory accounts for these effects, but is restricted to isothermal behavior and intraparticle mass transfer only by diffusion. If the reaction is highly exothermic and the particle is a poor heat conductor, the temperature in the particle center may rise above that in the contacting fluid and cause the overall rate to be higher than in the absence of heat- and mass-transfer limitations. Moreover, gas-phase reactions with change in mole number cause forced inward or outward convection that assists or counteracts reactant penetration into the particle and so enhances or depresses the rate. 

The particle is isothermal, i.e. flat intraparticle temperature profile, with the temperature difference between the pellet surface and the bulk fluid concentrated across the external heat transfer resistance. 

Heat transfer within catalyst particles occurs by conduction and an effective thermal conductivity /.g for the pellet is used with Fourier s law, to describe the intraparticle heat conduction. 

Particle Breakup, Inter- and Intraparticle Mass and Heat Transfer Resistance Models... 

The model reaction of p-xylene hydrogenation was chosen in order to provide the mild conditions of the experiments in both gas and capillary condensed phases, and to avoid the influence of side reaction and catalyst deactivation. The recycle type of gradientless reactor was used that provides uniform temperature and concentration profiles within all the catalyst packing. The catalyst particles (0.25-0.50 mm) provide a negligible intraparticle limitation of mass- and heat-transfer. 

Single particle models inter- and intraparticle mass and heat transfer... 

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. 

For heat transfer the relative importance of the internal and external resistances is reversed. For a gaseous system X,/Xy--10 -10 so it is evident from Eqs. 7.20 and 7.23 that at any reasonable Reynolds number (Bi) < 1.0, indicating that the external temperature gradient is much greater than the temperature gradient within the particle. The model of an isothermal particle in which all resistance to mass transfer is due to intraparticle diffusion while resistance tp heat transfer is confined to the external film thus emerges as a realistic representation for most conditions of practical importance. The validity of this approximation has been verified experimentally for a sin e isolated adsorbent particle. ... 

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