Kinetics lumping

K1NPTR Star.t-of-Cycle Kinetic Lumps (Index)... 

In this chapter the following topics will be reviewed KINPTR s start-of-cycle and deactivation kinetics, the overall program structure of KINPTR, the rationale for the kinetic lumping schemes, the model s accuracy, and examples of KINPTR use within Mobil. As an example, the detailed kinetics for the C6 hydrocarbons are provided. 

The same criteria were used for start-of-cycle and deactivation lumping. Start-of-cycle lumping was based on thermodynamics and molecular-reaction similarity. The deactivation kinetic lumps contain the start-of-cycle lumps as a subset. The additional deactivation lumps were required to properly describe the effect of carbon number on aging rate. 

Start-of-cycle kinetic lumps in KINPTR are summarized in Table V. A C5-light gas lump is required for mass balance. Thirteen hydrocarbon lumps are defined. The reforming kinetic behavior can be modeled without splitting the lumps into their individual isomers (e.g., isohexane and n-hexane). Also, the component distribution within the C5- lump can be described by simple correlations, as discussed later. The start-of-cycle reaction network that defines the interconversions between the 13 kinetic lumps is shown in Fig. 9. This reaction network results from kinetic studies on pure components and narrow boiling fractions of naphthas. It includes the basic reforming reactions... 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

Following the same arguments, the ring isomerization deactivation rate expression can be directly extended to include the effects of all kinetic lumps (defined in Table VII) ... 

While the 13 hydrocarbon lumps accurately represent the hydrocarbon conversion kinetics, they must be delumped for the deactivation kinetics. In addition, delumping is necessary to estimate many of the product properties and process conditions important to an effective reformer process model. These include H2 consumption, recycle gas H2 purity, and key reformate properties such as octane number and vapor pressure. The following three lump types had to be delumped the C5- kinetic lump into Cl to C5 light gas components, the paraffin kinetic lumps into isoparaffin and n-paraffin components, and the Cg+ kinetic lumps into Cg, C9, C10, and Cn components by molecular type. 

The paraffin isomer and Cg+ kinetic lumps are delumped in a more rigorous fashion than the C5-. Semikinetic delumping equations have been developed for both the Cg+ lumps and paraffin distribution (Table VIII). The paraffin distribution is constrained by known equilibrium. 

One has to be careful when using these global rate laws, as there may be more than one solution. The overall rate expression may provide some information on the kinetics however, individual parameters cannot be used separately to predict their effect on the rate. Kinetic lumping is another method that is often used by scientists to derive a simple rate formula avoiding the use of elementary reactions [85]. 

Li L, Crain N, Gloyna EF. Kinetic lumping applied to wastewater treatment. Water Environ Res 1996 68(5) 841-854. 

Pseudo-kinetic Lumped constituents models Molecular reactions schemes... 

Cicarelli, R, Astarita, G., and Gallifuoco, A., Continuous kinetic lumping of catalytic cracking processes. AIChE J. 38,1038 (1992). 

K. B. Bischoff, Some current issues in kinetic lumping of discrete mixtures, Chapter 9 in Chemical reactions in complex mixtures, A. V. Sapre and F. J. Krambeck, eds., Van Nostrand Reinhold, New York, 1990, ISBN 0442007256. 

The purpose of this chapter was to provide a broad-brush survey of available theoretical tools for the two t) es of kinetic lumping problems. The emphasis will be on the general concept. As such, literature citations are merely illustrative rather than comprehensive. And there are very few examples of applying these tools the reader should consult the original references for details. Throughout the chapter, scalars are denoted by italic letters, vectors by lower case boldface letters and matrices by capital boldface letters. 

Research on mathematical lumping has focused on constructing kinetic lumps and determining the conditions under which the lumped system can at least approximate the underlying unlumped system. In so doing, one often needs to impose some constraints. Take catalytic reforming as an example. Kinetically and analytically, it makes sense to lump iso and normal paraffins together, but these hydrocarbons have so different octane numbers that they should be separated. 

This traditional approach starts with a number of preselected, measurable kinetic lumps and determines the best reaction network and kinetics through experimental design and parameter estimation. The number of lumps depends on the level of detail desired. The lumps, satisfying the conservation law and stoichiometric constraints, are usually selected based on known chemistry, measurability and physicochemical properties (boiling range, solubility, etc.). 

The second step assumes that the reactivity of the ensemble is dominated by a few selected functionalities. The task then is to determine the reaction kinetics for each of the functional groups. Here the art of lumping applies in order to keep the number of kinetic lumps small. Information on reaction pathways and kinetics can be independently obtained from experiments using representative model compounds. For example, butyl benzene pyrolysis may serve as a model system for the pyrolysis of alkyl aromatics moieties in resids. 

The simplified fractionator includes a delumper model to convert the 21 kinetic lumps into >80 pure- and pseudo-components, which are then divided into user-specified boiling fractions. A non-linear distribution function generates ideal distillation curves with realistic fraction-to-fraction overlap. The fractionator can inter-convert distillation methods, so a user can calculate D-86, D-1160, D-2887, and/or TBP curves for gasoline and LCO. 

Table 3.4 Determination of the Number of Kinetic Lumps in Figure 3.6...

Suppose that there are n kinetic lumps that need to be added to the structure between I and B. as shown in Figure 3.6. The transfer function (Caughanowr and Koppel 1965) relating a change in the concentration of / to the corresponding change in B in terms of a Laplace transformation variable s is ... 

Here the quantity in the square brackets is included for better accuracy since A 100 and kzoo are known. The left hand side of Eq. 3.20 should match the right hand side if there is only one kinetic lump between I and B. In general, if there are n kinetic lumps (Akella and Lee 1981), one has ... 

It follows then that if the right hand side of Eq. 3.21 is evaluated for various n at different values of 5 and if a value of n is found that matches the left hand side, this n is the number of kinetic lumps that should be added to the kinetic structure. For the structure shown in Figure 3.4, one should find that = 1, leading to the structure in Figure 3.7. The same procedures can be followed to show that there are no kinetic lumps between B and C. The only question remaining is whether there is a direct reaction path between A1 and C. The transfer function relating / to C in terms of deviation variables is ... 

Kinetic analysis of the complex MTG reaction is somewhat simplified by the finding (Fig. 11) [2] that the methanol-DME-water equilibrium (dashed curves) is rapidly established and maintained along the initial segment of reaction path. Experimental data in Figure 11 demonstrate that this holds for pure methanol as well as pure DME feed. Thus OJQ genates can be treated as a single pseudospecies or kinetic "lump."... 

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