Question 6 of 6: Storage, Boundary Effects, Velocity Measurement and Field Test Selection

Question 6: Storage, Boundary Effects, Velocity Measurement and Field Test Selection (equal value)

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.

Part (a) — storativity vs. specific yield. Storativity $S$ describes water release from a confined aquifer: the aquifer remains fully saturated at all times, and the small volume of water released per unit head decline comes from the elastic compressibility of the water and the aquifer skeleton as the effective stress increases (a purely elastic, reversible mechanism). This makes $S$ dimensionless and very small, typically $10^{-5}$–$10^{-3}$. Specific yield $S_y$ describes water release from an unconfined aquifer: as the water table declines, pores actually drain by gravity, physically dewatering the sediment above the new water table. This releases far more water per unit head decline — typically 0.1–0.3 — because it is bounded by the material's true drainable porosity rather than by elastic compressibility. (An unconfined aquifer technically also has a small elastic component, but it is negligible next to $S_y$.)

Part (b) — ordering of drawdown by boundary condition. For the same $Q$, $t$ and $r$, the smallest-to-largest order is: leaky-confined < ordinary confined (Theis, infinite) < confined bounded by an impermeable boundary. A leaky aquitard supplies additional water to the pumped aquifer by vertical leakage, throttling drawdown below the ideal (no-leakage) Theis case. An impermeable (no-flow) boundary, by contrast, is simulated by a positive image well of the same sign as the real well, which adds rather than subtracts drawdown once its effect reaches the observation point — so a barrier boundary always produces drawdown greater than the equivalent infinite aquifer, and a leaky boundary always produces less.

Part (c) — groundwater velocity from a borehole dilution test. A tracer of known concentration $C_0$ is introduced into a section of the borehole isolated by packers and thoroughly mixed; natural groundwater flow through that section then dilutes the tracer, and its concentration is monitored over time. Because the borehole itself distorts the natural flow lines around it, the point (seepage) velocity is recovered from the measured concentration decay $C(t)$ using a distortion-corrected dilution equation, in the general form $$v=\frac{d}{2\alpha t}\ln\!\left(\frac{C_0}{C(t)}\right),$$ where $d$ is the borehole (test-section) diameter, $t$ the elapsed time, and $\alpha$ an empirical flow-distortion factor (of order 2 for an open, uncased hole) that accounts for the borehole channelling more flow through it than would have crossed that same cross-section of undisturbed aquifer. In words: the faster the true groundwater velocity, the faster the tracer is flushed out and the faster $C(t)$ falls, so the exponential decay rate of concentration is a direct, calibrated proxy for velocity.

Part (d) — three methods to determine hydraulic conductivity. (1) Pumping (aquifer) tests — pump a well at a known rate and match the drawdown at one or more observation wells to the Theis or Thiem type curve, yielding both $K$ (via $T=Kb$) and storage parameters over a large aquifer volume. (2) Slug tests — instantaneously raise or lower the water level in a single well and record its recovery, analyzed by the Hvorslev or Bouwer-Rice method, giving a local $K$ near that well with minimal water handling. (3) Laboratory permeameter tests — constant-head (for coarse, permeable samples) or falling-head (for fine-grained, low-$K$ samples) tests on an undisturbed core, giving a direct point measurement of $K$ under controlled conditions (grain-size correlations such as the Hazen approximation are a quick, less rigorous fourth option worth mentioning as a screening tool).

Part (e) — slug tests vs. pump tests. Slug tests are quick, inexpensive, and require only a single well and no water disposal, which makes them attractive at contaminated sites (no pumped water to manage) and for rapid site characterization of many wells. Their disadvantage is that they sample only a small aquifer volume immediately around the well, so they are highly sensitive to well development, skin effects and near-well heterogeneity, cannot reliably determine storativity, and give no information about aquifer boundaries at distance. Pump tests are more expensive and time-consuming — they require sustained pumping, one or more observation wells, and disposal of the pumped water — but they stress a much larger volume of the aquifer, so they yield reliable estimates of both transmissivity and storativity together, and (as in Question 5) can reveal real boundary conditions such as rivers or impermeable barriers that a slug test would never detect.