Lumped kinetic model

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). 

An analogous situation occurs in the catalytic cracking of mixed feed gas oils, where certain components of the feed are more difficult to crack (less reactive or more refractory) than the others. The heterogeneity in reactivities (in the form of Equations 3 and 5) makes kinetic modelling difficult. However, Kemp and Wojclechowskl (11) describe a technique which lumps the rate constants and concentrations into overall quantities and then, because of the effects of heterogeneity, account for the changes of these quantities with time, or extent of reaction. First a fractional activity is defined as... 

The very basis of the kinetic model is the reaction network, i.e. the stoichiometry of the system. Identification of the reaction network for complex systems may require extensive laboratory investigation. Although complex stoichiometric models, describing elementary steps in detail, are the most appropriate for kinetic modelling, the development of such models is time-consuming and may prove uneconomical. Moreover, in fine chemicals manufacture, very often some components cannot be analysed or not with sufficient accuracy. In most cases, only data for key reactants, major products and some by-products are available. Some components of the reaction mixture must be lumped into pseudocomponents, sometimes with an ill-defined chemical formula. Obviously, methods are needed that allow the development of simple... 

The following reaction system of industrial importance was studied a liquid reactant A simultaneously reacts with a liquid B and a gas G to give products R and S and by-products lumped as L. For proprietary reasons, the names of the species are not specified. The reaction is carried out in semibatch mode. The amounts of A, B, G, R, and S at the end of experiments leading to identification of the kinetic model were determined analytically while the amount of L was evaluated from the material balance. 

By lumping pseudo-components, we can formulate five three-component models of interest. Pseudo-components shown together in a circle are treated as one pseudo-component for the corresponding kinetic model. 

The first reaction vi (Gx. ATP) describes the upper part of glycolysis, converting one (external) molecule of glucose (Gx) into two molecules of triosephosphate (TP), using two molecules of ATP. The second reaction v2 (TP, ADP) describes the synthesis of two molecules ATP from each molecule of TP. The third reaction v3 (ATP) describes a (lumped) overall ATP utilization. To obtain a minimal kinetic model for the glycolytic pathway, we adopt rate function similar to [96], using... 

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. 

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. 

E. Ranzi, M. Dente, A. Goldaniga, G. Bozzano, and T. Faravelli. Lumping Procedures in Detailed Kinetic Modeling of Gasification, Pyrolysis, Partial Oxidation, and Combustion of Hydrocarbon Mixtures. Prog. Combust. Sci. Techn., 27 99-139, 2001. 

The most simple version of our model considers the two-phase nature of the fluidized beds in the reactor and in the regenerator in a simplified way. The kinetic model that we use considers three pseudocomponents in modeling type IV FCC units. This model is a consecutive-parallel model formed of three lumped components and coke as follows ... 

The chapter ends with a case study. Four different reduced kinetic models are derived from the detailed kinetic model of the phenol-formaldehyde reaction presented in the previous chapter, by lumping the components and the reactions. The best estimates of the relevant kinetic parameters (preexponential factors, activation energies, and heats of reaction) are computed by comparing those models with a wide set of simulated isothermal experimental data, obtained via the detailed model. Finally, the reduced models are validated and compared by using a different set of simulated nonisothermal data. 

In this section, the phenol-formaldehyde reactive system is considered as an example of identification of reduced kinetic models. The kinetic model containing 13 components and 89 reactions, developed in Sect. 2.4 to study the production of 1,3,5-methylolphenol, is too detailed and complex for control and monitoring purposes. Thus, in this section this model is referred to as detailed model, while four reduced kinetic models, based on lumped components and reactions, are developed. 

First, the detailed model is used to simulate the behavior of the real system, and a set of simulated isothermal experimental data is generated including the total heat released by reaction. Then, these data are used to estimate the kinetic parameters of the reduced models and the heats of reaction of the lumped reactions. Finally, the reduced kinetic models are tested in a validation procedure which simulates the operation of a batch reactor and allows one to identify the best reduced model. 

Two different reduced kinetic models have been considered, both involving four lumped chemical species and three and four lumped reactions, respectively. These models describe the time evolution of the following components ... 

Many working groups have modeled the performance of diesel particulate traps during the past few decades. Concentrated parameter models (CSTR assumption) have been applied for the evaluation of formal kinetic models and model parameters. The formal kinetic parameters lump the heat and mass transfer effects with the reaction kinetics of the complicated reaction network of diesel soot combustion. Those models and model parameters were used for the characterization of the performance of different filter geometries and filter materials, as well as of the performance of a variety of catalytically active coatings and fuel additives [58],... 

Figure 5. The Amoco Easy-Hard kinetic model for resid hydrotreating. The reaction products are characterized by seven distinct lumps, the three feedstock species which are shaded in gray (resid hard, resid easy, and gas oil) and the four new components which are not shaded (gas, naphtha, distillate, and gas oil). The kinetic interconversion of these groups is described by the 14 constants (3).

In this report, a kinetic model based on the solid film linear driving force assumption is used. Unlike the equilibrium-dispersive model, which lumps all transfer and kinetic effects into an effective dispersion term, the kinetic model is effective when the column efficiency is low and the effects of column kinetics are significant. 

Kinetic Model 2 (KM 2) lumped acids and CO2 production The kinetic model 1 considers only the oxidation of the major aromatic intermediates. As shown in the previous section, when most of the major intermediates have been depleted, there is still a substantial concentration of other remaining organic intermediates, as the TOC profile indicates. Therefore, it is of particular interest to calculate and predict the total mineralization times. Also, with TOC measurements, it is possible to approximate the amount of CO2 produced in the course of the reaction. In this new series-parallel model, the formation and disappearance of carboxylic acids as well as the production of CO2 has been incorporated. 

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). 

Recentlyr Schockaert and Proment [ref. 41] simulated the catalytic cracking of gasoil in both fluidized bed or riser reactors, connected with a fluidized bed regenerator. The kinetic model for the cracking was based upon the lO- lump loodel of Mobil [ ref 42 ]. Only one deactivation function was used for all the coking reactions and it was exponential in the coke content ... 

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