ASTM D6034-96
(Test Method)Standard Test Method (Analytical Procedure) for Determining the Efficiency of a Production Well in a Confined Aquifer from a Constant Rate Pumping Test
Standard Test Method (Analytical Procedure) for Determining the Efficiency of a Production Well in a Confined Aquifer from a Constant Rate Pumping Test
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 D 4050.
1.3 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.
1.4 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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Designation: D 6034 – 96
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope D4750 Test Method for Determining Subsurface Liquid
Levels in a Borehole or Monitoring Well (Observation
1.1 This test method describes an analytical procedure for
Well)
determining the hydraulic efficiency of a production well in a
D5521 Guide for Development of Ground-Water Monitor-
confinedaquifer.Itinvolvescomparingtheactualdrawdownin
ing Wells in Granular Aquifers
the well to the theoretical minimum drawdown achievable and
D5850 Test Method (Analytical Procedure) for Determin-
is based upon data and aquifer coefficients obtained from a
ing Transmissivity, Storage Coefficient, and Anisotropy
constant rate pumping test.
RatiofromaNetworkofPartiallyPenetratingWellsUsing
1.2 Thisanalyticalprocedureisusedinconjunctionwiththe
Distance-Drawdown Data and Iterative Procedure
field procedure, Test Method D4050.
1.3 Limitations—The limitations of the technique for deter-
3. Terminology
mination of well efficiency are related primarily to the corre-
3.1 Definitions—For definitions of terms used in this test
spondence between the field situation and the simplifying
method, see Terminology D653.
assumption of this test method.
3.2 Definitions of Terms Specific to This Standard:
1.4 This standard does not purport to address all of the
3.2.1 aquifer, confined, n—an aquifer bounded above and
safety concerns, if any, associated with its use. It is the
below by confining beds and in which the static head is above
responsibility of the user of this standard to establish appro-
the top of the aquifer.
priate safety and health practices and determine the applica-
3.2.2 confining bed, n—a hydrogeologic unit of less perme-
bility of regulatory limitations prior to use.
able material bounding one or more aquifers.
2. Referenced Documents 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
2.1 ASTM Standards:
imposing a constant change of head.
D653 Terminology Relating to Soil, Rock, and Contained
3.2.4 drawdown, n—vertical distance the static head is
Fluids
lowered due to the removal of water.
D4043 Guide for Selection of Aquifer Test Method in
3.2.5 hydraulic conductivity, n—(field aquifer test) the vol-
Determining Hydraulic Properties by Well Techniques
umeofwaterattheexistingkinematicviscositythatwillmove
D4050 Test Method (Field Procedure) for Withdrawal and
in a unit time under a unit hydraulic gradient through a unit
Injection Well Tests for Determining Hydraulic Properties
2 area measured at right angles to the direction flow.
of Aquifer Systems
3.2.6 observation well, n—a well open to all or part of an
D4105 Test Method (Analytical Procedure) for Determin-
aquifer.
ing Transmissivity and Storage Coefficient of Nonleaky
3.2.7 piezometer, n—a device so constructed and sealed as
Confined Aquifers by the Modified Theis Nonequilibrium
to measure hydraulic head at a point in the subsurface.
Method
3.2.8 storage coeffıcient, n—the volume of water an aquifer
D4106 Test Method (Analytical Procedure) for Determin-
releases from or takes into storage per unit surface area of the
ing Transmissivity and Storage Coefficient of Nonleaky
aquifer per unit change in head.
Confined Aquifers by the Theis Nonequilibrium Method
3.2.9 transmissivity, n—the volume of water at the existing
kinematic viscosity that will move in a unit time under a unit
This test method is under the jurisdiction of ASTM Committee D-18 on Soil hydraulic gradient through a unit width of the aquifer.
andRockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWater
and Vadose Zone Investigation.
Current edition approved Oct. 10, 1996. Published June 1997.
2 3
Annual Book of ASTM Standards, Vol 04.08. Annual Book of ASTM Standards, Vol 04.09.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D6034–96
3.2.10 well effıciency, n—the ratio, usually expressed as a (s ) is determined from the pumping test data by either
r
w
percentage, of the measured drawdown inside the control well extrapolation or direct calculation.
divided into the theoretical drawdown which would occur in 4.2 During the drilling of a well, the hydraulic conductivity
the aquifer just outside the borehole if there were no drilling of the sediments in the vicinity of the borehole wall is reduced
damage, that is, no reduction in the natural permeability of the significantly by the drilling operation. Damaging effects of
sediments in the vicinity of the borehole. drilling include mixing of fine and coarse formation grains,
3.3 Symbols:Symbols and Dimensions: invasion of drilling mud, smearing of the borehole wall by the
−1
3.3.1 K—hydraulic conductivity [LT ]. drillingtools,andcompactionofsandgrainsneartheborehole.
The added head loss (drawdown) associated with the perme-
3.3.1.1 Discussion—The use of the symbol K for the term
hydraulic conductivity is the predominant usage in ground- ability reduction due to drilling damage increases the draw-
downinthepumpedwellandreducesitsefficiency(seeFig.1).
water literature by hydrogeologists, whereas the symbol k is
commonly used for this term in soil and rock mechanics and Well development procedures help repair the damage (see
Guide D5521) but generally cannot restore the sediments to
soil science.
3.3.2 K—hydraulicconductivityintheplaneoftheaquifer, their original, natural permeability.
r
4.2.1 Additional drawdown occurs from head loss associ-
radially from the control well (horizontal hydraulic conductiv-
−1
ated with flow through the filter pack, through the well screen
ity) [LT ].
and vertically upward inside the well casing to the pump
3.3.3 K —hydraulic conductivity normal to the plane of the
z
−1
intake. While these drawdown components contribute to inef-
aquifer (vertical hydraulic conductivity) [ LT ].
ficiency, they usually are minor in comparison to the head loss
3.3.4 K (x)—modified Bessel function of the second kind
resulting from drilling damage.
and zero order [nd].
3 −1
4.2.2 Thewellefficiency,usuallyexpressedasapercentage,
3.3.5 Q—discharge [L T ].
is defined as the theoretical drawdown, also called aquifer
3.3.6 S—storage coefficient [nd].
2 −1
drawdown, which would have occurred just outside the well if
3.3.7 T—transmissivity [L T ].
there were no drilling damage divided by the actual drawdown
3.3.8 s—drawdown in the aquifer at a distance r from the
r
inside the well. The head losses contributing to inefficiency
control well [ L].
generally are constant with time while aquifer drawdown
3.3.9 s—drawdown which would occur in response to
f
gradually increases with time. This causes the computed
pumping a fully penetrating well [L].
efficiencytoincreaseslightlywithtime.Becausetheefficiency
3.3.10 r —borehole radius of control well [L].
w
issomewhattimedependent,usuallyitisassumedthatthewell
3.3.11 s —theoreticaldrawdownwhichwouldoccurinthe
rw
efficiency is the calculated drawdown ratio achieved after one
aquifer just outside the borehole if there were no drilling
day of continuous pumping. It is acceptable, however, to use
damage, that is, no reduction in the natural permeability of the
other pumping times, as long as the time that was used in the
sediments in the vicinity of the borehole [L].
efficiency calculation is specified. The only restriction on the
3.3.12 s —drawdown measured inside the control well [L].
w
pumping time is that sufficient time must have passed so that
3.3.13 u—(r S)/(4Tt)[nd].
wellbore storage effects are insignificant. In the vast majority
3.3.14 W(u)—an exponential integral known in hydrology
of cases, after one day of pumping, the effects of wellbore
as the Theis well function of u [nd].
storage have long since become negligible.
3.3.15 A—K /K , anisotropy ratio [nd].
z r
4.2.3 Efficiency is also somewhat discharge dependent.
3.3.16 b—thickness of aquifer [ L].
Boththeaquiferdrawdownandtheinefficiencydrawdowncan
3.3.17 d—distance from top of aquifer to top of screened
include both laminar (first order) and turbulent (approximately
interval of control well [L].
second order) components. Because the proportion of laminar
3.3.18 d8—distance from top of aquifer to top of screened
interval of observation well [L].
3.3.19 f —incremental dimensionless drawdown compo-
s
nent resulting from partial penetration [nd].
3.3.20 l—distancefromtopofaquifertobottomofscreened
interval of control well [L].
3.3.21 l8—distance from top of aquifer to bottom of
screened interval of observation well [L].
3.3.22 r—radial distance from control well [L].
3.3.23 t—time since pumping began [ T].
3.3.24 E—well efficiency [nd].
4. Summary of Test Method
4.1 Thistestmethodusesdatafromaconstantratepumping
test to determine the well efficiency. The efficiency is calcu-
latedastheratioofthetheoreticaldrawdownintheaquiferjust
outsidethewellbore(s )tothedrawdownmeasuredinsidethe
r
w
pumped well (s ). The theoretical drawdown in the aquifer FIG. 1 Illustration of Drawdown Inside and Outside Pumping Well
w
D6034–96
versusturbulentflowcanbedifferentintheundisturbedaquifer pumping time or anisotropy and assumes that the screen in the
than it is in the damaged zone and inside the well, the aquifer control well reaches either the top or the bottom of the aquifer.
drawdown and inefficiency drawdown can increase at different
4.3.4 The presence of a positive boundary (for example,
rates as Q increases. When this happens, the calculated
recharge) causes the drawdown in the aquifer to be less than
efficiency is different for different pumping rates. Because of
predicted by Eq 1-6, while a negative boundary (for example,
this discharge dependence, efficiency testing usually is per-
the aquifer pinching out) results in more drawdown. The
formed at or near the design discharge rate.
boundary-induced increases or decreases in drawdown usually
4.3 Thedrawdownintheaquiferaroundawellpumpedata
canbedeterminedfromthepumpingtestdata.Theseincreases/
constant rate can be described by one of several equations.
decreases can be combined with calculations using Eq 1-7 to
4.3.1 For fully penetrating wells, the Theis equation (1) is
determine the drawdown just outside the well bore.
used.
4.4 The efficiency of a production well is calculated as
Q
follows:
s 5 W~u! (1)
r
4pT
s
r
w
where: E 5 (8)
s
w
2x
e
`
W~u! 5 dx (2) where:
*u
x
s = denominator, the drawdown measured inside the
w
and
well, and
s = numerator, must be determined from field data.
rw
r S
u 5 (3)
4Tt Two procedures are available for determining s —
rw
extrapolation and direct calculation.
4.3.2 For sufficiently small values of u, the Theis equation
4.4.1 Extrapolation—Extrapolation can be used to deter-
may be approximated by the Cooper-Jacob equation (2).
mine s if data from two or more observation wells are
r
2.3Q 2.25Tt
w
s 5 log (4)
r 2 available. Distance drawdown data can be plotted from these
S D
4pT
r S
wells on either log-log or semilog graphs. If a log-log plot is
4.3.2.1 Examplesoferrorsinthisapproximationforsome u
used,theTheistypecurveisusedtoextrapolatethedrawdown
values are as follows:
data to the borehole radius to determine s . If a semilog plot
r
w
u Error
is used, extrapolation is done using a straight line of best fit.
0.01 0.25 %
The semilog method can be used only if the u value for each
0.03 1.01 %
0.05 2.00 %
observation well is sufficiently small that the error introduced
0.10 5.35 %
by the log approximation to the Theis equation is minimal.
4.3.3 For partially penetrating wells, the drawdown can be
4.4.1.1 Forpartiallypenetratingwells,theobservationwells
described by either the Hantush equation (3-5) or the Kozeny
must be located beyond the zone affected by partial penetra-
equation (6).
tion, that is, at a distance r from the pumped well such that:
4.3.3.1 The Hantush equation is similar to the Theis equa-
1.5b
tion but includes a correction factor for partial penetration.
r$ (9)
K /K
=
z r
Q
s 5 ~W~u! 1 f ! (5)
r s
4.4.1.2 The extrapolated drawdown obtained in this case is
4pT
s, the theoretical drawdown, which would have occurred just
f
4.3.3.2 According to Hantush, at late pumping times, when
outside the borehole of a fully penetrating pumped well. The
t > b S/(2TA), f can be expressed as follows:
s
aquifer drawdown corresponding to partial penetration is then
`
4b 1 npr K /K
=
z r
computed with the Hantush equation as follows:
f 5 K (6)
(
s 2 S 2D 0S D
b
n 51
p ~l– d!~l8– d8! n
Q
s 5 s 1 f (10)
npl npd npl npd r f s
w 4pT
sin –sin sin – sin
F S D S DGF S D S DG
b b b b
4.4.1.3 The second term on the right-hand side of Eq 10
4.3.3.3 The Kozeny equation is as follows:
represents the incremental aquifer drawdown caused by partial
s
f
penetration.
s 5 (7)
r
l 2 d r p l 2 d!
~
4.4.1.4 Using the Kozeny equation, the aquifer drawdown
1 17 cos
S ΠD
b 2b
2~l– d!
for partial penetration is computed from Eq 7 with r set equal
4.3.3.4 In this equation, sis the drawdown for a fully
to the borehole radius r :
f
w
penetrating well system and can be computed from Eq 1-4.
s
f
While easier to compute than the Hantush equation, the s 5 (11)
r
w
l 2 d r p~l 2 d!
w
Kozeny equation is not as accurate. It does not incorporate 1 17 cos
S D
Œ
b 2~l 2 d! 2b
4.4.1.5 If the extrapolation method is used for determining
aquifer drawdown, it is not necessary to make a separate
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this test method. adjustment to account for boundaries or recharge.
D6034–96
4.4.2 Direct Calculation—If the aquifer drawdown s can- discharging water from the well at a constant rate for the
rw
not be obtained by extrapolation, direct calculation must be durationofthetest.Afullypenetratingcontrolwellispreferred
used to determine its value. though not essential.
6.3 Construction and Placement of Observation Wells—If
4.4.2.1 For fully penetrating wells, s can be obtained by
rw
observationwellsareused,theyshouldbelocatedonastraight
direct calculation using either the Theis or Cooper-Jacob
lineextendingfromthecontrolwellandpositionedatdifferent
equations (Eq 1-4).
distances so that they span a good portion of the anticipated
4.4.2.2 For partially penetrating wells, s is calc
...
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