1、Designation: D6034 17Standard Test Method (Analytical Procedure) forDetermining the Efficiency of a Production Well in aConfined Aquifer from a Constant Rate Pumping Test1This standard is issued under the fixed designation D6034; the number immediately following the designation indicates the year of
2、original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test method describes an analytical procedure fordete
3、rmining the hydraulic efficiency of a production well in aconfined aquifer. It involves comparing the actual drawdown inthe well to the theoretical minimum drawdown achievable andis based upon data and aquifer coefficients obtained from aconstant rate pumping test.1.2 This analytical procedure is us
4、ed in conjunction with thefield procedure, Test Method D4050.1.3 The values stated in inch-pound units are to be regardedas standard, except as noted below. The values given inparentheses are mathematical conversions to SI units, whichare provided for information only and are not consideredstandard.
5、1.3.1 The gravitational system of inch-pound units is usedwhen dealing with inch-pound units. In this system, the pound(lbf) represents a unit of force (weight), while the unit for massis slugs.1.4 LimitationsThe limitations of the technique for deter-mination of well efficiency are related primaril
6、y to the corre-spondence between the field situation and the simplifyingassumption of this test method.1.5 All observed and calculated values shall conform to theguidelines for significant digits and round established inPractice D6026, unless superseded by this standard.1.5.1 The procedures used to
7、specify how data are collected/recorded or calculated, in this standard are regarded as theindustry standard. In addition, they are representative of thesignificant digits that generally should be retained. The proce-dures used do not consider material variation, purpose forobtaining the data, speci
8、al purpose studies, or any consider-ations for the users objectives; and it is common practice toincrease or reduce significant digits of reported date to becommensurate with these considerations. It is beyond the scopeof this standard to consider significant digits used in analysismethod for engine
9、ering design.1.6 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2.
10、 Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD3740 Practice for Minimum Requirements for AgenciesEngaged in Testing and/or Inspection of Soil and Rock asUsed in Engineering Design and ConstructionD4050 Test Method for (Field Procedure) for With
11、drawaland Injection Well Testing for Determining HydraulicProperties of Aquifer SystemsD5521 Guide for Development of Groundwater MonitoringWells in Granular AquifersD6026 Practice for Using Significant Digits in GeotechnicalData3. Terminology3.1 DefinitionsFor definitions of common terms used inthi
12、s test method, see Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 well effciency, nthe ratio, usually expressed as apercentage, of the measured drawdown inside the control welldivided into the theoretical drawdown which would occur inthe aquifer just outside the borehole i
13、f there were no drillingdamage, that is, no reduction in the natural permeability of thesediments in the vicinity of the borehole.3.3 Symbols:3.3.1 Symbols and Dimensions:3.3.2 Khydraulic conductivity LT1.1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the dir
14、ect responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved Jan. 1, 2017. Published January 2017. Originallyapproved in 1996. Last previous edition approved in 2010 as D603496(2010)1.DOI: 10.1520/D6034-17.2For referenced ASTM standards, visit the A
15、STM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr
16、Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommen
17、dations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.13.3.2.1 DiscussionThe use of the symbol K for the termhydraulic conductivity is the predominant usage in groundwa-ter literature by hydrogeologists, whereas the symbol k iscommonly used for this term in soil
18、and rock mechanics andsoil science.3.3.3 Krhydraulic conductivity in the plane of the aquifer,radially from the control well (horizontal hydraulic conductiv-ity) LT1.3.3.4 Kzhydraulic conductivity normal to the plane of theaquifer (vertical hydraulic conductivity) LT1.3.3.5 K0(x)modified Bessel func
19、tion of the second kindand zero order nd.3.3.6 Qdischarge L3T1.3.3.7 Sstorage coefficient nd.3.3.8 Ttransmissivity L2T1.3.3.9 srdrawdown in the aquifer at a distance r from thecontrol well L.3.3.10 sfdrawdown which would occur in response topumping a fully penetrating well L.3.3.11 rwborehole radius
20、 of control well L.3.3.12 srwtheoretical drawdown which would occur in theaquifer just outside the borehole if there were no drillingdamage, that is, no reduction in the natural permeability of thesediments in the vicinity of the borehole L.3.3.13 swdrawdown measured inside the control well L.3.3.14
21、 u(r2S)/(4Tt)nd.3.3.15 W(u)an exponential integral known in hydrologyas the Theis well function of u nd.3.3.16 AKz/Kr, anisotropy ratio nd.3.3.17 bthickness of aquifer L.3.3.18 ddistance from top of aquifer to top of screenedinterval of control well L.3.3.19 ddistance from top of aquifer to top of s
22、creenedinterval of observation well L.3.3.20 fsincremental dimensionless drawdown componentresulting from partial penetration nd.3.3.21 ldistance from top of aquifer to bottom of screenedinterval of control well L.3.3.22 ldistance from top of aquifer to bottom of screenedinterval of observation well
23、 L.3.3.23 rradial distance from control well L.3.3.24 ttime since pumping began T.3.3.25 Ewell efficiency nd.4. Summary of Test Method4.1 This test method uses data from a constant rate pumpingtest to determine the well efficiency. The efficiency is calcu-lated as the ratio of the theoretical drawdo
24、wn in the aquifer justoutside the well bore (srw) to the drawdown measured inside thepumped well (sw). The theoretical drawdown in the aquifer(srw) is determined from the pumping test data by eitherextrapolation or direct calculation.4.2 During the drilling of a well, the hydraulic conductivityof th
25、e sediments in the vicinity of the borehole wall is reducedsignificantly by the drilling operation. Damaging effects ofdrilling include mixing of fine and coarse formation grains,invasion of drilling mud, smearing of the borehole wall by thedrilling tools, and compaction of sand grains near the bore
26、hole.The added head loss (drawdown) associated with the perme-ability reduction due to drilling damage increases the draw-down in the pumped well and reduces its efficiency (see Fig. 1).Well development procedures help repair the damage (seeGuide D5521) but generally cannot restore the sediments tot
27、heir original, natural permeability.4.2.1 Additional drawdown occurs from head loss associ-ated with flow through the filter pack, through the well screenand vertically upward inside the well casing to the pumpintake. While these drawdown components contribute toinefficiency, they usually are minor
28、in comparison to the headloss resulting from drilling damage.4.2.2 The well efficiency, usually expressed as a percentage,is defined as the theoretical drawdown, also called aquiferdrawdown, which would have occurred just outside the well ifthere were no drilling damage divided by the actual drawdow
29、ninside the well. The head losses contributing to inefficiencygenerally are constant with time while aquifer drawdowngradually increases with time. This causes the computedefficiency to increase slightly with time. Because the efficiencyis somewhat time dependent, usually it is assumed that the well
30、efficiency is the calculated drawdown ratio achieved after oneday of continuous pumping. It is acceptable, however, to useother pumping times, as long as the time that was used in theefficiency calculation is specified. The only restriction on thepumping time is that sufficient time must have passed
31、 so thatwellbore storage effects are insignificant. In the vast majorityof cases, after one day of pumping, the effects of wellborestorage have long since become negligible.4.2.3 Efficiency is also somewhat discharge dependent.Both the aquifer drawdown and the inefficiency drawdown caninclude both l
32、aminar (first order) and turbulent (approximatelysecond order) components. Because the proportion of laminarversus turbulent flow can be different in the undisturbed aquiferthan it is in the damaged zone and inside the well, the aquiferFIG. 1 Illustration of Drawdown Inside and Outside PumpingWellD6
33、034 172drawdown and inefficiency drawdown can increase at differentrates as Q increases. When this happens, the calculatedefficiency is different for different pumping rates. Because ofthis discharge dependence, efficiency testing usually is per-formed at or near the design discharge rate.4.3 The dr
34、awdown in the aquifer around a well pumped at aconstant rate can be described by one of several equations.4.3.1 For fully penetrating wells, the Theis equation (1)3isused.sr5Q4TWu! (1)where:Wu! 5 *u e2xxdx (2)andu 5r2S4Tt(3)4.3.2 For sufficiently small values of u, the Theis equationmay be approxima
35、ted by the Cooper-Jacob equation (2).sr52.3Q4TlogS2.25Ttr2SD(4)4.3.2.1 Examples of errors in this approximation for some uvalues are as follows:u Error0.01 0.25 %0.03 1.01 %0.05 2.00 %0.10 5.35 %4.3.3 For partially penetrating wells, the drawdown can bedescribed by either the Hantush equation (3-5)
36、or the Kozenyequation (6).4.3.3.1 The Hantush equation is similar to the Theis equa-tion but includes a correction factor for partial penetration.sr5Q4TWu!1fs! (5)4.3.3.2 According to Hantush, at late pumping times, whent b2S/(2TA), fscan be expressed as follows:fs54b22l 2 d!l2d!(n51S1n2DK0Snr =Kz/K
37、rbD (6)FsinSnlbD2 sinSndbDGFsinSnlbD2 sinSndbDG4.3.3.3 The Kozeny equation is as follows:sr5sfl 2 dbS117 r2l 2 d!cosl 2 d!2bD(7)4.3.3.4 In this equation, sfis the drawdown for a fullypenetrating well system and can be computed from Eq 1-4.While easier to compute than the Hantush equation, theKozeny
38、equation is not as accurate. It does not incorporatepumping time or anisotropy and assumes that the screen in thecontrol 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 thanpredict
39、ed by Eq 1-6, while a negative boundary (for example,the aquifer pinching out) results in more drawdown. Theboundary-induced increases or decreases in drawdown usuallycan be determined from the pumping test data.These increases/decreases can be combined with calculations using Eq 1-7 todetermine the
40、 drawdown just outside the well bore.4.4 The efficiency of a production well is calculated asfollows:E 5srwsw(8)where:sw= denominator, the drawdown measured inside the well,andsrw= numerator, must be determined from field data.Two procedures are available for determining srwextrapolation and direct
41、calculation.4.4.1 ExtrapolationExtrapolation can be used to deter-mine srwif data from two or more observation wells areavailable. Distance drawdown data can be plotted from thesewells on either log-log or semilog graphs. If a log-log plot isused, the Theis type curve is used to extrapolate the draw
42、downdata to the borehole radius to determine srw. If a semilog plot isused, extrapolation is done using a straight line of best fit. Thesemilog method can be used only if the u value for eachobservation well is sufficiently small that the error introducedby the log approximation to the Theis equatio
43、n is minimal.4.4.1.1 For partially penetrating wells, the observation wellsmust be located beyond the zone affected by partialpenetration, that is, at a distance r from the pumped well suchthat:r $1.5b= Kz/Kr(9)4.4.1.2 The extrapolated drawdown obtained in this case issf, the theoretical drawdown, w
44、hich would have occurred justoutside the borehole of a fully penetrating pumped well. Theaquifer drawdown corresponding to partial penetration is thencomputed with the Hantush equation as follows:srw5 sf1Q4Tfs(10)4.4.1.3 The second term on the right-hand side of Eq 10represents the incremental aquif
45、er drawdown caused by partialpenetration.4.4.1.4 Using the Kozeny equation, the aquifer drawdownfor partial penetration is computed from Eq 7 with r set equalto the borehole radius rw:srw5sfl 2 dbS 117rw2l 2 d!cosl 2 d!2bD(11)3The boldface numbers in parentheses refer to the list of references at th
46、e end ofthis test method.D6034 1734.4.1.5 If the extrapolation method is used for determiningaquifer drawdown, it is not necessary to make a separateadjustment to account for boundaries or recharge.4.4.2 Direct CalculationIf the aquifer drawdown srwcan-not be obtained by extrapolation, direct calcul
47、ation must beused to determine its value.4.4.2.1 For fully penetrating wells, srwcan be obtained bydirect calculation using either the Theis or Cooper-Jacobequations (Eq 1-4).4.4.2.2 For partially penetrating wells, srwis calculated fromthe Hantush equation (Eq 5 and 6) or the Kozeny equation (Eq11)
48、.4.4.2.3 The presence of aquifer boundaries or recharge willtend to increase or decrease, respectively, the drawdown in andaround the pumped well. When they are present, the calculatedvalue of srwmust be adjusted to reflect the impact of theboundary conditions.5. Significance and Use5.1 This test me
49、thod allows the user to compute the truehydraulic efficiency of a pumped well in a confined aquiferfrom a constant rate pumping test. The procedures describedconstitute the only valid method of determining well efficiency.Some practitioners have confused well efficiency with percent-age of head loss associated with laminar flow, a parametercommonly determined from a step-drawdown test. Wellefficiency, however, cannot be determined from a step-drawdown test but only c
