ASTM D5850-95(2000)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.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:D5850–95 (Reapproved 2000)
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope D4105 Test Method for (Analytical Procedure for) Deter-
mining Transmissivity and Storativity of Nonleaky Con-
1.1 This test method covers an analytical procedure for
fined Aquifers by the Modified Theis Nonequilibrium
determining the transmissivity, storage coefficient, and ratio of
Method
vertical to horizontal hydraulic conductivity of a confined
D4106 Test Method for (Analytical Procedure for) Deter-
aquifer using observation well drawdown measurements from
mining Transmissivity and Storativity of Nonleaky Con-
a constant-rate pumping test. This test method uses data from
fined Aquifers by the Theis Nonequilibrium Method
a minimum of four partially penetrating, properly positioned
D4750 Test Method for Determining Subsurface Liquid
observation wells around a partially penetrating control well.
Levels in a Borehole or Monitoring Well (Observation
1.2 The analytical procedure is used in conjunction with the
Well)
field procedure in Test Method D4050.
D5473 Test Method (Analytical Procedure) for Analyzing
1.3 Limitations—The limitations of the technique for deter-
the Effects of Partial Penetration of Control Well and
mination of the horizontal and vertical hydraulic conductivity
Determining the Horizontal and Vertical Hydraulic Con-
ofaquifersareprimarilyrelatedtothecorrespondencebetween
ductivity in a Nonleaky Confined Aquifer
the field situation and the simplifying assumption of this test
method.
3. Terminology
1.4 The values stated in inch-pound units are to be regarded
3.1 Definitions:
as the standard. The SI units given in parentheses are for
3.1.1 aquifer, confined—an aquifer bounded above and
information only.
below by confining beds and in which the static head is above
1.5 This standard does not purport to address all of the
the top of the aquifer.
safety concerns, if any, associated with its use. It is the
3.1.2 confining bed—a hydrogeologic unit of less perme-
responsibility of the user of this standard to establish appro-
able material bounding one or more aquifers.
priate safety and health practices and determine the applica-
3.1.3 control well—well by which the head and flow in the
bility of regulatory limitations prior to use.
aquifer is changed, for example, by pumping, injection, or
2. Referenced Documents imposing a constant change of head.
3.1.4 drawdown—vertical distance the static head is low-
2.1 ASTM Standards:
ered due to the removal of water.
D653 Terminology Relating to Soil, Rock, and Contained
2 3.1.5 hydraulic conductivity—(fieldaquifertest)thevolume
Fluids
of water at the existing kinematic viscosity that will move in a
D4043 Guide for Selection of Aquifer Test Method in
unit time under a unit hydraulic gradient through a unit area
Determining Hydraulic Properties by Well Techniques
measured at right angles to the direction of flow.
D4050 Test Method for (Field Procedure for) Withdrawal
3.1.6 observation well—a well open to all or part of an
and Injection Well Tests for Determining Hydraulic Prop-
aquifer.
erties of Aquifer Systems
3.1.7 piezometer—a device so constructed and sealed as to
measure hydraulic head at a point in the subsurface.
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland 3.1.8 storage coeffıcient—the volume of water an aquifer
RockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWaterand
releases from or takes into storage per unit surface area of the
Vadose Zone Investigations.
aquifer per unit change in head.
Current edition approved Oct. 10, 1995. Published December 1995.
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.
D5850–95 (2000)
3.1.9 transmissivity—the volume of water at the existing hydraulic conductivity is less than the horizontal hydraulic
kinematic viscosity that will move in a unit time under a unit conductivity. The effects of partial penetration diminish with
hydraulic gradient through a unit width of the aquifer. increasing distance from the pumped well, becoming negli-
1/2
3.1.10 For definitions of other terms used in this test gible at a distance of about 1.5b/(K /K ) . This test method
z r
method, see Terminology D653. relies on obtaining drawdown measurements at a minimum of
3.2 Symbols:Symbols and Dimensions: two locations within this distance of the pumped well and at
3.2.1 A—K /K , anisotropy ratio [nd]. each location obtaining data from observation wells completed
z r
3.2.2 b—thickness of aquifer [L]. to two different depths.At each location, one observation well
3.2.3 C—drawdown correction factor, equal to the ratio of shouldbescreenedataboutthesameelevationasthescreenin
f
the drawdown for a fully penetrating well network to the the pumped well, while the other observation well should be
drawdown for a partially penetrating well network (W(u)/ screened in sediments not screened by the pumped well.
(W(u) + f )). 4.2 According to Theis (1), the drawdown around a fully
s
3.2.4 d—distance from top of aquifer to top of screened penetrating control well pumped at a constant rate and tapping
interval of control well [L]. a homogeneous, confined aquifer is as follows:
3.2.5 d8—distance from top of aquifer to top of screened
Q
s 5 W u (1)
~ !
interval of observation well [L]. f
4pT
3.2.6 f —incremental dimensionless drawdown component
s
where:
resulting from partial penetration [nd].
–x
−1
e
3.2.7 K—hydraulic conductivity [LT ].
`
W~u! 5 dx (2)
*
u
x
3.2.7.1 Discussion—The use of symbol K for the term
hydraulic conductivity is the predominant usage in ground-
4.2.1 Drawdown near a partially penetrating control well
water literature by hydrogeologists, whereas the symbol k is
pumped at a constant rate and tapping a homogeneous,
commonly used for this term in the rock and soil mechanics
anisotropic, confined aquifer is presented by Hantush (2, 3, 4):
literature.
3.2.8 K —modified Bessel function of the second kind and
o
Q
zero order. s 5 ~W~u! 1 f ! (3)
s
4pT
3.2.9 K—hydraulicconductivityintheplaneoftheaquifer,
r
According to Hantush (2, 3, 4), at late pumping times, when
radially from the control well (horizontal hydraulic conductiv-
−1
t>b S/(2TA), f can be expressed as follows:
s
ity) [LT ].
2 `
3.2.10 K —hydraulic conductivity normal to the plane of
4b 1 npr K /K
z =
z r
−1
f 5 K (4)
(
s 2 S 2D oS D
the aquifer (vertical hydraulic conductivity) [LT ]. b
p ~l 2 d! ~l8 2 d8!n 51 n
3.2.11 l—distancefromtopofaquifertobottomofscreened
npi npd npl8 npd8
interval of control well [L]. sin –sin sin –sin
F S D S DGF S D S DG
b b b b
3.2.12 l8—distance from top of aquifer to bottom of
4.2.2 For a given observed drawdown, it is possible to
screened interval of observation well [L].
3 −1 compute a correction factor, C, defined as the ratio of the
f
3.2.13 Q—discharge [L T ].
drawdown for a fully penetrating well to the drawdown for a
3.2.14 r—radial distance from control well [L].
partially penetrating well:
3.2.15 S—storage coefficient [nd].
3.2.16 s—drawdown observed in partially penetrating well W~u!
C 5 (5)
f
W~u! 1 f
network [L].
s
3.2.17 s—drawdown observed in fully penetrating well
f The observed drawdown for each observation well may be
network [L].
corrected to the fully penetrating equivalent drawdown by
2 −1
3.2.18 T—transmissivity [L T ].
multiplying by the correction factor:
3.2.19 t—time since pumping began [T].
s 5 Cs (6)
2 f f
3.2.20 u—(r S)/(4Tt)[nd].
The drawdown values corresponding to the fully penetrating
3.2.21 W(u)—an exponential integral known in hydrology
casemaythenbeanalyzedbyconventionaldistance-drawdown
as the Theis well function of u[nd].
methods to compute transmissivity and storage coefficient.
4. Summary of Test Method
4.2.3 The correction factors are a function of both transmis-
sivity and storage coefficient, that are the parameters being
4.1 This test method makes use of the deviations in draw-
down near a partially penetrating control well from those that sought. Because of this, the test method relies on an iterative
procedureinwhichaninitialestimateofTandSaremadefrom
wouldoccurnearacontrolwellfullypenetratingtheaquifer.In
general, drawdown within the screened horizon of a partially which initial correction factors are computed. Using these
correction factors, fully penetrating drawdown values are
penetrating control well tends to be greater than that which
would have been observed near a fully penetrating well, computed and analyzed using distance-drawdown methods to
whereasthedrawdownaboveorbelowthescreenedhorizonof
the partially penetrating control well tends to be less than the
corresponding fully penetrating case. Drawdown deviations
The boldface numbers given in parentheses refer to a list of references at the
due to partial penetration are amplified when the vertical end of the text.
D5850–95 (2000)
determine revised values for T and S. The revised T and S 6.2 Construction of the Control Well—Screen the control
values are used to compute revised correction factors, C. This wellthroughonlypartoftheverticalextentoftheaquifertobe
f
process is repeated until the calculated T and S values change tested.Theexactdistancesfromthetopoftheaquifertothetop
only slightly from those obtained in the previous iteration. andbottomofthepumpedwellscreenintervalmustbeknown.
4.2.4 The correction factors are also a function of the 6.3 Construction and Placement of Observation Wells—The
anisotropy ratio, A. For this reason, all of the calculations procedure will work for arbitrary positioning of observation
described above must be performed for several different wells and placement of their screens, as long as three or more
assumed anisotropy ratios. The assumed anisotropy value that observation wells are used and some of the observation wells
leads to the best solution, that is, best straight line fit or best fall inside the zone where flow is affected by partial penetra-
curve match, is deemed to be the actual anisotropy ratio. tion, that is, the area where significant vertical flow compo-
nents exists. However, strategic selection of the number and
5. Significance and Use location of observation wells will maximize the quality of the
data set and improve the reliability of the interpretation.
5.1 This test method is one of several available for deter-
6.3.1 Optimumresultswillbeobtainedbyusingaminimum
mining vertical anisotropy ratio.Among other available meth-
of four observation wells incorporating two pairs of observa-
ods are Weeks ((5); see Test Method D5473), that relies on
tion wells located at two different distances from the pumped
distance-drawdowndata,andWayandMcKee (6),thatutilizes
well, both within the zone where flow is affected by partial
time-drawdown data. An important restriction of the Weeks
penetration. Each well pair should consist of a shallow well
distance-drawdown method is that the observation wells must
and a deep well, that span vertically the area in which vertical
have identical construction (screened intervals) and two or
anisotropy is sought. For each well pair, one observation well
more of the observation wells must be located at a distance
screen should be at the same elevation as the screen in the
fromthepumpedwellbeyondtheeffectsofpartialpenetration.
pumpedwell,whereastheotherobservationwellscreenshould
The procedure described in this test method general distance-
be at a different elevation than the screen in the pumped well.
drawdown method, in that it works in theory for any observa-
6.3.2 This test method relies on choosing several arbitrary
tion well configuration incorporating three or more wells,
anisotropy ratios, correcting the observed drawdowns for
provided some of the wells are within the zone where flow is
partialpenetration,andevaluatingtheresults.Ifallobservation
affected by partial penetration.
wellsarescreenedatthesameelevation,thequalityofthedata
5.2 Assumptions:
traceproducedbycorrectingtheobserveddrawdownmeasure-
5.2.1 Control well discharges at a constant rate, Q.
ments is not sensitive to the choice of anisotropy, making it
5.2.2 Control well is of infinitesimal diameter and partially
difficult to determine this parameter accurately. If, however,
penetrates the aquifer.
observation well screens are located both within the pumped
5.2.3 Dataareobtainedfromanumberofpartiallypenetrat-
zone (where drawdown is greater than the fully penetrating
ing observation wells, some screened at elevations similar to
case)andtheunpumpedzone(wheredrawdownislessthanthe
that in the pumped well and some screened at different
fully penetrating case), the quality of the corrected data is
elevations.
sensitive to the choice of anisotropy ratio, making it easier to
5.2.4 The aquifer is confined, homogeneous and areally
quantify this parameter.
extensive. The aquifer may be anisotropic, and, if so, the
directions of maximum and minimum hydraulic conductivity
7. Procedure
are horizontal and vertical, respectively.
7.1 Pre-testpreparations,pumpingtestguidelines,andpost-
5.2.5 Discharge from the well is derived exclusively from
test procedures associated with the pumping test itself are
storage in the aquifer.
described in Test Method D4050.
5.3 Calculation Requirements—Application of this method
7.2 Verify the quality of the data set. Review the record of
is computationally intensive. The function, f , shown in (Eq 4)
s
measured flow rates to make sure the rate was held constant
must be evaluated numerous times using arbitrary input pa-
during the test. Check to see that hand measurements of
rameters. It is not practical to use existing, somewhat limited,
drawdown agree well with electronically measured values.
tables of values for f and, because this equation is rather
s
Finally, check the background water-level fluctuations ob-
formidable, it is not readily tractable by hand. Because of this,
served prior to or following the pumping test to see if
it is assumed the practitioner using this test method will have
adjustmentsmustbemadetotheobserveddrawdownvaluesto
available a computerized procedure for evaluating the function
account for background fluctuations. If appropriate, adjust the
f . This can be accomplished using commercially available
s
...