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
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