Optimizing Grinding Circuits: Calculating Separator Rejects via Sieve Analysis

In a closed-circuit ball mill, the separator’s primary role is to split the mill discharge into two streams: the finished product (fines) and the material that requires further comminution (rejects). Calculating the mass flow of these rejects is essential for understanding the Circulating Load (CL), which is a key driver of specific power consumption and mill throughput.

Core Concepts and Definitions

To calculate rejects on a mass flow basis using sieve analysis, we define the circuit via three material streams:

  • Separator Feed (A): The total material entering the separator, typically the mill discharge.
  • Fines (F): The finished product that meets the target fineness.
  • Rejects (R): The coarse material returned to the mill inlet.
  • Fineness Parameters (a,f,r): These represent the percentage of material passing (or retained on) a specific sieve for the Feed, Fines, and Rejects, respectively.

The Mathematical Foundation

The calculation relies on the principle of mass conservation: the amount of a specific size fraction entering the separator must equal the amount leaving it.

The Mass Balance Equation:

A×a=F×f+R×r

Since A=F+R, we can derive the Circulation Factor (u), which is the ratio of Separator Feed to Fines: u=FA​=(r−f​)/(r−a)

Calculating Rejects (R): If the production rate (F) is known via a weigh feeder, the mass flow of rejects is calculated as:

R=F×(u−1)

Or more directly from sieve data:

R=F×[(a−f​)/(r−a)]

OR R=CLXF/100; CL is circulation load

 

Typical Operational Benchmarks

The target circulating load varies significantly depending on the separator technology employed:

Parameter

Mechanical Separator

High Efficiency (HES)

Typical Circulating Load (CL%)

200% – 300%

150% – 200%

Circulation Factor (u)

3.0 – 4.0

2.5 – 3.0

Separation Efficiency

25% – 40%

75% – 85%

 

Importance for Process Optimization:

  • Preventing Over-grinding...
  • Specific Power Consumption (SPC)...
  • Capacity Management...

Influence on Cement Manufacturing...

Summary Table...

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