Intraphase gradient

Figure 7.13 Differential and overall selectivities in an isothermal Type III reaction with both interphase and intraphase gradients. [After J.J. Carberry, Chem. Eng. Sci., 17, 675, with permission of Pergamon Press, Ltd., London, England, (1962).]...

What particle dimension would be required in the case of problem 17 to eliminate the net effects of inter- and intraphase gradients ... 

This observation is very important because kinetic studies should de carried out preferably in upflow system in order to avoid mass transfer limitations (interphase). Of course, additional experiments have to be performed to study intraphase gradients consists of determining the conversion for particles of different size at constant space velocity [4]. If conversion is constant indicates that the system is imder chemical kinetic control. 

Figure6.18.17 Interphase and intraphase gradients of NO (cNo/< No,g) under the reaction conditions at the entrance of the channel ofthe monolith (i.e., for zero conversion of NO) the concentration gradient in the bulk phase is only given schematically ( /waii= 1 mm).

As noted earlier, previous theoretical studies (7-8) have shown that the selectivity to ethylene oxide is maximized, when the active material is located at the external surface of the pellet. This behavior results primarily from the fact that the main undesired reaction 2 has a higher activation energy than the desired one. Therefore, intraphase temperature gradients are detrimental to the selectivity. Indeed, in Figure 2, where results for Type 1 pellets are presented, it is shown that for all the temperatures studied, selectivity decreases when the active layer is located deeper inside the pellet. This behavior was observed for all the inlet ethylene concentrations investigated. 

Criteria have also been developed for evaluating the importance of intraphase and interphase heat transfer on a catalytic reaction. The Anderson criterion for estimating the significance of intraphase temperature gradients is [J. B. Anderson, Chem. Eng. Sci., 18 (1963) 147] ... 

To this point we have dealt only with transport effects within the porous catalyst matrix (intraphase), and the mathematics have been worked out for boundary conditions that specify concentration and temperature at the catalyst surface. In actual fact, external boundaries often exist that offer resistance to heat and mass transport, as shown in Figure 7.1, and the surface conditions of temperature and concentration may differ substantially from those measured in the bulk fluid. Indeed, if internal gradients of temperature exist, interphase gradients in the boundary layer must also exist because of the relative values of the pertinent thermal conductivities [J.J. Carberry, Ind. Eng. Chem., 55(10), 40 (1966)]. 

Since the major thermal resistances in nonisothermal reaction systems are encountered in the boundary layer, while the major mass transfer resistances occur within the particle, we can entertain some simplification of the overall effectiveness factor problem we have been considering. This simplified model envisions interphase temperature gradients and intraphase concentration gradients only. For this case... 

As outlined in the section Effects of the Operating Variables, the approach to design and analysis of monolith SCR reactors customarily adopted in the technical literature has been based on simple pseudo-homogeneous models accovmt-ing only for axial concentration gradients. The effects of inter- and intraphase mass transfer limitations were lumped into effective pseudo-first-order rate constants, such as in equation 14, which were specific for each type of catalyst. Such constants actually varied not only with temperature, but included dependences on the gas flow velocity, on the monolith channel geometry, and on the catalyst pore structure as well. 

Butt JB, Downing DM, Lee JW. Inter-intraphase temperature gradients in fresh and deactivated catalyst particles. Industrial Engineering Chemistry Fundamentals 1977 16(2) 270-272. 

External gradients were experimentally eliminated by increasing the recycle ratio until the characteristic "jump" temperatures were no longer affected. Extensive calculations of interphase and intraphase heat and mass transfer also indicate the absence of gradients. 

A tentative answer to this question may be sought from characteristic parameters, namely the reaction time tR an intraphase mass transfer time tj) = 1 / Z) or 16/<0 where 1 = 1/a is the reciprocal of the specific interfacial area of the dispersion, the diffusivity and 6 the equivalent diffu-sional film thickness the heat transfer time tj = 1 /a or 16/a where a is the heat diffusivity the adiabatic temperature rise J = (- AH)Cq/pCp. From these parameters the following criteria may be tentatively proposed, Local concentration and temperature gradients are negligible and the pseudo-homogeneous assumption is valid if... 

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