What is Theoretical Oxygen Demand (ThOD)?

Theoretical Oxygen Demand (ThOD) is the stoichiometric amount of oxygen required to completely oxidize a specific organic compound to its ultimate mineralized products (CO2, H2O, HNO3, SO2, and P2O5).

How does ThOD relate to BOD and COD in industrial wastewater?

ThOD represents the absolute upper limit of oxygen demand. Chemical Oxygen Demand (COD) typically equals 90% to 100% of ThOD for pure organic chemicals. Biological Oxygen Demand (BOD5) measures the 5-day biodegradable fraction, usually ranging from 50% to 70% of ThOD for readily biodegradable organics.

Why does nitrogen in organic compounds increase oxygen demand?

Organic nitrogen is first converted to ammonia (NH3) during carbonaceous oxidation. Nitrifying bacteria subsequently oxidize ammonia to nitrate (NO3-), consuming 2 moles of O2 per mole of NH3 (or 4.57 g O2 per gram of nitrogen), creating a significant Nitrogenous Oxygen Demand (NOD).

ThOD calculation step by step

Theoretical oxygen demand (thod) calculation

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1. STEP 1 : Gather data for theoretical oxygen demand calculation
2. STEP 2 : Calculate the ThOD
3. Interactive In-Browser ThOD Calculator (#calc-app)

Environment protection is now a priority and water effluents form factories must be controlled to make sure they do not carry too much organic material. When introducing a new component in a factory, it can be interesting to understand what will be the oxygen demand in the effluents in case the component is released. This page explains how to calculate the theoretical oxygen demand for a component of known formula.

1. STEP 1 : Gather data for theoretical oxygen demand calculation

In order to calculate the theoretical Oxygen Demand (ThOD), a chemical formula of the component must be determined as well as the reactions that are implied in the biodegradation of the material. The following example is the one of glycine.

Carbonaceous oxygen demand :

\[ \text{CH}_2(\text{NH}_2)\text{COOH} + \frac{3}{2} \text{O}_2 \longrightarrow \text{NH}_3 + 2 \text{CO}_2 + \text{H}_2\text{O} \]

CH₂(NH₂)COOH + 3/2 O₂ -> NH₃+2 CO₂+H₂O

Nitrogenous oxygen demand :

\[ \text{NH}_3 + \frac{3}{2} \text{O}_2 \longrightarrow \text{HNO}_2 + \text{H}_2\text{O} \]

NH₃ + 3/2 O₂ -> HNO₂+H₂O

\[ \text{HNO}_2 + \frac{1}{2} \text{O}_2 \longrightarrow \text{HNO}_3 \]

HNO₂+1/2 O₂ -> HNO₃

that can be simplified as :

\[ \text{NH}_3 + 2 \text{O}_2 \longrightarrow \text{HNO}_3 + \text{H}_2\text{O} \]

NH₃ + 2 O₂ -> HNO₃ + H₂O

2. STEP 2 : Calculate the ThOD

The theoretical oxygen demand can then be calculated from the equations above. It can be seen that for every mole of glycine, there will be a consumption of $ \frac{3}{2} + 2 = \frac{7}{2} = 3.5 $ moles of O₂.

Considering that the molecular weight of O₂ is $ 16 \times 2 = 32 \text{ g/mol} $, the mass of oxygen to be consumed to degrade one mole of glycine can be calculated :

\[ \text{ThOD}_{\text{molar}} = 3.5 \text{ moles of O}_2 / \text{mole of glycine} \]

ThOD = 3.5 moles of O₂/mole of glycine

\[ \text{ThOD}_{\text{mass/mole}} = 3.5 \times 32 \text{ g of O}_2 / \text{mole of glycine} = 112 \text{ g of O}_2 / \text{mole of glycine} \]

ThOD = 3.5 * 32 g of O₂/mole of glycine

ThOD = 11 g of O₂/mole of glycine

Note: 3.5 × 32 g/mol equals 112 g O₂/mole of glycine. Expressed as a mass ratio per gram of glycine (molar mass = 75.07 g/mol), $ \text{ThOD} = \frac{112}{75.07} = 1.492 \text{ g O}_2/\text{g glycine} $.

🧪 Interactive Theoretical Oxygen Demand (ThOD) Calculator

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

Preset Organic Compound:

Carbon Atoms (c):

Hydrogen Atoms (h):

Oxygen Atoms (o):

Nitrogen Atoms (n):

Sulfur Atoms (s):

Phosphorus Atoms (p):

Include Nitrification (NOD)?

Solute Concentration (mg/L):

Effluent Flow Rate (m³/h):

Stoichiometric & Oxygen Demand Results

Compound Molar Mass: 75.07 g/mol

Carbonaceous O₂ Demand: 1.50 mol O₂ / mol solute

Nitrogenous O₂ Demand (NOD): 2.00 mol O₂ / mol solute

Total Stoichiometric O₂ Ratio: 3.50 mol O₂ / mol solute

Mass Demand Ratio (ThOD): 1.492 g O₂ / g solute

Effluent Equivalent ThOD Concentration: 149.18 mg O₂ / L

Total Oxygen Mass Flow Requirement: 1.492 kg O₂ / h

💡 Industrial Wastewater Best Practices & Engineering Rules of Thumb

ThOD vs. COD vs. BOD: Theoretical Oxygen Demand (ThOD) represents the ultimate upper bound. For pure organic compounds, Chemical Oxygen Demand (COD) is generally 90% – 100% of ThOD. 5-day Biochemical Oxygen Demand (BOD₅) is typically 60% – 70% of ultimate BOD for readily biodegradable substances.
Nitrification Stoichiometry: Complete nitrification of ammonia requires 4.57 g O₂ per gram of Total Kjeldahl Nitrogen (TKN) oxidized ($ 1.14 \text{ g O}_2/\text{g N} $ to nitrite + $ 3.43 \text{ g O}_2/\text{g N} $ to nitrate).
Aeration Power Sizing: Standard aeration efficiency ($SAE$) in activated sludge systems typically ranges between 1.2 and 2.2 kg O₂ / kWh under process conditions.
Blower Design Margins: Apply a peak-to-average loading safety factor of 1.3 to 1.5 when sizing aeration blowers and diffusers to handle hydraulic and organic surges.

Sources

[Chopey] Handbook of Chemical Engineering calculations, Chopey et al, McGraw Hill, 2004