Kinetic and Transport Model

Suppose now that a pilot-plant or full-scale reactor has been built and operated. How can its performance be used to confirm the kinetic and transport models and to improve future designs Reactor analysis begins with an operating reactor and seeks to understand several interrelated aspects of actual performance kinetics, flow patterns, mixing, mass transfer, and heat transfer. This chapter is concerned with the analysis of flow and mixing processes and their interactions with kinetics. It uses residence time theory as the major tool for the analysis. 

In this chapter, we will review the fundamental models that we developed to predict cathode carbon-support corrosion induced by local H2 starvation and start-stop in a PEM fuel cell, and show how we used them to understand experiments and provide guidelines for developing strategies to mitigate carbon corrosion. We will discuss the kinetic model,12 coupled kinetic and transport model,14 and pseudo-capacitance model15 sequentially in the three sections that follow. Given the measured electrode kinetics for the electrochemical reactions appearing in Fig. 1, we will describe a model, compare the model results with available experimental data, and then present... 

COUPLED KINETIC AND TRANSPORT MODEL 3.1. Model Description... 

We use the coupled kinetic and transport model to predict when local H2 starvation occurs and how it affects carbon corrosion rate. 

The two-dimensional, coupled kinetic and transport model can also be used to simulate start-stop processes. Figure 14 plots cathode potential and carbon corrosion current distribution at three instants when the H2/02 front passes through 10, 50, and 90% of anode flow path during the start process. As H2 displaces air in the anode flow-field, the size of the power source increases and the load size decreases accordingly. The balanced current density becomes larger, causing higher carbon corrosion current density. 

The pseudo-capacitive effect can be incorporated in the coupled kinetic and transport model through Eqs. (19) and (20). Here we choose to illustrate the effect through the kinetic model for simplicity. With considering the pseudo-capacitive current density, the kinetic model becomes... 

Heterogeneous reaction systems are modelled by detailed chemical kinetics and transport models and numerically simulated for two simple configurations, an cataJytically active wire and disk. As special case for the latter configuration, chemical vapour deposition of diamond is simulated. Elementary reaction mechanisms are applied in the gas phase and on the surface, and the coupling of the catalytic surface with the surrounding reactive fiow is accounted for by a detailed transport model. 

The experimentalist often formulates a mathematical model in order to describe the observed behavior. In general, the model consists of a set of equations based on the principles of chemistry, physics, thermodynamics, kinetics and transport phenomena and attempts to predict the variables, y, that are being measured. In general, the measured variables y are a function of x. Thus, the model has the following form... 

Wilkinson, K. J. and Buffle, J. (2004). Critical evaluation of physicochemical parameters and processes for modelling the biological uptake of trace metals in environmental (aquatic) systems. In Physio chemical Kinetics and Transport at Biointerfaces, eds. van Leeuwen, H. P. and Koster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley Sons, Ltd, Chichester, UK, pp. 445-533. 

The model framework for describing the void problem is schematically shown in Figure 6.3. It is, of course, a part of the complete description of the entire processing sequence and, as such, depends on the same material properties and process parameters. It is therefore intimately tied to both kinetics and viscosity models, of which there are many [3]. It is convenient to consider three phases of the void model void formation and stability at equilibrium, void growth or dissolution via diffusion, and void transport. 

Many thermodynamic, chemical kinetic, and transport quantities are needed in the description of a chemically reacting flow, and for constructing numerical simulations. The required molecular parameters must be accumulated before we are able to model a particular chemical system. In the ideal world we would be able to find all such information from tabulated values in the literature. However, in reacting flow problems of real interest there are often gaps in the available chemical and transport data that have to be filled in with the aid of theory. 

Since around the mid-1990s, there has been a proliferation of hydrate time-dependent studies. These include macroscopic, mesoscopic, and molecular-level measurements and modeling efforts. A proliferation of kinetic measurements marks the maturing of hydrates as a field of research. Typically, research efforts begin with the consideration of time-independent thermodynamic equilibrium properties due to relative ease of measurement. As an area matures and phase equilibrium thermodynamics becomes better defined, research generally turns to time-dependent measurements such as kinetics and transport properties. 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

A fourth type of rate law, transport with apparent rate law, is a form of apparent rate law that includes transport processes. This type of rate-law determination is ubiquitous in the modeling literature (Cho, 1971 Rao et al., 1976 Selim et al., 1976a Lin et al., 1983). Kinetic-based transport models are more fully described in Chapter 9. With these rate laws, transport-controlled kinetics are emphasized more and chemical kinetics... 

Bahr BA, Clarkson ED, Rogers GA, Noremberg K, Parsons SM (1992) A kinetic and allosteric model for the acetylcholine transporter-vesamicol receptor in synaptic vesicles. Biochemistry 31 5752-5762. 

A model for transient simulation of radial and axial composition and temperature profiles In pressurized dry ash and slagging moving bed gasifiers Is described. The model Is based on mass and energy balances, thermodynamics, and kinetic and transport rate processes. Particle and gas temperatures are taken to be equal. Computation Is done using orthogonal collocation In the radial variable and exponential collocation In time, with numerical Integration In the axial direction. 

Unlike groundwater flow and transport models, thermodynamic models, in principal, do not need any calibration. However, considering surface-controlled or kinetically controlled reaction models might be subject to calibration. 

Chemical vapor deposition and heterogeneous catalysis share many kinetic and transport features, but CVD reactor design lags the corresponding catalytic reactor analysis both in level of sophistication and in scope. In the following we review the state of CVD reactor modelling and demonstrate how catalytic reactor design concepts may be applied to CVD processes. This is illustrated with an example where fixed bed reactor concepts are used to describe a commercial "multiple-wafers-in-tube" low pressure CVD reactor. 

Overall, geochemical computer models can be extremely useful in the description of chemical equilibria occurring in the aquatic environment. In some cases, predictions about reaction kinetics and transport of species can also be made. The application of geochemical models is not limited to natural aquatic systems but has been usefully extended to predict the eflfectiveness of certain remediation strategies in the treatment of waters emanating from contaminated sites." ... 

These equations have further been coupled to the kinetics and transport relationships associated with the heterogeneous and homogeneous reactions of coal gasification. This coupled system of equations provides the theoretical basis of our computer model of coal gasification reactors. 

As the kinetic and transport limitations of the process are modelled by the interlink of the reaction zones, the zones themselves can be treated assuming thermochemical equilibrium. Although derived with regard to the decarburisation reaction, the present model is also valid for other chemical components with similar behaviour present in hot metal and slag. Processes determined by other kinetic phenomena, such as the melting of scrap and the dissolution of lime, need to be modelled separately. 

The fundamental concepts used to mathematically represent mechanistic mathematical models are borrowed from chemical reaction kinetics and transport phenomena.1920 However, the application of these concepts in biology requires an understanding of the biological literature. The biological data to build a mechanistic model of mAh action typically include... 

The key interplay of reaction kinetics and transport phenomena in a catalytic combustor must be treated using rigorous reactor models. In the next section, we use a simple model to describe the behavior of a catalytic combustor and to interpret the technology breakthroughs that led to the successful implementation of catalytic combustion to reduce NO in power generation. The model will be kept simple, even though its additional complexities are readily incorporated, because our purpose is to show the main characteristics of a catalytic combustor rather than to provide accurate simulations of expected performance. 

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