Kinetic model parameterization

Overall, catalytic processes in industry are more commonly described by simple power rate law kinetics, as discussed in Chapter 2. However, power rate laws are simply a parameterization of experimental data and provide little insight into the underlying processes. A micro-kinetic model may be less accurate as a description, but it enables the researcher to focus on those steps in the reaction that are critical for process optimization. 

Hinrichsen, Muhler, and co workers—micro kinetic analysis parameterized by redox model. Hinrichsen et al.317 investigated the elementary steps by micro kinetic analysis by applying temperature and concentration-programmed experiments over Cu/Zn0/Al203, and modeling the data with the simplified redox mechanism in the spirit of Ovesen, Topsoe, and coworkers.303 This included 3 steps (1) dissociative adsorption of H2 on Cu metallic surface (2) dissociative adsorption of H20 leading to an adsorbed H2 molecule and an O adatom and a reduction step by CO to form gas phase C02 and a free active site (see Scheme 71). 

The development and application of a rigorous model for a chemically reactive system typically involves four steps (1) development of a thermodynamic model to describe the physical and chemical equilibrium (2) adoption and use of a modeling framework to describe the mass transfer and chemical reactions (3) parameterization of the mass-transfer and kinetic models based upon laboratory, pilot-plant, or commercial-plant data and (4) use of the integrated model to optimize the process and perform equipment design. 

Parameterization of Mass-Transfer and Kinetic Models The mass-transfer and chemical kinetic rates required in the rigorous model are typically obtained from the literature, but must be carefully evaluated and fine-tuning through pilot-plant and commercial data is highly recommended. 

The second method relies on the experimental determination of the kinetic parameters using techniques from biophysics or enzymology. Also in this case problems exist (1) the kinetic parameters are often determined under conditions different from the conditions in the cytoplasm (2) an enormous number of experiments need to be done, even for a network of moderate size, to determine all kinetic parameters experimentally. When the second method is used to parameterize a kinetic model then the resulting model is considered a silicon cell model. A number of silicon cell models exist [25-27, 29, 75-77]. 

Since the thermodynamic properties of the reactants and products are known, it is essential to ensure that the kinetic model is constructed so that it is consistent with these properties. Depending on how the model is parameterized (e.g., in terms of /c,, 0r and Ki eq, in terms of kl JCV and Ki eq, or in terms of kuOI and A-,.rcv), one of the previous equations of thermodynamic consistency must be used for each linear combination of steps that leads to an overall stoichiometric reaction. 

A. Parameterization of the Kinetic Model in Terms of Transition States... 

The previous two cases illustrate situations in which a specific reactant proceeds to a single specific product. More commonly, many products are formed. Accordingly, it is desired to develop quantitative kinetic models that incorporate the necessary elementary reaction pathways to account for the observed products. Furthermore, it is desired to parameterize the elementary steps so that these steps may be applied to related reaction systems under similar conditions. 

The next step in the reaction kinetics analysis is to choose for each family of reactions (i.e., adsorption/desorption, oligomerization//-) -scission, isomerization, and hydride transfer) whether to parameterize the kinetic model in terms of either the forward or the reverse rate constant (kj,for or khrey) since the ratio of the forward and the reverse rate constants must equal the known value of Kit q ... 

The rate constants for isomerization steps are similar in the forward and the reverse directions. For convenience, we choose to parameterize the kinetic model in terms of the forward rate constants. In this respect, we use the concept of single-event rate coefficients developed by Froment (127). According to Froment, the rate constant for a particular step is obtained by multiplying a single-event rate coefficient by the number of single events, ne, possible for the reactant. The expression for ne is... 

In summary, we have parameterized our kinetic model for isobutane conversion (containing 312 steps, 78 olefins, 73 paraffins, and 74 surface species) in terms of the following 19 parameters AH, au, Ehx, E, EmilJh, EmUCUx Ep,ss, Eptst, Ep, Tiso.b / -iso.nb, Ec3, Eq, Eq, Eq+, ASq, ASq, ASg, and ASq. Not all of these parameters will be kinetically significant in the final reaction kinetics analysis. 

No prediction of cell potential evolution and MEA durabihty. The kinetic models use to represent steady-state regimes with time-independent local operating conditions (e.g. local water content within the CL assumption of liquid water fully-saturated CL) and they show for instance poor predictive capability. One reason is that many of these models are parameterized by using ex situ experiments which are not representative enough of real operating conditions (e.g. potential holding between 1.2 and 1.6 V in [202]). Another reason is that... 

The methodology to answering these parameter estimation and set-based questions relies on different mathematical approaches. In principle, the parameter identification of chemical kinetic models can be posed as classical statistical inference [17,19-21] given a mathematical model and a set of experimental observations for the model responses, determine the best-fit parameter values, usually those that produce the smallest deviations of the model predictions from the measurements. The validity of the model and the identification of outliers are then determined using analysis of variance. The general optimizations are computationally intensive even for well-behaved, well-parameterized algebraic functions. Further complications arise from the highly ill-structured character... 

Eidsvik (1980) proposed an entrainment model where the combined effect of mechanical and convective turbulence production was expressed by the turbulence kinetic energy parameterized by e = i.lul + 0.5w2... 

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