There are several methods available for calculating the oxygen demand in a bioreactor and each of those will be compared in the discussion that follows. The initial operating assumptions to be used in comparing methods are listed below.

- Influent flow = 2,500 gpm = 3.6 mgd = 568 m
^{3}/hr - Influent BOD
_{5}= 229 mg/L - Effluent BOD
_{5}= 0 mg/L (to be conservative in estimating oxygen requirements) - Mean COD/BOD
_{5}ratio = 2.3 - Influent ammonia = 20 mg/L
- Aeration basin volume = 2,200,000 gallons = 8,328 m
^{3} - Waste activated sludge flow rate = 45 gpm = 0.0648 mgd = 10.2 m
^{3}/hr *Y*= 0.4 lb MLVSS/lb BOD_{5 }removed

**Note: For municipal wastewater plants, the typical value of ***Y *ranges from 0.5 to 0.7 g MLVSS/g BOD_{5} removed. In the stressed environment of an industrial wastewater system the value of *Y* is much smaller.

There is an approximate rule of thumb that can be used to estimate carbonaceous oxygen demand very quickly. The rule of thumb, though it differs among textbooks, goes like this: The amount of oxygen required in a bioreactor is in the range of 1.2 to 2.5 lb O_{2}/lb BOD_{5} removed. This is a broad range so let’s, somewhat arbitrarily, use the value of 1.5 lb O_{2}/lb BOD_{5} removed. The oxygen demand for ammonia reduction is 4.6 lb O_{2}/lb NH_{3}.

The pounds of BOD entering the bioreactor are calculated using Equation 1.

**Equation 1: Pounds of BOD Entering the Bioreactor**

The pounds of ammonia entering the bioreactor are calculated using Equation 2.

**Equation 2: Pounds of Ammonia Entering the Bioreactor**

Given the flow and loading conditions listed above, the actual pounds of oxygen required for carbon are calculated using Equation 3.

**Equation 3: Oxygen Requirement for Carbon**

The actual pounds of oxygen required for nitrogen are calculated using Equation 4.

**Equation 4: Oxygen Requirement for Nitrogen**

The total estimated oxygen demand for carbon + nitrogen is calculated using Equation 5.

**Equation 5: Total Oxygen Requirement Carbon + Nitrogen**

There is another method for calculating oxygen demand with the “standard form” of the equation that uses a BOD conversion factor of 0.68, explained in detail below. This equation takes into account the solids removed through sludge wasting and deducts the oxygen demand of those solids.

Using a second method, the carbonaceous oxygen demand is calculated using Equation 6.

**Equation 6: Oxygen Requirement for Carbon**

The conversion factor for converting all carbonaceous BOD_{5} to end products (CO_{2} and H_{2}O) is 0.68 for municipal wastewater plants, ≤0.20 to 0.68 for industrial wastewater plants with lower values directly correlated with an increasing percentage of refractory compounds.

The quantity of waste activated sludge removed each day is calculated using Equation 7.

**Equation 7: Waste Pounds**

Where 1.42 represents the stoichiometric relationship between bacterial cells (C_{5}H_{7}NO_{2}) and the oxygen required to stabilize organic substrate (1.42 g O_{2}/g biodegradable solids) and Y* _{obs}* is the observed yield coefficient that reflects the net sludge production.

The nitrogenous oxygen demand is calculated using Equation 8.

**Equation 8: Oxygen Requirement for Nitrogen**

For industrial wastewater systems with varying amounts of biodegradable, slowly biodegradable, and non-biodegradable organic fractions the ratio of COD to BOD is highly variable. This variability needs to be accounted for in the BOD conversion factor and it is done using Equation 9.

**Equation 9: BOD Conversion Factor**

The actual pounds of oxygen required for carbon are calculated using Equations 10, 11, and 12.

**Equation 10: Oxygen Requirement for Carbon**

The quantity of waste activated sludge removed each day and the oxygen associated with it is calculated using Equation 11.

**Equation 11: Oxygen Requirement for Waste Sludge**

The actual pounds of oxygen required for carbon, after deducting the oxygen requirement removed through sludge wasting is calculated using Equation 12.

**Equation 12: Final Oxygen Requirement for Carbon**

The nitrogenous oxygen demand is calculated using Equation 13.

**Equation 13: Oxygen Requirement for Nitrogen**

The total estimated oxygen demand for carbon + nitrogen is calculated using Equation 14.

**Equation 14: Total Oxygen Requirement Carbon + Nitrogen**

In Example 1 the estimated oxygen consumption was 13,073 lb O_{2}/day which is 42.3% higher than the 9,187 lb O_{2}/day estimate from the second method. Given such a large difference in values it’s hard to be particularly confident with either method. But we’ve overlooked something. We used a BOD conversion factor of 0.68 which does not adjust for the elevated COD/BOD_{5} ratio of 2.3. Let’s make that adjustment and recalculate the oxygen demand. The adjustment to the BOD conversion factor is made using Equation 15.

**Equation 15: Adjustment to BOD Conversion Factor**

The revised estimate for the pounds of oxygen required for carbon, after adjusting the BOD conversion factor, is recalculated using Equations 16 and 17.

**Equation 16: Revised Oxygen Requirement for Carbon**

**Equation 17: Final Oxygen Requirement for Carbon**

The total estimated oxygen demand for carbon + nitrogen is calculated using Equation 18.

**Equation 18: Total Oxygen Requirement Carbon + Nitrogen**

Now method 2 has an estimate that is 13.9% higher than method 1. So we’ve closed the gap but it is still fairly wide. Since we adjusted the oxygen consumption in method 2 to account for the elevated COD/BOD_{5} ratio that tells us that our use of 1.5 lb O_{2}/lb BOD_{5} removed in method is likely to be unreasonably low given the fact that there is an elevated amount of slowly biodegradable organics in the wastewater.

This method, which requires field testing to determine the oxygen uptake rate, produces a precise result for the oxygen required to treat a particular wastewater at a specific flow rate. In this case, a sample of the influent wastewater to the aeration basin was collected and used to perform oxygen uptake rate (OUR) testing. The result of the testing established an OUR of 19.22 mg/L/hr. The result of the OUR test and the estimation of oxygen demand is calculated using Equation 19.

**Equation 19: Oxygen Requirement From OUR Test**

Method 1: 13,073 lb O_{2}/day

Method 2: 14,889 lb O_{2}/day

Method 3: 13,826 lb O_{2}/day

OUR testing produces a data value that can be used to accurately calculate the oxygen consumption of a wastewater. It does not require any guessing in determing the oxygen demand. With Method 1 you have to pick (guess at) a value for lb O_{2}/lb BOD_{5} removed. And with Method 2 you have to guess at a *Y* value. In each case an unknown degree of error has been introduced into the calculation. Regardless, the fact is, if you are unable to generation an OUR value you have no choice but to use either Method 1 or Method 2, or both, as a check on the validity of the results.

In terms of accuracy, using Method 3 (based on the OUR) as the most accurate measurement and the baseline for comparison, Method 1 generated an oxygen demand rate 5.4% less than Method 3, not too bad. And Method 2, compared to Method 3, generated an oxygen demand 7.7% greater than Method 3, again, not too bad. It should be realized that Method 3 can be used as a means to estimate the key lb O_{2}/lb BOD_{5} removed parameter required with Method 1. And the OUR result can also be used to estimate the *Y* value required with Method 2.

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