Cone of Depression
Flow to Wells – Hydraulic Testing
Objective: to determine hydraulic properties (K,T, S, and Ss) for an aquifer 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
1 Solution for Radial, SS Flow to Well – Theim Equation
Example: SS, Radial Flow to Well
2 Example: SS, Radial Flow to Well
Groundwater Flow in an Unconfined Aquifer:
Confined:
Unconfined (Boussinesq eq):
Unconfined: s << b
3 Groundwater Flow in an Unconfined Aquifer:
Summary of Steady State Solutions:
1-D
2-D
Radial Flow to a Well
4 Superposition of Linear Differential Equations
Analytical Element Method (AEM)
Superposition Examples
Multiple Wells:
Capture Zone of a Well in a Uniform Flow:
5 Uniform Flow + Radial Flow to Well
= Flow to a Well in a Uniform Flow Field
6 Geometry of Capture Zone
Don’t forget – use radians not degrees.
7 Capture Zone Example. A capture well is pumping at a rate of 37,000 ft3/dy from a confined aquifer with 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
8 Aside: erf and erfc functions
Transient Flow in a Confined Aquifer
9 Example: Transient Flow in a Confined Aquifer
Your neighbor drills a well 1000 m from your well and starts pumping water out of the same aquifer that you rely upon. Estimate how long it will take for some head drop to occur in your well?
Transient Flow to a Well in a Confined Aquifer
Described by Theis Equation
10 Aquifer Response to Pumping
Transient Flow to a Well in a Confined Aquifer
Theis Eq. :
11 W(u) - Well Function
Well Function Values (Table 9.2)
12 Assumptions of Theis Equation
1.
2.
3.
4.
5.
6.
7.
Theis Type-Curve Method
13 Theis Example. Estimate a pumping rate.
You are to design a pump test for a confined aquifer. The best available estimates For 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 about 1.0 meter in an observation well located 150 m from the pumped well after 6 hrs of pumping.
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
14 Basis for log-log matching with Theis equation
Or, http://www.aqtesolv.com/
Modifications of Theis equation (a.k.a. Donut model or nonequilibrium equation)
Cooper and Jacob Approximation after well has been pumping for awhile
15 Deviations from Theis
Deviations from Theis
16 Pump Test in Unconfined Aquifer: Steady state
Single Well Tests –Slug/Bailor Test
17 Slug Test
Hvorslev Method
18 Example
SS in Unconfined Aquifer:
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 11.73 38 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.
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