Stochastic Model for a Countercurrent Flow with Recycling

2 Cellular Stochastic Model for a Countercurrent Flow with Recycling 

The example presented in this section is a system where two countercurrent fluids flow through N identical cells Fig. 4.43 describes this system schematically. In this simplified case, we consider that, at each cell level, we have a perfect mixing flow and that for a k cell, the actual transition probabilities are PuiPklc-i. Indeed, these probabilities are expressed as  

When we have the same fraction of recycling in the system and when the cells have the same volume, we can rewrite relation (4.345) as  

We can observe that the first and the last cell of the system are in contact with only one cell cell number 2 and number N - 1 respectively. So, in the matrix of the transition probabilities, the values pi3 and Pn-2n will be zero. It is easily noticed that, if we have a complete matrix of the transition probabilities, then we can compute the mean residence time, the dispersion around the mean residence time and the mixing intensity for our cells assembly. The relations (4.324)-(4.326) are used for this purpose. 

besides hydrodynamics and mixing, we want to consider other phenomena, such as a chemical reaction, we have to separate the probabilities characterizing each particular phenomenon  

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