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FSM: Liquid Desander – Classification Performance (i.e. Graded Efficiency Curve) (B-FSM050)

Figures 13 and 14 from Reference 3 (Yoshioka and Hotta, 1955)

As mentioned several times, a cyclonic device separates based on particle weight (not size). If all the particles have the same density, the only size matters for separation. However, in mixed density situations, the particle weight determines what is captured or rejected.

In comparison, a screen separates based on size only. A screen with 100-micron aperture will separate peanuts, bowling balls, sand, Styrofoam beads, or lead weights at the same size at all conditions – all that matters is size. Anything larger than 100 microns stays on one side of the screen and anything smaller goes through. A cyclone however takes into consideration the particle weight for separation – therefore a tiny piece of lead, a peanut, and huge chunk of Styrofoam will act the same within a cyclone.

Hydrocyclones are imperfect separators (however their size:throughput ratio makes them very attractive). All cyclones exhibit an imperfect separation as shown on a graded efficiency curve. Also called a classification curve, recovery curve, cyclone curve, or Tromp curve – the graded efficiency curve plots particle size (x-axis) versus recovery to underflow (y-axis). An example of the graded efficiency curve is shown in the following graphic. (Note: this curve is only applicable for a desander – a hydrocyclone has a similar shape actual recovery curve but with vertical offset – that discussion is neglected as it deviates too much from the focus on desander operation).

General Notes on Graded Efficiency Curve

  • Plots particle size versus recovery to underflow (U/F)
  • The cut size (D50) is the equiprobable size that may go to U/F or O/F. It is used in cyclone size and selection – used to define performance at specific conditions

Specific Notes on Graded Efficiency Curve (for Desanders)

  • X-axis is normalized by dividing particle size (D) by cut size (D50). A size of “1.0” is the same size particle as the cut size.
  • The shape of the curve fits the Yoshioka-Hotta equation
  • The slope (α) is the sharpness of separation. It is 4.0 for normal sand in water, <4 for low density or flat shape particles, and >4 for high density or very spherical particles. (Note: α=4 is used for all subsequent calculations and discussions unless otherwise stated). Plitt (see references) provides a method of estimating α from operating and geometric parameters.
  • The separation size (D98) for a desander is ~2X the D50 at α=4.

The next article will (finally) discuss general design and operation of a desander. 


  1. Plitt, L.R., “A mathematical model of the hydrocyclone classifier”, CIM Bulletin, December, 1976, pp. 115-123.
  2. Svarovsky, L., “Hydrocyclones”, Technomics Publishing Co. Inc., Lancaster, PA, 1984.
  3. Yoshioka, N. and Hotta, Y., “Liquid cyclone as a hydraulic classifier”, Chemical Engineering Japan, 19 (12), 1955, pp. 632-340.

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