Multicomponent mixtures kinetics

Vynckier, E., and Froment, G. F., Modeling of the kinetics of complex processes based upon elementary steps , in Kinetic and Thermodynamic Lumping of Multicomponent Mixtures (G. Astaiita and S. I. Sandler, Eds.) Elsevier, Amsterdam (1991) 131-161. 

Astarita, G. and Sandler, S.I. (Eds.), 1991, Proc. ACS Symposium on Kinetic and Themodynamic Lumping of Multicomponent Mixtures, Elsevier, Amsterdam. 

Raffaella Ocone and Gianni Astarita, Kinetics and Thermodynamics in Multicomponent Mixtures... 

Astarita G, Sandler SI. Kinetic and Thermodynamic Lumping of Multicomponent Mixtures. Amsterdam Elsevier, 1991. 

Raffaella Ocone and Gianni Astarita, Kinetics and Thermodynamics in Multicomponent Mixtures Arvind Varma, Alexander S. Rogachev, Alexandra S. Mukasyan, and Stephen Hwang, Combustion Synthesis of Advanced Materials Principles and Applications J. A. M. Kuipers and W. P. Mo, van Swaaij, Computional Fluid Dynamics Applied to Chemical Reaction Engineering... 

Nigam, A., M. Neurock, and M.T. Klein, Reconcilliationof Molecular Detail and Lumping An Asphaltene Thermolysis Example, in Kinetic and Thermodynamic Lumping of Multicomponent Mixtures. G. Astarita and S.I. Sandler, eds., Elsevier Science Publishers B.V., 1991. 

For binary and multicomponent mixtures of gases the viscosity coefficient depends on the concentrations, and the results of the accurate kinetic theory are quite complicated. In terms of the viscosities of the pure of the pure components at the same pressure and temperature, //,, a useful empirical formula is [5], [9]. 

The appropriate generalization of equation (33) to arbitrary geometries in multicomponent mixtures can be shown from kinetic theory [5] or from a reasonable continuum treatment to be... 

For binary and multicomponent mixtures, the thermal conductivity depends on the concentrations as well as on temperature, and the formulas of the accurate kinetic theory are quite complicated [5]. Empirical expressions for X are therefore more useful for both binary [9] and ternary [6], [26] mixtures, although few data exist for ternary mixtures. Tabulations of available experimental and theoretical results for thermal conductivities may be found in [5], [6], [13], and [18]-[21], for example. The thermal diffusivity, defined as 2p/Cp, often arises in combustion problems its pressure and temperature dependences in gases are XjpCp T7p ( < a < 2), and its typical values in combustion lie between 10 cm /s and 1 cm s at atmospheric pressure. 

In principle, mixtures containing a very large number of components behave in a way described by the same general laws that regulate the behavior of mixtures containing only a comparatively small number of components. In practice, however, the procedures for the description of the thermodynamic and kinetic behavior of mixtures that are usually adopted for mixtures of a few components rapidly become cumbersome in the extreme as the number of components grows. As a result, alternate procedures have been developed for multicomponent mixtures. Particularly in the field of kinetics, and to a lesser extent in the field of phase equilibria thermodynamics, there has been a flurry of activity in the last several years, which has resulted in a variety of new results. This article attempts to give a reasoned review of the whole area, with particular emphasis on recent developments. 

In this section, we attack the problem of kinetics in multicomponent mixtures, and we dedicate attention mostly to the case where one is only interested in, or may only be able to determine experimentally, some overall concentration of species of a certain class, such as sulfurated compounds in an oil cut during a hydrodesulfurization process. The presentation is given in terms of a continuous description special cases of the corresponding discrete description are discussed as the need arises. Instead of working with the masses of individual species, we will work with their mass concentration distribution c x). In the case of a batch reactor, the distinction is irrelevant, but in the case of a plug flow reactor the concentration-based description is clearly preferable. The discussion is presented in purely kinetic terms for, say, a batch reactor. 

In this section, we still restrict ourselves to the consideration of systems where only the overall behavior is of interest, but we extend the analysis to actual chemical reactors. Indeed, the discussion in the previous section was limited to the overall kinetics of multicomponent mixtures seen from the viewpoint of chemical reaction engineering, the discussion was in essence limited to the behavior in isothermal batch reactors, or, equivalently, in isothermal plug flow reactors. In this section, we present a discussion of reactors other than these two equivalent basic ones. The fundamental problem in this area is concisely discussed next for a very simple example. 

Aris (1991a), in addition to the case of M CSTRs in series, has also analyzed two other homotopies the plug flow reactor with recycle ratio R, and a PFR with axial diffusivity and Peclet number P, but only for first-order intrinsic kinetics. The values M = 1(< ), R = >(0), and P = 0( o) yield the CSTR (PFR). The M CSTRs in series were discussed earlier in Section IV,C,1. The solutions are expressed in terms of the Lerch function for the PFR with recycle, and in terms of the Niemand function for the PFR with dispersion. The latter case is the only one that has been attacked for the case of nonlinear intrinsic kinetics, as discussed below in Section IV,C,7,b. Guida et al. (1994a) have recently discussed a different homotopy, which is in some sense a basically different one no work has been done on multicomponent mixture systems in such a homotopy. 

Alberty, R. A., Kinetics and equilibrium of the polymerization of benzene series aromatic hydrocarbons in a flame. In Kinetic and Thermodynamic Lumping of Multicomponent Mixtures. (As-tarita, G., and Sandler, R. I., eds.), Elsevier, Amsterdam, 1991, p. 277. 

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