Chemical reactions Multicomponent

Though illustrated here by the Scott and Dullien flux relations, this is an example of a general principle which is often overlooked namely, an isobaric set of flux relations cannot, in general, be used to represent diffusion in the presence of chemical reactions. The reason for this is the existence of a relation between the species fluxes in isobaric systems (the Graham relation in the case of a binary mixture, or its extension (6.2) for multicomponent mixtures) which is inconsistent with the demands of stoichiometry. If the fluxes are to meet the constraints of stoichiometry, the pressure gradient must be left free to adjust itself accordingly. We shall return to this point in more detail in Chapter 11. 

Selectivity Selectivity is rarely a problem in molecular absorption spectrophotometry. In many cases it is possible to find a wavelength at which only the analyte absorbs or to use chemical reactions in a manner such that the analyte is the only species that absorbs at the chosen wavelength. When two or more species contribute to the measured absorbance, a multicomponent analysis is still possible, as shown in Example 10.6. 

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without compHcations isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and Hquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisotherma1 operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the stmcture and properties of a soHd phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particularly active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust control, industrial). Eor these kinds of appHcations psychrometric charts for systems other than air—water would be useful. The constmction of such has been considered (54). 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

Gibb s Phase Rule. The phase rule derived by W. J. Gibbs applies to multiphase equilibria in multicomponent systems, in the absence of chemical reactions. It is written as... 

The application of NMR to the study of chemical reactions has been expanded to a wide range of experimental conditions, including high pressure and temperatures. In 1993, Funahashi et al. [16] reported the construction of a high pressure 3H NMR probe for stopped-flow measurements at pressures <200 MPa. In the last decade, commercial flow NMR instrumentation and probes have been developed. Currently there are commercially available NMR probes for pressures of 0.1-35 MPa and temperatures of 270-350 K (Bruker) and 0.1-3.0 MPa and 270-400 K (Varian). As reported recently, such probes can be used to perform quantitative studies of complicated reacting multicomponent mixtures [17]. 

Here va and va are the stoichiometric coefficients for the reaction. The formulation is easily extended to treat a set of coupled chemical reactions. Reactive MPC dynamics again consists of free streaming and collisions, which take place at discrete times x. We partition the system into cells in order to carry out the reactive multiparticle collisions. The partition of the multicomponent system into collision cells is shown schematically in Fig. 7. In each cell, independently of the other cells, reactive and nonreactive collisions occur at times x. The nonreactive collisions can be carried out as described earlier for multi-component systems. The reactive collisions occur by birth-death stochastic rules. Such rules can be constructed to conserve mass, momentum, and energy. This is especially useful for coupling reactions to fluid flow. The reactive collision model can also be applied to far-from-equilibrium situations, where certain species are held fixed by constraints. In this case conservation laws... 

Because it is based on chemical reactions, the double layer model can be integrated into the equations describing the equilibrium state of a multicomponent system, as developed in Chapter 3. The basis appears as before (Table 3.1),... 

A similar approach was undertaken by Mah et al. (1976) in their attempt to organize the analysis of process data and to systematize the estimation and measurement correction problem. In this work, a simple graph-theoretic procedure for single component flow networks was developed. They then extended their treatment to multicomponent flow networks (Kretsovalis and Mah, 1987), and to generalized process networks, including bilinear energy balances and chemical reactions (Kretsovalis and Mah, 1988a,b). 

To calculate the multicomponent vapor-liquid equilibrium, equilibrium constants for chemical reactions 1-9 are taken from literature in comparison to the original publication, in the present work different numerical values for the second dissociations of hydrogen sulfide and sulfur dioxide were chosen (cf. Appendix III). Henry s constants are evaluated from single solute solubility data without neglecting Poynting corrections ... 

Vanni, M. and Baldi, G., 1991, Mass transfer and chemical reaction with multicomponent diffusion. Chem. Engng Sci. 46, 2465-2472. 

Yeh and Keeler 244) extended the method of laser-scattering spectroscopy to probe systems undergoing rapid chemical reactions. They observed the spectral line broadening in light from a singlemode He-Ne laser scattered from multicomponent solutions, as a function of time. The experiment employed a pressure-scanned Fabry-Perrot interferometer and photon counting techniques. 

For a multicomponent fluid (the only situation of interest with chemical reactions) we next have to solve mass balances for the individual chemical species. This has been implicitly the subject of this book until now. The species balance is written as flow in minus flow... 

P.I. Gold, Chemical species and chemical reactions of importance in nonequilibrium propellant performance calculations, NASA Accession No N66-33714, Rept No NASA-CR-65442, avail CFSTI, SciTechAerosp Rept 4 (19), 3722 (1966) CA 67, 4484 (1967) 47) S.S. Cherry L.J. van Nice, Pyrodynamics 6 (3-4), 275 (1969) CA 70, 98394 (1969) 48) R.E. Lo, Theoretical performance of the multicomponent rocket propellant system (oxygen, fluorine/ beryllium, lithium hydride)/hydrogen, Deutsche Versuchsanst Luft- und Raumfehri Rept11968, DLR-Mitt-68-21 (Ger), avail CFSTI, SciTech Aerosp Rept 7 (1), 161 (1969) CA 71,... 

When considering the mass continuity of an individual species in a multicomponent mixture, there can be, and typically is, diffusive transport across the control surfaces and the production or destruction of an individual species by volumetric chemical reaction. Despite the fact that individual species may be transported diffusively across a surface, there can be no net mass that is transported across a surface by diffusion alone. Moreover homogeneous chemical reaction cannot alter the net mass in a control volume. For these reasons the overall mass continuity need not consider the individual species. At the conclusion of this section it is shown that that the overall mass continuity equation can be derived by a summation of all the individual species continuity equations. 

A multicomponent mixture flows through a tube, which is selectively permeable for species A, which is one of the components in the mixture (Fig. 3.21). Assume steady flow. Assume that the flux of A out of the tube depends on the internal partial pressure of A, K. Futher, assume that the flow conditions are such that the system may be modeled as a plug flow, for which there are no radial gradients. Assume that there may be homogeneous chemical reaction, with the molar volumetric chemical-production rates given as m. ... 

Chemical Equilibrium. Although CVD is a nonequilibrium process controlled by chemical kinetics and transport phenomena, equilibrium analysis is usefiil in understanding the CVD process. The chemical reactions and phase equilibria determine the feasibility of a particular process and the final state attainable. Equilibrium computations with intentionally limited reactants can provide insights into reaction mechanisms, and equilibrium analysis can be used also to estimate the defect concentrations in the solid phase and the composition of multicomponent films. 

Hot-Wall Reactors. Because of the large mass diffusivities and nearly isothermal conditions (except for the entrance zone) in hot-wall, low-pressure reactors (50 Pa), multicomponent diffusion and chemical reactions are critical... 

Reactive absorption, distillation, and extraction have much in common. First of all, they involve at least one liquid phase, and therefore the properties of the liquid state become significant. Second, they occur in moving systems, thus the process hydrodynamics plays an important part. Third, these processes are based on the contact of at least two phases, and therefore the interfacial transport phenomena have to be considered. Further common features are multicomponent interactions of mixture components, a tricky interplay of mass transport and chemical reactions, and complex process chemistry and thermodynamics. 

Because of their multicomponent nature, RSPs are affected by a complex thermodynamic and difihisional coupling, which, in turn, is accompanied by simultaneous chemical reactions (57-59). To describe such phenomena adequately, specially developed mathematical models capable of taking into consideration column hydrodynamics, mass transfer resistances, and reaction kinetics are required. 

Suzuki I, Yagi H, Komatsu H, Hirata M. Calculation of multicomponent distillation accompanied by a chemical reaction. J Chem Eng Japan 1971 4 26-33. 

The mass balance equations of the traditional multicomponent rate-based model (see, e.g., Refs. 57 and 58) are written separately for each phase. In order to give a common description to all three considered RSPs (where it is possible, of course) we will use the notion of two contacting fluid phases. The first one is always the liquid phase, whereas the second fluid phase represents the gas phase for RA, the vapor phase for RD and the liquid phase for RE. Considering homogeneous chemical reactions taking place in the fluid phases, the steady-state balance equations should include the reaction source terms ... 

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... 

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