Mass Balance Using BOD Removal

The amount of BOD removed by a treatment process is directly related to the quantity of solids the process will generate. Because the actual amount of solids generated will vary with operational conditions and design, exact figures must be determined on a case-by-case basis;


Process Type

Conversion Factor (lb solids/lb BOD removal)

Primary treatment Trickling filters Rotating biological contactors Activated biosolids with primary Activated biosolids without primary

Conventional Extended air Contact stabilization Step feed Oxidation ditch

however, research has produced general conversion rates for many of the common treatment processes. These values are given in Table 3.2 and can be used if plant-specific information is unavailable.

Using these factors, the mass balance procedure determines the amount of solids the process is anticipated to produce. This is compared with the actual biosolids production to determine the accuracy of the sampling, the potential for solids buildup in the system, or unrecorded solids discharges.

1. BODin = Influent BOD x Flow x 8.34

4. Solids generated (lb) = BOD removed (lb) x Factor

5. Solids removed (lb/day) = Sludge pumped (gpd) x %Solids x 8.34

problem: A conventional activated biosolids system with primary treatment is operating at the levels listed below. Does the mass balance for the activated biosolids system indicate that a problem exists?

Plant influent BOD = 250 mg/L

Primary effluent BOD = 166 mg/L

Activated biosolids system effluent BOD = 25 mg/L

Activated biosolids system effluent TSS = 19 mg/L

Plant flow = 11.40 MGD

Waste concentration = 6795 mg/L

Waste flow = 0.15 MGD


BODin = 166 mg/L x 11.40 MGD x 8.34 = 15,783 lb/day

BOD removed = 15,783 lb/day - 2377 lb/day = 13,406 lb/day

Solids produced = 13,406 lb/day x 0.7 lb solids/lb BOD = 9384 lb/day

Solids removed = 6795 mg/L x 0.15 MGD x 8.34 = 8501 lb/day

Difference = 9384 lb/day - 8501 lb/day = 883 lb/day, or 9.4%

These results are within the acceptable range.

Note: We have demonstrated two ways in which mass balance can be used; however, it is important to note that the mass balance concept can be used for all aspects of wastewater and solids treatment. In each case, the calculations must take into account all of the sources of material entering the process and all of the methods available for removal of solids.


Before we review calculations involving force, pressure, and head, we must first define these terms:

• Force—The push exerted by water on any confined surface. Force can be expressed in pounds, tons, grams, or kilograms.

• Pressure—The force per unit area. The most common way of expressing pressure is in pounds per square inch (psi).

• Head.—The vertical distance or height of water above a reference point. Head is usually expressed in feet. In the case of water, head and pressure are related.

• Force vs. pressure—Figure 3.9 helps to illustrate these terms. A cubical container measuring 1 ft on each side can hold 1 ft3 of water. A basic fact of science states that 1 ft3 of water weighs 62.4 lb and contains 7.48 gal. The force acting on the bottom of the container

1 ft

Figure 3.9 One cubic foot of water weighs 62.4 lb.

1 ft

Figure 3.9 One cubic foot of water weighs 62.4 lb.

would be 62.4 pounds per square foot (lb/ft2). The area of the bottom in square inches is:

1 ft2 = 12 in. x 12 in. = 144 in.2 Therefore, the pressure in pounds per square inch (psi) is:

1ft2 144 in.2/ft2

If we use the bottom of the container as our reference point, then the head would be 1 ft. From this, we can see that 1 ft of head is equal to 0.433 psi, which is an important parameter to remember. Figure 3.10 illustrates some other important relationships between pressure and head. Based on this information, we can develop the following equations for calculating pressure and head:

Key Point: Force acts in a particular direction. Water in a tank exerts force down on the bottom and out of the sides. Pressure, however, acts in all directions. A marble at a water depth of 1 ft would have 0.433 psi of pressure acting inward on all sides.

Pressure (psi) = 0.433 x Head (ft) Head (ft) = 2.31 x Pressure (psi)

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