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Hydrometallurgy

Filtration Mass Balance Calculator

This calculator runs the single-unit mass and water balance across a filter — the dewatering step downstream of the thickener. From a measured feed dry-solids rate, the feed percent solids by mass, and the filter-cake moisture (wet basis, a value you measure or specify), it returns the cake solids, the water held in the cake, the total wet cake mass, the water removed to filtrate, the solids recovery to cake, and the solids lost to filtrate. An optional filtrate solids-loss fraction handles a non-clean filtrate (it defaults to 0 = clean filtrate, full solids recovery). The balance uses the same two-phase engine as the slurry and thickener calculators: feed slurry = dry solids ÷ feed fraction, and total mass closes (feed = wet cake + filtrate water + any lost solids). It is a preliminary, formula-based, educational mass/water balance on measured data. It is NOT a cake-moisture, filtration-rate, or recovery predictor, does NOT model rheology, washing, or filtration kinetics, and is NOT a filtration simulator. Cake moisture and any filtrate solids loss are user inputs, not predicted values. Final design requires representative, reconciled stream data and qualified review.

TypeInteractive engineering calculator

Calculator

t/h

dry solids in the filter feed

wt%

percent solids by mass in the feed slurry

wt%

measured or specified — a value you supply

%

optional; 0 = clean filtrate (full recovery)

Result
Filtrate water removed211.382 t/h
Solids recovery to cake100 %
Cake solids100 t/h
Cake water21.9512 t/h
Total wet cake mass121.951 t/h
Solids lost to filtrate0 t/h
Feed slurry mass333.333 t/h
Water removed (of feed water)90.5923 %
  • !Preliminary two-phase mass/water balance on measured data — it balances the feed slurry into a wet cake and a filtrate from the feed dry-solids rate, feed % solids, and a cake moisture YOU supply.
  • !It does NOT predict cake moisture, filtration rate, or recovery, does NOT model rheology, washing, or kinetics, and is NOT a filtration simulator. Final design requires representative, reconciled stream data and qualified review.

Preliminary, formula-based two-phase mass/water balance across a filter from measured feed tonnage, feed % solids, and a supplied cake moisture. Not a cake-moisture, filtration-rate, or recovery predictor, not a rheology/washing/kinetics model, and not a filtration simulator. Final design requires representative, reconciled stream data and qualified review.

Related: Filtration & Dewatering Calculations Explained · Filter Cake Moisture & Solids · Thickener Water Recovery · Percent Solids Mass ↔ Volume · Hydromet & Slurry Calculations

Formulas

Feed slurry mass
ṁ_feed = ṁ_s / Cw_feed
Feed water
ṁ_wf = ṁ_feed − ṁ_s
Cake solids
ṁ_sc = ṁ_s × (1 − L)
Total wet cake
ṁ_cake = ṁ_sc / (1 − M_cake)
Cake water
ṁ_wc = ṁ_cake − ṁ_sc
Filtrate water removed
ṁ_filt = ṁ_wf − ṁ_wc
Solids recovery to cake
R_s = ṁ_sc / ṁ_s
Solids lost to filtrate
ṁ_sl = ṁ_s × L

Diagram

Filtration mass balance — feed slurry splits into wet cake and filtrate waterfeed slurryfiltercloth / mediumwet cakesolids + waterfiltrate (water removed)ṁ_feed = ṁ_s / Cwṁ_cake = ṁ_sc / (1−M)ṁ_filt = ṁ_wf − ṁ_wcR_s = ṁ_sc / ṁ_sbalance on measured data — not a performance predictor or simulator

Worked example

A filter feed carries 100 t/h of dry solids at 30 wt% solids; the discharged cake is at 18 wt% moisture (82 wt% solids) with a clean filtrate. Find the cake streams, the water removed, and the solids recovery.

  1. 01Feed slurry mass: ṁ_feed = 100 / 0.30 = 333.33 t/h
  2. 02Feed water: 333.33 − 100 = 233.33 t/h
  3. 03Cake solids (clean filtrate): ṁ_sc = 100 × (1 − 0) = 100.00 t/h
  4. 04Total wet cake: ṁ_cake = 100 / 0.82 = 121.95 t/h
  5. 05Cake water: 121.95 − 100 = 21.95 t/h
  6. 06Filtrate water removed: 233.33 − 21.95 = 211.38 t/h (90.6% of feed water)
  7. 07Solids recovery: R_s = 100 / 100 = 100.0%; balance closes: 333.33 = 121.95 + 211.38 ✓
Result

Cake 121.95 t/h (100 t/h solids + 21.95 t/h water), filtrate water 211.38 t/h, solids recovery 100.0% — a preliminary mass/water balance, not a filtration-performance result.

FAQ

What does this filtration mass balance compute?
From the feed dry-solids rate, the feed % solids, and the cake moisture, it returns the cake solids, the cake water, the total wet cake mass, the water removed to filtrate, the solids recovery to cake, and the solids lost to filtrate. It answers "filtrate recovery", "solids recovery", "water removed by filtration", and "thickener-to-filter balance" in one page.
Where does the cake moisture come from?
You supply it — from a measured cake sample, a target specification, or the filter-cake moisture calculator. This balance does not predict the moisture a filter will achieve; it takes the cake moisture as an input and balances the streams around it. That is the key boundary: it balances measured streams, it does not predict performance.
How is this different from the thickener water recovery calculator?
The thickener water-recovery calculator balances a thickener: feed in, thickened underflow out, and clarified water to the overflow. This calculator balances the next unit downstream — a filter — where the streams are a wet filter cake and a filtrate. Different unit, different outputs (filtrate + wet cake vs overflow), so it is a separate page rather than a duplicate.
What is the filtrate solids loss input for?
It is the fraction of feed solids that report to the filtrate rather than the cake (cloth blinding, fines bleed, a torn cloth). It defaults to 0 — a clean filtrate and 100% solids recovery. Enter a small percentage to model a non-clean filtrate; the solids recovery and solids-lost outputs then update accordingly. It is a supplied value, not a prediction.
Does the mass balance close?
Yes. The feed slurry equals the total wet cake plus the filtrate water plus any solids lost to the filtrate. In the worked example 333.33 t/h feed = 121.95 t/h wet cake + 211.38 t/h filtrate water (with zero solids lost), which closes exactly — a built-in cross-check on the inputs.

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