Residence time distribution function perfectly mixed reactors

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. 

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. 

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 ... 

The residence time distribution function E i) of the growing latex particles in a perfectly mixed stirred tank reactor is defined as follows ... 

The limiting cases of continuous reactors considered in most reactor design textbooks are the perfectly mixed stirred tank and the plug-flow tube. These reactors can differ significantly in the amount of mixing and, therefore, the residence time distribution. The plug-flow tube (PFT) is assumed to be without any axial mixing. Hence, at steady state, the residence time distribution of the material in the effluent stream is represented by the Dirac function as shown by Equation (8.1) ... 

These models are usually applied to continuous mixed reactors. In order to be able to calculate the conversion in the exit, an assumption has to be made concerning the residence time distribution (see section 7.2.1). In the first and third models it was assumed that the mixed reactor has the residence time distribution (RTD) of a perfectly mixed CSTR. In the second model a measured RTD-function was included... 

The ideal cases are the piston flow reactor (PFR), also known as a plug flow reactor, and the continuous flow stirred tank reactor (CSTR). A third kind of ideal reactor, the completely segregated CSTR, has the same distribution of residence times as a normal, perfectly mixed CSTR. The washout function for a CSTR has the simple exponential form... 

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