ASTM D5270-96(2014)
(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
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, isotropic, 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 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.
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 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.
5.2.2 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.
5.2.3 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 pr...
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 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.5 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 2014)
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
2.1 ASTM Standards:
1.1 This test method covers an analytical procedure for
D653Terminology Relating to Soil, Rock, and Contained
determiningthetransmissivity,storagecoefficient,andpossible
Fluids
location of boundaries for a confined aquifer with a linear
D3740Practice for Minimum Requirements for Agencies
boundary. This test method is used to analyze water-level or
Engaged in Testing and/or Inspection of Soil and Rock as
head data from one or more observation wells or piezometers
Used in Engineering Design and Construction
during the pumping of water from a control well at a constant
D4043Guide for Selection of Aquifer Test Method in
rate. This test method also applies to flowing artesian wells
Determining Hydraulic Properties by Well Techniques
discharging at a constant rate. With appropriate changes in
D4050Test Method for (Field Procedure) for Withdrawal
sign, this test method also can be used to analyze the effects of
and Injection Well Testing for Determining Hydraulic
injecting water into a control well at a constant rate.
Properties of Aquifer Systems
1.2 The analytical procedure in this test method is used in
D4105Test Method for (Analytical Procedure) for Deter-
conjunction with the field procedure in Test Method D4050.
mining Transmissivity and Storage Coefficient of Non-
leaky ConfinedAquifers by the Modified Theis Nonequi-
1.3 Limitations—Thevaliduseofthistestmethodislimited
librium Method
todeterminationoftransmissivitiesandstoragecoefficientsfor
D4106Test Method for (Analytical Procedure) for Deter-
aquifers in hydrogeologic settings with reasonable correspon-
mining Transmissivity and Storage Coefficient of Non-
dence to the assumptions of the Theis nonequilibrium method
leaky Confined Aquifers by the Theis Nonequilibrium
(see Test Method D4106) (see 5.1), except that the aquifer is
Method
limitedinarealextentbyalinearboundarythatfullypenetrates
D6026Practice for Using Significant Digits in Geotechnical
the aquifer. The boundary is assumed to be either a constant-
Data
head boundary (equivalent to a stream or lake that hydrauli-
cally fully penetrates the aquifer) or a no-flow (impermeable)
3. Terminology
boundary (equivalent to a contact with a significantly less
permeable rock unit). The Theis nonequilibrium method is 3.1 Definitions—For definitions of general technical terms
used within this practice, refer to Terminology D653.
described in Test Methods D4105 and D4106.
3.2 Definitions of Terms Specific to This Standard:
1.4 The values stated in SI units are to be regarded as
3.2.1 constant-head boundary—the conceptual representa-
standard. No other units of measurement are included in this
tion of a natural feature such as a lake or river that effectively
standard.
fully penetrates the aquifer and prevents water-level change in
1.5 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
3.2.2 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.
3.2.3 image well—an imaginary well located opposite a
control well such that a boundary is the perpendicular bisector
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
Vadose Zone Investigations. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Feb. 1, 2014. Published February 2014. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1992. Last previous edition approved in 2008 as D5270–96 (2008). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/D5270-96R14. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5270−96 (2014)
of a straight line connecting the control and image wells; used
to simulate the effect of a boundary on water-level changes.
3.2.4 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.
3.3 Symbols and Dimensions:
3.3.1 K [nd]—constant of proportionality, r ⁄r .
l i r
3 −1
3.3.2 Q [L T ]—discharge.
3.3.3 r [L]—radial distance from control well.
3.3.4 r [L]—distance from observation well to image well.
i
3.3.5 r [L]—distancefromobservationwelltocontrolwell.
r
3.3.6 S [nd]—storage coefficient.
3.3.7 s [L]—drawdown.
3.3.8 s [L]—component of drawdown due to image well.
i
3.3.9 s [L]—drawdown at an observation well.
o
3.3.10 s [L]—component of drawdown due to control well.
r
2 −1
3.3.11 T [L T ]—transmissivity.
3.3.12 t [T]—time since pumping or injection began.
3.3.13 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
defined by the Theis nonequilibrium method (see Test Method
D4106) or from straight-line segments defined by the modified
Theis nonequilibrium method (see Test Method D4105).
NOTE 1—Modified from Ferris and others (1) and Heath (2).
FIG. 1Diagram Showing Constant-Head Boundary
4.2 Aconstant-head boundary such as a lake or stream that
fully penetrates the aquifer prevents drawdown or build up of
head at the boundary, as shown in Fig. 1. Likewise, an
impermeable boundary provides increased drawdown or build 3
4.3 Solution—The solution given by Theis (3) can be
up of head, as shown in Fig. 2. These effects are simulated by
expressed as follows:
treating the aquifer as if it were infinite in extent and
2y
Q ` e
introducing an imaginary well or “image well” on the opposite
s 5 dy (1)
*
u
4πT y
side of the boundary a distance equal to the distance of the
controlwellfromtheboundary.Alinebetweenthecontrolwell
and:
and the image well is perpendicular to the boundary. If the
r S
boundary is a constant-head boundary, the flux from the image
u 5 (2)
4Tt
well is opposite in sign from that of the control well; for
example,theimageofadischargingcontrolwellisaninjection where:
well, whereas the image of an injecting well is a discharging
2y
` e
* dy 5 W~u! (3)
well. If the boundary is an impermeable boundary, the flux
u
y
from the image well has the same sign as that from the control
2 3 4
well. Therefore, the image of a discharging well across an u u u
520.577216 2 log u1u 2 1 2 1…
e
impermeable boundary is a discharging well. Because the
2!2 3!3 4!4
effects are symmetrical, only discharging control wells will be
described in the remainder of this test method, but this test
method is equally applicable, with the appropriate change in
The boldface numbers in parentheses refer to a list of references at the end of
sign, to control wells into which water is injected. this standard.
D5270−96 (2014)
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,
isotropic, 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
conditions,aquifertestscanbesuccessfullyanalyzedwhenthe
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
needed. If only two observation wells are available, two
possible locations of the boundary are defined, and if only one
NOTE 1—Modified from Ferris and others (1) and Heath (2).
observation well is used, a circle describing all possible
FIG. 2Diagram Showing Impermeable Boundary
locations of the image well is defined.
5.2.3 The effects of a constant-head boundary are often
indistinguishable from the effects of a leaky, confined aquifer.
4.4 According to the principle of superposition, the draw-
Therefore, care must be taken to ensure that a correct concep-
down at any point in the aquifer is the sum of the drawdown
tualmodelofthesystemhasbeencreatedpriortoanalyzingthe
due to the real and image wells (3) and (4):
test. See Guide D4043.
s 5 s 6s (4)
o r i
5.3 Practice D3740 provides evaluation factors for the
Equation (5) can be rewritten as follows:
activities in this standard.
Q Q
s 5 @W~u !6W~u !# 5 W~u! (5) NOTE 2—The quality of the result produced by this standard is
o r i (
4πT 4πT
dependent on the competence of the personnel performing it, and the
suitability of the equipment and facilities used. Agencies that meet the
where:
criteria of Practice D3740 are generally considered capable of competent
2 2
r S r S
and objective testing/sampling/inspection/etc. Users of this standard are
r i
u 5 , u 5 (6)
r i
cautioned that compliance with Practice D3740 does not in itself assure
4Tt 4Tt
reliable results. Reliable results depend on many factors; Practice D3740
so that:
provides a means of evaluating some of those factors.
r
i
6. Apparatus
u 5 u , u 5 K u (7)
S D
i r i l r
r
r
6.1 Analysis of the data from the field procedure (see Test
where:
Method D4050) by this test method requires that the control
r
well and observation wells meet the requirements specified in
i
K 5 (8)
l
r the following subsections.
r
D5270−96 (2014)
6.2 Construction of Control Well—Installthecontrolwellin 7.2 Analysis of the field data consists of two steps: deter-
theaquiferandequipwithapumpcapableofdischargingwater mination of the properties of the aquifer and the nature and
from the well at a constant rate for the duration of the test. distance to the image well from each observation well, and
Preferably, the control well should be open throughout the full determination of the location of the boundary.
thickness of the aquifer. If the control well partially penetrates
7.3 Two methods of analysis can be used to determine the
the aquifer, take special precautions in the placement or design
aquifer properties and the nature and distance to the image
of observation wells (see 5.2.1).
well. One method is based on the Theis nonequilibrium
6.3 Construction of Observation Wells and Piezometers— method; the other method is based on the modified Theis
Construct one or more observation wells or piezometers at
nonequilibrium method.
specified distances from the control well.
7.3.1 Theis Nonequilibrium Method—ExpressionsinEq5-8
are used to generate a family of curves of 1/u versus ∑ W( u)
6.4 Location of Observation Wells and Piezometers —Wells r
for values of K for recharging and discharging image wells as
l
maybelocatedatanydistancefromthecontrolwellwithinthe
shown in Fig. 3 (4). Table 1 gives values of W(u) versus 1/u.
area of influence of pumping. However, if vertical flow
Thistablemaybeusedtocreateatableof ∑W(u)versus 1/ufor
componentsareexpectedtobesignificantnearthecontrolwell
each value of K by picking values for W(u ) and W(u), and
l r i
andifpartiallypenetratingobservationwellsaretobeused,the
computing the ∑ W(u) for the each value of 1/u.
observation wells should be located at a distance beyond the
7.3.1.1 Transmissivity, storage coefficient, and the possible
effectofverticalflowcomponents.Iftheaquiferisunconfined,
location of one or more boundaries are calculated from
constraints are imposed on the distance to partially penetrating
parameters determined from the match point and a curve
observation wells and on the validity of early time measure-
selected from a family of type curves.
ments (see Test Method D4106).
7.3.2 Modified Theis Nonequilibrium Method—The sum of
NOTE 3—To ensure that the effects of the boundary may be observed
the terms to the right of log u in Eq 3 is not significant when
e
during the tests, some of the wells should be located along lines parallel
u becomes small, that is, equal to or less than 0.01.
to the suspected boundary, no farther from the boundary than the control
well.
NOTE 4—The limiting value for u of less than 0.01 may be excessively
restrictive in some applications. The errors for small values of u, from
7. Procedure
Kruseman and DeRidder (7) are as follows:
7.1 The general procedure consists of conducting the field Error less than, %: 1 2 5 10
For u smaller than: 0.03 0.05 0.1 0.15
procedure for withdrawal or injection wells tests (see Test
Method D4050) and analyzing the
...
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