Question 8 of 11: In-Pit Tandem Pump Dewatering; Deep-Well Alternative

Question 3: In-Pit Tandem Pump Dewatering; Deep-Well Alternative (20 marks, optional)

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 → crest), since the tandem pump sits at the one accessible bench roughly mid-lift; friction loss negligible (stated); Fig. 3.1 pump curves read at zero flow (shut-off head): 433 (HT) $\approx56$ m, 431 (MT) $\approx33$ m, both declining with increasing flow.

Find. Whether MT alone can do the job, the resulting maximum discharge, the pressure at each pump, and the required pipe pressure rating.

Approach. With friction negligible, the two pumps act purely against static lift, plumbed in series on one pipe (so both carry the same flow $Q$); each pump's head, read off its own curve at that common $Q$, must sum to the 90 m total lift.

1. 3.1.1 – Can MT alone do both stages? Even at zero flow (shut-off head, the BEST case for available head), two MT pumps in series give only $2\times33=\boxed{66\text{ m}}$ – well short of the 90 m lift, so MT can never meet it at any flow. One HT + one MT in series gives at best (zero flow) $56+33=89$ m – still marginally short of 90 m. Only two 433 (HT) pumps in series/tandem can meet the 90 m lift: the answer to 3.1.1 is No.
2. 3.1.2 – Maximum discharge. With two identical HT pumps in series carrying the same flow $Q$, each must supply half the total lift: $$H_{HT}(Q)=90/2=\boxed{45\text{ m each}}$$ Reading the 433 (HT) curve (flat near 50–56 m up to about 50 l/s, then falling off steeply) at $H=45$ m gives an operating point of approximately $$Q\approx\boxed{60\ \text{l/s}\ (\approx950\ \text{US gpm})}$$

3.1.3 – Inlet/outlet pressures. Bottom (submersible) pump: inlet draws directly from the open sump, essentially atmospheric ($\approx0$ m gauge); it discharges into the riser and supplies 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 water the 45 m up to the tandem pump (friction negligible), so the top (tandem) pump's inlet arrives at essentially $\approx0$ m gauge too; it then supplies the remaining 45 m stage to the crest, so its outlet is also $\approx45$ m of water.

3.1.4 – Pipe schedule at the outlets. Converting the 45 m outlet head to pressure with the given conversion 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 at a moderate wall dimension ratio (e.g. DR17, typically rated 125–200 psi / 860–1380 kPa depending on nominal diameter) comfortably exceeds the 63.5 psi static working pressure with a healthy margin against the water-hammer transient of Question 1.3/3.1.5 – a thinner-wall (higher DR) pipe should NOT be chosen on the static figure alone without also checking the transient surge allowance.

3.1.5 – Modifications for a check (gate) valve at the top pump outlet. A check valve stops water in the upper riser draining back to the sump when the top pump stops, but it also creates a closed, pressurised section between the two pumps with nowhere for a transient to go – if the top pump trips while the bottom pump keeps running, the closing check valve can generate a Question 1.3-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 surge magnitude; (ii) a pressure-relief/surge-relief valve immediately downstream of the bottom pump (upstream of the check valve) to bleed off deadhead over-pressure; (iii) an interlock that trips the bottom pump whenever the top pump stops (or a low-flow/high-pressure cutout), 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.

3.2.1 – Transmissibility and storativity from pumping-test wells. A constant-rate pumping test in one well, with drawdown observed over time at nearby observation wells, is analysed by fitting the drawdown-vs-time (or 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 large-time approximation, the Cooper–Jacob straight-line method (drawdown plotted against $\log t$, linear once $u$ is small): the slope of that line gives transmissivity $T=\dfrac{2.3Q}{4\pi\Delta s}$ ($\Delta s=$ drawdown per log cycle of time), and the time-axis intercept at zero drawdown gives storativity $S=\dfrac{2.25Tt_0}{r^2}$.

3.2.2 – Pump layout and depth. With $T$ and $S$ known, the same Theis/Jacob equations are run FORWARD (predictive, not fitted) to estimate the drawdown any candidate well would produce at any distance and pumping rate; wells are laid out around the pit perimeter (and along the access ramp where practical) at a spacing chosen so 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.

3.2.3 – Feasibility and cost. Feasibility follows from the same forward model: predicted total well yield is compared against the aquifer's sustainable supply and against the mine's dewatering target; cost is the number of wells (from 3.2.2's spacing) times unit drilling/casing/pump cost, plus power cost driven by total lift and flow (a parametric approach directly analogous to Question 6.3), compared against the in-pit sump/pump system (Question 3.1) on a total lifecycle-cost basis.

3.2.4 – Operational advantages. A perimeter deep-well system dewaters the rock mass AHEAD of mining (improving highwall stability and reducing slope pore pressure – a geotechnical benefit the in-pit sump system cannot provide), keeps the active 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 3.1 entirely, since the wells discharge to a perimeter collection system well outside the active mining area.