1、Designation: D6034 96 (Reapproved 2010)1Standard 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 in
2、dicates the year oforiginal 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.1NOTEA units statement was added editorially in Augu
3、st 2010.1. Scope1.1 This test method describes an analytical procedure fordetermining 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
4、 obtained from aconstant rate pumping test.1.2 This analytical procedure is used 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
5、 units, whichare provided for information only and are not consideredstandard.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 limitatio
6、ns of the technique for deter-mination of well efficiency are related primarily to the corre-spondence between the field situation and the simplifyingassumption of this test method.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresp
7、onsibility 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. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD4050 Test Method for (Field Pr
8、ocedure) for Withdrawaland Injection Well Tests for Determining Hydraulic Prop-erties of Aquifer SystemsD5521 Guide for Development of Ground-Water Monitor-ing Wells in Granular Aquifers3. Terminology3.1 DefinitionsFor definitions of terms used in this testmethod, see Terminology D653.3.2 Definition
9、s of Terms Specific to This Standard:3.2.1 aquifer, confined, nan aquifer bounded above andbelow by confining beds and in which the static head is abovethe top of the aquifer.3.2.2 confining bed, na hydrogeologic unit of less perme-able material bounding one or more aquifers.3.2.3 control well, na w
10、ell by which the head and flow inthe aquifer is changed, for example, by pumping, injection, orimposing a constant change of head.3.2.4 drawdown, nvertical distance the static head islowered due to the removal of water.3.2.5 hydraulic conductivity, n(field aquifer test) the vol-ume of water at the e
11、xisting kinematic viscosity that will movein a unit time under a unit hydraulic gradient through a unitarea measured at right angles to the direction flow.3.2.6 observation well, na well open to all or part of anaquifer.3.2.7 piezometer, na device so constructed and sealed asto measure hydraulic hea
12、d at a point in the subsurface.3.2.8 storage coeffcient, nthe volume of water an aquiferreleases from or takes into storage per unit surface area of theaquifer per unit change in head.3.2.9 transmissivity, nthe volume of water at the existingkinematic viscosity that will move in a unit time under a
13、unithydraulic gradient through a unit width of the aquifer.3.2.10 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 if there were no drilling1Th
14、is test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Aug. 1, 2010. Published September 2010. Originallyapproved in 1996. Last previous edition appro
15、ved in 2004 as D603496(2004).DOI: 10.1520/D6034-96R10E01.2For referenced ASTM standards, visit the ASTM 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.1Cop
16、yright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.damage, that is, no reduction in the natural permeability of thesediments in the vicinity of the borehole.3.3 Symbols:Symbols and Dimensions:3.3.1 Khydraulic conductivity LT1.3.3.1.1 Discus
17、sionThe use of the symbol K for the termhydraulic conductivity is the predominant usage in ground-water literature by hydrogeologists, whereas the symbol k iscommonly used for this term in soil and rock mechanics andsoil science.3.3.2 Krhydraulic conductivity in the plane of the aquifer,radially fro
18、m the control well (horizontal hydraulic conductiv-ity) LT1.3.3.3 Kzhydraulic conductivity normal to the plane of theaquifer (vertical hydraulic conductivity) LT1.3.3.4 K0(x)modified Bessel function of the second kindand zero order nd.3.3.5 Qdischarge L3T1.3.3.6 Sstorage coefficient nd.3.3.7 Ttransm
19、issivity L2T1.3.3.8 srdrawdown in the aquifer at a distance r from thecontrol well L.3.3.9 sfdrawdown which would occur in response topumping a fully penetrating well L.3.3.10 rwborehole radius of control well L.3.3.11 srwtheoretical drawdown which would occur in theaquifer just outside the borehole
20、 if there were no drillingdamage, that is, no reduction in the natural permeability of thesediments in the vicinity of the borehole L.3.3.12 swdrawdown measured inside the control well L.3.3.13 u(r2S)/(4Tt)nd.3.3.14 W(u)an exponential integral known in hydrologyas the Theis well function of u nd.3.3
21、.15 AKz/Kr, anisotropy ratio nd.3.3.16 bthickness of aquifer L.3.3.17 ddistance from top of aquifer to top of screenedinterval of control well L.3.3.18 d8distance from top of aquifer to top of screenedinterval of observation well L.3.3.19 fsincremental dimensionless drawdown compo-nent resulting fro
22、m partial penetration nd.3.3.20 ldistance from top of aquifer to bottom of screenedinterval of control well L.3.3.21 l8distance from top of aquifer to bottom ofscreened interval of observation well L.3.3.22 rradial distance from control well L.3.3.23 ttime since pumping began T.3.3.24 Ewell efficien
23、cy 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 drawdown in the aquifer justoutside the well bore (srw) to the drawdown measured inside thepumped well (sw).
24、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 the sediments in the vicinity of the borehole wall is reducedsignificantly by the drilling operation. Dam
25、aging 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 borehole.The added head loss (drawdown) associated with the perme-ability reduction due to drilling damage
26、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 totheir original, natural permeability.4.2.1 Additional drawdown occurs from head loss associ-ated with fl
27、ow through the filter pack, through the well screenand vertically upward inside the well casing to the pumpintake. While these drawdown components contribute to inef-ficiency, they usually are minor in comparison to the head lossresulting from drilling damage.4.2.2 The well efficiency, usually expre
28、ssed 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 drawdowninside the well. The head losses contributing to inefficiencygenerally are constant with time while
29、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 wellefficiency is the calculated drawdown ratio achieved after oneday of continuous pumping. It is accept
30、able, 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 so thatwellbore storage effects are insignificant. In the vast majorityof cases, after one day of pu
31、mping, 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 laminar (first order) and turbulent (approximatelysecond order) components. Because the proportion of
32、laminarversus turbulent flow can be different in the undisturbed aquiferthan it is in the damaged zone and inside the well, the aquiferdrawdown and inefficiency drawdown can increase at differentrates as Q increases. When this happens, the calculatedefficiency is different for different pumping rate
33、s. Because ofFIG. 1 Illustration of Drawdown Inside and Outside Pumping WellD6034 96 (2010)12this discharge dependence, efficiency testing usually is per-formed at or near the design discharge rate.4.3 The drawdown in the aquifer around a well pumped at aconstant rate can be described by one of seve
34、ral equations.4.3.1 For fully penetrating wells, the Theis equation (1)3isused.sr5Q4pTWu! (1)where:Wu! 5*ue2xxdx (2)andu 5r2S4Tt(3)4.3.2 For sufficiently small values of u, the Theis equationmay be approximated by the Cooper-Jacob equation (2).sr52.3Q4pTlogS2.25Ttr2SD(4)4.3.2.1 Examples of errors in
35、 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) or the Kozenyequation (6).4.3.3.1 The Hantush equation is similar to the Theis equa-tion but
36、 includes a correction factor for partial penetration.sr5Q4pTWu! 1 fs! (5)4.3.3.2 According to Hantush, at late pumping times, whent b2S/(2TA), fscan be expressed as follows:fs54b2p2l d!l8 d8!(n 5 1S1n2DK0 Snpr =Kz/KrbD(6)FsinSnplbD sinSnpdbDGFsinSnplbD sinSnpdbDG4.3.3.3 The Kozeny equation is as fo
37、llows:sr5sfl 2 dbS1 1 7r2l d!cospl 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 equation is not as accurate. It does not incorporatepumping time or anisotropy and
38、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 thanpredicted by Eq 1-6, while a negative boundary (for example,the aquifer pinching out) resu
39、lts 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 drawdown just outside the well bore.4.4 The efficiency of a production well is cal
40、culated asfollows:E 5srwsw(8)where:sw= denominator, the drawdown measured inside thewell, andsrw= numerator, must be determined from field data.Two procedures are available for determining srwextrapolation and direct calculation.4.4.1 ExtrapolationExtrapolation can be used to deter-mine srwif data f
41、rom 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 drawdowndata to the borehole radius to determine srw. If a semilog plot isused, extrapo
42、lation 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 equation is minimal.4.4.1.1 For partially penetrating wells, the observation wellsmust be
43、located beyond the zone affected by partial penetra-tion, that is, at a distance r from the pumped well such that:r$1.5b= Kz/Kr(9)4.4.1.2 The extrapolated drawdown obtained in this case issf, the theoretical drawdown, which would have occurred justoutside the borehole of a fully penetrating pumped w
44、ell. Theaquifer drawdown corresponding to partial penetration is thencomputed with the Hantush equation as follows:srw5 sf1Q4pTfs(10)4.4.1.3 The second term on the right-hand side of Eq 10represents the incremental aquifer drawdown caused by partialpenetration.4.4.1.4 Using the Kozeny equation, the
45、aquifer drawdownfor partial penetration is computed from Eq 7 with r set equalto the borehole radius rw:srw5sfl 2 dbS1 1 7rw2l 2 d!cospl 2 d!2bD(11)4.4.1.5 If the extrapolation method is used for determiningaquifer drawdown, it is not necessary to make a separateadjustment to account for boundaries
46、or recharge.4.4.2 Direct CalculationIf the aquifer drawdown srwcan-not be obtained by extrapolation, direct calculation 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).3The boldfa
47、ce numbers in parentheses refer to the list of references at the end ofthis test method.D6034 96 (2010)134.4.2.2 For partially penetrating wells, srwis calculated fromthe Hantush equation (Eq 5 and Eq 6) or the Kozeny equation(Eq 11).4.4.2.3 The presence of aquifer boundaries or recharge willtend to
48、 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 method allows the user to compute the truehydraulic efficiency of a p
49、umped 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. Well effi-ciency, however, cannot be determined from a step-drawdowntest but only can be determined from a constant rate test.5.2 Assumption
