ASTM D5850-95(2006)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: D5850 − 95(Reapproved 2006)
Standard Test Method for (Analytical Procedure)
Determining Transmissivity, Storage Coefficient, and
Anisotropy Ratio from a Network of Partially Penetrating
Wells
This standard is issued under the fixed designation D5850; 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 erties of Aquifer Systems
D5473Test Method for (Analytical Procedure for) Analyz-
1.1 This test method covers an analytical procedure for
ing the Effects of Partial Penetration of Control Well and
determining the transmissivity, storage coefficient, and ratio of
Determining the Horizontal and Vertical Hydraulic Con-
vertical to horizontal hydraulic conductivity of a confined
ductivity in a Nonleaky Confined Aquifer
aquifer using observation well drawdown measurements from
a constant-rate pumping test. This test method uses data from
3. Terminology
a minimum of four partially penetrating, properly positioned
observation wells around a partially penetrating control well.
3.1 Definitions:
3.1.1 aquifer, confined—an aquifer bounded above and be-
1.2 Theanalyticalprocedureisusedinconjunctionwiththe
lowbyconfiningbedsandinwhichthestaticheadisabovethe
field procedure in Test Method D4050.
top of the aquifer.
1.3 Limitations—The limitations of the technique for deter-
3.1.2 confining bed—ahydrogeologicunitoflesspermeable
mination of the horizontal and vertical hydraulic conductivity
material bounding one or more aquifers.
ofaquifersareprimarilyrelatedtothecorrespondencebetween
the field situation and the simplifying assumption of this test
3.1.3 control well—well by which the head and flow in the
method.
aquifer is changed, for example, by pumping, injection, or
imposing a constant change of head.
1.4 The values stated in inch-pound units are to be regarded
as the standard. The SI units given in parentheses are for
3.1.4 drawdown—vertical distance the static head is low-
information only.
ered due to the removal of water.
1.5 This standard does not purport to address all of the
3.1.5 hydraulic conductivity—(fieldaquifertest)thevolume
safety concerns, if any, associated with its use. It is the
of water at the existing kinematic viscosity that will move in a
responsibility of the user of this standard to establish appro-
unit time under a unit hydraulic gradient through a unit area
priate safety and health practices and determine the applica-
measured at right angles to the direction of flow.
bility of regulatory limitations prior to use.
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 storage coeffıcient—the volume of water an aquifer
D4050Test 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.
3.1.9 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 December 2006. Originally
3.1.10 For definitions of other terms used in this test
approved in 1995. Last previous edition approved in 2000 as D5850–95 (2000).
method, see Terminology D653.
DOI: 10.1520/D5850-95R06.
2 3.2 Symbols and Dimensions:
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.2.1 A—K /K , anisotropy ratio [nd].
z r
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. 3.2.2 b—thickness of aquifer [L].
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5850 − 95 (2006)
1/2
3.2.3 C —drawdown correction factor, equal to the ratio of gible at a distance of about 1.5b/(K /K ) . This test method
f z r
the drawdown for a fully penetrating well network to the relies on obtaining drawdown measurements at a minimum of
drawdown for a partially penetrating well network (W(u)/ two locations within this distance of the pumped well and at
(W(u) + f )). each location obtaining data from observation wells completed
s
to two different depths.At each location, one observation well
3.2.4 d—distance from top of aquifer to top of screened
shouldbescreenedataboutthesameelevationasthescreenin
interval of control well [L].
the pumped well, while the other observation well should be
3.2.5 d`—distance from top of aquifer to top of screened
screened in sediments not screened by the pumped well.
interval of observation well [L].
4.2 According to Theis (1), the drawdown around a fully
3.2.6 f —incremental dimensionless drawdown component
s
penetrating control well pumped at a constant rate and tapping
resulting from partial penetration [nd].
a homogeneous, confined aquifer is as follows:
−1
3.2.7 K—hydraulic conductivity [LT ].
Q
3.2.7.1 Discussion—The use of symbol K for the term
s 5 W~u! (1)
f
4πT
hydraulic conductivity is the predominant usage in groundwa-
ter literature by hydrogeologists, whereas the symbol k is
where:
commonly used for this term in the rock and soil mechanics
2x
` e
literature.
W~u! 5 dx (2)
*
u
x
3.2.8 K —modified Bessel function of the second kind and
o
4.2.1 Drawdown near a partially penetrating control well
zero order.
pumped at a constant rate and tapping a homogeneous,
3.2.9 K —hydraulic conductivity in the plane of the aquifer,
r
anisotropic, confined aquifer is presented by Hantush (2, 3, 4):
radially from the control well (horizontal hydraulic conductiv-
−1
ity) [LT ].
Q
3.2.10 K —hydraulicconductivitynormaltotheplaneofthe
s 5 W u 1f (3)
~ ~ ! !
z s
4πT
−1
aquifer (vertical hydraulic conductivity) [LT ].
According to Hantush (2, 3, 4), at late pumping times, when
3.2.11 l—distancefromtopofaquifertobottomofscreened
t>b S/(2TA), f can be expressed as follows:
s
interval of control well [L].
`
3.2.12 l`—distance from top of aquifer to bottom of
4b 1 nπr=K /K
z r
f 5 K S D (4)
2 S 2D
s ( o
screened interval of observation well [L]. π l 2 d l`2d` n b
~ !~ !
n51
3 −1
3.2.13 Q—discharge [L T ].
nπi nπd nπl' nπd'
sin 2 sin sin 2 sin
F S D S DGF S D S DG
3.2.14 r—radial distance from control well [L].
b b b b
3.2.15 S—storage coefficient [nd].
4.2.2 For a given observed drawdown, it is possible to
3.2.16 s—drawdown observed in partially penetrating well
compute a correction factor, C, defined as the ratio of the
f
network [L].
drawdown for a fully penetrating well to the drawdown for a
3.2.17 s —drawdown observed in fully penetrating well
partially penetrating well:
f
network [L].
W~u!
2 −1 C 5 (5)
f
3.2.18 T—transmissivity [L T ].
W u 1f
~ !
s
3.2.19 t—time since pumping began [T].
The observed drawdown for each observation well may be
3.2.20 u—(r S)/(4Tt)[nd ].
corrected to the fully penetrating equivalent drawdown by
multiplying by the correction factor:
3.2.21 W(u)—an exponential integral known in hydrology
as the Theis well function of u[nd].
s 5 C s (6)
f f
The drawdown values corresponding to the fully penetrating
4. Summary of Test Method
casemaythenbeanalyzedbyconventionaldistance-drawdown
4.1 This test method makes use of the deviations in draw-
methods to compute transmissivity and storage coefficient.
down near a partially penetrating control well from those that
4.2.3 The correction factors are a function of both transmis-
wouldoccurnearacontrolwellfullypenetratingtheaquifer.In
sivity and storage coefficient, that are the parameters being
general, drawdown within the screened horizon of a partially
sought. Because of this, the test method relies on an iterative
penetrating control well tends to be greater than that which
procedureinwhichaninitialestimateof Tand Saremadefrom
would have been observed near a fully penetrating well,
which initial correction factors are computed. Using these
whereasthedrawdownaboveorbelowthescreenedhorizonof
correction factors, fully penetrating drawdown values are
the partially penetrating control well tends to be less than the
computed and analyzed using distance-drawdown methods to
corresponding fully penetrating case. Drawdown deviations
determine revised values for T and S. The revised T and S
due to partial penetration are amplified when the vertical
hydraulic conductivity is less than the horizontal hydraulic
conductivity. The effects of partial penetration diminish with
The boldface numbers given in parentheses refer to a list of references at the
increasing distance from the pumped well, becoming negli- end of the text.
D5850 − 95 (2006)
values are used to compute revised correction factors, C. This 6.2 Construction of the Control Well—Screen the control
f
process is repeated until the calculated T and S values change wellthroughonlypartoftheverticalextentoftheaquifertobe
only slightly from those obtained in the previous iteration. tested.Theexactdistancesfromthetopoftheaquifertothetop
4.2.4 The correction factors are also a function of the andbottomofthepumpedwellscreenintervalmustbeknown.
anisotropy ratio, A. For this reason, all of the calculations
6.3 Construction and Placement of Observation Wells—The
described above must be performed for several different
procedure will work for arbitrary positioning of observation
assumed anisotropy ratios. The assumed anisotropy value that
wells and placement of their screens, as long as three or more
leads to the best solution, that is, best straight line fit or best
observation wells are used and some of the observation wells
curve match, is deemed to be the actual anisotropy ratio.
fall inside the zone where flow is affected by partial penetra-
tion, that is, the area where significant vertical flow compo-
5. Significance and Use
nents exists. However, strategic selection of the number and
location of observation wells will maximize the quality of the
5.1 This test method is one of several available for deter-
data set and improve the reliability of the interpretation.
mining vertical anisotropy ratio.Among other available meth-
6.3.1 Optimumresultswillbeobtainedbyusingaminimum
ods are Weeks ((5); see Test Method D5473), that relies on
of four observation wells incorporating two pairs of observa-
distance-drawdowndata,andWayandMcKee (6),thatutilizes
tion wells located at two different distances from the pumped
time-drawdown data. An important restriction of the Weeks
well, both within the zone where flow is affected by partial
distance-drawdown method is that the observation wells must
penetration. Each well pair should consist of a shallow well
have identical construction (screened intervals) and two or
and a deep well, that span vertically the area in which vertical
more of the observation wells must be located at a distance
anisotropy is sought. For each well pair, one observation well
fromthepumpedwellbeyondtheeffectsofpartialpenetration.
screen should be at the same elevation as the screen in the
The procedure described in this test method general distance-
pumpedwell,whereastheotherobservationwellscreenshould
drawdown method, in that it works in theory for any observa-
be at a different elevation than the screen in the pumped well.
tion well configuration incorporating three or more wells,
6.3.2 This test method relies on choosing several arbitrary
provided some of the wells are within the zone where flow is
anisotropy ratios, correcting the observed drawdowns for
affected by partial penetration.
partialpenetration,andevaluatingtheresults.Ifallobservation
5.2 Assumptions:
wellsarescreenedatthesameelevation,thequalityofthedata
5.2.1 Control well discharges at a constant rate, Q.
traceproducedbycorrectingtheobserveddrawdownmeasure-
5.2.2 Control well is of infinitesimal diameter and partially
ments is not sensitive to the choice of anisotropy, making it
penetrates the aquifer.
difficult to determine this parameter accurately. If, however,
5.2.3 Dataareobtainedfromanumberofpartiallypenetrat-
observation well screens are located both within the pumped
ing observation wells, some screened at elevations similar to
zone (where drawdown is greater than the fully penetrating
that in the pumped well and some screened at different
case)andtheunpumpedzone(wheredrawdownislessthanthe
elevations.
fully penetrating case), the quality of the corrected data is
5.2.4 The aquifer is confined, homogeneous and areally
sensitive to the choice of anisotropy ratio, making it easier to
extensive. The aquifer may be anisotropic, and, if so, the
quantify this parameter.
directions of maximum and minimum hydraulic conductivity
7. Procedure
are horizontal and vertical, respectively.
5.2.5 Discharge from the well is derived exclusively from
7.1 Pre-testpreparations,pumpingtestguidelines,andpost-
storage in the aquifer.
test procedures associated with the pumping test itself are
described in Test Method D4050.
5.3 Calculation Requirements—Application of this method
is computationally intensive. The function, f , shown in (Eq 4)
s 7.2 Verify the quality of the data set. Review the record of
must be evaluated numerous times using arbitrary input pa-
measured flow rates to make sure the rate was held constant
rameters. It is not practical to use existing, somewhat limited,
during the test. Check to see that hand measurements of
tables of values for f and, because this equation is rather
s drawdown agree well with electronically measured values.
formidable, it is not readily tractable by hand. Because of this,
Finally, check the background water-level fluctuations ob-
it is assumed the practitioner using this test method will have
served prior to or following the pumping test to see if
available a computerized procedure for evaluating the function
adjustmentsmustbemadetotheobserveddrawdownvaluesto
f . This can be accomplished using commercially available
s account for background fluctuations. If appropriate, adjust the
mathematical software including some spreadsheet applica-
observed drawdown values accordingly.
tions, or by writing programs in languages such as Fortran or
7.3 Analysis of the field data is described in Section 8.
C.
8. Calculation and Int
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