Assumptions:

The control well discharges at a constant rate, Q.

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

The aquifer is homogeneous, isotropic, and areally extensive.

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

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.

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

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

Implications of Assumptions:

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.

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.”

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:

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 test method 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 test method 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 test method 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) is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Hantush-Jacob method (Test Method D6029) 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).

1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.

1.5 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.

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) )