Biochemical Oxygen Demand Calculator

BOD₅ gives a snapshot of oxygen demand at 5 days, but the rate at which that demand is exerted — the kinetic constant k — determines how quickly oxygen is depleted in a river and where the minimum dissolved oxygen concentration occurs. The BOD kinetics calculator fits first-order kinetic parameters to your time-series BOD data, providing the rate constant and ultimate BOD that models need for dissolved oxygen sag curve analysis.

First-Order BOD Kinetics: The Fundamental Model

Aerobic decomposition of organic matter follows approximate first-order kinetics:

BOD_t = BOD_u × (1 − e^(−k×t))

where BOD_t is oxygen demand at time t (days), BOD_u is ultimate BOD (total oxygen demand when decomposition is complete), and k is the first-order rate constant (day⁻¹). Linearized form for fitting: ln(BOD_u − BOD_t) = ln(BOD_u) − k×t. From this: measuring BOD at multiple time points (day 1, 2, 3, 5, 7, 10, 20) allows fitting of both k and BOD_u by least squares regression. Typical k values at 20°C: raw domestic sewage: k = 0.15–0.25 day⁻¹; secondary effluent: k = 0.06–0.10 day⁻¹; industrial wastewater with complex organics: k = 0.03–0.08 day⁻¹. Use this online calculator to fit kinetic parameters to your data. The BOD₅ calculator handles single time-point measurements.

Temperature Correction: From 20°C to Field Conditions

BOD rate constants are temperature-dependent, following the van 't Hoff-Arrhenius relationship:

k_T = k_20 × θ^(T−20)

where θ (theta) is the temperature coefficient, typically 1.047 for BOD kinetics (commonly rounded to 1.05). At 10°C (typical winter stream temperature): k_10 = k_20 × 1.047^(−10) ≈ 0.63 × k_20 — decomposition rate is 37% lower. At 30°C (summer): k_30 ≈ 1.59 × k_20. This temperature dependence is critical for river water quality modeling — the same wastewater discharge has much greater oxygen impact in summer (faster decomposition rate, lower oxygen saturation, less reaeration) than winter, which is why summer low-flow periods are the critical design condition for wastewater discharge permits.

Nitrogenous BOD: The Second-Stage Oxygen Demand

Standard BOD analysis measures carbonaceous BOD (CBOD) — oxygen consumed in oxidizing organic carbon. A second-stage BOD from nitrification occurs when nitrifying bacteria oxidize ammonium to nitrite and then nitrate:

• NH₄⁺ + 1.5O₂ → NO₂⁻ + 2H⁺ + H₂O (uses 3.43 g O₂ per g NH₄⁺-N)
• NO₂⁻ + 0.5O₂ → NO₃⁻ (uses 1.14 g O₂ per g NO₂⁻-N)
• Total nitrogenous BOD: approximately 4.57 g O₂ per g NH₃-N

Nitrification typically begins after day 5–10 in untreated or partially treated samples, causing the BOD curve to show a "second stage" uptick. Using ATH (allylthiourea) or TCMP as nitrification inhibitors suppresses this second stage, allowing pure CBOD measurement. The dissolved oxygen calculator and water quality calculators provide complementary water quality assessment tools.

BOD in Treatment Plant Design

BOD kinetics directly determines wastewater treatment unit sizing. For a complete-mix activated sludge system, the required hydraulic retention time (HRT) to achieve target effluent BOD:

HRT = (S₀ − S) / (μ_max × S × X / Y − k_d × X)

where S₀ = influent BOD (mg/L), S = target effluent BOD, X = MLSS concentration, Y = yield coefficient, k_d = decay rate. This design equation requires the ultimate BOD (not just BOD₅) as the correct substrate concentration — another reason why k and BOD_u determination from kinetic analysis is essential in treatment design rather than simply using the 5-day surrogate measurement.