GROUND WATER FLOW TO WELLS

PREPARED BY : RASHEED MATTER

JAMILA TIMRAZ

Al-Azhar University-Gaza Master Program of Water and Environmental

Science

INTRODUCTION :-A WATER WELL 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 .

WATER WELLS ARE USED FOR :-

EXTRACTION OF GROUND WATER CONTROL SALT WATER INTRUSIONREMOVE CONTAMINATED WATERLOWER THE WATER TABLE FOR CONSTRUCTION PROJECTRELIEVE PRESSURE UNDER THE DAMSDRAIN FARM LANDINJECT FLUID TO GROUND WATERARTIFICIALLY RECHARGE AQUIFER

PUMPING CON. (CON. OF DEPRESSION )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 WELLS :-

STATIC WATER LEVEL [SWL] (HO) IS THE EQUILIBRIUM WATER LEVEL BEFORE PUMPING

COMMENCES

PUMPING WATER LEVEL [PWL] (H)

IS THE WATER LEVEL DURING PUMPING

DRAWDOWN (S = HO - H)

IS THE DIFFERENCE BETWEEN SWL AND PWL

WELL YIELD (Q)

IS THE VOLUME OF WATER PUMPED PER UNIT TIME

SPECIFIC CAPACITY (Q/S)

IS THE YIELD PER UNIT DRAWDOWN

BASIC ASSUMPTIONS1. 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% efficient

Computing Drawdown Causing By A pumping Well: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 TWO – DIMENSIONAL EQUATION FOR CONFINED FLOW , IF THERE IS RECHARGE TO THE AQUIFER , IS GIVEN BY EQUATION :

CAN BE TRANSFORMED INTO RADIAL COORDINATES BECOMING

•

The First Mathematical Analysis Of A transient Draw Down Effect On Confined Aquifer Was Published By C.V. Theis

UNSTEADY FLOW TO A WELL IN A CONFINED AQUIFER

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 Well 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: DRAWDOWN 1 KM FROM WELL AFTER 1 YEARANSWER:

FIRSTLY FIND WELL FUNCTION U, THEN W(U(

FIND W(U) FROM APPENDIX 1

u = r2S4Tt

= (1000m)2 (4x10−4 )

4(600m2 /d)(365d)= 4.6x10−4

( )uWT

Qhho

π4=−

12.7)( =uW

mdm

dmuW

T

Qhho 42.112.7*

)/600(4

/1500)(

4 2

3

===−ππ

THEIS EQUATION - EXAMPLE WELL FUNCTION

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 AquiferTheoretical 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 thecoordinates 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 semi-log 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

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)

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 :-

WELL PUMPING FROM A LEAKY AQUIFER

Transient flow in a leaky , confide aquifer with no storage :

Hantush infection – point method

Walton graphic method

Log-log plot for hantush method

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)

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.

CROSS-SECTION OF A PUMPED UNCONFINED AQUIFER

FLOW EQUATIONS :

Type curves for unconfined aquifers

RECOVERY TEST

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

THE IMPORTANCE OF PUMPING TESTS* Pumping tests are carried out to determine:1- how much groundwater can be extracted from a well based on long-term 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.

PUMPING TEST IN THE FIELD