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.

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, everywhere by a confining bed having a uniform hydraulic conductivity and thickness. It is assumed that there is no change of water storage in this confining bed and that the hydraulic gradient across this bed changes instantaneously with a change in head in the aquifer. This confining bed is bounded on the distal side by a uniform head source where the head does not change with time.

5.1.6 The other confining bed is impermeable.

5.1.7 Leakage into the aquifer is vertical and proportional to the drawdown, and flow in the aquifer is strictly horizontal.

5.1.8 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. Section 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.

5.3.2 The leaky confining bed problem considered by the Hantush-Jacob solution requires that the control well has an infinitesimal diameter and has no storage. Abdul Khader and Ramadurgaiah (5) developed graphs of a solution for the drawdowns in a large-diameter control well discharging at a constant rate from an aquifer confined by a leaky confining bed. Fig. 2 (Fig. 3 of Abdul Khader and Ramadurgaiah (5)) gives a graph showing variation of dimensionless drawdown with dimensionless time in the control well assuming the aquifer storage coefficient, S = 10⁻³, and the leakage parameter, Note that at early dimensionless times the curve for a large-diameter well in a non-leaky aquifer (BCE) and in a leaky aquifer (BCD) are coincident. At later dimensionless times, the curve for a large diameter well in a leaky aquifer coalesces with the curve for an infinitesimal diameter well (ACD) in a leaky aquifer. They coalesce about one logarithmic cycle of dimensionless time before the drawdown becomes sensibly constant. For a value of r_w/B smaller than 10⁻³, the constant drawdown (D) would occur at a greater value of dimensionless drawdown and there would be a longer period during which well-bore storage effects are negligible (the period where ACD and BCD are coincident) before a steady drawdown is reached. For values of greater than 10⁻³, the constant drawdown (D) would occur at a smaller value of drawdown and there would be a shorter period of dimensionless time during which well-storage effects are negligible (the period where ACD and BCD are coincident) before a steady drawdown is reached. Abdul Khader and Ramadurgaiah (5)present graphs of dimensionless time versus dimensionless drawdown in a discharging control well for values of S = 10⁻¹, 10⁻², 10⁻³, 10⁻⁴, and 10⁻⁵ and ^r_w/_B = 10⁻², 10⁻³, 10⁻⁴, 10⁻⁵, 10⁻⁶, and 0. These graphs can be used in an analysis prior to the aquifer test making use of estimates of the hydraulic properties to estimate the time period during which well-bore storage effects in the control well probably will mask other effects and the drawdowns would not fit the Hantush-Jacob solution.

1.1 This test method covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer and the leakance value of an overlying or underlying confining bed for the case where there is negligible change of water in storage in a confining bed. 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 Hantush-Jacob method is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis nonequilibrium method (Test Method D4106) with the exception that in this case the aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and thickness, and in which the gain or loss of water in storage is assumed to be negligible, and that bed, in turn, is bounded on the distal side by a zone in which the head remains constant. The hydraulic conductivity of the other bed confining the aquifer is so small that it is assumed to be impermeable (see Fig. 1).

1.4 The values stated in SI units are to be regarded as standard. The values given in parentheses are mathematical conversions to inch-pound units, which are provided for information only and are not considered standard.

1.4.1 The converted inch-pound units use the gravitational system of units. In this system, the pound (lbf) represents a unit of force (weight), while the unit for mass is slugs. The converted slug unit is not given, unless dynamic (F = ma) calculations are involved.

1.5 All observed and calculated values shall conform to the guidelines for significant digits and round established in Practice D6026, unless superseded by this standard.

1.5.1 The procedures used to specify how data are collected/recorded or calculated, in this 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 date to be commensurate with these considerations. It is beyond the scope of this standard to consider significant digits used in analysis method for engineering design.

1.6 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.