Stochastic Models for Processes with Discrete Displacement

Stochastic Models for Processes with Discrete Displacement 

This type of model with compartment flow pattern can easily be applied in many chemical engineering devices such as chemical reactors, mechanical stirrers, absorption, rectification and liquid-liquid extraction columns [4.18, 4.19, 4.94]. Nevertheless, the practical applications of these models present some difficulties because of their high number of parameters. For example, in the application of Section 4.12 (the numerical application of the mechanical stirring of a liq- 

If we observe this type of modelling from the point of view of the general theory of the stochastic models, we can presume that it is not very simple. Indeed, the specific process which takes place in one compartment k= 1, 2, 3., N, defines the possible states of a fluid element (the elementary processes of the global stochastic process) and the transition describing the fluid element flowing from one compartment to another represents the stochastic connections. Consequently, p ]  

P]j(t) is the probability of having, at time t, the fluid element inside the k compartment. With these notations, the probability balances for P]j(t + At) can be written as follows  

Because, when r = nAr, the discrete case is usually applied, relation (4.321) becomes  

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