Ground water Flow To Wells

1. Al-Azhar University-Gaza
Master Program of W
ater and Environmental
Science
GROUND W
ATER FLOW TO W
ELLS
 PREPAR BY :
ED
 RASHEED MATTER
 JAMILA TIMRAZ

2. INTRODUCTION :-
AW
ATER W
ELL IS A HOLE CREATED IN THE GROUND, BY
DIGGING, OR DRILLING
IN TO AN AQUIFER WITH A PIPE , A SCREEN
.AND PUMP TO PULL WATER OUT OF THE GROUND

3. W
ATER W
ELLS ARE USED FOR :
EXTRACTION OF GROUND WATER
 CONTROL SALT WATER INTRUSION
REMOVE CONTAMINATED WATER
LOWER THE WATER TABLE FOR CONSTRUCTION PROJECT
RELIEVE PRESSURE UNDER THE DAMS
DRAIN FARM LAND
INJECT FLUID TO GROUND WATER
ARTIFICIALLY RECHARGE AQUIFER

4.  PUMPING
CON.
DEPRESSION
(CON.
OF
)
THE AREA AROUND A DISCHARGING WELL WHERE
THE WATER LEVEL IN THE AQUIFER DROPS IN THE
SHAPE OF A CON. DUE TO PUMPING

5.  HYDRAULIC OF W
ELLS : STATIC W
ATER LEVEL [SW (HO)
L]
IS THE EQUILIBRIUM W
ATER LEVEL BEFORE PUMPING
COMMENCES
 PUMPING W
ATER LEVEL [PW (H)
L]
IS THE W
ATER LEVEL DURING PUMPING
 DRAW
DOW (S = HO - H)
N
IS THE DIFFERENCE BETW
EEN SW AND PW
L
L
W
ELL YIELD (Q)
IS THE VOLUME OF W
ATER PUMPED PER UNIT TIME
 SPECIFIC CAPACITY (Q/
S)
IS THE YIELD PER UNIT DRAW
DOW
N

6.  BASIC ASSUMPTIONS
1. The aquifer is bounded on the bottom by a confining layer.
2. All geological formations are horizontal and of infinite horizontal extent.
3. The potentiometric surface of the aquifer is horizontal prior to the start
of the pumping.
4. The potentiometric surface of the aquifer is not changing with time prior
to the start of the pumping.
5. All changes in the position of the potentiometric surface are due to the
effect of the pumping well alone.
6. The aquifer is homogeneous and isotropic.

7. 7. All flow is radial toward the well.
8. Groundwater flow is horizontal.
9. Darcy’s law is valid.
10. Groundwater has a constant density and viscosity.
11. The pumping well and the observation wells are fully penetrating;
i.E., They are screened over the entire thickness of the aquifer.
12. The pumping well has an infinitesimal diameter and is 100%
efficient

8.  Computing Drawdown Causing By A
pumping W
ell:
un steady radial flow:
the use of polar coordinates to describe the position of
appoint in aplane . it lies the distance r from the origin and
the angle between the polar axis and aline connecting the
point and the origin is

9.  Two – dimensional flow in confined aquifer has
previously been derived as equation :
:THE RESULT IS EQUATION IN RADIAL COORDINATES

10. THE TW – DIMENSIONAL EQUATION FOR CONFINED FLOW , IF
O
THERE IS RECHARGE TO THE AQUIFER , IS GIVEN BY EQUATION :
CAN BE TRANSFOR
MED INTO R
ADIAL COOR
DINATES BECOMING
•

11.  The First Mathematical Analysis Of A transient
Draw Down Effect On Confined Aquifer W
as
Published By C.V. Theis

12.  UNSTEADY FLOW TO A W
ELL IN A
CONFINED AQUIFER

14.  The Integral In Equation Is Called The Exponential
Integral . It Can Be Approximated By An Infinite
Series So The Theis Equation Becomes :
Infinite Series Term Of Equation Has Been Called The W Function •
ell
( : And Is Generally Designated As W (U

15.  THEIS EQUATION - EXAMPLE
Q = 1500 M3/
DAY, T = 600 M2/
DAY S= 4 X 10-4
FIND: DR DOW 1 KM FR
AW
N
OM W
ELL AFTER 1 YEAR
: ANSW
ER
Q
ho − h =
W (u)
4πT
( FIRSTLY FIND WELL FUNCTION U, THEN W(U
r 2 S (1000 m)2 (4x10−4 )
u=
=
= 4.6x10−4
4Tt 4(600m 2 /d)(365 d)
W (u ) = 7.12
FIND W(U) FROM APPENDIX 1
Q
1500m 3 / d
ho − h =
W (u ) =
* 7.12 = 1.42m
2
4πT
4π (600m / d )

16. THEIS EQUATION - EXAMPLE W
ELL
FUNCTION
u = 4.6x10−4
W (u) = 7.12

17. The Data Required For The Theis Solution Are :
1 Drawdown Vs. Time Data At An Observation Well,
2 Distance From The Pumping Well To The Observation Well,
3 Pumping Rate Of The Well.

18.  The Non-equilibrium Reverse Type Curve (Theis
Curve) For A Fully Confined Aquifer
Theoretical Curve W(u) Versus 1/U Is Plotted On A Log-log Paper.
This Can Be Done Using Tabulated Values Of The Well Function
(See Appendix 1).

19.  Field Data Plot On Logarithmic Paper For Theis
Curve-marching Technique :
The Field Measurements Are Similarly Plotted On A Log-log Plot With
(T) Along The X-axis and (Sw) along the Y-axis

20.  MATCH OF FIELD DATA PLOT TO THEIS TYPE CURVE :
keeping the axes correctly aligned, superimposed the type curve on the
plot of the data (the data analysis is done by matching the observed
data to the type curve)
select any convenient point on the graph paper (a match point) and
read off the
coordinates of the point on both sets of axes. this gives coordinates
( 1/u, w(u)) and (t,sw) use the previous equations to determine t and s .

21.  The log function lets us plot this as a straight line on semilog paper
Jacob method of solution of pumping-test data for a fully confined
aquifer. Drawdown is plotted as a function of time on semi-logarithmic
paper

22. Thiem equation for steady radial flow in confide
: aquifer
• In the case of steady radial flow in a confide aquifer , the following
assumptions are necessary :• 1- the aquifer is confide top and bottom
• 2- the well is pumped at a constant rate
• Equillibrium has been reached that is , there is no farther change in draw
down with time.
• T= kb = Q/ 2 Π (σ1−σ2 ) ∗ λν ( ρ2/ρ1)
• η0−η = θ / 2 π τ ∗ λν ( ρ2/ρ1)

23.  FLOW IN A LEAKY, CONFIDE AQUIFER :
FLOW EQUATION :
Most Confide Aquifers Are Not Totally Isolated From Sources Of
Vertical Recharge . Aquitards , rather Above Or Below The Aquifer ,
Can Leak Water Into The Aquifer If The Direction Of The Hydraulic
Gradient Is Favorable :-

25.  WELL PUMPING FROM A LEAKY AQUIFER

26. Transient flow in a leaky , confide aquifer with no
: storage
Hantush infection – point method
W
alton graphic method

28.  Log-log plot for hantush method

29.  Unsteady radial flow in an unconfined aquifer
(non-equilibrium radial flow)
• The flow of water in an unconfined aquifer toward a pumping well is described by the
following
Equation (neuman & witherspoon 1969)

30. Neumann's solution assumes the following, in addition to
the basic assumptions:
Flow description :
Initial flow : the Theis – like ( horizontal ) from release of compression ,
specific storage component
Intermediate flow :
has gravity drainage component ( both horizontal & vertical flow )
Late – time flow :
becomes horizontal again from specific yield components

31.  Type curves of drawdown versus time illustrating the effect of delayed
yield for pumping tests in unconfined aquifers.

33. CROSS-SECTION OF A PUMPED UNCONFINED
AQUIFER

34.  FLOW EQUATIONS :

36.  Type curves for unconfined aquifers

37.  RECOVERY TEST

38.  DESIGN OF PUMPING TESTS :
PARAMETERS :
. Test well location, depth, capacity (unless existing well used).
. Observation well number, location, depth.
. Pump regime
GENERAL GUIDANCE:
• CONFINED AQUIFERS:
• Transmissivity more important than storativity: observation wells not
always needed (although accuracy lost without them!).
• Unconfined aquifers: storativity much larger, and has influence over
transmissivity estimates: observation wells important as is larger
test duration. Care needed if aquifer only partly screened

39.  THE IMPORTANCE OF PUMPING TESTS
* Pumping tests are carried out to determine:
1- how much groundwater can be extracted from a well based on longterm yield, and well efficiency?
2 - the hydraulic properties of an aquifer or aquifers.
3 - spatial effects of pumping on the aquifer.
4 - determine the suitable depth of pump.
5- information on water quality and its variability with time.

40.  PUMPING TEST IN THE FIELD