Multicomponent mixtures reactors

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. 

The two additional calibration gases required are typically a multicomponent mixture to accurately determine the relative sensitivities and a back-groimd gas for measuring the background signals at the various masses used in the analysis. As an example, consider the case of the reactor outlet gas from an ethylene oxide (EO) plant. Table 2 shows the components and their typical concentration levels, relative sensitivities, and fragmentation patterns. Note only a minimum set of masses has been considered for the analysis, i.e., the number of masses = the number of components = 8. 

The GAMMA-F code (Lim, 2014) has been developed by KAERI for system and safety analysis of VHTR. The code has the capabilities for multidimensional analyses of the fluid flow and heat conduction as well as the chemical reactions related to the air or steam ingress event in a multicomponent mixture system. As a system thermo-fluid and network simulation code, GAMMA-F includes a nonequilibrium porous media model for pebble-bed and prismatic reactor core, thermal radiation model, point reactor kinetics, and special component models such as pump, circulator, gas turbine, valves, and more. 

For non-ideal multicomponent mixtures the multiphase flow calculation can be combined with a more rigorous thermodynamic equilibrium calculation to determine the mixture properties at the interface as discussed by [60, 70, 98]. However, describing the chemical reactor performance under industrial operation conditions the heat balance is normally dominated by the heat of reaction term, the transport terms and the external heating/cooling boundary conditions, hence for chemical processes in which the phase change rates are relatively small the latent heat term is often neglected. 

Figure 3.1 provides a detailed flowsheet of the process and the notation used. The reaction occurs in a CSTR with molar holdup V. There are two fresh feedstreams Fqa and Fqb that contain pure reactants A and B, respectively, and a recycle stream Z>2 returns from a downstream distillation column. The reactor effluent contains a multicomponent mixture because complete one-pass conversion is not achieved. Two columns are needed to separate the two products from the intermediate-boiling reactants. The reactor effluent F with composition zj is fed into the first distillation column to separate product C from unreacted reactants A and B and heavy product D. Product C goes out in the distillate of the first colunm with the desired 95 mol% purity, and the other components go out in the bottoms, which is fed to the second column. This column produces a bottoms stream of D with the desired 95 mol% purity and a distillate of unreacted reactants A and B that is recycled back to the reactor with specific amounts of product impurities Xd2,c nd X/)2,d-... 

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). 

On its way downwards, the liquid phase is of course depleted with respect to its more volatile component(s) and enriched in its heavier component(s). At the decisive locus, however, where both phases have their final contact (i.e., the top of the column), the composition of the liquid is obviously stationary. For a desired composition of the gas mixture, the appropriate values for the liquid phase composition and the saturator temperature must be found. This is best done in two successive steps, viz. by phase equilibrium calculations followed by experimental refinement of the calculated values. The multicomponent saturator showed an excellent performance, both in a unit for atmospheric pressure [18] and in a high-pressure apparatus [19, 20] So far, the discussion of methods for generating well defined feed mixtures in flow-type units has been restricted to gaseous streams. As a rule, liquid feed streams are much easier to prepare, simply by premixing the reactants in a reservoir and conveying this mixture to the reactor by means of a pump with a pulsation-free characteristic. 

In reactive flow analysis the Pick s law for binary systems (2.285) is frequently used as an extremely simple attempt to approximate the multicomponent molecular mass fluxes. This method is based on the hypothesis that the pseudo-binary mass flux approximations are fairly accurate for solute gas species in the particular cases when one of the species in the gas is in excess and acts as a solvent. However, this approach is generally not recommend-able for chemical reactor analysis because reactive mixtures are normally not sufficiently dilute. Nevertheless, many industrial reactor systems can be characterized as convection dominated reactive flows thus the Pickian diffusion model predictions might still look acceptable at first, but this interpretation is usually false because in reality the diffusive fluxes are then neglectable compared to the convective fluxes. 

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