Aquifer Tests in Unconfined Aquifers

Lauren CameronSpring 2014

Topics•Unconfined vs. Confined•Parameters to Measure•Delayed Gravity Drainage

Effects•Steady and Transient

Solutions•Example Analysis with

AQTESOLV

What does “Unconfined” Mean?

•Upper boundary of aquifer is a water table, lower boundary is no-flow

•Delayed gravity drainage occurs within the drawdown cone near well

•Transmissivity is not constant near the pumping well

•Vertical components to flow near well

Basic Conceptual SketchDelayed Gravity Drainage in the drawdown cone

Saturated thickness decreases near the well

Vertical components to flow – vadose & saturated zones

Analytical Solution Accommodations

• Variable transmissivity– Drawdown assumed to be small relative to the

saturated thickness – so it can be neglected– Transmissivity is therefore assumed to be

constant– Otherwise, one must use a numerical solution

• Components of vertical flow – Vertical conductivity, Kv, is a parameter– Controls the duration of delayed yield– And the specific yield = aquifer storativity

Specific Yield

•Volume of water that will drain by gravity per unit area per unit decline in head.

• Inversely related to grain size – lab ranges :– Sand/gravel: 20 to 35% (0.2 to 0.35)– Silt/clays: < 10 % (< 0.1)

•Strongly time-dependent parameter

Drainage Near Falling Water Table

Source: Bear (1972)

Aquifer Storativity Ranges Inferred from Aquifer

Tests

•Confined: 10-7 to 10-4

•Semi-confined: 10-4 to 10-2

•Unconfined: 10-2 to 10-1

Consider the Following…

• Given two aquifers that have the same transmissivity.

• One is confined the other unconfined.

• You pump both at the same rate for the same amount of time.

• Which direction would the type curve shift when matching the drawdown-time data …– Up or down … along the vertical

drawdown axis?– Right or left … along the horizontal time

axis?

Answer: Shift Horizontally to the Right

Theis Curve fit to Early-Time Data

0.001

0.01

0.1

1

10

0 1 10 100 1000 10000

Elapsed time, minutes

Dra

wod

own,

feet

MW-18STheis Curve

Theis Curve fit to Late-Time Data

0.001

0.01

0.1

1

10

0 1 10 100 1000 10000

Elapsed time, minutesD

raw

odow

n, fe

et

MW-18STheis Curve

Shift Right – Why?• We’re shifting along the time scale is

in the direction of increasing Storativity.

• The larger the storativity, the slower the drawdown response.

• Recall hydraulic diffusivity, T/S …

• The smaller the diffusivity, the slower the drawdown cone spreads from the pumping well.

Drawdown-Time at Observation Wells

•Three drawdown segments observed

– Early time: Behaves as confined aquifer response

– Middle time: Flattens due to delayed yield

– Late time: Behaves as delayed confined aquifer

Steady-State Solution

•Based on Dupuit assumptions:– Flow is essentially horizontal– Drawdowns are small relative to total

sat’d thickness– Well was pumped long enough that

further drawdown is not measureable

•Must be used with caution as these conditions are generally not met

Dupuit Solution with 2 Observation Wells

Transient Solutions

• Jacob (1950) – Theis type curve solution when the first two Dupuit assumptions are met in late-time.

•Neuman (1972, 1975) – Generates the three segments of drawdown curve. Accounts for delayed gravity drainage. Includes Kh and Kv, position of screen, and the change in storativity with time.

Neuman Equations & Type Curves