3.6 How can we estimate the required volume of filter media and space?

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 kg_BOD/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 kg_BOD/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, Q_total :

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).