Selection Correction of Ball Mill in HPGR-BM Process

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In mineral processing circuits, the crushing and grinding system represents a significant capital investment and energy consumption. With the increasing complexity of ore characteristics and stringent energy efficiency requirements, high-pressure grinding rolls (HPGR) have emerged as a critical technology for achieving “more crushing and less grinding.” This innovation reduces ball mill feed size while enhancing grindability through micro-crack generation. However, traditional Bond formula calculations for ball mill sizing in HPGR-ball mill (BM) circuits exhibit substantial deviations from actual operational data, often underestimating throughput by 10-20%. This discrepancy primarily stems from unaccounted variations in particle size distribution (PSD) and grindability enhancements induced by HPGR.

Field Performance Analysis

A case study at a molybdenum concentrator revealed significant discrepancies between calculated and actual ball mill performance after HPGR integration. Operational data before and after HPGR installation are compared below:

Table 1: Operational Parameters of φ4.8m×7.0m Ball Mill
Parameter Pre-HPGR (Crusher Feed) Post-HPGR (Theoretical) Post-HPGR (Actual)
Motor Power (kW) 2,460 2,460 2,465
F80 (µm) 8,000 3,200 3,200
Bond Work Index (kWh/t) 12.46 11.64 11.64
Throughput (t/h) 240 310 350

The conventional Bond formula underestimated actual ball mill throughput by 11.4% (350 t/h actual vs. 310 t/h calculated). Particle size distribution analysis revealed the core issue:

Table 2: Feed PSD Comparison at Identical P80
Size Fraction (mm) Crusher Product (% Passing) HPGR Product (% Passing)
0.075 5.56 14.16
0.180 12.25 30.74
2.000 32.90 66.04

For identical P80 values, HPGR products contain 17% more fines below the target grind size (170 µm for this case). This material bypasses grinding, reducing specific energy consumption. The standard Bond work index test fails to capture this phenomenon.

Corrected Ball Mill Sizing Methodology

The modified specific energy consumption for HPGR-ball mill circuits is calculated as:

$$W_h = \frac{W}{K}$$

Where:
– \(W_h\) = Corrected specific energy (kWh/t)
– \(W\) = Bond-calculated specific energy (kWh/t)
– \(K\) = HPGR synergy coefficient

The synergy coefficient \(K\) quantifies the increased proportion of target-sized material in HPGR feed compared to crusher feed at equivalent P80. \(K\)-values vary with feed size and product fineness:

Table 3: HPGR Synergy Coefficient (K) Values
Max Feed Size F100 (mm) -0.074mm Content 55% -0.074mm Content 60% -0.074mm Content 65% -0.074mm Content 70%
12 1.108 1.105 1.102 1.099
10 1.111 1.108 1.105 1.102
8 1.115 1.112 1.114 1.106
5 1.122 1.120 1.117 1.115
3 1.127 1.126 1.124 1.123

Validation Case Studies

Case 1: Molybdenum Concentrator (φ4.8m×7.0m Ball Mill)
Applying the correction with \(K\) = 1.117:

$$W_h = \frac{310}{1.117} = 346 \text{ t/h}$$

Resulting in 1.1% error vs. actual 350 t/h throughput.

Table 4: Ball Mill Throughput Validation (Molybdenum Plant)
Method Throughput (t/h) Error vs. Actual
Bond Formula 310 -11.4%
K-Corrected 346 -1.1%
Actual Operation 350 0%

Case 2: Copper Concentrator (φ3.2m×4.5m Ball Mill)
With \(K\) = 1.105:

$$W_h = \frac{83.0}{1.105} = 91.7 \text{ t/h}$$

Resulting in 1.9% error vs. actual 90 t/h throughput.

Table 5: Ball Mill Throughput Validation (Copper Plant)
Method Throughput (t/h) Error vs. Actual
Bond Formula 83.0 -7.8%
K-Corrected 91.7 +1.9%
Actual Operation 90.0 0%

Implementation Considerations

For precise ball mill sizing in HPGR-BM circuits:

  1. Conduct comparative PSD analysis between HPGR and crusher products
  2. Determine target grind size (P80) for downstream processes
  3. Calculate the mass fraction of feed material already below target size
  4. Select \(K\)-value from Table 3 based on F100 and target fineness
  5. Apply energy correction before final ball mill specification

The synergy effect intensifies with finer grinding requirements. For P80 values below 100 µm, \(K\) can exceed 1.15, making accurate correction essential for avoiding under-sized ball mill selection. This methodology reduces over-design while ensuring sufficient capacity for ore variability.

Conclusions

  1. Traditional Bond calculations underestimate ball mill capacity in HPGR-BM circuits by 7-12% due to unaccounted particle distribution effects.
  2. HPGR products contain significantly more target-sized particles than crusher products at identical P80, reducing specific grinding energy.
  3. The synergy coefficient \(K\) corrects Bond calculations by accounting for fines content in HPGR discharge.
  4. Validated across multiple operations, the \(K\)-correction method reduces ball mill sizing errors to below 5%.
  5. Accurate ball mill specification requires integrated analysis of HPGR feed size, product PSD, and target grind fineness.
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