1、Designation: D5881 18Standard Practice 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 designatio
2、n 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 practice covers determination
3、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 level; ov
4、erdamped 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/D5785M, D4043.1.2 The analytical procedure in this practice is used inconjunctio
5、n with Guide D4043 and the field procedure in TestMethod D4044/D4044M 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 th
6、e 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 All observed and calculated values shall conform to theguidelines for significant digits and rounding established in
7、Practice D6026.1.4.1 The procedures used to specify how data are collected/recorded and calculated in this standard are regarded as theindustry standard. In addition, they are representative of thesignificant digits that should generally be retained. The proce-dures used do not consider material var
8、iation, purpose forobtaining the data, special purpose studies, or any consider-ations for the users objectives; and it is common practice toincrease or reduce significant digits of reported data to com-mensurate with these considerations. It is beyond the scope ofthis standard to consider significa
9、nt digits used in analysismethods for engineering design.1.5 UnitsThe values stated in SI units are to be regardedas standard. No other units of measurement are included in thisstandard. Reporting of test results in units other than SI shallnot be regarded as nonconformance with this standard.1.6 Th
10、is practice offers a set of instructions for performingone or more specific operations. This document cannot replaceeducation or experience and should be used in conjunction withprofessional judgment. Not all aspects of the practice may beapplicable in all circumstances. This ASTM standard is notint
11、ended to represent or replace the standard of care by whichthe adequacy of a given professional service must be judged,nor should this document be applied without the considerationof a projects many unique aspects. The word “Standard” in thetitle of this document means only that the document has bee
12、napproved through he ASTM consensus process.1.7 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, health, and environmental practices and deter-mine the applicab
13、ility of regulatory limitations prior to use.1.8 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the
14、World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD4043 Guide for Selection of Aquifer Test Method inDetermining Hydraulic Properties by Well Techniques1This test method is under
15、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 Dec. 1, 2018. Published December 2018. Originallyapproved in 1995. Last previous edition approved in 2013 as D5881 13. D
16、OI:10.1520/D5881-18.2For 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 Changes section appears at
17、the end of this standardCopyright ASTM International, 100 Barr 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
18、 theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1D4044/D4044M Test Method for (Field Procedure) for In-stantaneous Change in Head (Slug) Tests for DeterminingHydraulic Properties of AquifersD571
19、7 Guide for Design of Ground-Water Monitoring Sys-tems in Karst and Fractured-Rock Aquifers (Withdrawn2005)3D5785/D5785M Test Method for (Analytical Procedure) forDetermining Transmissivity of Confined Nonleaky Aqui-fers by Underdamped Well Response to InstantaneousChange in Head (Slug Test)D6026 Pr
20、actice for Using Significant Digits in GeotechnicalData3. Terminology3.1 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, confined, nin ground water, an aquiferbounded above and below by
21、confining beds and in which thestatic head is above the top of the aquifer.3.2.2 critically damped well response, nin ground water,characterized by the water level responding in a transitionalrange between underdamped and overdamped following asudden change in water level.3.2.3 observation well, nin
22、 ground water, a well open toall or part of an aquifer.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 Lc+(rc2/rs2)(b/2) L.3.3.5 Lclength of water c
23、olumn 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 rcradius of well casing L.3.3.12 rsradius of well sc
24、reen 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 inertial parameter nd.3.3.20 damping constant T
25、1.3.3.21 wavelength T.3.3.22 angular frequency T1.3.3.23 dimensionless damping factor nd.4. Summary of Practice4.1 This practice describes the analytical procedure foranalyzing data collected during an instantaneous head (slug)test for well and aquifer response at and near critical damping.Procedure
26、s in conducting a slug test are given in Test MethodD4044/D4044M. The analytical procedure consists of analyz-ing the response of water level in the well following the changein water level induced in the well.4.2 TheoryThe equations that govern the response of wellto an instantaneous change in head
27、are treated at length byKipp (1).4The 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 theouter boundary conditio
28、n 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 bore relates thedisplacement
29、 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 hsand w, comes from a momentum balance equ
30、ation 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.3The last approved version of this historical standard
31、is referenced onwww.astm.org.4The boldface numbers in parentheses refer to a list of references at the end ofthis standard.D5881 182The numerical 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 dif
32、ferential equation torepresent for the response of the displacement of water level inthe well:d2wdt21SgLeDw 5ghs2 ho!/Le(4)where:Le= effective water 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
33、Kipp (1) introduces dimensionless variables and param-eters in converting these equations to dimensionless form,solves the equations by Laplace transforms, and inverts thesolution by a Laplace-transform-inversion algorithm.5.2.1 The following dimensionless parameters are amongthose given by Kipp (1)
34、:dimensionless water-level displacement:w 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 dec
35、ay parameter: 51 1n!2(16)and dimensionless 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
36、systemresponds as if the inertial effects can be neglected and thesolution of Cooper et al. (3) (given in Guide D4043)isapplicable. For about 0.2 or less, the approximate solution ofvan der Kamp (4) is valid (given in Test Method D5785/D5785M). The solution of Kipp (1), the subject of this testmetho
37、d, is applicable for the transition zone between systemsthat are underdamped and overdamped. Solutions are givenhere 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
38、lower confining boundaries.6.1.2 The aquifer is of 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 aqui
39、fer is fully screened.FIG. 1 Well and Aquifer Geometry from Kipp (1)D5881 1836.1.5 The well is 100 % efficient, 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
40、 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 thickness.6.2.4 Change in momentum from the water velocity chang-ing from radial flow through the
41、 screen to vertical flow in thewell are negligible.NOTE 1The function of wells in any unconfined setting in a fracturedterrain might make the determination of k problematic because the wellsmight only intersect tributary or subsidiary channels or conduits. Theproblems determining the k of a channel
42、or conduit notwithstanding, thepartial penetration of tributary channels may make a determination of ameaningful number difficult. If plots of k in carbonates and other fracturedsettings are made and compared, they may show no indication that thereare conduits or channels present, except when with t
43、he lowest probabilityone maybe intersected by a borehole and can be verified, such problemsare described by (5) Smart (1999). Additional guidance can be found inGuide D5717.7. Procedure7.1 The overall procedure consists of conducting the slugtest field procedure (see Test Method D4044/D4044M) andana
44、lysis of the field data using this practice.NOTE 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-level displacementand the water-level displacement needs to be calcul
45、ated 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 level displacement, w, versus dimension-less time, t, using the sam
46、e 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, record the values of t, and w from the type curve.From the data plo
47、t, 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, within20 %, with the effective length calculated from the systemgeometry
48、(Eq 5).8.6 Calculate the dimensionless inertial parameter, , itera-tively from the following expression: 5 1n !/8#2(20)FIG. 2 Slug-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 Dime
49、nsionless Time, t, for Construction of TypeCurves, = 0.1 and = 9988.1tw tw3.162278E02 9.994887E01 3.162278E + 00 7.100277E013.636619E02 9.993281E01 3.636619E + 00 6.204110E013.952847E02 9.992086E01 3.952847E + 00 4.871206E014.269075E02 9.990793E01 4.269075E + 00 3.138511E014.743416E02 9.988666E01 4.743416E + 00 2.218683E025.375872E02 9.985483E01 5.375872E + 00 3.226809E016.32
