24-MMP-A5 Surface Mining Methods and Design · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-MMP-A5 Surface Mining Methods and Design, 2014-Dec. 3 hours duration, closed book; one hand-written 8.5×11 inch reference sheet and an approved Casio or Sharp calculator permitted. Question 1 is compulsory (40 marks, all seven parts 1.1–1.7); a candidate then selects THREE of Questions 2–7 (each worth 20 marks).
Reference texts: Hartman & Mutmansky (eds.), SME Mining Engineering Handbook, 3rd ed. (dragline stripping systems, truck-shovel productivity, mine dewatering, mine cost estimation); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design, 3rd ed. (block-model economics, floating/moving-cone algorithm, the Lerchs–Grossmann graph-theoretic pit-optimization method); Kennedy, B.A. (ed.), Surface Mining, 2nd ed., SME (dragline range-diagram geometry, stripping methods); Lerchs, H. & Grossmann, I.F. (1965), “Optimum Design of Open-Pit Mines,” CIM Bulletin, 58, 47–54; Mular, A.L. & Poulin, R. (1998), CapCosts: A Handbook for Estimating Mining and Mineral Processing Equipment Costs, CIM Special Volume 47 (parametric open-pit capital-cost formulae used throughout Question 7).
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.
Given. Total static lift $=1740-1650=90$ m, split into two equal 45 m stages (sump→1695 m tandem pump, then 1695 m→crest), the only accessible intermediate bench; friction loss negligible (stated); pump curves (Fig. 5.1) read as: 433 (HT) shutoff head $\approx56$ m, declining to $\approx30$ m at the curves' mutual crossing point near 95 l/s; 431 (MT) shutoff head $\approx33$ m, also $\approx30$ m at that same crossing point.
Find. Whether the stated (433, HT)+(433, HT) pairing can meet the 90 m lift and at what discharge, the outcome of every other pairing, the inlet/outlet pressure at each pump, the required pipe rating, and the check-valve modifications; then the deep-well alternative's design methodology.
Approach. With negligible friction, two pumps plumbed in series (the unvented tandem coupling) carry the same flow $Q$, and each pump's head, read off its OWN curve at that shared flow, must sum to the 90 m total lift; the operating point is therefore found where the sum of the two head-vs-flow curves equals 90 m.
5.1.b – Maximum discharge, all configurations. Checking each pairing's SHUTOFF head (the most favourable possible case) against the 90 m lift: MT+MT $=2\times33=66$ m $<90$ m – cannot lift the water at ANY flow, $Q=0$; HT+MT (either order) $=56+33=89$ m $<90$ m – also cannot meet the lift (Check callout above); HT+HT $=2\times56=112$ m $>90$ m – the ONLY configuration that can deliver water to the crest, at the $\approx40$ l/s operating point found in 5.1.a.
5.1.c – Inlet/outlet pressures. The bottom (submersible) pump draws directly from the open sump, so its inlet is essentially atmospheric, $\approx0$ m gauge; it discharges into the riser carrying its full 45 m share of the lift, so its outlet is $\approx45$ m of water. With friction negligible (stated) over the 45 m rise to the tandem pump, that head is entirely consumed reaching the top pump's level, so the top pump's inlet also arrives at $\approx0$ m gauge (it is coupled directly, not vented, so no atmospheric reference is re-established); it then supplies the remaining 45 m stage to the crest, so its outlet is likewise $\approx45$ m of water.
5.1.d – Pipe schedule at the inlets. Converting the 45 m outlet head using the given factors: $$45\text{ m}\times1.41\ \dfrac{\text{psi}}{\text{m}}=\boxed{63.5\text{ psi}}\qquad63.5\text{ psi}\times6.9\ \dfrac{\text{kPa}}{\text{psi}}=\boxed{438\text{ kPa}}$$ A standard large-diameter HDPE (PE100) pressure pipe in a moderate wall-thickness dimension ratio (e.g. DR17, commonly rated on the order of 860–1380 kPa depending on nominal diameter) comfortably exceeds this 438 kPa static working pressure with margin for the water-hammer transient discussed in 5.1.e; a thinner-wall (higher DR) pipe should not be chosen on the static figure alone without also checking the surge allowance.
5.1.e – Check-valve modifications. A check valve at the top pump's outlet stops back-flow to the sump when that pump stops, but it also seals the riser between the two pumps into a closed, pressurised section with nowhere for a pressure transient to go: if the top pump trips while the bottom pump keeps running, the closing valve can generate a water-hammer surge, and the bottom pump would effectively deadhead against the closed valve. Required modifications: (i) a slow-closing (non-slam) check valve rather than an instantaneous swing check, to limit surge magnitude; (ii) a pressure-relief valve immediately downstream of the bottom pump (upstream of the check valve) to bleed off deadhead over-pressure; (iii) an interlock tripping the bottom pump whenever the top pump stops, so it cannot run indefinitely against a closed valve; and (iv) an air-vacuum valve at the high point to admit air and prevent column separation if the top pump loses suction after tripping.
| Item | Value |
|---|---|
| 5.1.a Discharge, HT+HT | ≈ 40 l/s at 45 m per stage |
| 5.1.b MT+MT / HT+MT / HT+HT vs. 90 m lift | 66 m (fails) / 89 m (fails) / 112 m (only workable pairing) |
| 5.1.c Each pump inlet / outlet | ≈ 0 m / ≈ 45 m of water |
| 5.1.d Required pipe pressure rating | ≥ 63.5 psi (438 kPa) static, plus surge allowance |
5.2.a – Transmissibility and storativity from test wells. A constant-rate pumping test in one well, with drawdown logged over time in nearby observation wells, is fitted to the Theis non-equilibrium type curve (log-log overlay of the well function $W(u)$ against $1/u$) or, for large times, the simpler Cooper–Jacob straight-line method (drawdown vs. $\log t$, linear once $u$ is small): the line's slope gives transmissivity $T=2.3Q/(4\pi\Delta s)$ ($\Delta s=$ drawdown per log cycle of time), and its zero-drawdown time-intercept gives storativity $S=2.25Tt_0/r^2$.
5.2.b – Pump layout and depth. With $T$ and $S$ known, the same equations are run FORWARD to predict the drawdown any candidate well would produce at any distance/rate; wells are laid out around the pit perimeter (and along the ramp where practical) at a spacing chosen so neighbouring drawdown cones overlap enough to depress the water table below the advancing pit floor everywhere along the highwall, with intake depth set below the lowest predicted dynamic water level plus a safety margin.
5.2.c – Feasibility and cost. Predicted total well yield (from the same forward model) is compared against the aquifer's sustainable yield and the mine's dewatering target; cost is estimated from well count (from the 5.2.b spacing) × unit drilling/casing/pump cost, plus pumping-power cost driven by total lift and flow (the same parametric-cost logic as Question 7), then compared against the in-pit tandem-pump alternative (5.1) on a lifecycle-cost basis.
5.2.d – Operational advantages. A perimeter deep-well system dewaters the rock mass AHEAD of mining, improving highwall stability by lowering pore pressure on the slope (a geotechnical benefit Question 1.5.2's monitoring cannot itself provide, only detect the lack of); it keeps the working floor and faces dry for equipment traction and blast-hole integrity without any pipe run or pump that must be relocated as the pit deepens (unlike the in-pit tandem system of 5.1, whose pumps must follow the advancing bench); and it avoids the water-hammer/tandem-pump complications of 5.1.e entirely, discharging instead to a perimeter collection system outside the active mining area.
