Intraparticle gradient effects reactions

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

For working in absence of intraparticle gradients the criterium generally utilised is to decrease the catalyst particle size until no effect in the rate of reaction is obtained. 

The presence of pores, for which the observed reaction rate is lower than the kineti-cally controlled intrinsic one, in the particles or pellets affects the reaction rate due to diffusion limitations. This intraparticle diffusion effect causes a concentration gradient within the pores. If diffusion is fast, then the concentration gradient is negligible. 

The effect of intraparticle gradients was assumed to have been included in the estimated parameters, i.e. the reaction rates at the whole catalyst particle was calculated with the surface conditions. The intr article gradients were not calculated, because a commercial FCC catalyst was used in the experiments. The bulk gas temperature was assumed to remain constant along the reactor length due to the surrounding heating oven. 

The effective reaction rate tm eff (related to the mass of catalyst/solid) already considers all extra- and intraparticle mass and heat transfer effects (Sections 4.5-4.7). Thus the pseudo-homogeneous model does not distinguish between the conditions in the fluid and in the sohd phase, as more sophisticated heterogeneous models do, as discussed, for example, in Baerns ef al. (2006), Froment and Bischoff (1990), and Westerterp, van Swaaij, and Beenackers (1998). Thus, gradients of temperature and concentration within the particle and in the thermal and diffusive boundary layers are combined by the use of an overall effectiveness factor that enables the system of four equations (mass and heat balances for solid and fluid phase) to be replaced by just two equations, Eqs. (4.10.125) and (4.10.126). 

Table 2 lists most of the available experimental criteria for intraparticle heat and mass transfer. These criteria apply to single reactions only, where it is additionally supposed that the kinetics may be described by a simple nth order power rate law. The most general of the criteria, 5 and 8 in Table 2, ensure the absence of any net effects (combined) of intraparticle temperature and concentration gradients on the observable reaction rate. However, these criteria do not guarantee that this may not be due to a compensation of heat and mass transfer effects (this point has been discussed in the previous section). In fact, this happens when y/J n [12]. 

Another aspect concerns catalyst particles with intraparticle temperature gradients. In general the temperature inside a catalyst pellet will not be uniform, due to the heat effects of the reaction occurring inside the catalyst pellet. The temperature inside the catalyst can be related to the concentration with (see for example [4]) ... 

Volume changes due to the reaction may become considerable. This may lead to intraparticle pressure gradients, which will influence the effectiveness factor because ... 

Many complex situations have not been addressed, such as simultaneous intraparticle temperature and pressure gradients and nondiluted gases with anisotropic catalyst pellets. Calculations for these and other complex situations proceed along the same line as demonstrated for bimolecular reactions and nondiluted gases. A framework that can be used to investigate the effect of complex situations on the effectiveness factor is given. Also presented are criteria that can be used for a quick estimate as to whether or not certain phenomena are important. 

The intraparticle temperature gradients result in an increase in the effectiveness factor. This is obvious since the reaction is strongly exothermic. The increase, however, is only 2 % relative. Thus in this case intraparticle temperature gradients can be neglected. 

For a BSR built up of cylindrical catalyst rods (i.e., infinitely long catalyst cylinders), the boundary condition of Eq. (14) will result in circumferential variation of both the mass flux and the surface concentration. Because of the varying surface concentration, the concentration profile in the rod will not be axisymmetric, which will influence the effectiveness factor of the rod. Fortunately, the influence can be expected to be limited. This is because the strongest (relative to the flux) circumferential variations of the surface concentration are obtained for the boundary condition of constant flux, but this boundary condition corresponds to a relatively low reaction rate, which will usually correspond to small intraparticle concentration gradients. 

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. 

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