Siting a Second Municipal Well: Interference Drawdown vs Pump Setting
A municipal wellfield pumps from a sand aquifer with transmissivity 850 m²/d and an estimated storativity of 4×10⁻⁴. Well A, screened across the full 18 m saturated thickness, has produced 2,500 m³/d for years. Static water level is 35 m below land surface and the pump intake sits at 60 m. A 24-hour pumping test on A produced 8.2 m of drawdown in the pumping well itself. The utility proposes Well B, 400 m from A, at 2,000 m³/d, and asks whether both can run simultaneously without breaking suction. Regional data hint the sand may be semi-confined, with effective storativity nearer 1×10⁻². There are no observation wells between the two proposed pumping centers, and the drilling contract must be signed this week.
1. Estimate the interference drawdown each well imposes on the other at 400 m separation after one year of pumping, and show how the storativity uncertainty changes the answer.
Read the worked answer
Use the Cooper–Jacob approximation to Theis, valid here because u is small at these times and distances:
s = [2.303 Q / (4πT)] · log₁₀(2.25 T t / (r² S))
Interference at A caused by B (Q = 2,000 m³/d, r = 400 m, t = 365 d):
- 2.25 T t = 2.25 × 850 × 365 = 698,000 m²
- r²S = (400)² × 4×10⁻⁴ = 64 m²
- ratio = 10,900 → log₁₀ = 4.04
- coefficient = 2.303 × 2,000 / (4π × 850) = 0.431
- s_B→A = 0.431 × 4.04 ≈ 1.74 m
Interference at B caused by A (Q = 2,500 m³/d): coefficient = 0.539, so s_A→B ≈ 2.18 m.
Sensitivity to storage: with S = 1×10⁻² the ratio drops to about 436 → log₁₀ = 2.64, giving s_B→A ≈ 1.14 m and s_A→B ≈ 1.42 m.
The conclusion is robust: interference is between roughly 1.1 and 2.2 m regardless of which storativity is correct. That is small relative to the 25 m of available drawdown, so the storativity question does not control the decision - but the answer should state the range rather than a single number.
2. Using the interference estimates, decide whether the 60 m pump setting is adequate, and identify the assumptions that could invalidate your answer.
Read the worked answer
Well A: own pumping drawdown 8.2 m plus 1.7 m of interference ≈ 9.9 m → water level about 45 m below land surface. That leaves ~15 m of submergence above the intake - adequate, and well above the few metres of submergence a pump needs to avoid vortexing.
Well B: its own drawdown is not yet measured. Scaling from A's specific capacity (2,500/8.2 ≈ 305 m³/d per metre), B at 2,000 m³/d would draw down ~6.6 m, plus 2.2 m of interference ≈ 8.8 m → water level about 44 m. Also adequate.
Assumptions that could break this:
- The 8.2 m is a 24-hour value in a pumping well; it includes well losses and is not steady. Drawdown grows with log(t), so multi-year operation will exceed it.
- Specific capacity is not transferable between wells - a lower-permeability screen interval at B would give more drawdown.
- Regional water-level decline, seasonal low, and partial penetration are not represented.
- If the aquifer is leaky or river-bounded, drawdown will be less; if bounded by a barrier, much more.
Recommendation: proceed, but set both intakes at 62–65 m rather than 60 m, install a variable-frequency drive and a low-level cutoff, and require a 72-hour step test plus one observation well at B before finalizing the pump selection.
3. The driller proposes moving B to only 150 m from A to save pipeline cost. Evaluate this change quantitatively and give a recommendation.
Read the worked answer
Rerun Cooper–Jacob at r = 150 m:
- r²S = (150)² × 4×10⁻⁴ = 9 m² (with S = 10⁻²: 225 m²)
- ratio = 698,000 / 9 = 77,600 → log₁₀ = 4.89 (or 3.49 with the higher S)
- s_B→A = 0.539 × 4.89 ≈ 2.64 m (1.88 m if S = 10⁻²)
- s_A→B = 0.431 × 4.89 ≈ 2.11 m (1.50 m if S = 10⁻²)
Interference rises by roughly 50% and, more importantly, the rate of increase is steep: interference scales with log(1/r²), so halving the distance costs far less than a linear intuition would suggest - but it still consumes margin that is already partly committed to long-term drawdown growth.
Judgement: at 150 m, A's total drawdown would be ~10.8 m (level ~46 m), still within the pump's capability, so the move is not fatal. However, the pipeline saving is a one-time capital cost, while the interference penalty is permanent and grows with time; and should the higher-storativity model prove wrong, the pair becomes more coupled. Keep the 400 m spacing unless the pipeline cost difference exceeds the present value of the lost pumping margin - a comparison the utility can now actually make.