ASTM D4106-96(2002)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: D 4106 – 96 (Reapproved 2002)
Standard Test Method
(Analytical Procedure) for Determining Transmissivity and
Storage Coefficient of Nonleaky Confined Aquifers by the
Theis Nonequilibrium Method
This standard is issued under the fixed designation D4106; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.2 confining bed—a hydrogeologic unit of less perme-
able material bounding one or more aquifers.
1.1 This test method covers an analytical procedure for
3.1.3 control well—well by which the head and flow in the
determining the transmissivity and storage coefficient of a
aquifer is changed, for example, by pumping, injection, or
nonleaky confined aquifer. It is used to analyze data on
imposing a constant change of head.
water-level response collected during radial flow to or from a
3.1.4 drawdown—vertical distance the static head is low-
well of constant discharge or injection.
ered due to the removal of water.
1.2 Thisanalyticalprocedureisusedinconjunctionwiththe
3.1.5 head—see head, static.
field procedure given in Test Method D4050.
3.1.6 head, static—theheightaboveastandarddatumofthe
1.3 Limitations—The limitations of this test method for
surface of a column of water (or other liquid) that can be
determination of hydraulic properties of aquifers are primarily
supported by the static pressure at a given point.
related to the correspondence between the field situation and
3.1.7 hydraulic conductivity (field aquifer tests)—the vol-
the simplifying assumptions of this test method (see 5.1).
umeofwaterattheexistingkinematicviscositythatwillmove
1.4 The values stated in SI units are to be regarded as
in a unit time under a unit hydraulic gradient through a unit
standard.
area measured at right angles to the direction of flow.
1.5 This standard does not purport to address all of the
3.1.8 observation well—a well open to all or part of an
safety concerns, if any, associated with its use. It is the
aquifer.
responsibility of the user of this standard to establish appro-
3.1.9 piezometer—a device so constructed and sealed as to
priate safety and health practices and determine the applica-
measure hydraulic head at a point in the subsurface.
bility of regulatory limitations prior to use.
3.1.10 specific storage—the volume of water released from
2. Referenced Documents ortakenintostorageperunitvolumeoftheporousmediumper
unit change in head.
2.1 ASTM Standards:
3.1.11 storage coeffıcient—the volume of water an aquifer
D653 Terminology Relating to Soil, Rock, and Contained
releases from or takes into storage per unit surface area of the
Fluids
aquifer per unit change in head. For a confined aquifer, the
D4043 Guide for Selection of Aquifer Test Method in
storagecoefficientisequaltotheproductofthespecificstorage
Determining of Hydraulic Properties by Well Techniques
and aquifer thickness. For an unconfined aquifer, the storage
D4050 Test Method (Field Procedure) for Withdrawal and
coefficient is approximately equal to the specific yield.
Injection Well Tests for Determining Hydraulic Properties
3.1.12 transmissivity—the volume of water at the existing
of Aquifer Systems
kinematic viscosity that will move in a unit time under a unit
3. Terminology
hydraulic gradient through a unit width of the aquifer.
3.1.13 unconfined aquifer—an aquifer that has a water
3.1 Definitions:
table.
3.1.1 aquifer, confined—an aquifer bounded above and
3.1.14 For definitions of other terms used in this test
below by confining beds and in which the static head is above
method, see Terminology D653.
the top of the aquifer.
3.2 Symbols:Symbols and Dimensions:
−1
3.2.1 K [LT ]—hydraulic conductivity.
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
3.2.2 K —hydraulic conductivity in the horizontal plane,
RockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWaterand xy
Vadose Zone Investigations. radially from the control well.
Current edition approved Oct. 10, 1996. Published June 1997. Originally
3.2.3 K —hydraulic conductivity in the vertical direction.
z
published as D4106–91.
3 −1
2 3.2.4 Q [L T ]—discharge.
Annual Book of ASTM Standards, Vol 04.08.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 4106
3.2.5 S [nd]—storage coefficient.
−1
3.2.6 S [L ]—specific storage.
s
2 −1
3.2.7 T [L T ]—transmissivity.
3.2.8 W(u) [nd]—well function of u.
3.2.9 b [L]—thickness of aquifer.
3.2.10 r [L]—radial distance from control well.
3.2.11 s [L]—drawdown.
4. Summary of Test Method
4.1 This test method describes an analytical procedure for
analyzing data collected during a withdrawal or injection well
test. The field procedure (see Test Method D4050) involves
pumping a control well at a constant rate and measuring the
FIG. 1 Cross Section Through a Discharging Well in a Nonleaky
water level response in one or more observation wells or
Confined Aquifer
piezometers. The water-level response in the aquifer is a
function of the transmissivity and storage coefficient of the
totheaquiferthroughitsfullthickness.Ifthecontrolwelldoes
aquifer. Alternatively, this test method can be performed by
not fully penetrate the aquifer, the nearest piezometer or
injecting water at a constant rate into the aquifer through the
partially penetrating observation well should be located at a
control well.Analysis of buildup of water level in response to
distance, r, beyond which vertical flow components are negli-
injection is similar to analysis of drawdown of water level in
gible, where according to Reed (2):
response to withdrawal in a confined aquifer. Drawdown of
b
water level is analyzed by plotting drawdown against factors
r 51.5 (4)
K
incorporating either time or distance from the control well, or z
Œ
K
both, and matching the drawdown response with a type curve. xy
4.2 Solution—The solution given by Theis (1) may be
This section applies to distance-drawdown calculations of
expressed as follows:
transmissivity and storage coefficient and time-drawdown cal-
2y culations of storage coefficient. If possible, compute transmis-
`
Q e
s 5 dy (1)
* sivity from time-drawdown data from wells located within a
4pT u y
distance, r, of the pumped well using data measured after the
where:
effectsofpartialpenetrationhavebecomeconstant.Thetimeat
r S which this occurs is given by Hantush (3) by:
u 5 (2)
4Tt
t 5 b s/2T K /K (5)
~ !
z r
2y
`
e
Fully penetrating observation wells may be placed at less
dy 5 W~u!
*
y
u
than distance r from the control well. Observation wells may
be on the same or on various radial lines from the control well.
2 3 4
u u u
520.577216 2log u 1 u 2 1 2 1. 5.2.2 The Theis method assumes the control well is of
e
2!2 3!3 4!4
infinitesimal diameter. Also, it assumes that the water level in
(3)
the control well is the same as in the aquifer contiguous to the
5. Significance and Use well. In practice these assumptions may cause a difference
between the theoretical drawdown and field measurements of
5.1 Assumptions:
drawdown in the early part of the test and in and near the
5.1.1 Well discharges at a constant rate, Q.
control well. Control well storage is negligible after a time, t,
5.1.2 Well is of infinitesimal diameter and fully penetrates
given by the Eq 6 after Weeks (4).
the aquifer.
5.1.3 The nonleaky aquifer is homogeneous, isotropic, and
r
c
t 525 3 (6)
aerially extensive. A nonleaky aquifer receives insignificant T
contribution of water from confining beds.
where:
5.1.4 Discharge from the well is derived exclusively from
r = the radius of the control well in the interval in which
c
storage in the aquifer.
the water level changes.
5.1.5 The geometry of the assumed aquifer and well condi-
5.2.3 Application of Theis Method to Unconfined Aquifers:
tions are shown in Fig. 1.
5.2.3.1 Although the assumptions are applicable to artesian
5.2 Implications of Assumptions:
or confined conditions, the Theis solution may be applied to
5.2.1 Implicitintheassumptionsaretheconditionsofradial
unconfined aquifers if drawdown is small compared with the
flow. Vertical flow components are induced by a control well
saturated thickness of the aquifer or if the drawdown is
thatpartiallypenetratestheaquifer,thatis,thewellisnotopen
corrected for reduction in thickness of the aquifer, and the
effects of delayed gravity yield are small.
5.2.3.2 Reduction in Aquifer Thickness—In an unconfined
The boldface numbers in parentheses refer to a list of references at the end of
the text. aquifer dewatering occurs when the water levels decline in the
D 4106
vicinity of a pumping well. Corrections in drawdown need to 7.2 The integral expression in Eq 1 and Eq 2 can not be
be made when the drawdown is a significant fraction of the evaluated analytically. A graphical procedure is used to solve
aquifer thickness as shown by Jacob (5). The drawdown, s, for the two unknown parameters transmissivity and storage
needs to be replaced by s8, the drawdown that would occur in coefficient where:
an equivalent confined aquifer, where:
Q
s 5 W~u! (10)
4pT
s
s8 5 s 2 (7)
S D
2b
and:
5.2.3.3 Gravity Yield Effects—In unconfined aquifers, de-
r S
u 5 (11)
layed gravity yield effects may invalidate measurements of
4Tt
drawdownduringtheearlypartofthetestforapplicationtothe
Theismethod.Effectsofdelayedgravityyieldarenegligiblein
8. Calculation
partially penetrating observation wells at and beyond a dis-
8.1 The graphical procedure used to calculate test results is
tance, r, from the control well, where:
based on the functional relations between W (u) and s and
b
between u and t or t/r .
r 5 (8)
K
z
8.1.1 Plot values of W (u) versus 1/u on logarithmic-scale
Œ
K
xy
paper (see Table 1). This plot is referred to as the type curve
plot.
After the time, t, as given in Eq 9 from Neuman (6).
8.1.2 On logarithmic tracing paper of the same scale and
t 510 3 S ~r /T! (9)
y
size as the W (u) versus 1/u type curve, plot values of
drawdown, s, on the vertical coordinate versus either time on
where:
S = the specific yield. For fully penetrating observation the horizontal coordinate if one observation well is used or
y
versus t/r on the horizontal coordinate if more than one
wells, the effects of delayed yield are negligible at the
distance, r,inEq8afteronetenthofthetimegivenin observation well is used.
the Eq 9. 8.1.3 Overlaythedataplotonthetypecurveplotand,whi
...