Groundwater Flow to Wells

I. Overview A. Water well uses 1. Extraction 2. Injection

I. Overview A. Water well uses B. Terms 1. Cone of depression 2. Drawdown 3. Unsteady Flow

I. Overview A. Water well uses B. Terms C. Goals 1. Compute dh/dt given knowledge of the properties of the aquifer 2. Determine the properties of the aquifer based on the rate of dh/dt.

I. Overview A. Water well uses B. Terms C. Goals D. General Assumptions

General Assumptions

General Assumptions (continued)

I. Overview A. Water well uses B. Terms C. Goals D. General Assumptions E. Radial Flow

II. Theis Method

II. Theis Method A. Additional Assumptions The aquifer is confined on the top and bottom There is no source of recharge to the aquifer The aquifer is compressible, and water is released instantaneously from the aquifer as the hydraulic head is lowered.

The well is pumped at a constant rate.

II. Theis Method A. Additional Assumptions B. The Equations

II. Theis Method A. Additional Assumptions B. The Equations s = h o -h t h o -h t = Q* * w u 4 πT u = r 2 *S 4Tt

THEIS CURVE

II. Theis Method C. Examples (with known values) A well is located in an aquifer with a hydraulic conductivity of 15 m/d, storativity is 0.005, aquifer thickness is 20 m, and the pumping of the water well is occurring at a rate of 2725 m3/d. What is the drawdown at a distance of 7 m from the well after 1 day of pumping?

h o -h t = Q* * w u 4 πT u = r 2 *S 4Tt

II. Theis Method A. Additional Assumptions B. The Equations C. Examples (with known values) D. Examples (with unknown values)

THEIS CURVE

DRAWDOWN DATA

Problem: A well in a confined aquifer was pumped at a rate of 42,400 ft3/d for 500 minutes. The aquifer is 48 ft. thick. Time drawdown data from an observation well located 824 ft away yields the following data (see previous slide of drawdown data).

Find T, K, and S.

III. Jacob Straight Line Method A. Overview B. Conditions C. The Equation D. Example T = 2.3Q

4 πΔh S = 2.25T*t 0 r 2

III. Jacob Straight Line Method D. Example T = 2.3Q

4 πΔh S = 2.25T*t 0 r 2 Problem: A well in a confined aquifer was pumped at a rate of 42,400 ft3/d for 500 minutes. The aquifer is 48 ft. thick. Time drawdown data from an observation well located 824 ft away yields the following data (see previous slide of drawdown data).

Find T, K, and S.

IV. Distance Drawdown Method A. Overview B. Equations C. Example T = 2.3Q

2 πΔh S = 2.25T*t r 0 2

Distance Drawdown Method

16 14 4 2 0 1 8 6 12 10 10

Distance (ft)

100 1000

IV. Distance Drawdown Method

Distance Drawdown Method

C. Example 16 14 T = 2.3Q

2 πΔh 12 10 S = 2.25T*t r 0 2 8 6 4 2 0 1 10

Distance (ft)

100 A well is pumping 77,000 ft3/d, and has observational wells located 10, 40, 150, 300, and 400 ft away from the pumping well. After 0.14 days of pumping, the Following drawdowns were observed in the observation wells (see graph).

Determine T (ft2/d) and S of the aquifer.

1000

V.

Hzorslev Method (Slug or Bail Test) K = r 2 *ln(L/R) 2Lt 0.37

Hzorslev Method Time since injection 0 1 2 3 4 5 6 7 8 9 h 0.88

0.6

0.38

0.21

0.12

0.06

0.04

0.02

0.01

0 h/ho 1.000

0.682

0.432

0.239

0.136

0.068

0.045

0.023

0.011

0.000

Hzorslev Method 1 0.1

0.01

0 1 2 3 4 5

Tim e (s)

6 7 8 9 10

V.

Hzorslev Method (Slug or Bail Test) K = r 2 *ln(L/R) 2Lt 0.37

1 0.1

0.01

0 1 2 3 4 5

Tim e (s)

6 7 8 9 10 A slug test is performed by lowering a metal cylinder into a piezometer that is screened in coarse sand. The inside of the bore hole has a radius of 0.500 ft, and the inside radius of the piezometer is 0.083 ft. The screened section of the well is 10 ft. The well recovery data is shown via tables and the respective graph. Determine the Hydraulic Conductivity of the aquifer.

VI. Intersecting Pumping Cones and Well Interference A.

General Example

A.

Bounded Aquifers 1. Impermeable boundary

A.

Bounded Aquifers 1. Constant Head boundary

VII. Recovery of Pumping Wells A. Purpose B. Example

VII. Recovery of Pumping Wells Time(min) 0 0.2

Elevation (ft) 520 520.2

0.4

0.8

1 2 3 4 5 520.3

520.6

521 522 523 524 525

526 525 524 523 522 521 520 519 0 VII. Recovery of Pumping Wells 1 ft 3 = 7.48 gallons

Well Recovery

Time(min) y = 1.0134x + 519.94

0 0.2

Elevation (ft) 520 520.2

0.4

0.8

1 2 3 4 5 520.3

520.6

521 522 523 524 525 2 3 4 5 6 1