Biosolids Management, Decanter Centrifuges & Mass Balance
Sludge Centrifuge Solids Capture % & Cake Tonnage Formula
Calculate Decanter Centrifuge / Belt Press Solids Capture Recovery (%) from Lab %TS Samples, Daily Dry Solids Captured (t/d), Hauled Wet Cake Tonnage (t/d), and Volume Reduction (%).
Compute exact Solids Capture % from 3 grab samples—without needing flowmeters on cake conveyors!
Measuring wet biosolids mass on a screw conveyor is notoriously inaccurate, yet solving simultaneous total-mass and dry-solids conservation across a decanter centrifuge or belt filter press eliminates flowmeters completely! Given just three lab Total Solids (%TS) oven-dish tests—Feed Sludge C_f (%TS), Dewatered Cake C_k (%TS), and Centrate/Filtrate Return C_c (%TS)—exact Solids Capture Recovery (%) is Capture_Pct = ((C_k * (C_f - C_c)) / (C_f * (C_k - C_c))) * 100! Dirty centrate (high C_c from under-dosing cationic polymer) recycles fine solids back to the headworks, overloading plant aeration!
Verify on a 200 Wet-Ton/Day Digested-Sludge Decanter Centrifuge—Wet_Sludge_Feed = 200.0 t/d (B2), Feed_Solids C_f = 3.00% TS (6.00 dry t/d, B3), Dewatered_Cake_Solids C_k = 25.00% TS (B4), and Centrate_Solids C_c = 0.15% TS (1,500 mg/L, B5): Solids Capture Recovery hits (25 * (3.00 - 0.15)) / (3.00 * (25.00 - 0.15)) * 100 = 95.57% (E2), Captured Dry Biosolids equal 5.73 t/d (E3), Hauled Wet Cake drops from 200.0 t/d down to 5.734 / 0.25 = 22.94 wet t/d (E4), achieving an 88.53% Haulage Mass Reduction (E5)!
| Centrifuge Dewatering KPI (200 t/d Wet Feed, Cf=3.0%, Ck=25.0%, Cc=0.15%) | Formula | Verified Output |
|---|---|---|
| Solids Capture Recovery (%) | ((Ck * (Cf - Cc)) / (Cf * (Ck - Cc))) * 100 | 95.57% (86.56% @ Cc = 0.45%) |
| Captured Dry Biosolids (t/d) | Wet_Feed * (Cf / 100) * (Capture_Pct / 100) | 5.73 t/d |
| Hauled Wet Cake Mass (t/d) | Captured_Dry_t_d / (Ck / 100) | 22.94 t/d (20.77 @ Cc = 0.45%) |
| Wet Haulage Mass Reduction (%) | ((Wet_Feed - Wet_Cake) / Wet_Feed) * 100 | 88.53% |
Three-Concentration Solids Capture Recovery Formula
Validate Wet_Feed > 0 and strict concentration ordering 0 <= Centrate_Cc < Feed_Cf < Cake_Ck <= 60!
=LET(wf_t, B2, cf_p, B3, ck_p, B4, cc_p, B5, IF(OR(wf_t <= 0, cc_p < 0, cf_p <= cc_p, ck_p <= cf_p, ck_p > 60), "Invalid Dewatering Input", ROUND(((ck_p * (cf_p - cc_p)) / (cf_p * (ck_p - cc_p))) * 100, 2)))Polymer Under-Dose Dirty Centrate Check (Set Centrate Solids C_c = 0.45% TS)
Simulate a polymer-pump clog where Centrate_Solids B5 triples from 0.15% to 0.45% TS: Solids Capture Recovery E2 plunges from 95.57% down to 86.56%—dumping nearly 13.4% of digested solids back into the primary clarifiers!
=IF(ISTEXT(E2), E2, LET(cp_f, (B4 * (B3 - B5)) / (B3 * (B4 - B5)), ck_w, (B2 * (B3 / 100) * cp_f) / (B4 / 100), ROUND(((B2 - ck_w) / B2) * 100, 2)))Try the example
Use the original values or change them to test your understanding.