Pre-design problem: You are designing a wetland for nitrate removal; PFRs can be

Question

Pre-design problem: You are designing a wetland for nitrate removal; PFRs can be narrow pools and CSTRs can be rock sequence riffles (assume you have plenty of elevation head with which to work). For each of the following conditions, determine how much of the original material will remain if first order kinetics apply with k-0.5 hr1, Rank your results and make a recommendation for best treatment approach. a. CSTR 2 hours b. PFR : 2 hours c. CSTR 1 hour then CSTR 1 hour d. PFR e 1 hour then PFR -1 hour e. CSTR -1 hour then PFR : 1 hour f. PFR e 1 hour then CSTR 1 hour

Explanation / Answer

a)For an Initial concentration of CAi(mol/litre) , final conversion x, Rate Constant k=0.5

For a CSTR of space time()= 2 hours, the equation will be CAi = x/(k* CAi*(1-x))

We get final conversion over here as 0.5, so finally 0.5 CAi(mol/litre) of the original material remains.

b) For an Initial concentration of CAi(mol/litre) , final conversion x, Rate Constant k=0.5

For a PFR of space time()= 2 hours, the equation will be CAi =

   By inserting the value for k=0.5, = 2hr and integrating the equation we get x= 0.632

Original matter = 0.367 CAi(mol/litre).

c) For a series of two CSTRs, with time()= 1 hour each, to find the final conversion xi of the initial reactor, we follow the same procedure over here as stated in problem a) and we get xi = 0.333.

for the next cstr, procedure will be the same, but there will be a slight change in the equation. Here the final conversion in x.

CAi = (x-xi)/( k* CAi*(1-x)). By inserting the value of xi= 0.333, we get x value as 0.556.

Final original matter present over here is 0.444 CAi(mol/litre).

d) For a series of two PFRs, with time()= 1 hour each, to find the final conversion xi of the initial reactor, we follow the same procedure over here as stated in problem b) and we get xi= 0.394.

for the next pfr, procedure will be the same, but there will be a slight change in the equation. Here the final conversion in x.

CAi = we get x= 0.632.

Final Original matter = 0.367 CAi(mol/litre).

e) For a series of a CSTR Of space time = 1 hour and PFR = 1 hour. , to find the final conversion xi of the initial reactor, we follow the same procedure over here as stated in problem a) and we get xi = 0.333. For the next pfr, procedure will be the same, but there will be a slight change in the equation. Here the final conversion in x.

CAi = we get x= 0.595.

Final Original matter = 0.4045 CAi(mol/litre).

f) For a first order reaction, a cstr and pfr of same space time will yield same conversion finally when you connect them in series irrespective of which is the first one in the series. So answer in e will be the answer in f.

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