含义Meaning
微生物氧化水中有机物所消耗的溶解氧随时间按一级动力学趋近总需氧量 L₀。通常测定 20 °C 下 5 天的 BOD₅。斯特里特–菲尔普斯（1925）把耗氧与复氧结合，预测河流排污口下游的溶解氧下垂。
Oxygen consumed by microbes oxidising organic matter approaches the ultimate demand L₀ with first-order kinetics; the standard test is BOD₅ at 20 °C. Streeter–Phelps (1925) combined deoxygenation and reaeration to predict the dissolved-oxygen sag below an outfall.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(L_0\) | 最终（总）生化需氧量ultimate BOD | mg·L⁻¹ |
| \(k_1\) | 耗氧速率常数deoxygenation rate constant | d⁻¹ |
| \(k_2\) | 复氧速率常数reaeration rate constant | d⁻¹ |
| \(D\) | 氧亏（饱和溶解氧 − 实际溶解氧）oxygen deficit | mg·L⁻¹ |
推导Derivation
剩余可降解有机物 L 按一级消耗：\(dL/dt = -k_1L\)，\(L = L_0e^{-k_1t}\)。
Remaining demand decays first order.
已消耗氧 = \(L_0 - L\)。
Oxygen used = L₀ − L.
河流中氧亏 \(dD/dt = k_1L - k_2D\)，与连续反应 A→B→C 同型，解得下垂曲线。
In a river dD/dt = k₁L − k₂D, the same form as consecutive reactions.
适用条件与局限Assumptions & limitations
k₁ 随温度和水样而异（θ 校正 \(k_T = k_{20}\cdot1.047^{T-20}\)）；硝化作用会额外耗氧。COD（化学需氧量，重铬酸钾法）测的是可被化学氧化的全部有机物，一般 COD > BOD。
k₁ varies with temperature and water; nitrification adds demand. COD (dichromate) measures all chemically oxidisable matter, usually exceeding BOD.