1. Flow to Wells – 1 Steady flow to a well in a confined aquifer
Groundwater Hydraulics
Daene C. McKinney

2. Summary Some Information on Wells
Steady flow to a well in a confined aquifer

3. Some Information on Wells

4. Domestic Hand Pumped Well
Domestic dug well with rock curb, concrete seal, and hand pump
~20 m depth
> 1 m diameter
< 500 m3/day
Hand dug well in Beirut, Lebanon
Hand dug well in Trets, France

5. Augers Hand-driven augers ~15 m depth > 20 cm diameter
Power-driven augers
~30 m depth
> 1 m diameter

6. Power Auger
Auger drilling is done with a helical screw driven into the ground with rotation; cuttings are lifted up the borehole by the screw
~ 30 m depth
< cm diameter
< 500 m3/day

7. Drilled Well - Cable Tool
Traditional way of drilling large diameter water supply wells.
The Rig raises and drops the drill string with a heavy carbide tipped drill bit that chisels through the rock and pulverizes the materials.
8 – 60 cm
600 m

8. Mud/Air Rotary
Rotary drilling relies on continuous circular motion of the bit to break rock at the bottom of the hole.
Cuttings are removed as drilling fluids circulate through the bit and up the wellbore to the surface.

9. Drilling Mud Circulation
Lift cuttings from the borehole and carry to pit;
Cuttings drop out in the pit;
Length of drill pipe is added;
Film on the borehole wall prevents caving;
Seals borehole wall to reduce fluid loss;
Cools and cleans bit; and
Lubricates bit, bearings, mud pump and drill pipe .

10. Well Completion After drilling, must “complete” the well
Placement of casing
Placement of well screen
Placement of gravel packing
Open hole

11. Well Construction Well casing Lining to maintain open hole
Seals out other water (surface, formations)
Structural support against cave-in

12. Well in Limestone Surface casing
From ground surface through unconsolidated upper material

13. Placing the Pack

14. Steady Flow to a Well in a Confined Aquifer

15. Flow to a Well in a Confined Aquifer

16. Drawdown in a Well
Drawdown in a pumped well consists of two components:
Aquifer losses
Head losses that occur in the aquifer where the flow is laminar
Tme-dependent
Vary linearly with the well discharge
Well losses
Aquifer damage during drilling and completion
Turbulent friction losses adjacent to well, in the well and pipe

17. Drawdown to a pumping well in a confined aquifer
Uncased hole
Screened well
Gravel-packed well
Bear, 1979, Fig. 8.3

18. Groundwater Notation Confined aquifer
𝛻∙𝑇𝛻ℎ= 𝜕 𝜕𝑥 𝑇 𝑥 𝜕ℎ 𝜕𝑥 + 𝜕 𝜕𝑦 𝑇 𝑦 𝜕ℎ 𝜕𝑦 =S 𝜕ℎ 𝜕𝑡
General equation,
rectangular coordinates
𝛻 2 ℎ= 𝜕 2 ℎ 𝜕 𝑥 𝜕 2 ℎ 𝜕 𝑦 2 =0
Steady state flow, homogeneous
and Isotropic aquifer
𝛻∙𝑇𝛻ℎ= 1 𝑟 𝜕 𝜕𝑟 𝑇 𝑟 𝑟 𝜕ℎ 𝜕𝑟 𝑟 2 𝜕 𝜕𝜃 𝑇 𝜃 𝜕ℎ 𝜕𝜃 =𝑆 𝜕ℎ 𝜕𝑡
General equation,
radial coordinates
𝛻 2 ℎ= 1 𝑟 𝜕 𝜕𝑟 𝑟 𝜕ℎ 𝜕𝑟 𝑟 2 𝜕 2 ℎ 𝜕 𝜃 2 =0
Steady state flow, homogeneous
and Isotropic aquifer

19. Steady Flow to a Well in a Confined Aquifer
2rw
Ground surface
Bedrock
Confined aquifer Q h0
Pre-pumping
head
Confining Layer b r1 r2 h2 h1 hw
Observation wells
Drawdown curve
Pumping well
Governing equation
in radial coordinates
𝛻 2 ℎ= 1 𝑟 𝜕 𝜕𝑟 𝑟 𝜕ℎ 𝜕𝑟 𝑟 2 𝜕 2 ℎ 𝜕 𝜃 2 = 𝑆 𝑇 𝜕ℎ 𝜕𝑡
Homogeneous and
Isotropic aquifer
𝑑 𝑑𝑟 𝑟 𝑑ℎ 𝑑𝑟 =0
Steady state flow

20. Steady Flow to a Well in a Confined Aquifer
𝑑 𝑑𝑟 𝑟 𝑑ℎ 𝑑𝑟 =0
2rw
Ground surface
Bedrock
Confined aquifer Q h0
Pre-pumping
head
Confining Layer b r1 r2 h2 h1 hw
Observation wells
Drawdown curve
Pumping well
𝑟 𝑑ℎ 𝑑𝑟 = 𝐶 1
Darcy’s law
𝑄=𝐴𝑞= 2𝜋𝑟𝑏 𝐾 𝑑ℎ 𝑑𝑟
𝑟 𝑑ℎ 𝑑𝑟 = 𝑄 2𝜋𝑏𝐾 =𝐶 1
𝑑ℎ= 𝑄 2𝜋𝑇 𝑑𝑟 𝑟
ℎ= 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 + 𝐶 2

21. Steady Flow to a Well in a Confined Aquifer
ℎ= 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 + 𝐶 2
2rw
Ground surface
Bedrock
Confined aquifer Q h0
Pre-pumping
head
Confining Layer b r1 r2 h2 h1 hw
Observation wells
Drawdown curve
Pumping well
Boundary condition:
ℎ= ℎ 1 @ 𝑟= 𝑟 1
ℎ 1 = 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 1 + 𝐶 2
𝐶 2 =ℎ 1 − 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 1
ℎ= 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 + ℎ 1 − 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 1
ℎ= ℎ 1 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑟 1

22. Example - Steady Flow to a Well in a Confined Aquifer
Q = 400 m3/hr
b = 40 m
Two observation wells,
h1 = 85.3 m r1 = 25 m)
h2 = 89.6 m r2 = 75 m)
Find: Transmissivity (T)
2rw
Ground surface
Bedrock
Confined aquifer Q h0
Confining Layer b r1 r2 h2 h1 hw
Pumping well
ℎ= ℎ 1 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑟 1
ℎ 2 = ℎ 1 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 2 𝑟 1

23. Drawdown, s ℎ= ℎ 0 @ 𝑟= 𝑟 0 ℎ= ℎ 0 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑟 0 𝑠= ℎ 0 −ℎ
ℎ= ℎ 0 @ 𝑟= 𝑟 0
ℎ= ℎ 0 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑟 0
𝑠= ℎ 0 −ℎ
𝑠= ℎ 0 − ℎ 0 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑟 0
𝑠(𝑟)= 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 0 𝑟

24. Example - Steady Flow to a Well in a Confined Aquifer
1-m diameter well
Q = 113 m3/hr
b = 30 m
h0= 40 m
Two observation wells,
h1 = 38.2 m r1 = 15 m)
h2 = 39.5 m r2 = 50 m)
Find: Head and drawdown at the well
2rw
Ground surface
Bedrock
Confined aquifer Q h0
Confining Layer b r1 r2 h2 h1 hw
Pumping well
Drawdown
ℎ= ℎ 1 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑟 1
𝑠 1 = ℎ 0 − ℎ 1
𝑠 2 = ℎ 0 − ℎ 2
𝑠 1 − 𝑠 2 = ℎ 2 − ℎ 1 = 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 2 𝑟 1
𝑇= 𝑄 2𝜋 𝑠 1 − 𝑠 2 𝑙𝑛 𝑟 2 𝑟 1 = 113 𝑚 3 /ℎ𝑟 2𝜋 1.8−0.5 𝑚 𝑙𝑛 = 𝑚 2 /ℎ𝑟

25. Example - Steady Flow to a Well in a Confined Aquifer
2rw
Ground surface
Bedrock
Confined aquifer Q h0
Confining Layer b r1 r2 h2 h1 hw
well
ℎ= ℎ 1 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑟 1
ℎ 𝑤 = ℎ 1 + 𝑄 2𝜋𝑇 𝑙𝑛 𝑟 𝑤 𝑟 1
ℎ 𝑤 =38.2 𝑚 𝑚 3 /ℎ𝑟 2𝜋 𝑚 2 /ℎ𝑟 𝑙𝑛
ℎ 𝑤 =34.5 𝑚
Head at the well
𝑠 𝑤 = ℎ 0 −ℎ=40−34.5 𝑚=5.5 𝑚
Drawdown at the well

26. Flow to a Partially Penetrating Well in a Confined Aquifer

27. Summary Some Information on Wells
Steady flow to a well in a confined aquifer