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Exercise set

Mineral Processing and Ore Handling Systems Exercises

Worked mining engineering exercises for mineral processing and ore handling covering ore grade, metal recovery, mass balance, slurry flow, conveyor capacity, screen efficiency, circulating load, pumping power, thickener water balance, metallurgical reconciliation, and failure-mode risk.

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Mining and Georesources Engineering
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Exercise set
Updated
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v1.1.0 ยท reviewed

These exercises practise first-pass calculations used in mineral processing and ore handling systems. They connect ore grade, recovery, concentrate mass, tailings mass, slurry density, conveyor capacity, screen performance, circulating load, pump power, thickener water balance, metallurgical reconciliation, and failure-mode risk.

Assume simplified nominal values unless an exercise states otherwise. Real processing decisions require representative sampling, mineralogy, liberation testing, plant operating data, water chemistry, equipment curves, wear condition, control-loop review, safety controls, tailings constraints, and reconciliation against measured production.

How to Use These Exercises

For each problem:

  1. define the process boundary and whether the basis is dry solids, wet slurry, component mass, or volumetric flow;
  2. keep tonnes, kilograms, cubic metres, hours, days, percentages, and fractions consistent;
  3. separate valuable component balance, total solids balance, water balance, and equipment capacity;
  4. state which measurement or sample would validate the calculation;
  5. identify the downstream consequence for recovery, tailings, water, maintenance, or safety.

The most common mistake is trusting a plant calculation without checking its measurement basis. Moisture, sampling bias, stockpile accumulation, recycle load, density error, and delayed assays can make a precise-looking recovery number physically weak.

Use the exercises as plant-control gates: correct a recovery estimate, rebalance a slurry circuit, resize ore handling capacity, reduce feed, clean a screen or chute, investigate a reconciliation mismatch, or change blending rules when sampling, density, moisture, recycle, or equipment evidence contradicts the calculation.

Exercise 1: Metal Feed from Ore Grade

A concentrator processes 12{,}000\ \text{t/day} of ore at copper grade 1.25\% by mass.

Estimate copper metal entering the plant per day.

Solution

Convert grade to fraction:

1.25\%=0.0125

Copper metal feed:

m_{Cu,in}=12{,}000(0.0125)=150\ \text{t/day}

Engineering Comment

This is a dry mass basis only if the ore tonnage is dry. If the belt scale reports wet tonnes, moisture correction is required before grade, recovery, and metal accounting can be reconciled.

Exercise 2: Concentrate Mass and Tailings Grade

The plant feed from Exercise 1 contains 150\ \text{t/day} of copper. Copper recovery to concentrate is 88\%. The concentrate grade is 24\% copper by mass. Assume total dry ore feed is 12{,}000\ \text{t/day}.

Estimate copper in concentrate, concentrate mass, dry tailings mass, and copper grade in tailings.

Solution

Copper recovered to concentrate:

m_{Cu,c}=0.88(150)=132\ \text{t/day}

Concentrate mass:

\displaystyle m_c=\frac{m_{Cu,c}}{0.24}=\frac{132}{0.24}=550\ \text{t/day}

Dry tailings mass:

m_t=12{,}000-550=11{,}450\ \text{t/day}

Copper reporting to tailings:

m_{Cu,t}=150-132=18\ \text{t/day}

Tailings copper grade:

\displaystyle G_t=\frac{18}{11{,}450}=0.00157=0.157\%

Engineering Comment

This balance is useful for a first metallurgical check. The actual reconciliation should include sampling uncertainty, moisture, stockpile changes, unmeasured recycle, intermediate inventory, and assay bias.

Exercise 3: Slurry Flow from Solids Rate and Density

A grinding circuit handles dry solids at 900\ \text{t/h}. The slurry is 65\% solids by mass and has bulk slurry density \rho_s=1.75\ \text{t/m}^3.

Estimate total slurry mass flow and volumetric flow.

Solution

Total slurry mass flow:

\displaystyle \dot{m}_{slurry}=\frac{\dot{m}_{solids}}{0.65}
\displaystyle \dot{m}_{slurry}=\frac{900}{0.65}=1384.6\ \text{t/h}

Volumetric slurry flow:

\displaystyle Q=\frac{\dot{m}_{slurry}}{\rho_s}
\displaystyle Q=\frac{1384.6}{1.75}=791.2\ \text{m}^3/\text{h}

Convert to cubic metres per second:

\displaystyle Q=\frac{791.2}{3600}=0.220\ \text{m}^3/\text{s}

Engineering Comment

Slurry flow affects pump selection, cyclone pressure, pipe velocity, wear, water balance, and control stability. The density measurement must represent the actual solids concentration and particle-size distribution.

Exercise 4: Conveyor Capacity

A crushed-ore conveyor has effective loaded cross-sectional area A=0.095\ \text{m}^2, belt speed v=2.7\ \text{m/s}, and bulk density \rho_b=1.80\ \text{t/m}^3.

Estimate mass capacity in tonnes per hour.

Solution

Volumetric flow:

Q=Av=0.095(2.7)=0.2565\ \text{m}^3/\text{s}

Mass flow:

\dot{m}=\rho_b Q=1.80(0.2565)=0.4617\ \text{t/s}

Convert to tonnes per hour:

\dot{m}=0.4617(3600)=1662\ \text{t/h}

Engineering Comment

The calculation assumes stable loading. Real conveyor capacity also depends on feed control, lump size, moisture, belt width, surcharge angle, skirt leakage, spillage, belt tension, drive power, and transfer chute performance.

Exercise 5: Screen Undersize Recovery

A screen receives 500\ \text{t/h} of feed. Size analysis shows that 35\% of the feed is true undersize. The measured undersize product is 150\ \text{t/h}.

Estimate undersize recovery to the undersize product.

Solution

True undersize in feed:

\dot{m}_{u,in}=0.35(500)=175\ \text{t/h}

Undersize recovery:

\displaystyle R_u=\frac{150}{175}=0.857
R_u=85.7\%

Engineering Comment

The missing undersize reports with oversize, increasing circulating load or sending near-size material downstream. Causes may include overloaded deck area, blinding, pegging, moisture, worn media, poor distribution, or vibration problems.

Exercise 6: Grinding Circuit Circulating Load

A grinding circuit receives fresh feed of 250\ \text{t/h}. Cyclone underflow returns 500\ \text{t/h} to the mill.

Estimate circulating load ratio and total mill feed.

Solution

Circulating load ratio:

\displaystyle CL=\frac{\dot{m}_{return}}{\dot{m}_{fresh}}
\displaystyle CL=\frac{500}{250}=2.00=200\%

Total mill feed:

\dot{m}_{mill}=250+500=750\ \text{t/h}

Engineering Comment

High circulating load is not automatically bad, but it changes mill power draw, cyclone pressure, slurry density, classification sharpness, liner wear, and the ability to respond to harder or wetter ore.

Exercise 7: Slurry Pumping Power

A slurry pump delivers Q=0.20\ \text{m}^3/\text{s} at bulk density \rho=1650\ \text{kg/m}^3 against total dynamic head H=38\ \text{m}. Overall efficiency is \eta=0.68.

Estimate hydraulic power and required input power.

Solution

Hydraulic power:

P_h=\rho gQH
P_h=1650(9.81)(0.20)(38)=123{,}077\ \text{W}
P_h=123\ \text{kW}

Input power:

\displaystyle P_{in}=\frac{P_h}{\eta}=\frac{123}{0.68}=181\ \text{kW}

Engineering Comment

Slurry pump selection also requires a pump curve, solids size, wear allowance, suction condition, settling velocity, cavitation margin, gland water, flushing, and isolation plan. Clear-water calculations are not enough.

Exercise 8: Thickener Water Balance

A thickener receives 600\ \text{t/day} of dry solids at 22\% solids by mass. Underflow leaves at 55\% solids by mass. Assume solids loss in overflow is negligible.

Estimate water reporting to overflow.

Solution

Feed total mass:

\displaystyle m_f=\frac{600}{0.22}=2727\ \text{t/day}

Feed water:

m_{w,f}=2727-600=2127\ \text{t/day}

Underflow total mass:

\displaystyle m_u=\frac{600}{0.55}=1091\ \text{t/day}

Underflow water:

m_{w,u}=1091-600=491\ \text{t/day}

Overflow water:

m_{w,o}=2127-491=1636\ \text{t/day}

Engineering Comment

Overflow water affects reclaim, process-water chemistry, pond balance, and treatment load. Thickener performance should be checked against flocculant dosage, feed variability, torque, bed level, underflow density, and clarity.

Exercise 9: Metallurgical Reconciliation Check

During a reporting period, measured dry feed is 10{,}000\ \text{t} at 1.10\% copper. Concentrate production is 420\ \text{t} at 22.0\% copper. Tailings production is 9580\ \text{t} at 0.18\% copper.

Check the copper balance mismatch as a percentage of feed copper.

Solution

Feed copper:

m_{Cu,f}=10{,}000(0.0110)=110.0\ \text{t}

Concentrate copper:

m_{Cu,c}=420(0.220)=92.4\ \text{t}

Tailings copper:

m_{Cu,t}=9580(0.0018)=17.24\ \text{t}

Measured copper out:

m_{Cu,out}=92.4+17.24=109.64\ \text{t}

Mismatch:

\Delta m=109.64-110.0=-0.36\ \text{t}

Percentage of feed copper:

\displaystyle \frac{-0.36}{110.0}(100\%)=-0.33\%

Engineering Comment

This mismatch is small for a simplified example, but reconciliation should still check sample representativeness, moisture basis, assay method, stockpile change, unmeasured losses, and whether the reporting period reached steady operation.

Exercise 10: Failure-Mode Risk for Chute Plugging

A transfer chute can plug during wet clay-rich ore campaigns. A failure-mode review assigns severity S=8, occurrence O=6, and detection ranking D=4.

After moisture-triggered feed blending, chute inspection, and differential power alarms are added, occurrence is estimated at O=3 and detection at D=2. Compare the traditional risk priority numbers.

Solution

Initial risk priority number:

RPN_1=SOD=8(6)(4)=192

Revised risk priority number:

RPN_2=8(3)(2)=48

Reduction:

\Delta RPN=192-48=144

Engineering Comment

The revised ranking is lower, but the plant still needs verified controls: ore-domain tracking, moisture measurement, cleanout access, guarding, lockout, alarm response, and a rule for reducing feed before the chute becomes a safety and production incident.

Review Checklist

When reviewing a mineral-processing or ore-handling calculation, ask:

  • Is the basis explicit: dry solids, wet tonnes, slurry mass, volumetric flow, component mass, or assay period?
  • Are feed, concentrate, tailings, recycle, stockpile, and intermediate inventories included before interpreting recovery?
  • Are moisture, sampling bias, delayed assays, density error, and meter calibration small enough for the decision margin?
  • Are equipment capacities checked against variability in ore hardness, clay, moisture, particle size, wear, and control-loop response?
  • Are water balance, reagent addition, tailings constraints, and environmental discharge connected to the processing decision?
  • Are chute, conveyor, pump, screen, and thickener risks controlled with alarms, access, lockout, inspection, and response rules?
  • Does reconciliation trigger a specific investigation before the plant calculation is used for planning or reporting?

Good mineral-processing evidence connects mass balance to plant reality. A recovery number is credible only when samples, meters, inventories, operating state, and equipment limits support the same physical account.

REF

See also

  1. Mineral Processing and Ore Handling Systems Mining and Georesources Engineering
  2. Tailings, Mine Waste, and Closure Engineering Mining and Georesources Engineering
  3. Tailings, Mine Waste, and Closure Engineering Exercises Mining and Georesources Engineering
  4. Mine Dewatering and Groundwater Control Systems Mining and Georesources Engineering
  5. Mine Dewatering and Groundwater Control Systems Exercises Mining and Georesources Engineering
  6. Mine Ventilation and Underground Safety Systems Mining and Georesources Engineering
  7. Mine Ventilation and Underground Safety Systems Exercises Mining and Georesources Engineering
  8. Mine Slope Stability and Excavation Design Mining and Georesources Engineering
  9. Mine Slope Stability and Excavation Design Exercises Mining and Georesources Engineering
  10. Mine Planning, Production Scheduling, and Georesource Risk Mining and Georesources Engineering
  11. Mine Planning, Production Scheduling, and Georesource Risk Exercises Mining and Georesources Engineering
  12. Chemical Process Balances and Reactors Chemical Engineering
  13. Chemical Process Balances and Reactors Exercises Chemical Engineering
  14. Separation Processes and Distillation Engineering Chemical Engineering
  15. Separation Processes and Distillation Engineering Exercises Chemical Engineering
  16. Chemical Process Control and Plant Operations Chemical Engineering
  17. Chemical Process Safety and Hazard Control Chemical Engineering
  18. Mechanical Fluid Flow and Piping Systems Mechanical Engineering
  19. Materials Processing and Manufacturing Routes Materials Engineering
  20. Materials Processing and Manufacturing Routes Exercises Materials Engineering
  21. Production Systems and Supply Chain Operations Industrial and Management Engineering
  22. Solid Waste and Resource Recovery Systems Environmental Engineering
  23. Solid Waste and Resource Recovery Systems Exercises Environmental Engineering
  24. Environmental Water and Wastewater Systems Environmental Engineering
  25. Environmental Water and Wastewater Systems Exercises Environmental Engineering
  26. Georesource Model Mining and Georesources Engineering model
  27. Ore Grade Mining and Georesources Engineering quantity
  28. Grade Control Mining and Georesources Engineering process
  29. Tailings Storage Facility Mining and Georesources Engineering device
  30. Mass Balance Chemical Engineering model
  31. Density Materials Engineering quantity
  32. Flow Rate Mechanical Engineering quantity
  33. Continuity Equation Mechanical Engineering model
  34. Hydraulics Mechanical Engineering concept
  35. Bernoulli Equation Mechanical Engineering model
  36. Reynolds Number Mechanical Engineering quantity
  37. Laminar Flow Mechanical Engineering phenomenon
  38. Turbulence Mechanical Engineering phenomenon
  39. Viscosity Mechanical Engineering quantity
  40. Rheology Chemical Engineering term
  41. Zeta Potential Chemical Engineering quantity
  42. Oxidation Chemical Engineering process
  43. Chemical Reactor Chemical Engineering device
  44. Permeability Materials Engineering quantity
  45. Infiltration Environmental Engineering process
  46. Hydrostatic Pressure Mechanical Engineering quantity
  47. Gauge Pressure Mechanical Engineering quantity
  48. Water Hammer Mechanical Engineering phenomenon
  49. Cavitation Mechanical Engineering phenomenon
  50. Power Electrical Engineering quantity
  51. Efficiency Energy Engineering metric
  52. Bearing Mechanical Engineering device
  53. Torque Mechanical Engineering quantity
  54. Stress Mechanical Engineering quantity
  55. Fatigue Materials Engineering phenomenon
  56. Corrosion Rate Materials Engineering metric
  57. Galvanic Corrosion Materials Engineering phenomenon
  58. Closed-Loop Control Automation and Control Engineering concept
  59. PID Controller Automation and Control Engineering device
  60. Feedforward Control Automation and Control Engineering method
  61. Interlock Industrial and Management Engineering device
  62. Failure Mode Industrial and Management Engineering concept
  63. Reliability Industrial and Management Engineering metric
  64. Risk Priority Number Industrial and Management Engineering metric
  65. Validation Industrial and Management Engineering method
  66. Uncertainty Analysis Mathematical Engineering method
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