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Flotation

Flotation Cell Capacity Explained

The concept anchor for flotation capacity — what flotation cell capacity is, how a bank is sized from the slurry flow and a supplied target residence time, and how the number of cells, installed volume, and actual mean residence time follow. Carries the capacity-vs-performance boundary: it sizes volume, it does not predict recovery, kinetics, or the RTD.

TypeEngineering guide — concept explainer

Definition

Flotation cell capacity is the volumetric sizing of a flotation or conditioning bank: how much total cell volume — and so how many cells — are needed to hold the slurry for a chosen residence time, and what mean residence time a given installed bank actually delivers. It is the flotation application of the generic residence-time relationship τ = V / Q. Given a slurry flow, a target residence time you supply (from testwork or the literature), and the working volume of a single cell, the calculation returns the required total flotation volume, the number of cells (rounded up to a whole cell), the installed working volume, and the actual mean residence time. It is a preliminary, formula-based, educational sizing — the everyday arithmetic of laying out a flotation row — scoped strictly to capacity and residence time. It is not, and does not attempt to be, a model of how well the flotation will actually work.

Why it matters

The sharpest line in flotation is capacity versus performance. This calculation sizes the volume and counts the cells; it says nothing about how much mineral floats. The residence time it uses is an input you bring from flotation kinetics testwork, the literature, or a comparable operation — it is never predicted here. That distinction matters because 'flotation' strongly connotes recovery and grade, and it is easy to mistake a residence-time sizing for a performance promise. It is not one: a bank sized for 20 minutes of residence does not thereby recover any particular percentage of the valuable mineral. Recovery and grade depend on kinetics (rate constants, ultimate recovery), reagent suite, particle size and liberation, aeration, froth behaviour, and circuit configuration — none of which this calculation touches. Rounding up to a whole cell also means the installed bank usually delivers a little more residence time than the target (four 20 m³ cells give 80 m³ and 24 minutes for a 66.67 m³, 20-minute duty at 200 m³/h), which is the safe direction. Get the capacity-versus-performance boundary right and the sizing is a useful, honest first pass; blur it and the number is dangerously misread.

Formula

Required total flotation volume
V_req = Q × τ_target / 60
Cells required (rounded up)
N = ⌈ V_req / V_cell ⌉
Installed working volume
V_installed = N × V_cell
Actual mean residence time
τ = V_installed / Q × 60

Units involved

  • slurry flow Q — volumetric flow (m³/h)
  • target / actual residence time τ — minutes
  • cell working volume V_cell, required & installed volume — m³
  • number of cells N — dimensionless count, rounded up to a whole cell

Concept diagram

Flotation cell capacity — volumetric sizing from a supplied residence time, not performance predictionslurry Qfroth (concentrate)N cells · V_cell eachtailsV_req = Q · τ / 60 · N = ⌈V_req / V_cell⌉τ_actual = installed volume / Q · 60volumetric capacity from a supplied τ — not recovery, kinetics, or cell design

Worked example

A flotation duty has 200 m³/h of slurry and a 20-minute target residence time from testwork; each cell has a 20 m³ working volume. Size the bank and find the residence time it actually delivers.

  1. 01Required total volume: V_req = 200 × 20 / 60 = 66.67 m³
  2. 02Cells required: N = ⌈66.67 / 20⌉ = ⌈3.33⌉ = 4 cells
  3. 03Installed working volume: 4 × 20 = 80 m³
  4. 04Actual residence time: τ = 80 / 200 × 60 = 24.0 min
  5. 05Read this as a volumetric capacity sizing for a supplied target — not a recovery prediction
Result

Required volume 66.67 m³, 4 cells, installed 80 m³, actual residence time 24.0 min — a preliminary capacity sizing, not a flotation performance result.

Common mistakes

  • Reading a residence-time sizing as a recovery or grade prediction — it sizes volume only.
  • Treating the target residence time as a calculated value — it is a user input from testwork or the literature.
  • Forgetting to round the cell count up to a whole cell, then under-installing capacity.
  • Expecting the actual residence time to equal the target — rounding up makes it equal or longer.
  • Confusing the mean residence time with the residence-time distribution — this is a perfect-mixing mean, not an RTD.
  • Using a nominal cell volume where a working/effective volume is needed, or vice versa, without stating which.

When to use the calculator

Use the flotation cell capacity calculator to size a flotation or conditioning bank: enter the slurry flow, a target residence time from testwork or the literature, and the cell working volume to get the required total volume, the number of cells, the installed volume, and the actual mean residence time. Use the pulp / slurry volumetric flow calculator first if you have dry tonnage and percent solids rather than a slurry m³/h. For flotation recovery, grade, kinetics, residence-time distribution, cell mechanical or aeration design, equipment selection, or circuit optimisation, use testwork, kinetic modelling, vendor methods, and qualified review — those are outside this calculator.

FAQ

Does this calculator predict flotation recovery?
No. It sizes volumetric capacity and mean residence time only. Recovery and grade depend on flotation kinetics, reagents, particle size and liberation, aeration, froth behaviour, and circuit configuration — none of which this calculation models. Use flotation testwork and kinetic modelling for performance.
Where does the target residence time come from?
You supply it, from flotation kinetics testwork, the literature, or a comparable operation. The calculator never predicts the residence time; it uses your value to size the volume and count the cells. That is the core capacity-versus-performance boundary of this page.
Why is the actual residence time longer than the target?
Because the number of cells is rounded up to a whole cell, so the installed volume meets or exceeds the requirement. In the worked example a 66.67 m³ requirement becomes four 20 m³ cells (80 m³), giving 24.0 minutes instead of the 20-minute target — the safe direction.
Is the mean residence time the same as the residence-time distribution?
No. This calculation gives a single mean residence time on a perfect-mixing basis (τ = V / Q). It does not model the residence-time distribution — the spread of times individual particles spend in the bank — which depends on mixing, short-circuiting, and the number of cells in series, and requires RTD modelling.
How do I get the slurry flow if I only have dry tonnage?
Use the pulp / slurry volumetric flow calculator: it converts a dry solids tonnage, percent solids by mass, solids SG, and liquid density into a slurry volumetric flow in m³/h, which you then feed into this flotation cell capacity calculation.

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