Start-of-cycle kinetics

The model includes fundamental hydrocarbon conversion kinetics developed on fresh catalysts (referred to as start-of-cycle kinetics) and also the fundamental relationships that modify the fresh-catalyst kinetics to account for the complex effects of catalyst aging (deactivation kinetics). The successful development of this model was accomplished by reducing the problem complexity. The key was to properly define lumped chemical species and a minimum number of chemical reaction pathways between these lumps. A thorough understanding of the chemistry, thermodynamics, and catalyst... 

The start-of-cycle kinetic problem was uncoupled from the deactivation kinetics by taking advantage of their widely different time constants. 

For the start-of-cycle kinetics, the following assumptions were made. 

The model followed single-site, nondissociative, Langmuir-Hinshelwood poisoning. This resulted in the same adsorption coefficients for deactivation and start-of-cycle kinetics. 

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... 

KINPTR Start-of-Cycle Kinetic Lumps (Index)... 

In order to solve the complete aging model, Eq. (37) must be solved with the start-of-cycle kinetic equations illustrated as follows ... 

Data used to develop the start-of-cycle kinetics consisted of over 300 material balances on several commercial catalysts of three types Pt/Al203, Pt-Re/Al203, and Pt-Ir/Al203. 

By following this multistep procedure, the kinetics were evaluated on a wide range of data (both conditions and feedstock) not used in the parameter estimation. The start-of-cycle kinetics were extended to other catalysts and catalyst states by defining an appropriate catalyst state vector (a = aD, al5 a , ac), which is different from 1 at the start of cycle. A catalyst characterization test was developed to estimate parameters for new catalysts. 

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 hydrocarbon lumps and reaction network for both the start-of-cycle and the deactivation kinetics were defined. 

An experimental design was developed which uncoupled the overall problem into a number of smaller parameter estimation problems. This approach reduced confounding between parameters, for both start-of-cycle and deactivation kinetics. 

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. 

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 ... 

To effectively determine the start-of-cycle reforming kinetics, a set of experimental isothermal data which covers a wide range of feed compositions and process conditions is needed. From these data, selectivity kinetics can be determined from Eq. (12). With the selectivity kinetics known, Eqs. (17) and (18a)-(18c) are used to determine the activity parameters. It is important to emphasize that the original definition of pseudomonomolecular kinetics allowed the transformation of a highly nonlinear problem [Eq. (5)] into two linear problems [Eqs. (12) and (15)]. Not only are the linear problems easier to solve, the results are more accurate since confounding between kinetic parameters is reduced. 

The elements of range in value from 0 to 1 and are the ratio of the reformer kinetic constants at time on stream t to the values at start of cycle. At any time on stream t, the deactivation rate constant matrix K(a) is determined by modifying the start-of-cycle K with a. From the catalytic chemistry, it is known that each reaction class—dehydrogenation, isomerization, ring closure, and cracking—takes place on a different combination of metal and acid sites (see Section II). As the catalyst ages, the catalytic sites deactivate at... 

The start-of-cycle rate constant for ring isomerization X° is modified to include deactivation by multiplying its kinetic equations by a, ... 

The matrix K(a) is the start-of-cycle matrix K at t = 0, appropriately modified by the a s. Equation (40) represents the complete reformer model kinetic expressions. 

The expanded set of 34 lumps necessary to define the reforming process is shown in Table VIII. Note that this 34-lump set is sufficient for both start-of-cycle and aging kinetics. 

The deactivation kinetics were determined through a series of seven separate parameter estimation problems. As with the start-of-cycle case, separate estimating problems resulted from uncoupling the reactions of each carbon number by properly selecting the charge stock. This allowed the independent determination of submatrices in the rate constant matrix Dp [Eq. (37)]. 

The start-of-cycle (fresh catalyst) kinetics for a pseudo-monomolecular reforming reaction system may be determined In two steps (IJ ... 

Predictions of reforming catalyst activity, such as the reactor inlet temperature (RIT) required to make a specific octane, are determined by the activity kinetics. In the monitoring of Mobil s commercial reformers, inlet temperatures are continually compared to model predicted start-of-cycle (SOC) RlT s to assess commercial catalyst SOC activity and catalyst activity loss over a reformer cycle. Accurate predictions of activity cure therefore essential. 

Most catalytic cycles are characterized by the fact that, prior to the rate-determining step [18], intermediates are coupled by equilibria in the catalytic cycle. For that reason Michaelis-Menten kinetics, which originally were published in the field of enzyme catalysis at the start of the last century, are of fundamental importance for homogeneous catalysis. As shown in the reaction sequence of Scheme 10.1, the active catalyst first reacts with the substrate in a pre-equilibrium to give the catalyst-substrate complex [20]. In the rate-determining step, this complex finally reacts to form the product, releasing the catalyst... 

These were lumped Into a much smaller number of pseudo components identified by carbon number and chemical nature. The lumps vary with the age of the catalyst. The table shows the 13 lumps adopted for the "start of kinetic cycle". The kinetic characteristics of these lumps are proprietary data. 

The fast stage of relaxation of a complex reaction network could be described as mass transfer from nodes to correspondent attractors of auxiliary dynamical system and mass distribution in the attractors. After that, a slower process of mass redistribution between attractors should play a more important role. To study the next stage of relaxation, we should glue cycles of the first auxiliary system (each cycle transforms into a point), define constants of the first derivative network on this new set of nodes, construct for this new network an (first) auxiliary discrete dynamical system, etc. The process terminates when we get a discrete dynamical system with one attractor. Then the inverse process of cycle restoration and cutting starts. As a result, we create an explicit description of the relaxation process in the reaction network, find estimates of eigenvalues and eigenvectors for the kinetic equation, and provide full analysis of steady states for systems with well-separated constants. 

We start our analysis of the TCA cycle kinetics by examining the predicted steady state production of NADH as a function of the NAD and ADP concentrations. From Equation (6.31) we see that there can be no net flux through the TCA cycle when concentration of either NAD or ADP, which serve as substrates for reactions in the cycle, is zero. Thus when the ratios [ATP]/[ADP] and [NADH]/[NAD] are high, we expect the TCA cycle reaction fluxes to be inhibited by simple mass action. In addition, the allosteric inhibition of several enzymes (for example inhibition of pyruvate dehydrogenase by NADH and ACCOA) has important effects. 

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