1、Designation: D 5881 95 (Reapproved 2005)Standard 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 D 5881; the number immediately f
2、ollowing the designation 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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test me
3、thod covers determination 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
4、changes in water level; 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 D 4043; underdampedresponse is covered in D 5785.1.2 The analytical procedure in this test method is
5、used inconjunction with Guide D 4043 and the field procedure in TestMethod D 4044 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, z,
6、 is within the range 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 The values stated in SI units are to be regarded asstandard.1.5 This standard does not purport to addre
7、ss 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. Referenced Documents2.1 ASTM Standards:2D 653 Terminolo
8、gy Relating to Soil, Rock, and ContainedFluidsD 4043 Guide for Selection of Aquifer-Test Method inDetermining of Hydraulic Properties by Well TechniquesD 4044 Test Method (Field Procedure) for InstantaneousChange in Head (Slug Test) for Determining HydraulicProperties of AquifersD 4750 Test Method f
9、or Determining Subsurface LiquidLevels in a Borehole or Monitoring Well (ObservationWell)D 5785 Test Method for (Analytical Procedure) Determin-ing Transmissivity of Confined Nonleaky Aquifers byUnderdamped Well Response to Instantaneous Change inHead (Slug Test)3. Terminology3.1 Definitions:3.1.1 a
10、quifer, confinedan aquifer bounded above andbelow by confining beds and in which the static head is abovethe top of the aquifer.3.1.2 confining beda hydrogeologic unit of less perme-able material bounding one or more aquifers.3.1.3 control wella well by which the head and flow in theaquifer is chang
11、ed by pumping, injecting, or imposing aconstant change of head.3.1.4 critically damped well responsecharacterized by thewater level responding in a transitional range between under-damped and overdamped following a sudden change in waterlevel.3.1.5 head, staticthe height above a standard datum thesu
12、rface of a column of water can be supported by the staticpressure at a given point.3.1.6 observation wella well open to all or part of anaquifer.3.1.7 overdamped well responsecharacterized by the wa-ter level returning to the static level in an approximatelyexponential manner following a sudden chan
13、ge in water level.(See for comparison underdamped well response.)3.1.8 sluga volume of water or solid object used to inducea sudden change of head in a well.1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Gro
14、und Water andVadose Zone Investigations.Current edition approved Nov. 1, 2005. Published December 2005. Originallyapproved in 1995. Last previous edition approved in 2000 as D 5881 95 (2000).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serv
15、iceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.9 storage coeffcientthe volume of water an aquiferr
16、eleases from or takes into storage per unit surface area of theaquifer per unit change in head. For a confined aquifer, thestorage coefficient is equal to the product of the specific storageand aquifer thickness.3.1.10 transmissivitythe volume of water at the existingkinematic viscosity that will mo
17、ve in a unit time under a unithydraulic gradient through a unit width of the aquifer.3.1.11 underdamped well responseresponse characterizedby the water level oscillating about the static water levelfollowing a sudden change in water level (See for comparisonoverdamped-well response).3.1.12 For defin
18、itions of other terms used in this testmethod, see Terminology D 653.3.2 Symbols:Symbols and Dimensions:3.2.1 Ttransmissivity L2T1.3.2.2 Sstorage coefficient nd.3.2.3 Lstatic water column length above top of aquiferL.3.2.4 Leeffective length of water column in a well, equalto Lc+(rc2/rs2)(b/2) L.3.2
19、.5 Lclength of water column within casing L.3.2.6 Lslength of water column within well screen L.3.2.7 gacceleration of gravity LT2.3.2.8 hhydraulic head in the aquifer L.3.2.9 hoinitial hydraulic head in the aquifer L.3.2.10 hshydraulic head in the well screen L.3.2.11 rcradius of well casing L.3.2.
20、12 rsradius of well screen L.3.2.13 ttime T.3.2.14 t8dimensionless time nd.3.2.15 tdimensionless time nd.3.2.16 wwater level displacement from the initial staticlevel L.3.2.17 woinitial water level displacement L.3.2.18 adimensionless storage parameter nd.3.2.19 bdimensionless inertial parameter nd.
21、3.2.20 gdamping constant T1.3.2.21 twavelength T.3.2.22 vangular frequency T1.3.2.23 zdimensionless 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 aquifer response at
22、and near critical damping.Procedures in conducting a slug test are given in Test MethodD 4044. 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 of wellto an in
23、stantaneous 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 and h = ho, and
24、 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 balance on the well b
25、ore relates thedisplacement of the water level in the well riser to the flow intothe well:prc2dwdt5 2prsTdhdr|r 5 rs(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 hsand w, co
26、mes from a momentum balance equation of Bird et al(2) as referenced in Kipp (1):ddt*b0prs2pvdz 5 pv221 p12 p22rgb! prs2(3)where:v = velocity in the well screen interval,b = aquifer thickness,p = pressure,r = fluid density,g = gravitational acceleration, andrs= well screen radius.The numerical subscr
27、ipts 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 water co
28、lumn length, defined as:Le5 L 1 rc2/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 trans
29、forms, and inverts thesolution by a Laplace-transform-inversion algorithm.3The boldface numbers in parentheses refer to a list of references at the end ofthe text.D 5881 95 (2005)25.2.1 The following dimensionless parameters are amongthose given by Kipp (1):dimensionless water-level displacement:w8
30、52w/wo(9)dimensionless time:t8 5 tT! / rs2S! (10)and:t5 t8/b(11)dimensionless storage:a5rc2! 2rs2S! (12)dimensionless inertial parameter:b5Le / g!T / rs2S!2(13)dimensionless skin factor:FIG. 1 Well and Aquifer Geometry from Kipp (1)FIG. 2 Slug-Test Data Overlaid on Type Curves for Three DifferentDam
31、ping Factors, Modified from Kipp (1)D 5881 95 (2005)3s5f/rs(14)dimensionless frequency parameter:v52d2s11nb! 1 4b2b(15)dimensionless decay parameter:g5as11nb!2b(16)and dimensionless damping factor:z5as11nb!2b(17)5.3 For z less than one, the system is underdamped; for zgreater than one, the system is
32、 overdamped. For z equal to one,the system is critically damped, yet the inertial effects are quiteimportant (1). For z greater than about five, the systemresponds as if the inertial effects can be neglected and thesolution of Cooper et al (3) (given in Guide D 4043)isapplicable. For z about 0.2 or
33、less, the approximate solution ofvander Kamp (4) is valid (given in Test Method D 5785). Thesolution of Kipp (1), the subject of this test method, isapplicable for the transition zone between systems that areunderdamped and overdamped. Solutions are given here for zranging from 0.2 to 5.0.6. Signifi
34、cance 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 of constant homogeneous porosity andmatrix compressibility and constant homogeneous and isotro-pic hydrauli
35、c 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 % efficient, that is, the skin factor, f,and dimensionless skin factor, s, are zero.6.2 The assumptions made in
36、 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 well arenegligible.6.2.3 Flow through the well screen is uniformly distributedover the entire aquifer thickn
37、ess.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.7. Procedure7.1 The overall procedure consists of conducting the slugtest field procedure (see Test Method D 4044) and analysis ofthe field data using this te
38、st method.NOTE 1The 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-level displacementand the water-level displacement needs to be calculated independently.8. Calculation
39、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 fromTables 1-10 by plottingdimensionless water level displacement, w8, versus dimension-less time, t, using the same scale as in plotting the observe
40、dwater-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 z; from thematch point, record the values of t, and w8 from the type curve.From the data plot, record the values of time, t,
41、 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, within20 %, with the effective length calculated from the systemgeometry, (Eq 5).TABLE 1 Values of the Di
42、mensionless Water Level Displacement,w*, Versus Dimensionless Time, t, for Construction of TypeCurves, z = 0.1 and a = 9988.1tw8 tw83.162278E02 9.994887E01 3.162278E + 00 7.100277E013.636619E02 9.993281E01 3.636619E + 00 6.204110E013.952847E02 9.992086E01 3.952847E + 00 4.871206E014.269075E02 9.9907
43、93E01 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 5.191564E017.115125E02 9.974688E01 7.115125E + 00 3.413663E017.905694E02 9.968794E01 7.905694E + 00 3.445623E058.696264E02 9.9622
44、84E01 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 + 01 2.109260E021.581139E01 9.876230E01 1.581139E + 01 1.919487E011.739253E01 9.8504
45、56E01 1.739253E + 01 2.455328E021.897367E01 9.822293E01 1.897367E + 00 1.392019E012.213594E01 9.758851E01 2.213594E + 01 9.826209E022.529822E01 9.686026E01 2.529822E + 01 7.129166E022.846050E01 9.603946E01 2.846050E + 01 4.976069E023.162278E01 9.512748E01 3.162278E + 01 3.626029E023.636619E01 9.3591
46、83E01 3.636619E + 01 9.997386E033.952847E01 9.259452E01 3.952847E + 01 7.200932E034.269075E01 9.084819E01 4.743416E + 01 5.892951E034.743416E01 8.947298E01 5.375872E + 01 2.737128E035.375872E01 8.632514E01 6.324555E + 01 1.254582E036.324555E01 8.135785E01 7.115125E + 01 2.961127E047.115125E01 7.6730
47、17E01 7.905694E + 01 5.757717E057.905694E01 7.169702E01 8.696264E + 01 2.991356E048.696264E01 6.629659E01 9.486833E + 01 1.835296E049.486833E01 6.056883E01 1.106797E + 02 1.426791E041.106797E + 00 4.829810E01 1.264911E + 02 1.249977E041.264911E + 00 3.522848E01 1.423025E + 02 1.115579E041.423025E +
48、00 2.171309E01 1.581139E + 02 1.001696E041.581139E + 00 8.105198E02 1.739253E + 02 9.109389E051.739253E + 00 5.974766E02 1.897367E + 02 8.347056E051.897367E + 00 1.802728E01 2.213594E + 02 7.152232E052.213594E + 00 4.066508E01 2.529822E + 02 6.256450E052.529822E + 00 5.647406E01 2.846050E + 02 5.560200E052.846050E + 00 6.811030E01 . .D 5881 95 (2005)48.6 Calculate the dimensionless inertial parameter, b, itera-tively from the following expression:b5a 1n b !/8z2(20)where:z = damping parameter,a = dimensionless storage parameter as given in (Eq 12).8.7 Calculate transmissivity from the f
