Chemical reactions models

E. Clement, P. Leroux-Hugon, L. M. Sander. Exact results for a chemical reaction model. Phys Rev Lett 67 1661-1664, 1991. 

We use computational solution of the steady Navier-Stokes equations in cylindrical coordinates to determine the optimal operating conditions.Fortunately in most CVD processes the active gases that lead to deposition are present in only trace amounts in a carrier gas. Since the active gases are present in such small amounts, their presence has a negligible effect on the flow of the carrier. Thus, for the purposes of determining the effects of buoyancy and confinement, the simulations can model the carrier gas alone (or with simplified chemical reaction models) - an enormous reduction in the problem size. This approach to CVD modeling has been used extensively by Jensen and his coworkers (cf. Houtman, et al.) ... 

The "two classes of chemical reactions model" represented by Equations 10 and 11 can be represented mathematically by the following ... 

Kramer, M. A., Kee, R. J., and Rabitz, H., CHEMSEN A computer Code for Sensitivity Analysis of Elementary Chemical Reaction Models. SAND82-8230, Sandia National Laboratories, Livermore, August, 1982a. 

As a third step, the relations between the various model components have to be specified in terms of mathematical expressions, once the model structure is fixed. In contrast to the common chemical reaction models which describe the reaction kinetics under laboratory conditions (e.g., in a test tube), environmental models usually contain two kinds of processes (1) the familiar reaction processes discussed in Parts II and III of this book, and (2) the transport processes. These processes are linked by the concept of mass balance. 

J.E. Broadwell and A.E. Lutz. A Turbulent Jet Chemical Reaction Model NO Production in Jet Flames. Combust. Flame, 114 319-335,1998. 

The knowledge of the two-minima energy surface is sufficient theoretically to determine the microscopic and static rate of reaction of a charge transfer in relation to a geometric variation of the molecule. In practice, the experimental study of the charge-transfer reactions in solution leads to a macroscopic reaction rate that characterizes the dynamics of the intramolecular motion of the solute molecule within the environment of the solvent molecules. Stochastic chemical reaction models restricted to the one-dimensional case are commonly used to establish the dynamical description. Therefore, it is of importance to recall (1) the fundamental properties of the stochastic processes under the Markov assumption that found the analysis of the unimolecular reaction dynamics and the Langevin-Fokker-Planck method, (2) the conditions of validity of the well-known Kramers results and their extension to the non-Markovian effects, and (3) the situation of a reaction in the absence of a potential barrier. 

Fig. 1. Data and biphasic chemical reaction model predictions of xylan conversion vs time for batch pretreatment of corn stover with only water at 160,180,200, and 220°C and 5% solids concentration.

Figure 2 Chemical reaction models for (a) isodesmic and (b) nucleated supramolecular assembly. 1 and K 2>1 are equilibrium constants for the elongation reactions, and Ka 1 and K a those for the conversion between assembly active and inactive forms of the monomer units. If /f aKa, then the nucleated assembly is self-catalyzed ( autosteric ) and if K a = Ka this is not so.

Rigorous Model with Chemical Reactions - Model Type V... 

Discussion of Results and Conclusions. The results of regression analysis show that a chemical reaction model, first order with respect to fractional carbon conversion, with a production and a decomposition step for each of CH4, C2H5, BTX and Oils, satisfactorily describes the dilute phase flash hydrogenation of both lignite and subbltumlnous coal. 

The kinetics of all these chemical processes must be modeled in the same way as typical chemical processes. Then, it has to be taken in mind that for a given chemical process the kinetic expression must be proposed separately taking into account the experimental performance of this process. However, in the general case, chemical reaction modeling can be performed assuming a second-order kinetic depending on the concentrations of the electrochemically formed species or mediator ( [5med]) and the pollutant ([5, ]), as shown in (4.26). In this equation is the kinetic constant... 

Table 2. In each case, it is found that the DSMC computations provide excellent agreement with the experimental data. However, it should be noted that these flow conditions gave chemically frozen flow. These comparisons indicate that the DSMC method is an accurate simulation method, but they do not aid in the assessment of chemical reaction models.

Chapter 2 deals with principles of chemical reaction modeling and gives some model forms for use in later chapters. A strong distinction is maintained between rates of reaction and of species production by defining reaction rates as frequencies of particular reaction events per unit reactor space. Various levels of reactor modeling are considered in Chapter 3 and implemented in Athena s samples of its solvers. 

Chemical reaction models play a major role in chemical engineering as tools for process analysis, design, and discovery. This chapter provides an introduction to structures of chemical reaction models and to ways of formulating and investigating them. Each notation in this chapter is defined when introduced. Chapter 3 gives a complementary introduction to chemical reactor models, including their physical and chemical aspects. 

A chemical reaction model consists of a list of chemical steps, each described by its stoichiometric equation and rate expression. The degree of detail included depends on the intended use of the model, the means available for solving it, and the range of phenomena to be described. Thus, the list of steps is always postulated and needs to be tested against experiments. 

M. Frenklach, Reduction of Chemical Reaction Models, in Numerical Approaches to Combustion Modelling, Prog. Astronaut, and Aeronaut. 135 (AIAA, Washington, 1990). 

F. Schlogl, Chemical reaction models for non-equilibrium phase transition. Z. Physik. 253, 147-161 (1972)... 

Finally, this study provides an extensive set of data on thick wood pyrolysis which can be better interpreted and generalized by the use of mathematical models taking into account the effects of transport phenomena and chemical reactions. Models including such features are already available in the literature (for instance, see References 23,24) and have proven to give quantitative predictions of temperature dynamics, but product yield predictions are still unacceptable, mainly because of unreliable kinetic constants. Therefore, this issue deserves further investigation before extensive computer simulation and/or development of more advanced physical models of thick wood pyrolysis are proposed. 

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