Flotation Rate Constant Calculator
Extract actual two-point apparent flotation residual decay with independent ultimate recovery, signed inverse-rate retained; distinct from existing multi-point unconstrained-intercept fit. Caller independently verifies units, applicability and matching conditions; no operational recipe, safety certification, causal efficacy or legal/resource classification is inferred.
Description
A two-point apparent flotation rate compares log residuals relative to an independently established ultimate recovery.
A two-point apparent flotation rate compares log residuals relative to an independently established ultimate recovery.1
A decreasing recovery can produce a negative apparent rate.
When to use Flotation Rate Constant Calculator
Use this tool to calculate or review the supplied observations under the stated rules. Match completed survey or ledger observations by block, segment or stage and confirm their units and boundaries.
How to use Flotation Rate Constant Calculator and understand its results
- Match completed survey or ledger observations by block, segment or stage and confirm their units and boundaries.
- Enter observedTwoFlotationTimesSeconds, observedRecoveryFractions, callerIndependentlyEstablishedUltimateFraction, using the field meanings and rules below, then run the tool.
- Read twoPointApparentFlotationRatePerSecond. Inspect nested result fields where present, and review unknown records separately from known matches.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedTwoFlotationTimesSeconds | Observed two flotation times seconds | list of number | Required |
| observedRecoveryFractions | Observed recovery fractions | list of number | Required |
| callerIndependentlyEstablishedUltimateFraction | Caller independently established ultimate fraction | number | Required |
Require exactly two nonnegative strictly increasing times and two fractions in [0,1], plus an ultimate fraction>0≤1. Each recovery must be strictly below ultimate. Transform ln(1−r/ultimate), take the negative secant slope and retain its sign.
rate=−[ln(1−r2/ultimate)−ln(1−r1/ultimate)]/(t2−t1) Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| twoPointApparentFlotationRatePerSecond | Two point apparent flotation rate per second | number |
{
"input": {
"observedTwoFlotationTimesSeconds": [
1,
3
],
"observedRecoveryFractions": [
0.2,
0.6
],
"callerIndependentlyEstablishedUltimateFraction": 0.8
},
"output": {
"twoPointApparentFlotationRatePerSecond": 0.5493061443340546
}
}Limitations and assumptions
Units, ledger boundaries, survey interpretation and model applicability must be independently established. These summaries do not assign reserve/resource classifications or establish support adequacy, ventilation safety or an operating setting.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries; ordinary string lists allow at most 128 strings of 128 UTF-16 units each; numeric matrices allow at most 128 rows and 128 columns, subject to narrower requirements above.
Alternative or Complementary methods
For a related step, use Flotation Recovery vs Time Calculator: Incremental flotation collections can be accumulated into a recovery history. For a complementary comparison, use Leaching Rate Constant Calculator: A first-order residual fit relates log unrecovered fraction to elapsed leach time.
References
-
Flotation Rate Constant Calculator — tool.io
Similar or alternative tools
- Flotation Recovery vs Time Calculator
Incremental flotation collections can be accumulated into a recovery history.
- Leaching Rate Constant Calculator
A first-order residual fit relates log unrecovered fraction to elapsed leach time.