- Reading & Lecture
- Partition Analysis
- Partition Curve Observations
- Corrected Partition Number
- Separation Efficiency
- Separation Performance Projection
Upon completing this lesson students should be able to:
- Explain the method used to assess the performance of separators.
- Illustrate partition analysis for comminution circuit.
- Analyze different types of partition curves.
- Explain the methods to access separation efficiency from partition curve.
Reading & Lecture
- One of the most insightful methods for quantifying the performance of separators is a “partition analysis”.
- This detailed assessment is commonly performed using a “partition curve”.
- Partition curves show the probability of a particular particle having a given characteristics reporting to a given product stream.
- Can be achieved for any separation: particle size, density, magnetics, floatability, etc.
- To explain partition curves, let’s take a look at a “perfect” particle size separation at 0.45 mm.
- As shown, 100% of particles > 0.45 mm in each in each size class in the feed report to oversize.
- If the separation is less than perfect, then particles can be “misplaced” to the wrong streams.
- This includes:
- Misplacement of coarser particles to undersize
- Misplacement of finer particles to oversize
- If ideal, curve runs parallel to abscissa at the “cutsize”.
- More deviation from axis means more misplaced material.
- Shape is characteristic of separator type and operation.
- Cut – Point
= 0.45 mm
- Ecart Probability (Ep)
=(0.5-0.4)/2=0.05 mmImperfection (I)
=0.05/2 = 0.025
- Curve shape is an inherent characteristic of the type of separator employed.
- Commonly reported values for imperfection range from 0.005 to more than 0.50.
- Depends on:
- Type of equipment (e.g., screens, cyclones hydraulic sizers, etc)
- Characteristics of feed material (e.g., particle size, shape, density, etc.)
- Production demands (feed rate, water quality, etc.)
- Another important issue is “bypass”.
- Bypass can occur to both oversize and undersize.
- Oversize bypass is not unusual for screens
- Undersize bypass very common for classifiers.
- Bypass is the misplacement of fines via entrainment into the oversize product.
- Quantified by zero-size offset on the partition curve.
- Can sometimes >30°/o for fine sizing applications.
- Bypass typically has a large adverse downstream impact.
- Classifiers are often used in multiple stages to reduce bypass (i.e., retreat oversize).
- Type 1- Ideal Symmetrical
- represents perfect processes (e.g., laboratory sieve data)
- Type 2 – Efficient Symmetrical
- OK for efficient units (e.g., well designed/operated screen)
- Type 3 – Inefficient Symmetrical
- OK for less efficient units (e.g., fine hydraulic classifiers)
- Type 4- Oversize Nonsymmetrical
- shows loss of coarse to undersize (e.g., holes in screens)
- Type 5 – Undersize Nonsymmetrical
- shows loss of fines to oversize (e.g., overloaded screen)
Inherent unit characteristic, poor circuit design, excessive rates, mechanical failure, poor operating practices, others …
Step 1- Collect Samples
- Collect representative samples of the feed, oversize and undersize streams.
- Make sure that all streams have been taken into account.
Step 2 – Perform Size Analysis
- Perform a laboratory particle size analysis on each sample.
- Assess data to make sure that it is reliable (discussed later).
|Size Class (Mesh)||Mean Size (mm)||Feed Mass (%)||U/S (%)||O/S (%)|
Step 3 – Conduct Calculations
- Plot (u-f) versus (u-o).
Data should form a line passing through zero .
- Line slope is the fraction of feed tonnage that reports to oversize.
- You may disregard unreliable points that do not appear to fall along the line.
|Size Class (Mesh)||Mean Size (mm)||Feed Mass (%)||U/S (%)||O/S (%)||X-axis (u-o)||Y-axis (u-f)|
Step 4 – Construct Partition Curve
- Calculate oversize partition for each size class using [(u-f)o]/[(u o)f].
- Plot mean size versus partition factor .
- Compute performance indicators (cutsize, imperfection, bypass, etc.).
|Mean Size (mm)||Feed Mass (%)||U/S (%)||O/S (%)||Y-axis (u-f)||X-axis (u-o)||Percent Feed Weight|
|Percent Feed Weight|
|Reconstituted Feed Weight||Partition Number|
Yield to Oversize Stream – 46.92%
Partition Curve Observations
- The partition curve completed for a particle size separation utilized the weight distribution of all process streams including the feed stream.
- Depending on the breakage characteristics of the material and the location of the sample points, particle breakage could occur which affects the component balance around the process.
- As such, it is sometimes preferred to use component assays (e.g., solid concentration or assays such as iron content) and the two-product equation to determine mass yield.
- Using the mass yield, the feed is then reconstituted to determine the partition numbers.
Corrected Partition Number
The equation for determining the corrected Partition Number is:
Y’ is the corrected partition number, Y the actual partition number, R1 , the fractional amount of ultrafines by-passing to the underflow stream and R2 , the fractional amount of coarsest particles by-passing to the flow stream.
- The by-pass of coarse material to the overflow stream is rare but may occur due to a worn vortex finder.
- R2 =0 can be assumed in most cases.
Separation efficiency should always be measured from the corrected partition numbers.
- Bypassed particles were not subjected to the separation forces .
For particle size separations, the imperfection value (I) is the preferred measurement:
d75, d50 , and d25= the particle size having 75 %, 50% and 25% probabilities, respectively, of reporting to the underflow stream.
Separation Performance Projection
- Many equations are available that model typical performance curves associated with
- Lynch and Rao found that the Reduces Efficiency curve can be modeled by the following expression:
X= d/d 50(c)
α = the curve slope and the value is indicative of the classification efficiency.
- The Lynch model can be used to predict the performance of a classifying cyclones.
Example: Performance Prediction
Given a feed particle size distribution and an alpha value of 2.5, predict the performance of a cyclone. The amount of ultrafine by-pass is assumed to be 20% by weight.
|Mean Particle Size (microns)||Weight (%)||d/d50(c)||Corrected Partition Number||Actual Partition Number||Underflow Weight (%)||Normalized Underflow Weight (%|
Mass Yield to Underflow = 61.57%
- “Partition factor” represents the probability that a given particle size in the feed stream will report to the oversize product.
- “Partition analysis” makes it possible to determine key performance indicators.
- Cutsize (D50)
- Imperfection (I)
- Plant personnel should monitor and strive to maintain sizing “efficiencies ” since this greatly impacts other plant operations.