ASTM D5785/D5785M-20

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Designation: D5785/D5785M − 15 D5785/D5785M − 20
Standard Test Method Practice for
(Analytical Procedure) for Determining Transmissivity of
Confined Nonleaky Aquifers by Underdamped Well
Response to Instantaneous Change in Head (Slug Test)
This standard is issued under the fixed designation D5785/D5785M; the number immediately following the designation indicates the
year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last
reapproval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This test method covers determination of transmissivity from the measurement of the damped oscillation about the
equilibrium water level of a well-aquifer system to a sudden change of water level in a well. Underdamped response of water level
in a well to a sudden change in water level is characterized by oscillatory fluctuation about the static water level with a decrease
in the magnitude of fluctuation and recovery to initial water level. Underdamped response may occur in wells tapping highly
transmissive confined aquifers and in deep wells having long water columns.
1.2 This analytical procedure is used in conjunction with the field procedure Test Method D4044 for collection of test data.
1.3 Limitations—Slug tests are considered to provide an estimate of transmissivity of a confined aquifer. This test method
requires that the storage coefficient be known. Assumptions of this test method prescribe a fully penetrating well (a well open
through the full thickness of the aquifer), but the slug test method is commonly conducted using a partially penetrating well. Such
a practice may be acceptable for application under conditions in which the aquifer is stratified and horizontal hydraulic
conductivity is much greater than vertical hydraulic conductivity. In such a case the test would be considered to be representative
of the average hydraulic conductivity of the portion of the aquifer adjacent to the open interval of the well. The method assumes
laminar flow and is applicable for a slug test in which the initial water-level displacement is less than 0.1 or 0.2 of the length of
the static water column.
1.4 This test method of analysis presented here is derived by van der Kamp (1) based on an approximation of the underdamped
response to that of an exponentially damped sinusoid. A more rigorous analysis of the response of wells to a sudden change in water
level by Kipp (2) indicates that the method presented by van der Kamp (1) matches the solution of Kipp (2) when the damping
parameter values are less than about 0.2 and time greater than that of the first peak of the oscillation (2).
1.5 Units—The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values in each
system may not be exact equivalents; therefore each system shall be used independently of the other. Combining values from the
two systems may result in non-conformance with the standard. Reporting of test results in units other than SI shall not be regarded
as nonconformance with this test method.
1.6 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice
D6026.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
D653 Terminology Relating to Soil, Rock, and Contained Fluids
This test method practice is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater
and Vadose Zone Investigations.
Current edition approved Nov. 1, 2015May 15, 2020. Published November 2015May 2020. Originally approved in 1995. Last previous edition approved in 20132015 as
D5785 – 95 (2013).D5785 – 15. DOI: 10.1520/D5785_D5785M-15.10.1520/D5785_D5785M-20.
The boldface numbers given in parentheses refer to a list of references at the end of the text.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5785/D5785M − 20
D3740 Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in
Engineering Design and Construction
D4043 Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques
D4044 Test Method for (Field Procedure) for Instantaneous Change in Head (Slug) Tests for Determining Hydraulic Properties
of Aquifers
D6026 Practice for Using Significant Digits in Geotechnical Data
3. Terminology
3.1 Definitions—For definitions of other terms used in this test method, see Terminology D653.
3.1.1 observation well—a well open to all or part of an aquifer.
3.1.2 storage coeffıcient—the volume of water an aquifer releases from or takes into storage per unit surface area of the aquifer
per unit change in head. For a confined aquifer, the storage coefficient is equal to the product of specific storage and aquifer
thickness. For an unconfined aquifer, the storage coefficient is approximately equal to the specific yield.
3.1.3 transmissivity—the volume of water at the existing kinematic viscosity that will move in a unit time under a unit hydraulic
gradient through a unit width of the aquifer.
3.2 Symbols and Dimensions:
2 −1
3.2.1 T—transmissivity [L T ].
3.2.2 S—storage coefficient [nd].
3.2.3 L—effective length of water column, equal to L +
c
2 2
(r /r ) (m/2).
c s
3.2.3.1 Discussion—This expression for the effective length is given by Kipp (2). The expression for the effective length of the
water column from Cooper et al. (3) is given as L + 3 ⁄8L and assumes that the well screen and well casing have the same
c s
diameter.
3.2.4 L —length of water column within casing [L].
c
3.2.5 L —length of water column within well screen [L].
s
−2
3.2.6 g—acceleration of gravity [LT ].
3.2.7 h—hydraulic head in the aquifer [L].
3.2.8 h —initial hydraulic head in the aquifer [L].
o
3.2.9 h —hydraulic head in the well screen [L].
s
3.2.10 r —radius of well casing [L].
c
3.2.11 r —radius of well screen [L].
s
3.2.12 t—time [T].
3.2.13 w—water level displacement from the initial static level [L].
3.2.14 w —initial water level displacement [L].
o
−1
3.2.15 γ—damping constant [T ].
3.2.16 τ—wavelength [T].
−1
3.2.17 ω—angular frequency [T ].
3.2.18 m—aquifer thickness, [L].
4. Summary of Test Method
4.1 This test method describes the analytical procedure for analyzing data collected during an instantaneous head (slug) test
using a well in which the response is underdamped. The field procedures in conducting a slug test are given in Test Method D4044.
The analytical procedure consists of analyzing the response of water level in the well following the change in water level induced
in the well.
4.2 Theory—The equations that govern the response of well to an instantaneous change in head are treated at length by Kipp
(2). The flow in the aquifer is governed by the following equation for cylindrical flow:
S dh 1 d dh
5 r (1)
S D
T dt r dr dr
where:
h = hydraulic head,
T = aquifer transmissivity, and
S = storage coefficient.
4.2.1 The initial condition is at t = 0 and h = h and the outer boundary condition is as r → ∞ and h → h .
o o
4.3 The flow rate balance on the well bore relates the displacement of the water level in the well-riser to the flow into the well:
D5785/D5785M − 20
dw ]h
πr 5 2πr T (2)
U U
c s
dt ]r
r5r
s
where:
r = radius of the well casing, and
c
w = displacement of the water level in the well from its initial position.
4.3.1 The third equation describing the system, relating h and w, comes from a momentum balance of Bird et al. (4) as
s
referenced in Kipp (2).
d 0
2 2 2
πr pv z 5 @2pv 1p 2 p 2 pgm#πr (3)
*
s d 2 1 2 s
2m
dt
where:
v = velocity in the well screen interval,
m = aquifer thickness,
p = pressure,
ρ = fluid density,
g = gravitational acceleration, and
r = well screen radius. Well and aquifer geometry are shown in Fig. 1.
s
Atmospheric pressure is taken as zero.
5. Solution
5.1 The method of van der Kamp (1) assumes the water level response to a sudden change for the underdamped case, except
near critical damping conditions, can be approximately described as an exponentially damped cyclic fluctuation that decays
exponentially. The water-level fluctuation would then be given by:
2γt
w~t! 5 w e cos wt (4)
o
FIG. 1 Well and Aquifer Geometry
D5785/D5785M − 20
5.1.1 The following solution is given by van der Kamp (1).
2 1/2 2 1/2
2r ~g/L! 1n@0.79 r ~S/T! ~g/L!
c s
d 5 (5)
8T
that may be written as:
T 5 b1a 1nT (6)
where:
2 1/2
b 5 a 1n@0.79 r S ~g/L! (7)
s
2 1/2
r g/L
~ !
c
a 5 (8)
8d
1/2
d 5 γ/~g/L! (9)
and
2 2
L 5 g/ ω 1γ (10)
~ !
NOTE 1—Other analytical solutions are proposed by Kipp (2); Krauss (5); Kruseman and de Ridder (6); and Kabala, Pinder, and Milly (7).
6. Significance and Use
NOTE 2—The quality of the result produced by this standard is dependent on the competence of the personnel performing it, and the suitability of the
equipment and facilities used. Agencies that meet the criteria of Practice D3740 are generally considered capable of competent and objective
testing/sampling/inspection/etc. Users of this standard are cautioned that compliance with Practice D3740 does not in itself assure reliable results. Reliable
results depend on many factors; Practice D3740 provides a means of evaluating some of those factors.
6.1 The assumptions of the physical system are given as follows:
6.1.1 The aquifer is of uniform thickness and confined by impermeable beds above and below.
6.1.2 The aquifer is of constant homogeneous porosity and matrix compressibility and of homogeneous and isotropic hydraulic
conductivity.
6.1.3 The origin of the cylindrical coordinate system is taken 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 balance are as follows:
6.2.1 The average water velocity in the well is approximately constant over the well-bore section.
6.2.2 Flow is laminar and frictional head losses from flow across the well screen are negligible.
6.2.3 Flow through the well screen is uniformly distributed over the entire aquifer thickness.
6.2.4 Change in momentum from the water velocity changing from radial flow through the screen to vertical flow in the well
are negligible.
6.2.5 The system response is an exponentially decaying sinusoidal function.
7. Procedure
7.1 The overall procedure consists of:
7.1.1 Conducting the slug test field procedure (see Test Method D4044), and
7.1.2 Analyzing the field data, that is addressed in this test method.
NOTE 3—The initial displacement of water level should not exceed 0.1 or 0.2 of the length of the static water column in the well, because of
considerations for calculating L . Practically, the displacement should be small, a few times larger than the well radius, to minimize frictional losses. The
c
measurement of displacement should be within 1 % of the initial water-level displacement. The water-level displacement needs to be calculated
independently for comparison to the observed initial displacement.
8. Calculation and Interpretation of Test Data
8.1 Plot the water-level response in the well to the sudden change in head, as in Fig. 2.
8.2 Calculate the angular frequency, ω:
ω5 2π/τ (11)
where:
τ = t − t , and t and t are times of successive maxima or minima of the oscillatory wave.
1 2 1 2
8.3 Calculate the damping factor, γ:
γ51n w t /w t /t 2 t (12)
@ ~ ! ~ !#
1 2 2 1
where:
w(t ) and w(t ) are the water-level displacements at times t and t , respectively.
1 2 1 2
8.4 Determine transmissivity, T,
D5785/D5785M − 20
FIG. 2 Underdamped Response of Water Level to a Sudden Change in Head
T 5 b1a 1nT (13)
where:
2 1/2
a 5 @r ~g/L! #/8d (14)
c
1/2
d 5 γ/~g/L! (15)
2 2
L 5 g/ ω 1γ (16)
~ !
and:
b 52a 1n@0# (17)
8.4.1 Solve for transmissivity iteratively using an initial estimate value for transmissivity, T, and a known or estimated value
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:
2 2
L 5 g/ ω 1γ (18)
~ !
and:
2 2
L 5 L 1 r /r m/2 (19)
~ !
c c s
The values of L should agree within 20 %.
8.5.2 Check to see that the value of α << 0.1, where:
1/2 2 2 1/4
α5 0.89 S/T ω 1γ r ,0.1 (20)
~ ! ~ !
s
8.5.3 Check to see that the value of d << 0.7, where:
1⁄2
d 5 γ⁄ g ⁄ L (21)
~ !
8.5.4 Example—The following data are taken from the underdamped response to a slug test shown in Fig. 2:
w(t ) = –1.0 ft
w(t ) = –0.5 ft
t = 4.9 s
D5785/D5785M − 20
t = 16.9 s
r = 0.25 ft
c
r = 0.25 ft
s
L = 95 ft
c
L = 55 ft
s
τ = t – t = 16.9 – 4.9 = 12 s
2 1
–1
ω = 2π/τ = 2* 3.1416/12.0 = 0.5236 s
–1
γ = 1n(w(t )/w(t ))/τ = 1n(–1.0/–0.5)/12 = 0.6931/12 = 0.05776 s
1 2
T = b + a 1nT
1/2 2 2 1/2 2 2 1/2 1/2 1/2
(g/L) = (ω + γ ) = ((0.5236) + (0.05776) ) = ((0.2742) + (0.0033362)) = (0.2775) = 0.5268
1/2
d = γ(g/L) = 0.05776/0.5268 = 0.1096
2 1/2 2 2
a = (r (g/L) )/8d = (0.25) (0.5268)/8(0.1096) = 0.03755 ft /s
c
−5
Assume S = 1.5 × 10
2 1/2
b = a 1n(0.79 r S(g/L) )
s
2 2
= (–0.03755)1n(0.79(0.25) (0.000015)(0.5268) = 0.5541 ft /s
T = b + a 1nT
1 0
Assume T > b,
T = 0.5541 + (0.03755)1n(0.5541) = 0.5319 ft /s
T = 0.5541 + (0.03755)1n(0.5319) = 0.5304 ft /s
2 2
T = 0.5304 ft /s * 86 400 s/day = 45 826 ft /day
Check the results:
2 2
L = g/(ω + γ ) = 32/(0.2775) = 115.3 ft
2 2
L = L + (r /r )m/2 = 95 + 27.5 = 122.5
c c s
122.5 – 115.3 = 7.2, 7.2/115.3 = 6.2 < 20 %
1/2 2 2 1/4
α = 0.89(S/T) (ω + γ ) r < 0.1
s
= 0.89 (0.005318)(0.7258) 0.25 = 0.000859 < 0.1
d = 0.1096 < 0.7
9. Report
9.1 Report the following information described as follows. The final report of the analytical procedure will include information
from the report on test method selection, Guide D4043, and the field testing procedure, Test Method D4044.
9.1.1 Introduction—The introductory section is intended to present the scope and purpose of the slug test method for
determining transmissivity and storativity. Summarize the field hydrogeologic conditions, the field equipment and instrumentation
including the construction of the control well, the method of measurement of head, and the method of effecting the change in head.
Discuss the rationale for selecting this test method.
9.1.2 Hydrogeologic Setting—Review information available on the hydrogeology of the site; interpret and describe the
hydrogeology of the site as it pertains to the method selected for conducting and analyzing an aquifer test. Compare hydrogeologic
characteristics of the site as it conforms and differs from assumptions made in the solution to the aquifer test method.
9.1.3 Equipment—Report the field installation and equipment for the aquifer test. Include in the report, well construction
information, diameter, depth, and open interval to the aquifer, and location of control well and pumping equipment. The
construction, diameter, depth, and open interval of observation wells should be recorded.
9.1.3.1 Report the techniques used for observing water levels, and other environmental conditions pertinent to the test. Include
a list of measuring devices used during the test; the manufacturer’s name, model number, and basic specifications for each major
item; and the name and date of the last calibration, if applicable.
9.1.4 Testing Procedures—Report the steps taken in conducting the pretest and test phases. Include the frequency of head
measurements made in the control well, and other environmental data recorded before and during the testing procedure.
9.1.5 Presentation and Interpretation of Test Results:
9.1.5.1 Data—Present tables of data collected during the test.
9.1.5.2 Data Plots—Present data plots used in analysis of the data.
9.1.5.3 Show calculation of transmissivity and coefficient of storage.
9.1.5.4 Evaluate the overall quality of the test on the basis of the adequacy of instrumentation and observations of stress and
response and the conformance of the hydrogeologic conditions and the performance of the test to the assumptions (see 5.1).
10. Precision and Bias
10.1 Precision—Test data on precision is not presented due to the nature of this test method. It is either not feasible or too costly
at this time to have ten or more agencies participate in an in situ testing program at a given site.
D5785/D5785M − 20
10.2 Bias—There is no accepted reference value for this test method, therefore, bias cannot be determined.
11. Keywords
11.1 aquifers; aquifer tests; control wells; groundwater; hydraulic conductivity; slug test; storage coefficient; transmissivity
REFERENCES
(1) van der Kamp, Garth, “Determining Aquifer Transmissivity by Means of Well Response Tests: The Underdamped Case,” Water Resources Research,
Vol 12, No. 1, 1976, pp. 71–77.
(2) Kipp, K. L., Jr., “Type Curve Analysis of Inertial Effects in the Response of a Well to a Slug Test,” Water Resources Research, Vol 21, No. 9, 1985,
pp. 1397–1408.
(3) Cooper, H. H., Jr., Bredehoeft, J. D., and Papadopulos, I. S., “Response of a Finite-Diameter Well to an Instantaneous Charge of Water,” Water
Resources Research, Vol 3, No. 1, 1967, pp. 263–269.
(4) Bird, R. B., Stewart, W. E., and Lightfoot, E. N., Transport Phenomena, John Wiley, New York, 1960.
(5) Krauss, I., “Determination of the Transmissibility from the Free Water Level Oscillation in Well-Aquifer Systems,” Surface and Subsurface
Hydrology, Proceedings of the Third International Hydrology Symposium, Colorado State University, 1977, pp. 179–268.
(6) Kruseman and de Ridder, “Analysis and Evaluation of Pumping Test Data,” Publication 47, International Institute for Land and Reclamation and
Improvement, Wageningen, The Netherlands, 1991.
(7) Kabala, Z. J., Pinder, G. F., and Milly, P. C. D., “Analysis of Well-Aquifer Response to a Slug Test,” Water Resources Research, Vol 21, No. 9, 1985,
pp. 1433–1436.
SUMMARY OF CHANGES
Committee D18 has identified the location of selected changes to this standard since the last issue (D5785 – 95
(2013)) that may impact the use of this standard. (November 1, 2015)
(1) Added D3740 to Referenced Documents section.
(2) Added Note 2 to Section 6 regarding the use of Practice D3740.
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