Attached-Growth Biological Wastewater Treatment, NRC (1946) Trickling-Filter BOD Formula
Trickling Filter NRC Recirculation & BOD5 Removal Formula
Calculate Daily Settled BOD5 Organic Load (kg/d), NRC Effective Biofilm Pass Factor F, Single-Stage + Clarifier BOD5 Removal Efficiency (%), and Final Effluent BOD5 (mg/L).
Cranking trickling-filter recirculation R past 8.0 does NOT climb endlessly—NRC’s (1 + 0.1·R)^2 treatability decay peaks F at R = 8 and shuts off wetting benefits if recycle pumps trip!
**Attached-Growth Rock and Slag Trickling Filters** (`Media Volume V` m³ fed Primary-Clarified Wastewater `Q` m³/d at Settled `BOD_5` `C_0` mg/L -> **Daily Organic Load `W = (Q * C_0) / 1,000`** kg `BOD_5`/d) recycle `Q_r = R * Q` (`Recirculation Ratio R = Q_r / Q`) to keep rotary distributor arms flushing sloughed zoogloeal biofilm and dilute incoming strength! Analyzing `34` full-scale wastewater plants, the **U.S. National Research Council (`NRC`, `1946`)** derived **Effective Biofilm Pass Factor `F = (1 + R) / ((1 + 0.1 * R)^2)`** (accounting for diminishing `10%` substrate treatability per pass!) and the **SI-Converted First-Stage + Secondary-Clarifier Efficiency `E = 100 / (1 + 0.4432 * sqrt(W / (V * F)))`** (`%`, where `0.4432` converts imperial `0.0085` lb/(ac·ft) to `kg/(m³·d)`), fixing **Clarified Effluent `C_e = C_0 * (1 - E / 100)`** (`mg/L`)!
Verify on a Municipal Single-Stage Rock Trickling Filter—Influent_Flow `Q` = 4,800 m³/d (B2), Primary-Settled_`BOD_5` `C_0` = 175 mg/L (B3), Media_Volume `V` = 1,650 m³ (B4), and Recirculation_Ratio `R` = 1.50 (B5): Daily Organic Load `W` equals `840.0` kg `BOD_5`/d (E2), NRC Effective Pass Factor `F` equals `1.890` (E3), Overall `BOD_5` Removal Efficiency reaches **`81.30%`** (E4), and Secondary-Clarifier Effluent `BOD_5` equals **`32.7` mg/L** (E5)!
| NRC (1946) Trickling-Filter KPI (Media Volume V=1,650 m³) | Formula | Verified Output |
|---|---|---|
| Daily Organic Load W (kg BOD5/d) | (Influent_Q_m3_d * Settled_BOD_mg_L) / 1000 | 840.0 kg/d (2,444.0 kg/d cannery surge) |
| NRC Effective Pass Factor F | (1 + R) / ((1 + 0.1 * R) ^ 2) | 1.890 @ R=1.5 (1.000 @ recycle pump off) |
| First-Stage BOD5 Removal E (%) | 100 / (1 + 0.4432 * SQRT(W / (V * F))) | 81.30% (64.96% overloaded!) |
| Clarified Effluent BOD5 (mg/L) | Settled_BOD_mg_L * (1 - Removal_Pct / 100) | 32.7 mg/L (91.1 mg/L permit violation!) |
NRC (1946) SI Trickling-Filter Organic Loading & Effective Pass Formula
Validate `Flow_Rate Q` in `[50, 250,000]` m³/d, `Settled_BOD5 C_0` in `[30, 1,500]` mg/L, `Media_Volume V` in `[20, 50,000]` m³, and `Recirculation_Ratio R` in `[0, 8.0]`!
=LET(qf_d, B2, cz_m, B3, vm_c, B4, rr_x, B5, wb_k, (qf_d * cz_m) / 1000, fp_x, (1 + rr_x) / ((1 + 0.1 * rr_x) ^ 2), ef_p, 100 / (1 + 0.4432 * SQRT(wb_k / (vm_c * fp_x))), IF(OR(qf_d < 50, qf_d > 250000, cz_m < 30, cz_m > 1500, vm_c < 20, vm_c > 50000, rr_x < 0, rr_x > 8), "Invalid NRC Input", ROUND(cz_m * (1 - ef_p / 100), 1)))Seasonal Food-Processing Load (`Q = 9,400` m³/d, `C_0 = 260` mg/L) + Recycle Off (`R = 0`) Check
Take a seasonal fruit-cannery surge (`B2 = 9,400` m³/d at `B3 = 260` mg/L -> `2,444.0` kg/d in E2) while turning off recirculation (`B5 = 0` -> `F = 1.000` in E3): NRC Removal E4 sags to **`64.96%`**, pushing Effluent `BOD_5` E5 nearly `3x` higher to **`91.1` mg/L** alongside Psychoda filter-fly breeding on dry stones!
=IF(ISTEXT(E5), E5, LET(wb_k, (B2 * B3) / 1000, fp_x, (1 + B5) / ((1 + 0.1 * B5) ^ 2), ROUND(100 / (1 + 0.4432 * SQRT(wb_k / (B4 * fp_x))), 2)))Try the example
Use the original values or change them to test your understanding.