Aquifer Tests in Unconfined Aquifers

Lauren Cameron Spring 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 Sketch

Delayed Gravity Drainage in the drawdown cone Vertical components to flow – vadose & saturated zones Saturated thickness decreases near the well

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, K v , 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

10 1 0.1

0.01

0.001

0 MW-18S Theis Curve 1 10 100

Elapsed time, minutes

1000 10000

Theis Curve fit to Late-Time Data

10 1 0.1

0.01

0.001

0 MW-18S Theis Curve 1 10 100

Elapsed time, minutes

1000 10000

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: aquifer Behaves as delayed confined

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 K h and K v , position of screen, and the change in storativity with time.

Neuman Equations & Type Curves