ASTM D5270-96(2008)
(Test Method)Standard Test Method for Determining Transmissivity and Storage Coefficient of Bounded, Nonleaky, Confined Aquifers
Standard Test Method for Determining Transmissivity and Storage Coefficient of Bounded, Nonleaky, Confined Aquifers
SIGNIFICANCE AND USE
Assumptions:
The well discharges at a constant rate.
Well is of infinitesimal diameter and is open through the full thickness of the aquifer.
The nonleaky confined aquifer is homogeneous, isotropic, and areally extensive except where limited by linear boundaries.
Discharge from the well is derived initially from storage in the aquifer; later, movement of water may be induced from a constant-head boundary into the aquifer.
The geometry of the assumed aquifer and well are shown in Fig. 1 or Fig. 2.
Boundaries are vertical planes, infinite in length that fully penetrate the aquifer. No water is yielded to the aquifer by impermeable boundaries, whereas recharging boundaries are in perfect hydraulic connection with the aquifer.
Observation wells represent the head in the aquifer; that is, the effects of wellbore storage in the observation wells are negligible.
Implications of Assumptions:
Implicit in the assumptions are the conditions of a fully-penetrating control well and observation wells of infinitesimal diameter in a confined aquifer. Under certain conditions, aquifer tests can be successfully analyzed when the control well is open to only part of the aquifer or contains a significant volume of water or when the test is conducted in an unconfined aquifer. These conditions are discussed in more detail in Test Method D4105.
In cases in which this test method is used to locate an unknown boundary, a minimum of three observation wells is needed. If only two observation wells are available, two possible locations of the boundary are defined, and if only one observation well is used, a circle describing all possible locations of the image well is defined.
The effects of a constant-head boundary are often indistinguishable from the effects of a leaky, confined aquifer. Therefore, care must be taken to ensure that a correct conceptual model of the system has been created prior to analyzing the test. See Guide D4043.
SCOPE
1.1 This test method covers an analytical procedure for determining the transmissivity, storage coefficient, and possible location of boundaries for a confined aquifer with a linear boundary. This test method is used to analyze water-level or head data from one or more observation wells or piezometers during the pumping of water from a control well at a constant rate. This test method also applies to flowing artesian wells discharging at a constant rate. With appropriate changes in sign, this test method also can be used to analyze the effects of injecting water into a control well at a constant rate.
1.2 The analytical procedure in this test method is used in conjunction with the field procedure in Test Method D4050.
1.3 Limitations—The valid use of this test method is limited to determination of transmissivities and storage coefficients for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis nonequilibrium method (see Test Method D4106) (see 5.1), except that the aquifer is limited in areal extent by a linear boundary that fully penetrates the aquifer. The boundary is assumed to be either a constant-head boundary (equivalent to a stream or lake that hydraulically fully penetrates the aquifer) or a no-flow (impermeable) boundary (equivalent to a contact with a significantly less permeable rock unit). The Theis nonequilibrium method is described in Test Methods D4105 and D4106.
1.4 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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Standards Content (Sample)
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Designation:D5270 −96(Reapproved 2008)
Standard Test Method for
Determining Transmissivity and Storage Coefficient of
Bounded, Nonleaky, Confined Aquifers
This standard is issued under the fixed designation D5270; 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 2. Referenced Documents
1.1 This test method covers an analytical procedure for 2.1 ASTM Standards:
determiningthetransmissivity,storagecoefficient,andpossible D653Terminology Relating to Soil, Rock, and Contained
location of boundaries for a confined aquifer with a linear Fluids
boundary. This test method is used to analyze water-level or D4043Guide for Selection of Aquifer Test Method in
head data from one or more observation wells or piezometers Determining Hydraulic Properties by Well Techniques
during the pumping of water from a control well at a constant D4050Test Method for (Field Procedure) for Withdrawal
rate. This test method also applies to flowing artesian wells and Injection Well Tests for Determining Hydraulic Prop-
discharging at a constant rate. With appropriate changes in erties of Aquifer Systems
sign, this test method also can be used to analyze the effects of D4105Test Method for (Analytical Procedure) for Deter-
injecting water into a control well at a constant rate. mining Transmissivity and Storage Coefficient of Non-
leaky ConfinedAquifers by the Modified Theis Nonequi-
1.2 The analytical procedure in this test method is used in
librium Method
conjunction with the field procedure in Test Method D4050.
D4106Test Method for (Analytical Procedure) for Deter-
1.3 Limitations—Thevaliduseofthistestmethodislimited
mining Transmissivity and Storage Coefficient of Non-
todeterminationoftransmissivitiesandstoragecoefficientsfor
leaky Confined Aquifers by the Theis Nonequilibrium
aquifers in hydrogeologic settings with reasonable correspon-
Method
dence to the assumptions of the Theis nonequilibrium method
D4750Test Method for Determining Subsurface Liquid
(see Test Method D4106) (see 5.1), except that the aquifer is
Levels in a Borehole or Monitoring Well (Observation
limitedinarealextentbyalinearboundarythatfullypenetrates 3
Well) (Withdrawn 2010)
the aquifer. The boundary is assumed to be either a constant-
head boundary (equivalent to a stream or lake that hydrauli-
3. Terminology
cally fully penetrates the aquifer) or a no-flow (impermeable)
3.1 Definitions:
boundary (equivalent to a contact with a significantly less
3.1.1 constant-head boundary—the conceptual representa-
permeable rock unit). The Theis nonequilibrium method is
tion of a natural feature such as a lake or river that effectively
described in Test Methods D4105 and D4106.
fully penetrates the aquifer and prevents water-level change in
1.4 This standard does not purport to address all of the
the aquifer at that location.
safety concerns, if any, associated with its use. It is the
3.1.2 equipotential line—a line connecting points of equal
responsibility of the user of this standard to establish appro-
hydraulic head. A set of such lines provides a contour map of
priate safety and health practices and determine the applica-
a potentiometric surface.
bility of regulatory limitations prior to use.
1 2
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Vadose Zone Investigations. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Sept. 15, 2008. Published October 2008. Originally the ASTM website.
approved in 1992. Last previous edition approved in 2002 as D5270–96 (2002). The last approved version of this historical standard is referenced on
DOI: 10.1520/D5270-96R08. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5270−96 (2008)
3.1.3 image well—an imaginary well located opposite a
control well such that a boundary is the perpendicular bisector
of a straight line connecting the control and image wells; used
to simulate the effect of a boundary on water-level changes.
3.1.4 impermeable boundary—the conceptual representa-
tion of a natural feature such as a fault or depositional contact
that places a boundary of significantly less-permeable material
laterally adjacent to an aquifer.
3.1.5 See Terminology D653 for other terms.
3.2 Symbols and Dimensions:
3.2.1 K [nd]—constant of proportionality, r /r .
l i r
3 −1
3.2.2 Q [L T ]—discharge.
3.2.3 r [L]—radial distance from control well.
3.2.4 r [L]—distance from observation well to image well.
i
3.2.5 r [L]—distancefromobservationwelltocontrolwell.
r
3.2.6 S [nd]—storage coefficient.
3.2.7 s [L]—drawdown.
3.2.8 s [L]—component of drawdown due to image well.
i
3.2.9 s [L]—drawdown at an observation well.
o
3.2.10 s [L]—component of drawdown due to control well.
r
2 −1
3.2.11 T [L T ]—transmissivity.
3.2.12 t [T]—time since pumping or injection began.
3.2.13 t [T]—time at projection of zero drawdown.
o
4. Summary of Test Method
4.1 This test method prescribes two analytical procedures
for analysis of a field test. This test method requires pumping
water from, or injecting water into, a control well that is open
to the entire thickness of a confined bounded aquifer at a
constant rate and measuring the water-level response in one or
more observation wells or piezometers. The water-level re-
sponse in the aquifer is a function of the transmissivity and
storagecoefficientoftheaquifer,andthelocationandnatureof
the aquifer boundary or boundaries. Drawdown or build up of
the water level is analyzed as a departure from the type curve
NOTE 1—Modified from Ferris and others (6) and Heath (7) .
defined by the Theis nonequilibrium method (see Test Method
FIG. 1Diagram Showing Constant-Head Boundary
D4106) or from straight-line segments defined by the modified
Theis nonequilibrium method (see Test Method D4105).
method is equally applicable, with the appropriate change in
4.2 Aconstant-head boundary such as a lake or stream that
sign, to control wells into which water is injected.
fully penetrates the aquifer prevents drawdown or build up of
4.3 Solution—The solution given by Theis (1) can be
head at the boundary, as shown in Fig. 1. Likewise, an
expressed as follows:
impermeable boundary provides increased drawdown or build
2y
up of head, as shown in Fig. 2. These effects are simulated by
Q ` e
s 5 dy (1)
*
treating the aquifer as if it were infinite in extent and
u
4πT y
introducing an imaginary well or “image well” on the opposite
and:
side of the boundary a distance equal to the distance of the
controlwellfromtheboundary.Alinebetweenthecontrolwell r S
u 5 (2)
and the image well is perpendicular to the boundary. If the
4Tt
boundary is a constant-head boundary, the flux from the image
where:
well is opposite in sign from that of the control well; for
2y
` e
example,theimageofadischargingcontrolwellisaninjection
* dy 5 W ~u! (3)
u
y
well, whereas the image of an injecting well is a discharging
well. If the boundary is an impermeable boundary, the flux
2 3 4
u u u
from the image well has the same sign as that from the control
520.577216 2log u1u 2 1 2 1…
e
2!2 3!3 4!4
well. Therefore, the image of a discharging well across an
impermeable boundary is a discharging well. Because the
effects are symmetrical, only discharging control wells will be
The boldface numbers in parentheses refer to a list of references at the end of
described in the remainder of this test method, but this test this standard.
D5270−96 (2008)
NOTE 1—K is a constant of proportionality between the radii, not to be
l
confused with hydraulic conductivity.
5. Significance and Use
5.1 Assumptions:
5.1.1 The well discharges at a constant rate.
5.1.2 Well is of infinitesimal diameter and is open through
the full thickness of the aquifer.
5.1.3 The nonleaky confined aquifer is homogeneous, iso-
tropic, and areally extensive except where limited by linear
boundaries.
5.1.4 Discharge from the well is derived initially from
storage in the aquifer; later, movement of water may be
induced from a constant-head boundary into the aquifer.
5.1.5 The geometry of the assumed aquifer and well are
shown in Fig. 1 or Fig. 2.
5.1.6 Boundaries are vertical planes, infinite in length that
fullypenetratetheaquifer.Nowaterisyieldedtotheaquiferby
impermeableboundaries,whereasrechargingboundariesarein
perfect hydraulic connection with the aquifer.
5.1.7 Observation wells represent the head in the aquifer;
that is, the effects of wellbore storage in the observation wells
are negligible.
5.2 Implications of Assumptions :
5.2.1 Implicit in the assumptions are the conditions of a
fully-penetrating control well and observation wells of infini-
tesimal diameter in a confined aquifer. Under certain condi-
tions, aquifer tests can be successfully analyzed when the
control well is open to only part of the aquifer or contains a
significant volume of water or when the test is conducted in an
unconfined aquifer. These conditions are discussed in more
detail in Test Method D4105.
5.2.2 In cases in which this test method is used to locate an
unknown boundary, a minimum of three observation wells is
NOTE 1—Modified from Ferris and others (6) and Heath (7) .
FIG. 2Diagram Showing Impermeable Boundary needed. If only two observation wells are available, two
possible locations of the boundary are defined, and if only one
observation well is used, a circle describing all possible
locations of the image well is defined.
4.4 According to the principle of superposition, the draw-
5.2.3 The effects of a constant-head boundary are often
down at any point in the aquifer is the sum of the drawdown
indistinguishable from the effects of a leaky, confined aquifer.
due to the real and image wells (1) and (2):
Therefore, care must be taken to ensure that a correct concep-
s 5 s 6s (4)
o r i
tualmodelofthesystemhasbeencreatedpriortoanalyzingthe
test. See Guide D4043.
Equation (4) can be rewritten as follows:
Q Q
6. Apparatus
s 5 @W~u !6W~u !# 5 W~u! (5)
o r i (
4πT 4πT
6.1 Analysis of the data from the field procedure (see Test
where:
Method D4050) by this test method requires that the control
2 2
r S r S
r i well and observation wells meet the requirements specified in
u 5 , u 5 (6)
r i
4Tt 4Tt
the following subsections.
so that:
6.2 Construction of Control Well—Installthecontrolwellin
theaquiferandequipwithapumpcapableofdischargingwater
r
i
u 5 u , u 5 K u (7)
S D
i r i l r from the well at a constant rate for the duration of the test.
r
r
Preferably, the control well should be open throughout the full
where:
thickness of the aquifer. If the control well partially penetrates
r theaquifer,takespecialprecautionsintheplacementordesign
i
K 5 (8)
l
r of observation wells (see 5.2.1).
r
D5270−96 (2008)
6.3 Construction of Observation Wells and Piezometers— 7.3.1 Theis Nonequilibrium Method—ExpressionsinEq5-8
Construct one or more observation wells or piezometers at are used to generate a family of curves of 1/u versus∑ W( u)
r
specified distances from the control well.
for values of K for recharging and discharging image wells as
l
shown in Fig. 3 (2). Table 1 gives values of W(u) versus 1/u.
6.4 Location of Observation Wells and Piezometers —Wells
Thistablemaybeusedtocreateatableof∑W(u)versus 1/ufor
maybelocatedatanydistancefromthecontrolwellwithinthe
each value of K by picking values for W(u ) and W(u), and
l r i
area of influence of pumping. However, if vertical flow
computing the ∑ W(u) for the each value of 1/u.
componentsareexpectedtobesignificantnearthecontrolwell
andifpartiallypenetratingobservationwellsaretobeused,the 7.3.1.1 Transmissivity, storage coefficient, and the possible
observation wells should be located at a distance beyond the
location of one or more boundaries are calculated from
effectofverticalflowcomponents.Iftheaquiferisunconfined, parameters determined from the match point and a curve
constraints are imposed on the distance to partially penetrating
selected from a family of type curves.
observation wells and on the validity of early time measure-
7.3.2 Modified Theis Nonequilibrium Method—The sum of
ments (see Test Method D4106).
the terms to the right of log u in Eq 3 is not significant when
e
u becomes small, that is, equal to or less than 0.01.
NOTE 2—To ensure that the effects of the boundary may be observed
during the tests, some of the wells should be located along lines parallel
NOTE 3—The limiting value for u of less than 0.01 may be excessively
to the suspected boundary, no farther from the boundary than the control
restrictive in some applications. The errors for small values of u, from
well.
Kruseman and DeRidder (3) are as follows:
7. Procedure
Error less than, %: 1 2 5 10
For u smaller than: 0.03 0.05 0.1 0.15
7.1 The general procedure consists of conducting the field
7.3.2.1 The value of u decreases as time, t, increases and
procedure for withdrawal or injection wells tests (see Test
decreases as radial distance, r, decreases. Therefore, for large
Method D4050) and analyzing the field data, as addressed in
this test method. values of t and small values of r, the terms to the right of log
eu in Eq 3 may be neglected, as recognized by Theis (1). The
7.2 Analysis of the field data consists of two steps: deter-
modified Theis equation can then be written as follows:
mination of the properties of the aquifer and the nature and
Q r S
distance to the image well from each observation well, and
s 5 20.577216 2log (9)
S S DD
e
determination of the location of the boundary. 4πT 4Tt
7.3 Two methods of analysis can be used to determine the
from which it has been shown by Lohman (4) that:
aquifer properties and the nature and distance to the image
2.3Q
well. One method is based on the Theis nonequilibrium
T 5 (10)
4π∆s
method; the other method is based on the modified Theis
nonequilibrium method. where:
NOTE 1—From Stallman (2).
FIG. 3Family of Type Curves for the Solution of the Modified Theis Formula
D5270−96 (2008)
TABLE 1 Values of Theis equation W(u) for values of 1/u (8)
−1 2 3 4 4 4
1/u 1/u ×10 110 10 10 10 10 10
A
1.0 0.00000 0.21938 1.82292 4.03793 6.33154 8.63322 10.93572 13.23830
1.2 0.00003 0.29255 1.98932 4.21859
...
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