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.
Description
A closed two-product assay balance can infer concentrate yield from feed, concentrate and tailings grades.
A closed two-product assay balance can infer concentrate yield from feed, concentrate and tailings grades. The feed-to-concentrate mass ratio is the inverse of that yield.1
The tool returns concentrationMassRatio, concentrateMassFraction, inferredMetalRecovery. The computation uses supplied observations and parameters rather than acquiring measurements.
When to use Concentration Ratio
Use this for the following task: 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. Prepare observations and calibration parameters on the same unit and reporting basis.
How to use Concentration Ratio and understand its results
- Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
- Enter feedGradeFraction, concentrateGradeFraction, tailingsGradeFraction according to the field table, then run the tool.
- Read concentrationMassRatio, concentrateMassFraction, inferredMetalRecovery. 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 |
|---|---|---|---|
| feedGradeFraction | Feed grade fraction | number | Required |
| concentrateGradeFraction | Concentrate grade fraction | number | Required |
| tailingsGradeFraction | Tailings grade fraction | number | Required |
Use grade fractions in [0,1] with strict concentrate > feed > tailings ordering. Compute inferred yield, mass ratio and metal recovery.
yield = (feedGrade−tailingsGrade)/(concentrateGrade−tailingsGrade); concentration ratio = 1/yield The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| concentrationMassRatio | Concentration mass ratio | number |
| concentrateMassFraction | Concentrate mass fraction | number |
| inferredMetalRecovery | Inferred metal recovery | number |
{
"input": {
"feedGradeFraction": 0.1,
"concentrateGradeFraction": 0.5,
"tailingsGradeFraction": 0.02
},
"output": {
"concentrationMassRatio": 5.999999999999999,
"concentrateMassFraction": 0.16666666666666669,
"inferredMetalRecovery": 0.8333333333333334
}
}Limitations and assumptions
Representative dry assays and a closed two-product balance are assumed. Unlike measured mass pull, the result is inferred without supplied product masses.
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 Mass Pull when you need its operation: Calculate dry mass pull from separate wet masses and moisture assays; unlike assay-inferred concentration ratio, this uses measured moisture-corrected quantities. Choose Grade Recovery Curve for the complementary operation: 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.
Background reference: Material balance in mineral processing.
References
-
Material balance in mineral processing — NPTEL, Indian Institute of Technology Kanpur
Similar or alternative tools
- Mass Pull
Calculate dry mass pull from separate wet masses and moisture assays; unlike assay-inferred concentration ratio, this uses measured moisture-corrected quantities.
- 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.