24-MMP-A2 Underground Mining Methods and Design · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
09-MMP-A2 Underground Mining Methods and Design — National Exam, December 2017. Compulsory Question 1 (Section A, 40 marks) plus three optional questions (two from Section B, one from Section C) constitute a graded 100-mark paper; every optional question (2–6) is answered in full below as a complete study resource.
Reference texts: Hartman, H. & Mutmansky, J., Introductory Mining Engineering, 2nd ed., Wiley (2002); Hartman, H. (ed.), SME Mining Engineering Handbook, 2nd/3rd ed., SME; Hartman, H., Mutmansky, J., Ramani, R. & Yang, Y., Mine Ventilation and Air Conditioning, 3rd ed., Wiley (1991) — the three texts named on the exam's own reference line.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
3.1.1 Pitot tube and manometer. A pitot tube measures the difference between total (impact) and static pressure at a single point in the airstream; connected to a sensitive (inclined or digital) manometer, that differential pressure is converted to point velocity via V = √(2Δp/ρ). Because it reads only one point, a full-cross-section traverse (typically a 5×5 or log-Tchebycheff grid) is needed to get a representative mean velocity; it is most accurate at moderate-to-high velocities (roughly >2–3 m/s, where Δp is large enough to read reliably) in relatively clean, larger airways such as shafts and main intakes, and gives no direct reading of contaminant concentration — its role in dilution assessment is purely to confirm the design airflow Q is actually being delivered so the contaminant-dilution calculation (based on that Q) is valid.
3.1.2 Vane anemometer. A small, freely rotating multi-bladed rotor is held in the airstream (or, for continuous monitoring, permanently mounted); rotor RPM is proportional to velocity and is read directly off a calibrated dial or digital counter, averaged over a timed traverse. It works well over a wide low-to-moderate velocity range (roughly 0.25–20 m/s) typical of headings, crosscuts and return airways, is quick and simple for routine face and split surveys, but reads only velocity (not concentration) and is less accurate very close to a wall or obstruction where flow is non-uniform — like the pitot tube, its dilution-assessment role is to verify the delivered quantity Q against the ventilation plan/legislated minimum, not to measure contaminant levels directly.
3.1.3 Smoke tube. A glass tube packed with a chemical (typically titanium tetrachloride or stannic chloride) that produces a visible white smoke trail when air is pumped through it with a hand bulb; the smoke's travel time over a known distance gives a rough velocity, but its real value is qualitative — it makes airflow DIRECTION and PATTERN visible (recirculation, dead air pockets, short-circuiting between intake and return, leakage past stoppings/doors) that a point-velocity instrument cannot show. It is the most direct of the three for judging dilution QUALITY (does contaminated air actually leave the working face along the intended path, or recirculate) even though it is the least precise for quantitative velocity/quantity measurement.
3.2.1 Oxygen depletion. Normal air is ≈20.9% O2; underground consumption (diesel combustion, blasting, oxidation of sulphide ore/timber, human respiration) can draw this down, and the exam's own Reg. 854 threshold (>18 kPa partial pressure O2, roughly 18% at sea level) is the statutory minimum below which physiological impairment begins. 3.2.2 Carbon dioxide (CO2)2 both displaces O2 and directly increases breathing rate and fatigue. 3.2.3 Methane (CH4) ‑ an explosive strata gas (flammable range roughly 5–15% in air) released from coal/some hard-rock formations; even where not itself acutely toxic, it is a fire/explosion hazard requiring continuous monitoring and forced dilution. 3.2.4 Carbon monoxide (the source's list repeats "carbon dioxide" here, evidently intending carbon monoxide, CO, the other principal diesel/blasting combustion gas) ‑ a highly toxic, odourless product of incomplete combustion from diesel equipment and blasting fumes, dangerous at concentrations far below those noticeable by smell, making instrumented monitoring essential. 3.2.5 Hydrogen sulfide (H2S) and sulfur dioxide (SO2) ‑ H2S (rotten-egg odour at low concentration but rapidly deadens the sense of smell at higher, more dangerous concentrations) arises from sulphide ore oxidation and stagnant water; SO2 arises mainly from sulphide-ore blasting and roasting-related processes, both severe respiratory irritants. 3.2.6 Oxides of nitrogen (NOx) ‑ produced by diesel combustion and by blasting (especially with wet or poorly primed ANFO), toxic and, unlike CO, with delayed-onset pulmonary effects that can appear hours after exposure.
3.2.7 Measurement and detection equipment. Gas volumes/concentrations are measured with a combination of fixed, continuous multi-gas monitoring stations (electrochemical/catalytic sensors for O2, CO, NOx, H2S, non-dispersive infrared for CO2/CH4) tied into a mine-wide SCADA/gas-monitoring system with alarm setpoints, portable multi-gas detectors carried by supervisors and diesel-equipment operators for spot checks, and, historically, colorimetric detector tubes for periodic verification/calibration checks. Airborne particulate (diesel particulate matter and respirable dust) is measured gravimetrically (personal/area sampling pumps drawing a known volume through a pre-weighed filter, weighed before/after) and, increasingly, with real-time laser photometers for immediate feedback; DPM specifically is also assessed via elemental/organic carbon analysis of the collected filter, since mass alone does not distinguish diesel soot from other dust sources.
Vane-axial fans move air parallel to the shaft axis through a ring of aerofoil-section blades (often with adjustable pitch); they are compact, give good efficiency at high volume/moderate pressure, and their straight-through flow path makes them well suited to auxiliary/duct ventilation and as booster fans in confined headings; adjustable pitch lets output be trimmed to match a changing face-advance resistance without a full speed change. Centrifugal fans throw air radially outward off a rotating impeller into a scroll (volute) casing; they generate substantially higher pressure per stage than an equivalent axial fan (a stable, steep pressure-quantity curve resistant to stall/surge), which is why the large, fixed MAIN mine fans handling the whole mine's resistance (as in Question 3.4) are almost always centrifugal rather than axial. Blade design trades efficiency against pressure-rise stability: backward-curved/backward-inclined blades give the highest efficiency and a stable, non-overloading power curve (power falls as flow rises past the design point) and are the standard choice for main fans; forward-curved blades give a more compact, lower-tip-speed (quieter) machine for a given duty but a power curve that keeps rising with flow, risking motor overload if system resistance drops unexpectedly; radial blades are simplest/most robust for dusty, abrasive service. Noise for both families scales strongly with tip speed, so larger, slower-turning impellers (favoured for main fans) are inherently quieter for the same duty than a small, high-speed unit, and both fan families are commonly fitted with inlet/outlet silencers on the surface installation for community-noise compliance.
Given. Downcast shaft airflow Q = 66.1 m3/s (140,000 ft3/min — the two values are consistent to within 0.1%, so 66.1 m3/s, the value carried in the source's own data table, is used); Atkinson friction factor K = 8.35×10−3 kg/m3; shaft circumference O = 12.5 m; shaft depth (airway length) L = 2,000 m; shaft cross-sectional area A = 12.6 m2; 1 inch water = 249 Pa.
| Quantity | Value |
|---|---|
| Airflow Q | 66.1 m3/s |
| Friction factor K | 8.35×10−3 kg/m3 |
| Shaft circumference O | 12.5 m |
| Shaft depth L | 2,000 m |
| Shaft area A | 12.6 m2 |
Find. The frictional pressure difference (loss) H across the downcast shaft, in Pa and in inches of water gauge.
Approach. Substitute directly into the Atkinson equation H = KOLQ2/A3 (the same relation explained conceptually in Question 1.3.2), then convert Pa to inches H2O with the given factor.
| Quantity | Value |
|---|---|
| Downcast-shaft pressure loss H | 455.9 Pa ≈ 1.83 in. H2O |
A shock load in a ventilation airway is a sudden, short-duration surge in the contaminant concentration or airflow demand of an airway that is well in excess of its normal, steady-state design condition — the classic examples being the pulse of blasting fumes released the instant a round fires, a sudden diesel-equipment concentration spike when several machines start together in one heading, or an abrupt airflow-quantity change when a ventilation door/regulator is opened or a fan trips. Unlike the steady contaminant generation rate a ventilation system is normally sized to dilute continuously, a shock load must be cleared by CLEARANCE TIME (re-entry/clearing period after blasting) or by transient system capacity (regulator/fan response, auxiliary fan reserve capacity) rather than by the airway's nominal design quantity, and mine ventilation plans must explicitly provide for it (statutory blast re-entry/clearance periods, auxiliary fan sizing with reserve capacity above the steady-state minimum) rather than assuming the average design airflow alone is adequate at every instant.
3.7.1 Refrigeration. A mechanical vapour-compression (or, less commonly now, absorption) refrigeration plant — compressor, condenser, expansion device, evaporator — extracts sensible and latent heat from the downcast air by passing it over chilled coils (or through a direct-contact spray chamber) below its dew point, which both cools the air and, by condensing moisture out of it, dehumidifies it (removing latent as well as sensible heat, important since latent heat removal is what actually improves a worker's evaporative cooling capacity at depth). The heat absorbed at the evaporator is rejected at the condenser to a surface (or, in deep mines, an underground) cooling-water circuit, which is itself rejected to atmosphere at a surface cooling tower or heat-exchanger radiator — so the refrigeration plant does not destroy the heat, it pumps it from the downcast air stream to the surface where it can be discarded. This is the method of choice where the required air temperature is low enough (deep, hot mines) that simple evaporative cooling cannot reach it.
3.7.2 Cooling towers. Warm water (returning from underground heat exchangers, or, in a direct-contact tower, air itself) is sprayed or cascaded down through a packed tower against a counter-flow of ambient (surface) air; a fraction of the water evaporates, and because evaporation draws its latent heat from the remaining water, the bulk water leaving the tower is cooled to close to the ambient wet-bulb temperature. That chilled water is then piped underground and used in air-to-water heat exchangers (cooling coils) to cool the downcast airstream by sensible (and, if the coil surface runs below the air's dew point, some latent) heat transfer. Cooling towers are cheaper to operate than mechanical refrigeration (no compressor) but are limited by the SURFACE wet-bulb temperature they can reach — effective mainly in drier climates or as first-stage pre-cooling ahead of mechanical refrigeration in hot, humid settings, which is why the exam scenario (refrigeration plus cooling-tower assist) commonly uses both in series.
3.8.1 Sketch. Plot the entering air's measured dry-bulb/wet-bulb pair as state 1 on the chart; locate the saturation curve; the coil process line runs from state 1 down toward the saturation curve, terminating at state 2 (the coil's saturated leaving-air condition), as drawn in Fig. 3.8 above.
3.8.2 Determining the heat change. Read the specific enthalpy h1 and h2 (kJ/kg dry air) directly off the psychrometric chart at states 1 and 2 (or compute them from the Carrier/ASHRAE humidity-ratio relation, h = 1.006T + W(2501+1.86T)); the specific heat removed is q = h1−h2 (kJ/kg dry air), and multiplying by the actual dry-air mass flow rate G (kg/s) through the coil gives the total rate of heat removal in kW (or, with the imperial specific-enthalpy values and G in lb/hr, in Btu/hr).
3.8.3 Determining the moisture content removed. Read the humidity ratios W1 and W2 (kg water/kg dry air) at the same two states, either off the chart or from the saturation-vapour-pressure relation at each state's dry-bulb/wet-bulb pair; the specific moisture removed is ΔW = W1−W2, and multiplying by the dry-air mass flow rate G gives the actual condensate (moisture removal) rate in kg/s (or lb/hr) — the water that must be drained from the coil pan/sump.
