5.1 Assumptions: 

5.1.1 The control well discharges at a constant rate, Q.

5.1.2 The control well is of infinitesimal diameter and fully penetrates the aquifer.

5.1.3 The aquifer is homogeneous, isotropic, and areally extensive.

Note 1: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information.

5.1.4 The aquifer remains saturated (that is, water level does not decline below the top of the aquifer).

5.1.5 The aquifer is overlain or underlain, or both, everywhere by confining beds individually having uniform hydraulic conductivities, specific storages, and thicknesses. The confining beds are bounded on the distal sides by one of the cases shown in Fig. 1.

5.1.6 Flow in the aquifer is two-dimensional and radial in the horizontal plane.

5.2 The geometry of the well and aquifer system is shown in Fig. 1.

5.3 Implications of Assumptions: 

5.3.1 Paragraph 5.1.1 indicates that the discharge from the control well is at a constant rate. Paragraph 8.1 of Test Method D4050 discusses the variation from a strictly constant rate that is acceptable. A continuous trend in the change of the discharge rate could result in misinterpretation of the water-level change data unless taken into consideration.

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.

5.3.2 The leaky confining bed problem considered by the modified Hantush method requires that the control well has an infinitesimal diameter and has no storage. Moench (6) generalized the field situation addressed by the modified Hantush (1) method to include the well bore storage in the pumped well. The mathematical approach that he used to obtain a solution for that more general problem results in a Laplace transform solution whose analytical inversion has not been developed and probably would be very complicated, if possible, to evaluate. Moench (6) used a numerical Laplace inversion algorithm to develop type curves for selected situations. The situations considered by Moench indicate that large well bore storage may mask effects of leakage derived from storage changes in the confining beds. The particular combinations of aquifer and confining bed properties and well radius that result in such masking is not explicitly given. However, Moench ((6), p. 1125) states “Thus observable effects of well bore storage are maximized, for a given well diameter, when aquifer transmissivity Kb and the storage coefficient S_sb are small.” Moench (p. 1129) notes that “...one way to reduce or effectively eliminate the masking effect of well bore storage is to isolate the aquifer of interest with hydraulic packers and repeat the pump test under pressurized conditions. Because well bore storage C will then be due to fluid compressibility rather than changing water levels in the well”...“the dimensionless well bore storage parameter may be reduced by 4 to 5 orders of magnitude.”

5.3.3 The modified Hantush method assumes, for Cases 1 and 3 (see Fig. 1), that the heads in source layers on the distal side of confining beds remain constant. Neuman and Witherspoon (7) developed a solution for a case that could correspond to Hantush's Case 1 with K" = O  = S" except that they do not require the head in the unpumped aquifer to remain constant. For that case, they concluded that the drawdowns in the pumped aquifer would not be affected by the properties of the other, unpumped, aquifer when (Neuman and Witherspoon (7) p. 810) time satisfies:

5.3.4 Implicit in the assumptions are the conditions that the flow in the confining beds is essentially vertical and in the aquifer is essentially horizontal. Hantush's (8) analysis of an aquifer bounded only by one leaky confining bed suggested that these assumptions are acceptably accurate wherever

That form of relation between aquifer and confining bed properties may also be a useful guide for the case of two leaky confining beds.

1.1 This practice covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer taking into consideration the change in storage of water in overlying or underlying confining beds, or both. This practice is used to analyze water-level or head data collected from one or more observation wells or piezometers during the pumping of water from a control well at a constant rate. With appropriate changes in sign, this practice also can be used to analyze the effects of injecting water into a control well at a constant rate.

1.2 This analytical procedure is used in conjunction with Test Method D4050.

1.3 Limitations—The valid use of the modified Hantush method (1)2 is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Hantush-Jacob method (Practice D6029/D6029M) with the exception that in this case the gain or loss of water in storage in the confining beds is taken into consideration (see 5.1). All possible combinations of impermeable beds and source beds (for example, beds in which the head remains uniform) are considered on the distal side of the leaky beds that confine the aquifer of interest (see Fig. 1).

FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Water in the Confining Beds, Illustrating Three Different Cases of Boundary Conditions (from Reed (2) )

1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026.

1.4.1 The procedures used to specify how data are collected/recorded and calculated in the standard are regarded as the industry standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objectives; and it is common practice to increase or reduce significant digits of reported data to be commensurate with these considerations. It is beyond the scope of these test methods to consider significant digits used in analysis methods for engineering data.

1.5 The values stated in SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values for the two systems may result in nonconformance with the standard. Reporting of results in units other than SI shall not be regarded as nonconformance with this standard.

1.6 This practice offers a set of instructions for performing one or more specific operations. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of the practice may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without the consideration of a project’s many unique aspects. The word “Standard” in the title of this document means only that the document has been approved through the ASTM consensus process.

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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.

1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.