ASTM D5473-93(2000)
(Test Method)Standard Test Method for (Analytical Procedure for) Analyzing the Effects of Partial Penetration of Control Well and Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer
Standard Test Method for (Analytical Procedure for) Analyzing the Effects of Partial Penetration of Control Well and Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer
SCOPE
1.1 This test method covers an analytical solution for determining the horizontal and vertical hydraulic conductivity of an aquifer by analysis of the response of water levels in the aquifer to the discharge from a well that partially penetrates the aquifer.
1.2 Limitations -The limitations of the technique for determination of the horizontal and vertical hydraulic conductivity of aquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this test method.
1.3 The values stated in either inch-pound or SI units are to be regarded separately as the standard. The values given in parentheses are for information only.
1.4 This standard does not purport to address all of the safety problems, 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.
General Information
Relations
Buy Standard
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.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: D 5473 – 93 (Reapproved 2000)
Standard Test Method for
(Analytical Procedure for) Analyzing the Effects of Partial
Penetration of Control Well and Determining the Horizontal
and Vertical Hydraulic Conductivity in a Nonleaky Confined
Aquifer
This standard is issued under the fixed designation D5473; 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 3. Terminology
1.1 This test method covers an analytical solution for 3.1 Definitions:
determining the horizontal and vertical hydraulic conductivity 3.1.1 aquifer, confined—an aquifer bounded above and
of an aquifer by analysis of the response of water levels in the below by confining beds and in which the static head is above
aquifertothedischargefromawellthatpartiallypenetratesthe the top of the aquifer.
aquifer. 3.1.2 confining bed—a hydrogeologic unit of less perme-
1.2 Limitations—The limitations of the technique for deter- able material bounding one or more aquifers.
mination of the horizontal and vertical hydraulic conductivity 3.1.3 control well—well by which the head and flow in the
ofaquifersareprimarilyrelatedtothecorrespondencebetween aquifer is changed, for example, by pumping, injection, or
the field situation and the simplifying assumption of this test imposing a constant change of head.
method. 3.1.4 drawdown—vertical distance the static head is low-
1.3 The values stated in either inch-pound or SI units are to ered due to the removal of water.
be regarded separately as the standard. The values given in 3.1.5 hydraulic conductivity—(field aquifer tests), the vol-
parentheses are for information only. umeofwaterattheexistingkinematicviscositythatwillmove
1.4 This standard does not purport to address all of the in a unit time under a unit hydraulic gradient through a unit
safety problems, if any, associated with its use. It is the area measured at right angles to the direction of flow.
responsibility of the user of this standard to establish appro- 3.1.6 observation well—a well open to all or part of an
priate safety and health practices and determine the applica- aquifer.
bility of regulatory limitations prior to use. 3.1.7 piezometer—a device so constructed and sealed as to
measure hydraulic head at a point in the subsurface.
2. Referenced Documents
3.1.8 specific storage—the volume of water released from
2.1 ASTM Standards:
ortakenintostorageperunitvolumeoftheporousmediumper
D653 Terminology Relating to Soil, Rock, and Contained unit change in head.
Fluids
3.1.9 storage coeffıcient—the volume of water an aquifer
D4050 Test Method for (Field Procedure for) Withdrawal releases from or takes into storage per unit surface area of the
and Injection Well Tests for Determining Hydraulic Prop-
aquifer per unit change in head.
erties of Aquifer Systems 3.1.10 transmissivity—the volume of water at the existing
D4105 Test Method for (Analytical Procedure for) Deter-
kinematic viscosity that will move in a unit time under a unit
mining Transmissivity and Storativity of Nonleaky Con- hydraulic gradient through a unit width of the aquifer.
fined Aquifers by the Modified Theis Nonequilibrium
3.1.11 unconfinedaquifer—anaquiferthathasawatertable.
Method 3.1.12 For definitions of other terms used in this test
D4750 Test Method for Determining Subsurface Liquid
method, see Terminology D653.
Levels in a Borehole or Monitoring Well (Observation 3.2 Symbols:Symbols and Dimensions:
2 1/2
Well)
3.2.1 a [nd]—( K /K ) .
z r
3.2.2 b [L]—thickness of aquifer.
3.2.3 d [L]—distance from top of aquifer to top of screened
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
interval of control well.
RockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWaterand
3.2.4 d8[L]—distancefromtopofaquifertotopofscreened
Vadose Zone Investigations.
Current edition approved Nov. 15, 1993. Published January 1994. interval of observation well.
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 5473
3.2.5 f [nd]—dimensionless drawdown factor. 4. Summary of Test Method
s
−1
3.2.6 K [LT ]—hydraulic conductivity.
4.1 This test method uses the deviations in drawdown near
−1
3.2.7 K [LT ]—hydraulic conductivity in the plane of the apartiallypenetratingcontrolwellfromthosethatwouldoccur
r
aquifer, radially from the control well.
near a control well fully penetrating the aquifer. These devia-
−1
tions occur when a well partially penetrating the aquifer is
3.2.8 K [LT ]—hydraulic conductivity normal to the
z
pumped because water levels are drawn down more near the
plane of the aquifer.
levelofthescreen,andlessatlevelssomewhataboveorbelow
3.2.9 K — modified Bessel function of the second kind and
the screened interval, than they would be if the pumped well
zero order.
fully penetrated the aquifer. These effects are shown in Fig. 1
3.2.10 l [L]—distance from top of aquifer to bottom of
by comparing drawdown and flow lines for fully penetrating
screened interval of control well.
and partially penetrating control wells in an isotropic aquifer.
3.2.11 l8 [L]—distance from top of aquifer to bottom of
Drawdown deviations due to partial penetration are amplified
screened interval of observation well.
when the vertical permeability is less than the horizontal
3 −1
3.2.12 Q [L T ]—discharge.
permeability, as often occurs in stratified sediments (1).
3.2.13 r [L]—radial distance from control well.
Hantush (2) has shown that at a distance, r, from the control
3.2.14 r — distance from pumped well at which an ob-
c well the drawdown deviation due to pumping a partially
served drawdown deviation, ds, would occur in the equivalent
penetrating well at a constant rate is the same as that at a
1/2
isotropic aquifer.
distance r (K /K ) if the aquifers were transformed into an
z r
3.2.15 S [nd]—storage coefficient.
equivalent isotropic aquifer.
3.2.16 s [L]—drawdown. 4.2 Solutions—Solutions are given by Hantush (2) for the
−1
drawdown near a partially penetrating control well being
3.2.17 S [L ]—specific storage.
s
2 −1
pumped at a constant rate and tapping a homogeneous,
3.2.18 T [L T ]—transmissivity.
isotropic artesian aquifer:
3.2.19 u [nd]—(r S)/(4 Tt).
Q
3.2.20 W(u)[nd]—anexponentialintegralknowninhydrol-
s 5 @W~u! 1 f # (1)
s
4pT
ogy as the well function of u.
where:
3.2.21 W(u, f )—partial-penetration control well function.
s
3.2.22 ds [L]—drawdown deviation due to partial penetra-
tion from that given by equations for purely radial flow.
3.2.23 z [L]—distance from top of aquifer to bottom of
The boldface numbers in parentheses refer to a list of references at the end of
piezometer. the text.
NOTE 1—Solid lines are for a well screened in the bottom three tenths of the aquifer; dashed lines are for a well screened the full thickness.
FIG. 1 Vertical Section Showing Drawdown Lines and Approximate Flow Paths Near a Pumped Well in an Ideal Artesian Aquifer
D 5473
2y
drawdown caused by partial penetration of the control well.
` e
W~u! 5 dy (2)
*
y This term is designated as the drawdown deviation by Weeks
u
(1) and is given by:
and f is the dimensionless drawdown correction factor. The
s
function [ W (u)+ f ] in Eq 1 can be referred to as the partial Q
s
ds 5 f (7)
s
4pT
penetration well function.
4.2.1 The dimensionless drawdown correction factor for a
4.2.4 Theeffectsofpartialpenetrationneedtobeconsidered
piezometer is given by:
for ar/b<1.5.Thereisaresponsecurveforeachvalueof ar/b,
ar l d z d/b, l/b, and either z/b for piezometers, or l8/ b and d8/b for
f 5 f u, , , , (3)
S D
s
b b b b
observation wells.Atable of dimensionless drawdown factors
` forpiezometersfromWeeks (1)isgiveninTable1covering56
2b 1 npl npd npz npar
5 sin 2sin cos W u,
( S D S D
different partial-penetration situations. A graph of one of the
p l 2 d! n b b b b
~
n 51
many families of curves showing the dimensionless drawdown
and the solution for the dimensionless drawdown correction
factor f versus ar/b for a control well screened, or open, from
s
factor for an observation well is given by:
z =0.6b to z =0.9b for various values of piezometer penetra-
ar l d l8 d8
tion, z/b, is shown in Fig. 3. Because of the even greater
f 5 f u, , , , , (4)
S D
s
b b b b b
number of possible drawdown factors for observation wells,
2 `
drawdown correction factors for wells are not tabulated.
2b 1 npl npd
5 ~l8 2 d8! sin 2sin
( S D
2 2
b b
p ~l 2 d! n 51 n
5. Significance and Use
npl8 npd8 npar
sin 2sin W u,
S D S D
5.1 Assumptions:
b b b
5.1.1 Control well discharges at a constant rate, Q.
where:
5.1.2 Control well is of infinitesimal diameter and partially
x
penetrates the aquifer.
expS 2y 2 D
` 4y
W m, x 5 dy (5) 5.1.3 The nonleaky artesian aquifer is homogeneous, and
~ !
*
u y
aerially extensive. The aquifer may also be anisotropic and, if
The hydrogeologic conditions and symbols used in connec-
so, the directions of maximum and minimum hydraulic con-
tion with piezometer and well geometries are shown in Fig. 2.
ductivityarehorizontalandvertical,respectively.Themethods
2 2
4.2.2 For large values of time, that is, for t > b S/(2a T)or
may be used to analyze tests on unconfined aquifers under
t > bS/(2K ), the effects of partial penetration are constant in
z
conditions described in a following section.
time, and W(u, (npar)/b)) can be approximated by 2K
5.1.4 Discharge from the well is derived exclusively from
0((npar)/b) (2). K is the modified Bessel function of the
storage in the aquifer.
second kind of order zero.
5.1.5 The geometry of the assumed aquifer and well condi-
4.2.3 Eq 1 can be written
tions are shown in Fig. 2.
Q Q
5.2 Implications of Assumptions—The vertical flow compo-
s 5 W~u! 1 f (6)
s
4pT 4pT
nents in the aquifer are induced by a control well that partially
The first term in Eq 6 is the drawdown in an isotropic penetrates the aquifer, that is, a well that is not open to the
homogeneous confined aquifer under radial flow, as given by aquifer through its full thickness. The effects of vertical flow
Theis (3). The second term is deviation from the Theis componentsaremeasuredinpiezometersnearthecontrolwell,
FIG. 2 Cross Section Through a Discharging Well That is Screened in a Part of a Nonleaky Aquifer
D 5473
5.3.3 The transmissivity decreases as a result of decreasing
thicknessoftheunconfinedaquifernearthecontrolwell.Jacob
(4)hasshownthattheeffectofdecreasingtransmissivityonthe
drawdown may be corrected by the equation:
s8 5 s 2 ~s /2b! (11)
where sistheobserveddrawdownand s8isthedrawdownin
an equivalent confined aquifer.
6. Apparatus
6.1 Apparatus for withdrawal tests is given in Test Method
D4050. The apparatus described as follows are those compo-
nents of the apparatus that require special attributes for this
specific test method.
6.2 Construction of Control Well—Screen the control well
through only part of the vertical extent of the aquifer to be
tested.Thescreenedintervalofthecontrolwellmustbeknown
as a function of aquifer thickness.
6.3 Construction and Placement of Piezometers and Obser-
vation Wells—The requirements for observation wells and
piezometers are related to the method of analysis to be used.
Two methods of analysis are prescribed in Section 8; the
observationwellandpiezometerrequirementsforeachmethod
are given as follows. The piezometers and observation wells
may be on the same or various radial lines from the control
FIG. 3 Graph of Dimension Less Drawdown Factor, f , versus
s
ar/b for a Pumped Well Screened from z = 0.66 to z =0.96 for
well.
Values of Piezometer Penetration, z/b
6.3.1 The type curve fitting methods require one or more
piezometers near the control well within the radial distance
that is, within a distance, r, in which vertical flow components affectedbyverticalflowcomponents.Thisdistanceisgivenby
1/2
are significant, that is:
r<1.5b/(K /K ) .Thedepthofthepiezometeropeningmust
z r
be known as a function of the aquifer thickness. Construction
r ,1.5b Kr/Kz (8)
=
ofpiezometersorwellsforaspecifictestshallbeidenticalwith
5.3 Application of Method to Unconfined Aquifers:
respect to distance from the top of the aquifer to the bottom of
5.3.1 Althoughtheassumptionsareapplicabletoartesianor
the piezometers or the screened interval of the wells.
confinedconditions,Weeks(1)haspointedoutthatthesolution
6.3.2 Method 1 of the drawdown deviation methods re-
may be applied to unconfined aquifers if drawdown is small
quires one or more piezometers or wells near the control well
compared with the saturated thickness of the aquifer or if the
withintheradialdistanceaffectedbyverticalflowcomponents.
drawdowniscorrectedforreductioninthicknessoftheaquifer,
The depth of these piezometers and the screened interval of
and the effects of delayed gravity response are small. The
wells must be known as a function of aquifer thickness.
effects of gravity response become negligible after a time as
Construction of piezometers or wells for a specific test within
given, for piezometers near the water table, by the equation:
the distance affected by vertical flow components shall be
bS
identical with respect to distance from the top of the aquifer to
y
t 5 (9)
K
z the bottom of the piezometers or the screened interval of the
wells.Inaddition,themethodrequirestwoormoreobservation
for values of ar/b < 0.4 and by the equation:
wellsorpiezometersatadistancefromthecontrolwellbeyond
bS r K
y z
the effect of vertical flow components.
t 5 S0.5 11.25 D (10)
Œ
K b K
z r
6.3.3 Method 2 of the drawdown deviation methods re-
for greater values of ar/b.
quires two or more piezometers within the radial distance
5.3.2 Drawdowninanunconfinedaquiferisalsoaffectedby
affected by vertical flow components. Construction of piezom-
curvature of the water table or free surface near the control
eters or wells for a specific test within the distance affected by
well,andbythedecreaseinsaturatedthickness,thatcausesthe
vertical flow components shall be identical with respect to
transmissivity to decline toward the control well. This test
distance from the top of the aquifer to the bottom of the
method should be applicable to analysis of tests on water-table
piezometers or the screened interval of the wells.
aquifers for which the control well is cased to a depth below
NOTE 1—The drawdown deviation methods were originated by Weeks
the pumping level and the drawdown in the control well is less
(1) who published tables of the drawdown correction factors for piezom-
than0.2
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.