1、Designation: D5785 95 (Reapproved 2013)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 D5785; the number immediately
2、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 () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test m
3、ethod 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 oscillato
4、ry 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 conj
5、unction 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 pen
6、etrating 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 gre
7、ater 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
8、 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 re
9、sponse 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
10、in either 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
11、 test 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 conce
12、rns, 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,
13、 and ContainedFluidsD4043 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 Determining HydraulicProperties of AquifersD6026 Practice for Using Significant Digits in
14、 GeotechnicalData1This test method 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 March 15, 2013. Published April 2013. Originallyapproved in 1995. Last previ
15、ous edition approved in 2006 as D5785 95 (2006).DOI: 10.1520/D5785-95R13.2The boldface numbers given in parentheses refer 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
16、 Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13. Terminology
17、3.1 DefinitionsFor definitions of other terms used in thistest method, see Terminology D653.3.1.1 observation wella well open to all or part of anaquifer.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 h
18、ead. 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.3.1.3 transmissivitythe volume of water at the existingkinematic viscosity that will mo
19、ve 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 Sstorage 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 g
20、iven 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 within well screen L.3.2.6 gac
21、celeration 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 from the initial staticlevel
22、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.4. Summary of Test Method4.1 This test method describes the analytical procedure foranalyzing data collected during an instantaneous head (slug)test u
23、sing a well in which the response is underdamped. Thefield procedures in conducting a slug test are given in TestMethod D4044. The analytical procedure consists of analyzingthe response of water level in the well following the change inwater level induced in the well.4.2 TheoryThe equations that gov
24、ern 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 coefficient.4.2.1 The initial condi
25、tion 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:Urc2dwdt5 2rsT hrUr5rs(2)where:rc= radius of the well casing, andw = displacement of the water
26、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 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 = pre
27、ssure, = 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 underdamped case,except near c
28、ritical damping conditions, can be approximatelydescribed as an exponentially damped cyclic fluctuation thatdecays exponentially. The water-level fluctuation would thenbe given by:w t! 5 woe2tcos wt (4)5.1.1 The following solution is given by van der Kamp (1).d 52rc2g/L!1/21n0.79rs2S/T!g/L!1/28T(5)t
29、hat 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 solutions are proposed by Kipp (2); KraussD5785 95 (2013)2(5); Kruseman and de Ridder (6); and Kabala, Pinder, and Milly (7).6. Significance and Use6.1 The
30、 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 The origin of
31、 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 well-bore se
32、ction.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 to vertica
33、l 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 D4044), and7.1.2 Analyzing the field data, that is addressed in this testmethod.
34、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. The measur
35、ement 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 well to the
36、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, : 5 1nw t1!/w t2! #/t22 t1(12)where:w(t1) and w(t2) are the water-level displacements at tim
37、es 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 initialestimate value for transmissivity, T, and a known or estimatedvalue of storage coefficien
38、t, 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)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 b,T1= 0.5541 + (0.03755)1n(0.5541) = 0.5319 ft2
39、/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/rs2)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 = 0.00085
40、9 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, GuideD4043, and the field testing procedure, Test Method D4044.9.1.1 IntroductionThe introductory secti
41、on 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 measurement of head, and the method
42、 of effectingthe change in head. Discuss the rationale for selecting this testmethod.9.1.2 Hydrogeologic SettingReview information availableon the hydrogeology of the site; interpret and describe theFIG. 2 Underdamped Response of Water Level to a Sudden Change in HeadD5785 95 (2013)4hydrogeology of
43、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 installation and equip-ment for the
44、 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 Report the techniques used
45、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 applicable.9.1.4 Testing Pr
46、oceduresReport 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:9.1.5.1 DataPresent tables
47、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 andrespons
48、e and the conformance of the hydrogeologic conditionsand the performance of the test to the assumptions (see 5.1).10. Precision and Bias10.1 PrecisionTest data on precision is not presented dueto the nature of this test method. It is either not feasible or toocostly at this time to have ten or more
49、agencies participate inan in situ testing program at a given site.10.2 BiasThere is no accepted reference value for this testmethod, therefore, bias cannot be determined.11. Keywords11.1 aquifers; aquifer tests; control wells; groundwater;hydraulic conductivity; slug test; storage coefficient; transmis-sivityREFERENCES(1) van der Kamp, Garth, “DeterminingAquifer Transmissivity by Meansof Well Response Tests: The Underdamped Case,” Water Resources
