ASTM D6034-20

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

SIGNIFICANCE AND USE
5.1 This practice allows the user to compute the true hydraulic efficiency of a pumped well in a confined aquifer from a constant rate pumping field 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.  
5.2 Assumptions:  
5.2.1 Control well discharges at a constant rate, Q.  
5.2.2 Control well is of infinitesimal diameter.  
5.2.3 Data are obtained from the control well and, if available, a number of observation wells.  
5.2.4 The aquifer is confined, homogeneous, and extensive. The aquifer may be anisotropic, and if so, the directions of maximum and minimum hydraulic conductivity are horizontal and vertical, respectively.  
5.2.5 Discharge from the well is derived exclusively from storage in the aquifer.  
5.3 Calculation Requirements—For the special case of partially penetrating wells, application of this practice may be computationally intensive. The function fs shown in Eq 6 should 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 may not be tractable by hand. Because of this, it is assumed the practitioner using this practice will have available a computerized procedure for evaluating the function fs. This can be accomplished using commercially available mathematical software including some spreadsheet applications. If calculating fs is not practical, it is recommended to substitute the Kozeny equation for the Hantush equation as previously described.
Note 1: The quality of the result produced by this standard is dependent on the competence of the personnel performing it, and the suitability o...
SCOPE
1.1 This practice 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 practice 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. The reporting of results in units other than inch-pound shall not be regarded as nonconformance with this 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 practice.  
1.5 All observed and calculated values shall conform to the guidelines for significant digits and round established in Practice D6026, unless superseded by this standard.  
1.5.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as the industry standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objectives; and it is common practice to increase or reduce significant digits of reported date to be commensurate with these considerations. It is beyond the scope of this standard to ...

General Information

• Status: Published
• Publication Date: 31-May-2020
• ICS: 93.160 - Hydraulic construction
• Technical Committee: D18 - Soil and Rock
• Drafting Committee: D18.21 - Groundwater and Vadose Zone Investigations

Relations

• Replaces: 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-Jun-2020
• Refers: ASTM D3740-23 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Nov-2023
• Refers: ASTM D4050-20 - Standard Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of Aquifer Systems
• Effective Date: 01-Jan-2020
• Refers: ASTM D3740-19 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Oct-2019
• Refers: ASTM D5521/D5521M-18 - Standard Guide for Development of Groundwater Monitoring Wells in Granular Aquifers
• Effective Date: 01-Jun-2018
• Refers: ASTM D653-14 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-2014
• Refers: ASTM D4050-14 - Standard Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of Aquifer Systems
• Effective Date: 01-Jun-2014
• Refers: ASTM D3740-12a - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-May-2012
• Refers: ASTM D3740-12 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Mar-2012
• Refers: ASTM D653-11 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Sep-2011
• Refers: ASTM D3740-11 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Sep-2011
• Refers: ASTM D3740-10 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Mar-2010
• Refers: ASTM D653-09 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jan-2009
• Refers: ASTM D653-08a - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Dec-2008
• Refers: ASTM D653-08 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2008

Overview

ASTM D6034-20 is the internationally recognized standard practice for determining the efficiency of a production well in a confined aquifer using data from a constant rate pumping test. Developed by ASTM International, this standard provides analytical procedures to accurately evaluate the hydraulic efficiency of a well by comparing the measured drawdown inside the well to the theoretical minimum drawdown achievable in the surrounding aquifer. This practice is fundamental for groundwater professionals interested in well performance assessment, aquifer characterization, and optimizing resource management.

Key Topics

• Hydraulic Efficiency of Production Wells: The standard defines well efficiency as the ratio (usually expressed as a percentage) of the theoretical drawdown just outside the well bore (if no drilling damage occurred) to the actual drawdown measured within the pumped well.
• Constant Rate Pumping Test: The procedure specifically relies on data from a constant rate pumping test to determine aquifer and well parameters. Efficiency determination by this method is more valid than attempting to use step-drawdown tests.
• Key Assumptions:
  • The control well operates at a truly constant discharge rate.
  • The well's diameter is considered infinitesimal for calculation purposes.
  • The aquifer is confined, homogeneous, and extensive, though anisotropy may be present.
  • Drawdown data are collected from both the control (pumped) well and, if present, observation wells.
• Extrapolation and Direct Calculation: Two accepted data analysis methods include:
  • Extrapolation using data from observation wells, typically via log-log or semilog graph plotting.
  • Direct calculation using analytical solutions (e.g., Theis, Cooper-Jacob, Hantush, or Kozeny equations), especially when only the control well is available.
• Correction Factors: Adjustments are incorporated for factors such as partial well penetration, aquifer boundaries, or recharge conditions.

Applications

ASTM D6034-20 is widely used in hydrogeology, water resources management, and well design:

• Well Performance Assessment: Quantifying well efficiency helps identify the extent of drilling-induced formation damage, evaluate development effectiveness, and determine whether further rehabilitation is needed.
• Groundwater Resource Management: Understanding the true hydraulic efficiency of wells aids in the sustainable management of aquifers, especially in settings where groundwater is a critical resource.
• Well Design and Optimization: Engineers and hydrogeologists use this standard to guide the design and construction of highly efficient wells, minimizing energy costs and maximizing water yield.
• Compliance and Reporting: The standard specifies data collection, calculation, and reporting requirements, supporting regulatory compliance and best practices in geotechnical documentation.
• Project Feasibility Studies: The method is integral to aquifer tests and feasibility studies for municipal, industrial, or agricultural groundwater supply projects.

Related Standards

• ASTM D4050: Field procedure for withdrawal and injection well testing to determine hydraulic properties of aquifer systems; often used in conjunction with D6034-20 for complete aquifer evaluations.
• ASTM D653: Terminology standard relating to soil, rock, and contained fluids.
• ASTM D3740: Practice for minimum requirements for testing/inspection agencies involved in soil and rock investigations.
• ASTM D5521/D5521M: Guide for development of groundwater monitoring wells.
• ASTM D6026: Practice for using significant digits in geotechnical data, addressing data reporting and accuracy in accordance with D6034-20.

Keywords: confined aquifer, well efficiency, production well, constant rate pumping test, drawdown, aquifer test, hydraulic conductivity, observation well, ASTM D6034-20, groundwater monitoring, transmissivity, storage coefficient

By implementing ASTM D6034-20, hydrogeologists and water professionals can ensure accurate, repeatable assessment of well efficiency, supporting effective groundwater management and well optimization in diverse field settings.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation:D6034 −20
Standard Practice for
(Analytical Procedure) 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.
1. Scope* ations for the user’s objectives; and it is common practice to
increase or reduce significant digits of reported date to be
1.1 This practice describes an analytical procedure for
commensuratewiththeseconsiderations.Itisbeyondthescope
determining the hydraulic efficiency of a production well in a
of this standard to consider significant digits used in analysis
confinedaquifer.Itinvolvescomparingtheactualdrawdownin
method for engineering design.
the well to the theoretical minimum drawdown achievable and
is based upon data and aquifer coefficients obtained from a 1.6 This practice offers a set of instructions for performing
constant rate pumping test. one or more specific operations.This document cannot replace
educationorexperienceandshouldbeusedinconjunctionwith
1.2 This analytical practice is used in conjunction with the
professional judgment. Not all aspects of the practice may be
field procedure, Test Method D4050.
applicable in all circumstances. This ASTM standard is not
1.3 The values stated in inch-pound units are to be regarded
intended to represent or replace the standard of care by which
as standard, except as noted below. The values given in
the adequacy of a given professional service must be judged,
parentheses are mathematical conversions to SI units, which
nor should this document be applied without the consideration
are provided for information only and are not considered
ofaproject’smanyuniqueaspects.Theword“Standard”inthe
standard. The reporting of results in units other than inch-
title of this document means only that the document has been
pound shall not be regarded as nonconformance with this
approved through the ASTM consensus process.
standard.
1.7 This standard does not purport to address all of the
1.3.1 The gravitational system of inch-pound units is used
safety concerns, if any, associated with its use. It is the
when dealing with inch-pound units. In this system, the pound
responsibility of the user of this standard to establish appro-
(lbf)representsaunitofforce(weight),whiletheunitformass
priate safety, health, and environmental practices and deter-
is slugs.
mine the applicability of regulatory limitations prior to use.
1.4 Limitations—The limitations of the technique for deter-
1.8 This international standard was developed in accor-
mination of well efficiency are related primarily to the corre-
dance with internationally recognized principles on standard-
spondence between the field situation and the simplifying
ization established in the Decision on Principles for the
assumption of this practice.
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
1.5 All observed and calculated values shall conform to the
Barriers to Trade (TBT) Committee.
guidelines for significant digits and round established in
Practice D6026, unless superseded by this standard.
2. Referenced Documents
1.5.1 Theproceduresusedtospecifyhowdataarecollected/
recorded or calculated, in this standard are regarded as the
2.1 ASTM Standards:
industry standard. In addition, they are representative of the
D653Terminology Relating to Soil, Rock, and Contained
significant digits that generally should be retained. The proce-
Fluids
dures used do not consider material variation, purpose for
D3740Practice for Minimum Requirements for Agencies
obtaining the data, special purpose studies, or any consider-
Engaged in Testing and/or Inspection of Soil and Rock as
Used in Engineering Design and Construction
This practice is under the jurisdiction of ASTM Committee D18 on Soil and
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 June 1, 2020. Published June 2020. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1996. Last previous edition approved in 2010 as D6034–17. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/D6034-20. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D6034−20
D4050Test Method for (Field Procedure) for Withdrawal 3.3.19 d'—distance from top of aquifer to top of screened
and Injection Well Testing for Determining Hydraulic interval of observation well [L].
Properties of Aquifer Systems
3.3.20 f —incrementaldimensionlessdrawdowncomponent
s
D5521/D5521MGuide for Development of Groundwater
resulting from partial penetration [nd].
Monitoring Wells in Granular Aquifers
3.3.21 l—distancefromtopofaquifertobottomofscreened
D6026Practice for Using Significant Digits in Geotechnical
interval of control well [L].
Data
3.3.22 l'—distancefromtopofaquifertobottomofscreened
interval of observation well [L].
3. Terminology
3.3.23 r—radial distance from control well [L].
3.1 Definitions—For definitions of common technical terms
3.3.24 t—time since pumping began [T].
used in this standard, refer to Terminology D653.
3.3.25 E—well efficiency [nd].
3.2 Definitions of Terms Specific to This Standard:
3.2.1 well effıciency, n—the ratio, usually expressed as a
4. Summary of Practice
percentage, of the measured drawdown inside the control well
divided into the theoretical drawdown which would occur in 4.1 Thispracticeusesdatafromaconstantratepumpingtest
to determine the well efficiency.The efficiency is calculated as
the aquifer just outside the borehole if there were no drilling
damage, that is, no reduction in the natural permeability of the theratioofthetheoreticaldrawdownintheaquiferjustoutside
sediments in the vicinity of the borehole. the well bore (s ) to the drawdown measured inside the
r
w
pumped well (s ). The theoretical drawdown in the aquifer
w
3.3 Symbols:
(s ) is determined from the field pumping test data by either
r
w
3.3.1 Symbols and Dimensions:
−1 extrapolation or direct calculation.
3.3.2 K—hydraulic conductivity [LT ].
4.2 During the drilling of a well, the hydraulic conductivity
3.3.2.1 Discussion—The use of the symbol K for the term
of the sediments in the vicinity of the borehole wall is reduced
hydraulic conductivity is the predominant usage in ground
significantly by the drilling operation. Damaging effects of
water literature by hydrogeologists, whereas the symbol k is
drilling include mixing of fine and coarse formation grains,
commonly used for this term in soil and rock mechanics and
invasion of drilling mud, smearing of the borehole wall by the
soil science.
drillingtools,andcompactionofsandgrainsneartheborehole.
3.3.3 K —hydraulic conductivity in the plane of the aquifer,
r
The added head loss (drawdown) associated with the perme-
radially from the control well (horizontal hydraulic conductiv-
ability reduction due to drilling damage increases the draw-
−1
ity) [LT ].
downinthepumpedwellandreducesitsefficiency(seeFig.1).
3.3.4 K —hydraulic conductivity normal to the plane of the
z
Well development procedures help repair the damage (see
−1
aquifer (vertical hydraulic conductivity) [LT ].
Guide D5521/D5521M) but generally cannot restore the sedi-
3.3.5 K (x)—modified Bessel function of the second kind ments to their original, natural permeability.
and zero order [nd].
4.2.1 Additional drawdown occurs from head loss associ-
3 −1
ated with flow through the filter pack, through the well screen
3.3.6 Q—discharge [L T ].
and vertically upward inside the well casing to the pump
3.3.7 S—storage coefficient [nd].
intake. While these drawdown components contribute to
2 −1
3.3.8 T—transmissivity [L T ].
inefficiency, they usually are minor in comparison to the head
loss resulting from drilling damage.
3.3.9 s —drawdown in the aquifer at a distance r from the
r
control well [L].
3.3.10 s —drawdown which would occur in response to
f
pumping a fully penetrating well [L].
3.3.11 r —borehole radius of control well [L].
w
3.3.12 s —theoretical drawdown which would occur in the
rw
aquifer just outside the borehole if there were no drilling
damage, that is, no reduction in the natural permeability of the
sediments in the vicinity of the borehole [L].
3.3.13 s —drawdown measured inside the control well [L].
w
3.3.14 u—(r S)/(4Tt)[nd].
3.3.15 W(u)—an exponential integral known in hydrology
as the Theis well function of u [nd].
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
FIG. 1 Illustration of Drawdown Inside and Outside Pumping
interval of control well [L]. Well
D6034−20
4.2.2 Thewellefficiency,usuallyexpressedasapercentage, 4.3.3 For partially penetrating wells, the drawdown can be
is defined as the theoretical drawdown, also called aquifer described by either the Hantush equation (3-5) or the Kozeny
drawdown, which would have occurred just outside the well if
equation (6).
there were no drilling damage divided by the actual drawdown
4.3.3.1 The Hantush equation is similar to the Theis equa-
inside the well. The head losses contributing to inefficiency
tion but includes a correction factor for partial penetration.
generally are constant with time while aquifer drawdown
Q
gradually increases with time. This causes the computed
s 5 ~W~u!1f ! (5)
r s
4πT
efficiencytoincreaseslightlywithtime.Becausetheefficiency
issomewhattimedependent,usuallyitisassumedthatthewell
4.3.3.2 According to Hantush, at late pumping times, when
efficiency is the calculated drawdown ratio achieved after one
t > b S/(2TA), f can be expressed as follows:
s
day of continuous pumping. It is acceptable, however, to use
2 `
4b 1 nπr =K /K
other pumping times, as long as the time that was used in the
z r
f 5 K S D (6)
S D
s 2 ( 2 0
efficiency calculation is specified. The only restriction on the π l 2 d l'2d' n b
~ !~ ! n51
pumping time is that sufficient time should have passed so that
nπl nπd nπl nπd
wellbore storage effects are insignificant. In the vast majority
sin 2 sin sin 2 sin
F S D S DGF S D S DG
b b b b
of cases, after one day of pumping, the effects of wellbore
storage have long since become negligible.
4.3.3.3 The Kozeny equation is as follows:
4.2.3 Efficiency is also somewhat discharge dependent.
s
f
Boththeaquiferdrawdownandtheinefficiencydrawdowncan
s 5 (7)
r
include both laminar (first order) and turbulent (approximately
l 2 d r π~l 2 d!
S117 cos D
Œ
second order) components. Because the proportion of laminar
b 2 l 2 d 2b
~ !
versusturbulentflowcanbedifferentintheundisturbedaquifer
4.3.3.4 In this equation, s is the drawdown for a fully
than it is in the damaged zone and inside the well, the aquifer f
penetrating well system and can be computed from Eq 1-4.
drawdown and inefficiency drawdown can increase at different
While easier to compute than the Hantush equation, the
rates as Q increases. When this happens, the calculated
Kozeny equation is not as accurate. It does not incorporate
efficiency is different for different pumping rates. Because of
pumping time or anisotropy and assumes that the screen in the
this discharge dependence, efficiency testing usually is per-
control well reaches either the top or the bottom of the aquifer.
formed at or near the design discharge rate.
4.3.4 The presence of a positive boundary (for example,
4.3 Thedrawdownintheaquiferaroundawellpumpedata
recharge) causes the drawdown in the aquifer to be less than
constant rate can be described by one of several equations.
predicted by Eq 1-6, while a negative boundary (for example,
4.3.1 For fully penetrating wells, the Theis equation (1) is
the aquifer pinching out) results in more drawdown. The
used.
boundary-induced increases or decreases in drawdown usually
Q
can be determined from the field pumping test data. These
s 5 W u (1)
~ !
r
4πT
increases/decreases can be combined with calculations using
where: Eq 1-7 to determine the drawdown just outside the well bore.
2x
` e
4.4 The efficiency of a production well is calculated as
W u 5 dx (2)
~ ! *
u x
follows:
s
and
r
w
E 5 (8)
s
w
r S
u 5 (3)
4Tt
where:
s = denominator, the drawdown measured inside the well,
w
4.3.2 For sufficiently small values of u, the Theis equation
and
may be approximated by the Cooper-Jacob equation (2).
s = numerator, determined from field data.
rw
2.3Q 2.25Tt
s 5 log (4)
S D
r 2
Two procedures are available for determining s —
4πT r S rw
extrapolation and direct calculation.
4.3.2.1 Examplesoferrorsinthisapproximationforsome u
4.4.1 Extrapolation—Extrapolation can be used to deter-
values are as follows:
mine s if data from two or more observation wells are
r
w
u Error
available. Distance drawdown data can be plotted from these
0.01 0.25 %
wells on either log-log or semilog graphs. If a log-log plot is
0.03 1.01 %
0.05 2.00 %
used,theTheistypecurveisusedtoextrapolatethedrawdown
0.10 5.35 %
datatotheboreholeradiustodetermine s .Ifasemilogplotis
r
w
used, extrapolation is done using a straight line of best fit. The
semilog method can be used only if the u value for each
3 observation well is sufficiently small that the error introduced
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this practice. by the log approximation to the Theis equation is minimal.
D6034−20
4.4.1.1 Forpartiallypenetratingwells,theobservationwells 5.2.3 Data are obtained from the control well and, if
should be located beyond the zone affected by partial available, a number of observation wells.
penetration, that is, at a distance r from the pumped well such
5.2.4 The aquifer is confined, homogeneous, and extensive.
that: The aquifer may be anisotropic, and if so, the directions of
maximum and minimum hydraulic conductivity are horizontal
1.5b
r$ (9)
and vertical, respectively.
= K /K
z r
5.2.5 Discharge from the well is derived exclusively from
storage in the aquifer.
4.4.1.2 The extrapolated drawdown obtained in this case is
s, the theoretical drawdown, which would have occurred just
f
5.3 Calculation Requirements—For the special case of par-
outside the borehole of a fully penetrating pumped well. The
tially penetrating wells, application of this practice may be
aquifer drawdown corresponding to partial penetration is then
computationally intensive. The function f shown in Eq 6
s
computed with the Hantush equation as follows:
should be evaluated using arbitrary input parameters. It is not
Q practicaltouseexisting,somewhatlimited,tablesofvaluesfor
s 5 s 1 f (10)
r f s
w
4πT f and,becausethisequationisratherformidable,itmaynotbe
s
tractablebyhand.Becauseofthis,itisassumedthepractitioner
4.4.1.3 The second term on the right-hand side of Eq 10
using this practice will have available a computerized proce-
represents the incremental aquifer drawdown caused by partial
dure for evaluating the function f . This can be accomplished
s
penetration.
using commercially available mathematical software including
4.4.1.4 Using the Kozeny equation, the aquifer drawdown
some spreadsheet applications. If calculating f is not practical,
s
for partial penetration is computed from Eq 7 with r set equal
it is recommended to substitute the Kozeny equation for the
to the borehole radius r :
w
Hantush equation as previously described.
s
f
NOTE 1—The quality of the result produced by this standard is
s 5 (11)
r
w
l 2 d r π l 2 d
~ ! dependent on the competence of the personnel performing it, and the
w
S 117Πcos D
suitability of the equipment and facilities used. Agencies that meet the
b 2~l 2 d! 2b
criteria of Practice D3740 are generally considered capable of competent
and objective testing/sampling/inspection/etc. Users of this standard are
4.4.1.5 If the extrapolation method is used for determining
cautioned that compliance with Practice D3740 does not in itself assure
aquifer drawdown, it is not necessary to make a separate
reliable results. Reliable results depend on many factors; Practice D3740
adjustment to account for boundaries or recharge.
provides a means of evaluating some of those factors.
4.4.2 Direct Calculation—If the aquifer drawdown s can-
rw
NOTE 2—Commercially available software is available for the
not be obtained by extrapolation, direct calculation should be
calculating, graphing, plotting, and analyses of this practice. The user is
responsibleforverifyingthecorrectnessoftheformulas,graphs,plotsand
used to determine its value.
analyses of the software.
4.4.2.1 For fully penetrating wells, s can be obtained by
rw
direct calculation using either the Theis or Cooper-Jacob
6. Apparatus
equations (Eq 1-4).
6.1 Apparatus for field withdrawal tests is given in Test
4.4.2.2 Forpartiallypenetratingwells, s iscalculatedfrom
r
w
MethodD4050.Thefollowingapparatusarethosecomponents
the Hantush equation (Eq 5 and 6) or the Kozeny equation (Eq
of the apparatus that require special attributes for this specific
11).
test.
4.4.2.3 The presence of aquifer boundaries or recharge will
tendtoincreaseordecrease,respectively,t
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D6034 − 17 D6034 − 20
Standard Test Method (Analytical Procedure) Practice for
(Analytical Procedure) 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. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. 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 correspon-
dence between the field situation and the simplifying assumption of this test method.
1.5 All observed and calculated values shall conform to the guidelines for significant digits and round established in Practice
D6026, unless superseded by this standard.
1.5.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as the industry
standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not
consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objectives;
and it is common practice to increase or reduce significant digits of reported date to be commensurate with these considerations.
It is beyond the scope of this standard to consider significant digits used in analysis method for engineering design.
1.6 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.
2. Referenced Documents
2.1 ASTM Standards:
D653 Terminology Relating to Soil, Rock, and Contained Fluids
D3740 Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in
Engineering Design and Construction
D4050 Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of
Aquifer Systems
D5521 Guide for Development of Groundwater Monitoring Wells in Granular Aquifers
D6026 Practice for Using Significant Digits in Geotechnical Data
3. Terminology
3.1 Definitions—For definitions of common terms used in this test method, see Terminology D653.
3.2 Definitions of Terms Specific to This Standard:
This test method practice is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater
and Vadose Zone Investigations.
Current edition approved Jan. 1, 2017June 1, 2020. Published January 2017June 2020. Originally approved in 1996. Last previous edition approved in 2010 as
ɛ1
D6034–96(2010)D6034 .–17. DOI: 10.1520/D6034-17.10.1520/D6034-20.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D6034 − 20
3.2.1 well effıciency, n—the ratio, usually expressed as a percentage, of the measured drawdown inside the control well divided
into the theoretical drawdown which would occur in the aquifer just outside the borehole if there were no drilling damage, that
is, no reduction in the natural permeability of the sediments in the vicinity of the borehole.
3.3 Symbols:
3.3.1 Symbols and Dimensions:
−1
3.3.2 K—hydraulic conductivity [LT ].
3.3.2.1 Discussion—
The use of the symbol K for the term hydraulic conductivity is the predominant usage in groundwater literature by hydrogeologists,
whereas the symbol k is commonly used for this term in soil and rock mechanics and soil science.
3.3.3 K —hydraulic conductivity in the plane of the aquifer, radially from the control well (horizontal hydraulic conductivity)
r
−1
[LT ].
−1
3.3.4 K —hydraulic conductivity normal to the plane of the aquifer (vertical hydraulic conductivity) [LT ].
z
3.3.5 K (x)—modified Bessel function of the second kind and zero order [nd].
3 −1
3.3.6 Q—discharge [L T ].
3.3.7 S—storage coefficient [nd].
2 −1
3.3.8 T—transmissivity [L T ].
3.3.9 s —drawdown in the aquifer at a distance r from the control well [L].
r
3.3.10 s —drawdown which would occur in response to pumping a fully penetrating well [L].
f
3.3.11 r —borehole radius of control well [L].
w
3.3.12 s —theoretical drawdown which would occur in the aquifer just outside the borehole if there were no drilling damage,
rw
that is, no reduction in the natural permeability of the sediments in the vicinity of the borehole [L].
3.3.13 s —drawdown measured inside the control well [L].
w
3.3.14 u—(r S)/(4Tt)[nd].
3.3.15 W(u)—an exponential integral known in hydrology as the Theis well function of u [nd].
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 —incremental dimensionless drawdown component resulting from partial penetration [nd].
s
3.3.21 l—distance from top of aquifer to bottom of screened interval of control well [L].
3.3.22 l'—distance from top of aquifer to bottom of screened interval of observation well [L].
3.3.23 r—radial distance from control well [L].
3.3.24 t—time since pumping began [T].
3.3.25 E—well efficiency [nd].
4. Summary of Test Method
4.1 This test method uses data from a constant rate pumping test to determine the well efficiency. The efficiency is calculated
as the ratio of the theoretical drawdown in the aquifer just outside the well bore (s ) to the drawdown measured inside the pumped
r
w
well (s ). The theoretical drawdown in the aquifer (s ) is determined from the pumping test data by either extrapolation or direct
w r
w
calculation.
4.2 During the drilling of a well, the hydraulic conductivity of the sediments in the vicinity of the borehole wall is reduced
significantly by the drilling operation. Damaging effects of drilling include mixing of fine and coarse formation grains, invasion
of drilling mud, smearing of the borehole wall by the drilling tools, and compaction of sand grains near the borehole. The added
head loss (drawdown) associated with the permeability reduction due to drilling damage increases the drawdown in the pumped
well and reduces its efficiency (see Fig. 1). Well development procedures help repair the damage (see Guide D5521) but generally
cannot restore the sediments to their original, natural permeability.
4.2.1 Additional drawdown occurs from head loss associated with flow through the filter pack, through the well screen and
vertically upward inside the well casing to the pump intake. While these drawdown components contribute to inefficiency, they
usually are minor in comparison to the head loss resulting from drilling damage.
D6034 − 20
FIG. 1 Illustration of Drawdown Inside and Outside Pumping Well
4.2.2 The well efficiency, usually expressed as a percentage, is defined as the theoretical drawdown, also called aquifer
drawdown, which would have occurred just outside the well if there were no drilling damage divided by the actual drawdown
inside the well. The head losses contributing to inefficiency generally are constant with time while aquifer drawdown gradually
increases with time. This causes the computed efficiency to increase slightly with time. Because the efficiency is somewhat time
dependent, usually it is assumed that the well efficiency is the calculated drawdown ratio achieved after one day of continuous
pumping. It is acceptable, however, to use other pumping times, as long as the time that was used in the efficiency calculation is
specified. The only restriction on the pumping time is that sufficient time must have passed so that wellbore storage effects are
insignificant. In the vast majority of cases, after one day of pumping, the effects of wellbore storage have long since become
negligible.
4.2.3 Efficiency is also somewhat discharge dependent. Both the aquifer drawdown and the inefficiency drawdown can include
both laminar (first order) and turbulent (approximately second order) components. Because the proportion of laminar versus
turbulent flow can be different in the undisturbed aquifer than it is in the damaged zone and inside the well, the aquifer drawdown
and inefficiency drawdown can increase at different rates as Q increases. When this happens, the calculated efficiency is different
for different pumping rates. Because of this discharge dependence, efficiency testing usually is performed at or near the design
discharge rate.
4.3 The drawdown in the aquifer around a well pumped at a constant rate can be described by one of several equations.
4.3.1 For fully penetrating wells, the Theis equation (1) is used.
Q
s 5 W~u! (1)
r
4πT
where:
2x
` e
W~u! 5* dx (2)
u x
and
r S
u 5 (3)
4Tt
4.3.2 For sufficiently small values of u, the Theis equation may be approximated by the Cooper-Jacob equation (2).
2.3Q 2.25Tt
s 5 log (4)
S D
r 2
4πT r S
4.3.2.1 Examples of errors in this approximation for some u values are as follows:
u Error
0.01 0.25 %
0.03 1.01 %
0.05 2.00 %
0.10 5.35 %
4.3.3 For partially penetrating wells, the drawdown can be described by either the Hantush equation (3-5) or the Kozeny
equation (6).
The boldface numbers in parentheses refer to the list of references at the end of this test method.practice.
D6034 − 20
4.3.3.1 The Hantush equation is similar to the Theis equation but includes a correction factor for partial penetration.
Q
s 5 W u 1f (5)
~ ~ ! !
r s
4πT
4.3.3.2 According to Hantush, at late pumping times, when t > b S/(2TA), f can be expressed as follows:
s
`
4b 1 nπr =K /K
z r
f 5 K S D (6)
S D
s 2 ( 2 0
π ~l 2 d!~l'2d'! n b
n51
nπl nπd nπl nπd
sin 2 sin sin 2 sin
F S D S DG F S D S DG
b b b b
4.3.3.3 The Kozeny equation is as follows:
s
f
s 5 (7)
r
l 2 d r π~l 2 d!
S 117 cos D
Œ
b 2 l 2 d 2b
~ !
4.3.3.4 In this equation, s is the drawdown for a fully penetrating well system and can be computed from Eq 1-4. While easier
f
to compute than the Hantush equation, the Kozeny equation is not as accurate. It does not incorporate pumping time or anisotropy
and assumes that the screen in the control well reaches either the top or the bottom of the aquifer.
4.3.4 The presence of a positive boundary (for example, recharge) causes the drawdown in the aquifer to be less than predicted
by Eq 1-6, while a negative boundary (for example, the aquifer pinching out) results in more drawdown. The boundary-induced
increases or decreases in drawdown usually can be determined from the pumping test data. These increases/decreases can be
combined with calculations using Eq 1-7 to determine the drawdown just outside the well bore.
4.4 The efficiency of a production well is calculated as follows:
s
r
w
E 5 (8)
s
w
where:
s = denominator, the drawdown measured inside the well, and
w
s = numerator, must be determined from field data.
rw
Two procedures are available for determining s —extrapolation and direct calculation.
rw
4.4.1 Extrapolation—Extrapolation can be used to determine s if data from two or more observation wells are available.
r
w
Distance drawdown data can be plotted from these wells on either log-log or semilog graphs. If a log-log plot is used, the Theis
type curve is used to extrapolate the drawdown data to the borehole radius to determine s . If a semilog plot is used, extrapolation
r
w
is done using a straight line of best fit. The semilog method can be used only if the u value for each observation well is sufficiently
small that the error introduced by the log approximation to the Theis equation is minimal.
4.4.1.1 For partially penetrating wells, the observation wells must be located beyond the zone affected by partial penetration,
that is, at a distance r from the pumped well such that:
1.5b
r $ (9)
= K /K
z r
4.4.1.2 The extrapolated drawdown obtained in this case is s , the theoretical drawdown, which would have occurred just outside
f
the borehole of a fully penetrating pumped well. The aquifer drawdown corresponding to partial penetration is then computed with
the Hantush equation as follows:
Q
s 5 s 1 f (10)
r f s
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
penetration.
4.4.1.4 Using the Kozeny equation, the aquifer drawdown for partial penetration is computed from Eq 7 with r set equal to the
borehole radius r :
w
s
f
s 5 (11)
r
w
l 2 d r π~l 2 d!
w
S 117Πcos D
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 adjustment
to account for boundaries or recharge.
D6034 − 20
4.4.2 Direct Calculation—If the aquifer drawdown s cannot be obtained by extrapolation, direct calculation must be used to
rw
determine its value.
4.4.2.1 For fully penetrating wells, s can be obtained by direct calculation using either the Theis or Cooper-Jacob equations
rw
(Eq 1-4).
4.4.2.2 For partially penetrating wells, s is calculated from the Hantush equation (Eq 5 and 6) or the Kozeny equation (Eq 11).
r
w
4.4.2.3 The presence of aquifer boundaries or recharge will tend to increase or decrease, respectively, the drawdown in and
around the pumped well. When they are present, the calculated value of s must be adjusted to reflect the impact of the boundary
r
w
conditions.
5. Significance and Use
5.1 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.
5.2 Assumptions:
5.2.1 Control well discharges at a constant rate, Q.
5.2.2 Control well is of infinitesimal diameter.
5.2.3 Data are obtained from the control well and, if available, a number of observation wells.
5.2.4 The aquifer is confined, homogeneous, and extensive. The aquifer may be anisotropic, and if so, the directions of
maximum and minimum hydraulic conductivity are horizontal and vertical, respectively.
5.2.5 Discharge from the well is derived exclusively from storage in the aquifer.
5.3 Calculation Requirements—For the special case of partially penetrating wells, application of this test method may be
computationally intensive. The function f shown in Eq 6 should be evaluated using arbitrary input parameters. It is not practical
s
to use existing, somewhat limited, tables of values for f and, because this equation is rather formidable, it may not be tractable
s
by hand. Because of this, it is assumed the practitioner using this test method will have available a computerized procedure for
evaluating the function f . This can be accomplished using commercially available mathematical software including some
s
spreadsheet applications. If calculating f is not practical, it is recommended to substitute the Kozeny equation for the Hantush
s
equation as previously described.
NOTE 1—The quality of the result produced by this standard is dependent on the competence of the personnel performing it, and the suitability of the
equipment and facilities used. Agencies that meet the criteria of Practice D3740 are generally considered capable of competent and objective
testing/sampling/inspection/etc. Users of this standard are cautioned that compliance with Practice D3740 does not in itself assure reliable results. Reliable
results depend on many factors; Practice D3740 provides a means of evaluating some of those factors.
6. Apparatus
6.1 Apparatus for withdrawal tests is given in Test Method D4050. The following apparatus are those components of the
apparatus that require special attributes for this specific test.
6.2 Construction of the Control Well—Install the control well in the aquifer and equip with a pump capable of discharging water
from the well at a constant rate for the duration of the test. A fully penetrating control well is preferred.
6.3 Construction and Placement of Observation Wells—If observation wells are used, they should be located on a straight line
extending from the control well and positioned at different distances so that they span a good portion of the anticipated cone of
depression. It is preferable that the wells be fully penetrating. If the control well and observation wells are partially penetrating,
the extrapolation method of determining well efficiency can be used only if the observation wells are located outside the zone
effected by partial penetration.
7. Procedure
7.1 Pretest preparations, pumping test guidelines, and posttest procedures associated with the pumping test itself are described
in Test Method D4050.
7.2 Verify the quality of the data set. Review the record of measured flow rates to make sure the rate was held constant during
the test. Check to see that hand measurements of drawdown agree well with electronically measured values. Check the background
water-level fluctuations observed prior to or following the pumping test to see if adjustments should be made to the observed
drawdown values to account for background fluctuations. If appropriate, adjust the observed drawdown values accordingly.
7.3 Analysis of the field data is described in Section 8.
8. Calculation and Interpretation of Test Data
8.1 Methods:
D6034 − 20
8.1.1 Extrapolation—This test method relies on extrapolating observation well drawdown data to estimate the theoretical
drawdown just outside the well bore. It requires a single drawdown observation for the control well and each observation well used
in the test, preferably after one day of continuous pumping. If the wells are penetrating partially, the observation wells must be
located outside the zone effected by partial penetration as described by Eq 9.
8.1.1.1 Log-Log Method—Plot the observation well distance drawdown data on a log-log graph with drawdown on the vertical
axis and the reciprocal of the distance squared on the horizontal axis. On a separate graph having the same scale as the data graph,
prepare a standard Theis type curve by plotting W(u) on the vertical axis versus l/u on the horizontal axis (Fig. 2). Overlay the data
plot on the type curve, and while keeping the coordinate axes of the two plots parallel, shift the data plot to align with the type
curve effecting a match position. On the data graph, follow the type curve to a horizontal axis coordinate of l/r and read s from
w r
w
the graph. For partially penetrating wells, the extrapolated value must be corrected for partial penetration using Eq 10 or Eq 11.
Calculate well efficiency using Eq 8.
8.1.1.2 Semilog Method—This test method can be used if the u value for each observation well is sufficiently small that the
Cooper-Jacob equation represents an adequate approximation to the Theis equation. Plot the observation well distance drawdown
data on a semilog graph with drawdown on the linear scale and distance on the log scale. Construct a straight line of best fit through
the data points and extrapolate it to a radius value of r . Read s from the graph. If the control well is partially penetrating, the
w r
w
extrapolated value must be corrected for partial penetration using Eq 10 or Eq 11. Calculate well efficiency using Eq 8.
8.1.2 Direct Calculation—Aquifer parameters including transmissivity, storage coefficient, and anisotropy ratio (T, S, A) are
determined using conventional pumping test analysis techniques. Then s is computed directly from Eq 1-7 and Eq 11.
rw
8.1.2.1 Fully Penetrating Wells—Determine T and S from the pumping test. If no observation wells are available, S cannot be
determined from the test data. In this case, S must be estimated.
−5 −6
NOTE 2—An acceptable procedure for estimating S is to multiply the aquifer thickness in feet by a factor between 10 and 10 . Determine the aquifer
drawdown, s , by direct calculation using either Eq 1-3 or Eq 4. The time parameter used in the calculation should be the time at which s was measured
rw w
inside the control well. Determine well efficiency using Eq 8.
8.1.2.2 Partially Penetrating Wells—Determine T, S, and A from the pumping test. Often it is difficult to determine the
anisotropy ratio, A, accurately from the pumping test data. If this is the case, A must be estimated. Likewise, if S cannot be
calculated from the data, it must be estimated. Calculate s from Eq 5 and Eq 6 or Eq 11 and well efficiency from Eq 8.
r
w
8.1.2.3 Boundary Conditions—If boundary conditions affect the magnitude of the observed drawdown, follow 8.1.2.1 or 8.1.2.2
to calculate an initial value for s . This value then must be increased or decreased by the magnitude of the boundary effect.
r
w
Determine this value in accordance with 8.1.2.4.
8.1.2.4 Use the time drawdown graph for either the control well or an observation well where the u value is sufficiently small
(approximately u < 0.05). Extrapolate the early time drawdown trend to a pumping time of one day to obtain the drawdown that
would have been observed if no boundary had been present. Determine the difference between this value and the actual drawdown
at one day. Increase (negative boundary) or decrease (positive boundary) the initial value of s by this amount to obtain a final
rw
value for s . Use Eq 8 to compute well efficiency.
rw
8.2 Example Calculations:
8.2.1 Semilog Extrapolation:
8.2.1.1 Table 1 shows distance drawdown data obtained from a 24-h constant rate pumping test incorporating three observation
wells located 30 ft, 100 ft, and 400 ft from the control well. The control well was completed with a 24-in. diameter borehole
(radius = 1 ft).
FIG. 2 Theis Type Curve
D6034 − 20
TABLE 1 Distance-Drawdown Data After 24 h of Continuous
Pumping at 600 gpm (115 000 cfd)
Well Distance, ft Drawdown at 24 h, ft
A
Control well 1 46.2
Observation Well 1 30 20.3
Observation Well 2 100 15.5
Observation Well 3 400 9.7
A
Borehole radius.
8.2.1.2 The distance drawdown data have been plotted on the graph shown in Fig. 3. A straight line of best fit constructed
through the data points extrapolates to a drawdown value of 34 ft at the borehole radius. The actual drawdown measured in the
pumped well is 46.2 ft. The efficiency is calculated as follows:
E 5 5 74 % (12)
46.2
8.2.2 Log-Log Extrapolation—The data from Table 1 have been replotted on the log-log graph shown in Fig. 4. On this graph,
drawdown is plotted against the reciprocal of the square of the distance to the observation well. Theis type curve matching results
in the type curve position shown on the graph. The extrapolated drawdown corresponding to the borehole radius of 1 ft is 34 ft,
the same as the value obtained from the semilog analysis. The efficiency calculation is identical to that in the previous section.
8.2.3 Direct Calculation:
8.2.3.1 Fig. 5 shows a semilog time drawdown graph for a control well pumped at 800 gpm for 24 h. The transmissivity
determined using standard analysis techniques from the early time drawdown trend is 8690 ft /day.
8.2.3.2 About 100 min into the test, the influence of a negative boundary is seen in the data plot. Extrapolating the early time
drawdown trend to a pumping time of one day results in a predicted drawdown of 35.3 ft. The measured one-day drawdown in
the well was 43.9 ft. The difference of 8.6 ft is the incremental drawdown attributable to the presence of the negative boundary.
8.2.3.3 Since there were no observation wells available for this pumping test, direct calculation will be used to determine well
efficiency. Eq 4 is used to compute a trial value for s , that is, the expected theoretical aquifer drawdown assuming no boundary
rw
condition. Inputs to the equation are as follows:
Q = 154 000 cfd,
T = 8690 ft /day,
−4
S = 5 × 10 (estimated),
r = 1 ft, and
w
t = 1 day
NOTE 3—Storage coefficient had to be estimated to facilitate the calculation. The trial value for s is as follows:
rw
2.3 3154 000 2.25 38690 31
trial s 5 log 5 24.6 ft (13)
S D
r 2
w
4π8690 1 0.0005
8.2.3.4 Since it is known that the presence of the boundary causes an additional 8.6 ft of drawdown above that which would
be theoretically predicted, the theoretical aquifer drawdown at the borehole face including the effect of the boundary is as follows:
FIG. 3 Extrapolation of Straight Line on Semilog Graph
D6034 − 20
FIG. 4 Extrapolation of Theis Type Curve on Log-Log Graph
FIG. 5 Pumped Well Time-Drawdown Graph
s 5 24.618.6 (14)
r
w
533.2 ft
8.2.3.5 The efficiency is calculated from Eq 8 as follows:
33.2
E 5 5 76 % (15)
43.9
8.2.4 Log-Log Extrapolation with Partial Penetration—Table 2 shows distance drawdown data obtained from a 90-gpm, 24-h
constant rate pumping test incorporating two observation wells located 360 and 2200 ft from the control well. The control well
was completed with an 18-in. diameter borehole (radius = 0.75 ft) and penetrated 30 ft of an 80-ft thick aquifer.
TABLE 2 Distance-Drawdown Data After 24 h of Continuous
Pumping at 90 gpm (17 325 cfd)
Well Distance, ft Drawdown at 24 h, ft
A
Control Well 0.75 116.0
Observation Well 1 360 9.2
Observation Well 2 2200 0.8
A
Borehole radius
D6034 − 20
8.2.5 Fig. 6 shows a Theis curve match from which transmissivity and storage coefficient were computed as 485 ft /day and
0.00034, respectively. This analysis assumes that both observation wells lie outside the zone affected by partial penetration, a
reasonable assumption for moderately antisotropic to isotropic conditions. The theoretical drawdown extrapolated at the borehole
2 −2
radius of 0.75 ft (1/r = 1.78 ft ) is 44 ft as shown on the figure.
8.2.5.1 The calculated value of u for the distant observation well using Eq 3 is as follows:
2200 5 30.00034
u 5 (16)
43485 31
50.848
This large value of u precludes using the straight-line, semilog method for extrapolating theoretical drawdown at the borehole.
8.2.5.2 Because the control well does not fully penetrate the aquifer, the extrapolated drawdown must be corrected for partial
penetration using either Eq 10 or Eq 11. Since no antisotropy information is available, a value of A must be estimated if Eq 10
is used. In this example, Eq 11 will be used to determine the corrected drawdown value. Inputs to the equation are as follows:
l = 30 ft,
d = 0 ft,
b = 80 ft,
r = 0.75 ft, and
w
s = 44 ft (extrapolated from graph).
f
From Eq 11:
s 5 (17)
r
w
30 0.75 π30
S 117 cos D
Œ
80 2330 2380
568.5 ft
The efficiency is calculated from Eq 8 as follows:
68.5
E 5 5 59 % (18)
9. Report: Test Data Sheet(s)/Form(s)
9.1 Record as a minimum the following general information (data).
9.1.1 Introduction—The introductory section is intended to present the scope and purpose of the test method for determining
the efficiency of a pumped well in a confined aquifer. Briefly summarize the field hydrogeologic conditions and the field equipment
and instrumentation, including the construction of the control well and observation wells, the method of measurement of discharge
and water levels, and the duration of the test and pumping rate.
FIG. 6 Extrapolated Drawdown for Partially Penetrating Well
D6034 − 20
9.1.2 Conceptual Model—Review the information available on the hydrogeology of the site. Interpret and describe the
hydrogeology of the site as it pertains to the selection of this test method for conducting and analyzing an aquifer test. Compare
the hydrogeologic characteristics of the site as it conforms and differs from the assumptions in the solution to the aquifer test
method.
9.1.3 Equipment—Report the field installation and equipment for the aquifer test, including the construction; diameter; depth
of screened and filter-packed intervals; location of control well and pumping equipment; and the construction, diameter, depth, and
screened interval of observation wells.
9.1.4 Instrumentation—Describe the field instrumentation for observing water levels, pumping rate, barometric changes, and
other environmental conditions pertinent to this test method. Include a list of measuring devices used during the test method; the
manufacturer’s name, model number, and basic specifications for each major item; and the name, date, and method of the last
calibration, if applicable.
9.1.5 Testing Procedures—List the steps taken in conducting pretest, drawdown, and recovery phases of the test. Include the
frequency of measurements of discharge rate, water level in observation wells, and other environmental data recorded during the
testing procedure.
9.1.6 Presentation and Interpretation of Test Results:
9.1.6.1 Data—Present tables of data collected during the test. Show methods of adjusting water levels for background
water-level and barometric changes and calculation of drawdown and residual drawdown.
9.1.6.2 Data Plots—Present data plots used in analysis of the data. Show overlays of data plots and type curve with match points
and corresponding values of parameters at match points.
9.1.7 Calculations—Show calculations of transmissivity, storage coefficient, and coefficient of leakage. Show the calculation of
transmissivity and storage coefficient in accordance with Practice D6026.
9.1.8 Evaluate qualitatively the overall accuracy of the test, the corrections and adjustments made to the original water-level
measurements, the adequacy and accuracy of instrumentation, accuracy of observations of stress and response, and the
conformance of the hydrogeologic conditions and the conformance of the test to the model assumptions.
10. Precision and Bias
10.1 Precision—Test data on precision is not presented due to the nature of this test method. It is either not feasible or too costly
at this time to have ten or more agencies participate in an in situ testing program at a given site.
10.1.1 The subcommittee D18.21 is seeking data for the users of this test method that might be used to make a limited statement
on precision.
10.2 Bias—There is no accepted reference value for this test method, therefore bias cannot be determined.
11. Keywords
11.1 anisotropy; aquifers; aquifer tests; control wells; groundwater; hydraulic conductivity; observation wells; storage
coefficient; transmissivity; well efficiency
REFERENCES
(1) Theis, C. V., “The Relation Between the Lowering of the Piezometric Surface and the Rate and Duration of Discharge of a Well Using Groundwater
Storage,” Trans. Am. Geophys. Union, Vol 16, 1935, pp. 519–524.
(2) Cooper, H. H., Jr., and Jacob, C. E., “A Generalized Graphical Method for Evaluating Formation Constants and Summarizing Well Field History,”
Trans. Am. Geophys. Union, Vol 27, No. 4, 1946.
(3) Hantush, M. S., “Drawdown Around a Partially Penetrating Well,” Am. Soc. Civil Eng. Proc., Vol 87, HY4, 1961, pp. 83–93.
(4) Hantush, M. S., “Aquifer Tests on Partially Penetrating Wells,” Am. Soc., Civil Eng. Proc., Vol 87, HY5, 1961, pp. 171–195.
(5) Hantush, M. S., “Hydraulics of Wells,” Advances in Hydroscience, Academic Press, Ney York, NY, Vol 1, edited by Ven Te Chow, 1964, pp. 281–432.
(6) Kozeny, J., “Theorie and Berechnung der Brunnen,” Vasserkraft u. Wasser Wirtschaft, “Methods of Determining Permeability, Transmissibility, and
Drawdown,” Geological Survey Water-Supply Paper, Vol 29, 1933, p. 101.
D6034 − 20
SUMMARY OF CHANGES
In accordance with Committee D18 policy, this section identifies the location of changes to this standard since
ɛ1
the last edition (1996 (2010) ) that may impact the use of this standard. (January 1, 2017)
(1) Added references, notes for D3740 and D6026.
(2) Removed terminology that was not used in the text or is already available in D653.
(3) Removed/revised jargon.
(4) Removed wording for dated technology.
(5) Updated precision and bias to current D18 wording.
(6) Added missing data for Reference 6.
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1. Scope*
1.1 This practice 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 practice 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. The reporting
of results in units other than inch-pound shall not be regarded as nonconformance with this 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 correspon-
dence between the field situation and the simplifying assumption of this practice.
1.5 All observed and calculated values shall conform to the guidelines for significant digits and round established in Practice
D6026, unless superseded by this standard.
1.5.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as the industry
standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not
consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objectives;
and it is common practice to increase or reduce significant digits of reported date to be commensurate with these considerations.
It is beyond the scope of this standard to consider significant digits used in analysis method for engineering design.
1.6 This practice offers a set of instructions for performing one or more specific operations. This document cannot replace
education or experience and should be used in conjunction with professional judgment. Not all aspects of the practice may be
applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the
adequacy of a given professional service must be judged, nor should this document be applied without the consideration of a
project’s many unique aspects. The word “Standard” in the title of this document means only that the document has been approved
through the ASTM consensus process.
1.7 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, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.8 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
D6034 − 20
2. Referenced Documents
2.1 ASTM Standards:
D653 Terminology Relating to Soil, Rock, and Contained Fluids
D3740 Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in
Engineering Design and Construction
D4050 Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of
Aquifer Systems
D5521/D5521M Guide for Development of Groundwater Monitoring Wells in Granular Aquifers
D6026 Practice for Using Significant Digits in Geotechnical Data
3. Terminology
3.1 Definitions—For definitions of common technical terms used in this standard, refer to Terminology D653.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 well effıciency, n—the ratio, usually expressed as a percentage, of the measured drawdown inside the control well divided
into the theoretical drawdown which would occur in the aquifer just outside the borehole if there were no drilling damage, that
is, no reduction in the natural permeability of the sediments in the vicinity of the borehole.
3.3 Symbols:
3.3.1 Symbols and Dimensions:
−1
3.3.2 K—hydraulic conductivity [LT ].
3.3.2.1 Discussion—
The use of the symbol K for the term hydraulic conductivity is the predominant usage in ground water literature by
hydrogeologists, whereas the symbol k is commonly used for this term in soil and rock mechanics and soil science.
3.3.3 K —hydraulic conductivity in the plane of the aquifer, radially from the control well (horizontal hydraulic conductivity)
r
−1
[LT ].
−1
3.3.4 K —hydraulic conductivity normal to the plane of the aquifer (vertical hydraulic conductivity) [LT ].
z
3.3.5 K (x)—modified Bessel function of the second kind and zero order [nd].
3 −1
3.3.6 Q—discharge [L T ].
3.3.7 S—storage coefficient [nd].
2 −1
3.3.8 T—transmissivity [L T ].
3.3.9 s —drawdown in the aquifer at a distance r from the control well [L].
r
3.3.10 s —drawdown which would occur in response to pumping a fully penetrating well [L].
f
3.3.11 r —borehole radius of control well [L].
w
3.3.12 s —theoretical drawdown which would occur in the aquifer just outside the borehole if there were no drilling damage,
rw
that is, no reduction in the natural permeability of the sediments in the vicinity of the borehole [L].
3.3.13 s —drawdown measured inside the control well [L].
w
3.3.14 u—(r S)/(4Tt)[nd].
3.3.15 W(u)—an exponential integral known in hydrology as the Theis well function of u [nd].
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 —incremental dimensionless drawdown component resulting from partial penetration [nd].
s
3.3.21 l—distance from top of aquifer to bottom of screened interval of control well [L].
3.3.22 l'—distance from top of aquifer to bottom of screened interval of observation well [L].
3.3.23 r—radial distance from control well [L].
3.3.24 t—time since pumping began [T].
3.3.25 E—well efficiency [nd].
D6034 − 20
4. Summary of Practice
4.1 This practice uses data from a constant rate pumping test to determine the well efficiency. The efficiency is calculated as
the ratio of the theoretical drawdown in the aquifer just outside the well bore (s ) to the drawdown measured inside the pumped
r
w
well (s ). The theoretical drawdown in the aquifer (s ) is determined from the field pumping test data by either extrapolation or
w r
w
direct calculation.
4.2 During the drilling of a well, the hydraulic conductivity of the sediments in the vicinity of the borehole wall is reduced
significantly by the drilling operation. Damaging effects of drilling include mixing of fine and coarse formation grains, invasion
of drilling mud, smearing of the borehole wall by the drilling tools, and compaction of sand grains near the borehole. The added
head loss (drawdown) associated with the permeability reduction due to drilling damage increases the drawdown in the pumped
well and reduces its efficiency (see Fig. 1). Well development procedures help repair the damage (see Guide D5521/D5521M) but
generally cannot restore the sediments to their original, natural permeability.
4.2.1 Additional drawdown occurs from head loss associated with flow through the filter pack, through the well screen and
vertically upward inside the well casing to the pump intake. While these drawdown components contribute to inefficiency, they
usually are minor in comparison to the head loss resulting from drilling damage.
4.2.2 The well efficiency, usually expressed as a percentage, is defined as the theoretical drawdown, also called aquifer
drawdown, which would have occurred just outside the well if there were no drilling damage divided by the actual drawdown
inside the well. The head losses contributing to inefficiency generally are constant with time while aquifer drawdown gradually
increases with time. This causes the computed efficiency to increase slightly with time. Because the efficiency is somewhat time
dependent, usually it is assumed that the well efficiency is the calculated drawdown ratio achieved after one day of continuous
pumping. It is acceptable, however, to use other pumping times, as long as the time that was used in the efficiency calculation is
specified. The only restriction on the pumping time is that sufficient time should have passed so that wellbore storage effects are
insignificant. In the vast majority of cases, after one day of pumping, the effects of wellbore storage have long since become
negligible.
4.2.3 Efficiency is also somewhat discharge
...