Master Program of W
ater and Environmental
ATER FLOW TO W
PREPAR BY :
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
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
THE AREA AROUND A DISCHARGING WELL WHERE
THE WATER LEVEL IN THE AQUIFER DROPS IN THE
SHAPE OF A CON. DUE TO PUMPING
HYDRAULIC OF W
ELLS : STATIC W
ATER LEVEL [SW (HO)
IS THE EQUILIBRIUM W
ATER LEVEL BEFORE PUMPING
ATER LEVEL [PW (H)
IS THE W
ATER LEVEL DURING PUMPING
DOW (S = HO - H)
IS THE DIFFERENCE BETW
EEN SW AND PW
ELL YIELD (Q)
IS THE VOLUME OF W
ATER PUMPED PER UNIT TIME
SPECIFIC CAPACITY (Q/
IS THE YIELD PER UNIT DRAW
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. 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%
Computing Drawdown Causing By A
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
Two – dimensional flow in confined aquifer has
previously been derived as equation :
:THE RESULT IS EQUATION IN RADIAL COORDINATES
THE TW – DIMENSIONAL EQUATION FOR CONFINED FLOW , IF
THERE IS RECHARGE TO THE AQUIFER , IS GIVEN BY EQUATION :
CAN BE TRANSFOR
MED INTO R
The First Mathematical Analysis Of A transient
Draw Down Effect On Confined Aquifer W
Published By C.V. Theis
UNSTEADY FLOW TO A W
ELL IN A
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 •
( : And Is Generally Designated As W (U
THEIS EQUATION - EXAMPLE
Q = 1500 M3/
DAY, T = 600 M2/
DAY S= 4 X 10-4
FIND: DR DOW 1 KM FR
ELL AFTER 1 YEAR
ho − h =
( FIRSTLY FIND WELL FUNCTION U, THEN W(U
r 2 S (1000 m)2 (4x10−4 )
4Tt 4(600m 2 /d)(365 d)
W (u ) = 7.12
FIND W(U) FROM APPENDIX 1
1500m 3 / d
ho − h =
W (u ) =
* 7.12 = 1.42m
4π (600m / d )
THEIS EQUATION - EXAMPLE W
u = 4.6x10−4
W (u) = 7.12
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.
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).
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
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 .
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
Thiem equation for steady radial flow in confide
• 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)
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 :-
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
Equation (neuman & witherspoon 1969)
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
Type curves of drawdown versus time illustrating the effect of delayed
yield for pumping tests in unconfined aquifers.
DESIGN OF PUMPING TESTS :
. Test well location, depth, capacity (unless existing well used).
. Observation well number, location, depth.
. Pump regime
• 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
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.