Groundwater, Aquifers & Well Hydraulics Notes

Last reviewed 16 Sept 2026 · 7 min read

Occurrence of groundwater

Below the ground surface, water occurs in two main zones:

Zone	Description
Zone of aeration (vadose zone)	Pores contain both air and water. Sub-zones: soil-water zone (root zone), intermediate vadose zone, capillary fringe (just above the water table, held by capillarity)
Zone of saturation	All pores filled with water under pressure ≥ atmospheric; its water is groundwater

The water table (phreatic surface) is the upper surface of the zone of saturation in an unconfined aquifer, where pressure is atmospheric.

Geological formations

Formation	Stores water?	Transmits water?	Example
Aquifer	Yes	Yes, readily	Sand, gravel, fractured rock, cavernous limestone
Aquitard	Yes	Slowly	Sandy clay
Aquiclude	Yes (porous)	No (practically)	Clay
Aquifuge	No	No	Massive unfractured granite

Types of aquifers

Unconfined (water-table) aquifer — upper boundary is the water table; recharged directly from the surface.
Confined (artesian) aquifer — sandwiched between impervious layers; water is under pressure. The level to which water rises in a well is the piezometric surface. If the piezometric surface is above the ground, the well flows naturally (flowing artesian well).
Perched aquifer — a small body of groundwater held above the main water table by a local impervious lens.
Leaky (semi-confined) aquifer — bounded by an aquitard that allows some leakage.

Aquifer properties

FormulaAquifer parameters

Porosity $n = V_{v} / V$
Specific yield $S_{y}$ — volume of water drained by gravity ÷ total volume
Specific retention $S_{r}$ — water retained against gravity ÷ total volume

n = S_{y} + S_{r}

Hydraulic conductivity (coefficient of permeability) $K$ (m/s or m/day)
Intrinsic permeability $k_{0} = \frac{K μ}{ρ g}$ (m² or darcy) — property of the medium alone
Transmissivity $T = K b$ (m²/day) — flow through a unit-width strip of the full aquifer thickness $b$ under unit gradient
Storage coefficient (storativity) $S$ — volume of water released per unit surface area per unit decline of head
- Confined aquifers: very small, about $5 \times 1 0^{- 5}$ to $5 \times 1 0^{- 3}$ (from compression of the aquifer and expansion of water)
- Unconfined aquifers: $S \approx S_{y}$ (typically a few per cent to about 30%)

Clay has high porosity but very low specific yield (high retention); coarse sand and gravel have high specific yield.

Darcy's law

V = K i, Q = K i A

$V$ = discharge (Darcy) velocity over the gross area; the actual average seepage velocity $V_{s} = V / n_{e}$ ( $n_{e}$ = effective porosity).

Validity: laminar flow — Reynolds number $R e = V d_{10} / ν$ below about 1 (up to about 10 in practice). Not valid for flow through coarse gravel, fractures with turbulent flow or karst conduits.

Steady radial flow to wells (equilibrium equations)

Assumptions (Dupuit–Thiem): homogeneous, isotropic aquifer of infinite extent; well fully penetrating; flow horizontal and laminar; steady state reached; pumping rate constant.

FormulaConfined aquifer

Q = \frac{2 π K b ( h _{2} - h _{1} )}{ln ( r _{2} / r _{1} )} = \frac{2 π T ( s _{1} - s _{2} )}{ln ( r _{2} / r _{1} )}

With well radius $r_{w}$ , drawdown $s_{w}$ and radius of influence $R$ : $Q = \frac{2 π T s _{w}}{ln ( R / r _{w} )}$

FormulaUnconfined aquifer

Q = \frac{π K ( h _{2}^{2} - h _{1}^{2} )}{ln ( r _{2} / r _{1} )} or Q = \frac{π K ( H ^{2} - h _{w}^{2} )}{ln ( R / r _{w} )}

$H$ = saturated thickness before pumping; $h_{w}$ = depth of water in the well while pumping.

Radius of influence — distance beyond which drawdown is negligible; Sichardt's formula: $R = 3000 s_{w} K$ ( $R$ , $s_{w}$ in m; $K$ in m/s).
Cone of depression — the drawdown surface around the pumped well.
Discharge is only moderately sensitive to $R$ (it appears inside a logarithm).
Specific capacity $= Q / s_{w}$ — a measure of well productivity (decreases with time and pumping rate).

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Groundwater, Aquifers & Well Hydraulics