ASTM D5785-95(2006)
(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
The assumptions of the physical system are given as follows:
The aquifer is of uniform thickness and confined by impermeable beds above and below.
The aquifer is of constant homogeneous porosity and matrix compressibility and of homogeneous and isotropic hydraulic conductivity.
The origin of the cylindrical coordinate system is taken to be on the well-bore axis at the top of the aquifer.
The aquifer is fully screened.
The assumptions made in defining the momentum balance are as follows:
The average water velocity in the well is approximately constant over the well-bore section.
Flow is laminar and frictional head losses from flow across the well screen are negligible.
Flow through the well screen is uniformly distributed over the entire aquifer thickness.
Change in momentum from the water velocity changing from radial flow through the screen to vertical flow in the well are negligible.
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) 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 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:D5785 −95(Reapproved 2006)
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
1.5 This standard does not purport to address all of the
water level in a well to a sudden change in water level is
safety concerns, if any, associated with its use. It is the
characterized by oscillatory fluctuation about the static water
responsibility of the user of this standard to establish appro-
level with a decrease in the magnitude of fluctuation and
priate safety and health practices and determine the applica-
recovery to initial water level. Underdamped response may
bility of regulatory limitations prior to use.
occur in wells tapping highly transmissive confined aquifers
and in deep wells having long water columns.
2. Referenced Documents
1.2 Thisanalyticalprocedureisusedinconjunctionwiththe
2.1 ASTM Standards:
field procedure Test Method D4044 for collection of test data.
D653Terminology Relating to Soil, Rock, and Contained
1.3 Limitations—Slug tests are considered to provide an
Fluids
estimate of transmissivity of a confined aquifer. This test
D4043Guide for Selection of Aquifer Test Method in
method requires that the storage coefficient be known. As-
Determining Hydraulic Properties by Well Techniques
sumptionsofthistestmethodprescribeafullypenetratingwell
D4044Test Method for (Field Procedure) for Instantaneous
(a well open through the full thickness of the aquifer), but the
Change in Head (Slug) Tests for Determining Hydraulic
slug test method is commonly conducted using a partially
Properties of Aquifers
penetrating well. Such a practice may be acceptable for
application under conditions in which the aquifer is stratified
3. Terminology
and horizontal hydraulic conductivity is much greater than
3.1 Definitions:
verticalhydraulicconductivity.Insuchacasethetestwouldbe
3.1.1 aquifer, confined—an aquifer bounded above and be-
considered to be representative of the average hydraulic
lowbyconfiningbedsandinwhichthestaticheadisabovethe
conductivity of the portion of the aquifer adjacent to the open
top of the aquifer.
interval of the well. The method assumes laminar flow and is
3.1.2 confining bed—ahydrogeologicunitoflesspermeable
applicable for a slug test in which the initial water-level
material bounding one or more aquifers.
displacement is less than 0.1 or 0.2 of the length of the static
water column. 3.1.3 control well—wellbywhichtheaquiferisstressed,for
example, by pumping, injection, or change in head.
1.4 Thistestmethodofanalysispresentedhereisderivedby
3.1.4 head, static—theheightaboveastandarddatumofthe
van der Kamp (1) based on an approximation of the under-
surface of a column of water (or other liquid) that can be
damped response to that of an exponentially damped sinusoid.
supported by the static pressure at a given point.
3.1.5 observation well—a well open to all or part of an
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
aquifer.
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
Vadose Zone Investigations.
Current edition approved Sept. 15, 2006. Published December 2006. Originally
approved in 1995. Last previous edition approved in 2000 as D5785–95 (2000). For referenced ASTM standards, visit the ASTM website, www.astm.org, or
DOI: 10.1520/D5785-95R06. 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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5785−95 (2006)
3.1.6 overdamped well response—characterized by the wa- 4.2 Theory—The equations that govern the response of well
ter level returning to the static level in an approximately to an instantaneous change in head are treated at length by
exponential manner following a sudden change in water level. Kipp (2). The flow in the aquifer is governed by the following
(See for comparison underdamped well response.) equation for cylindrical flow:
3.1.7 slug—avolumeofwaterorsolidobjectusedtoinduce S dh 1 d dh
5 r (1)
S D
a sudden change of head in a well.
T dt r dr dr
3.1.8 storage coeffıcient—the volume of water an aquifer
where:
releases from or takes into storage per unit surface area of the
h = hydraulic head,
aquifer per unit change in head. For a confined aquifer, the
T = aquifer transmissivity, and
storage coefficient is equal to the product of specific storage
S = storage coefficient.
and aquifer thickness. For an unconfined aquifer, the storage
4.2.1 The initial condition is at t =0 and h = h and the
coefficient is approximately equal to the specific yield.
o
outer boundary condition is as r→∞ and h→ h .
o
3.1.9 transmissivity—the volume of water at the existing
kinematic viscosity that will move in a unit time under a unit 4.3 The flow rate balance on the well bore relates the
hydraulic gradient through a unit width of the aquifer.
displacementofthewaterlevelinthewell-risertotheflowinto
the well:
3.1.10 underdamped well response—response characterized
by the water level oscillating about the static water level
dw ] h
πr 52πr T (2)
U U
c s
following a sudden change in water level (See for comparison
dt ]r
r5r
s
overdamped well response.)
where:
3.1.11 For definitions of other terms used in this test
r = radius of the well casing, and
c
method, see Terminology D653.
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
is given by Kipp (2).The expression for the effective length of
2m
dt
the water column from Cooper et al (3) is given as 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].
o shown in Fig. 1.
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
−1
described as an exponentially damped cyclic fluctuation that
3.2.15 γ—damping constant [T ].
decays exponentially. The water-level fluctuation would then
3.2.16 τ—wavelength [T].
−1 be given by:
3.2.17 ω—angular frequency [T ].
2γt
3.2.18 m—aquifer thickness, [L]. w ~t! 5 w e cos wt (4)
o
5.1.1 The following solution is given by van der Kamp (1).
4. Summary of Test Method
4.1 This test method describes the analytical procedure for
2 1/2 2 1/2
2r g/L 1n[0.79r S/T g/L
~ ! ~ !~ !
c s
d 5 (5)
analyzing data collected during an instantaneous head (slug)
8T
test using a well in which the response is underdamped. The
field procedures in conducting a slug test are given in Test that may be written as:
MethodD4044.Theanalyticalprocedureconsistsofanalyzing
T 5 b1a 1nT (6)
the response of water level in the well following the change in
water level induced in the well. where:
D5785−95 (2006)
6.2.1 The average water velocity in the well is approxi-
mately 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 chang-
ing from radial flow through the screen to vertical flow in the
well are negli
...
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