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**Significance and Use**

Assumptions:

Well discharges at a constant rate, Q.

Well is of infinitesimal diameter and fully penetrates the aquifer.

The nonleaky aquifer is homogeneous, isotropic, and aerially extensive. A nonleaky aquifer receives insignificant contribution of water from confining beds.

Discharge from the well is derived exclusively from storage in the aquifer.

The geometry of the assumed aquifer and well conditions are shown in Fig. 1.

Implications of Assumptions:

Implicit in the assumptions are the conditions of radial flow. Vertical flow components are induced by a control well that partially penetrates the aquifer, that is, the well is not open to the aquifer through its full thickness. If the control well does not fully penetrate the aquifer, the nearest piezometer or partially penetrating observation well should be located at a distance, r, beyond which vertical flow components are negligible, where according to Reed (2):

This section applies to distance-drawdown calculations of transmissivity and storage coefficient and time-drawdown calculations of storage coefficient. If possible, compute transmissivity from time-drawdown data from wells located within a distance, r, of the pumped well using data measured after the effects of partial penetration have become constant. The time at which this occurs is given by Hantush (3) by:

Fully penetrating observation wells may be placed at less than distance r from the control well. Observation wells may be on the same or on various radial lines from the control well.

The Theis method assumes the control well is of infinitesimal diameter. Also, it assumes that the water level in the control well is the same as in the aquifer contiguous to the well. In practice these assumptions may cause a difference between the theoretical drawdown and field measurements of drawdown in the early part of the test and in and near the control well. Control well storage is negligible after a time, t, given by the Eq 6 after Weeks (4).

where: | ||
---|---|---|

_{c} | = | the radius of the control well in the interval in which the water level changes. |

Application of Theis Method to Unconfined Aquifers:

Although the assumptions are applicable to artesian or confined conditions, the Theis solution may be applied to unconfined aquifers if drawdown is small compared with the saturated thickness of the aquifer or if the drawdown is corrected for reduction in thickness of the aquifer, and the effects of delayed gravity yield are small.

Reduction in Aquifer Thickness—In an unconfined aquifer dewatering occurs when the water levels decline in the vicinity of a pumping well. Corrections in drawdown need to be made when the drawdown is a significant fraction of the aquifer thickness as shown by Jacob (5). The drawdown, s, needs to be replaced by s′, the drawdown that would occur in an equivalent confined aquifer, where:

Gravity Yield Effects—In unconfined aquifers, delayed gravity yield effects may invalidate measurements of drawdown during the early part of the test for application to the Theis method. Effects of delayed gravity yield are negligible in partially penetrating observation wells at and beyond a distance, r, from the control well, where:

After the time, t, as given in Eq 9 from Neuman (6).

where: | ||
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_{y} | = | the specific yield. For fully penetrating observation wells, the effects of delayed yield are negligible at the distance, r, in Eq 8 after one tenth of the time given in the Eq 9. |

FIG. 1 Cross Section Through a Discharging Well in a Nonleaky Confined Aquifer

**1. Scope**

1.1 This test method covers an analytical procedure for determining the transmissivity and storage coefficient of a nonleaky confined aquifer. It is used to analyze data on water-level response collected during radial flow to or from a well of constant discharge or injection.

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

1.3 Limitations—The limitations of this test method for determination of hydraulic properties of aquifers are primarily related to the correspondence between the field situation and the simplifying assumptions of this test method (see 5.1).

1.4 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** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**ASTM Standards**

D653 Terminology Relating to Soil, Rock, and Contained Fluids

D4043 Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques

D4050 Test Method for (Field Procedure) for Withdrawal and Injection Well Tests for Determining Hydraulic Properties of Aquifer Systems

**ICS Code**

ICS Number Code 93.160 (Hydraulic construction)

**UNSPSC Code**

UNSPSC Code

**DOI:** 10.1520/D4106-96R08

ASTM International is a member of CrossRef.

**Citation Format**

ASTM D4106-96(2008), Standard Test Method for (Analytical Procedure) for Determining Transmissivity and Storage Coefficient of Nonleaky Confined Aquifers by the Theis Nonequilibrium Method, ASTM International, West Conshohocken, PA, 2008, www.astm.org

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