ASTM D5473-93(2006)
(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of Control Well and Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer (Withdrawn 2015)
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of Control Well and Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer (Withdrawn 2015)
SIGNIFICANCE AND USE
Assumptions:
Control well discharges at a constant rate, Q.
Control well is of infinitesimal diameter and partially penetrates the aquifer.
The nonleaky artesian aquifer is homogeneous, and aerially extensive. The aquifer may also be anisotropic and, if so, the directions of maximum and minimum hydraulic conductivity are horizontal and vertical, respectively. The methods may be used to analyze tests on unconfined aquifers under conditions described in a following section.
Discharge from the well is derived exclusively from storage in the aquifer.
The geometry of the assumed aquifer and well conditions are shown in Fig. 2.
Implications of Assumptions—The vertical flow components in the aquifer are induced by a control well that partially penetrates the aquifer, that is, a well that is not open to the aquifer through its full thickness. The effects of vertical flow components are measured in piezometers near the control well, that is, within a distance, r, in which vertical flow components are significant, that is:
Application of Method to Unconfined Aquifers:
Although the assumptions are applicable to artesian or confined conditions, Weeks (1) has pointed out that the solution may be applied to unconfined aquifers if drawdown is small compared with the saturated thickness of the aquifer or if the drawdown is corrected for reduction in thickness of the aquifer, and the effects of delayed gravity response are small. The effects of gravity response become negligible after a time as given, for piezometers near the water table, by the equation:
for values of ar/b 0.4 and by the equation:
for greater values of ar/b.
Drawdown in an unconfined aquifer is also affected by curvature of the water table or free surface near the control well, and by the decrease in saturated thickness, that causes the transmissivity to decline toward the control well. This test method should be applicable to analysis of tests on water-table aquifers for whic...
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.
WITHDRAWN RATIONALE
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.
Formerly under the jurisdiction of Committee D18 on Soil and Rock, this test method was withdrawn in July 2015 in accordance with section 10.6.3 of the Regulations Governing ASTM Technical Committees, which requires that standards shall be updated by the end of the eighth year since the last approval date.
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Designation:D5473 −93(Reapproved 2006)
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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope leaky ConfinedAquifers by the Modified Theis Nonequi-
librium Method
1.1 This test method covers an analytical solution for
determining the horizontal and vertical hydraulic conductivity
3. Terminology
of an aquifer by analysis of the response of water levels in the
3.1 Definitions:
aquifertothedischargefromawellthatpartiallypenetratesthe
3.1.1 aquifer, confined—an aquifer bounded above and be-
aquifer.
lowbyconfiningbedsandinwhichthestaticheadisabovethe
1.2 Limitations—The limitations of the technique for deter-
top of the aquifer.
mination of the horizontal and vertical hydraulic conductivity
3.1.2 confining bed—ahydrogeologicunitoflesspermeable
ofaquifersareprimarilyrelatedtothecorrespondencebetween
material bounding one or more aquifers.
the field situation and the simplifying assumption of this test
method. 3.1.3 control well—well by which the head and flow in the
aquifer is changed, for example, by pumping, injection, or
1.3 The values stated in either inch-pound or SI units are to
imposing a constant change of head.
be regarded separately as the standard. The values given in
3.1.4 drawdown—vertical distance the static head is low-
parentheses are for information only.
ered due to the removal of water.
1.4 This standard does not purport to address all of the
3.1.5 hydraulic conductivity—(field aquifer tests), the vol-
safety problems, if any, associated with its use. It is the
umeofwaterattheexistingkinematicviscositythatwillmove
responsibility of the user of this standard to establish appro-
in a unit time under a unit hydraulic gradient through a unit
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use. area measured at right angles to the direction of flow.
3.1.6 observation well—a well open to all or part of an
2. Referenced Documents
aquifer.
2.1 ASTM Standards:
3.1.7 piezometer—a device so constructed and sealed as to
D653Terminology Relating to Soil, Rock, and Contained
measure hydraulic head at a point in the subsurface.
Fluids
3.1.8 specific storage—the volume of water released from
D4050Test Method for (Field Procedure) for Withdrawal
ortakenintostorageperunitvolumeoftheporousmediumper
and Injection Well Testing for Determining Hydraulic
unit change in head.
Properties of Aquifer Systems
3.1.9 storage coeffıcient—the volume of water an aquifer
D4105Test Method for (Analytical Procedure) for Deter-
releases from or takes into storage per unit surface area of the
mining Transmissivity and Storage Coefficient of Non-
aquifer per unit change in head.
3.1.10 transmissivity—the volume of water at the existing
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
kinematic viscosity that will move in a unit time under a unit
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
hydraulic gradient through a unit width of the aquifer.
Vadose Zone Investigations.
Current edition approved Sept. 15, 2006. Published October 2006. Originally
3.1.11 unconfined aquifer—anaquiferthathasawatertable.
approved in 1993. Last previous edition approved in 2000 as D5473–93(2000).
DOI: 10.1520/D5473-93R06.
3.1.12 For definitions of other terms used in this test
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
method, see Terminology D653.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.2 Symbols and Dimensions:
Standards volume information, refer to the standard’s Document Summary page on
1/2
the ASTM website. 3.2.1 a [nd]—(K /K ) .
z r
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5473−93 (2006)
3.2.2 b [L]—thickness of aquifer. 3.2.20 W(u) [nd]—an exponential integral known in hydrol-
ogy as the well function of u.
3.2.3 d [L]—distance from top of aquifer to top of screened
interval of control well. 3.2.21 W(u, f )—partial-penetration control well function.
s
3.2.4 d'[L]—distancefromtopofaquifertotopofscreened
3.2.22 δs [L]—drawdown deviation due to partial penetra-
interval of observation well.
tion from that given by equations for purely radial flow.
3.2.23 z [L]—distance from top of aquifer to bottom of
3.2.5 f [nd]—dimensionless drawdown factor.
s
piezometer.
−1
3.2.6 K [LT ]—hydraulic conductivity.
−1
3.2.7 K [LT ]—hydraulic conductivity in the plane of the
4. Summary of Test Method
r
aquifer, radially from the control well.
4.1 This test method uses the deviations in drawdown near
−1
3.2.8 K [LT ]—hydraulicconductivitynormaltotheplane
z apartiallypenetratingcontrolwellfromthosethatwouldoccur
of the aquifer.
near a control well fully penetrating the aquifer. These devia-
tions occur when a well partially penetrating the aquifer is
3.2.9 K — modified Bessel function of the second kind and
zero order. pumped because water levels are drawn down more near the
levelofthescreen,andlessatlevelssomewhataboveorbelow
3.2.10 l [L]—distance from top of aquifer to bottom of
the screened interval, than they would be if the pumped well
screened interval of control well.
fully penetrated the aquifer. These effects are shown in Fig. 1
3.2.11 l' [L]—distance from top of aquifer to bottom of
by comparing drawdown and flow lines for fully penetrating
screened interval of observation well.
and partially penetrating control wells in an isotropic aquifer.
3 −1
3.2.12 Q [L T ]—discharge.
Drawdown deviations due to partial penetration are amplified
when the vertical permeability is less than the horizontal
3.2.13 r [L]—radial distance from control well.
permeability, as often occurs in stratified sediments (1).
3.2.14 r —distancefrompumpedwellatwhichanobserved
c
Hantush (2) has shown that at a distance, r, from the control
drawdown deviation, δs, would occur in the equivalent isotro-
well the drawdown deviation due to pumping a partially
pic aquifer.
penetrating well at a constant rate is the same as that at a
3.2.15 S [nd]—storage coefficient. 1/2
distance r(K /K ) if the aquifers were transformed into an
z r
3.2.16 s [L]—drawdown.
equivalent isotropic aquifer.
−1
3.2.17 S [L ]—specific storage.
s
2 −1
3.2.18 T [L T ]—transmissivity.
The boldface numbers in parentheses refer to a list of references at the end of
3.2.19 u [nd]—(r S)/(4 Tt). thetext.
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. 1Vertical Section Showing Drawdown Lines and Approximate Flow Paths Near a Pumped Well in an Ideal Artesian Aquifer
D5473−93 (2006)
2 2
4.2 Solutions—Solutions are given by Hantush (2) for the 4.2.2 For large values of time, that is, for t > b S/(2a T)or
drawdown near a partially penetrating control well being t > bS/(2K ), the effects of partial penetration are constant in
z
pumped at a constant rate and tapping a homogeneous, time, and W(u, (nπar)/b)) can be approximated by
isotropic artesian aquifer: 2K ((nπar)/b) (2). K is the modified Bessel function of the
0 0
second kind of order zero.
Q
s 5 @W~u!1f # (1)
s 4.2.3 Eq 1 can be written
4πT
Q Q
where:
s 5 W u 1 f (6)
~ !
s
4πT 4πT
`
2y
e
W u 5 dy (2)
~ ! *
The first term in Eq 6 is the drawdown in an isotropic
y
u
homogeneous confined aquifer under radial flow, as given by
and f is the dimensionless drawdown correction factor. The
Theis (3). The second term is deviation from the Theis
s
function [ W(u)+ f ]in Eq 1 can be referred to as the partial drawdown caused by partial penetration of the control well.
s
penetration well function.
This term is designated as the drawdown deviation by Weeks
4.2.1 The dimensionless drawdown correction factor for a (1) and is given by:
piezometer is given by:
Q
δs 5 f (7)
s
ar l d z
4πT
f 5 f u, , , , (3)
S D
s
b b b b
4.2.4 Theeffectsofpartialpenetrationneedtobeconsidered
`
for ar/b<1.5.Thereisaresponsecurveforeachvalueof ar/b,
2b 1 nπl nπd nπz nπar
5 sin 2 sin cos W u,
S D S D
(
d/b, l/b, and either z/b for piezometers, or l'/ b and d'/b for
π~l 2 d! n b b b b
n51
observation wells.Atable of dimensionless drawdown factors
and the solution for the dimensionless drawdown correction
forpiezometersfromWeeks (1)isgiveninTable1covering56
factor for an observation well is given by:
different partial-penetration situations. A graph of one of the
ar l d l' d'
many families of curves showing the dimensionless drawdown
f 5 f u, , , , , (4)
S D
s
b b b b b
factor f versus ar/b for a control well screened, or open, from
s
z =0.6b to z =0.9b for various values of piezometer
`
2b 1 nπl nπd
penetration, z/b,isshowninFig.3.Becauseoftheevengreater
5 l'2d' sin 2 sin
~ ! S D
2 2
(
π l 2 d n b b
~ !
n51
number of possible drawdown factors for observation wells,
drawdown correction factors for wells are not tabulated.
nπl' nπd' nπar
sin 2 sin W u,
S D S D
b b b
5. Significance and Use
where:
5.1 Assumptions:
x
5.1.1 Control well discharges at a constant rate, Q.
`
exp 2y 2
S D
4y
W m, x 5 dy (5) 5.1.2 Control well is of infinitesimal diameter and partially
~ ! *
y
u
penetrates the aquifer.
The hydrogeologic conditions and symbols used in connec- 5.1.3 The nonleaky artesian aquifer is homogeneous, and
tion with piezometer and well geometries are shown in Fig. 2. aerially extensive. The aquifer may also be anisotropic and, if
FIG. 2 Cross Section Through a Discharging Well That is Screened in a Part of a Nonleaky Aquifer
D5473−93 (2006)
TABLE 1 Tabulated Values of the Dimensionless Drawdown Correction Factor
All values, including those for piezometer depth, are listed for percentages of the aquifer thickness, as measured from the top of the aquifer or from the pumped
well.
The f(s) values listed are for an isotropic aquifer. For an anisotropic aquifer the value of f(s) would be read as the value of r/b[Kz/Kr) ⁄2 ], expressed as a
percentage, equivalent to the r value listed.
Each of the tables listed below may also be used for the situation where values for the bottom and the top of the screen are reversed by reading the z value in the
table equivalent to (100 z) for the field situation. For example, the first table listed could also be used to determine values of fs for a well screened from the top of
the aquifer down to a depth equal to 90 % of the adapter thickness. If the piezometers penetrated 20 % of the aquifer thickness, the correction value for a given r/b
value would be found from the z = 80 listing.
Frequently it would be necessary to make a double or triple interpolation to use the data from these tables. Such interpolation probably would be best
accomplished from a plot of f(s) versus log r/b for each of the d/b, zw/b, and z/b values bounding the actual values of these parameters.
Bottom of Screen in Pumped Well is 100. Per Cent of Aquifer Thickness Below Top of Aquifer
Top of Screen in Pumped Well is 90. Per Cent of Aquifer Thickness Below Top of Aquifer
Piez. Depth Distance of Piezometer from Pumped Well, as Per Cent of Aquifer Thickness
5.00 10.00 15.00 20.00 25.00 30.00 40.00 50.00 60.00 80.00 100.00 120.00 150.00
0.0 −4.828 −3.457 −2.674 −2.134 −1.732 −1.421 −0.972 −0.673 −0.468 −0.229 −0.113 −0.056 −0.020
10. −4.785 −3.415 −2.633 −2.095 −1.696 −1.387 −0.944 −0.650 −0.451 −0.219 −0.219 −0.053 −0.019
20. −4.651 −3.284 −2.506 −1.976 −1.585 −1.284 −0.860 −0.584 −0.400 −0.191 −0.093 −0.046 −0.016
30. −4.408 −3.048 −2.280 −1.763 −1.388 −1.104 −0.715 −0.471 −0.315 −0.145 −0.069 −0.034 −0.012
40. −4.020 −2.674 −1.925 −1.434 −1.086 −0.833 −0.503 −0.312 −0.198 −0.085 −0.039 −0.018 −0.006
50. −3.415 −2.095 −1.387 −0.944 −0.650 −0.451 −0.219 −0.108 −0.053 −0.013 −0.003 −0.001 0.000
60. −2.444 −1.185 −0.566 −0.225 −0.035 0.067 0.138 0.135 0.111 0.063 0.033 0.017 0.006
70. −0.736 0.341 0.725 0.829 0.808 0.736 0.556 0.399 0.280 0.137 0.067 0.033 0.012
80. 2.897 3.170 2.791 2.312 1.875 1.511 0.983 0.648 0.432 0.199 0.095 0.046 0.016
90. 13.344 8.218 5.575 3.974 2.926 2.207 1.322 0.831 0.539 0.241 0.113 0.055 0.019
100. 21.264 11.404 7.087 4.778 3.395 2.499 1.454 0.899 0.578 0.256 0.120 0.058 0.020
Top of Screen in Pumped Well is 80. Per Cent of Aquifer Thickness Below Top of Aquifer
Piez. Depth Distance of Piezometer from Pumped Well, as Per Cent of Aquifer Thickness
5.00 10.00 15.00 20.00 25.00 30.00 40.00 50.00 60.00 80.00 100.00 120.00 150.00
0.0 −4.785 −3.415 −2.633 −2.095 −1.696 −1.387 −0.944 −0.650 −0.451 −0.219 −0.108 −0.053 −0.019
10. −4.739 −3.371 −2.590 −2.055 −1.658 −1.352 −0.916 −0.628 −0.434 −0.210 −0.103 −0.051 −0.018
20. −4.597 −3.232 −2.457 −1.929 −1.542 −1.246 −0.829 −0.561 −0.383 −0.182 −0.089 −0.044 −0.015
30. −4.336 −2.979 −2.216 −1.705 −1.335 −1.059 −0.681 −0.448 −0.299 −0.138 −0.066 −0.032 −0.011
40. −3.912 −2.572 −1.834 −1.354 −1.019 −0.778 −0.467 −0.290 −0.184 −0.079 −0.036 −0.017 −0.006
50. −3.232 −1.929 −1.246 −0.829 −0.561 −0.383 −0.182 −0.089 −0.044 −0.011 −0.003 −0.001 0.000
60. −2.076 −0.877 −0.331 −0.057 0.079 0.142 0.168 0.145 0.114 0.062 0.032 0.016 0.006
70. 0.227 0.992 1.113 1.044 0.920 0.789 0.561 0.391 0.272 0.131 0.064 0.032 0.011
80. 6.304 4.280 3.150 2.401 1.867 1.471 0.939 0.615 0.410 0.189 0.090 0.044 0.015
90. 12.080 7.287 4.939 3.545 2.635 2.005 1.219 0.773 0.505 0.228 0.107 0.052 0.018
100. 13.344 8.218 5.575 3.973 2.926 2.207 1.322 0.831 0.539 0.241 0.113 0.055 0.019
Top of Screen in Pumped Well is 70. Per Cent of Aquifer Thickness Below Top of Aquifer
Piez. Depth Distance of Piezometer from Pumped Well, as Per Cent of Aquifer Thickness
5.00 10.00 15.00 20.00 25.00 30.00 40.00 50.00 60.00 80.00 100.00 120.00 150.00
0.0 −4.710 −3.342 −2.562 −2.029 −1.634 −1.330 −0.897 −0.613 −0.423 −0.204 −0.100 −0.049 −0.017
10. −4.659 −3.293 −2.515 −1.985 −1.593 −1.293 −0.868 −0.591 −0.406 −0.195 −0.095 −0.047 −0.017
20. −4.500 −3.138 −2.368 −1.848 −1.468 −1.179 −0.778 −0.523 −0.355 −0.168 −0.082 −0.040 −0.014
30. −4.203 −2.853 −2.100 −1.601 −1.245 −0.981 −0.626 −0.410 −0.273 −0.126 −0.600 −0.029 −0.010
40. −3.705 −2.381 −1.666 −1.212 −0.902 −0.683 −0.408 −0.254 −0.162 −0.071 −0.033 −0.016 −0.005
50. −2.853 −1.601 −0.981 −0.626 −0.410 −0.273 −0.126 −0.060 −0.029 −0.007 −0.002 −0.000 0.000
60. −1.189 −0.2
...
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