Engineering calculators · Sludge
Sludge dewatering mass balance calculator
Run a solids and water mass balance through sludge thickening and dewatering. From the sludge flow and dry solids, or the tonnes of dry solids a day, the calculator gives the cake or thickened sludge produced in tonnes and cubic metres, the filtrate or centrate flow and the solids it returns to the works, the polymer needed as active and as product, the cost per tonne of dry solids and per year, the tanker loads a week and the throughput each machine must handle. Presets cover gravity, belt, drum and centrifuge thickeners and belt, centrifuge, screw and plate presses.
Inputs
Results
- Gravity belt thickener: thickened solids of 6% is within the typical 5 to 7%.
- Dewatering centrifuge: cake solids of 25% is within the typical 22 to 30%.
- Dewatering centrifuge: polymer dose of 8 kg active/tDS is within the typical 6 to 12 kg/tDS.
- 488 kg/d of solids (10% of feed) return to the works in liquors. Returned liquors also carry ammonia and phosphorus and should be included in the works load.
Stage by stage
| Quantity | Thickening | Dewatering | Notes |
|---|---|---|---|
| Feed solids, tDS/d | 5.00 | 4.75 | to this stage |
| Feed volume, m³/d | 200 | 79.2 | |
| Feed dry solids, % | 2.50 | 6.00 | |
| Captured solids, tDS/d | 4.75 | 4.51 | feed × capture |
| Product, t/d wet | 79.2 | 18.1 | captured ÷ product DS |
| Product, m³/d | 79.2 | 17.2 | wet ÷ density |
| Filtrate or centrate, m³/d | 121 | 61.1 | feed volume − product |
| Solids in liquor, kg/d | 250 | 238 | feed − captured |
| Liquor solids, mg/L | 2,069 | 3,886 | |
| Polymer, kg active/d | 15.0 | 38.0 | dose × feed tDS |
| Throughput per machine, m³/h | 12.5 | 4.95 | feed ÷ (hours × machines) |
| Throughput per machine, kgDS/h | 313 | 297 |
Sensitivity to cake dry solids
| Product DS, % | Wet, t/d | Volume, m³/d | Loads/week | Wet, t/year | Liquor, m³/d |
|---|---|---|---|---|---|
| 21 | 21.5 | 20.5 | 5.7 | 7,843 | 179 |
| 23 | 19.6 | 18.7 | 5.2 | 7,161 | 180 |
| 25 | 18.1 | 17.2 | 4.8 | 6,588 | 182 |
| 27 | 16.7 | 15.9 | 4.5 | 6,100 | 183 |
| 29 | 15.6 | 14.8 | 4.1 | 5,680 | 184 |
How the calculation works
- Feed solids. Mfeed (tDS/d) = Q (m³/d) × DS ÷ 100, taking liquid sludge at 1 t/m³ [M&E].
- Captured solids. Mout = Mfeed × capture. Solids to liquor = Mfeed − Mout.
- Product. Wet mass = Mout ÷ DSproduct; volume = wet mass ÷ bulk density. Thickened sludge is taken at 1 t/m³.
- Liquor. Filtrate or centrate volume = feed volume − wet product mass (water balance at 1 t/m³). Its solids concentration = solids to liquor ÷ volume.
- Two stages. The thickener product becomes the dewatering feed, so solids losses compound: overall capture = capture1 × capture2 [WEF].
- Polymer. Active kg/d = dose (kg/tDS) × stage feed tDS/d. Product kg/d = active ÷ strength. Solution L/d = active ÷ (concentration % ÷ 100) [EPA]. Cost = product × price; per tDS = cost ÷ feed tDS.
- Throughput. Feed per machine = stage feed ÷ (hours × machines), in m³/h and kgDS/h, for comparison with the supplier's hydraulic and solids ratings [EPA].
Worked example with the default inputs
200 m³/d at 2.5% DS is 5 tDS/d. A gravity belt thickener at 6% DS and 95% capture keeps 4.75 tDS/d in 79.2 t/d (79.2 m³/d) of thickened sludge and sends 120.8 m³/d of filtrate carrying 250 kg/d back to the works. The dewatering centrifuge at 25% DS and 95% capture keeps 4.5125 tDS/d, giving 18.05 t/d of cake, 17.2 m³/d at 1.05 t/m³, and 61.1 m³/d of centrate with 237.5 kg/d of solids. Overall capture is 0.95 × 0.95 = 90.25%. Polymer is 3 × 5 + 8 × 4.75 = 53 kg active/d; at 100% strength and £3/kg that is £159/d, £31.80 per tDS fed and £58,035 a year. Cake haulage is 17.2 × 7 ÷ 25 = 4.8 loads a week. The centrifuge must take 79.2 ÷ 16 = 4.95 m³/h and 297 kgDS/h.
What this cannot tell you. It is a steady-state balance with the performance you enter. It does not predict what cake solids or capture a given sludge will reach; those depend on sludge type, digestion, volatile solids, conditioning and the machine, and come from bench tests, pilot trials or supplier guarantees. It ignores washwater on belt presses, dilution water in polymer make-down, sludge density above 1 t/m³, grit, and the ammonia and phosphorus in liquors. Use it for sizing, cost estimates and checking operating data, not as a performance guarantee.
Sources
- US EPA (2000) Biosolids Technology Fact Sheet: Centrifuge Thickening and Dewatering (cake solids, capture, polymer dose)
- US EPA (2000) Biosolids Technology Fact Sheet: Belt Filter Press (cake solids, capture, polymer dose)
- US EPA (2000) Biosolids Technology Fact Sheet: Recessed-Plate Filter Press (cake solids 30 to 45%)
- US EPA (2003) Biosolids Technology Fact Sheet: Gravity Thickening (thickened solids 2 to 8%, capture)
- Water Environment Federation, Manual of Practice No. 8: Design of Water Resource Recovery Facilities, 6th ed., ch. on solids thickening and dewatering
- Metcalf & Eddy / AECOM (2014) Wastewater Engineering: Treatment and Resource Recovery, 5th ed., ch. 14 (sludge mass balances, thickening and dewatering performance)
Frequently asked questions
How do I convert sludge flow and dry solids to tonnes of dry solids?
Multiply the volume by the dry solids fraction, treating liquid sludge as 1 tonne per cubic metre: 200 m³/d at 2.5% DS is 200 × 0.025 = 5 tDS/d. The small error from sludge density (1.00 to 1.03 t/m³ for liquid sludge) is well within the uncertainty of the sampling.
What is solids capture and why does it matter?
Capture is the share of feed solids that ends up in the cake rather than in the filtrate or centrate. At 95% capture on 5 tDS/d, 250 kg/d of solids go back to the head of the works in the liquors, along with ammonia and phosphorus released in digestion. Low capture raises the works load, fouls the liquor system and wastes polymer, so it is the first thing to check when a machine underperforms.
How much polymer does dewatering use?
Doses are quoted as kg of active polymer per tonne of dry solids. Belt presses use about 3 to 8 kg/tDS, centrifuges 6 to 12, screw presses 5 to 10 and plate presses, which often use lime or ferric instead, 0 to 4. Digested and surplus activated sludges need more than primary sludge. Emulsion polymers are 40 to 50% active, so the product quantity is roughly double the active dose; powders are near 100% active.
Why is cake volume different from cake mass?
Cake is weighed in tonnes for disposal contracts but hauled by volume. The calculator divides wet cake mass by the cake bulk density, typically 1.0 to 1.1 t/m³, to give m³/d and tanker or skip loads. Drier cake is both lighter and smaller: going from 20 to 25% DS cuts wet cake mass by 20%.