Study guide
8.1 Crushing, Grinding & Bond Work Index Calculations
PRC Mining Engineer Licensure Examination Philippines
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1 Chapter 1: Surface Mining Methods & Pit Optimization
1.1 Surface Mining Unit Operations & Method Selection 1.2 Bench Geometry, Slope Stability & Geotechnical Pit Design 1.3 Cut-Off Grade Optimization & Lerchs-Grossmann Pit Limits
2 Chapter 2: Underground Mining Methods & Strata Control
2.1 Underground Mining Method Classification & Selection 2.2 Rock Mechanics, Stress Analysis & Strata Control 2.3 Underground Ground Support Systems & Excavation Design
3 Chapter 3: Materials Handling, Equipment & Mine Economics
3.1 Drilling, Blasting & Explosives Engineering 3.2 Mine Loading, Haulage & Materials Handling Systems 3.3 Mine Capital (CAPEX), Operating Costs (OPEX) & Financial Evaluation
4 Chapter 4: Mine Safety, Ventilation & Philippine Mining Laws
4.1 Mine Ventilation Network Analysis & Environmental Quality 4.2 Philippine Mine Safety Rules, Health & Disaster Prevention 4.3 Philippine Mining Act of 1995 (RA 7942), DAO 2010-21 & Mining Ethics
5 Chapter 5: Physical Geology, Mineralogy & Philippine Deposit Types
5.1 Structural Geology, Tectonics & Ore Controls 5.2 Igneous, Metamorphic & Sedimentary Ore Mineralogy 5.3 Major Philippine Ore Deposit Models
6 Chapter 6: Mineral Exploration, Geophysics & Core Logging
6.1 Geochemical & Remote Sensing Exploration Techniques 6.2 Geophysical Exploration Methods in Mining Geology 6.3 Diamond Drilling, Core Logging & QA/QC Protocols
7 Chapter 7: Geostatistics, Resource Estimation & PMRC Code
7.1 Ore Body Block Modeling & Spatial Variography 7.2 Inverse Distance & Ordinary Kriging Grade Estimation 7.3 Philippine Mineral Reporting Code (PMRC 2020) & Resource Classification
8 Chapter 8: Comminution, Sizing & Physical Mineral Separation
8.1 Crushing, Grinding & Bond Work Index Calculations 8.2 Particle Screening, Hydrocyclone Classification & Sizing 8.3 Gravity Concentration & Magnetic/Electrostatic Separation
9 Chapter 9: Froth Flotation & Extractive Hydrometallurgy
9.1 Froth Flotation Chemistry, Reagents & Cell Kinetics 9.2 Leaching Technologies (Heap, Agitation & Tank) 9.3 Precious Metal Recovery: CIP, CIL, Merrill-Crowe & Electrowinning
10 Chapter 10: Process Plant Flowsheets & Environmental Tailings Management
10.1 Metallurgical Plant Flowsheets & Pulp Mass Balances 10.2 Tailings Storage Facility (TSF) Design & Dam Safety 10.3 Acid Mine Drainage (AMD) Mitigation & Environmental Protection (EPEP/FMR/DP)
11 Chapter 11: 2025 PRC Blueprint, Prospecting Tools & Exploration Decisions
11.1 Official 2025 TOS, Three-Paper Structure & Exam Strategy 11.2 Prospecting Instruments, Base Maps & Surface Geological Mapping 11.3 Integrating Direct and Indirect Evidence for Exploration Decisions
12 Chapter 12: Mine Infrastructure, Sustainable Development & Climate
12.1 Power, Water, Drainage & Support-Facility Selection 12.2 Sustainable Development, Progressive Rehabilitation & Community Impact 12.3 Mining, Climate, Reforestation, Coal & Energy-Transition Minerals
13 Chapter 13: Mine Valuation, Financial Analysis & Due Diligence
13.1 Time Value of Money, Future Value & Present Value 13.2 Financial Statements, Mine Economics & External Price Drivers 13.3 Exploration Provenance, Technical Review & Legal Due Diligence
14 Chapter 14: Mine Organization, Communication & Accountable Leadership
14.1 Line and Staff Functions in a Mining Organization 14.2 Communication With Superiors, Peers & Subordinates 14.3 Authority, Responsibility, Delegation & Safety Accountability
15 Chapter 15: Philippine Mining Law, Indigenous Rights & Professional Ethics
15.1 Legal Hierarchy, Mineral Tenure & Compliance Analysis 15.2 Constitutional Participation, IPRA, FPIC & Ancestral Domains 15.3 RA 4274, Professional Scope, Ethics & Document Integrity
16 Chapter 16: Applied Mathematics & Mine Surveying
16.1 Engineering Mathematics for Safe, Efficient Mine Decisions 16.2 Survey Control, Instruments, Traverses & Error Adjustment 16.3 Topographic Maps, Underground Set-Out & Survey Timeliness
17 Chapter 17: Feasibility Studies, Data Quality & Project Decisions
17.1 Scoping, Pre-Feasibility & Final Feasibility Study Maturity 17.2 Data Accuracy, Assumption Control & Go/No-Go Decisions 17.3 Multidisciplinary Integration, Interfaces & Independent Review
18 Chapter 18: Mining Computer Applications, Digital Control & Global Developments
18.1 Computer Functions, Office Applications & Data Governance 18.2 Geological Modeling, Mine Planning, Scheduling & Valuation Software 18.3 Real-Time Control, Critical Minerals & Regional Mining Developments
19 Chapter 19: Earth Systems, Geologic Time & Philippine Hazards
19.1 Solar-System Origin, Earth Interior & Atmospheric Layers 19.2 Rock Cycle, Landforms & the Geologic Time Scale 19.3 Philippine Tectonics, Geologic Hazards & Mitigation
20 Chapter 20: Metallurgy, Foundry Practice & Assaying
20.1 Extractive, Physical & Adaptive Metallurgy Principles 20.2 Foundry Materials, Casting, Solidification & Defects 20.3 Sampling, Fire Assay, Cupellation, Parting & Assay Calculations
21 Chapter 21: Solid–Liquid Separation, Environmental Law & Mine Ecology
21.1 Thickening, Filtration & Solid–Liquid Separation 21.2 Philippine Air, Water, Waste & Hazardous-Substance Controls 21.3 Mine Ecology, Closure, Tailings, Waste & Community Livelihood
8.1 Crushing, Grinding & Bond Work Index Calculations
Key Takeaways Explain This Topic AI
Kick, Rittinger, and Bond relations are idealized energy-size models often associated with coarse, very fine, and intermediate reduction respectively; their domains overlap and must be calibrated rather than divided by universal size boundaries.
Bond's Third Theory of Comminution calculates specific energy requirement (W in kWh/tonne) using W = 10 * Wi * (1/sqrt(P80) - 1/sqrt(F80)), where Wi is the Bond Work Index and P80 and F80 are the 80% passing sizes in micrometers.
Primary crushing machinery (jaw and gyratory crushers) achieves reduction ratios of 4:1 to 8:1, while secondary/tertiary cone crushers and High-Pressure Grinding Rolls (HPGR) reduce feed down to fine sizes with high energy efficiency.
Tumbling mill critical speed is the rotational speed at which centrifugal force equals gravitational force (Nc = 42.3 / sqrt(D - d) in rpm); commercial ball and rod mills operate at 65% to 80% of critical speed to promote cataract/cascade grinding action.
Circulating-load ratio compares classifier return to fresh feed; its appropriate value follows the mill-classifier balance, product target, ore response, capacity, water balance, and stability rather than a universal 200%–400% optimum.
Last updated: August 2026
Crushing, Grinding & Bond Work Index Calculations
Comminution is the process of physical size reduction of ore particles through crushing and grinding. In many mineral-processing plants, comminution is a major consumer of energy and operating cost, but its share is orebody-, flowsheet-, tariff-, and accounting-dependent. Ranges such as 30%–50% are context examples, not a universal plant fraction. The primary objectives of comminution are to liberate valuable economic minerals from barren gangue matrix at the coarse economic liberation size and to prepare mineral surfaces for downstream physical or chemical separation processes.
Classical Comminution Theories & Energy-Size Reduction Laws
The fundamental relationship between energy input ( E E E ) and particle size reduction ( x x x ) is expressed by the general differential comminution equation: d E = − C d x x n dE = -C \frac{dx}{x^n} d E = − C x n d x
Where C C C is a material constant, x x x is the characteristic particle size, and n n n is an exponent determining the specific comminution regime.
1. Kick's Law ( n = 1 n = 1 n = 1 )
Kick's Law states that the energy required to crush a given quantity of material is directly proportional to the reduction ratio ( F 80 P 80 \frac{F_{80}}{P_{80}} P 80 F 80 ), regardless of original particle size: E = C K ln ( F 80 P 80 ) E = C_K \ln\left( \frac{F_{80}}{P_{80}} \right) E = C K ln ( P 80 F 80 )
Where F 80 F_{80} F 80 is the 80% passing size of the feed and P 80 P_{80} P 80 is the 80% passing size of the product. Kick's Law is commonly used as a coarse-reduction approximation over a calibrated range; the model has no universal particle-size boundary.
2. Rittinger's Law ( n = 2 n = 2 n = 2 )
Rittinger's Law states that the energy consumed in comminution is directly proportional to the new surface area created during size reduction: E = C R ( 1 P 80 − 1 F 80 ) E = C_R \left( \frac{1}{P_{80}} - \frac{1}{F_{80}} \right) E = C R ( P 80 1 − F 80 1 )
Rittinger's Law relates energy to new surface area and is often used as a fine-size approximation over a calibrated range; it does not have a universal particle-size boundary.
3. Bond's Third Theory of Comminution ( n = 1.5 n = 1.5 n = 1.5 )
Fred C. Bond established an empirical relationship bridging the gap between Kick's and Rittinger's laws, asserting that the work input is proportional to the new crack length produced per unit volume. Bond's equation calculates specific power consumption ( W W W , in kWh/tonne \text{kWh/tonne} kWh/tonne or kWh/short ton \text{kWh/short ton} kWh/short ton ): W = 10 W i ( 1 P 80 − 1 F 80 ) W = 10 W_i \left( \frac{1}{\sqrt{P_{80}}} - \frac{1}{\sqrt{F_{80}}} \right) W = 10 W i ( P 80 1 − F 80 1 )
Where:
W W W = Specific energy required ( kWh/tonne \text{kWh/tonne} kWh/tonne )
W i W_i W i = Bond Work Index ( kWh/tonne \text{kWh/tonne} kWh/tonne ), defined as the total specific energy required to reduce ore from infinite particle size to an 80% passing size of 100 μ m 100\ \mu\text{m} 100 μ m
- P 80 P_{80} P 80 = 80% passing size of the grinding circuit product ( μ m \mu\text{m} μ m )
- F 80 F_{80} F 80 = 80% passing size of the primary feed ( μ m \mu\text{m} μ m )
If P 80 P_{80} P 80 and F 80 F_{80} F 80 are given in micrometers ( μ m \mu\text{m} μ m ), the constant 10 10 10 converts units into standard specific energy. Bond's relation is empirical and must use a compatible test Work Index, size basis, units, and circuit correction factors.
Crushing Machinery & Equipment Selection
Crushing is performed dry in multi-stage sequences (primary, secondary, tertiary) using mechanical compression or impact forces.
Primary Crushers
Blake Jaw Crusher : Heavy-duty primary crusher with a fixed jaw and a movable swing jaw pivoted at the top. This configuration provides maximum motion at the discharge throat, preventing clogging under coarse ROM (run-of-mine) feed up to 1.5 m 1.5\ \text{m} 1.5 m .
Dodge Jaw Crusher : Swing jaw pivoted at the bottom, creating a constant discharge throat opening but variable feed opening. Prone to choking; used mainly for small-scale sampling plants.
Gyratory Crusher : Features a heavy conical crushing head mounted on a central vertical shaft that gyrates inside a concave shell. Delivers continuous crushing action with higher throughput capacity ( 2 , 000 – 10 , 000 tph 2,000\text{--}10,000\ \text{tph} 2 , 000 – 10 , 000 tph ) than jaw crushers.
Secondary & Tertiary Crushers
Cone Crushers : Modified gyratory crushers with a shortened shaft supported from below. Standard Cone Crushers feature steep crushing cavities for coarse secondary feed ( 50 – 100 mm 50\text{--}100\ \text{mm} 50 – 100 mm ), while Short Head Cone Crushers feature flatter parallel crushing zones for fine tertiary feed ( 10 – 25 mm 10\text{--}25\ \text{mm} 10 – 25 mm ).
High-Pressure Grinding Rolls (HPGR) : Consists of two counter-rotating rolls applying high hydraulic pressures ( 50 – 150 MPa 50\text{--}150\ \text{MPa} 50 – 150 MPa ) to an ore bed. HPGR promotes interparticle crushing, generating micro-cracks in mineral grains that reduce downstream ball mill grinding energy by 15% to 25%.
Grinding Machinery & Mill Dynamics
Grinding utilizes tumbling mills loaded with grinding media (steel balls, steel rods, or coarse ore rocks) operating wet at high solids concentrations (65% to 80% solids by weight).
Tumbling Mill Types
Rod Mills : Utilize high-carbon steel rods as media. Rods exhibit line contact, selectively grinding coarse particles while shielding fine particles, producing a uniform product ( 0.5 – 3.0 mm 0.5\text{--}3.0\ \text{mm} 0.5 – 3.0 mm ) with minimal slimes.
Ball Mills : Utilize forged steel balls ( 20 – 100 mm 20\text{--}100\ \text{mm} 20 – 100 mm diameter). Point contact promotes intense impact and attrition grinding, achieving fine product sizes ( < 74 μ m <74\ \mu\text{m} < 74 μ m / -200 mesh).
Autogenous (AG) & Semi-Autogenous (SAG) Mills : AG mills grind ore using large coarse ore rocks as media without steel media. SAG mills add a light steel ball charge (4% to 15% mill volume) to assist ore breakage, achieving extreme reduction ratios ( F 80 = 300 mm F_{80} = 300\ \text{mm} F 80 = 300 mm to P 80 = 1 mm P_{80} = 1\ \text{mm} P 80 = 1 mm ) in a single stage.
Mill Critical Speed Calculation
The Critical Speed ( N c N_c N c ) of a tumbling mill is the rotational speed at which centrifugal force acting on a grinding ball equals gravitational force, causing media to cling to the mill shell throughout the revolution: N c = 42.3 D − d ( rpm ) N_c = \frac{42.3}{\sqrt{D - d}} \quad (\text{rpm}) N c = D − d 42.3 ( rpm )
Where D D D is the internal mill diameter ( m \text{m} m ) and d d d is the media diameter ( m \text{m} m ). If d ≪ D d \ll D d ≪ D , the equation simplifies to N c = 42.3 D N_c = \frac{42.3}{\sqrt{D}} N c = D 42.3 . Commercial ball mills operate at 65% to 80% of critical speed to create a cataracting regime (balls lift and impact the mill toe) combined with cascading (balls roll down the charge face producing attrition).
Closed-Circuit Grinding & Circulating Load Ratio
To prevent overgrinding of liberated mineral grains, tumbling mills operate in closed circuit with hydrocyclones or vibrating screens.
Circulating Load Ratio ( C L R CLR C L R )
The Circulating Load Ratio evaluates the mass flow rate of coarse classifier underflow ( C C C ) returned to the mill relative to fresh plant feed ( F F F ): C L R = C F × 100 % = t o − t m t m − t u × 100 % CLR = \frac{C}{F} \times 100\% = \frac{t_o - t_m}{t_m - t_u} \times 100\% C L R = F C × 100% = t m − t u t o − t m × 100%
Where t o t_o t o , t m t_m t m , and t u t_u t u are cumulative mass fractions passing a specified sieve mesh in the classifier overflow, mill discharge, and classifier underflow, respectively. The suitable circulating load follows the ore, mill, classifier, water balance, power draw, product target, and stability; a quoted range is only a reference case and cannot ensure optimum grinding.
Summary of Comminution Machinery
- Equipment Type Mechanism Reduction Ratio Typical Product Size Key Application
- Blake Jaw Crusher Compression (top pivot) 4:1 to 7:1 100 – 200 mm Primary ROM rock crushing
- Gyratory Crusher Continuous compression 4:1 to 8:1 75 – 150 mm High-capacity primary crushing
- Standard Cone Crusher High-speed compression 4:1 to 6:1 20 – 40 mm Secondary crushing
- HPGR Interparticle compression 4:1 to 8:1 2 – 6 mm Tertiary crushing / SAG alternative
- SAG Mill Impact & attrition 30:1 to 100:1 1 – 3 mm Primary wet ore grinding
- Ball Mill Point impact & attrition 10:1 to 50:1 0.045 – 0.15 mm Secondary / fine grinding