Filtration and Dewatering Calculations Explained
The concept anchor for filtration — what filtration is and how it follows thickening, what cake moisture, filtrate, and solids recovery mean, how the filter mass/water balance works, and what required filter area means. Carries the operating-calculation-vs-equipment-sizing / performance-prediction boundary: it balances streams and sizes area from supplied rates, it does not select or design equipment.
Definition
Filtration is the dewatering step that separates a slurry into a wet solid filter cake and a (largely) clear liquid filtrate by passing the slurry through a filter medium. In a mineral-processing flowsheet it usually follows thickening: the thickener raises the percent solids of the slurry by settling and removing clarified overflow water, and the filter then removes most of the remaining water mechanically, producing a handleable cake. The everyday filtration calculations are three: the filter-cake moisture (the water held in the cake, on a wet or dry basis), the filter mass/water balance (how the feed splits into cake solids, cake water, and filtrate, and what fraction of solids reports to the cake), and the required filter area (the area needed to pass a throughput at a supplied filtration rate). All three are preliminary, formula-based, educational operating calculations on measured or supplied data — they balance streams and size area, they do not select or design filtration equipment.
Why it matters
The defining boundary of these calculations is operating calculation versus equipment sizing and performance prediction. The filter mass balance balances measured streams; the cake-moisture calculation splits a measured cake; the filter-area calculation sizes area from a filtration rate you supply. None of them predicts the moisture a filter will achieve, the filtration rate an ore will give, or the recovery a circuit will deliver — those depend on the material, particle size, cake thickness, air or pressure, cycle time, washing, and filter type, and require filtration testwork (leaf tests, pilot work) and vendor methods. It is easy to misread a tidy area number as 'the filter I need' or a cake-moisture figure as 'the moisture I will get'; neither is true. Thickening and filtration are complementary: thickeners are cheap bulk water removal that get the slurry to perhaps 50–65% solids, while filters do the expensive final dewatering to a low-moisture cake. The water balance ties them together — the thickener-to-filter sequence is exactly what the filter mass balance quantifies. Get the operating-versus-design boundary right and these are honest first-pass checks; blur it and the numbers are dangerously over-read as equipment selection or guarantees.
Formula
Units involved
- •feed dry-solids rate ṁ_s and throughput G — t/h (G also kg/h for the area calc)
- •feed % solids Cw and cake moisture M_cake — by mass (wet basis)
- •cake, filtrate, and water streams — t/h
- •specific filtration rate R — kg dry solids / m²·h (a user input)
- •required filter area A — m²; on-stream factor f — dimensionless fraction
Concept diagram
Worked example
A filter feed carries 100 t/h of dry solids at 30 wt% solids; the cake is at 18 wt% moisture (82 wt% solids), clean filtrate. Separately, a 20 t/h duty has a leaf-test filtration rate of 200 kg/m²·h. Run the balance and the area check.
- 01Feed slurry: 100 / 0.30 = 333.33 t/h; feed water = 233.33 t/h
- 02Wet cake: 100 / 0.82 = 121.95 t/h; cake water = 21.95 t/h
- 03Filtrate water removed: 233.33 − 21.95 = 211.38 t/h; solids recovery = 100.0%
- 04Mass balance closes: 333.33 = 121.95 (cake) + 211.38 (filtrate) ✓
- 05Required area: A = 20 000 kg/h / (200 × 1) = 100 m² — at a SUPPLIED rate, an operating check
Filtrate 211.38 t/h at 100% solids recovery, and 100 m² required at the supplied 200 kg/m²·h — operating calculations, not equipment selection or a performance guarantee.
Common mistakes
- •Reading a required filter area as "the filter to buy" — it is an area from a supplied rate, not equipment selection or design.
- •Treating cake moisture or the filtration rate as predicted — both are measured or supplied inputs.
- •Confusing the thickener water balance (overflow) with the filter water balance (filtrate + wet cake).
- •Mixing wet-basis and dry-basis cake moisture without stating which (the dry basis is always larger).
- •Assuming a clean filtrate when fines bleed through — set a filtrate solids loss and recovery drops below 100%.
- •Ignoring the on-stream factor, then under-sizing the area for a filter that is not filtering 100% of the time.
When to use the calculator
Use the filtration mass balance calculator to split a measured feed into cake solids, cake water, total wet cake, filtrate water, solids recovery, and solids lost to filtrate. Use the filter cake moisture & solids calculator to convert a wet/dry cake mass into moisture on both bases and the cake % solids. Use the filter area & capacity calculator (an operating check only) to get the required area and cake production rate from a throughput and a filtration rate you supply. For the moisture a filter will actually achieve, the filtration rate for your ore, filter selection or sizing, vacuum/pressure-system design, media selection, or any performance guarantee, use filtration testwork, vendor methods, and qualified review — those are outside these calculators.