ASTM D5269-96(2008)

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Designation:D5269 −96(Reapproved 2008)
Standard Test Method for
Determining Transmissivity of Nonleaky Confined Aquifers
by the Theis Recovery Method
This standard is issued under the fixed designation D5269; 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 D4106Test Method for (Analytical Procedure) for Deter-
mining Transmissivity and Storage Coefficient of Non-
1.1 This test method covers an analytical procedure for
leaky Confined Aquifers by the Theis Nonequilibrium
determining the transmissivity of a confined aquifer. This test
Method
method is used to analyze data from the recovery of water
D4750Test Method for Determining Subsurface Liquid
levels following pumping or injection of water to or from a
Levels in a Borehole or Monitoring Well (Observation
control well at a constant rate.
Well) (Withdrawn 2010)
1.2 The analytical procedure given in this test method is
used in conjunction with the field procedure in Test Method
3. Terminology
D4050.
3.1 Definitions:
1.3 Limitations—The valid use of the Theis recovery
3.1.1 aquifer, confined—an aquifer bounded above and be-
method is limited to determination of transmissivities for
lowbyconfiningbedsandinwhichthestaticheadisabovethe
aquifers in hydrogeologic settings with reasonable correspon-
top of the aquifer.
dence to the assumptions of the Theis theory (see 5.1).
3.1.2 confining bed—ahydrogeologicunitoflesspermeable
1.4 This standard does not purport to address all of the
material bounding one or more aquifers.
safety concerns, if any, associated with its use. It is the
3.1.3 control well—a well by which the aquifer is stressed,
responsibility of the user of this standard to establish appro-
for example, by pumping, injection, or change of head.
priate safety and health practices and determine the applica-
3.1.4 drawdown—vertical distance the static head is low-
bility of regulatory limitations prior to use.
ered due to the removal of water.
2. Referenced Documents
3.1.5 hydraulic conductivity (field aquifer tests)—the vol-
umeofwaterattheexistingkinematicviscositythatwillmove
2.1 ASTM Standards:
in a unit time under unit hydraulic gradient through a unit area
D653Terminology Relating to Soil, Rock, and Contained
measured at right angles to the direction of flow.
Fluids
D4043Guide for Selection of Aquifer Test Method in 3.1.6 observation well—a well open to all or part of an
Determining Hydraulic Properties by Well Techniques
aquifer.
D4050Test Method for (Field Procedure) for Withdrawal
3.1.7 piezometer—a device used to measure head at a point
and Injection Well Testing for Determining Hydraulic
in the subsurface.
Properties of Aquifer Systems
3.1.8 residual drawdown—The difference between the pro-
D4105Test Method for (Analytical Procedure) for Deter-
jected prepumping water-level trend and the water level in a
mining Transmissivity and Storage Coefficient of Non-
well or piezometer after pumping or injection has stopped.
leaky ConfinedAquifers by the Modified Theis Nonequi-
3.1.9 specific storage—the volume of water released from
librium Method
ortakenintostorageperunitvolumeoftheporousmediumper
unit change in head.
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
3.1.10 step-drawdown test—a test in which a control well is
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
Vadose Zone Investigations.
pumped at constant rates in “steps” of increasing discharge.
Current edition approved Sept. 15, 2008. Published October 2008. Originally
Each step is approximately equal in duration, although the last
approved in 1992. Last previous edition approved in 2002 as D5269–96 (2002).
step may be prolonged.
DOI: 10.1520/D5269-96R08.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on The last approved version of this historical standard is referenced on
the ASTM website. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5269−96 (2008)
3.1.11 storage coeffıcient—the volume of water an aquifer is used by plotting residual drawdown against either a function
releases from or takes into storage per unit surface area of the oftimeorafunctionoftimeanddischargeanddeterminingthe
aquifer per unit change in head. For a confined aquifer it is slope of a straight line fitted to the points.
equal to the product of specific storage and aquifer thickness. 4
4.2 Solution—The solution given by Theis (1) can be
For an unconfined aquifer, the storage coefficient is approxi-
expressed as follows:
mately equal to the specific yield.
2y
Q ` e
3.1.12 transmissivity—thevolumeofwateroftheprevailing s 5 dy (1)
*
u
4πT y
kinematic viscosity transmitted in a unit time through a unit
and:
width of the aquifer under a unit hydraulic gradient.
r S
3.2 Symbols and Dimensions:
u 5 (2)
4Tt
3.2.1 b [L]—aquifer thickness.
−1
4.3 At a control well, observation well, or piezometer, for
3.2.2 K [LT ]—hydraulic conductivity.
large values of time, t, and small values of radius, r, the Theis
3.2.2.1 Discussion—The use of the symbol K for the term
equationreduces,asshownbyCooperandJacob (2)andJacob
hydraulic conductivity is the predominant usage in groundwa-
(3) to the following:
ter literature by hydrogeologists, whereas the symbol k is
commonly used for this term in rock mechanics and soil
Q
s' 5 ln t/t' (3)
~ !
science.
4πT
3.2.3 K —hydraulic conductivity in the plane of the aquifer,
r
where:
radially from the control well.
t = the time after pumping began and
3.2.4 K —hydraulic conductivity in the vertical direction.
z
t' = the time after pumping ceases. From which it can be
3.2.5 ln—natural logarithm.
shown that:
3.2.6 log —logarithm to the base 10. 2.3Q
3 −1 T 5 (4)
3.2.7 Q [L T ]—discharge. 4π∆s'
3.2.8 r [L]—radial distance from control well.
where:
3.2.9 r [L]—equivalent inside radius of control well.
∆s' = the measured or projected residual drawdown over
c
one log cycle of t/t'.
3.2.10 S [nd]—storage coefficient.
3.2.11 s [L]—drawdown. 4.4 A similar analysis (see 4.3) may also be used for a
step-drawdown test in which a well is pumped at a constant
3.2.12 s [L]—drawdown corrected for the effects of reduc-
c
rateforaninitialperiod,andthenthepumpingrateisincreased
tion in saturated thickness.
through several new constant rates in a series of steps. Harrill
3.2.13 S [nd]—specific yield.
y
(4) shows that:
3.2.14 s' [L]—residual drawdown.
2.3∆Q t 2.3∆Q t
1 1 2 2
s' 5 log 1 log (5)
S D S D
10 10
3.2.15 ∆s' [L]—change in residual drawdown over one log
4πT t' 4πT t'
cycle of t/t'.
2 −1
2.3∆Q t
3.2.16 T [L T ]—transmissivity. n n
1… log
S D
4πT t'
3.2.17 t [T]—time since pumping or injection began.
where:
3.2.18 t' [T]—time since pumping or injection stopped.
t ,t , . t = the elapsed times since either pumping
1 2 n
3.2.19 u—dimensionless parameter, equal to r S/4Tt.
was begun or the discharge rate was
3.2.20 u'—dimensionless parameter, equal to r S/4Tt'.
increased,
Q ,Q , . Q = the well discharge rates, and
1 2 n
4. Summary of Test Method
∆Q , ∆Q . ∆Q = the incremental increases in discharge.
1 2 n
4.1 This test method describes an analytical procedure for
Eq 5 can be rewritten as follows:
determining transmissivity using data collected during the
2.3Q
n
recovery phase of a withdrawal or injection well test.The field
T 5 log f t, Q (6)
~ !
4πs'
test (see Test Method D4050) requires pumping or injecting a
control well that is open to the entire thickness of a confined where:
aquifer at a constant rate for a specified period. The water- ∆Q /Q ∆Q /Q ∆Q /Q ∆Q /Q
1 n 2 n 3 n n n
t t t … t
1 2 3 n
f t, Q 5 (7)
levelsinthecontrolwell,observationwells,orpiezometersare ~ !
t'
measured after pumping is stopped and used to calculate the
and:
transmissivity of the aquifer using the procedures in this test
method. Alternatively, this test method can be performed by
injecting water into the control well at a constant rate. With
somemodification,thistestmethodcanalsobeusedtoanalyze
The boldface numbers in parentheses refer to a list of references at the end of
the residual drawdown following a step test. This test method this standard.
D5269−96 (2008)
2.3Q 5.2.3 Application of Theis Recovery Method for Unconfined
n
T 5 (8)
4π∆s' Aquifers:
h
5.2.3.1 Although the assumptions are applicable to artesian
where:
or confined conditions, the Theis solution may be applied to
∆s' = the residual drawdown over one log cycle of the
h
unconfined aquifers if (A) drawdown is small compared with
expression f(t, Q)in Eq 6.
the saturated thickness of the aquifer or if the drawdown is
Eq 8 can also be used to analyze the residual drawdown
corrected for reduction in thickness of the aquifer and (B) the
followingatestinwhichdischargevariessignificantly,solong
effects of delayed gravity yield are small. See 5.2.3 of Test
as the discharge can be generalized as a series of constant-
Method D4106 for guidance in treating reduction in saturated
discharge steps.
thickness and delayed gravity drainage in unconfined aquifers.
5. Significance and Use
6. Apparatus
5.1 Assumptions:
6.1 Analysis of data by this test method from the field
5.1.1 Thewelldischargesataconstantrate, Q,oratstepsof
procedure given in Test Method D4050 requires that the
constant rate Q , Q . Q .
1 2 n control well and observation wells meet the requirements
5.1.2 Well is of infinitesimal diameter and is open through
specified in the following subsections.
the full thickness of the aquifer.
6.2 Construction of Control Well—Installthecontrolwellin
5.1.3 The nonleaky aquifer is homogeneous, isotropic, and
theaquiferandequipwithapumpcapableofdischargingwater
areally extensive.
from the well at a constant rate, or several steps at constant
5.1.4 Discharge from the well is derived exclusively from
rate, for the duration of the test. Preferably, the control well
storage in the a
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