Mass balances, activated sludge plants
116
Example 4.1
Find the activated sludge concentration, X6,2, in an activated sludge plant without recycle where the influent and effluent concentrations are 500 g COD(S)/m 3 and 80 g
COD(S)/m 3 , respectively.
The observed yield constant is known and is 0.35 kg COD(B)/kg COD(S) or 0.25 kg
VSS/kg COD(S).
From Expression (4.4) is found:
Xs,2 = Yob~ (C1 - Ca) = (0.35 kg COD(B)Ikg COD(S)) (0.5 kg COD(S)/m 3 - 0.08 kg
COD(S)/m ) = 0.147 kg COD(B)tm 3
X6,2 can also be calculated in the unit kg of VSS/m 3 if the yield constant with the unit
VSS is used, that is, Yobs = 0.25 kg VSS/kg COD. Hence X6 ,2 = 0.105 kg VSS/m 3 .
Example 4.2
Design an activated sludge plant (find the necessary volume) corresponding to the one
shown in Fig 4.1. The following quantities are known:
Influent:
01 = 1,000 m 3 td
C1 = 500 g COD(S)/m 3
Effluent:
Oa = 1,000 m 3 td
Ca = 60 g COD(S)/m 3 (value required by the authorities)
Furthermore the following quantities are known:
rx,s = 3 kg COD(S)/(kg COD(B) · d)
Yobs = 0.3 kg COD(B)Ikg COD(S)
From Expression (4.2) the necessary volume, V2, of the aeration tank can be found:
V2 = (01 · c1 - oa · Ca)t(rx.s · Xs.2l
The only unknown is X6,2. It is found in the same way as shown in Example 4.1
Xs.2 = Y obs · (C1 - Ca) = 0.3 · (0.5 - 0.06) = 0.132 kg COD(B)tm 3 .
Substitution of these values gives:
V2 = (1,000 · 500-1,000. 60)/(3 · 0.132) = 1.111.111 m 3 .
It is a good idea to substitute the specific units and not just the numbers as shown above, thus checking whether commensurable quantities have been substituted and whether the expression as such is correct in terms of design.
Substitution of these values gives:
V2 = (1,000 m 3 /d · 500 g COD(S)/m 3 -1,000 m 3 /d ·
60 g COD(S)/m 3 )/(3 kg COD(S)/(kg COD(B) · d) ·
0.132 kg COD(B)/m 3 ) = 1,111,111 m 3 · g COD(S)/kg COD(S).
However, it is seen that something is wrong. It may be corrected by either substituting
C1 and C3 into the unit kg of COD(S)/m 3 , or by converting the result by means of the
conversion factor 1 ,000 g COD(S)/kg COD(S).
116
Example 4.1
Find the activated sludge concentration, X6,2, in an activated sludge plant without recycle where the influent and effluent concentrations are 500 g COD(S)/m 3 and 80 g
COD(S)/m 3 , respectively.
The observed yield constant is known and is 0.35 kg COD(B)/kg COD(S) or 0.25 kg
VSS/kg COD(S).
From Expression (4.4) is found:
Xs,2 = Yob~ (C1 - Ca) = (0.35 kg COD(B)Ikg COD(S)) (0.5 kg COD(S)/m 3 - 0.08 kg
COD(S)/m ) = 0.147 kg COD(B)tm 3
X6,2 can also be calculated in the unit kg of VSS/m 3 if the yield constant with the unit
VSS is used, that is, Yobs = 0.25 kg VSS/kg COD. Hence X6 ,2 = 0.105 kg VSS/m 3 .
Example 4.2
Design an activated sludge plant (find the necessary volume) corresponding to the one
shown in Fig 4.1. The following quantities are known:
Influent:
01 = 1,000 m 3 td
C1 = 500 g COD(S)/m 3
Effluent:
Oa = 1,000 m 3 td
Ca = 60 g COD(S)/m 3 (value required by the authorities)
Furthermore the following quantities are known:
rx,s = 3 kg COD(S)/(kg COD(B) · d)
Yobs = 0.3 kg COD(B)Ikg COD(S)
From Expression (4.2) the necessary volume, V2, of the aeration tank can be found:
V2 = (01 · c1 - oa · Ca)t(rx.s · Xs.2l
The only unknown is X6,2. It is found in the same way as shown in Example 4.1
Xs.2 = Y obs · (C1 - Ca) = 0.3 · (0.5 - 0.06) = 0.132 kg COD(B)tm 3 .
Substitution of these values gives:
V2 = (1,000 · 500-1,000. 60)/(3 · 0.132) = 1.111.111 m 3 .
It is a good idea to substitute the specific units and not just the numbers as shown above, thus checking whether commensurable quantities have been substituted and whether the expression as such is correct in terms of design.
Substitution of these values gives:
V2 = (1,000 m 3 /d · 500 g COD(S)/m 3 -1,000 m 3 /d ·
60 g COD(S)/m 3 )/(3 kg COD(S)/(kg COD(B) · d) ·
0.132 kg COD(B)/m 3 ) = 1,111,111 m 3 · g COD(S)/kg COD(S).
However, it is seen that something is wrong. It may be corrected by either substituting
C1 and C3 into the unit kg of COD(S)/m 3 , or by converting the result by means of the
conversion factor 1 ,000 g COD(S)/kg COD(S).