ASTM D4106-96(2008)
(Test Method)Standard Test Method for (Analytical Procedure) for Determining Transmissivity and Storage Coefficient of Nonleaky Confined Aquifers by the Theis Nonequilibrium Method
Standard Test Method for (Analytical Procedure) for Determining Transmissivity and Storage Coefficient of Nonleaky Confined Aquifers by the Theis Nonequilibrium Method
SIGNIFICANCE AND USE
Assumptions:
Well discharges at a constant rate, Q.
Well is of infinitesimal diameter and fully penetrates the aquifer.
The nonleaky aquifer is homogeneous, isotropic, and aerially extensive. A nonleaky aquifer receives insignificant contribution of water from confining beds.
Discharge from the well is derived exclusively from storage in the aquifer.
The geometry of the assumed aquifer and well conditions are shown in Fig. 1.
Implications of Assumptions:
Implicit in the assumptions are the conditions of radial flow. Vertical flow components are induced by a control well that partially penetrates the aquifer, that is, the well is not open to the aquifer through its full thickness. If the control well does not fully penetrate the aquifer, the nearest piezometer or partially penetrating observation well should be located at a distance, r, beyond which vertical flow components are negligible, where according to Reed (2):
This section applies to distance-drawdown calculations of transmissivity and storage coefficient and time-drawdown calculations of storage coefficient. If possible, compute transmissivity from time-drawdown data from wells located within a distance, r, of the pumped well using data measured after the effects of partial penetration have become constant. The time at which this occurs is given by Hantush (3) by:
Fully penetrating observation wells may be placed at less than distance r from the control well. Observation wells may be on the same or on various radial lines from the control well.
The Theis method assumes the control well is of infinitesimal diameter. Also, it assumes that the water level in the control well is the same as in the aquifer contiguous to the well. In practice these assumptions may cause a difference between the theoretical drawdown and field measurements of drawdown in the early part of the test and in and near the control well. Control well storage is negligible after a time, t, given by the Eq 6 aft...
SCOPE
1.1 This test method covers an analytical procedure for determining the transmissivity and storage coefficient of a nonleaky confined aquifer. It is used to analyze data on water-level response collected during radial flow to or from a well of constant discharge or injection.
1.2 This analytical procedure is used in conjunction with the field procedure given in Test Method D4050.
1.3 Limitations—The limitations of this test method for determination of hydraulic properties of aquifers are primarily related to the correspondence between the field situation and the simplifying assumptions of this test method (see 5.1).
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation:D4106 −96(Reapproved 2008)
Standard Test Method for
(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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.1 aquifer, confined—an aquifer bounded above and be-
lowbyconfiningbedsandinwhichthestaticheadisabovethe
1.1 This test method covers an analytical procedure for
top of the aquifer.
determining the transmissivity and storage coefficient of a
nonleaky confined aquifer. It is used to analyze data on 3.1.2 confining bed—ahydrogeologicunitoflesspermeable
material bounding one or more aquifers.
water-level response collected during radial flow to or from a
well of constant discharge or injection.
3.1.3 control well—well by which the head and flow in the
aquifer is changed, for example, by pumping, injection, or
1.2 Thisanalyticalprocedureisusedinconjunctionwiththe
imposing a constant change of head.
field procedure given in Test Method D4050.
3.1.4 drawdown—vertical distance the static head is low-
1.3 Limitations—The limitations of this test method for
ered due to the removal of water.
determination of hydraulic properties of aquifers are primarily
related to the correspondence between the field situation and
3.1.5 head—see head, static.
the simplifying assumptions of this test method (see 5.1).
3.1.6 head, static—theheightaboveastandarddatumofthe
surface of a column of water (or other liquid) that can be
1.4 This standard does not purport to address all of the
supported by the static pressure at a given point.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
3.1.7 hydraulic conductivity (field aquifer tests)—the vol-
priate safety and health practices and determine the applica-
umeofwaterattheexistingkinematicviscositythatwillmove
bility of regulatory limitations prior to use.
in a unit time under a unit hydraulic gradient through a unit
area measured at right angles to the direction of flow.
2. Referenced Documents
3.1.8 observation well—a well open to all or part of an
2.1 ASTM Standards:
aquifer.
D653Terminology Relating to Soil, Rock, and Contained
3.1.9 piezometer—a device so constructed and sealed as to
Fluids
measure hydraulic head at a point in the subsurface.
D4043Guide for Selection of Aquifer Test Method in
3.1.10 specific storage—the volume of water released from
Determining Hydraulic Properties by Well Techniques
ortakenintostorageperunitvolumeoftheporousmediumper
D4050Test Method for (Field Procedure) for Withdrawal
unit change in head.
and Injection Well Testing for Determining Hydraulic
Properties of Aquifer Systems
3.1.11 storage coeffıcient—the volume of water an aquifer
releases from or takes into storage per unit surface area of the
3. Terminology
aquifer per unit change in head. For a confined aquifer, the
storagecoefficientisequaltotheproductofthespecificstorage
3.1 Definitions:
and aquifer thickness. For an unconfined aquifer, the storage
coefficient is approximately equal to the specific yield.
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
3.1.12 transmissivity—the volume of water at the existing
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
kinematic viscosity that will move in a unit time under a unit
Vadose Zone Investigations.
Current edition approved Sept. 15, 2008. Published October 2008. Originally
hydraulic gradient through a unit width of the aquifer.
approved in 1991. Last previous edition approved in 2002 as D4106–96 (2002).
3.1.13 unconfined aquifer—anaquiferthathasawatertable.
DOI: 10.1520/D4106-96R08.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3.1.14 For definitions of other terms used in this test
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
method, see Terminology D653.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. 3.2 Symbols and Dimensions:
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D4106−96 (2008)
−1
3.2.1 K [LT ]—hydraulic conductivity. 5.1.4 Discharge from the well is derived exclusively from
storage in the aquifer.
3.2.2 K —hydraulic conductivity in the horizontal plane,
xy
5.1.5 The geometry of the assumed aquifer and well condi-
radially from the control well.
tions are shown in Fig. 1.
3.2.3 K —hydraulic conductivity in the vertical direction.
z
3 −1
3.2.4 Q [L T ]—discharge. 5.2 Implications of Assumptions :
5.2.1 Implicitintheassumptionsaretheconditionsofradial
3.2.5 S [nd]—storage coefficient.
−1 flow. Vertical flow components are induced by a control well
3.2.6 S [L ]—specific storage.
s
thatpartiallypenetratestheaquifer,thatis,thewell is not open
2 −1
3.2.7 T [L T ]—transmissivity.
totheaquiferthroughitsfullthickness.Ifthecontrolwelldoes
3.2.8 W(u) [nd]—well function of u.
not fully penetrate the aquifer, the nearest piezometer or
partially penetrating observation well should be located at a
3.2.9 b [L]—thickness of aquifer.
distance, r, beyond which vertical flow components are
3.2.10 r [L]—radial distance from control well.
negligible, where according to Reed (2):
3.2.11 s [L]—drawdown.
b
r 5 1.5 (4)
4. Summary of Test Method
K
z
Œ
K
xy
4.1 This test method describes an analytical procedure for
analyzing data collected during a withdrawal or injection well
This section applies to distance-drawdown calculations of
test. The field procedure (see Test Method D4050) involves
transmissivity and storage coefficient and time-drawdown cal-
pumping a control well at a constant rate and measuring the
culations of storage coefficient. If possible, compute transmis-
water level response in one or more observation wells or
sivity from time-drawdown data from wells located within a
piezometers. The water-level response in the aquifer is a
distance, r, of the pumped well using data measured after the
function of the transmissivity and storage coefficient of the
effectsofpartialpenetrationhavebecomeconstant.Thetimeat
aquifer. Alternatively, this test method can be performed by
which this occurs is given by Hantush (3) by:
injecting water at a constant rate into the aquifer through the
t 5 b s/2T ~K /K ! (5)
z r
control well.Analysis of buildup of water level in response to
injection is similar to analysis of drawdown of water level in
Fully penetrating observation wells may be placed at less
response to withdrawal in a confined aquifer. Drawdown of
than distance r from the control well. Observation wells may
water level is analyzed by plotting drawdown against factors
be on the same or on various radial lines from the control well.
incorporating either time or distance from the control well, or
5.2.2 The Theis method assumes the control well is of
both, and matching the drawdown response with a type curve.
infinitesimal diameter. Also, it assumes that the water level in
4.2 Solution—The solution given by Theis (1) may be
the control well is the same as in the aquifer contiguous to the
expressed as follows:
well. In practice these assumptions may cause a difference
2y
between the theoretical drawdown and field measurements of
Q ` e
s 5 dy (1)
*
u drawdown in the early part of the test and in and near the
4πT y
control well. Control well storage is negligible after a time, t,
where:
given by the Eq 6 after Weeks (4).
r S
r
u 5 (2) c
t 5 25 3 (6)
4Tt
T
2y
` e
dy 5 W u
* ~ !
u
y
2 3 4
u u u
520.577216 2 log u1u 2 1 2 1…
e
2!2 3!3 4!4
(3)
5. Significance and Use
5.1 Assumptions:
5.1.1 Well discharges at a constant rate, Q.
5.1.2 Well is of infinitesimal diameter and fully penetrates
the aquifer.
5.1.3 The nonleaky aquifer is homogeneous, isotropic, and
aerially extensive. A nonleaky aquifer receives insignificant
contribution of water from confining beds.
The boldface numbers in parentheses refer to a list of references at the end of FIG. 1 Cross Section Through a Discharging Well in a Nonleaky
this standard. Confined Aquifer
D4106−96 (2008)
where: ofinfluenceofpumping.However,ifverticalflowcomponents
aresignificantandifpartiallypenetratingobservationwellsare
r = theradiusofthecontrolwellintheintervalinwhichthe
c
used, locate them at a distance beyond the effect of vertical
water level changes.
flow components (see 5.2.1). If the aquifer is unconfined,
5.2.3 Application of Theis Method to Unconfined Aquifers:
constraints are imposed on the distance to partially penetrating
5.2.3.1 Although the assumptions are applicable to artesian
observation wells and the validity of early time measurements
or confined conditions, the Theis solution may be applied to
(see 5.2.3).
unconfined aquifers if drawdown is small compared with the
saturated thickness of the aquifer or if the drawdown is
7. Procedure
corrected for reduction in thickness of the aquifer, and the
7.1 The overall procedure consists of conducting the field
effects of delayed gravity yield are small.
5.2.3.2 Reduction in Aquifer Thickness—In an unconfined procedure for withdrawal or injection well tests (described in
Test Method D4050) and analysis of the field data that is
aquifer dewatering occurs when the water levels decline in the
addressed in this test method.
vicinity of a pumping well. Corrections in drawdown need to
be made when the drawdown is a significant fraction of the
7.2 The integral expression in Eq 1 and Eq 2 can not be
aquifer thickness as shown by Jacob (5). The drawdown, s,
evaluated analytically. A graphical procedure is used to solve
needs to be replaced by s', the drawdown that would occur in
for the two unknown parameters transmissivity and storage
an equivalent confined aquifer, where:
coefficient where:
s
Q
s' 5 s 2 (7)
S D
s 5 W u (10)
2b ~ !
4πT
5.2.3.3 Gravity Yield Effects—In unconfined aquifers, de-
and:
layed gravity yield effects may invalidate measurements of
r S
drawdownduringtheearlypartofthetestforapplicationtothe
u 5 (11)
4Tt
Theismethod.Effectsofdelayedgravityyieldarenegligiblein
partially penetrating observation wells at and beyond a
8. Calculation
distance, r, from the control well, where:
8.1 The graphical procedure used to calculate test results is
b
r 5 (8)
based on the functional relations between W(u) and s and
K
z 2
between u and t or t/r .
Œ
K
xy
8.1.1 Plot values of W(u) versus 1/u on logarithmic-scale
After the time, t, as given in Eq 9 from Neuman (6).
paper (see Table 1). This plot is referred to as the type curve
...
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