ASTM D5785-95(2013)
(Test Method)Standard Test Method for (Analytical Procedure) for Determining Transmissivity of Confined Nonleaky Aquifers by Underdamped Well Response to Instantaneous Change in Head (Slug Test)
Standard Test Method for (Analytical Procedure) for Determining Transmissivity of Confined Nonleaky Aquifers by Underdamped Well Response to Instantaneous Change in Head (Slug Test)
SIGNIFICANCE AND USE
6.1 The assumptions of the physical system are given as follows:
6.1.1 The aquifer is of uniform thickness and confined by impermeable beds above and below.
6.1.2 The aquifer is of constant homogeneous porosity and matrix compressibility and of homogeneous and isotropic hydraulic conductivity.
6.1.3 The origin of the cylindrical coordinate system is taken to be on the well-bore axis at the top of the aquifer.
6.1.4 The aquifer is fully screened.
6.2 The assumptions made in defining the momentum balance are as follows:
6.2.1 The average water velocity in the well is approximately constant over the well-bore section.
6.2.2 Flow is laminar and frictional head losses from flow across the well screen are negligible.
6.2.3 Flow through the well screen is uniformly distributed over the entire aquifer thickness.
6.2.4 Change in momentum from the water velocity changing from radial flow through the screen to vertical flow in the well are negligible.
6.2.5 The system response is an exponentially decaying sinusoidal function.
SCOPE
1.1 This test method covers determination of transmissivity from the measurement of the damped oscillation about the equilibrium water level of a well-aquifer system to a sudden change of water level in a well. Underdamped response of water level in a well to a sudden change in water level is characterized by oscillatory fluctuation about the static water level with a decrease in the magnitude of fluctuation and recovery to initial water level. Underdamped response may occur in wells tapping highly transmissive confined aquifers and in deep wells having long water columns.
1.2 This analytical procedure is used in conjunction with the field procedure Test Method D4044 for collection of test data.
1.3 Limitations—Slug tests are considered to provide an estimate of transmissivity of a confined aquifer. This test method requires that the storage coefficient be known. Assumptions of this test method prescribe a fully penetrating well (a well open through the full thickness of the aquifer), but 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. The method assumes laminar flow and is applicable for a slug test in which the initial water-level displacement is less than 0.1 or 0.2 of the length of the static water column.
1.4 This test method of analysis presented here is derived by van der Kamp (1)2 based on an approximation of the underdamped response to that of an exponentially damped sinusoid. A more rigorous analysis of the response of wells to a sudden change in water level by Kipp (2) indicates that the method presented by van der Kamp (1) matches the solution of Kipp (2) when the damping parameter values are less than about 0.2 and time greater than that of the first peak of the oscillation (2).
1.5 Units—The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values in each system may not be exact equivalents; therefore each system shall be used independently of the other. Combining values from the two systems may result in non-conformance with the standard. Reporting of test results in units other than SI shall not be regarded as nonconformance with this test method.
1.6 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026.
1.7 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 sa...
General Information
Relations
Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation:D5785 −95(Reapproved 2013)
Standard Test Method for
(Analytical Procedure) for Determining Transmissivity of
Confined Nonleaky Aquifers by Underdamped Well
Response to Instantaneous Change in Head (Slug Test)
This standard is issued under the fixed designation D5785; 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* Amore rigorous analysis of the response of wells to a sudden
change in water level by Kipp (2) indicates that the method
1.1 This test method covers determination of transmissivity
presented by van der Kamp (1) matches the solution of Kipp
from the measurement of the damped oscillation about the
(2) when the damping parameter values are less than about 0.2
equilibrium water level of a well-aquifer system to a sudden
andtimegreaterthanthatofthefirstpeakoftheoscillation (2).
change of water level in a well. Underdamped response of
water level in a well to a sudden change in water level is
1.5 Units—The values stated in either SI units or inch-
characterized by oscillatory fluctuation about the static water
pound units are to be regarded separately as standard. The
level with a decrease in the magnitude of fluctuation and
values in each system may not be exact equivalents; therefore
recovery to initial water level. Underdamped response may
each system shall be used independently of the other. Combin-
occur in wells tapping highly transmissive confined aquifers
ing values from the two systems may result in non-
and in deep wells having long water columns.
conformance with the standard. Reporting of test results in
1.2 Thisanalyticalprocedureisusedinconjunctionwiththe
units other than SI shall not be regarded as nonconformance
field procedure Test Method D4044 for collection of test data.
with this test method.
1.3 Limitations—Slug tests are considered to provide an
1.6 All observed and calculated values shall conform to the
estimate of transmissivity of a confined aquifer. This test
guidelines for significant digits and rounding established in
method requires that the storage coefficient be known. As-
Practice D6026.
sumptionsofthistestmethodprescribeafullypenetratingwell
1.7 This standard does not purport to address all of the
(a well open through the full thickness of the aquifer), but the
safety concerns, if any, associated with its use. It is the
slug test method is commonly conducted using a partially
responsibility of the user of this standard to establish appro-
penetrating well. Such a practice may be acceptable for
application under conditions in which the aquifer is stratified priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
and horizontal hydraulic conductivity is much greater than
verticalhydraulicconductivity.Insuchacasethetestwouldbe
considered to be representative of the average hydraulic 2. Referenced Documents
conductivity of the portion of the aquifer adjacent to the open
2.1 ASTM Standards:
interval of the well. The method assumes laminar flow and is
D653Terminology Relating to Soil, Rock, and Contained
applicable for a slug test in which the initial water-level
Fluids
displacement is less than 0.1 or 0.2 of the length of the static
D4043Guide for Selection of Aquifer Test Method in
water column.
Determining Hydraulic Properties by Well Techniques
1.4 Thistestmethodofanalysispresentedhereisderivedby
D4044Test Method for (Field Procedure) for Instantaneous
van der Kamp (1) based on an approximation of the under-
Change in Head (Slug) Tests for Determining Hydraulic
damped response to that of an exponentially damped sinusoid.
Properties of Aquifers
D6026Practice for Using Significant Digits in Geotechnical
Data
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
Vadose Zone Investigations.
Current edition approved March 15, 2013. Published April 2013. Originally
approved in 1995. Last previous edition approved in 2006 as D5785–95 (2006). For referenced ASTM standards, visit the ASTM website, www.astm.org, or
DOI: 10.1520/D5785-95R13. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
The boldface numbers given in parentheses refer to a list of references at the Standards volume information, refer to the standard’s Document Summary page on
end of the text. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5785−95 (2013)
3. Terminology where:
h = hydraulic head,
3.1 Definitions—For definitions of other terms used in this
T = aquifer transmissivity, and
test method, see Terminology D653.
S = storage coefficient.
3.1.1 observation well—a well open to all or part of an
aquifer. 4.2.1 The initial condition is at t =0 and h = h and the
o
outer boundary condition is as r→∞ and h→ h .
o
3.1.2 storage coeffıcient—the volume of water an aquifer
releases from or takes into storage per unit surface area of the
4.3 The flow rate balance on the well bore relates the
aquifer per unit change in head. For a confined aquifer, the
displacementofthewaterlevelinthewell-risertotheflowinto
storage coefficient is equal to the product of specific storage
the well:
and aquifer thickness. For an unconfined aquifer, the storage
dw ] h
coefficient is approximately equal to the specific yield.
Uπr 52πr T U (2)
c s
dt ]r
r5r
s
3.1.3 transmissivity—the volume of water at the existing
where:
kinematic viscosity that will move in a unit time under a unit
r = radius of the well casing, and
hydraulic gradient through a unit width of the aquifer.
c
w = displacement of the water level in the well from its
3.2 Symbols and Dimensions:
initial position.
2 −1
3.2.1 T—transmissivity [L T ].
4.3.1 The third equation describing the system, relating h
3.2.2 S—storage coefficient [nd]. s
and w, comes from a momentum balance of Bird et al. (4) as
3.2.3 L—effective length of water column, equal to L +
c
2 2
referenced in Kipp (2).
(r /r ) (m/2).
c s
3.2.3.1 Discussion—This expression for the effective length d 0
2 2 2
πr pv z 5 @2pv 1p 2 p 2 pgm#πr (3)
*
s d 2 1 2 s
2m
is given by Kipp (2).The expression for the effective length of dt
thewatercolumnfromCooperetal. (3)isgivenas L +3⁄8L
c s
where:
andassumesthatthewellscreenandwellcasinghavethesame
v = velocity in the well screen interval,
diameter.
m = aquifer thickness,
3.2.4 L —length of water column within casing [L].
c
p = pressure,
3.2.5 L —length of water column within well screen [L].
s
ρ = fluid density,
−2
3.2.6 g—acceleration of gravity [LT ].
g = gravitational acceleration, and
3.2.7 h—hydraulic head in the aquifer [L].
r = well screen radius. Well and aquifer geometry are
s
3.2.8 h —initial hydraulic head in the aquifer [L]. shown in Fig. 1.
o
3.2.9 h —hydraulic head in the well screen [L].
s
Atmospheric pressure is taken as zero.
3.2.10 r —radius of well casing [L].
c
3.2.11 r —radius of well screen [L].
s 5. Solution
3.2.12 t—time [T].
5.1 The method of van der Kamp (1) assumes the water
3.2.13 w—water level displacement from the initial static
level response to a sudden change for the underdamped case,
level [L].
except near critical damping conditions, can be approximately
3.2.14 w —initial water level displacement [L].
o
described as an exponentially damped cyclic fluctuation that
−1
3.2.15 γ—damping constant [T ].
decays exponentially. The water-level fluctuation would then
3.2.16 τ—wavelength [T].
be given by:
−1
3.2.17 ω—angular frequency [T ].
2γt
w t 5 w e cos wt (4)
~ !
o
3.2.18 m—aquifer thickness, [L].
5.1.1 The following solution is given by van der Kamp (1).
2 1/2 2 1/2
4. Summary of Test Method
2r g/L 1n 0.79 r S/T g/L
~ ! @ ~ !~ !
c s
d 5 (5)
8T
4.1 This test method describes the analytical procedure for
analyzing data collected during an instantaneous head (slug)
that may be written as:
test using a well in which the response is underdamped. The
T 5 b1a 1nT (6)
field procedures in conducting a slug test are given in Test
MethodD4044.Theanalyticalprocedureconsistsofanalyzing
where:
the response of water level in the well following the change in
2 1/2
b 5 a 1n 0.79 r S g/L (7)
@ ~ !
s
water level induced in the well.
2 1/2
r g/L
~ !
c
a 5 (8)
4.2 Theory—The equations that govern the response of well
8d
to an instantaneous change in head are treated at length by
1/2
d 5 γ/ g/L (9)
~ !
Kipp (2). The flow in the aquifer is governed by the following
equation for cylindrical flow:
and
2 2
S dh 1 d dh
L 5 g/ ω 1γ (10)
~ !
5 r (1)
S D
T dt r dr dr NOTE 1—Other analytical solutions are proposed by Kipp (2); Krauss
D5785−95 (2013)
6.2.5 The system response is an exponentially decaying
sinusoidal function.
7. Procedure
7.1 The overall procedure consists of:
7.1.1 Conducting the slug test field procedure (see Test
Method D4044), and
7.1.2 Analyzing the field data, that is addressed in this test
method.
NOTE 2—The initial displacement of water level should not exceed 0.1
or 0.2 of the length of the static water column in the well, because of
considerations for calculating L . Practically, the displacement should be
c
small, a few times larger than the well radius, to minimize frictional
losses. The measurement of displacement should be within 1% of the
initialwater-leveldisplacement.Thewater-leveldisplacementneedstobe
calculated independently for comparison to the observed initial
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.