ASTM D4105-96(2002)
(Test Method)Standard Test Method (Analytical Procedure) for Determining Transmissivity and Storage Coefficient of Nonleaky Confined Aquifers by the Modified Theis Nonequilibrium Method
Standard Test Method (Analytical Procedure) for Determining Transmissivity and Storage Coefficient of Nonleaky Confined Aquifers by the Modified Theis Nonequilibrium Method
SCOPE
1.1 This test method covers an analytical procedure for determining transmissivity and storage coefficient of a nonleaky confined aquifer under conditions of radial flow to a fully penetrating well of constant flux. This test method is a shortcut procedure used to apply the Theis nonequilibrium method. The Theis method is described in Test Method D 4106.
1.2 This test method is used in conjunction with the field procedure given in Test Method D 4050.
1.3 Limitations—The limitations of this test method are primarily related to the correspondence between the field situation and the simplifying assumptions of this test method (see ). Furthermore, application is valid only for values of uless than 0.01 (u is defined in Eqn. 1, in ).
1.4 The values stated in SI units are to be regarded as standard.
1.5 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: D 4105 – 96 (Reapproved 2002)
Standard Test Method
(Analytical Procedure) for Determining Transmissivity and
Storage Coefficient of Nonleaky Confined Aquifers by the
Modified Theis Nonequilibrium Method
This standard is issued under the fixed designation D4105; 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. Terminology
1.1 This test method covers an analytical procedure for 3.1 Definitions:
determining transmissivity and storage coefficient of a non- 3.1.1 aquifer, confined—an aquifer bounded above and
leakyconfinedaquiferunderconditionsofradialflowtoafully below by confining beds and in which the static head is above
penetratingwellofconstantflux.Thistestmethodisashortcut the top of the aquifer.
procedureusedtoapplytheTheisnonequilibriummethod.The 3.1.2 aquifer, unconfined—an aquifer that has a water table.
Theis method is described in Test Method D4106. 3.1.3 confining bed—a hydrogeologic unit of less perme-
1.2 This test method is used in conjunction with the field able material bounding one or more aquifers.
procedure given in Test Method D4050. 3.1.4 controlwell—wellbywhichtheaquiferisstressed,for
1.3 Limitations—The limitations of this test method are example, by pumping, injection, or change of head.
primarily related to the correspondence between the field 3.1.5 drawdown—vertical distance the static head is low-
situation and the simplifying assumptions of this test method ered due to the removal of water.
(see 5.1). Furthermore, application is valid only for values of u 3.1.6 hydraulic conductivity—(field aquifer tests), the vol-
less than 0.01 (u is defined in Eq 2, in 8.6). umeofwaterattheexistingkinematicviscositythatwillmove
1.4 The values stated in SI units are to be regarded as in a unit time under unit hydraulic gradient through a unit area
standard. measured at right angles to the direction of flow.
1.5 This standard does not purport to address all of the 3.1.7 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- 3.1.8 piezometer—use to measure static head at a point in
priate safety and health practices and determine the applica- the subsurface.
bility of regulatory limitations prior to use. 3.1.9 specific storage—the volume of water released from
ortakenintostorageperunitvolumeoftheporousmediumper
2. Referenced Documents
unit change in head.
2.1 ASTM Standards:
3.1.10 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, it is
D4043 Guide for Selection of Aquifer-Test Method in equal to the product of specific storage and aquifer thickness.
Determining Hydraulic Properties by Well Techniques
For an unconfined aquifer, the storage coefficient is approxi-
D4050 Test Method (Field Procedure) for Withdrawal and mately equal to the specific yield.
Injection Well Tests for Determining Hydraulic Properties
3.1.11 transmissivity—the volume of water at the existing
of Aquifer Systems kinematic viscosity that will move in a unit time under a unit
D4106 Test Method (Analytical Procedure) for Determin-
hydraulic gradient through a unit width of the aquifer.
ing Transmissivity and Storage Coefficient of Nonleaky 3.1.12 For definitions of other terms used in this test
Confined Aquifers by the Theis Nonequilibrium Method
method, see Terminology D653.
3.2 Symbols:Symbols and Dimensions:
−1
3.2.1 K [LT ]—hydraulic conductivity.
3.2.2 K —hydraulic conductivity in the horizontal direc-
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
xy
RockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWaterand
tion.
Vadose Zone Investigations.
3.2.3 K —hydraulic conductivity in the vertical direction.
z
Current edition approved Oct. 10, 1996. Published June 1997. Originally
2 −1
3.2.4 T [L T ]—transmissivity.
published as D4105–91. Last previous edition D4105–91.
Annual Book of ASTM Standards, Vol 04.08. 3.2.5 S [nd]—storage coefficient.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 4105
−1
3.2.6 Ss [L ]—specific storage. and:
3.2.7 s [L]—drawdown.
2.3Q
3 −1
T52 (6)
3.2.8 Q [L T ]—discharge.
2pDs/Dlog r
3.2.9 r [L]—radial distance from control well.
where:
3.2.10 t [T]—time.
Ds/Dlog t = thedrawdown(measuredorprojected)over
3.2.11 b [L]—thickness of the aquifer. 10
one log cycle of time, and
4. Summary of Test Method Ds/Dlog r = thedrawdown(measuredorprojected)over
one log cycle of radial distance from the
4.1 This test method describes an analytical procedure for
control well.
analyzing data collected during a withdrawal or injection well
test. The field procedure (see Test Method D4050) involves
5. Significance and Use
pumping a control well at a constant rate and measuring the
5.1 Assumptions:
water level response in one or more observation wells or
5.1.1 Well discharges at a constant rate, Q.
piezometers. The water-level response in the aquifer is a
5.1.2 Well is of infinitesimal diameter and fully penetrates
function of the transmissivity and coefficient of storage of the
the aquifer, that is, the well is open to the full thickness of the
aquifer. Alternatively, the test can be performed by injecting
aquifer.
water at a constant rate into the aquifer through the control
5.1.3 The nonleaky aquifer is homogeneous, isotropic, and
well.Analysisofbuildupofwaterlevelinresponsetoinjection
areally extensive. A nonleaky aquifer receives insignificant
issimilartoanalysisofdrawdownofwaterlevelinresponseto
contribution of water from confining beds.
withdrawal in a confined aquifer. Drawdown of water level is
5.1.4 Discharge from the well is derived exclusively from
analyzed by plotting drawdown against factors incorporating
storage in the aquifer.
either time or distance from the control well, or both, and
5.1.5 The geometry of the assumed aquifer and well condi-
matching the drawdown response with a straight line.
tions are shown in Fig. 1.
4.2 Solution—The solution given by Theis (1) can be
5.2 Implications of Assumptions:
expressed as follows:
5.2.1 Implicitintheassumptionsaretheconditionsofradial
2y
`
Q e
flow. Vertical flow components are induced by a control well
s 5 dy (1)
*
4pT u y
that partially penetrates the aquifer, that is, not open to the
where: aquifer through its full thickness. If the control well does not
2 fully penetrate the aquifer, the nearest piezometer or partially
r S
u 5 (2)
penetrating observation well should be located at a distance, r,
4Tt
beyond which vertical flow components are negligible, where
and:
according to Reed (5)
2y
` e
1.5b
dy 5 W~u!520.577216 2log u (3)
*
e r 5 (7)
y
u
K
z
Œ
2 3 4
K
u u u xy
1 u 2 1 2 1 .
2!2 3!3 4!4
This section applies to distance-drawdown calculations of
transmissivity and storage coefficient and time-drawdown cal-
4.3 The sum of the terms to the right of log u in the series
e
culations of storage coefficient. If possible, compute transmis-
of Eq 3 is not significant when u becomes small.
sivity from time-drawdown data from wells located within a
NOTE 1—The errors for small values of u, from Kruseman and
distance, r, of the pumped well using data measured after the
DeRidder (1) are as follows:
effectsofpartialpenetrationhavebecomeconstant.Thetimeat
Error less than, %: 1 2 5 10
which this occurs is given by Hantush (6) by:
For u smaller than: 0.03 0.05 0.1 0.15
The value of u decreases with increasing time, t, and
decreases as the radial distance, r, decreases. Therefore, for
large values of t and reasonably small values of r, the terms to
the right of log u in Eq 3 may be neglected as recognized by
e
Theis (2)andJacob (3).TheTheisequationcanthenbewritten
as follows:
Q S
s 5 20.577216 2ln r (4)
F S DG
4pT 4Tt
from which it has been shown by Lohman (4) that
2.3Q
T 5 (5)
4pDs/Dlog t
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
the text. Confined Aquifer
D 4105
6. Apparatus
t 5 b s/2T ~K /K ! (8)
z r
6.1 Analysis of data from the field procedure (see Test
Fully penetrating observation wells may be placed at less
Method D4050) by this test method requires that the control
than distance r from the control well. Observation wells may
well and observation wells meet the requirements specified in
beonthesameoronvariousradiallinesfromthecontrolwell.
6.2-6.4.
5.2.2 The Theis method assumes the control well is of
6.2 Control Well—Screenthecontrolwellintheaquiferand
infinitesimal diameter. Also, it assumes that the water level in
equip with a pump capable of discharging water from the well
the control well is the same as in the aquifer contiguous to the
at a constant rate for the duration of the test. Preferably, screen
well. In practice these assumptions may cause a difference
the control well throughout the full thickness of the aquifer. If
between the theoretical drawdown and field measurements of
the control well partially penetrates the aquifer, take special
drawdown in the early part of the test and in and near the
precautionintheplacementordesignofobservationwells(see
control well. Control well storage is negligible after a time, t,
5.2.1).
given by the following equation after weeks (7). 6.3 Construction of Observation Wells—Construct one or
more observation wells or piezometers at a distance from the
25 r
c
t 5 (9) control well. Observation wells may be partially open or fully
T
open throughout the thickness of the aquifer.
where: 6.4 Location of Observation Wells—Locate observation
r = the radius of the control well in the interval that
wells at various distances from the control well within the area
c
includes the water level changes.
ofinfluenceofpumping.However,ifverticalflowcomponents
aresignificantandifpartiallypenetratingobservationwellsare
5.2.3 Application of Theis Nonequilibrium Method to Un-
used, locate them at a distance beyond the effect of vertical
confined Aquifers:
fl
...
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