Pumping Test Interpretation in a Layered Aquifer
A 24-hour constant-rate pumping test at 1,800 m³/d in a confined sand aquifer shows drawdown that plots as a straight line on semi-log axes for the first 6 hours, then steepens and curves. A nearby observation well 60 m away shows delayed drawdown beginning at ~7 hours. The aquifer is underlain by a clay aquitard and overlain by a leaky confining layer. A single-layer Theis analysis of the full dataset gives storativity S = 0.0004 and transmissivity T = 850 m²/d, but residuals are poor after 6 hours.
1. Diagnose why the Theis fit fails and what the late-time curvature indicates.
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Theis assumes a single homogeneous confined aquifer with no leakage and no boundaries. A semi-log straight line early, then steepening, with delayed observation-well response, indicates a layered/leaky system or a recharge boundary effect. The 7-hour delay at 60 m suggests either a low-permeability layer transmitting pressure slowly (leaky aquitard with storage) or a boundary. The poor late-time residuals mean the single-layer Theis parameters (S = 0.0004, T = 850 m²/d) are fit to only the early data and are unreliable for the full test. The steepening is consistent with leakage from the confining layer or a nearby low-permeability boundary, not simple Theis behavior.
2. Which analytical model would you apply, and what parameters would you extract?
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Apply a leaky-aquifer model (Hantush-Jacob for no aquitard storage, or Hantush with aquitard storage given the delayed response). Fit T and S from early-time data, then the leakage factor B (or leakage coefficient) from the late-time flattening/curvature. The delayed observation-well response supports the Hantush model with aquitard storage. Extract T from the early straight-line slope, S from the intercept, and the leakage coefficient from the deviation. Check consistency between pumping and observation wells. If the curve instead steepens without flattening, consider a barrier boundary and estimate distance to it. Report parameters with the model assumption stated; do not force Theis.
3. How would you translate the result into a safe yield or permit recommendation?
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Use the leaky-aquifer parameters to estimate sustainable yield: leakage provides some recharge but is finite. Compute the proportion of pumped water derived from leakage vs storage over the design period; if a large fraction comes from storage, the yield is not sustainable long-term. Recommend a yield below the rate at which drawdown approaches the aquitard or induces unacceptable leakage, and set a monitoring trigger (water level or leakage rate). The single-layer Theis yield would be over-optimistic because it ignores leakage limits and boundary effects. State the model, parameters, and the monitoring conditions for revisiting the permit.