Tromp Curve
Also known as: Partition Curve, Classification Efficiency Curve, Grade Recovery Curve
The Tromp Curve, introduced by K. Tromp in 1937, is an empirical model that quantifies the performance of size classifiers (cyclones, screens, jigs) by showing the fraction of particles at each size that report to the target stream (overflow or underflow). It is universally used in mineral processing to evaluate classifier performance, design circuits, and diagnose operational problems.
Key highlights
- Simple empirical model captures classifier imperfection with two interpretable parameters
- Enables prediction of product distributions from feed distributions; critical for circuit optimization
- Widely used in industry; comparable data from many operating plants available
- Useful for diagnostics: shift in d50c or sharpness indicates wear or configuration change
- Relatively easy to measure from plant samples; does not require instrumentation beyond sieves
Intuition
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How it works
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When to use it
Use Tromp Curves when designing or optimizing mineral processing circuits, especially those with multiple size classification stages. It is most applicable to conventionally operated classifiers (cyclones, screens, spirals). Assume the classifier is operating at steady-state and that the feed size distribution is well-characterized. For non-conventional separation methods (magnetic, density), use method-specific models.
Strengths & limitations
- Simple empirical model captures classifier imperfection with two interpretable parameters
- Enables prediction of product distributions from feed distributions; critical for circuit optimization
- Widely used in industry; comparable data from many operating plants available
- Useful for diagnostics: shift in d50c or sharpness indicates wear or configuration change
- Relatively easy to measure from plant samples; does not require instrumentation beyond sieves
- Empirical model does not explain why the curve has this shape; physical understanding requires fluid mechanics
- Tromp Curve can vary with feed concentration, temperature, and other process variables; single curve may not cover all operating ranges
- Bypass and entrainment mechanisms are distinct; using a single curve may mask changes in one or the other
- Curve fitting is sensitive to outliers in sieve data, especially at size extremes
- Model assumes the classifier has reached steady-state; transient operation is not captured
Common pitfalls
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Applications
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Frequently asked
What is a typical cut point (d50c) for industrial size classifiers?
Typical d50c values are 50-150 micrometers for fine classifiers (e.g., small cyclones) and 200-500 micrometers for coarse classifiers. d50c is primarily set by classifier design (diameter for cyclones, screen aperture for screens). It can shift ±10-20% with density or pulp concentration changes.
What does classifier sharpness (steepness of Tromp Curve) tell me?
Sharp curves (steep slope) indicate efficient separation with little bypass or entrainment. Sharpness >0.6 is excellent; <0.4 is poor. Wear, blockage, or size overlap (e.g., density overlap in dense-medium cyclones) reduces sharpness.
How do I diagnose classifier problems from Tromp Curve changes?
Shift in d50c indicates configuration change or viscosity change. Reduced sharpness indicates wear, blockage, or particle interaction problems. Compare current curve to baseline from the commissioning phase to isolate changes.
Can I use Tromp Curves from one ore type and apply them to another?
Not directly. While the shape of the curve is similar, d50c and sharpness are affected by particle density, shape, and surface properties. Always measure or calibrate Tromp Curves for your specific ore.
How often should I re-measure Tromp Curves in operating plants?
At commissioning and annually thereafter, or whenever equipment is modified. After major operational changes or if product distribution becomes inconsistent, re-test to ensure the circuit is still operating as designed.
Sources
- 1.Tromp, K. (1937). Separation of fine particles from slurries by hydrocyclone. Colliery Guardian, 155(4), 251-256.
- 2.Lynch, A. J., & Rao, T. C. (1997). Hydrocyclones in mineral processing. In Classification and segregation. Society for Mining, Metallurgy & Exploration.
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Cite this page
ScholarGate. (2026, June 3). Tromp Curve. ScholarGate. https://scholargate.app/mining-engineering/tromp-curve