4. A chemical reaction takes place in a series of four continuous stirred tank r

Question

4. A chemical reaction takes place in a series of four continuous stirred tank reactors arranged as shown in FigureE23. 100 lit/h 1000 lit/h 100 lit/h C, 1 mol/lit 1000 lit/h Figure E2.3 Series of continuous stirred tank reactors. The chemical reaction is a first-order irreversible reaction ofthe type A- B The conditions of temperature in each reactor are such that the value of the rate constant ki, is different in each reactor. Also, the volume of each reactor Vi, is different. The values of ki, and Vi, are given in Table E2.3. The following assumptions can be made regarding this system: 1. The system is at steady state. 2. The reactions are in the liquid phase. 3. There is no change in volume or density of the liquid. 4. The rate of disappearance of component A in each reactor is given by R. Vik,CA, mol/h Table E2.3 Reactor vi (L) k, (h Reactor VI (L) k, (h 1) 1000 0.1 100 0.4 1500 0.2 500 0.3

Explanation / Answer

a) rate of accumulation of component = rate of inflow of component-rate of outflow of component+rate of generation of component by chemical reaction.

material balance equation for continuous stirred tank reactor is given by

where, Qf (flow rate) and cjf (concentration) are for inlet and Q and cj are for outlet for each reactor. Rj is rate at different reactors For series the output of first tank is considered as the input of the second tank.

b) For series the output of first tank is considered as the input of the second tank. To calculate the output concentration at each tank the best method is by using “Damköhler number" (Da)= Reaction rate/flow

Exit concentration can be calculated as follows

for first reactor CA1 = CA0/ 1 + Da1

for second reactorCA2 = CA0/ (1 + Da1) (1+Da2 )

for third reactorCA3 = CA0/ (1 + Da1) (1+Da2 )(1+Da3 )

for fourth reactorCA4 = CA0/ (1 + Da1) (1+Da2 )(1+Da3 )(1+Da4 )

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