Topic 7
• Aquifer response to pumping
• Pumping/hydraulic tests and analytical solutions for
flow to a well (Thiem and Theis solutions)
Fetter: Chapter 5 (all except 5.8, 5.9)
Flow to pumping wells: basic application of groundwater hydrology
Pumping occurs for:
• Water supply (domestic, community, industrial)
• Irrigation
• Removal of contaminated water (pump-and-treat)
• Lowering water table for construction and mining (dewatering)
• Relieving pressure under dams
• Draining farmland
• Hydraulic tests
• Control of saltwater intrusion - injection (hydraulic barriers)
• Wastewater injection
What happens when you pump?
Side View
Top View
Flow to wells can be complex. For simplicity, the following discussion makes some basic
assumptions. These include (but are not limited to):
1.
2.
3.
4.
5.
6.
7.
8.
9.
The aquifer is bounded below by a confining (no-flow) unit
Geologic formations (aquifers and confining units) are horizontal and have infinite extent
Potentiometric surface is flat (no flow) and steady-state prior to onset of pumping
Aquifers are homogeneous and isotropic
Groundwater flow is horizontal
Darcy’s Law is valid (can be tricky very close to wells, but we’ll ignore that)
Fluid density and viscosity is constant
Pumping and observation wells are fully penetrating – screened over entire aquifer thickness
Pumping wells have ~0 diameter and are 100% efficient
Under these conditions, all flow will be toward (or away) from a well in 2 dimensions.
This means that flow is 1D, radially (there is radial symmetry)
Maintaining a Water Balance: Back to the groundwater flow equation
2D Flow in a confined aquifer:
  2h  2h 
h
S
T 2  2 
t
y 
 x
If water enters or exits the system (the REV) externally, another term is required
1) Source/sink term, w (examples are pumping wells, surface water inflow/outflow)
  2h  2h 
h
S
 T  2  2   w( x, y)
t
y 
 x
• w is volume rate of inflow per unit area [L/T]
• Units: easiest to look at on time derivative term (LHS)
• Sign of W is + for inflow (can tell this because LHS is + for increasing storage)
2) Source/sink term, Leakage through aquitard
  2 h  2 h  K ' (ho  h)
h
S
T 2  2 
t
b'
 x y 
Specific discharge through
aquitard: Darcy’s Law
Confined flow with a source/sink term (Cartesian coordinates):
  2h  2h 
h
S
T 2  2 w
t
y 
 x
Convert to Polar coordinates:
x  r cos 
y  r sin 
r  x2  y2
  2 h 1 h 
h
S
T 2 
w
t
r r 
 r
Why does the head gradient steepen
toward the well?
• Drawdown cone spreads and deepens
over time until it reaches a steady state
where the gradient can sustain the
pumping rate (w)
• Shape of the cone (depth, width) and
time to reach steady-state depend on:
–T
–S
–w
Steady-state flow: heads are
constant in time
Unsteady flow: heads change
with time
Where does pumped water come from?
Consider a simple case:
• Initial pre-pumping rate of recharge balances pre-pumping rate of discharge.
Initial Recharge = Initial Discharge (water balance at steady-state)
• At onset of pumping, water comes from storage and recharge within cone of
depression. Natural Discharge (to lakes) = Initial Discharge
Where does pumped water come from?
• Pumping creates cone of depression that reaches shoreline. Only then does:
Pumping Rate = Initial Recharge, Natural Discharge = 0
• Ultimately, Pumping = Initial Recharge + Flow in from boundaries (before well dries
up). If there is enough water available, the well will not dry up, and the system will
eventually reach steady-state.
• Ultimate production of water depends on:
1. Reduction/capture of natural discharge
2. How much water can be pulled in (from boundaries)
3. How much the rate of recharge can be changed (induced recharge not shown)
Where does pumped water come from?
Map View
A pump in a homogeneous
confined aquifer with regional
flow
Pre-pumping flow was uniform
and horizontal
Cross section
Where does pumped water come from?
Map View
A pump in a homogeneous
confined aquifer with regional
flow
Pre-pumping flow was uniform
and horizontal
Cross section
When recharge
is only at the
water table
What water can be captured?
•
•
•
•
•
•
rainwater recharge
water from a surface water body (stream, lake, ocean, river)
water from an adjacent aquifer
water in an adjacent confining unit
water from ‘storage’ (dropping water table)
water ‘not lost’ to drains or evapotranspiration-ET (lower water
table stops these from functioning)
• water that ‘would have’ discharged elsewhere
For transient systems, the origin of captured water may
change with time
Where does pumped water come from?
Note that:
• Steady-state production is not dependent on Sy (or S in a confined aquifer).
Flow in = Flow out (storage is 0 at steady-state)
• Pre-pumping rate of recharge = discharge is NOT the sustainable yield of the
aquifer (though it is often calculated as such!). In fact, it is almost irrelevant
(consider situation where rainfall is small, and water source to wells is ultimately
the lake). Remember that before pumping begins, initial recharge is already
balanced by the initial discharge.
Essential factors that determine response of an aquifer to well development:
• Distance to, and amount of, recharge (rainfall vs lake)
• Distance to, and amount of, natural discharge
• Character of cone of depression (function of T and S)
Prior to development, the aquifer is in equilibrium.
“All water discharged by wells is balanced by a loss of water from
somewhere” (Theis, 1940)
When pumping occurs, water comes from storage until a new equilibrium is
reached
Where does pumped water come from?
New equilibrium is arrived at by:
• Increase in recharge -> capture of a water source
• Decrease in discharge -> reduction of gradient toward outflow
• Both
Some water must always be mined (taken from storage) to create groundwater development.
This rearranges hydraulic gradients so that water flows toward the well.
Estimates of capture (where the water to the well is coming from, and how much) are
fundamentally important to long-term planning of groundwater development
• Important for supply
• Important for quality
Mathematically, the pumping water balance is:
Q = (R + R) – (D + D) – S(h/ t)
If, over time, R = D, and a new equilibrium (steady-state) is reached, (h/ t=0). This means
that initial recharge was increased or initial discharge was decreased, or both:
Q = R - D
Pumping Test Analysis
The idea of a pump test is to stress the aquifer by pumping water in or out, and then
observing changes in head (or drawdown) over space and in some cases, time.
Equations that relate pumping rate (Q) to aquifer parameters from the flow equation (T, S)
allow us to estimate the parameters.
HISTORY:
• The earliest model for interpretation of pumping test data was developed by Thiem
(1906) for:
– Constant pumping rate
– Equilibrium (steady-state) conditions
– Confined and unconfined aquifers
• Theis (1935) published the first analysis of transient (non steady-state) pump tests for:
– Constant pumping rate
– Confined aquifers
• Since then, many methods for analysis of transient tests have been designed for
increasingly complex conditions, including:
–
–
–
–
–
–
–
Aquitard leakage
Aquitard storage
Wellbore storage
Partial well penetration
Anisotropy
Slug tests
Recirculating well tests (water is not removed)
Development of the Thiem Equation
Steady radial flow in a confined aquifer:
Assume:
• Aquifer is confined (top and bottom) and laterally infinite
• Well is pumped at a constant rate
• Equilibrium is reached (no drawdown change with time)
• Wells are fully screened and only one is pumping
Confined Aquifers
Confined Aquifers
Development of the Thiem Equation
Steady radial flow in a confined aquifer:
Consider Darcy’s Law through a cylinder
(looking down) with radius, r, with flow toward
well:
QK
dh
dh
A K
2rb
dr
dr
rearrange : dh 
Q dr
2Kb r
h2
r
Q 2 dr
integrate from r1 , h1 to r2 , h 2 :  dh 
2Kb r1 r
h1
r 
Q
h2  h1 
ln  2  , noting that T  Kb :
2Kb  r1 
T
r 
Q
ln  2  This is the Thiem Equation!
2 (h2  h1 )  r1 
r 
527.7Q
or, T 
log  2 
(h2  h1 )  r1 
(USGS units)
Notes on the Thiem Equation:
• Good with any self-consistent units
• If drawdown has stabilized, can use any two
observation wells
• Water is not coming from storage (S doesn’t
appear) – cannot get S from this test
• Commonly used in USGS units and log10, T
in gpd/ft (gallons per day per foot), Q in gpm
(gallons per minute), r and h in ft.
Example: Determining T for a confined aquifer with a steady-state pumping test:
A well in a confined aquifer is pumped at a rate of 100 m3/d for a long time at a steady rate (the
system is in ~equilibrium). Observed heads in two wells located 25m and 85m from the pumping
well are 124m and 130m, respectively (above mean sea level). Estimate the value of aquifer
transmissivity.
Example: Determining T for a confined aquifer with a steady-state pumping test:
A well in a confined aquifer is pumped at a rate of 100 m3/d for a long time at a steady rate (the
system is in ~equilibrium). Observed heads in two wells located 25m and 85m from the pumping
well are 124m and 130m, respectively (above mean sea level). Estimate the value of aquifer
transmissivity.
If the aquifer is 200m thick, what is K?
Confined Aquifers
Pumping Test Analysis: Thiem Equation
Specific Capacity of a Well – Roughly estimating T:
Specific Capacity = Discharge Rate / Drawdown in the well
[this is a proxy for T because the more transmissive the aquifer, the less drawdown you will need to
produce the same Q (think Darcy’s Law…)]
1.A well is pumped to ~ equilibrium
2.A good well would produce 50 gpm per foot of drawdown, or 20 feet of drawdown for 1000 gpm
3.
Specific Capacity 
Q
T

(he  hw ) 527.7 log re
rw
he and re are the head and corresponding
distance from a well where drawdown is
effectively zero.
4.Rule of thumb: T ~ 1,800 x Specific Capacity [for units gpm/ft (SC) and gpd/ft (T)]
5.What is re? It doesn’t matter that much.
re=1,000 rw , log re/rw = 3
re=10,000 rw , log re/rw = 4
6.Case A -> T = Specific Capacity x 527 x 3 = 1581 x SC
Case B -> T = Specific Capacity x 527 x 4 = 2108 x SC
 If you use T ~ 1800 x SC you’re not too far off
7.Specific Capacity is NOT a storage parameter
8.If there are well (frictional) losses, then the T you get may be lower than the actual T of the aquifer
(seems harder to pull water out of the well than it should be)
Development of the Thiem Equation
Unconfined Aquifers
Steady radial flow in an unconfined aquifer:
Assume:
• Aquifer is unconfined but underlain by an impermeable horizontal unit,
and is laterally infinite
• Well is pumped at a constant rate
• Equilibrium is reached (no drawdown change with time)
• Wells are fully screened and only one is pumping
Unconfined Aquifers
Development of the Thiem Equation
Steady radial flow in an unconfined aquifer:
QK
dh
dh
A K
2rh
dr
dr
rearrange : hdh 
Q dr
2K r
h2
Q
integrate from r1 , h1 to r2 , h 2 :  hdh 
2K
h1
r 
h22  h12
Q

ln  2 
2
2K  r1 
K
r2
dr
r r
1
 r2 
Q
  This is the Thiem Equation for unconfined aquifers
ln
 (h22  h12 )  r1 
For locations near the well, r<1.5 hmax (where hmax is
the full saturated thickness), there will be errors using
this equation because of vertical flow near the well.
Confined Aquifers
Development of the Theis Equation
Transient radial flow in a confined aquifer:
Recall the 2D groundwater flow equation in radial
coordinates:
2
S
  h 1 h 
h
T 2 
w
t
r r 
 r
We want a solution that gives h(r, t) after pumping starts.
To solve it, we need IC’s (1) and BC’s (2):
IC: h(r, 0) = ho
Q
 h 

 r  2T
BC’s: h(, t) = ho & lim
r
r 0
for t  0
(which is Darcy’s Law at the well)
Development of the Theis Equation
Confined Aquifers
Transient radial flow in a confined aquifer:
Theis Equation:
In 1935, C.V. Theis solved this equation (using principles from heat conduction):

Q e  u du
ho  h(r , t ) 
4T u u
exponentia l integral is in math table s, call this " well function"
r 2S
where u 
4Tt
ho  h(r , t ) 
Q
W (u )
4T
Q
ho  h(r , t ) 
4T
well function is W(u), look up in tables
or approximat e as an infinte series :


u2
u3
u4

0
.
5772

ln
u

u




...


2

2
!
3

3
!
4

4
!


In USGS units of drawdown [ft], Q [gpm], T [gpd/ft], r [ft], t [days], S [decimal fraction]:
ho  h(r , t ) 
1.87 r 2 S
u
Tt
114.6 Q
W (u )
T
Pumping Test Analysis: Theis Equation
Confined Aquifers
Forward solution: predict drawdown at a particular point in space and time (r, t), knowing the
hydraulic properties of the system (S, T)
To predict drawdown: drawdown vs. distance or time
• put in r, S, T, t and solve for u
• find W(u) based on u (from above) and tables of W(u) vs. u (Fetter Appendix 1, pg. 535)
• Plug W, Q, and T into the equation: ho – h(r,t) is drawdown.
The analytical solution:
• Describes geometric characteristics of the cone of depression: steepening toward the well
• Quantifies changes in the cone of depression -> increases in depth and extent with time for
given aquifer properties
• Shows by inspection that drawdown at a time and location increases linearly with pumping
rate
• Shows that drawdown at a time and location is greater for lower T
• Shows that drawdown at a time and location is greater for lower S
A well screened in a confined aquifer is pumped for 10 days at a rate of 5000 ft3/d. The
aquifer is 50 ft thick, with a hydraulic conductivity of 10 ft/d. Aquifer specific storage is
1x10-4 ft-1. What are drawdowns 10 ft and 100 ft from the well?
Pumping Test Analysis: Theis Equation
Confined Aquifers
Determining T and S from Transient Pump Tests
Inverse solution (parameter estimation): Use solution to the differential equation (Theis solution) to
identify parameter values by matching observed heads (data) to simulated heads (from equation).
E.g., measure aquifer drawdown response given a known pumping rate and get T and S.
Method:
1. Identify pumping well and observation wells and their conditions (e.g., fully screened)
2. Determine aquifer type and make a quick estimate to predict what you think will happen during
the pumping test <- design test!
3. Theis Method: arrange Theis equation as follows:
 Q 
ho  h  
W (u )
4

T


u
2
r S
4Tt
r S  1
t

 4T  u
2

 Q 
logho  h   log 
  log W (u )
 4T 
r S 
1
log t  log 
  log
u
 4T 
2
• If Q is constant, then bracketed terms are constant
for aquifer observed at a point
• This constant will tell you about T and S
• Imagine first log terms = 0, then the graph log (1/u
vs W(u)) and log (t vs ho-h) would look identical.
They would overlay each other exactly.
If bracketed terms existed, then the graphs would
be translated by a constant (shifted)
Confined Aquifers
Pumping Test Analysis: Theis Equation
Determining T and S from Transient Pump Tests
Method (continued):
4. Plot the type curve: plot the well function W(u) vs. 1/u on log-log paper
5. Plot the field curve: plot drawdown vs time on log-log paper of same scale (this is from data at a
single observation well)
6. Superimpose the field curve on the type curve, keeping the axes parallel. Adjust the curves so
that most of the data fall on the type curve. You are trying to get the constants (bracketed terms)
that make the type curve axes translate into your axes.
7. Select a match point (any convenient point will do, like W(u) = 1.0 and 1/u = 1.0), and read off the
values for W(u) and 1/u. Then read off the values for drawdown and t.
Note: the drawdown corresponds to the match point. If the match point is not on the curve, then ho-h
and t will not correspond to the data you collected. That is OK for the match point as you are just
attempting to get the relationship (shift between the type curve axes and those of the data plot.
The match point registers the offset between the two graphs.
8. Compute the values of T and S from:
Using self-consistent units
T
Q W (u )
4 ho  h 
S
4T t u
r2
Using USGS units
T
S
114 .6 Q W (u )
ho  h
T tu
1.87 r 2
Theis Type Curve
Field Curve
Curve Matching
Curve Matching
Curve Matching
Confined Aquifers
Pumping Test Analysis: Theis Equation
Determining T and S from Transient Pump Tests
Method (continued):
4. Plot the type curve: plot the well function W(u) vs. 1/u on log-log paper
5. Plot the field curve: plot drawdown vs time on log-log paper of same scale (this is from data at a
single observation well)
6. Superimpose the field curve on the type curve, keeping the axes parallel. Adjust the curves so
that most of the data fall on the type curve. You are trying to get the constants (bracketed terms)
that make the type curve axes translate into your axes.
7. Select a match point (any convenient point will do, like W(u) = 1.0 and 1/u = 1.0), and read off the
values for W(u) and 1/u. Then read off the values for drawdown and t.
Note: the drawdown corresponds to the match point. If the match point is not on the curve, then ho-h
and t will not correspond to the data you collected. That is OK for the match point as you are just
attempting to get the relationship (shift between the type curve axes and those of the data plot.
The match point registers the offset between the two graphs.
8. Compute the values of T and S from:
Using self-consistent units
T
Q W (u )
4 ho  h 
S
4T t u
r2
Using USGS units
T
S
114 .6 Q W (u )
ho  h
T tu
1.87 r 2
You perform a pumping test on a confined aquifer. There is an observation well
located 25 m from a pumping well. The pumping well produces 3.0x10-3 m3/s. You
turn on the pump and measure the drawdown in the observation well over time.
Use the Theis type-curve method to estimate transmissivity and storativity of the
aquifer.
Confined Aquifers
Modified Nonequilibrium Solution: Jacob Equation
Recall from Theis solution:
Q
ho  h(r , t ) 
4T


u
e u du
u
C.E. Jacob noted that the well function (W(u)) can be represented by a series :
Q
ho  h(r , t ) 
4T


u2
u3
u4


 ...
 0.5772  ln u  u 
2  2! 3  3! 4  4!


For small values of r and large values of t, u becomes small (valid when u<0.01), and most terms can be
dropped, leaving:
ho  h(r , t ) 
Q
 0.5772  ln u 
4T
from rules of logarithms , - ln u  ln (1/u), and ln(1.78)  0.5772
ho  h(r , t ) 
Q
4T
 2.25Tt 
ln 2 
r S 

and ln(u)  2.3 log(u)
ho  h(r , t ) 
2.3Q 
2.25Tt 
log
10

4T 
r 2S 
See description of time-drawdown
and distance-drawdown methods in
Fetter (5.5.3.2 and 5.5.3.3)
Since Q, T, and S are constants,
drawdown vs log t should plot as a
straight line
Note that this form of the Theis equation
is very useful (don’t have to look up W(u)),
but should only be used when u is small
(late time)
Confined Aquifers
Modified Nonequilibrium Solution: Jacob Equation
ho  h(r , t ) 
2.3Q 
2.25Tt 
log
10
4T 
r 2 S 
Or
s(r , t ) 
2.3Q 
2.25Tt 
log
10
4T 
r 2 S 
Now Say, drawdown is s1 at time t1 and s2 at time t2
2.3Q 
2.25Tt1 
s1 (r , t1 ) 
log
10
4T 
r 2 S 
And
s2 ( r , t 2 ) 
2.3Q 
2.25Tt 2 
log
10
4T 
r 2 S 
Therefore;
s1 (r , t1 )  s2 (r , t 2 ) 
2.3Q 
2.25Tt1  2.3Q 
2.25Tt 2 
log

log
10
10
4T 
r 2 S  4T 
r 2 S 
s1 (r , t1 )  s2 (r , t 2 ) 
2.3Q 
2.25Tt1  
2.25Tt 2 
log

log
10
10
4T 
r 2 S  
r 2 S 
s1 (r , t1 )  s2 (r , t 2 ) 
2.3Q 
t2 
log
 10 
4T 
t1 
Confined Aquifers
Modified Nonequilibrium Solution: Jacob Equation
Therefore;
s1 (r , t1 )  s2 (r , t 2 )  s 
Back to the original equation
s(r , t ) 
2.3Q 
2.25Tt 
log
10
4T 
r 2 S 
At t0, s(r,t) = 0
Therefore;
0
2.3Q 
2.25Tt 
log
10
4T 
r 2 S 
2.25Tt 0
S
r2
2.3Q 
t2 
log
 10 
4T 
t1 
Or
T
2.3Q
4s
Confined Aquifers
Modified Nonequilibrium Solution: Jacob Equation
Distance-Drawdown Method
Using similar logic we can also apply the Jacob Equation for drawdown observed as a
function of distance.
T
2.3Q
4s
and
S
2.25Tt 0
r2
Transient Radial Flow in Unconfined Aquifers
Unconfined Aquifers
Flow in an unconfined aquifer toward a pumping well
Drawdown
3 Distinct phases once pumping begins:
1. Elastic response: behavior of a confined aquifer: water initially comes from elastic storage
(sensitive to Ss). Follows a Theis type curve with S=Ss. Flow is ~horizontal, water comes from
entire aquifer thickness.
2. Water table begins to decline: water comes from aquifer drainage. Flow is both horizontal and
vertical.
3. Approach to steady-state: rate of drawdown decreases, flow ~horizontal (driven more by
hydraulic gradient of drawdown cone). Again behaves like Theis type curve, but with S=Sy.
Pumping Test Analysis: Unconfined Aquifers (Neuman Type Curves)
Unconfined Aquifers
Neuman developed an analytical solution to the radial flow equation under the following assumptions:
1.
2.
3.
4.
5.
6.
7.
Aquifer is unconfined
Vadose zone has no influence on drawdown
Water initially pumped comes from instantaneous release of water from elastic storage
Eventually water comes from storage due to gravity drainage of connected pores
Drawdown is negligible compared to saturated aquifer thickness
Sy is > 10x Ss
Aquifer may be isotropic or anisotropic
Neuman’s solution:
ho  h(r , t ) 
r 2S
uA 
4Tt
uB 
r 2S y
4Tt
r 2 Kv
 2
b Kh
Q
W (u A , u B , )
4T
(for early drawdown data)
(for later drawdown data)
Values of W for this case found in
Appendix 6 in Fetter
Pumping Test Analysis: Unconfined Aquifers (Neuman Type Curves)
Unconfined Aquifers
Procedure to estimate Ss, Sy, Kv, Kh:
1. Superimpose early time-drawdown data on the Type-A curves, keeping axes parallel. At any match
point, determine W(uA, ), 1/uA, t, and ho-h.  comes directly from the type curve. Compute T and
S from first 2 equations above.
2. Superimpose late drawdown data on the Type-B curve for the  value determined and get a new
set of match points. The value of T should be nearly the same as calculated in #1. Calculate Sy
from third equation above.
3. Calculate Kh from:
Kh 
T
b
4. Calculate Kv from:
b 2 K h
Kv 
r2
Partial Penetration of Wells
If a pumping well is screened in only part of an aquifer, it creates vertical flow components.
This can cause problems with pumping tests.
In general:
• If an observation well fully penetrates the aquifer (is screened over the entire depth), or if it is
located more than 1.5b K h / K v distance units from the pumping well, effects are negligible.
• If both pumping and observation wells are partially penetrating, and if observation wells are
closer than 1.5b K h / K v , then the drawdown curves are more complex, and the methods
presented cannot be used to predict drawdowns or to estimate parameters.
Slug Tests (Cooper et al., 1967)
In a slug test, the water level in a well is raised (or lowered) instantaneously by
adding (or removing) a known quantity (or ‘slug’) of water. The return of the
water level to baseline is then monitored.
Advantages:
• Slug test is a single-well test
• May be quick, with less preparation
• An object (preferably attached to a rope) may be substituted for the slug of
water. This way:
 There is no water to dispose of (a problem if contaminated site), and no danger
of affecting groundwater chemistry
 Once the water level has returned to baseline, a ‘reverse’ test may be preformed
by removing the object quickly (bail test) and again monitoring the return to
baseline
Disadvantages:
• Generally does not give reliable values
of S (adding small volume doesn’t
induce enough stress to measure)
• Measures near-well environment only,
may not give representative large-scale
aquifer values (could be good or bad)
Slug Tests (Cooper et al., 1967)
Several different methods have been developed, for particular aquifer conditions.
Overdamped Response: water level recovers smoothly (exponentially) to its initial level following
the slug addition or removal
Applicable Methods:
• Cooper-Bredehoeft-Papadopulos Method (Fetter 5.6.2.1)
-> Fully penetrating well in a confined aquifer
• Hvorslev Method (Fetter 5.6.2.2)
-> Piezometer in any aquifer
• Bouwer and Rice Method (Fetter 5.6.2.3)
-> Open boreholes or screened wells, fully or partially penetrating
-> For unconfined aquifers or confined if screen is well below aquifer top
Underdamped Response: water level oscillates around static water level, magnitude decreases
with time. (Most likely in wells with long water column, high T aquifers).
Applicable Methods:
• Van der Kamp Method (Fetter 5.6.3.1)
-> Fully penetrating well in a confined aquifer
• Kipp (1985)
-> Fully penetrating well in a confined aquifer
• Butler (1997) variation on Hvorslev, Bouwer and Rice for underdamped
(From Topic 2)
How to estimate the value of hydraulic conductivity?
1. In the lab: permeameter tests
Re-do Darcy’s experiment using a sediment sample. Calculate K for a fixed h/l by measuring Q
induced by the gradient, and Darcy’s Law. Or, measure h created by a fixed Q.
2. Grain-size analysis: empirical grain size relationships
3. In the field: in-situ slug tests, pump tests.
4. Inverse modeling: using groundwater models to estimate K values (more later)
(From Topic 2)