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Aquifer Tests in Unconfined Aquifers Lauren Cameron Spring 2014

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Topics Unconfined vs. Confined Parameters to Measure Delayed Gravity Drainage Effects Steady and Transient Solutions Example Analysis with AQTESOLV

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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

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

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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

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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

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Drainage Near Falling Water Table Source: Bear (1972)

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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

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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?

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Answer: Shift Horizontally to the Right

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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.

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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

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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

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Dupuit Solution with 2 Observation Wells

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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.

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Neuman Equations & Type Curves

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