24-MMP-A5 Surface Mining Methods and Design · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
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, then 1695 m→crest), since the intermediate tandem pump sits exactly at the one accessible bench (1695 m); friction loss negligible (stated); pump curves for 433 (HT) and 431 (MT), read from Fig. 7.1: HT starts near 56 m head at zero flow, MT starts near 33 m at zero flow, both declining with flow.
Find. Whether MT alone can do the job, the resulting maximum discharge, the pressure at each pump, and the required pipe rating.
Approach. With negligible friction, the two pumps operate purely against static lift, in series on one pipe (so both carry the same flow); each pump’s head, read off its own curve at that shared flow, must sum to the 90 m total lift.
7.1.3 – Inlet/outlet pressures. Bottom (submersible) pump: inlet is drawing directly from the open sump, essentially atmospheric ($\approx0$ m gauge); it discharges into the riser and must supply the full 45 m of the lower stage, so its outlet pressure equals its developed head, $\approx45$ m of water. That head is entirely consumed lifting the water the 45 m to the tandem pump (friction negligible, as given), so the top (tandem) pump’s inlet arrives at essentially $\approx0$ m gauge as well; it then supplies the remaining 45 m stage to the crest, so its outlet is also $\approx45$ m of water.
7.1.4 – Pipe schedule at the outlets. Converting the 45 m outlet head to pressure using the given factors: $$45\text{ m}\times1.41\ \dfrac{\text{psi}}{\text{m}}=\boxed{63.5\text{ psi}}\qquad 63.5\text{ psi}\times6.9\ \dfrac{\text{kPa}}{\text{psi}}=\boxed{438\text{ kPa}}$$ Standard large-diameter HDPE (PE100) pressure pipe in a moderate-wall dimension ratio (e.g. DR17, rated on the order of 125–200 psi / 860–1380 kPa depending on nominal diameter) comfortably exceeds the 63.5 psi working pressure with a healthy margin against the water-hammer transients discussed in Question 1.7/7.1.5 – a thinner-wall (higher DR) pipe should NOT be selected purely on the static 63.5 psi figure without also checking the transient surge allowance.
7.1.5 – Modifications for a check (gate) valve at the top pump outlet. A check valve prevents water in the upper riser from draining back to the sump when the top pump stops, but it also creates a closed, pressurised section of pipe between the two pumps with nowhere for a pressure transient to go – if the top pump trips while the bottom pump keeps running (or on any sudden flow change), the closing check valve can generate a Question 1.7-style 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 the surge magnitude; (ii) a pressure-relief or surge-relief valve immediately downstream of the bottom pump (upstream of the check valve) to bleed off any deadhead over-pressure; (iii) an interlock that trips the bottom pump whenever the top pump stops (or a low-flow/high-pressure cutout on the bottom pump), 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/vacuum collapse if the top pump loses suction after tripping.
| Item | Value |
|---|---|
| 7.1.1 MT alone sufficient? | No – two 433 (HT) pumps required |
| 7.1.2 Maximum discharge | ≈ 60 l/s |
| 7.1.3 Each pump: inlet / outlet | ≈ 0 m / ≈ 45 m of water |
| 7.1.4 Required pipe pressure rating | ≥ 63.5 psi (438 kPa) static, plus surge allowance |
7.2.1 – Transmissibility and storativity from pumping-test wells. A constant-rate pumping test in one well, with drawdown observed over time in one or more nearby observation wells, is analysed by fitting the observed drawdown-vs-time (or drawdown-vs-distance) data to the Theis non-equilibrium type curve (log-log overlay of the well function $W(u)$ against $1/u$), or, for the simpler large-time approximation, the Cooper–Jacob straight-line method (drawdown plotted against $\log t$, which becomes linear once $u$ is small): the slope of that straight line gives transmissivity $T=\dfrac{2.3Q}{4\pi\Delta s}$ (where $\Delta s$ is drawdown per log cycle of time), and the time-axis intercept where drawdown $=0$ gives the storage coefficient $S=\dfrac{2.25Tt_0}{r^2}$.
7.2.2 – Pump layout and depth. Once $T$ and $S$ are known, the same Theis/Jacob equations are run FORWARD (rather than fitted) to predict the drawdown any candidate well would produce at any distance and pumping rate; wells are then laid out around the pit perimeter (and along the access ramp, where practical) at a spacing chosen so that neighbouring wells’ drawdown cones overlap enough to depress the water table below the advancing pit floor everywhere along the highwall, with pump-intake depth set below the lowest predicted dynamic water level at that location plus a safety margin.
7.2.3 – Feasibility and cost. Feasibility follows directly from the same forward model: predicted total pumping rate (sum of individual well yields) is compared against the aquifer’s sustainable yield and against the mine’s dewatering target (rate needed to keep the pit floor dry on schedule); cost is estimated from the number of wells (spacing from 7.2.2) times unit drilling/casing/pump cost, plus power cost driven by total lift and total flow (directly analogous to the parametric capital-cost approach of Question 1.1), and compared against the alternative in-pit sump/pump system (Question 7.1) on a total lifecycle-cost basis.
7.2.4 – Operational advantages. A perimeter deep-well system dewaters the rock mass AHEAD of mining (improving highwall stability and reducing pore pressure on the slope, a geotechnical benefit the in-pit sump system cannot provide), keeps the working pit floor and faces dry for equipment traction and blast-hole integrity without pipe runs and pumps that must be relocated as the pit deepens, and avoids the water-hammer/tandem-pump complications of Question 7.1 entirely, since the wells discharge to a perimeter collection system outside the active mining area.
