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Cone of Depression

Flow to Wells – Hydraulic Testing

Objective: to determine hydraulic properties (K,T, S, and Ss) for anaquifer and whether it can serve as a suitable water supply(quantity of water!).

1 – estimate rate of gw removal (Q!)

2 – effect of gw removal on storage

3 – well tests used to make in situ estimates of K (or T) and k

Potable water and Petroleum Reserves

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Solution for Radial, SS Flow to Well – Theim Equation

Example: SS, Radial Flow to Well

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Example: SS, Radial Flow to Well

Groundwater Flow in an Unconfined Aquifer:

Confined:

Unconfined(Boussinesq eq):

Unconfined: s << b

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Groundwater Flow in an Unconfined Aquifer:

Summary of Steady State Solutions:

1-D

2-D

Radial Flow to a Well

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Superposition of Linear Differential Equations

Analytical Element Method (AEM)

Superposition Examples

Multiple Wells:

Capture Zone of a Well in a Uniform Flow:

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Uniform Flow + Radial Flow to Well

= Flow to a Well in a Uniform Flow Field

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Geometry of Capture Zone

Don’t forget – use radians not degrees.

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Capture Zone Example. A capture well is pumping at a rate of 37,000 ft3/dy from a confined aquiferwith a hydraulic conductivity of 920 ft/dy, an initial hydraulic gradient of 0.0027, and an initial saturated thickness of 40 ft.

A. What is the max width of the capture zone?B. What is the distance from the well to the stagnation point?C. How would you calculate the extent of the capture zone?

Transient Flow in a Confined Aquifer

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Aside: erf and erfc functions

Transient Flow in a Confined Aquifer

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Example: Transient Flow in a Confined Aquifer

Your neighbor drills a well 1000 m from your well and starts pumping water out of thesame aquifer that you rely upon. Estimate how long it will take for some head drop tooccur in your well?

Transient Flow to a Well in a Confined Aquifer

Described by Theis Equation

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Aquifer Response to Pumping

Transient Flow to a Well in a Confined Aquifer

Theis Eq. :

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W(u) - Well Function

Well Function Values (Table 9.2)

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Assumptions of Theis Equation

1.

2.

3.

4.

5.

6.

7.

Theis Type-Curve Method

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You are to design a pump test for a confined aquifer. The best available estimatesFor T and S are 1.4E-2 m2/s and 1.0E-4, respectively. Assuming a Theis type solution,What pumping rate should be used? We want to generate a drawdown of about1.0 meter in an observation well located 150 m from the pumped well after 6 hrsof pumping.

Theis Example. Estimate a pumping rate.

Theis Matching Type Curve Solution Example Given Q = 0.1 m3/s, r = 90 m, and b = 30 m

from match point – W(u) and s - - - Estimate T or K

from match point – 1/u and t - - - Estimate S or Ss

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Basis for log-log matching with Theis equation

Or, http://www.aqtesolv.com/

Cooper and Jacob Approximation after well has been pumping for awhile

Modifications of Theis equation (a.k.a. Donut model or nonequilibrium equation)

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Deviations from Theis

Deviations from Theis

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Pump Test in Unconfined Aquifer: Steady state

Single Well Tests –Slug/Bailor Test

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Slug Test

Hvorslev Method

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Example

A steady state pumping test was conducted in an unconfined aquifer. The test was conducted to remediate a contamination problem. The idea is to place wells such that the entire plume falls within the zone of influence of the pumping wells. The saturated thickness is 50 ft and the static water level is at a depth of 5 ft. The pumping well has a radius of 0.5 ft. The well was pumped at 18 gpm. You have the following data:

obs well distance (ft) depth to water (ft)14 11.7338 9.47

a. What is the drawdown in the observation wells?

b. What is the total hydraulic head in obs. wells, relative to bottom of aquifer?

c. Find K (ft/dy) and T (gal / dy ft)

d. Find the radius of influence of the well

e. Using Jacob’s correction for Leaky aquifers, correct the above drawdowns and redetermine K and T for confined aquifer conditions.

SS in Unconfined Aquifer: