ASTM D5881-95(2000)
(Test Method)Standard Test Method for (Analytical Procedure) Determining Transmissivity of Confined Nonleaky Aquifers by Critically Damped Well Response to Instantaneous Change in Head (Slug)
Standard Test Method for (Analytical Procedure) Determining Transmissivity of Confined Nonleaky Aquifers by Critically Damped Well Response to Instantaneous Change in Head (Slug)
SCOPE
1.1 This test method covers determination of transmissivity from the measurement of water-level response to a sudden change of water level in a well-aquifer system characterized as being critically damped or in the transition range from underdamped to overdamped. Underdamped response is characterized by oscillatory changes in water level; overdamped response is characterized by return of the water level to the initial static level in an approximately exponential manner. Overdamped response is covered in Guide D4043; underdamped response is covered in D5785.
1.2 The analytical procedure in this test method is used in conjunction with Guide D4043 and the field procedure in Test Method D4044 for collection of test data.
1.3 The values stated in SI units are to be regarded as standard.
1.4 Limitations--Slug tests are considered to provide an estimate of the transmissivity of an aquifer near the well screen. The method is applicable for systems in which the damping parameter, [zeta], is within the range from 0.2 through 5.0. The assumptions of the method prescribe a fully penetrating well (a well open through the full thickness of the aquifer) in a confined, nonleaky aquifer.
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 5881 – 95 (Reapproved 2000)
Standard Test Method for
(Analytical Procedure) Determining Transmissivity of
Confined Nonleaky Aquifers by Critically Damped Well
Response to Instantaneous Change in Head (Slug)
This standard is issued under the fixed designation D5881; 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 Change in Head (Slug Test) for Determining Hydraulic
Properties of Aquifers
1.1 This test method covers determination of transmissivity
D4750 Test Method for Determining Subsurface Liquid
from the measurement of water-level response to a sudden
Levels in a Borehole or Monitoring Well (Observation
changeofwaterlevelinawell-aquifersystemcharacterizedas
Well)
being critically damped or in the transition range from under-
D5785 Test Method (Analytical Procedure) for Determin-
damped to overdamped. Underdamped response is character-
ing Transmissivity of Confined Nonleaky Aquifers by
ized by oscillatory changes in water level; overdamped re-
Underdamped Well Response to Instantaneous Change in
sponseischaracterizedbyreturnofthewaterleveltotheinitial
Head (Slug Test)
static level in an approximately exponential manner. Over-
damped response is covered in Guide D4043; underdamped
3. Terminology
response is covered in D5785.
3.1 Definitions:
1.2 The analytical procedure in this test method is used in
3.1.1 aquifer, confined—an aquifer bounded above and
conjunction with Guide D4043 and the field procedure inTest
below by confining beds and in which the static head is above
Method D4044 for collection of test data.
the top of the aquifer.
1.3 The values stated in SI units are to be regarded as
3.1.2 confining bed—a hydrogeologic unit of less perme-
standard.
able material bounding one or more aquifers.
1.4 Limitations—Slug tests are considered to provide an
3.1.3 controlwell—awellbywhichtheheadandflowinthe
estimate of the transmissivity of an aquifer near the well
aquifer is changed by pumping, injecting, or imposing a
screen. The method is applicable for systems in which the
constant change of head.
dampingparameter, z,iswithintherangefrom0.2through5.0.
3.1.4 critically damped well response—characterizedbythe
The assumptions of the method prescribe a fully penetrating
water level responding in a transitional range between under-
well (a well open through the full thickness of the aquifer) in
damped and overdamped following a sudden change in water
a confined, nonleaky aquifer.
level.
1.5 This standard does not purport to address all of the
3.1.5 head, static—the height above a standard datum the
safety concerns, if any, associated with its use. It is the
surface of a column of water can be supported by the static
responsibility of the user of this standard to establish appro-
pressure at a given point.
priate safety and health practices and determine the applica-
3.1.6 observation well—a well open to all or part of an
bility of regulatory limitations prior to use.
aquifer.
2. Referenced Documents 3.1.7 overdamped well response—characterized by the wa-
ter level returning to the static level in an approximately
2.1 ASTM Standards:
exponential manner following a sudden change in water level.
D653 Terminology Relating to Soil, Rock, and Contained
(See for comparison underdamped well response.)
Fluids
3.1.8 slug—avolumeofwaterorsolidobjectusedtoinduce
D4043 Guide for Selection of Aquifer-Test Method in
a sudden change of head in a well.
Determining of Hydraulic Properties by Well Techniques
3.1.9 storage coeffıcient—the volume of water an aquifer
D4044 Test Method (Field Procedure) for Instantaneous
releases from or takes into storage per unit surface area of the
aquifer per unit change in head. For a confined aquifer, the
storagecoefficientisequaltotheproductofthespecificstorage
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
RockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWaterand and aquifer thickness.
Vadose Zone Investigations.
Current edition approved Dec. 10, 1995. Published April 1996.
2 3
Annual Book of ASTM Standards, Vol 04.08. Annual Book of ASTM Standards, Vol 04.09.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 5881 – 95 (2000)
3.1.10 transmissivity—the volume of water at the existing
S = storage coefficient.
kinematic viscosity that will move in a unit time under a unit
4.2.1 The initial condition is at t =0 and h = h , and the
o
hydraulic gradient through a unit width of the aquifer.
outer boundary condition is as r − andh−h .
o
3.1.11 underdamped well response—response characterized
4.2.1.1 An equation is given by Kipp (1) for the skin factor,
by the water level oscillating about the static water level
that is, the effect of aquifer damage during drilling of the well.
following a sudden change in water level (See for comparison
However, this factor is not treated by Kipp (1) and is not
overdamped-well response).
considered in this procedure.
3.1.12 For definitions of other terms used in this test
4.2.2 The flow rate balance on the well bore relates the
method, see Terminology D653.
displacementofthewaterlevelinthewellrisertotheflowinto
3.2 Symbols:Symbols and Dimensions:
the well:
2 −1
3.2.1 T—transmissivity [L T ].
dw dh
3.2.2 S—storage coefficient [ nd].
pr 52pr T | (2)
c s r 5 rs
dt dr
3.2.3 L—static water column length above top of aquifer
[L].
where:
3.2.4 L —effective length of water column in a well, equal
e
r = radius of the well casing, and
c
2 2
to L +(r /r )(b/2) [L].
w = displacement of the water level in the well from its
c c s
3.2.5 L —length of water column within casing [L].
c initial position.
3.2.6 L —length of water column within well screen [L].
s
4.2.3 The fourth equation describing the system relating h
s
−2
3.2.7 g—acceleration of gravity [ LT ].
and w,comesfromamomentumbalanceequationofBirdetal
3.2.8 h—hydraulic head in the aquifer [L].
(2) as referenced in Kipp (1):
3.2.9 h —initial hydraulic head in the aquifer [L].
o
d 0
2 2 2
3.2.10 h —hydraulic head in the well screen [L].
pr pvdz 5 –pv 1 p 2 p 2rgb pr (3)
~ !
s * s 2 1 2 s
dt
–b
3.2.11 r —radius of well casing [L].
c
3.2.12 r —radius of well screen [L].
where:
s
3.2.13 t—time [T]. v = velocity in the well screen interval,
3.2.14 t8—dimensionless time [ nd]. b = aquifer thickness,
p = pressure,
3.2.15 t—dimensionless time [ nd].
r = fluid density,
3.2.16 w—water level displacement from the initial static
g = gravitational acceleration, and
level [L].
r = well screen radius.
s
3.2.17 w —initial water level displacement [L].
o
Thenumericalsubscriptsrefertotheplanesdescribedabove
3.2.18 a—dimensionless storage parameter [nd].
and shown in Fig. 1. Atmospheric pressure is taken as zero.
3.2.19 b—dimensionless inertial parameter [nd].
−1
3.2.20 g—damping constant [ T ].
5. Solution
3.2.21 t—wavelength [ T].
−1
3.2.22 v—angular frequency [T ].
5.1 Kipp (1) derives the following differential equation to
3.2.23 z—dimensionless damping factor [nd].
representfortheresponseofthedisplacementofwaterlevelin
the well:
4. Summary of Test Method
d w g g
4.1 This test method describes the analytical procedure for
1 w 5 / L (4)
S D
2 e
L
~h 2 h !
dt e
s o
analyzing data collected during an instantaneous head (slug)
test for well and aquifer response at and near critical damping.
where:
Procedures in conducting a slug test are given in Test Method
L = effective water column length, defined as:
e
D4044. The analytical procedure consists of analyzing the
2 2
L 5 L 1 r /r b/2 (5)
~ !~ !
e c s
response of water level in the well following the change in
water level induced in the well.
where:
4.2 Theory—Theequationsthatgoverntheresponseofwell
b = aquifer thickness with initial conditions:
to an instantaneous change in head are treated at length by
4 at t 50, w 5 w (6)
o
Kipp (1). Theflowintheaquiferisgovernedbythefollowing
dw/dt 5 w * (7)
equation for cylindrical flow:
o
h 5 L 5 h (8)
S dh 1 d dh s o
5 r (1)
S D
T dt r dr dr
5.2 Kipp (1) introduces dimensionless variables and param-
eters in converting these equations to dimensionless form,
where:
solves the equations by Laplace transforms, and inverts the
h = hydraulic head,
solution by a Laplace-transform-inversion algorithm.
T = aquifer transmissivity, and
5.2.1 The following dimensionless parameters are among
those given by Kipp (1):
dimensionless water-level displacement:
The boldface numbers in parentheses refer to a list of references at the end of
the text. w852w/w (9)
o
D 5881 – 95 (2000)
FIG. 2 Slug-Test Data Overlaid on Type Curves for Three Different
Damping Factors, Modified from Kipp (1)
and dimensionless damping factor:
a~s1¼1nb!
z5 (17)
½
2b
5.3 For z less than one, the system is underdamped; for z
greaterthanone,thesystemisoverdamped.For zequaltoone,
thesystemiscriticallydamped,yettheinertialeffectsarequite
important (1). For z greater than about five, the system
responds as if the inertial effects can be neglected and the
solution of Cooper et al (3) (given in Guide D4043) is
applicable. For z about 0.2 or less, the approximate solution of
vander Kamp (4) is valid (given in Test Method D5785). The
solution of Kipp (1), the subject of this test method, is
applicable for the transition zone between systems that are
underdamped and overdamped. Solutions are given here for z
ranging from 0.2 to 5.0.
FIG. 1 Well and Aquifer Geometry from Kipp (1)
6. Significance and Use
dimensionless time:
6.1 The assumptions of the physical system are given as
follows:
t8 5 ~tT!/ ~r S! (10)
s
6.1.1 Theaquiferisofuniformthickness,withimpermeable
and:
upper and lower confining boundaries.
½
ˆ
t 5 t8/b (11)
6.1.2 The aquifer is of constant homogeneous porosity and
matrix compressibility and constant homogeneous and isotro-
dimensionless storage:
pic hydraulic conductivity.
2 2
a5 ~r ! ~2r S! (12)
c s
6.1.3 The origin of the cylindrical coordinate system is
dimensionless inertial parameter:
taken to be on the well-bore axis at the top of the aquifer.
2 2
6.1.4 The aquifer is fully screened.
b5 ~Le/ g!~T/ ~r S!! (13)
s
6.1.5 The well is 100% efficient, that is, the skin factor, f,
dimensionless skin factor:
and dimensionless skin factor, s, are zero.
s5 f/r (14)
s 6.2 The assumptions made in defining the momentum bal-
ance are as follows:
dimensionless frequency parameter:
6.2.1 The average water velocity in the well is approxi-
2 ½
@2d ~s1¼1nb! 14b]
mately constant over the well-bore section.
v5 (15)
2b
6.2.2 Frictional head losses from flow in the well are
dimensionless decay parameter:
negligible.
a~s1¼1nb! 6.2.3 Flow through the well screen is uniformly distributed
g5 (16)
2b over the entire aquifer thickness.
D 5881 – 95 (2000)
TABLE 2 Values of the Dimensionless Water Level Displacement,
6.2.4 Change in momentum from the water velocity chang-
w*, Versus Dimensionless Time, t, for Construction of Type
ing from radial flow through the screen to vertical flow in the
Curves, z = 0.2 and a = 19976
well are negligible.
tw8 tw8
3.162278E−02 −9.994902E−01 3.162278E + 00 4.939368E−
7. Procedure
3.636619E−02 −9.993263E−01 3.636619E + 00 4.349310E−
7.1 The overall procedure consists of conducting the slug
3.952847E−02 −9.992107E−01 3.952847E + 00 3.465758E−
4.269075E−02 −9.990815E−01 4.269075E + 00 2.343067E−
test field procedure (see Test Method D4044) and analysis of
4.743416E−02 −9.988695E−01 4.743416E + 00 5.160353E−
the field data using this test method.
5.375872E−02 −9.985520E−01 5.375872E + 00 −1.543438E−
6.324555E−02 −9.980024E−01 6.324555E + 00 −2.671865E−
NOTE 1—The initial displacement of water level should not exceed 0.1
7.115125E−02 −9.974810E−01 7.115125E + 00 −1.818502E−
or 0.2 of the static water column in the well, the measurement of
7.905694E−02 −9.968908E−01 7.905694E + 00 −2.600650E−
displacement should be within 1% of the initial water-level displacement
8.696264E−02 −9.962437E−01 8.696264E + 00 9.764360E−
9.486833E−02 −9.955360E−01 9.486833E + 00 1.324266E−
and the water-level displacement needs to be calculated independently.
1.106797E−01 −9.939399E−01 1.106797E + 01 3.871680E−
1.264911E−01 −9.921040E−01 1.264911E + 01 −7.304361E−
8. Calculation and Interpretation of Results
1.423025E−01 −9.900304E−01 1.423025E + 01 −3.623751E−
8.1 Plotthenormalizedwater-leveldisplacementinthewell
1.581139E−01 −9.877207E−01 1.581139E + 01 3.430765E−
1.739253E−01 −9.851770E−01 1.739253E + 01 −2.397516E−
versus the logarithm of time.
1.897367E−01 −9.824014E−01 1.897367E + 01 −2.051297E−
8.2 PrepareasetoftypecurvesfromTables1-10byplotting
2.213594E−01 −9.761622E−01 2.213594E + 01 8.187383E−
dimensionlesswaterleveldisplacement, w8,versusdimension-
2.529822E−01 −9.690205E−01 2.529822E + 01 −6.259136E−
2.846050E−01 −9.609942E−01 2.846050E + 01 1.402892E−
ˆ
less time, t, using the same scale as in plotting the observed
3.162278E−01 −9.521021E−01 3.162278E + 01 −2.331164E−
water-level displacement.
3.636619E−01 −9.371834E−01 3.636619E + 01 −1.031248E−
3.952847E−01 −9.262139E−01 3.952847E + 01 −7.347959E−
8.3 Match the semilog plot of water-level displacement to
4.269075E−01 −9.105352E−01 4.269075E + 01 −8.050596E−
the type curves by translation of the time axis.
4.743416E−01 −8.975464E−01 4.743416E + 01 −6.352422E−
5.375872E−01 −8.673412E−01 5.375872E + 01 −5.870822E−
6.324555E−01 −8.201831E−01 6.324555E + 01 −5.087767E−
7.115125E−01 −7.766091E−01 7.115125E + 01 −4.500425E−
TABLE 1 Values of the Dimensionless Water Level Displacement,
7.905694E−01 −7.295735E−01 7.905694E + 01 −4.046973E−
w*, Versus Dimensionless Time, t, for Construction of Type
8.696264E−01 −6.794859E−01 8.696264E + 01 −3.675505E−
Curves, z = 0.1 and a = 9988.1
9.486833E−01 −6.267637E−01 9.486833E + 01 −3.366208E−
tw8 tw8
1.106797E + 00 −5.151022E−01 1.106797E + 02 −2.881191E−
1.264911E + 00 −3.979593E−01 1.264911E + 02 −2.518280E−
3.162278E−02 −9.994887E−01 3.162278E + 00 7.100277E−01
1.423025E + 00 −2.786373E−01 1.423025E + 02 −2.236385E−
3.636619E−02 −9.993281E−01 3.636619E + 00 6.204110E−01
1.581139E + 00 −1.602887E−01 1.581139E + 02 −2.011471E−
3.952847E−02 −9.992086E−01 3.952847E + 00 4.871206E−01
1.739253E + 00 −3.860371E−02 1.739253E + 02 −1.827551E−
4.269075E−02 −9.990793E−01 4.269075E + 00 3.138511E−01
1.897367E + 00 6.204784E−02 1.897367E + 02 −1.674534E−
4.743416E−02 −9.988666E−01 4.743416E + 00 2.218683E−02
2.213594E + 00 2.492937E−01 2.213594E + 02 −1.434090E−
5.375872E−02 −9.985483E−01 5.3758
...
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