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Process Design

Slurry Mass Balance Calculator

This calculator performs a single-stream slurry mass balance. Given the slurry volumetric flow, the slurry density, and the percent solids by mass, it splits the stream into solids and liquid mass flows. When you also supply the solids and liquid densities, it returns the component volumetric flows and the percent solids by volume. It is a preliminary single-stream balance — not a full plant mass balance, thickener model, or process simulator.

TypeInteractive engineering calculator

Calculator

0–100 %

Optional — for volume basis

Result
Slurry mass flow122.96 t/h
Solids mass flow36.888 t/h
Liquid mass flow86.072 t/h
Slurry volumetric flow100 m³/h
Solids volumetric flow13.92 m³/h
Liquid volumetric flow86.072 m³/h
Percent solids by mass30 %
Percent solids by volume13.9211 %

Formulas

Slurry mass flow
ṁ_slurry = Q_slurry × ρ_slurry
Solids mass flow
ṁ_solids = ṁ_slurry × Xs
Liquid mass flow
ṁ_liquid = ṁ_slurry × (1 − Xs)
Solids volume flow
Q_solids = ṁ_solids / ρ_solids
Liquid volume flow
Q_liquid = ṁ_liquid / ρ_liquid

Diagram

Slurry Mass Balance: Stream SplitQ × ρ_slurryṁ_slurryṁ_solids = ṁ·XsQ_solids = ṁ_solids/ρ_Sṁ_liquid = ṁ·(1−Xs)Q_liquid = ṁ_liquid/ρ_Lmass conserved across the split

Worked example

A slurry stream flows at 100 m³/h with a slurry density of 1229.6 kg/m³ at 30% solids by mass. Solids density is 2650 kg/m³ and liquid density is 1000 kg/m³. What are the mass and volume flows?

  1. 01ṁ_slurry = 100 × 1229.6 = 122,960 kg/h = 122.96 t/h
  2. 02ṁ_solids = 122.96 × 0.30 = 36.89 t/h
  3. 03ṁ_liquid = 122.96 × 0.70 = 86.07 t/h
  4. 04Q_solids = 36,888 / 2650 ≈ 13.92 m³/h
  5. 05Q_liquid = 86,072 / 1000 ≈ 86.07 m³/h
  6. 06Cv = 13.92 / (13.92 + 86.07) ≈ 13.9%
Result

Slurry 122.96 t/h; solids 36.89 t/h; liquid 86.07 t/h. Solids volume ≈ 13.92 m³/h, liquid volume ≈ 86.07 m³/h (total ≈ 99.99 m³/h). Percent solids by volume ≈ 13.9%.

FAQ

What is the minimum input I need?
Slurry volumetric flow, slurry density, and percent solids by mass. That gives you the slurry, solids, and liquid mass flows. Supplying the solids and liquid densities additionally unlocks the component volumetric flows and the percent solids by volume.
Where do I get the slurry density?
Measure it (e.g. Marcy cup, Coriolis, nuclear gauge) or estimate it with the Slurry Density Calculator from the liquid density, solids density, and percent solids.
Why might my component volumes not sum exactly to the slurry volume?
For a consistent set of inputs they should sum to the slurry volumetric flow within rounding. Small discrepancies usually mean the entered slurry density and percent solids are not perfectly consistent with the component densities.
Can this balance a whole plant or multiple streams?
No. This is a single-stream balance. Multi-stream reconciliation, thickeners, cyclones, and recovery models are out of scope.

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