Wastewater BOD Dilution Calculation

The dilution factor ($DF$) required for a Biochemical Oxygen Demand (BOD) test is calculated to ensure that the dissolved oxygen (DO) level in the diluted sample remains sufficient for the microorganisms to function and for accurate measurement after the incubation period.

Formula for Dilution Factor

The calculation is based on the initial DO, the minimum required DO, the sample's BOD concentration, and the dilution factor itself. The relationship is derived from the oxygen available for consumption:

Oxygen Available for Consumption = Initial DO - Minimum Remaining DO

This available oxygen must be greater than or equal to the oxygen consumed by the diluted sample ($BOD_s / DF$).

$ DO_{initial} - DO_{minimum} \ge \frac{BOD_s}{DF} $

Rearranging the formula to find the minimum required dilution factor:

$ DF \ge \frac{BOD_s}{DO_{initial} - DO_{minimum}} $

Applying the Values

Given:

• BOD of the sample ($BOD_s$) = 300 mg/L
• Initial DO of dilution water ($DO_{initial}$) = 8.5 mg/L
• Minimum DO that should remain ($DO_{minimum}$) = 1.5 mg/L

Substitute these values into the formula:

$ DF \ge \frac{300 \text{ mg/L}}{8.5 \text{ mg/L} - 1.5 \text{ mg/L}} $

$ DF \ge \frac{300 \text{ mg/L}}{7 \text{ mg/L}} $

$ DF \ge 42.857 $

Determining the Correct Dilution

The dilution factor must be at least 42.857. We need to choose the option that meets this requirement.

• Option 1: 100 times dilution (Meets requirement)
• Option 2: 50 times dilution (Meets requirement)
• Option 3: 200 times dilution (Meets requirement)
• Option 4: 150 times dilution (Meets requirement)

In BOD testing, the goal is to achieve the lowest possible dilution factor that still satisfies the DO requirement, as excessive dilution can introduce errors. Among the options provided, 50 is the smallest dilution factor that is greater than 42.857.

Therefore, a 50 times dilution is appropriate.