Plug Flow-Perfectly Mixed Reactor Systems

4 PLUG FLOW-PERFECTLY MIXED REACTOR SYSTEMS 

In the following, a variety of configurations will be treated, which find importance in practice and in simulation, as well as elaborate the application of the model in chapter 4.1. 

The basic scheme of a single plug flow reactor with recycle is shown below in Fig.4.4-1. Such a reactor may be described also as a combination of perfectly mixed reactors. Other simplified configurations are described in the following cases, 4.4-l(l) and 4.4-l(2). The states are the concentration of the tracer in the perfectly mixed reactors, i.e. SS = [Ci, C2,. ]. The residence time in the 

The corresponding probabilities are obtained from Eqs.(4-16), (4-18), (4-18a) and (4-19) yielding the following probability matrix  

A simplified approach for treating a plug flow reactor by comparison to case 

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Plug flow-perfectly mixed reactor systems (chapter 4.4). 

Deflnitions. The basic elements of Markov chains associated with Eq.(2-24) are the system, the state space, the initial state vector and the one-step transition probability matrix. Considering refs.[26-30], each of the elements will be defined in the following with special emphasize to chemical reactions occurring in a batch perfectly-mixed reactor or in a single continuous plug-flow reactor. In the latter case, which may simulated by perfectly-mixed reactors in series, all species reside in the reactor the same time. 

In treating a certain configuration, the first step is to define the states that the system can occupy. By a state is meant, the concentration Ci in a perfectly mixed reactor i or at the inlet or the exit of a plug-flow reactor, that the system (fluid element) can occupy. The states will be designated by Ci, C2,... whereas the state space SS, will read ... 

Fig.4.4-2 demonstrates a plug flow reactor containing a "dead water" element of volume Vd where the active part is of volume Vp. The system contains also two perfectly mixed reactors 1 and 2. A tracer in a form of a pulse is introduced into reactor 1 and is transferred by the flow Qi into reactor 2 where it accumulates. 

The following system comprises two plug flow reactors, perfectly mixed reactors and recycle streams Q45, Q53 and Q52. Reactors 2, 4 and 5 may be considered also as measurement points of the concentration, and in this case their i s are assigned a large value, say, 500. 

Fig.4.4-5a demonstrates the effect of p on the transient response of C2 and Cn, i.e. the first and the last perfectly mixed reactors in the upper plug flow reactor in Fig.4.4-5. The tracer was introduced into reactor 2. It is obsereved that by increasing p from 80 to 800, the number of oscillations for reaching the steady state concentration 1/22 in the system is increased. It should also be noted that for p = 800, the distance between two successive peaks corresponding to C2 and Cn is...

The following configuration demonstrates a general cell model of a continuous flow system described in ref. [77]. There are two possibilities to arrive at state 4, i.e. directly and via the upper plug flow reactor. However, in order to materialize these possibilities it was necessary to add state 3-a perfectly mixed reactor 3. The residence time in this reactor is controlled by the quantity [13. 

Consider a plug flow reactor, with mean residence time t, followed by a perfectly mixed reactor, with mean residence time, i2. The overall RTD for this system will merely be that for a perfectly mixed vessel, but with a time delay caused by the... 

The RTD in a system is a measure of the degree to which fluid elements mix. In an ideal plug flow reactor, there is no mixing, while in a perfect mixer, the elements of different ages are uniformly mixed. A real process fluid is neither a macrofluid nor a microfluid, but tends toward one or the other of these extremes. Fluid mixing in a vessel, as reviewed in Chapter 7, is a complex process and can be analyzed on both macroscopic and microscopic scales. In a non-ideal system, there are irregularities that account for the fluid mixing of different... 

Next the reactor system in which the CSTR is preceded by the PFR will be treated. If the pulse of tracer is introduced into the entrance of the plug-flow section, then the same pulse will appear at the entrance of the perfectly mixed section Xp seconds later, meaning that the RTD of the reactor system will be... 

The application of the equations to chemical reactions requires the proper definition of the above quantities as well as correctly defining the transition probabilities pjj and pjk this is established in the following. It should also be noted that the models derived below for numerous chemical reactions, are applicable to chemical reaction occurring in a perfectly-mixed batch reactor or in a single continuous plug-flow reactor. Other flow systems accompanied with a chemical reaction will be considered in next chapters. 

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