SAME
Q
T Q
t:
Q
High S
Low S
different
sameTTyields
yieldsdifferent
same gradient
gradient
at at
well
well
bore
bore
different
same SSyields
yieldssame
different
volume
volume
drawdown
drawdown
cone
cone
Q S yields
Q cone
smaller
but shape
variesproportionally
given differentlarger
gradient
High T
Steady state:
T differences
persist
S differences
do not
Low T
SAME
S Q
t:
Hydraulic Diffusivity D = T/S
relative rate at which the drawdown cone advances from the well
Q
Q
2
1
A
B
High S SAME
Q
1
T Q
t : Low S
Q
C
High T
2
D
SAME
S Q t : Low T
1
THINK in 3 Dimensions! … plan view:
??
Explore
the influence
of pumping
andsides
the
Notice that
water comes
in from the
gradient
on the flow
field(velocity=0)
using a groundand a stagnation
zone
forms
water
flow
model
Fromarea
The
the contours
is surrounded
of
at a point down gradient of the well.
by contours
head,
how do
42you
andknow
44,
the head
thus
heads
is must
higherbethan
42 in this these
between
area?values.
s vs. log r - is a straight line, if assumptions are met, drawdown
decreases logarithmically with distance from the well because
gradient decreases linearly with increasing area (2 rh)
Theim Eqtn
s
log r
T = transmissivity [L2/T]
Q = discharge from pumped well [L3/T]
r = radial distance from the well [L]
h = head at r [L]
and rearranging to get
T from field data:
Plot before applying equations
-WHY
to verify
you conditions
should plotare
theappropriate
data first? for application of equations
- to identify data problems
2
In an unconfined aquifer, T is not constant
If drawdown is small relative to saturated thickness, confined
equilibrium formulas can be applied with only minor errors
Otherwise call on Dupuit assumptions and use:
Q
pumping well
observation well 1
observation well 2
or, to
determine K
from field
measurements
of head:
s2
s1
r1
r2
Q = pumping rate [L3/T]
K = permeability [L/T]
hi = head @ a distance ri from well [L]
using the aquifer base as datum
Why
must the
aquifer
be datum
the datum?
The aquifer
base
mustbase
be the
because the head not only
represents the gradient but also reflects the aquifer thickness, hence
the flow area.
Predict Drawdown Using Theis Equation
Class
Are these
picks:
reasonable
T
and
S how do rwe know?t
-3
2
1x10 m /s 1x10-5
2m
year
Take 3 minutes to calculate: s
Q
0.01m/s
USE table of W(u)
from 3 slides back
What value did you get for s?
~15m
3