ASTM D6034-96(2010)e1

Standard Test Method (Analytical Procedure) for Determining the Efficiency of a Production Well in a Confined Aquifer from a Constant Rate Pumping Test

SIGNIFICANCE AND USE
This test method allows the user to compute the true hydraulic efficiency of a pumped well in a confined aquifer from a constant rate pumping test. The procedures described constitute the only valid method of determining well efficiency. Some practitioners have confused well efficiency with percentage of head loss associated with laminar flow, a parameter commonly determined from a step-drawdown test. Well efficiency, however, cannot be determined from a step-drawdown test but only can be determined from a constant rate test.
Assumptions:  
Control well discharges at a constant rate, Q.
Control well is of infinitesimal diameter.
Data are obtained from the control well and, if available, a number of observation wells.
The aquifer is confined, homogeneous, and areally extensive. The aquifer may be anisotropic, and if so, the directions of maximum and minimum hydraulic conductivity are horizontal and vertical, respectively.  
Discharge from the well is derived exclusively from storage in the aquifer.
Calculation Requirements—For the special case of partially penetrating wells, application of this test method may be computationally intensive. The function fs  shown in Eq 6 must be evaluated using arbitrary input parameters. It is not practical to use existing, somewhat limited, tables of values for fs and, because this equation is rather formidable, it is not readily tractable by hand. Because of this, it is assumed the practitioner using this test method will have available a computerized procedure for evaluating the function fs. This can be accomplished using commercially available mathematical software including some spreadsheet applications or by writing programs in languages, such as Fortran or C. If calculating fs  is not practical, it is possible to substitute the Kozeny equation for the Hantush equation as previously described.
SCOPE
1.1 This test method describes an analytical procedure for determining the hydraulic efficiency of a production well in a confined aquifer. It involves comparing the actual drawdown in the well to the theoretical minimum drawdown achievable and is based upon data and aquifer coefficients obtained from a constant rate pumping test.
1.2 This analytical procedure is used in conjunction with the field procedure, Test Method D4050.
1.3 The values stated in inch-pound units are to be regarded as standard, except as noted below. The values given in parentheses are mathematical conversions to SI units, which are provided for information only and are not considered standard.
1.3.1 The gravitational system of inch-pound units is used when dealing with inch-pound units. In this system, the pound (lbf) represents a unit of force (weight), while the unit for mass is slugs.
1.4 Limitations—The limitations of the technique for determination of well efficiency are related primarily to the correspondence between the field situation and the simplifying assumption of this test method.
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.

General Information

• Status: Historical
• Publication Date: 31-Jul-2010
• ICS: 93.160 - Hydraulic construction
• Technical Committee: D18 - Soil and Rock
• Drafting Committee: D18.21 - Groundwater and Vadose Zone Investigations

Relations

• Replaces: ASTM D6034-96(2004) - Standard Test Method (Analytical Procedure) for Determining the Efficiency of a Production Well in a Confined Aquifer from a Constant Rate Pumping Test
• Effective Date: 01-Aug-2010
• Replaced By: ASTM D6034-17 - Standard Test Method (Analytical Procedure) for Determining the Efficiency of a Production Well in a Confined Aquifer from a Constant Rate Pumping Test
• Effective Date: 01-Jan-2017

Standards Content (Sample)

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
´1
Designation:D6034 −96 (Reapproved 2010)
Standard Test Method (Analytical Procedure) for
Determining the Efficiency of a Production Well in a
Confined Aquifer from a Constant Rate Pumping Test
This standard is issued under the fixed designation D6034; 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.
ε NOTE—A units statement was added editorially in August 2010.
1. Scope D653Terminology Relating to Soil, Rock, and Contained
Fluids
1.1 This test method describes an analytical procedure for
D4050Test Method for (Field Procedure) for Withdrawal
determining the hydraulic efficiency of a production well in a
and Injection Well Testing for Determining Hydraulic
confinedaquifer.Itinvolvescomparingtheactualdrawdownin
Properties of Aquifer Systems
the well to the theoretical minimum drawdown achievable and
D5521Guide for Development of Groundwater Monitoring
is based upon data and aquifer coefficients obtained from a
Wells in Granular Aquifers
constant rate pumping test.
1.2 Thisanalyticalprocedureisusedinconjunctionwiththe
3. Terminology
field procedure, Test Method D4050.
3.1 Definitions—For definitions of terms used in this test
1.3 The values stated in inch-pound units are to be regarded
method, see Terminology D653.
as standard, except as noted below. The values given in
3.2 Definitions of Terms Specific to This Standard:
parentheses are mathematical conversions to SI units, which
3.2.1 aquifer, confined, n—an aquifer bounded above and
are provided for information only and are not considered
below by confining beds and in which the static head is above
standard.
the top of the aquifer.
1.3.1 The gravitational system of inch-pound units is used
when dealing with inch-pound units. In this system, the pound 3.2.2 confining bed, n—a hydrogeologic unit of less perme-
able material bounding one or more aquifers.
(lbf)representsaunitofforce(weight),whiletheunitformass
is slugs.
3.2.3 control well, n—a well by which the head and flow in
the aquifer is changed, for example, by pumping, injection, or
1.4 Limitations—The limitations of the technique for deter-
imposing a constant change of head.
mination of well efficiency are related primarily to the corre-
spondence between the field situation and the simplifying
3.2.4 drawdown, n—vertical distance the static head is
assumption of this test method.
lowered due to the removal of water.
1.5 This standard does not purport to address all of the
3.2.5 hydraulic conductivity, n—(field aquifer test) the vol-
safety concerns, 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-
area measured at right angles to the direction flow.
bility of regulatory limitations prior to use.
3.2.6 observation well, n—a well open to all or part of an
aquifer.
2. Referenced Documents
2 3.2.7 piezometer, n—a device so constructed and sealed as
2.1 ASTM Standards:
to measure hydraulic head at a point in the subsurface.
3.2.8 storage coeffıcient, n—the volume of water an aquifer
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
releases from or takes into storage per unit surface area of the
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
aquifer per unit change in head.
Vadose Zone Investigations.
Current edition approved Aug. 1, 2010. Published September 2010. Originally
3.2.9 transmissivity, n—the volume of water at the existing
approved in 1996. Last previous edition approved in 2004 as D6034–96(2004).
kinematic viscosity that will move in a unit time under a unit
DOI: 10.1520/D6034-96R10E01.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
hydraulic gradient through a unit width of the aquifer.
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
3.2.10 well effıciency, n—the ratio, usually expressed as a
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. percentage, of the measured drawdown inside the control well
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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D6034−96 (2010)
divided into the theoretical drawdown which would occur in 4. Summary of Test Method
the aquifer just outside the borehole if there were no drilling
4.1 Thistestmethodusesdatafromaconstantratepumping
damage, that is, no reduction in the natural permeability of the
test to determine the well efficiency. The efficiency is calcu-
sediments in the vicinity of the borehole.
latedastheratioofthetheoreticaldrawdownintheaquiferjust
3.3 Symbols: outsidethewellbore(s )tothedrawdownmeasuredinsidethe
r
w
pumped well (s ). The theoretical drawdown in the aquifer
3.3.1 Symbols and Dimensions:
w
−1
(s ) is determined from the pumping test data by either
3.3.2 K—hydraulic conductivity [LT ]. r
w
extrapolation or direct calculation.
3.3.2.1 Discussion—The use of the symbol K for the term
hydraulic conductivity is the predominant usage in groundwa-
4.2 During the drilling of a well, the hydraulic conductivity
ter literature by hydrogeologists, whereas the symbol k is
of the sediments in the vicinity of the borehole wall is reduced
commonly used for this term in soil and rock mechanics and
significantly by the drilling operation. Damaging effects of
soil science.
drilling include mixing of fine and coarse formation grains,
invasion of drilling mud, smearing of the borehole wall by the
3.3.3 K —hydraulic conductivity in the plane of the aquifer,
r
drillingtools,andcompactionofsandgrainsneartheborehole.
radially from the control well (horizontal hydraulic conductiv-
−1
The added head loss (drawdown) associated with the perme-
ity) [LT ].
ability reduction due to drilling damage increases the draw-
3.3.4 K —hydraulic conductivity normal to the plane of the
z
downinthepumpedwellandreducesitsefficiency(seeFig.1).
−1
aquifer (vertical hydraulic conductivity) [ LT ].
Well development procedures help repair the damage (see
3.3.5 K (x)—modified Bessel function of the second kind Guide D5521) but generally cannot restore the sediments to
and zero order [nd]. their original, natural permeability.
3 −1 4.2.1 Additional drawdown occurs from head loss associ-
3.3.6 Q—discharge [L T ].
ated with flow through the filter pack, through the well screen
3.3.7 S—storage coefficient [nd].
and vertically upward inside the well casing to the pump
2 −1
intake. While these drawdown components contribute to
3.3.8 T—transmissivity [L T ].
inefficiency, they usually are minor in comparison to the head
3.3.9 s —drawdown in the aquifer at a distance r from the
r
loss resulting from drilling damage.
control well [ L].
4.2.2 Thewellefficiency,usuallyexpressedasapercentage,
3.3.10 s —drawdown which would occur in response to
f is defined as the theoretical drawdown, also called aquifer
pumping a fully penetrating well [ L].
drawdown, which would have occurred just outside the well if
there were no drilling damage divided by the actual drawdown
3.3.11 r —borehole radius of control well [L].
w
inside the well. The head losses contributing to inefficiency
3.3.12 s —theoretical drawdown which would occur in the
rw
generally are constant with time while aquifer drawdown
aquifer just outside the borehole if there were no drilling
gradually increases with time. This causes the computed
damage, that is, no reduction in the natural permeability of the
efficiencytoincreaseslightlywithtime.Becausetheefficiency
sediments in the vicinity of the borehole [L].
issomewhattimedependent,usuallyitisassumedthatthewell
3.3.13 s —drawdown measured inside the control well [L].
w efficiency is the calculated drawdown ratio achieved after one
day of continuous pumping. It is acceptable, however, to use
3.3.14 u—(r S)/(4Tt)[nd].
other pumping times, as long as the time that was used in the
3.3.15 W(u)—an exponential integral known in hydrology
efficiency calculation is specified. The only restriction on the
as the Theis well function of u [nd].
pumping time is that sufficient time must have passed so that
3.3.16 A—K /K , anisotropy ratio [nd].
z r
3.3.17 b—thickness of aquifer [ L].
3.3.18 d—distance from top of aquifer to top of screened
interval of control well [L].
3.3.19 d'—distance from top of aquifer to top of screened
interval of observation well [L].
3.3.20 f —incrementaldimensionlessdrawdowncomponent
s
resulting from partial penetration [nd].
3.3.21 l—distancefromtopofaquifertobottomofscreened
interval of control well [L].
3.3.22 l'—distancefromtopofaquifertobottomofscreened
interval of observation well [L].
3.3.23 r—radial distance from control well [L].
3.3.24 t—time since pumping began [ T].
FIG. 1 Illustration of Drawdown Inside and Outside Pumping
3.3.25 E—well efficiency [nd]. Well
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D6034−96 (2010)
wellbore storage effects are insignificant. In the vast majority 4.3.3.3 The Kozeny equation is as follows:
of cases, after one day of pumping, the effects of wellbore
s
f
storage have long since become negligible. s 5 (7)
r
l 2 d r π l 2 d
~ !
4.2.3 Efficiency is also somewhat discharge dependent.
S117 cos D
Œ
b 2 l 2 d 2b
~ !
Boththeaquiferdrawdownandtheinefficiencydrawdowncan
include both laminar (first order) and turbulent (approximately
4.3.3.4 In this equation, s is the drawdown for a fully
f
second order) components. Because the proportion of laminar
penetrating well system and can be computed from Eq 1-4.
versusturbulentflowcanbedifferentintheundisturbedaquifer
While easier to compute than the Hantush equation, the
than it is in the damaged zone and inside the well, the aquifer
Kozeny equation is not as accurate. It does not incorporate
drawdown and inefficiency drawdown can increase at different
pumping time or anisotropy and assumes that the screen in the
rates as Q increases. When this happens, the calculated
control well reaches either the top or the bottom of the aquifer.
efficiency is different for different pumping rates. Because of
4.3.4 The presence of a positive boundary (for example,
this discharge dependence, efficiency testing usually is per-
recharge) causes the drawdown in the aquifer to be less than
formed at or near the design discharge rate.
predicted by Eq 1-6, while a negative boundary (for example,
the aquifer pinching out) results in more drawdown. The
4.3 Thedrawdownintheaquiferaroundawellpumpedata
boundary-induced increases or decreases in drawdown usually
constant rate can be described by one of several equations.
canbedeterminedfromthepumpingtestdata.Theseincreases/
4.3.1 For fully penetrating wells, the Theis equation (1) is
decreases can be combined with calculations using Eq 1-7 to
used.
determine the drawdown just outside the well bore.
Q
s 5 W u (1)
~ !
r
4.4 The efficiency of a production well is calculated as
4πT
follows:
where:
s
r
2x w
` e
E 5 (8)
s
W u 5 dx (2)
~ ! * w
u
x
where:
and
s = denominator,thedrawdownmeasuredinsidethewell,
w
r S
and
u 5 (3)
4Tt
s = numerator, must be determined from field data.
rw
4.3.2 For sufficiently small values of u, the Theis equation
Two procedures are available for determining s —
rw
may be approximated by the Cooper-Jacob equation (2).
extrapolation and direct calculation.
4.4.1 Extrapolation—Extrapolation can be used to deter-
2.3Q 2.25Tt
s 5 log (4)
S D
r 2 mine s if data from two or more observation wells are
4πT r S r
w
available. Distance drawdown data can be plotted from these
4.3.2.1 Examplesoferrorsinthisapproximationforsome u
wells on either log-log or semilog graphs. If a log-log plot is
values are as follows:
used,theTheistypecurveisusedtoextrapolatethedrawdown
u Error
datatotheboreholeradiustodetermine s .Ifasemilogplotis
r
w
0.01 0.25 %
used, extrapolation is done using a straight line of best fit. The
0.03 1.01 %
semilog method can be used only if the u value for each
0.05 2.00 %
0.10 5.35 %
observation well is sufficiently small that the error introduced
by the log approximation to the Theis equation is minimal.
4.3.3 For partially penetrating wells, the drawdown can be
described by either the Hantush equation (3-5) or the Kozeny 4.4.1.1 Forpartiallypenetratingwells,theobservationwells
must be located beyond the zone affected by partial
equation (6).
4.3.3.1 The Hantush equation is similar to the Theis equa- penetration, that is, at a distance r from the pumped well such
that:
tion but includes a correction factor for partial penetration.
1.5b
Q
r$ (9)
s 5 ~W~u!1f ! (5)
r s
4πT
= K /K
z r
4.3.3.2 According to Hantush, at late pumping times, when
4.4.1.2 The extrapolated drawdown obtained in this case is
t > b S/(2TA), f can be expressed as follows:
s
s, the theoretical drawdown, which would have occurred just
f
outside the borehole of a fully penetrating pumped well. The
`
=
4b 1 nπr K /K
z r
f 5 K S D (6)
S D aquifer drawdown corresponding to partial penetration is then
2 2
s ( 0
π l 2 d l'2d' n b
~ !~ !
n51
computed with the Hantush equation as follows:
nπl nπd nπl nπd
Q
sin 2 sin sin 2 sin
F S D S DGF S D S DG
s 5 s 1 f (10)
r f s
b b b b w
4πT
4.4.1.3 The second term on the right-hand side of Eq 10
represents the incremental aquifer drawdown caused by partial
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this test method. penetration.
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D6034−96 (2010)
4.4.1.4 Using the Kozeny equation, the aquifer drawdown gramsinlanguages,suchasFortranor C.Ifcalculating f isnot
s
for partial penetration is computed from Eq 7 with r set equal practical,itispossibletosubstitutetheKozenyequationforthe
to the borehole radius r : Hantush equation as previously described.
w
s
f
6. Apparatus
s 5 (11)
r
w
l 2 d r π l 2 d
~ !
w
6.1 Apparatus for withdrawal tests is given in Test Method
S 117Πcos D
b 2 l 2 d 2b
~ !
D4050. The following apparatus are those components of the
4.4.1.5 If the extrapolation method is used for determining apparatus that require special attributes for this specific test.
aquifer drawdown, it is not necessary to make a separate
6.2 Construction of the Control Well—Install the control
adjustment to account for boundaries or recharge.
well in the aquifer and equip with a pump capable of
4.4.2 Direct Calculation—If the aquifer drawdown s can-
rw
discharging water from the well at a constant rate for the
not be obtained by extrapolation, direct calculation must be
...