modelMixingUnit1

Information

Model of idealized stirred tank reactor from [1], p. 280. In the stirred tank there is a continuous intake of substance A which reacts with a catalyzer and brakes down into other substances. Since the content of the tank reactor is stired continuously, it can be supposed a homogenous distribution of all substances within the tank. Therefore, the tank reactor system can be described by means of concentrated parameters.

The chemical reaction in the tank reactor is exothermic, i.e. it produces themal energy which affects the stability of the reaction. To stabilize it, the tank reactor is cooled. The temperature T_c of cooling medium is the variable to be actuated by controller.

The speed γ of the reaction depends on the concentration c and temperature T as follows:

gamma = (1-x1) * k0 * e^(-eps/(1+x2))

with related concentration x1 and related temperature x2:

      c0 - c            T - T0
x1 = --------;    x2 = --------.
        c0                T0

Both variables x1 and  x2 are states of the model. Additionally, there is used related temperature u of cooling medium:

     T_c - T0
u = --------.
       T0

References

 [1] Föllinger O. (1998):

Nichtlineare Regelungen I. 8th Edition, Oldenbourg Verlag München.
 

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