Lumped kinetics

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

Lee, L.S., Chen, T.W., Haunh, T.N., and Pan, W.Y. (1989) Four lump kinetic model for fluid catalytic cracking process. Canadian Journal of Chemical Engineering, 67, 615. 

Singh, J., Kumar, M.M., Saxena, A.K., and Kumar, S. (2005) Reaction pathways and product yields in mild thermal cracking of vacuum residues A multi-lump kinetic... 

The lumped kinetic model can be obtained with further simplifications from the lumped pore model. We now ignore the presence of the intraparticle pores in which the mobile phase is stagnant. Thus, p = 0 and the external porosity becomes identical to the total bed porosity e. The mobile phase velocity in this model is the linear mobile phase velocity rather than the interstitial velocity u = L/Iq. There is now a single mass balance equation that is written in the same form as Equation 10.8. 

In the lumped kinetic model, various kinetic equations may describe the relationship between the mobile phase and stationary phase concentrations. The transport-dispersive model, for instance, is a linear film driving force model in which a first-order kinetics is assumed in the following form ... 

Note that this kinetic equation is rather similar to Equation 10.15. The major difference between Equations 10.15 and 10.19 is that the general rate and the lumped pore models assume that adsorption takes place from the stagnant mobile phase within the pores, while the lumped kinetic model assumes that the mobile phase concentration is the same in the pores and between the particles. 

The connection of the overall mass transfer coefficient of the lumped kinetic and the parameters of the general rate model is... 

It follows that the lumped kinetics is of apparent order... 

The rate expression can be rearranged into the following form in terms of three lumped kinetic parameters, /[Pg.177]

These lumped kinetic parameters are defined by the following relationships ... 

A simple model of lumped kinetics for supercritical water oxidation included in the partial differential equations for temperature and organic concentrations allows to qualitatively simulate the dynamic process behavior in a tubular reactor. Process parameters can be estimated from measured operational data. By using an integrated environment for data acquisition, simulation and parameter estimation it seems possible to perform an online update of the process parameters needed for prediction of process behavior. 

These equations mean that a linear dependence of the reaction rate with light intensity (LVRPA) is observed when intensities are small, while square root dependence is observed when intensity is high. This latter dependence occurs for high intensities because the recombination of electron-hole pairs starts to limit the efficient use of the available photons (Alfano et al., 1997). The intensity at which the crossover between these two types of behavior occurs depends on the value of the lumped kinetic parameter 7, which in turn depends on the specific reaction under consideration. 

From a plausible reaction sequence in Table 1 and reliable approximations, a local expression for the reaction kinetics in terms of observable and independent variables has been obtained. a and are lumped kinetic parameters. 

In Equations (51)-(54), it must be noted that (i) e (x) = e [(x), Can] to recall that the LVRPA is a strong fimction of the catalyst loading and (ii) there are eight lumped kinetic parameters that depend on intrinsic properties of the system according to... 

Activation energies are derived from the dynamic mechanical experiments assuming that the kinetic mechanism does not change with temperature. The thus arrived at activation energy represents a lumped kinetic parameter for the reactions which have led to the point in time of the dynamics mechanical dispersion being measured. Activation energies for the first dispersion by DSA... 

Cao, G., Viola, A., Baratti, R., Morbidelli, M., Sanseverino, L., and Cruccu, M., Lumped kinetic model for propene-butene mixtures oligomerization on a supported phosphoric acid catalyst. Adv. Catal. 41,301 (1988). 

Ho, T. C., and White, B. S., Experimental and theoretical investigation of the validity of asymptotic lumped kinetics. AIChE J. Submitted for publication (1994). 

It is clear that modeling of the coke deposition is essential for a satisfactory description of FCC unit operation. It is not useful to describe this phenomena based on a simple power rate law. A more sophisticated model has to be derived in which the initial effects are accounted for. It is shown that coke deposition and catalyst activity have to be divided in an initial process (typically within 0.15 s) and a process at larger residence times. A simplified lumped kinetic model can be adequately used for this purpose, but a realistic coke formation model has to be developed. 

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