V ¼ volume of filter media, volume, ac.-ft
F ¼ recirculation factor
R ¼ recirculation ratio
Q ¼ influent wastewater flow rate through the trickling filter, volume/time, MGD
Q r ¼ recirculation flow rate, volume/time, MGD
For the second-stage filter, the NRC model is:
E 2 ¼
100
1 þ K nrc W
0
=VF
ð
Þ
0:5 1 À E 1
ð
Þ
À1
ð3:37Þ
W
0
¼ 1 À E 1
ð
ÞW
ð3:38Þ
in which:
E 2 ¼ % efficiency of BOD removal for second-stage filtration, including
recirculation and settling
W
0
¼ BOD loading to second-stage filter, mass/time, lb/d
7.2 Velz Model
In 1948 Velz [30] postulated that the BOD removal per unit depth of trickling filter
was proportional to the BOD remaining.
dL=dD ¼ ÀK e L
ð3:39Þ
which integrates to:
L D =L ¼ e
ÀK e
D
¼ 10
ÀK 10 D
ð3:40Þ
in which:
D ¼ the depth of the trickling filter, length, ft
L D ¼ the BOD remaining in the effluent at depth D, mass/volume, mg/L
L 0 ¼ BOD of untreated wastewater, mass/volume, mg/L
L ¼ applied BOD (mass/volume, mg/L) which is removable, not over 0.90 L 0
K e ¼ rate of BOD removal, base e
K 10 ¼ rate of BOD removal, base 10
When recirculation is used, the applied BOD L may be determined from
Eq. (3.41):
3 Biological Processes
127