Grade Recovery Curve

Build observed grade/recovery operating points from matched concentrate masses and assay fractions; points are separate trials, not additive products or a fitted optimization curve.

Description

Grade and recovery describe competing outcomes of a concentration trial: concentrate quality and recovered feed metal.

Grade and recovery describe competing outcomes of a concentration trial: concentrate quality and recovered feed metal. Separate observed trials form operating points on a grade-recovery comparison.^[1]

The tool returns massPullFractions, metalRecoveryFractions, enrichmentRatios. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Grade Recovery Curve

Use this for the following task: Build observed grade/recovery operating points from matched concentrate masses and assay fractions; points are separate trials, not additive products or a fitted optimization curve. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Grade Recovery Curve and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter feedTonnes, feedGradeFraction, concentrateTonnes, concentrateGradeFractions according to the field table, then run the tool.
Read massPullFractions, metalRecoveryFractions, enrichmentRatios. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
Review the supplied assumptions and calibration before comparing or reporting the result.

Input field	Meaning	Value type and bounds	Requirement
feedTonnes	Feed tonnes	number	Required
feedGradeFraction	Feed grade fraction	number	Required
concentrateTonnes	Concentrate tonnes	list of number	Required
concentrateGradeFractions	Concentrate grade fractions	list of number	Required

Use positive feed tonnage and grade fraction with aligned concentrate masses and grade fractions. Require mass pull and metal recovery in [0,1] for every trial.

mass pull = concentrate/feed; recovery = mass pull×concentrateGrade/feedGrade; enrichment = concentrateGrade/feedGrade

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
massPullFractions	Mass pull fractions	list of number
metalRecoveryFractions	Metal recovery fractions	list of number
enrichmentRatios	Enrichment ratios	list of number

json

{
  "input": {
    "feedTonnes": 100,
    "feedGradeFraction": 0.1,
    "concentrateTonnes": [
      10,
      20
    ],
    "concentrateGradeFractions": [
      0.8,
      0.45
    ]
  },
  "output": {
    "massPullFractions": [
      0.1,
      0.2
    ],
    "metalRecoveryFractions": [
      0.8000000000000002,
      0.9
    ],
    "enrichmentRatios": [
      8,
      4.5
    ]
  }
}

Limitations and assumptions

Each point represents a separate trial against the same feed basis. The tool does not sum products, fit a curve or choose an optimal operating point.

Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.

Alternative or Complementary methods

Choose Concentration Ratio when you need its operation: Infer concentrate yield and feed/concentrate mass ratio from a closed two-product assay balance; distinct from measured mass pull and assumes representative dry assays. Choose Flotation Kinetics Rate for the complementary operation: Fit log residual recovery against time with caller ultimate flotation recovery; intercept is estimated and no asymptote is invented.

Background reference: Material balance in mineral processing.

References

Material balance in mineral processing — NPTEL, Indian Institute of Technology Kanpur

Similar or alternative tools

Concentration Ratio
Infer concentrate yield and feed/concentrate mass ratio from a closed two-product assay balance; distinct from measured mass pull and assumes representative dry assays.
Flotation Kinetics Rate
Fit log residual recovery against time with caller ultimate flotation recovery; intercept is estimated and no asymptote is invented.