ASTM D4104-96(2010)e1
(Test Method)Standard Test Method (Analytical Procedure) for Determining Transmissivity of Nonleaky Confined Aquifers by Overdamped Well Response to Instantaneous Change in Head (Slug Tests)
Standard Test Method (Analytical Procedure) for Determining Transmissivity of Nonleaky Confined Aquifers by Overdamped Well Response to Instantaneous Change in Head (Slug Tests)
SIGNIFICANCE AND USE
Assumptions of Solution of Cooper et al (1):
The head change in the control well is instantaneous at time t = 0.
Well is of finite diameter and fully penetrates the aquifer.
Flow in the nonleaky aquifer is radial.
Implications of Assumptions:
The mathematical equations applied ignore inertial effects and assume the water level returns the static level in an approximate exponential manner. The geometric configuration of the well and aquifer are shown in Fig. 1.
Assumptions are applicable to artesian or confined conditions and fully penetrating wells. However, this test method is commonly applied to partially penetrating wells and in unconfined aquifers where it may provide estimates of hydraulic conductivity for the aquifer interval adjacent to the open interval of the well if the horizontal hydraulic conductivity is significantly greater than the vertical hydraulic conductivity.
As pointed out by Cooper et al (1) the determination of storage coefficient by this test method has questionable reliability because of the similar shape of the curves, whereas, the determination of transmissivity is not as sensitive to choosing the correct curve. However, the curve selected should not imply a storage coefficient unrealistically large or small.
FIG. 1 Cross Section Through a Well in Which a Slug of Water is Suddenly Injected
SCOPE
1.1 This test method covers the determination of transmissivity from the measurement of force-free (overdamped) response of a well-aquifer system to a sudden change of water level in a well. Force-free response of water level in a well to a sudden change in water level is characterized by recovery to initial water level in an approximate exponential manner with negligible inertial effects.
1.2 The analytical procedure in this test method is used in conjunction with the field procedure in Test Method D4044 for collection of test data.
1.3 Limitations—Slug tests are considered to provide an estimate of transmissivity. Although the assumptions of this test method prescribe a fully penetrating well (a well open through the full thickness of the aquifer), the slug test method is commonly conducted using a partially penetrating well. Such a practice may be acceptable for application under conditions in which the aquifer is stratified and horizontal hydraulic conductivity is much greater than vertical hydraulic conductivity. In such a case the test would be considered to be representative of the average hydraulic conductivity of the portion of the aquifer adjacent to the open interval of the well.
1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this 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:D4104 −96 (Reapproved 2010)
Standard Test Method
(Analytical Procedure) for Determining Transmissivity of
Nonleaky Confined Aquifers by Overdamped Well Response
to Instantaneous Change in Head (Slug Tests)
This standard is issued under the fixed designation D4104; 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.
ε NOTE—The units statement in 1.4 was revised editorially in August 2010.
1. Scope 2. Referenced Documents
2.1 ASTM Standards:
1.1 This test method covers the determination of transmis-
D653Terminology Relating to Soil, Rock, and Contained
sivity from the measurement of force-free (overdamped) re-
Fluids
sponse of a well-aquifer system to a sudden change of water
D4043Guide for Selection of Aquifer Test Method in
level in a well. Force-free response of water level in a well to
Determining Hydraulic Properties by Well Techniques
a sudden change in water level is characterized by recovery to
D4044Test Method for (Field Procedure) for Instantaneous
initial water level in an approximate exponential manner with
Change in Head (Slug) Tests for Determining Hydraulic
negligible inertial effects.
Properties of Aquifers
1.2 The analytical procedure in this test method is used in
D4750Test Method for Determining Subsurface Liquid
conjunctionwiththefieldprocedureinTestMethodD4044for
Levels in a Borehole or Monitoring Well (Observation
collection of test data. 3
Well) (Withdrawn 2010)
D5912Test Method for (Analytical Procedure) Determining
1.3 Limitations—Slug tests are considered to provide an
Hydraulic Conductivity of an Unconfined Aquifer by
estimate of transmissivity. Although the assumptions of this
Overdamped Well Response to Instantaneous Change in
test method prescribe a fully penetrating well (a well open
Head (Slug) (Withdrawn 2013)
through the full thickness of the aquifer), the slug test method
is commonly conducted using a partially penetrating well.
3. Terminology
Such a practice may be acceptable for application under
conditions in which the aquifer is stratified and horizontal
3.1 Definitions:
hydraulic conductivity is much greater than vertical hydraulic
3.1.1 aquifer, confined—an aquifer bounded above and be-
conductivity. In such a case the test would be considered to be
lowbyconfiningbedsandinwhichthestaticheadisabovethe
representative of the average hydraulic conductivity of the
top of the aquifer.
portion of the aquifer adjacent to the open interval of the well.
3.1.2 confining bed—ahydrogeologicunitoflesspermeable
material bounding one or more aquifers.
1.4 The values stated in SI units are to be regarded as
standard. No other units of measurement are included in this
3.1.3 control well—wellbywhichtheaquiferisstressed,for
standard.
example, by pumping, injection, or change of head.
1.5 This standard does not purport to address all of the 3.1.4 head, static—theheightaboveastandarddatumofthe
surface of a column of water (or other liquid) that can be
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro- supported by the static pressure at a given point.
priate safety and health practices and determine the applica-
3.1.5 hydraulic conductivity—(field aquifer tests), the vol-
bility of regulatory limitations prior to use.
umeofwaterattheexistingkinematicviscositythatwillmove
1 2
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Vadose Zone Investigations. Standardsvolume information, refer to the standard’s Document Summary page on
Current edition approved Aug. 1, 2010. Published September 2010. Originally the ASTM website.
approved in 1991. Last previous edition approved in 2004 as D4104 – 96 (2004). The last approved version of this historical standard is referenced on
DOI: 10.1520/D4104-96R10E01. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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D4104−96 (2010)
in a unit time under a unit hydraulic gradient through a unit analytical procedure consists of analyzing the recovery of
area measured at right angles to the direction of flow. water level in the well following the change in water level
induced in the well.
3.1.6 observation well—a well open to all or part of an
aquifer.
4.2 Solution—The solution given by Cooper et al (1) is as
follows:
3.1.7 overdamped-well response—characterized by the wa-
`
ter level returning to the static level in an approximately
2H
o
exponential manner following a sudden change in water level. H 5 * @@exp ~2βu /α! @J ~ur/r ! (1)
0 w
π
(See for comparison underdamped-well response.)
3.1.8 slug—avolumeofwaterorsolidobjectusedtoinduce
@uY ~u! 2 2αY ~u!# 2 Y ~ur/r !
0 1 0 w
a sudden change of head in a well.
uJ u 2 2αJ u # / ∆ u #du
@ ~ ! ~ !# ~ !
0 1
3.1.9 specific storage—the volume of water released from
where:
ortakenintostorageperunitvolumeoftheporousmediumper
unit change in head. 2 2
α 5 r S/r ,
w c
3.1.10 storage coeffıcient—the volume of water an aquifer β 5 Tt/r ,
c
releases from or takes into storage per unit surface area of the
and:
aquifer per unit change in head. For a confined aquifer, the
2 2
∆~u! 5 @uJ ~u! 2 2αJ ~u!# 1@uY ~u! 2 2αY ~u!#
storage coefficient is equal to the product of specific storage 0 1 0 1
NOTE 1—See D5912 and Hvorslev (2) Bouwer and Rice (3), and
and aquifer thickness. For an unconfined aquifer, the storage
Bouwer (4) .
coefficient is approximately equal to the specific yield.
5. Significance and Use
3.1.11 transmissivity—the volume of water at the existing
kinematic viscosity that will move in a unit time under a unit
5.1 Assumptions of Solution of Cooper et al (1):
hydraulic gradient through a unit width of the aquifer.
5.1.1 Theheadchangeinthecontrolwellisinstantaneousat
3.1.12 underdamped-well response—response characterized time t =0.
by the water level oscillating about the static water level 5.1.2 Well is of finite diameter and fully penetrates the
following a sudden change in water level. (See for comparison aquifer.
overdamped-well response.) 5.1.3 Flow in the nonleaky aquifer is radial.
3.1.13 For definitions of other terms used in this test 5.2 Implications of Assumptions:
method, see Terminology D653. 5.2.1 The mathematical equations applied ignore inertial
3.2 Symbols: effects and assume the water level returns the static level in an
3.2.1 J [nd]—zero-order Bessel function of the first kind. approximate exponential manner. The geometric configuration
of the well and aquifer are shown in Fig. 1.
3.2.2 J [nd]—first-order Bessel function of the first kind.
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3.2.3 K [LT ]—hydraulic conductivity.
2 −1
3.2.4 T [L T ]—transmissivity.
The boldface numbers in parentheses refer to a list of references at the end of
the text.
3.2.5 S [nd]—storage coefficient.
3.2.6 Y [nd]—zero order Bessel function of the second
kind.
3.2.7 Y [nd]—firstorderBesselfunctionofthesecondkind.
3.2.8 r [L]—radius of control-well casing or open hole in
c
interval where water level changes.
3.2.9 r [L]—radius of control well screen or open hole
w
adjacent to water bearing unit.
3.2.10 u—variable of integration.
3.2.11 H [L]—change in head in control well.
3.2.12 H [L]—initial head rise (or decline) in control well.
o
3.2.13 t—time.
3.2.14 β—Tt/r .
c
2 2
3.2.15 α—r S/r .
w c
4. Summary of Test Method
4.1 This test method describes the analytical procedure for
analyzing data collected during an instantaneous head (slug)
test using an overdamped well. The field procedures in
FIG. 1 Cross Section Through a Well in Which a Slug of Water is
conducting a slug test are given in Test Method D4044. The SuddenlyInjected
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D4104−96 (2010)
TABLE 1 Values of H/H
5.2.2 Assumptions are applicable to artesian or confined
o
conditions and fully penetrating wells. However, this test From Cooper, Bredehoeft, and Papadopulos (1)
2 −1 −2 −3 −4 −5
β = Tt/r α 10 10 10 10 10
c
method is commonly applied to partially penetrating wells and
1.00 0.9771 0.9920 0.9969 0.9985 0.9992
in unconfined aquifers where it may provide estimates of
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10 2.15 0.9658 0.9876 0.9949 0.9974 0.9985
hydraulic conductivity for the aquifer interval adjacent to the
4.64 0.9490 0.9807 0.9914 0.9954 0.9970
open interval of the well if the horizontal hydraulic conduc- 1.00 0.9238 0.9693 0.9853 0.9915 0.9942
−2
10 2.15 0.8860 0.9505 0.9744 0.9841 0.9883
tivity is significantly greater than the vertical hydraulic con-
4.64 0.8293 0.9187 0.9545 0.9701 0.9781
ductivity.
1.00 0.7460 0.8655 0.9183 0.9434 0.9572
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5.2.3 AspointedoutbyCooperetal (1)thedeterminationof 10 2.15 0.6289 0.7782 0.8538 0.8935 0.9167
4.64 0.4782 0.6436 0.7436 0.8031 0.8410
storage coefficient by this test method has questionable reli-
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