1、Designation: D5881 13Standard Test Method for(Analytical Procedure) Determining Transmissivity ofConfined Nonleaky Aquifers by Critically Damped WellResponse to Instantaneous Change in Head (Slug)1This standard is issued under the fixed designation D5881; the number immediately following the designa
2、tion indicates 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.1. Scope*1.1 This test method covers determin
3、ation of transmissivityfrom the measurement of water-level response to a suddenchange of water level in a well-aquifer system characterized asbeing critically damped or in the transition range from under-damped to overdamped. Underdamped response is character-ized by oscillatory changes in water lev
4、el; overdamped re-sponse is characterized by return of the water level to the initialstatic level in an approximately exponential manner. Over-damped response is covered in Guide D4043; underdampedresponse is covered in D5785, D4043.1.2 The analytical procedure in this test method is used inconjunct
5、ion with Guide D4043 and the field procedure in TestMethod D4044 for collection of test data.1.3 LimitationsSlug tests are considered to provide anestimate of the transmissivity of an aquifer near the wellscreen. The method is applicable for systems in which thedamping parameter, , is within the ran
6、ge from 0.2 through 5.0.The assumptions of the method prescribe a fully penetratingwell (a well open through the full thickness of the aquifer) ina confined, nonleaky aquifer.1.4 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPract
7、ice D6026.1.5 UnitsThe values stated in SI units are to be regardedas standard. No other units of measurement are included in thisstandard.1.5.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as theindustry standard. In addition, they are
8、representative of thesignificant digits that generally should be retained. The proce-dures used do not consider material variation, purpose forobtaining the data, special purpose studies, or any consider-ations for the users objectives and it is common practice toincrease to reduce significant digit
9、s of reported data to becommensurate with these considerations. It is beyond the scopeof this standard to consider significant digits used in analyticalmethods for design.1.6 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility
10、 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 ContainedFluidsD3740 Practice for Minimum Requirements f
11、or AgenciesEngaged in Testing and/or Inspection of Soil and Rock asUsed in Engineering Design and ConstructionD4043 Guide for Selection of Aquifer Test Method inDetermining Hydraulic Properties by Well TechniquesD4044 Test Method for (Field Procedure) for InstantaneousChange in Head (Slug) Tests for
12、 Determining HydraulicProperties of AquifersD5785 Test Method for (Analytical Procedure) for Deter-mining Transmissivity of Confined Nonleaky Aquifers byUnderdamped Well Response to Instantaneous Change inHead (Slug Test)D6026 Practice for Using Significant Digits in GeotechnicalData3. Terminology3.
13、1 DefinitionsFor definitions of common technical termsin this standard, refer to Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 aquifer, confinedan aquifer bounded above and be-low by confining beds and in which the static head is above thetop of the aquifer.1This test met
14、hod is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved Nov. 15, 2013. Published December 2013. Originallyapproved in 1995. Last previous edition approved in 2005
15、as D5881 95 (2005).DOI: 10.1520/D5881-13.2For 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.*A Summary of Change
16、s section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.2 critically damped well responsecharacterized by thewater level responding in a transitional range between under-damped and overdamped f
17、ollowing a sudden change in waterlevel.3.2.3 observation wella well open to all or part of anaquifer.3.3 Symbols and Dimensions:3.3.1 Ttransmissivity L2T1.3.3.2 Sstorage coefficient nd.3.3.3 Lstatic water column length above top of aquiferL.3.3.4 Leeffective length of water column in a well, equalto
18、 Lc+(rc2/rs2)(b/2) L.3.3.5 Lclength of water column within casing L.3.3.6 Lslength of water column within well screen L.3.3.7 gacceleration of gravity LT2.3.3.8 hhydraulic head in the aquifer L.3.3.9 hoinitial hydraulic head in the aquifer L.3.3.10 hshydraulic head in the well screen L.3.3.11 rcradi
19、us of well casing L.3.3.12 rsradius of well screen L.3.3.13 ttime T.3.3.14 tdimensionless time nd.3.3.15 tdimensionless time nd.3.3.16 wwater level displacement from the initial staticlevel L.3.3.17 woinitial water level displacement L.3.3.18 dimensionless storage parameter nd.3.3.19 dimensionless i
20、nertial parameter nd.3.3.20 damping constant T1.3.3.21 wavelength T.3.3.22 angular frequency T1.3.3.23 dimensionless damping factor nd.4. Summary of Test Method4.1 This test method describes the analytical procedure foranalyzing data collected during an instantaneous head (slug)test for well and aqu
21、ifer response at and near critical damping.Procedures in conducting a slug test are given in Test MethodD4044. The analytical procedure consists of analyzing theresponse of water level in the well following the change inwater level induced in the well.4.2 TheoryThe equations that govern the response
22、 of wellto an instantaneous change in head are treated at length byKipp (1).3The flow in the aquifer is governed by the followingequation for cylindrical flow:STdhdt51rddrSrdhdrD(1)where:h = hydraulic head,T = aquifer transmissivity, andS = storage coefficient.4.2.1 The initial condition is at t = 0
23、 and h = ho, and theouter boundary condition is as r and hho.4.2.1.1 An equation is given by Kipp (1) for the skin factor,that is, the effect of aquifer damage during drilling of the well.However, this factor is not treated by Kipp (1) and is notconsidered in this procedure.4.2.2 The flow rate balan
24、ce on the well bore relates thedisplacement of the water level in the well riser to the flow intothe well:rc2dwdt5 2rsTdhdr?r5rs(2)where:rc= radius of the well casing, andw = displacement of the water level in the well from itsinitial position.4.2.3 The fourth equation describing the system relating
25、 hsand w, comes from a momentum balance equation of Bird et al(2) as referenced in Kipp (1):ddt*2b0rs2pvdz 52pv221p12 p22 gb!rs2(3)where:v = velocity in the well screen interval,b = aquifer thickness,p = pressure, = fluid density,g = gravitational acceleration, andrs= well screen radius.The numerica
26、l subscripts refer to the planes described aboveand shown in Fig. 1. Atmospheric pressure is taken as zero.5. Solution5.1 Kipp (1) derives the following differential equation torepresent for the response of the displacement of water level inthe well:d2wdt21SgLeDw 5ghs2 ho!/Le(4)where:Le= effective w
27、ater column length, defined as:Le5 L1rc2/rs2!b/2! (5)where:b = aquifer thickness with initial conditions:at t 5 0, w 5 wo(6)dw/dt 5 wo* (7)hs5 L 5 ho(8)5.2 Kipp (1) introduces dimensionless variables and param-eters in converting these equations to dimensionless form,solves the equations by Laplace
28、transforms, and inverts thesolution by a Laplace-transform-inversion algorithm.3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.D5881 1325.2.1 The following dimensionless parameters are amongthose given by Kipp (1):dimensionless water-level displacement:w
29、 52w/wo(9)dimensionless time:t 5 tT!/rs2S! (10)and:t5 t/(11)dimensionless storage: 5rc2! 2rs2S! (12)dimensionless inertial parameter: 5 Le/g!T/rs2S!2(13)dimensionless skin factor: 5 f/rs(14)dimensionless frequency parameter: 52d21 1n!14#2(15)dimensionless decay parameter: 51 1n!2(16)and dimensionles
30、s damping factor: 51 1n!2(17)5.3 For less than one, the system is underdamped; for greater than one, the system is overdamped. For equal to one,the system is critically damped, yet the inertial effects are quiteimportant (1). For greater than about five, the systemresponds as if the inertial effects
31、 can be neglected and thesolution of Cooper et al. (3) (given in Guide D4043)isapplicable. For about 0.2 or less, the approximate solution ofvander Kamp (4) is valid (given in Test Method D5785). Thesolution of Kipp (1), the subject of this test method, isapplicable for the transition zone between s
32、ystems that areunderdamped and overdamped. Solutions are given here for ranging from 0.2 to 5.0.6. Significance and Use6.1 The assumptions of the physical system are given asfollows:6.1.1 The aquifer is of uniform thickness, with impermeableupper and lower confining boundaries.6.1.2 The aquifer is o
33、f constant homogeneous porosity andmatrix compressibility and constant homogeneous and isotro-pic hydraulic conductivity.6.1.3 The origin of the cylindrical coordinate system istaken to be on the well-bore axis at the top of the aquifer.6.1.4 The aquifer is fully screened.6.1.5 The well is 100 % eff
34、icient, that is, the skin factor, f,and dimensionless skin factor, , are zero.6.2 The assumptions made in defining the momentum bal-ance are as follows:6.2.1 The average water velocity in the well is approxi-mately constant over the well-bore section.6.2.2 Frictional head losses from flow in the wel
35、l arenegligible.6.2.3 Flow through the well screen is uniformly distributedover the entire aquifer thickness.6.2.4 Change in momentum from the water velocity chang-ing from radial flow through the screen to vertical flow in thewell are negligible.NOTE 1The quality of the result produced by this stan
36、dard isdependent on the competence of the personnel performing it, and thesuitability of the equipment and facilities used. Agencies that meet thecriteria of Practice D3740 are generally considered capable of competentand objective testing/sampling/inspection/etc. Users of this standard arecautioned
37、 that compliance with Practice D3740 does not in itself assurereliable results. Reliable results depend on many factors; Practice D3740provides a means of evaluating some of those factors.7. Procedure7.1 The overall procedure consists of conducting the slugtest field procedure (see Test Method D4044
38、) and analysis ofthe field data using this test method.FIG. 1 Well and Aquifer Geometry from Kipp (1)D5881 133NOTE 2The initial displacement of water level should not exceed 0.1or 0.2 of the static water column in the well, the measurement ofdisplacement should be within 1 % of the initial water-lev
39、el displacementand the water-level displacement needs to be calculated independently.8. Calculation and Interpretation of Results8.1 Plot the normalized water-level displacement in the wellversus the logarithm of time.8.2 Prepare a set of type curves from Tables 1-10 by plottingdimensionless water l
40、evel displacement, w, versus dimension-less time, t, using the same scale as in plotting the observedwater-level displacement.8.3 Match the semilog plot of water-level displacement tothe type curves by translation of the time axis.8.4 From the type curve, record the value of ; from thematch point, r
41、ecord the values of t, and w from the type curve.From the data plot, record the values of time, t, and water-leveldisplacement, w.8.5 Calculate the effective static water column length, Le,from the following:t5tLe/g!1/2(18)Le5 t/t!2g (19)The effective static water column length should agree, within2
42、0 %, with the effective length calculated from the systemgeometry (Eq 5).8.6 Calculate the dimensionless inertial parameter, , itera-tively from the following expression: 5 1n !/8#2(20)where: = damping parameter, = dimensionless storage parameter as given in Eq 12.8.7 Calculate transmissivity from t
43、he following:T 5 g!/Le#rs2S (21)8.7.1 Kipp (1) gives an example application of the method,using data from vander Kamp (4) for York Point well 6-2. Thiswell has casing, screen, and well-bore radii of 0.051 m, a watercolumn above the aquifer of 6.5 m, an aquifer thickness of 15m, and an independently
44、estimated storage coefficient of8105.8.7.2 A type curve of dimensionless water-leveldisplacement, w, plotted against the log of dimensionless time,t, for three values of the dimensionless damping factor, , wasprepared. Water-level displacement was calculated using anestimated initial displacement of
45、 3.45 cm, and plotted againstthe log of elapsed time since maximum initial water-leveldisplacement of paper of the same scale as the type curve.8.7.3 The data curve was overlain on the type curve, andshifted horizontally, with the water-level displacement axescoincident, until the best match with th
46、e type curve was found.The best fit was for a dimensionless damping factor of 0.25. Amatch point of t = 7s for t = 5 was selected. The resultinggraph is shown in Fig. 2.8.7.4 The effective water column length can be calculatedfrom Eq 19 as follows:Le5 t/t!2g 5 7s/5!29.80 m/s2! 5 19.2 m (22)FIG. 2 Sl
47、ug-Test Data Overlaid on Type Curves for Three Differ-ent Damping Factors, Modified from Kipp (1)TABLE 1 Values of the Dimensionless Water Level Displacement,w, Versus Dimensionless Time, t, for Construction of TypeCurves, = 0.1 and = 9988.1tw tw3.162278E02 9.994887E01 3.162278E + 00 7.100277E013.63
48、6619E02 9.993281E01 3.636619E + 00 6.204110E013.952847E02 9.992086E01 3.952847E + 00 4.871206E014.269075E02 9.990793E01 4.269075E + 00 3.138511E014.743416E02 9.988666E01 4.743416E + 00 2.218683E025.375872E02 9.985483E01 5.375872E + 00 3.226809E016.324555E02 9.979965E01 6.324555E + 00 5.191564E017.11
49、5125E02 9.974688E01 7.115125E + 00 3.413663E017.905694E02 9.968794E01 7.905694E + 00 3.445623E058.696264E02 9.962284E01 8.696264E + 00 2.889492E019.486833E02 9.955161E01 9.486833E + 00 3.712172E011.106797E01 9.939077E01 1.106797E + 01 1.758246E021.264911E01 9.920552E01 1.264911E + 01 2.697976E011.423025E01 9.899599E01 1.423025E
