ASTM D5269-96(2002)
(Test Method)Standard Test Method for Determining Transmissivity of Nonleaky Confined Aquifers by the Theis Recovery Method
Standard Test Method for Determining Transmissivity of Nonleaky Confined Aquifers by the Theis Recovery Method
SCOPE
1.1 This test method covers an analytical procedure for determining the transmissivity of a confined aquifer. This test method is used to analyze data from the recovery of water levels following pumping or injection of water to or from a control well at a constant rate.
1.2 The analytical procedure given in this test method is used in conjunction with the field procedure in Test Method D 4050.
1.3 LimitationsThe valid use of the Theis recovery method is limited to determination of transmissivities for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis theory (see 5.1).
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 5269 – 96 (Reapproved 2002)
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 D4106 Test Method (Analytical Procedure) for Determin-
ing Transmissivity and Storage Coefficient of Nonleaky
1.1 This test method covers an analytical procedure for
Confined Aquifers by the Theis Nonequilibrium Method
determining the transmissivity of a confined aquifer. This test
D4750 Test Method for Determining Subsurface Liquid
method is used to analyze data from the recovery of water
Levels in a Borehole or Monitoring Well (Observation
levels following pumping or injection of water to or from a
Well)
control well at a constant rate.
1.2 The analytical procedure given in this test method is
3. Terminology
used in conjunction with the field procedure in Test Method
3.1 Definitions:
D4050.
3.1.1 aquifer, confined—an aquifer bounded above and
1.3 Limitations—The valid use of the Theis recovery
below by confining beds and in which the static head is above
method is limited to determination of transmissivities for
the top of the aquifer.
aquifers in hydrogeologic settings with reasonable correspon-
3.1.2 confining bed—a hydrogeologic unit of less perme-
dence to the assumptions of the Theis theory (see 5.1).
able material bounding one or more aquifers.
1.4 The values stated in SI units are to be regarded as
3.1.3 control well—a well by which the aquifer is stressed,
standard.
for example, by pumping, injection, or change of head.
1.5 This standard does not purport to address all of the
3.1.4 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-
3.1.5 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
2. Referenced Documents measured at right angles to the direction of flow.
3.1.6 observation well—a well open to all or part of an
2.1 ASTM Standards:
aquifer.
D653 Terminology Relating to Soil, Rock and Contained
3.1.7 piezometer—a device used to measure head at a point
Fluids
in the subsurface.
D4043 Guide for Selection of Aquifer-Test Method in
3.1.8 residual drawdown—The difference between the pro-
Determining Hydraulic Properties by Well Techniques
jected prepumping water-level trend and the water level in a
D4050 Test Method (Field Procedure) for Withdrawal and
well or piezometer after pumping or injection has stopped.
Injection Well Tests for Determining Hydraulic Properties
2 3.1.9 specific storage—the volume of water released from
of Aquifer Systems
ortakenintostorageperunitvolumeoftheporousmediumper
D4105 Test Method (Analytical Procedure) for Determin-
unit change in head.
ing Transmissivity and Storage Coefficient of Nonleaky
3.1.10 step-drawdown test—atestinwhichacontrolwellis
Confined Aquifers by the Modified Theis Nonequilibrium
pumped at constant rates in “steps” of increasing discharge.
Method
Each step is approximately equal in duration, although the last
step may be prolonged.
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
3.1.11 storage coeffıcient—the volume of water an aquifer
RockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWaterand
Vadose Zone Investigations. releases from or takes into storage per unit surface area of the
Current edition approved July 10, 2002. Published June 1997. Originally
aquifer per unit change in head. For a confined aquifer it is
published as D5269–92.
equal to the product of specific storage and aquifer thickness.
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 5269 – 96 (2002)
2y
For an unconfined aquifer, the storage coefficient is approxi-
Q ` e
s 5 dy (1)
*
mately equal to the specific yield. 4pT y
u
3.1.12 transmissivity—the volume of water of the prevail-
ingkinematicviscositytransmittedinaunittimethroughaunit
and:
width of the aquifer under a unit hydraulic gradient.
r S
3.2 Symbols:Symbols and Dimensions:
u 5 (2)
4Tt
3.2.1 b [L]—aquifer thickness.
−1
3.2.2 K [LT ]—hydraulic conductivity.
3.2.2.1 Discussion—The use of the symbol K for the term
4.3 At a control well, observation well, or piezometer, for
hydraulic conductivity is the predominant usage in ground-
large values of time, t, and small values of radius, r, the Theis
water literature by hydrogeologists, whereas the symbol k is
equationreduces,asshownbyCooperandJacob (2)andJacob
commonly used for this term in rock mechanics and soil
(3) to the following:
science.
Q
3.2.3 K —hydraulicconductivityintheplaneoftheaquifer,
r s8 5 ln~t/t8! (3)
4pT
radially from the control well.
3.2.4 K —hydraulic conductivity in the vertical direction.
z
3.2.5 ln—natural logarithm.
where:
3.2.6 log —logarithm to the base 10.
t = the time after pumping began and
3 −1
3.2.7 Q [L T ]—discharge. t8 = the time after pumping ceases. From which it can be
3.2.8 r [L]—radial distance from control well. shown that:
3.2.9 r [L]—equivalent inside radius of control well.
c
2.3Q
T 5 (4)
3.2.10 S [nd]—storage coefficient.
4pDs8
3.2.11 s [L]—drawdown.
3.2.12 s [L]—drawdown corrected for the effects of reduc-
c
where:
tion in saturated thickness.
Ds8 = the measured or projected residual drawdown over
3.2.13 S [nd]—specific yield.
y
one log cycle of t/t8.
3.2.14 s8 [L]—residual drawdown.
4.4 A similar analysis (see 4.3) may also be used for a
3.2.15 Ds8 [L]—change in residual drawdown over one log
step-drawdown test in which a well is pumped at a constant
cycle of t/t8.
2 −1
3.2.16 T [L T ]—transmissivity. rateforaninitialperiod,andthenthepumpingrateisincreased
3.2.17 t [T]—time since pumping or injection began. through several new constant rates in a series of steps. Harrill
3.2.18 t8 [T]—time since pumping or injection stopped. (4) shows that:
3.2.19 u—dimensionless parameter, equal to r S/4Tt.
2.3DQ t 2.3DQ t
1 1 2 2
s8 5 log 1 log (5)
3.2.20 u8—dimensionless parameter, equal to r S/4Tt8. S D S D
10 10
4pT t8 4pT t8
2.3DQ t
n n
4. Summary of Test Method 1. log
S D
4pT t8
4.1 This test method describes an analytical procedure for
where:
determining transmissivity using data collected during the
t,t , . t = the elapsed times since either pump-
1 2 n
recovery phase of a withdrawal or injection well test.The field
ing was begun or the discharge rate
test (see Test Method D4050) requires pumping or injecting a
was increased,
control well that is open to the entire thickness of a confined
Q,Q , . Q = the well discharge rates, and
1 2 n
aquifer at a constant rate for a specified period. The water-
DQ , DQ . DQ = theincrementalincreasesindischarge.
1 2 n
levelsinthecontrolwell,observationwells,orpiezometersare
measured after pumping is stopped and used to calculate the
Eq 5 can be rewritten as follows:
transmissivity of the aquifer using the procedures in this test
method. Alternatively, this test method can be performed by
2.3Q
n
T 5 log f~t, Q! (6)
injecting water into the control well at a constant rate. With 4ps8
somemodification,thistestmethodcanalsobeusedtoanalyze
the residual drawdown following a step test. This test method
where:
is used by plotting residual drawdown against either a function
DQ /Q DQ /Q DQ /Q DQ /Q
1 n 2 n 3 n n n
t t t . t
oftimeorafunctionoftimeanddischargeanddeterminingthe 1 2 3 n
f~t, Q! 5 (7)
t8
slope of a straight line fitted to the points.
4.2 Solution—The solution given by Theis (1) can be
and:
expressed as follows:
2.3Q
n
T 5 (8)
4pDs8
h
The boldface numbers given in parentheses refer to a list of references at the
where:
end of the text.
D 5269 – 96 (2002)
corrected for reduction in thickness of the aquifer and (B) the
Ds8 = the residual drawdown over one log cycle of the
h
effects of delayed gravity yield are small. See 5.2.3 of Test
expression f (t, Q)inEq6.
Method D4106 for guidance in treating reduction in saturated
Eq 8 can also be used to analyze the residual drawdown
thickness and delayed gravity drainage in unconfined aquifers.
followingatestinwhichdischargevariessignificantly,solong
as the discharge can be generalized as a series of constant-
6. Apparatus
discharge steps.
6.1 Analysis of data by this test method from the field
5. Significance and Use procedure given in Test Method D4050 requires that the
control well and observation wells meet the requirements
5.1 Assumptions:
specified in the following subsections.
5.1.1 Thewelldischargesataconstantrate, Q,oratstepsof
6.2 Construction of Control Well—Installthecontrolwellin
constant rate Q , Q . Q .
1 2 n
theaquiferandequipwithapumpcapableofdischargingwater
5.1.2 Well is of infinitesimal diameter and is open through
from the well at a constant rate, or several steps at constant
the full thickness of the aquifer.
rate, for the duration of the test. Preferably, the control well
5.1.3 The nonleaky aquifer is homogeneous, isotropic, and
should be open throughout the full thickness of the aquifer. If
areally extensive.
the control well partially penetrates the aquifer, take special
5.1.4 Discharge from the well is derived exclusively from
precautions in the placement or design of observation wells
storage in the aquifer.
(see 5.2.1).
5.1.5 The geometry of the assumed aquifer and well are
6.3 Construction of Observation Wells and Piezometers—
shown in Fig. 1.
Construct one or more observation wells or piez
...
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