Leaching Kinetics

Evaluate ideal reaction-controlled shrinking-core leaching 1−(1−X)^(1/3)=kt capped at complete conversion; excludes diffusion control and reagent depletion.

Description

Reaction-controlled shrinking-core kinetics describes conversion as a reaction front moves through an ideal particle.

Reaction-controlled shrinking-core kinetics describes conversion as a reaction front moves through an ideal particle. A supplied rate constant determines the time scale.^[1]

The tool returns predictedLeachedFractions. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Leaching Kinetics

Use this for the following task: Evaluate ideal reaction-controlled shrinking-core leaching 1−(1−X)^(1/3)=kt capped at complete conversion; excludes diffusion control and reagent depletion. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Leaching Kinetics and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter ratePerHour, timesHours according to the field table, then run the tool.
Read predictedLeachedFractions. 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
ratePerHour	Rate per hour	number	Required
timesHours	Times hours	list of number	Required

Require a positive hourly rate and a nonempty list of nonnegative elapsed hours. Evaluate each time in supplied order and cap the predicted leached fraction at one once k×t reaches one.

X(t) = 1−max(0,1−k×t)³

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

Output field	Meaning	Value type
predictedLeachedFractions	Predicted leached fractions	list of number

json

{
  "input": {
    "ratePerHour": 0.1,
    "timesHours": [
      0,
      1,
      5,
      10
    ]
  },
  "output": {
    "predictedLeachedFractions": [
      0,
      0.2709999999999999,
      0.875,
      1
    ]
  }
}

Limitations and assumptions

This ideal model excludes diffusion control, changing reagents and particle-size distributions. The tool does not fit the rate constant or identify which kinetic mechanism applies.

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 Leaching Recovery when you need its operation: Infer leached metal from ore and changing residue mass/assay; accounts for mass loss with matched dry samples. 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: Chemical Reaction Engineering 2: shrinking-core models.

References

Chemical Reaction Engineering 2: shrinking-core models — NPTEL, Indian Institute of Technology Madras

Similar or alternative tools

Leaching Recovery
Infer leached metal from ore and changing residue mass/assay; accounts for mass loss with matched dry samples.
Flotation Kinetics Rate
Fit log residual recovery against time with caller ultimate flotation recovery; intercept is estimated and no asymptote is invented.