Week 4

Question 1

Why are we interested in radial flow?

Answer 1

Generally interact with groundwater through wells

Pump = cone of depression

If system homogenous and isotropic, and aquifer is sufficiently large, flow = axisymmetric

Question 2

Flow to production wells is

Answer 2

Radially convergent

Question 3

Flow to injection wells is

Answer 3

Radially divergent

Question 4

Qw =

Answer 4

flow rate out of a well

Question 5

Derivation of the Thiem equation, basic gist:

Answer 5

1. Recall Darcy’s Law
2. A = 2piHr
3. Separate and integrate w.r.t r
4. Impose boundary conditions to eliminate C
5. Rearrange for (he-h) =
   (6. Recall law of logs to invert fraction and remove -ve)
6. S =

Question 6

What is the radius of influence?

Answer 6

re, the well has an insignificant effect on Q

At the extent of the radius of influence r=re and h=he

Question 7

S =

Answer 7

drawdown - the amount hydraulic head has been drawn down as a consequence of water flowing out

= he-h

Question 8

When is Q = -Qw

Answer 8

When water is moving in the opposite direction to r

Question 9

Thiem equation

Answer 9

S = (Qw/2piHK)ln(re/r)

or

S = (Qw/2piT)ln(re/r)

Question 10

Assumptions for Thiem equation

Answer 10

Homogenous

Isotropic

1D radial flow (head get only in radial direction)

Infinite aquifer

S-S conditions (no variation in time)

Darcy’s law applies i.e. head gradient linearly proportional to flow rate

Question 11

How can we use Thiem’s equation?

Answer 11

1. For given well radius rw and production rate Qw we can forecast the drawdown Sw
2. For a given well radius rw and drawdown Sw we can forecast the production rate Qw

Question 12

Principle of superposition

Answer 12

Can describe how a system will respond to multiple simultaneous events by adding together the responses that would be expected if each event occurred by itself

Question 13

Estimating T from Thiem, basic gist:

Answer 13

1. Form Thiem’s equation for the production well and observation well separately
2. Separate the ln(x/y) into lnx - lny
3. Take one away from the other to eliminate re
4. Rearrange so that T =

Question 14

Estimating re from Thiem, basic gist:

Answer 14

1. Form Thiem’s equation for the production well

2. Rearrange to that re =

Question 15

Flow to a well near a river, assumptions:

Answer 15

Constant stream stage therefore interface with aquifer = constant head/equipotential boundary

BOTH well and stream fully penetrate aquifer (not actually in practice but ~small error)

No sealing layer of fine sediment on streamed (full hydraulic connection)

Pseudo-steady state conditions

Question 16

Flow to a well near a river/impermeable boundary, basic gist:

Answer 16

“Method of images”
- whatever you have, do an image of the opposite

1. Drawdown due to production/injection well (Thiem’s equation)
2. Drawdown due to image well
3. Drawdown due to both = add

Question 17

Calculating the radii from the river/impermeable boundaries to the wells

Answer 17

Draw diagram

Use Pythagoras

Question 18

What is the drawdown at the river? (and how)

Answer 18

S = 0

• river exists where x = 0
• substitute this into Thiem equation with pythag radii
• Qw/2piT ln(1) = 0

Question 19

Sources of well losses

Answer 19

Near pumping well, flow velocities are artificially enhanced
Turbulent effects associated with flow through the well screen and the standpipe up to the well pump

= inertial/turbulent effects significant
= non-linearity in drawdown flow currents

Question 20

Step drawdown test

Answer 20

Pump a well at sequentially increasing rate (Qw)

After certain amount of time, drawdown reaches a steady value

Plot these against production rate

Sw = AQw + BQw^2 (Jacob’s equation)

Question 21

Using Jacob’s equation

Answer 21

Sw = AQw + BQw^2

2. Plot Sw/Qw by Qw:

Sw/Qw = A + BQw^2

• A and B can also be found = well quality (smaller B better)
  2. When Qw <=1, Sw~=AQw
  3. Compare to Thiem’s equation
  4. Rearrange to find T or A

Question 22

Good well, highly developed - B =

Answer 22

<675

Question 23

Mediocre well - B =

Answer 23

675 < B < 1350

Question 24

Clogged/deteriorated well - B =

Answer 24

1350 < B < 5400

Question 25

Well cannot be rehabilitated - B =

Answer 25

> 5400