ASTM D5785-95(2000)

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Designation: D 5785 – 95 (Reapproved 2000)
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope (2) when the damping parameter values are less than about 0.2
andtimegreaterthanthatofthefirstpeakoftheoscillation (2).
1.1 This test method covers determination of transmissivity
1.5 This standard does not purport to address all of the
from the measurement of the damped oscillation about the
safety concerns, if any, associated with its use. It is the
equilibrium water level of a well-aquifer system to a sudden
responsibility of the user of this standard to establish appro-
change of water level in a well. Underdamped response of
priate safety and health practices and determine the applica-
water level in a well to a sudden change in water level is
bility of regulatory limitations prior to use.
characterized by oscillatory fluctuation about the static water
level with a decrease in the magnitude of fluctuation and
2. Referenced Documents
recovery to initial water level. Underdamped response may
2.1 ASTM Standards:
occur in wells tapping highly transmissive confined aquifers
D653 Terminology Relating to Soil, Rock, and Contained
and in deep wells having long water columns.
Fluids
1.2 Thisanalyticalprocedureisusedinconjunctionwiththe
D4043 Guide for Selection of Aquifer-Test Method in
field procedureTest Method D4044 for collection of test data.
Determining of Hydraulic Properties by Well-Techniques
1.3 Limitations—Slug tests are considered to provide an
D4044 TestMethodfor(FieldProcedurefor)Instantaneous
estimate of transmissivity of a confined aquifer. This test
Change in Head (Slug Test) for Determining Hydraulic
method requires that the storage coefficient be known. As-
Properties of Aquifers
sumptionsofthistestmethodprescribeafullypenetratingwell
D4750 Test Method for Determining Subsurface Liquid
(a well open through the full thickness of the aquifer), but the
Levels in a Borehole or Monitoring Well (Observation
slug test method is commonly conducted using a partially
Well)
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
considered to be representative of the average hydraulic
below by confining beds and in which the static head is above
conductivity of the portion of the aquifer adjacent to the open
the top of the aquifer.
interval of the well. The method assumes laminar flow and is
3.1.2 confining bed—a hydrogeologic unit of less perme-
applicable for a slug test in which the initial water-level
able material bounding one or more aquifers.
displacement is less than 0.1 or 0.2 of the length of the static
3.1.3 controlwell—wellbywhichtheaquiferisstressed,for
water column.
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.
Amore rigorous analysis of the response of wells to a sudden
3.1.5 observation well—a well open to all or part of an
change in water level by Kipp (2) indicates that the method
aquifer.
presented by van der Kamp (1) matches the solution of Kipp
3.1.6 overdamped well response—characterized by the wa-
ter level returning to the static level in an approximately
exponential manner following a sudden change in water level.
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
(See for comparison underdamped well response.)
RockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWaterand
Vadose Zone Investigations.
Current edition approved Sept. 10, 1995. Published November 1995.
The boldface numbers given in parentheses refer to a list of references at the
end of the text. 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 5785
3.1.7 slug—avolumeofwaterorsolidobjectusedtoinduce
where:
a sudden change of head in a well.
h = hydraulic head,
3.1.8 storage coeffıcient—the volume of water an aquifer
T = aquifer transmissivity, and
releases from or takes into storage per unit surface area of the S = storage coefficient.
aquifer per unit change in head. For a confined aquifer, the
4.2.1 The initial condition is at t =0 and h = h and the
o
storage coefficient is equal to the product of specific storage outer boundary condition is as r→ ` and h→ h .
o
and aquifer thickness. For an unconfined aquifer, the storage
4.3 The flow rate balance on the well bore relates the
coefficient is approximately equal to the specific yield.
displacementofthewaterlevelinthewell-risertotheflowinto
3.1.9 transmissivity—the volume of water at the existing
the well:
kinematic viscosity that will move in a unit time under a unit
dw ]h
pr 52pr T (2)
hydraulic gradient through a unit width of the aquifer. U
c s
dt ]r
r5r
s
3.1.10 underdamped well response—responsecharacterized
by the water level oscillating about the static water level
where:
following a sudden change in water level (See for comparison r = radius of the well casing, and
c
overdamped well response.) w = displacement of the water level in the well from its
3.1.11 For definitions of other terms used in this test initial position.
method, see Terminology D653.
4.3.1 The third equation describing the system, relating
3.2 Symbols:Symbols and Dimensions: h and w, comes from a momentum balance of Bird et al (4) as
s
2 −1
3.2.1 T—transmissivity [L T ].
referenced in Kipp (2).
3.2.2 S—storage coefficient [ nd].
d
0 2 2 2
pr pv z 5 @– pv 1 p – p – pgm#pr (3)
3.2.3 L—effective length of water column, equal to L + *–m s d 2 1 2 s
c dt
2 2
( r /r ) (m/2).
c s
where:
3.2.3.1 Discussion—Thisexpressionfortheeffectivelength
v = velocity in the well screen interval,
is given by Kipp (2).The expression for the effective length of
m = aquifer thickness,
the water column from Cooper et al (3) is given as L +3/8L
c s
p = pressure,
andassumesthatthewellscreenandwellcasinghavethesame
r = fluid density,
diameter.
g = gravitational acceleration, and
3.2.4 L —length of water column within casing [L].
c
r = well screen radius. Well and aquifer geometry are
s
3.2.5 L —length of water column within well screen [L].
s
shown in Fig. 1.
−2
3.2.6 g—acceleration of gravity [ LT ].
Atmospheric pressure is taken as zero.
3.2.7 h—hydraulic head in the aquifer [L].
3.2.8 h —initial hydraulic head in the aquifer [L].
o
5. Solution
3.2.9 h —hydraulic head in the well screen [L].
s
5.1 The method of van der Kamp (1) assumes the water
3.2.10 r —radius of well casing [L].
c
level response to a sudden change for the underdamped case,
3.2.11 r —radius of well screen [L].
s
except near critical damping conditions, can be approximately
3.2.12 t—time [T].
described as an exponentially damped cyclic fluctuation that
3.2.13 w—water level displacement from the initial static
decays exponentially. The water-level fluctuation would then
level [L].
be given by:
3.2.14 w —initial water level displacement [L].
o
−1
–gt
3.2.15 g—damping constant [T ].
w~t! 5 w e cos wt (4)
o
3.2.16 t—wavelength [ T].
5.1.1 The following solution is given by van der Kamp (1).
−1
3.2.17 v—angular frequency [T ].
3.2.18 m—aquifer thickness, [ L].
2 1/2 2 1/2
–r ~g/L! 1n@0.79r ~S/T!~g/L!
c s
d 5 (5)
8T
4. Summary of Test Method
that may be written as:
4.1 This test method describes the analytical procedure for
analyzing data collected during an instantaneous head (slug)
T 5 b 1 a1nT (6)
test using a well in which the response is underdamped. The
where:
field procedures in conducting a slug test are given in Test
2 1/2
b 5 a1n 0.79 r S g/L! (7)
MethodD4044.Theanalyticalprocedureconsistsofanalyzing @ ~
s
the response of water level in the well following the change in
2 1/2
water level induced in the well.
r ~g/L!
c
a 5 (8)
4.2 Theory—Theequationsthatgoverntheresponseofwell
8d
to an instantaneous change in head are treated at length by
Kipp (2). The flow in the aquifer is governed by the following
1/2
d5g/~g/L! (9)
equation for cylindrical flow:
and
S dh 1 d dh
5 r (1) 2 2
S D
T dt r dr dr L 5 g/~v 1g ! (10)
D 5785
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
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