1、Designation: D5785/D5785M 15Standard Test Method for(Analytical Procedure) for Determining Transmissivity ofConfined Nonleaky Aquifers by Underdamped WellResponse to Instantaneous Change in Head (Slug Test)1This standard is issued under the fixed designation D5785/D5785M; the number immediately foll
2、owing the designation indicates theyear of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of lastreapproval. A superscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test metho
3、d covers determination of transmissivityfrom the measurement of the damped oscillation about theequilibrium water level of a well-aquifer system to a suddenchange of water level in a well. Underdamped response ofwater level in a well to a sudden change in water level ischaracterized by oscillatory f
4、luctuation about the static waterlevel with a decrease in the magnitude of fluctuation andrecovery to initial water level. Underdamped response mayoccur in wells tapping highly transmissive confined aquifersand in deep wells having long water columns.1.2 This analytical procedure is used in conjunct
5、ion with thefield procedure Test Method D4044 for collection of test data.1.3 LimitationsSlug tests are considered to provide anestimate of transmissivity of a confined aquifer. This testmethod requires that the storage coefficient be known. As-sumptions of this test method prescribe a fully penetra
6、ting well(a well open through the full thickness of the aquifer), but theslug test method is commonly conducted using a partiallypenetrating well. Such a practice may be acceptable forapplication under conditions in which the aquifer is stratifiedand horizontal hydraulic conductivity is much greater
7、 thanvertical hydraulic conductivity. In such a case the test would beconsidered to be representative of the average hydraulicconductivity of the portion of the aquifer adjacent to the openinterval of the well. The method assumes laminar flow and isapplicable for a slug test in which the initial wat
8、er-leveldisplacement is less than 0.1 or 0.2 of the length of the staticwater column.1.4 This test method of analysis presented here is derived byvan der Kamp (1)2based on an approximation of the under-damped response to that of an exponentially damped sinusoid.A more rigorous analysis of the respon
9、se of wells to a suddenchange in water level by Kipp (2) indicates that the methodpresented by van der Kamp (1) matches the solution of Kipp(2) when the damping parameter values are less than about 0.2and time greater than that of the first peak of the oscillation (2).1.5 UnitsThe values stated in e
10、ither SI units or inch-pound units are to be regarded separately as standard. Thevalues in each system may not be exact equivalents; thereforeeach system shall be used independently of the other. Combin-ing values from the two systems may result in non-conformance with the standard. Reporting of tes
11、t results inunits other than SI shall not be regarded as nonconformancewith this test method.1.6 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPractice D6026.1.7 This standard does not purport to address all of thesafety concerns,
12、 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:3D653 Terminology Relating to Soil, Rock, and
13、 ContainedFluidsD3740 Practice for Minimum Requirements for 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 Pr
14、ocedure) for InstantaneousChange in Head (Slug) Tests for Determining HydraulicProperties of AquifersD6026 Practice for Using Significant Digits in GeotechnicalData1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21
15、 on Groundwater andVadose Zone Investigations.Current edition approved Nov. 1, 2015. Published November 2015. Originallyapproved in 1995. Last previous edition approved in 2013 as D5785 95 (2013).DOI: 10.1520/D5785_D5785M-15.2The boldface numbers given in parentheses refer to a list of references at
16、 theend of the text.3For 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 States13. Terminology3.1 DefinitionsFor definitions of other terms used in thistest method, see Terminology D653.3.1.1 observation wella well open to all or part of anaq
18、uifer.3.1.2 storage coeffcientthe volume of water an aquiferreleases 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 specific storageand aquifer thickness. For an unconfined aquifer, the
19、 storagecoefficient is approximately equal to the specific yield.3.1.3 transmissivitythe volume of water at the existingkinematic viscosity that will move in a unit time under a unithydraulic gradient through a unit width of the aquifer.3.2 Symbols and Dimensions:3.2.1 Ttransmissivity L2T1.3.2.2 Sst
20、orage coefficient nd.3.2.3 Leffective length of water column, equal to Lc+(rc2/rs2) (m/2).3.2.3.1 DiscussionThis expression for the effective lengthis given by Kipp (2). The expression for the effective length ofthe water column from Cooper et al. (3) is given as Lc+38Lsand assumes that the well scr
21、een and well casing have the samediameter.3.2.4 Lclength of water column within casing L.3.2.5 Lslength of water column within well screen L.3.2.6 gacceleration of gravity LT2.3.2.7 hhydraulic head in the aquifer L.3.2.8 hoinitial hydraulic head in the aquifer L.3.2.9 hshydraulic head in the well sc
22、reen L.3.2.10 rcradius of well casing L.3.2.11 rsradius of well screen L.3.2.12 ttime T.3.2.13 wwater level displacement from the initial staticlevel L.3.2.14 woinitial water level displacement L.3.2.15 damping constant T1.3.2.16 wavelength T.3.2.17 angular frequency T1.3.2.18 maquifer thickness, L.
23、4. Summary of Test Method4.1 This test method describes the analytical procedure foranalyzing data collected during an instantaneous head (slug)test using a well in which the response is underdamped. Thefield procedures in conducting a slug test are given in TestMethod D4044. The analytical procedur
24、e consists of analyzingthe response 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 instantaneous change in head are treated at length byKipp (2). The flow in the aquifer is governed by the followingequat
25、ion 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 = hoand theouter boundary condition is as r and h ho.4.3 The flow rate balance on the well bore relates thedisplacement of the
26、water level in the well-riser to the flow intothe well:Urc2dwdt5 2rsT hrUr5rs(2)where:rc= radius of the well casing, andw = displacement of the water level in the well from itsinitial position.4.3.1 The third equation describing the system, relating hsand w, comes from a momentum balance of Bird et
27、al. (4) asreferenced in Kipp (2).ddt*2m0rs2pvdz 5 2pv221p12 p22 pgm#rs2(3)where:v = velocity in the well screen interval,m = aquifer thickness,p = pressure, = fluid density,g = gravitational acceleration, andrs= well screen radius. Well and aquifer geometry areshown in Fig. 1.Atmospheric pressure is
28、 taken as zero.5. Solution5.1 The method of van der Kamp (1) assumes the waterlevel response to a sudden change for the underdamped case,except near critical damping conditions, can be approximatelydescribed as an exponentially damped cyclic fluctuation thatdecays exponentially. The water-level fluc
29、tuation would thenbe given by:wt! 5 woe2tcos wt (4)5.1.1 The following solution is given by van der Kamp (1).d 52rc2g/L!1/21n0.79 rs2S/T!g/L!1/28T(5)that may be written as:T 5 b1a 1nT (6)where:b 5 a 1n0.79 rs2S g/L!1/2(7)a 5rc2g/L!1/28d(8)d 5 /g/L!1/2(9)andL 5 g/212! (10)NOTE 1Other analytical solut
30、ions are proposed by Kipp (2); KraussD5785/D5785M 152(5); Kruseman and de Ridder (6); and Kabala, Pinder, and Milly (7).6. Significance and UseNOTE 2The quality of the result produced by this standard isdependent on the competence of the personnel performing it, and thesuitability of the equipment a
31、nd 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 that compliance with Practice D3740 does not in itself assurereliable results. Reliable results depend
32、on many factors; Practice D3740provides a means of evaluating some of those factors.6.1 The assumptions of the physical system are given asfollows:6.1.1 The aquifer is of uniform thickness and confined byimpermeable beds above and below.6.1.2 The aquifer is of constant homogeneous porosity andmatrix
33、 compressibility and of homogeneous and isotropichydraulic 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.6.2 The assumptions made in defining the momentum bal-ance are as follows:6.
34、2.1 The average water velocity in the well is approxi-mately constant over the well-bore section.6.2.2 Flow is laminar and frictional head losses from flowacross the well screen are negligible.6.2.3 Flow through the well screen is uniformly distributedover the entire aquifer thickness.6.2.4 Change i
35、n momentum from the water velocity chang-ing from radial flow through the screen to vertical flow in thewell are negligible.6.2.5 The system response is an exponentially decayingsinusoidal function.7. Procedure7.1 The overall procedure consists of:7.1.1 Conducting the slug test field procedure (see
36、TestMethod D4044), and7.1.2 Analyzing the field data, that is addressed in this testmethod.NOTE 3The initial displacement of water level should not exceed 0.1or 0.2 of the length of the static water column in the well, because ofconsiderations for calculating Lc. Practically, the displacement should
37、 besmall, a few times larger than the well radius, to minimize frictionallosses. The measurement of displacement should be within 1 % of theinitial water-level displacement. The water-level displacement needs to becalculated independently for comparison to the observed initial displace-ment.8. Calcu
38、lation and Interpretation of Test Data8.1 Plot the water-level response in the well to the suddenchange in head, as in Fig. 2.8.2 Calculate the angular frequency, : 5 2/ (11)where: = t1t2, and t1and t2are times of successive maxima orminima of the oscillatory wave.8.3 Calculate the damping factor, :
39、 5 1nwt1!/wt2!#/t22 t1(12)where:w(t1) and w(t2) are the water-level displacements at times t1andt2, respectively.8.4 Determine transmissivity, T,T 5 b1a 1nT (13)where:a 5 rc2g/L!1/2#/8d (14)d 5 /g/L!1/2(15)L 5 g/212! (16)and:b 52a 1n0# (17)8.4.1 Solve for transmissivity iteratively using an initiale
40、stimate value for transmissivity, T, and a known or estimatedvalue of storage coefficient, S.8.5 Check the results.8.5.1 Compare the effective length of the water column, L,calculated by the following two relationships:L 5 g/212! (18)FIG. 1 Well and Aquifer GeometryD5785/D5785M 153and:L 5 Lc1rc2/rs2
41、!m/2 (19)The values of L should agree within 20 %.8.5.2 Check to see that the value of b,T1= 0.5541 + (0.03755)1n(0.5541) = 0.5319 ft2/sT2= 0.5541 + (0.03755)1n(0.5319) = 0.5304 ft2/sT = 0.5304 ft2/s * 86 400 s/day = 45 826 ft2/dayCheck the results:L = g/(2+ 2) = 32/(0.2775) = 115.3 ftL = Lc+(rc2/rs
42、2)m/2 = 95 + 27.5 = 122.5122.5 115.3 = 7.2, 7.2/115.3 = 6.2 20 % = 0.89(S/T)1/2(2+ 2)1/4rs 0.1= 0.89 (0.005318)(0.7258) 0.25 = 0.000859 0.1d = 0.1096 0.79. Report9.1 Report the following information described as follows.The final report of the analytical procedure will includeinformation from the re
43、port on test method selection, GuideD4043, and the field testing procedure, Test Method D4044.9.1.1 IntroductionThe introductory section is intended topresent the scope and purpose of the slug test method fordetermining transmissivity and storativity. Summarize the fieldhydrogeologic conditions, the
44、 field equipment and instrumen-tation including the construction of the control well, theFIG. 2 Underdamped Response of Water Level to a Sudden Change in HeadD5785/D5785M 154method of measurement of head, and the method of effectingthe change in head. Discuss the rationale for selecting this testmet
45、hod.9.1.2 Hydrogeologic SettingReview information availableon the hydrogeology of the site; interpret and describe thehydrogeology of the site as it pertains to the method selectedfor conducting and analyzing an aquifer test. Compare hydro-geologic characteristics of the site as it conforms and diff
46、ersfrom assumptions made in the solution to the aquifer testmethod.9.1.3 EquipmentReport the field installation and equip-ment for the aquifer test. Include in the report, well construc-tion information, diameter, depth, and open interval to theaquifer, and location of control well and pumping equip
47、ment.The construction, diameter, depth, and open interval of obser-vation wells should be recorded.9.1.3.1 Report the techniques used for observing waterlevels, and other environmental conditions pertinent to the test.Include a list of measuring devices used during the test; themanufacturers name, m
48、odel number, and basic specificationsfor each major item; and the name and date of the lastcalibration, if applicable.9.1.4 Testing ProceduresReport the steps taken in con-ducting the pretest and test phases. Include the frequency ofhead measurements made in the control well, and otherenvironmental
49、data recorded before and during the testingprocedure.9.1.5 Presentation and Interpretation of Test Results:9.1.5.1 DataPresent tables of data collected during thetest.9.1.5.2 Data PlotsPresent data plots used in analysis ofthe data.9.1.5.3 Show calculation of transmissivity and coefficient ofstorage.9.1.5.4 Evaluate the overall quality of the test on the basis ofthe adequacy of instrumentation and observations of stress andresponse and the conf
