Unmixed feed streams

Diffusion is important in reactors with unmixed feed streams since the initial mixing of reactants must occur inside the reactor under reacting conditions. Diffusion can be a slow process, and the reaction rate will often be limited by diffusion rather than by the intrinsic reaction rate that would prevail if the reactants were premixed. Thus, diffusion can be expected to be important in tubular reactors with unmixed feed streams. Its effects are difficult to calculate, and normal design practice is to use premixed feeds whenever possible. 

We turn now to the numerical solution of Equations (9.1) and (9.3). The solutions are necessarily simultaneous. Equation (9.1) is not needed for an isothermal reactor since, with a flat velocity profile and in the absence of a temperature profile, radial gradients in concentration do not arise and the model is equivalent to piston flow. Unmixed feed streams are an exception to this statement. By writing versions of Equation (9.1) for each component, we can model reactors with unmixed feed provided radial symmetry is preserved. Problem 9.1 describes a situation where this is possible. 

Packed-bed reactors can be adiabatic, and Equation 9.3 takes a particularly simple form with no radial gradients in temperature or composition arising when the feed is premixed. If the fluid is uniform in the radial direction when it enters the reactor, it remains uniform. Thus adiabatic packed beds are normally modeled as PERs. This assumption may be overly optimistic in terms of yields and selectivities. The axial dispersion model in Section 9.2 adds a correction term to avoid undue optimism. Unmixed feed streams can also be treated provided the reactants enter the reactor in a manner that preserves radial symmetry. 

Figure 5.9. The unmixed mixture-fraction PDF in turbulent flows with two feed streams has two peaks that can be approximated by a beta PDF. However, with three feed streams, the unmixed PDF has three peaks, and is therefore poorly approximated by a beta PDF. 

Another Lagrangian-based description of micromixing is provided by multienvironment models. In these models, the well macromixed reactor is broken up into sub-grid-scale environments with uniform concentrations. A four-environment model is shown in Fig. 5.16. In this model, environment 1 contains unmixed fluid from feed stream 1 environments 2 and 3 contain partially mixed fluid and environment 4 contains unmixed fluid from feed stream 2. The user must specify the relative volume of each environment (possibly as a function of age), and the exchange rates between environments. While some qualitative arguments have been put forward to fit these parameters based on fluid dynamics and/or flow visualization, one has little confidence in the general applicability of these rules when applied to scale up or scale down, or to complex reactor geometries. 

The case of reactors with two unmixed feedstreams is especially interesting (6), because more realistic for applications. It has been thoroughly investigated in a series of papers by researchers of Exeter University (UK). The BPT model offers a convenient picture of the reactor where both feed streams have their own RTD and the two bundles are placed side by side in such a manner that particles with the same life expectancy are situated as usual on the same vertical line (figure 6). In a first paper (60), a distinction is made between age mixedness and species mixedness Maximum age and species mixedness is achieved if particles with the same life expectancy are mixed. A more restrictive case is that where particles are able to mix only if they have both the same... 

Each Helikon module uses two axial-flow compressors, one for the emiched streams (point 1, Fig. 14.29) and a second for the feed streams (point 4). The nature of flow through this type of compressor is such that there is rather little mixing of material fed into the barrel at one angular position with material of another composition fed at another angular position. Such streams of different composition flow throu the compressor in helical paths and leave the compressor still relatively unmixed. 

The feed streams being unmixed, the fully segregated concentration would be y =1. 

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