Question 10 of 11: Pit dewatering — tandem pumps and deep wells (20 marks)

Question 5: Pit dewatering — tandem pumps and deep wells (20 marks)

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.

5.1 Tandem in-pit pump system

Given. Total static lift = 1740−1650 = 90 m; two pumps in series (bottom, submersible, at 1650 m; top, tandem-coupled, at 1695 m, i.e. 45 m of pipe rise to the top pump, then a further 45 m of pipe/elevation to the crest); friction assumed negligible; pump curves per Fig. 5.1 (below) for the high-head "433, HT" and high-volume "431, MT" configurations.

[Figure not reproduced: Fig. 5.1 (redrawn) — HT curve starts near 58 m head at shut-off and terminates near 20 m at ≈107 L/s; MT curve starts near 35 m and declines gently to ≈12 m at 250 L/s. The two-HT operating point (both pumps at 45 m, Q≈36 L/s) is marked. See the official exam paper.]

Approach. Because the two pumps run IN SERIES, the SAME flow Q passes through both, and their heads simply ADD: $H_1(Q)+H_2(Q)=90\text{ m}$ (friction negligible). In addition, the BOTTOM pump alone must supply at least the 45 m of elevation up to the top pump's inlet, or that inlet would be starved (sub-atmospheric/cavitating) — i.e. $H_1(Q)\ge45$ m is a hard floor on the bottom pump, independent of what the top pump does.

1. Test "both MT" (5.1.1). The MT curve's OWN maximum head, at zero flow, is only $\approx35$ m — below the 45 m floor the bottom pump alone must clear. Even summing two MT pumps at shut-off, $2\times35=70\ \text{m} < 90\ \text{m}$ required: MT can never reach the duty, at any flow. $$\boxed{\text{No} - \text{the 431, MT pump cannot be used for either position; at least the bottom pump must be the 433, HT.}}$$
2. Best configuration — both HT. Trying the top pump as HT too (both pumps identical, so $H_1(Q)=H_2(Q)=H_{HT}(Q)$ at the common flow): solve $2H_{HT}(Q)=90 \Rightarrow H_{HT}(Q)=45$ m. Reading Fig. 5.1's HT curve at $H=45$ m gives $$\boxed{Q_{max}\approx 36\ \text{L/s}}$$ Trying "HT bottom + MT top" instead requires $H_{HT}(Q)+H_{MT}(Q)=90$; since $H_{HT}(0)+H_{MT}(0)=58+35=93$ already only barely clears 90 m, the crossing happens at a MUCH lower Q (under 10 L/s) — worse than the all-HT pairing. Both pumps HT is therefore the best (highest-flow) configuration, at $H_1=H_2=45$ m each (which also exactly satisfies the $H_1\ge45$ m floor, at equality).
3. Pressures at each pump (5.1.3). Bottom pump: suction $\approx0$ m (submerged at the sump free surface); discharge $=H_1=\boxed{45\ \text{m}}$. This head is spent lifting 45 m to the top pump, so the top pump's OWN inlet arrives at $45-45=\boxed{0\ \text{m}}$ (borderline atmospheric — the reason the bottom pump cannot be allowed to develop less than 45 m). Top pump discharge $=0+H_2=\boxed{45\ \text{m}}$, which is then spent on the final 45 m rise to the crest, arriving at $45-45=0$ m (free discharge at the crest) — the system closes exactly.
4. Pipe schedule (5.1.4). Each pump discharges at 45 m of water $=45\times1.41=63.5$ psi $\approx438$ kPa. Allowing a normal design margin (1.5–2×), the HDPE discharge pipe at each pump outlet should be rated at least PN10 (1000 kPa, i.e. ≈145 psi) — comfortably above the 438 kPa working pressure with margin for surge.
5. Check-valve modification (5.1.5). A non-return valve at the TOP pump's outlet stops the column above it draining back to the sump on shutdown, but it also means the pipe and valve from that point to the crest permanently HOLD the full 45 m/438 kPa static head even while both pumps are off — so that section must be rated for continuous static pressure, not just running pressure, and the top pump must be sized/started against this full head every restart (no gradual ramp-up as in an un-valved column). A small air-release/vacuum-breaker valve is also needed just below the check valve, since the LOWER section (sump to top pump, unprotected by any check valve) will drain back to the sump on shutdown and could otherwise draw a vacuum against the now-sealed upper column.

5.2 Deep-well dewatering alternative

5.2.1 Transmissibility and storage. Transmissibility $T$ (m²/day) is the rate at which the pit-wall aquifer can transmit water through its full saturated thickness under a unit hydraulic gradient ($T=Kb$, hydraulic conductivity × aquifer thickness); the storage coefficient $S$ (dimensionless) is the volume of water released from (or taken into) storage per unit surface area per unit change in head. Both are found from a PUMPING TEST: a test well is pumped at a constant known rate while drawdown is logged with time in nearby observation wells, and the drawdown-vs-time (or drawdown-vs-distance) data is plotted against the THEIS (or, at late time, the Jacob straight-line simplification of Theis) TYPE CURVE; matching the field curve to the type curve (or reading the slope/intercept of the Jacob semi-log straight line) yields $T$ and $S$ directly from the match-point coordinates.

5.2.2 Well layout and depth. Wells are laid out in plan around the pit perimeter (and along the internal access ramp where the wall geometry allows) at a spacing set by the aquifer's own radius of influence (from the pumping test above) so that adjacent wells' cones of depression overlap and jointly draw the water table down below the advancing pit floor; each well is drilled/screened to a depth that keeps the pumping water level safely below the deepest bench the pit will reach at that location, with enough submergence over the pump intake to avoid air-entrainment.

5.2.3 Feasibility and cost. Feasibility is assessed from the SAME pumping-test $T$ and $S$ values, used to predict the well spacing/count and total pumping rate needed to achieve the target drawdown ahead of mining; cost is then estimated from the number of wells (drilling + casing + screen + submersible pump per well) plus the power cost of continuous pumping at the predicted combined rate, and compared against the in-pit pump alternative's own capital (pumps, pipe, tandem stations) and power cost.

5.2.4 Operational advantages. Deep wells dewater the rock mass AHEAD of the excavation, so the working faces and floor stay dry and stable (better wall/floor trafficability, reduced slope-failure risk from pore pressure) with no pumps or pipework occupying working benches inside the pit, unlike the in-pit tandem system of 5.1 which must be relocated as the pit deepens and occupies bench space needed for haulage.