MetPro

Flotation Kinetics & Bank Sizing Calculator

First-order flotation kinetics with the Garcia-Zuniga floatable-fraction model, N-cell bank sizing and grade-recovery curves with interactive charts.

Methodology & references

The kinetics tab implements first-order flotation kinetics with a finite floatable fraction: García-Zúñiga (1935) introduced the R_max framing on the batch form R(t) = R_max·[1 − exp(−kt)]. For a continuous bank of N equal cells the calculator uses the N-tanks-in-series closed form R = R_max·[1 − (1/(1 + kτ))^N], the extension formalized for flotation by Arbiter & Harris (1962). The closed form converges to R_max as N grows; simple iterative implementations that re-apply R_max per cell overpredict recovery by 4–5 percentage points at typical bank sizes, a defect this module fixed and now tests against.

Bank sizing finds the smallest number of cells that reaches a target recovery given the rate constant, per-cell residence time and cell volume (capped at 30 cells). The grade-recovery tab applies the same kinetics to mineral and gangue rate constants to trace the grade-recovery trade-off cell by cell.

The original 1935 García-Zúñiga paper, published in Santiago, is available as a scan from the Biblioteca Nacional Digital de Chile (reference below).

References

• García-Zúñiga, H. (1935). La eficiencia obtenida por flotación es una función exponencial del tiempo. Boletín Minero, Sociedad Nacional de Minería (Chile) 47, 83–86.
• Arbiter, N. & Harris, C.C. (1962). Flotation Kinetics. In Fuerstenau, D.W. (ed.), Froth Flotation: 50th Anniversary Volume, SME-AIME.
• Wills, B.A. & Finch, J.A. (2016). Wills' Mineral Processing Technology, 8th ed., Ch. 12.
• Yianatos, J.B. (2007). Fluid flow and kinetic modelling in flotation related processes. Chemical Engineering Research and Design 85(A12), 1591–1603.

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