Application of the Modeling and General Guidelines

The above modeling is applied to numerous flow configurations which have appeared in various Chemical Engineering textbooks as well as additional ones of particular interest, i.e. impinging-stream reactors [73]. In general, any flow configurations under consideration will consist of a series of perfectly-mixed reactors, plug-flow reactors, dead water elements as well as recycle streams, by pass and cross flow etc., or part of the above. 

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  

The next step is to break the complicated flow configuration into basic elements which were described above in sections 4.1-1 to 4.1-3 thus, the probabilities of remaining in a state, pjj, or of moving to a new state, pjk, can be deduced. This yields the transition probability matrix P. 

A further step is to specify the initial concentration of each state, i.e. the initial state vector S(0). This is defined by  

In the present case, the initial concentration is that of the pulse input introduced into the reactor. The concentration at some time t = nAt or step n, in the various reactors, i.e., the states of the system, is defined by the following state vector. 

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