1、Designation: D 5785 95 (Reapproved 2006)Standard 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 D 5785; the number immediatel
2、y following 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
3、 method 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 oscilla
4、tory fluctuation 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 co
5、njunction with thefield procedure Test Method D 4044 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
6、penetrating 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
7、greater 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 init
8、ial water-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
9、 response 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 This standard does n
10、ot 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 and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standar
11、ds:3D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 4043 Guide for Selection of Aquifer Test Method inDetermining Hydraulic Properties by Well TechniquesD 4044 Test Method (Field Procedure) for InstantaneousChange in Head (Slug) Tests for Determining HydraulicProperties of Aquifiers3.
12、 Terminology3.1 Definitions:3.1.1 aquifer, 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 wellwell by which the aqu
13、ifer is stressed, forexample, by pumping, injection, or change in head.3.1.4 head, staticthe height above a standard datum of thesurface of a column of water (or other liquid) that can besupported by the static pressure at a given point.3.1.5 observation wella well open to all or part of anaquifer.3
14、.1.6 overdamped well responsecharacterized by the wa-ter level returning to the static level in an approximatelyexponential manner following a sudden change in water level.(See for comparison underdamped well response.)1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock
15、and is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Sept. 15, 2006. Published December 2006. Originallyapproved in 1995. Last previous edition approved in 2000 as D 5785 95 (2000).2The boldface numbers given in parentheses re
16、fer to a list of references at 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.1Copyright
17、ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.7 sluga volume of water or solid object used to inducea sudden change of head in a well.3.1.8 storage coeffcientthe volume of water an aquiferreleases from or takes into storage per unit surfa
18、ce 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 storagecoefficient is approximately equal to the specific yield.3.1.9 transmissivitythe volume of water at th
19、e existingkinematic viscosity that will move in a unit time under a unithydraulic gradient through a unit width of the aquifer.3.1.10 underdamped well responseresponse characterizedby the water level oscillating about the static water levelfollowing a sudden change in water level (See for comparison
20、overdamped well response.)3.1.11 For definitions of other terms used in this testmethod, see Terminology D 653.3.2 Symbols and Dimensions:3.2.1 Ttransmissivity L2T1.3.2.2 Sstorage coefficient nd.3.2.3 Leffective length of water column, equal to Lc+( rc2/rs2) (m/2).3.2.3.1 DiscussionThis expression f
21、or 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+ 3/8Lsand assumes that the well screen and well casing have the samediameter.3.2.4 Lclength of water column within casing L.3.2.5 Lslength of water column with
22、in 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 screen 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 fro
23、m the initial staticlevel L.3.2.14 woinitial water level displacement L.3.2.15 gdamping constant T1.3.2.16 twavelength T.3.2.17 vangular frequency T1.3.2.18 maquifer thickness, L.4. Summary of Test Method4.1 This test method describes the analytical procedure foranalyzing data collected during an in
24、stantaneous head (slug)test using a well in which the response is underdamped. Thefield procedures in conducting a slug test are given in TestMethod D 4044.The analytical procedure consists of analyzingthe response of water level in the well following the change inwater level induced in the well.4.2
25、 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 followingequation for cylindrical flow:STdhdt51rddrSrdhdrD(1)where:h = hydraulic head,T = aquifer transmissivity, andS = storage coeffi
26、cient.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 water level in the well-riser to the flow intothe well:prc2dwdt5 2prsThrUr5rs(2)where:rc= radius of the well casing, andw
27、 = displacement of the water level in the well from itsinitial position.4.3.1 The third equation describing the system, relatinghsand w, comes from a momentum balance of Bird et al (4) asreferenced in Kipp (2).ddt*m0prs2pvdz 5 pv221 p1 p2 pgmprs2(3)where:v = velocity in the well screen interval,m =
28、aquifer thickness,p = pressure,r = fluid density,g = gravitational acceleration, andrs= well screen radius. Well and aquifer geometry areshown in Fig. 1.Atmospheric pressure is taken as zero.5. Solution5.1 The method of van der Kamp (1) assumes the waterlevel response to a sudden change for the unde
29、rdamped case,except near critical damping conditions, can be approximatelydescribed as an exponentially damped cyclic fluctuation thatdecays exponentially. The water-level fluctuation would thenbe given by:wt! 5 woegtcos wt (4)5.1.1 The following solution is given by van der Kamp (1).d 5rc2g/L!1/21n
30、0.79rs2S/T!g/L!1/28T(5)that may be written as:T 5 b 1 a 1nT (6)where:b 5 a 1n0.79 rs2Sg/L!1/2(7)a 5rc2g/L!1/28d(8)d 5g/g/L!1/2(9)andL 5 g/v21g2! (10)D 5785 95 (2006)2NOTE 1Other analytical solutions are proposed by Kipp (2), Krauss(5), Uffink (6) and Kabala, Pinder, and Milly (7).6. Significance and
31、 Use6.1 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 compressibility and of homogeneous and isotropichydraulic conductivity.6.1.3 Th
32、e 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:6.2.1 The average water velocity in the well is approxi-mately constant over the w
33、ell-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 in momentum from the water velocity chang-ing from radial flow through the screen
34、 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 TestMethod D 4044), and7.1.2 Analyzing the field data, that is addressed in this
35、 testmethod.NOTE 2The 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 besmall, a few times larger than the well radius, to minimize frictionallosses
36、. 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. Calculation and Interpretation of Test Data8.1 Plot the water-level response in the
37、well to the suddenchange in head, as in Fig. 2.8.2 Calculate the angular frequency, v:v52p/t (11)where:t = t1t2, and t1and t2are times of successive maxima orminima of the oscillatory wave.8.3 Calculate the damping factor, g:g51nwt1!/wt2!#/t2 t1(12)where:w(t1) and w(t2) are the water-level displacem
38、ents at times t1andt2, respectively.8.4 Determine transmissivity, T,T 5 b 1 a 1nT (13)where:a 5 rc2g/L!1/2#/8d (14)d 5g/g/L!1/2(15)L 5 g/v21g2! (16)and:b 5 a 1n0 (17)8.4.1 Solve for transmissivity iteratively using an initialestimate value for transmissivity, T, and a known or estimatedvalue of stor
39、age 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/v21g2! (18)and:L 5 Lc1 rc2/rs2!m/2 (19)The values of L should agree within 20 %.8.5.2 Check to see that the value of a b,T1= 0.5541 + (0.03755)1n (0.
40、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/(v2+ g2) = 32/(0.2775) = 115.3 ftL = Lc+(rc2/rs2!m/2 5 95 1 27.5 5122.5122.5 115.3 = 7.2, 7.2/115.3 = 6.2 20 %a = 0.89(S/T)1/2(v2+ g2)1/4rs 0.1= 0.89 (0.005318)
41、(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 report on test method selection, GuideD 4043, and the field testing procedure, Test Method D 4044.9.1.1 Introduct
42、ionThe introductory section is intended topresent the scope and purpose of the slug test method fordetermining transmissivity and storativity. Summarize the fieldhydrogeologic conditions, the field equipment and instrumen-tation including the construction of the control well, themethod of measuremen
43、t of head, and the method of effectingthe change in head. Discuss the rationale for selecting this testmethod.9.1.2 Hydrogeologic SettingReview information avail-able on the hydrogeology of the site; interpret and describe theFIG. 2 Underdamped Response of Water Level to a Sudden Change in HeadD 578
44、5 95 (2006)4hydrogeology 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 differsfrom assumptions made in the solution to the aquifer testmethod.9.1.3 EquipmentReport the field install
45、ation 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 equipment.The construction, diameter, depth, and open interval of obser-vation wells should be recorded.9.1.3.1
46、 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, model number, and basic specificationsfor each major item; and the name and date of the lastcalibration, if
47、 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 data recorded before and during the testingprocedure.9.1.5 Presentation and Interpretation of Test Results
48、: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 obser
49、vations of stress andresponse and the conformance of the hydrogeologic conditionsand the performance of the test to the assumptions (see 5.1).10. Precision and Bias10.1 It is not practicable to specify the precision of this testmethod because the response of aquifer systems during aquifertests is dependent upon ambient system stresses. No statementcan be made about bias because no true reference values exist.11. Keywords11.1 aquifers; aquifer tests; control well
