Depending on the type of filter media, two formulas can be applied to determine the required volume and space of the filter system.
3.6.1 Filter media: Stone or Rocks
The NRC (National Research Council) formula for trickling-filter performance is an empirical expression developed by the National Research Council from an extensive study of the operating data of trickling treatment plants at military bases within the United States during World War II in the early 1940s.
It may be applied to single-stage and multi-stage rock filters with varying recirculation ratios.
The equation to calculate the BOD removal efficiency for a single-stage or first stage of a two-stage rock filter is:
Where,
Parameter
Description
Unit
E1
Efficiency of BOD removal for the first stage at 20°C
%
OL
Organic load BOD
kg/d
V
Volume of the filter media
m3
F
Recirculation factor
–
To calculate the BOD removal efficiency for the second filter in a two-stage rock filter, the following formula is used:
Where,
Parameter
Description
Unit
E2
Efficiency of BOD removal for a second-stage filter at 20°C
%
OL’
Organic load BOD applied to the second-stage filter
kg/d
The recirculation factor (F) is calculated by: (If no recirculation is planned, then F = 1)
Where,
Parameter
Description
Unit
F
Recirculation factor
–
r
Recirculation ratio
QR/Q
QR
Recirculation flow
m3/d
Q
Influent flow
m3/d
The overall BOD removal efficiency of a two-stage filter system can be computed by
BOD removal efficiency in the biological treatment process is significantly influenced by wastewater temperature. Warmer temperatures generally enhance microbial activity, leading to more effective degradation of pollutants.
The effect of temperature can be calculated as
Exercise
Let us practice and apply the formula to determine the size of the trickling filter.
Determine the size of the single-stage trickling filter, without recirculation using the NRC equations. The assumption is as follows:
Parameter
Description
Value
Unit
T
Influent temperature
20
°C
Qin
Influent flow
100
m3/d
Cin
BOD5 influent
150
mg/L
Cout
BOD5 effluent
30
mg/L
D
Filter depth
1.5
m
F
Recirculation factor
1
–
Step 1: Determine the overall required removal efficiency (E)
Step 2: Calculate Organic Load BOD in kg/d (OL)
Be mindful of unit adjustments:
Step 3: Calculate the volume of the filter (V)
Step 4: Calculate the area of the rectangular filter (A)
Step 5: Cross-check if our result would also be within the suggested ranges for the Organic Loading Rate (0.08 – 0.22 kgBOD/m3/d) and Hydraulic Loading Rate (1 – 4 m3/m2/d)
The organic loading rate exceeds the recommended limits; therefore, the volume must be adjusted accordingly.
Step 5.1: Adjust the required filter volume. Defining an intended organic loading rate of 0.18 kgBOD/m3/d, the following volume is required:
Step 5.2: Adjust the required filter area.
3.6.2 Filter media: Plastic
1966 Germain applied the Schulze formulation to a plastic media trickling filter and proposed the following equation.
Where,
Parameter
Description
Unit
St
BOD5 effluent
mg/L
S0
BOD5 influent
mg/L
e
Euler number, a mathematical constant (e = 2.71828)
–
k
Empirical reaction rate (Schulze determined the value of k to be 0.69/d, at 20°C for plastic media)
d-1
D
Filter depth
m
HLR
Hydraulic loading rate
m3/m2d
n
Empirical constant of the filter media (Schulze determined the value of n = 0.67 for plastic media)
–
Please note that the value of k in these equations depends upon temperatures of 20°C. Therefore, a correction factor to any other temperature needs to be applied and is as follows:
Where,
Parameter
Description
Unit
kT
Reaction rate at the desired temperature
d-1
0
Temperature correction coefficient, usually assumed to be 1.035
–
k20
Reaction rate at 20°C
d-1
T
Temperature at which the value of k is desired
°C
Exercise
Let us practice and apply the formula and determine the size of the trickling filter.
The assumptions are as follows:
Parameter
Description
Value in Exercise
Unit
T
Influent temperature
25
°C
Qin
Influent flow
100
m3/d
Cin
BOD5 influent
150
mg/L
Cout (= St)
BOD5 effluent
30
mg/L
D
Filter depth
4.5
m
r
Recirculation ratio
2
–
k20
Reaction rate at 20°C
0.69
d-1
n
Empirical constant of the filter media (Plastic)
0.67
–
Step 1: Adjust reaction rate k according to the temperature.
Step 2: Calculate BOD5 influent after recirculation of the wastewater (S0).
Step 3: Calculate the Hydraulic Loading Rate (HLR) based on the BOD5 influent after recirculation of the wastewater.
Step 4: Calculate the required filter area (A).
Total Inflow to the filter, Qtotal:
Area of the filter, A :
Even in the scenario where wastewater is recirculated within the system twice, the area of the trickling filter with plastic media (33.37 m2) is smaller compared to the rock media (55.55 m2).
This website uses cookies so that we can provide you with the best user experience possible. Cookie information is stored in your browser and performs functions such as recognising you when you return to our website and helping our team to understand which sections of the website you find most interesting and useful.
Strictly Necessary Cookies
Strictly Necessary Cookie should be enabled at all times so that we can save your preferences for cookie settings.
If you disable this cookie, we will not be able to save your preferences. This means that every time you visit this website you will need to enable or disable cookies again.
3rd Party Cookies
This website uses Google Tag Manager to collect anonymous information such as the number of visitors to the site, and the most popular pages.
Keeping this cookie enabled helps us to improve our website.
Please enable Strictly Necessary Cookies first so that we can save your preferences!