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