Tailings Grade
Solve residual tailings mass and assay from a closed dry feed/concentrate balance; impossible negative or above-one assays return errors.
Description
A two-product dry mass and metal balance infers tailings mass and grade from feed and concentrate.
A two-product dry mass and metal balance infers tailings mass and grade from feed and concentrate. Assays must be represented as fractions of the same constituent.
The tool returns tailingsDryTonnes (tailings dry tonnes); tailingsAssayFraction (tailings assay fraction). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Tailings Grade
Use Tailings Grade when you already have feedDryTonnes, feedAssayFraction, concentrateDryTonnes, concentrateAssayFraction and want tailingsDryTonnes, tailingsAssayFraction. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Tailings Grade and understand its results
- Enter feedDryTonnes, feedAssayFraction, concentrateDryTonnes, concentrateAssayFraction using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read tailingsDryTonnes, tailingsAssayFraction. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| feedDryTonnes | Feed dry tonnes | number | Required |
| feedAssayFraction | Feed assay fraction | number | Required |
| concentrateDryTonnes | Concentrate dry tonnes | number | Required |
| concentrateAssayFraction | Concentrate assay fraction | number | Required |
Require positive feed and tailings mass, nonnegative concentrate and assay fractions in [0,1]. Reject inferred tailings assay outside [0,1].
tailingsTonnes = feed−concentrate; tailingsAssay = (feed×feedAssay−concentrate×concentrateAssay)/tailingsTonnes The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"feedDryTonnes": 100,
"feedAssayFraction": 0.1,
"concentrateDryTonnes": 10,
"concentrateAssayFraction": 0.8
},
"output": {
"tailingsDryTonnes": 90,
"tailingsAssayFraction": 0.022222222222222223
}
}Limitations and assumptions
The balance assumes only concentrate and tailings products with no other losses or additions. It does not reconcile measurement error.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Recovery Percentage: Balance metal recovery across multiple disjoint dry product streams; unlike analytical spike recovery, this checks both process mass and contained-metal feasibility. Screen Efficiency: Calculate screen class recoveries and their product from a two-class dry balance; explicitly a recovery product, not undersize purity.
Methodological background: Material balance in mineral processing.1
References
-
Material balance in mineral processing — NPTEL, Indian Institute of Technology Kanpur
Similar or alternative tools
- Recovery Percentage
Balance metal recovery across multiple disjoint dry product streams; unlike analytical spike recovery, this checks both process mass and contained-metal feasibility.
- Screen Efficiency
Calculate screen class recoveries and their product from a two-class dry balance; explicitly a recovery product, not undersize purity.