Wastewater Characteristics, BOD and Sewer Design

Before treating sewage, you need to know how much there is and how strong it is. The key measure of strength is BOD.

Quantity of sewage

• Dry weather flow ≈ 80% of the water supplied.
• Peak factor for sewers about 2–3 (higher for small populations).
• Storm water by the rational method (combined or separate systems).

BOD (biochemical oxygen demand)

The oxygen consumed by microbes oxidising organic matter.

BOD_t = L₀ (1 − e^(−k t)) (base e)

or BOD_t = L₀(1 − 10^(−k_D t)) with k = 2.303 k_D.

• L₀ = ultimate (first-stage) BOD. BOD₅ at 20 °C is the standard test.
• Rate constant varies with temperature: k_T = k₂₀ θ^(T−20), θ ≈ 1.047.
• Lab test: BOD = (DO_initial − DO_final)/(dilution fraction), with the dilution fraction = sample volume/bottle volume.
• COD (chemical oxygen demand, dichromate) ≥ BOD; BOD/COD ≈ 0.5 for biodegradable sewage. ThOD from stoichiometry.
• Population equivalent = industrial BOD load (kg/day) / per capita BOD (about 0.08 kg/day).

Solids

Total solids = suspended + dissolved. Volatile solids (lost at 550 °C) indicate organic content.

Sewer design

• Self-cleansing velocity: about 0.6–0.75 m/s at design flow, to stop solids settling. Maximum about 3 m/s to prevent erosion.
• Sewers are designed to flow partly full (about half to 0.8 full); a circular sewer runs at the same velocity at half full as at full.
• Manning's equation is used for slopes.

Stream self-purification

When sewage enters a river, BOD uses up oxygen while the surface re-aerates it. The dissolved oxygen sag curve (Streeter–Phelps):

D_t = (k_d L₀/(k_r − k_d))(e^(−k_d t) − e^(−k_r t)) + D₀ e^(−k_r t)

• D = DO deficit (saturation DO − actual DO); k_d = deoxygenation and k_r = reaeration rate constants.
• Self-purification factor f = k_r/k_d.
• The minimum DO occurs at the critical time t_c.

Worked example

A sample has BOD₅ = 200 mg/L and k = 0.23 per day (base e).

• L₀ = 200/(1 − e^(−1.15)) = 200/0.683 = 292.7 mg/L.

Practice