Reference ID: MET-DA2A | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Closed-circuit grinding with classification is a ubiquitous unit operation in mineral processing, cement, and chemical plants. It couples a mill (ball, rod, or vertical) with a classifier (mechanical air, hydrocyclone, or screen) that separates the ground product into a finished stream and a coarse stream. The coarse fraction is returned to the mill for additional comminution, creating an internal material loop. The ratio of returned solids to fresh feed—known as the recirculating load—directly influences mill residence time, specific energy consumption, and the final particle-size distribution. Accurate prediction of this load is therefore essential for equipment sizing, throughput optimisation, and control-system tuning.
Methodology & Formulas
The derivation assumes a perfectly mixed mill and a classifier whose performance is described by a single parameter: the classifier efficiency \(E\), defined as the mass fraction of classifier feed that reports to the fine (product) stream. A steady-state mass balance around the classifier yields the recirculating load \(R\) and the total mill discharge \(M\).
Classifier Efficiency Constraint
\(0 < E < 1\)
Mass Balance on Classifier
Let \(F\) denote the fresh feed rate. The classifier receives the mill discharge \(M\) and splits it into:
Fine product stream: \(E\,M\)
Coarse recycle stream: \((1-E)\,M\)
At steady state, the fine product must equal the fresh feed, hence:
\[
E\,M = F \quad\Longrightarrow\quad M = \frac{F}{E}.
\]
Recirculating Load
The recycle rate \(R\) is the difference between mill discharge and fresh feed:
\[
R = M - F = \frac{F}{E} - F = F\left(\frac{1-E}{E}\right).
\]
Improved product size control: Classification systems (e.g., cyclones, air classifiers) maintain consistent particle size distribution.
Energy efficiency: Reduces overgrinding by returning only oversized particles to the mill, lowering energy waste.
Flexibility: Adjust classifier settings to meet varying product specifications without stopping the process.
Monitor classifier efficiency: Regularly check and adjust classifier settings (e.g., air flow, vane angles) to ensure proper separation.
Balance feed rate: Match mill feed to its capacity to avoid overloading and maintain stable circulation load.
Optimize mill speed: Adjust rotational speed to achieve ideal grinding media motion and energy transfer.
Use real-time sensors: Implement particle size analyzers to provide feedback for dynamic process adjustments.
Worn classifier components: Replace worn vanes, nozzles, or screens to restore separation accuracy.
Incorrect air flow: Adjust air velocity to match the material's aerodynamic properties and desired cut size.
Moisture content: Dry feed material if high moisture causes agglomeration or clogging in the classifier.
Feed variability: Use a pre-classifier or buffer hopper to stabilize feed size and rate before entering the main circuit.
High circulation load: Increases mill throughput but may lead to overgrinding and higher energy consumption.
Low circulation load: Reduces recirculation, improving energy efficiency but potentially lowering production rates.
Optimal balance: Maintain a circulation load between 150–250% of the fresh feed, depending on material hardness and classifier efficiency.
Monitoring tools: Use mass balance calculations and particle size analysis to track and adjust circulation load dynamically.
Inspect classifier wear: Schedule regular checks for abrasion in classifier nozzles, vanes, and housing to prevent size distribution drift.
Mill liner condition: Replace worn liners to maintain grinding media trajectory and prevent metal contamination.
Seal integrity: Check for air leaks in classifier and mill seals to ensure consistent pressure and separation efficiency.
Lubrication systems: Monitor and maintain lubrication for mill bearings and classifier drive components to avoid mechanical failure.
Worked Example – Closed-Circuit Grinding with Classification
A mineral processing plant operates a closed-circuit grinding system that includes a ball mill and a hydro-cyclone classifier. The goal is to determine the recirculation flow rate and the total mill throughput required to achieve the desired product recovery.
F – Fresh feed to the mill = 1000 kg h−1
E – Classification efficiency (fraction of fine product removed) = 0.7
Esafe – Safety-adjusted efficiency (assumed equal to E) = 0.7
Calculate the fraction of material that must be recirculated:
\[
1 - E = 1 - 0.7 = 0.3
\]
Determine the recirculation flow rate (R) using the closed-circuit relationship:
\[
R = \frac{F\,(1 - E)}{E}
\]
Substituting the known values:
\[
R = \frac{1000 \times 0.3}{0.7} = \frac{300}{0.7} = 428.571 \text{ kg h}^{-1}
\]
Compute the total mill throughput (M), which is the sum of fresh feed and recirculated material:
\[
M = F + R = 1000 + 428.571 = 1428.571 \text{ kg h}^{-1}
\]
Verify that the safety-adjusted efficiency does not change the result (since Esafe = E):
\[
R_{\text{safe}} = \frac{F\,(1 - E_{\text{safe}})}{E_{\text{safe}}} = \frac{1000 \times 0.3}{0.7} = 428.571 \text{ kg h}^{-1}
\]
Final Answer: Recirculation flow rate R = 428.571 kg h−1; total mill throughput M = 1428.571 kg h−1.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
