ASTM D4105-96(2008)

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Designation:D4105 −96(Reapproved 2008)
Standard Test Method for
(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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope mining Transmissivity and Storage Coefficient of Non-
leaky Confined Aquifers by the Theis Nonequilibrium
1.1 This test method covers an analytical procedure for
Method
determining transmissivity and storage coefficient of a non-
leakyconfinedaquiferunderconditionsofradialflowtoafully
3. Terminology
penetratingwellofconstantflux.Thistestmethodisashortcut
procedureusedtoapplytheTheisnonequilibriummethod.The
3.1 Definitions:
Theis method is described in Test Method D4106. 3.1.1 aquifer, confined—an aquifer bounded above and be-
lowbyconfiningbedsandinwhichthestaticheadisabovethe
1.2 This test method is used in conjunction with the field
top of the aquifer.
procedure given in Test Method D4050.
3.1.2 aquifer, unconfined—an aquifer that has a water table.
1.3 Limitations—The limitations of this test method are
3.1.3 confining bed—ahydrogeologicunitoflesspermeable
primarily related to the correspondence between the field
material bounding one or more aquifers.
situation and the simplifying assumptions of this test method
(see 5.1). Furthermore, application is valid only for values of u
3.1.4 control well—wellbywhichtheaquiferisstressed,for
less than 0.01 (u is defined in Eq 2,in 8.6).
example, by pumping, injection, or change of head.
1.4 This standard does not purport to address all of the
3.1.5 drawdown—vertical distance the static head is low-
safety concerns, if any, associated with its use. It is the
ered due to the removal of water.
responsibility of the user of this standard to establish appro-
3.1.6 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 unit hydraulic gradient through a unit area
measured at right angles to the direction of flow.
2. Referenced Documents
3.1.7 observation well—a well open to all or part of an
2.1 ASTM Standards:
aquifer.
D653Terminology Relating to Soil, Rock, and Contained
3.1.8 piezometer—use to measure static head at a point in
Fluids
the subsurface.
D4043Guide for Selection of Aquifer Test Method in
Determining Hydraulic Properties by Well Techniques 3.1.9 specific storage—the volume of water released from
D4050Test Method for (Field Procedure) for Withdrawal
ortakenintostorageperunitvolumeoftheporousmediumper
and Injection Well Testing for Determining Hydraulic unit change in head.
Properties of Aquifer Systems
3.1.10 storage coeffıcient—the volume of water an aquifer
D4106Test Method for (Analytical Procedure) for Deter-
releases from or takes into storage per unit surface area of the
aquifer per unit change in head. For a confined aquifer, it is
equal to the product of specific storage and aquifer thickness.
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
For an unconfined aquifer, the storage coefficient is approxi-
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
mately equal to the specific yield.
Vadose Zone Investigations.
Current edition approved Sept. 15, 2008. Published October 2008. Originally
3.1.11 transmissivity—the volume of water at the existing
approved in 1991. Last previous edition approved in 2002 as D4105–96 (2002).
kinematic viscosity that will move in a unit time under a unit
DOI: 10.1520/D4105-96R08.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or hydraulic gradient through a unit width of the aquifer.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.1.12 For definitions of other terms used in this test
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. method, see Terminology D653.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D4105−96 (2008)
3.2 Symbols and Dimensions: The value of u decreases with increasing time, t, and
−1
3.2.1 K [LT ]—hydraulic conductivity. decreases as the radial distance, r, decreases. Therefore, for
large values of t and reasonably small values of r, the terms to
3.2.2 K —hydraulic conductivity in the horizontal direc-
xy
the right of log u in Eq 3 may be neglected as recognized by
e
tion.
Theis (2)andJacob (3).TheTheisequationcanthenbewritten
3.2.3 K —hydraulic conductivity in the vertical direction.
z
as follows:
2 −1
3.2.4 T [L T ]—transmissivity.
Q S
s 5 20.577216 2 ln r (4)
3.2.5 S [nd]—storage coefficient. F S DG
4πT 4Tt
−1
3.2.6 Ss [L ]—specific storage.
from which it has been shown by Lohman (4) that
3.2.7 s [L]—drawdown.
2.3Q
3 −1
T 5 (5)
3.2.8 Q [L T ]—discharge.
4π∆s/∆log t
3.2.9 r [L]—radial distance from control well.
and:
3.2.10 t [T]—time.
2.3Q
T52 (6)
3.2.11 b [L]—thickness of the aquifer.
2π∆s/∆log r
where:
4. Summary of Test Method
∆s/∆log t = the drawdown (measured or projected) over
4.1 This test method describes an analytical procedure for
one log cycle of time, and
analyzing data collected during a withdrawal or injection well
∆s/∆log r = the drawdown (measured or projected) over
test. The field procedure (see Test Method D4050) involves
one log cycle of radial distance from the
pumping a control well at a constant rate and measuring the
control well.
water level response in one or more observation wells or
piezometers. The water-level response in the aquifer is a
5. Significance and Use
function of the transmissivity and coefficient of storage of the
5.1 Assumptions:
aquifer. Alternatively, the test can be performed by injecting
5.1.1 Well discharges at a constant rate, Q.
water at a constant rate into the aquifer through the control
5.1.2 Well is of infinitesimal diameter and fully penetrates
well.Analysisofbuildupofwaterlevelinresponsetoinjection
the aquifer, that is, the well is open to the full thickness of the
issimilartoanalysisofdrawdownofwaterlevelinresponseto
aquifer.
withdrawal in a confined aquifer. Drawdown of water level is
5.1.3 The nonleaky aquifer is homogeneous, isotropic, and
analyzed by plotting drawdown against factors incorporating
areally extensive. A nonleaky aquifer receives insignificant
either time or distance from the control well, or both, and
contribution of water from confining beds.
matching the drawdown response with a straight line.
5.1.4 Discharge from the well is derived exclusively from
4.2 Solution—The solution given by Theis (1) can be
storage in the aquifer.
expressed as follows:
5.1.5 The geometry of the assumed aquifer and well condi-
2y
Q ` e
tions are shown in Fig. 1.
s 5 dy (1)
*
4πT u y
5.2 Implications of Assumptions:
where: 5.2.1 Implicitintheassumptionsaretheconditionsofradial
flow. Vertical flow components are induced by a control well
r S
u 5 (2)
that partially penetrates the aquifer, that is, not open to the
4Tt
aquifer through its full thickness. If the control well does not
and:
2y
` e
dy 5 W~u!520.577216 2 log u (3)
*
e
u
y
2 3 4
u u u
1u 2 1 2 1…
2!2 3!3 4!4
4.3 The sum of the terms to the right of log u in the series
e
of Eq 3 is not significant when u becomes small.
NOTE 1—The errors for small values of u, from Kruseman and
DeRidder(1) are as follows:
Error less than, %: 1 2 5 10
For u smaller than: 0.03 0.05 0.1 0.15
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
D4105−96 (2008)
fully penetrate the aquifer, the nearest piezometer or partially b
r 5 (11)
penetrating observation well should be located at a distance, r,
K
z
Œ
beyond which vertical flow components are negligible, where
K
xy
according to Reed (5)
after the time, t, as given in the following equation from
1.5b
Neuman (9):
r 5 (7)
K
z
r
Œ
K
t 5 10S (12)
xy
y
T
This section applies to distance-drawdown calculations of
where:
transmissivity and storage coefficient and time-drawdown cal-
S = the specific yield.
y
culations of storage coefficient. If possible, compute transmis-
sivity from time-drawdown data from wells located within a For fully penetrating observation wells, the effects of de-
layed yield are negligible at the distance, r,in Eq 11 after one
distance, r, of the pumped well using data measured after the
effectsofpartialpenetrationhavebecomeconstant.Thetimeat tenth of the time given in the Eq 12.
which this occurs is given by Hantush (6) by:
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).
25 r 6.3 Construction of Observation Wells—Construct one or
c
t 5 (9)
more observation wells or piezometers at a distance from the
T
control well. Observation wells may be partially open or fully
where:
open throughout the thickness of the aquifer.
r = theradiusofthecontrolwellintheintervalthatincludes
c
6.4 Location of Observation Wells—Locate observation
the water level changes.
wells at various
...