18-Geol-A2 Hydrogeology · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2019 — 18-Geol-A2 Hydrogeology. Three-hour, open-book exam; any non-communicating calculator permitted. Five questions constitute a complete paper and all five are of equal value; clarity and organization of the answers, with work shown in detail, are explicitly graded. Unless stated otherwise, water density is taken as 1000 kg/m³, water viscosity as 0.001 kg/m-sec, and g as 9.81 m/s².
Reference texts: Freeze & Cherry, Groundwater (Prentice-Hall, 1979) — Darcy's law and anisotropic conductivity tensors, the three-point head-gradient method, soil phase relations, layered-medium effective conductivity, freshwater-equivalent head across a density interface, elastic storage, the Theis and Hantush-Jacob (leaky) well equations, Cooper-Jacob straight-line analysis, and slug-test analysis (Cooper-Bredehoeft-Papadopulos); Todd & Mays, Groundwater Hydrology — supplementary well-test methods; EGBC Geoscience Professional Practice Guidelines for assumption-disclosure conventions on open-book calculations.
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.
This question is entirely descriptive — no numeric data are given, and the four parts are answered as connected essay responses drawing directly on the theory used quantitatively elsewhere in this paper (Q2, Q3, Q4).
Part (a) — storativity vs. specific yield. Storativity $S$ is the property of a confined aquifer: the volume of water released from (or taken into) storage per unit surface area per unit decline (or rise) in head, while the aquifer remains fully saturated. Release is entirely elastic — a small decline in pressure allows the water to expand slightly and the aquifer skeleton to compress slightly, and both effects together are captured in $S=S_sb$. Because it relies on the compressibility of water and grains, $S$ is typically very small, on the order of $10^{-3}$ to $10^{-5}$. Specific yield $S_y$, by contrast, applies to an unconfined (water-table) aquifer: as the water table falls, pores actually drain by gravity, physically releasing water from storage (with a residual specific retention left behind by capillary forces). Because it represents true dewatering of pore space rather than elastic expansion, $S_y$ is orders of magnitude larger than $S$, typically 0.05–0.30. A confined aquifer that is pumped hard enough to draw its head below the top of the aquifer converts locally to unconfined conditions and releases water via $S_y$ instead of $S$ from that point on — the reason a "confined-to-unconfined conversion" is flagged as a modelling complication in long-term confined pumping tests.
Part (b) — drawdown ordering. From smallest to biggest: leaky confined < (fully) confined < confined bounded by an impermeable boundary. A leaky confining layer allows vertical recharge into the pumped aquifer as drawdown develops (exactly as computed in Q3(b) vs. Q3(a), where the leaky drawdowns were a fraction of the fully-confined Theis values) — that extra source of water reduces how far the head must fall to supply the well, so drawdown is smallest. The fully confined (Theis) case has no such extra recharge and is the baseline. An impermeable (no-flow) boundary is modelled by an image well of the SAME sign and discharge, mirrored across the boundary; once the expanding cone of depression "feels" the boundary, its drawdown contribution adds directly to the real well's drawdown, so this case produces the LARGEST drawdown of the three for identical $Q$, $t$, and $r$.
Part (c) — saltwater encroachment. Causes: over-pumping of a coastal aquifer draws the freshwater head down faster than natural recharge replaces it, allowing the freshwater-saltwater interface to migrate landward (governed by the Ghyben-Herzberg relation, where every 1 m of freshwater head above sea level supports roughly 40 m of freshwater below it); reduced natural recharge from drought, paving, or land-use change; sea-level rise, which raises the reference saltwater elevation directly; and local up-coning beneath an individual pumping well screened too close to the interface, which can pull saline water upward into the well even without a regional-scale intrusion. Mitigation measures: reduce or relocate pumping away from the coast and spread demand across more, shallower wells rather than a few deep, high-capacity ones; limit individual well penetration depth to reduce up-coning risk; artificial recharge (spreading basins or injection wells) to maintain the freshwater head; dedicated injection or extraction "barrier" wells along the coast to hold the interface in place; and ongoing monitoring-well networks to detect early landward migration before production wells are affected.
Part (d) — investigative study for a new-subdivision water supply. The study proceeds in stages, broadly following the same logic used quantitatively in Q3(c) and Q4(c)/(d) of this paper. (1) Desktop review of existing geological maps, well records, and regional hydrogeological reports to identify candidate aquifers and rule out obviously unsuitable ones. (2) Surface geophysical survey (electrical resistivity or seismic refraction) to map aquifer geometry, depth, and likely boundaries before committing to drilling. (3) Test drilling with continuous lithologic logging (core or cuttings description) to confirm aquifer thickness, lithology, and confining layers directly. (4) Installation of monitoring wells/piezometers and a period of water-level monitoring to establish static heads, seasonal fluctuation, and natural gradient — the same three-point/regional-gradient technique used in Q1(b) and Q3(c). (5) Aquifer (pumping) testing at a representative test well, analyzed by Theis or Cooper-Jacob methods (as in Q3(a)/Q4(d) of this paper) to determine transmissivity $T$ and storativity $S$, plus a specific-capacity test to estimate a sustainable pumping rate. (6) Water-quality sampling and laboratory analysis for potability (major ions, TDS, coliform, and any regional contaminants of concern; salinity/chloride screening if the site is coastal). (7) A water-balance / recharge estimate to bound the long-term sustainable (safe) yield, distinct from the short-term pumping-test transmissivity. (8) Simple analytical or numerical modelling of long-term drawdown under the proposed subdivision pumping schedule, checking against the daily demand the way Q3(c) checks a natural-gradient discharge against 1000 m³/day. Equipment needed: a drill rig capable of continuous sampling, geophysical survey instrumentation, a submersible test pump with flow metering, pressure transducers/data loggers for the pumping test and long-term monitoring, and field/laboratory water-quality testing equipment. Aquifer properties to determine: $T$, $S$ (or $S_y$ if unconfined), hydraulic conductivity $K$, saturated thickness, boundary conditions (recharge or barrier boundaries, leakage), natural gradient and flow direction, water quality, and estimated natural recharge rate and sustainable yield.
