Distribution function reaction time, mixing

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

Mixing Models. The assumption of perfect or micro-mixing is frequently made for continuous stirred tank reactors and the ensuing reactor model used for design and optimization studies. For well-agitated reactors with moderate reaction rates and for reaction media which are not too viscous, this model is often justified. Micro-mixed reactors are characterized by uniform concentrations throughout the reactor and an exponential residence time distribution function. 

Volume changes also can be mechanically determined, as in the combustion cycle of a piston engine. If V=V(i) is an explicit function of time. Equations like (2.32) are then variable-separable and are relatively easy to integrate, either alone or simultaneously with other component balances. Note, however, that reaction rates can become dependent on pressure under extreme conditions. See Problem 5.4. Also, the results will not really apply to car engines since mixing of air and fuel is relatively slow, flame propagation is important, and the spatial distribution of the reaction must be considered. The cylinder head is not perfectly mixed. 

Figure 10-7 shows the concentrations of R and S and the product distribution Xs as a function of time for the feed location just above the impeller. The values are normalized with respect to the final values. R and S increase steadily with time. Xs increases at first, reaching a local maximum just before the species are mixed by the impeller. The improved quality of the mixture favors the first reaction and Xs decreases until it reaches a local minimum. At this point there is enough R present to allow the second reaction to occur even in relatively well mixed regions, and Xs increases again until it asymptotically reaches a final value. Figures 10-8a through 10-8h show the local concentrations of species A, R, and S as a function of time for the 600-1 tank at 100 rpm. 

Given the reaction stoichiometry and rate laws for an isothermal system, a simple representation for targeting of reactor networks is the segregated-flow model (see, e.g., Zwietering, 1959). A schematic of this model is shown in Fig. 2. Here, we assume that only molecules of the same age, t, are perfectly mixed and that molecules of different ages mix only at the reactor exit. The performance of such a model is completely determined by the residence time distribution function,/(f). By finding the optimal/(f) for a specified reactor network objective, one can solve the synthesis problem in the absence of mixing. 

The RTD function E(0) or E(0), obtained from the tracer experiment conducted on the reaction vessel, can be used to characterise the non-ideality as the fluid mixing pattern in the vessel has a strong influence on the distribution of residence time. Given the RTD for a reaction vessel, we would first like to know if the mixing patterns in the reaction vessel match well with the mixing patterns assumed for ideal reactors (ideal CSTR or ideal PER). This can be done by comparing the RTD function (F-curve or E-curve) for the given reactors with the RTD functions for the ideal CSTR or ideal PER. For this, we should know the RTD functions for ideal reactors. As the ideal CSTR and ideal PER are theoretical reactors, the RTD function equations for these reactors are derived theoretically. 

There is another practical method for estimating conversions in reactors with residence time distribution, for perfect micro-mixing, that is also applicable to other reaction orders. To this end the reactor is simulated by a model that consists of a cascade on N perfectly mixed equal reactors (section 3.3.3). The RTD-function of the cascade with total residence time x can be calculated ... 

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