3.5.1 Designing an Aerobic Digester Tank: An Exercise

Let us design an aerobic digester with the following assumptions:

Parameter	Value
Input Sludge	5 m3/d
Total Solids	2% (after thickening)
Volatile Solids	75% TS
Lowest Temperature during Winter	17°C
Oxygen Demand	2.3 kgO2/kgVS destroyed
Air Density	1.2 kg/m3
Oxygen Concentration in the Air	23%

Step 1: Select Retention Time (RT) and Calculate Digester Volume (V_D)

The lowest temperature during winter in the region is 17°C, which will result in a retention time of 31 days, based on the recommendation from the table presented in Topic 3.5 (Table: Design parameters for conventional aerobic sludge digesters).

The following formula can be applied to calculate the digester volume.

Where,

Parameter	Description	Value in Exercise	Unit
VD	Digester Volume	–	m3
VIN	Volume Input	5	m3/d
RT	Retention Time	31	d (day)

Let’s calculate the digester volume based on the recommended retention time of 31 days.

Solution:

Step 2: Verify the Organic Loading Rate (OLR) (within the range 1.6 – 4.8 kg_VS/m³d)

The following formula can be applied to calculate the organic loading rate.

Where,

Parameter	Description	Value in Exercise	Unit
OLR	Organic Loading Rate	–	kgVS/m3/d
VIN	Volume Input	5	m3/d
ρ	Density of Water	1,000	kg/m3
CTS	TS Concentration	2	%TS
CVS(TS)	VS Concentration from TS	75	%VS from TS
VD	Digester Volume	155	m3

Now, we calculate the organic loading rate and verify if it is within the specified range.

Solution:

The calculated organic loading rate is not within the specified range.

Step 3: Calculate the Total Solids Concentration in the Aerobic Digester (C_TS)

Firstly, we calculate the fixed solids (FS), the undigested part which remains constant throughout the process for both the influent and effluent.

Where,

Parameter	Description	Value in Exercise	Unit
FS	Fixed Solids	–	kg/d
FSIN	Fixed Solids of Influent	–	kg/d
FSEFF	Fixed Solids of Effluent	–	kg/d
TSIN	Total Solids of Influent	100	kg/d
VSIN	Volatile Solids of Influent	75	kg/d

Solution:

Secondly, we calculate VS of the effluent, VS_EFF . We assume a VS removal efficiency of 40% for aerobic digestion.

Where,

Parameter	Description	Value in Exercise	Unit
VSEFF	Volatile Solids of Effluent	–	kgVS/d
REVS	Removal Efficiency	40	%
VSIN	Volatile Solids of Influent	75	kgVS/d

Solution:

Thirdly, we calculate the TS of the effluent, TS_EFF

Solution:

Finally, we can determine the TS concentration that is maintained in the digester tank (C_TS).

Where,

Parameter	Description	Value in Exercise	Unit
CTS	TS Concentration in digester tank	–	%
ρ	Density of Water	1,000	kg/m3
TSEFF	Total Solids of Effluent	70	kg/d
VSEFF	Volatile Solids of Effluent	5	m3/d

Solution:

Step 4: Determine the Area Requirements for the Digester (A)

Next, we calculate the area requirements for 4 rounded tanks if one tank has a diameter of 10 m. As a reminder, the formula for the area is A= π r² .

Where,

Parameter	Description	Value in Exercise	Unit
A	Area required	–	m2
π	Constant	3.14	–
r	Radius of the digester tank	5	m

Solution:

Step 5: Determine the Air Requirements for the Digester (V_AIR)

Firstly, we need to quantify the VS removed per day, VS_REM .

Where,

Parameter	Description	Value in Exercise	Unit
VSREM	Volatile Solids Removed	–	kg/d
REVS	Removal Efficiency	40	%
VSIN	Volatile Solids of Influent	75	kg/d

Solution:

Secondly, we need to quantify the oxygen requirement for the removal of VS_REM of 30 kg/d.

Where,

Parameter	Description	Value in Exercise	Unit
OM	Mass of Oxygen	–	kgO2
VSREM	VS Removed	30	kgVS/d
ODM	Oxygen Demand	2.3	kgO2/ kgVS

Solution:

Finally, we can determine the volume of air (V_AIR) required per day if the oxygen concentration is assumed to be 30%. As calculated in the previous example, the oxygen required is 69 kg_O2/d.

We use the following formula to calculate the volume of air, V_AIR , required per day.

Where,

Parameter	Description	Value in Exercise	Unit
VAIR	Volume of Air	–	m3/d
OM	Mass of Oxygen	69	kgO2
ρAIR	Density of Oxygen	1.2	kgO2 /m3
CO	Oxygen Concentration	30	%

Solution:

We then check the airflow mixing capacity and confirm if it exceeds the minimum requirements as suggested in the table presented in Topic 3.5 (Table: Design parameters for conventional aerobic sludge digesters): The minimum airflow mixing capacity should be between 20 – 40 L/m³/min.

Where,

Parameter	Description	Value in Exercise	Unit
MIX	Airflow Mixing Capacity	–	L/m3/min
VAIR	Volume of Air	191.7	m3/d
VD	Volume of the Digester	155	m3

Solution:

The airflow mixing capacity is lower than the minimum requirements; therefore, the amount of air needs to be increased based on the minimum flow mixing capacity of 20L/m³/min or 29 m³/m³ d.

Let us now calculate the revised air volume.

Solution: