Estimation of Hydraulic Parameters from an Unconfined Aquifer Test Conducted in a Glacial Outwash Deposit, Cape Cod, Massachusetts

by Allen F. Moench, Stephen P. Garabedian, and Denis R. LeBlanc

U.S. Geological Survey Professional Paper 1629

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An aquifer test conducted in a sand and gravel, glacial outwash deposit on Cape Cod, Massachusetts was analyzed by means of a model for flow to a partially penetrating well in a homogeneous, anisotropic unconfined aquifer. The model is designed to account for all significant mechanisms expected to influence drawdown in observation piezometers and in the pumped well. In addition to the usual fluid-flow and storage processes, additional processes include effects of storage in the pumped well, storage in observation piezometers, effects of skin at the pumped-well screen, and effects of drainage from the zone above the water table. The aquifer was pumped at a rate of 320 gallons per minute for 72-hours and drawdown measurements were made in the pumped well and in 20 piezometers located at various distances from the pumped well and various depths below the land surface. To facilitate the analysis, an automatic parameter estimation algorithm was used to obtain relevant unconfined aquifer parameters, including the saturated thickness and a set of empirical parameters that relate to gradual drainage from the unsaturated zone.

Drainage from the unsaturated zone is treated in this paper as a finite series of exponential terms, each of which contains one empirical parameter that is to be determined. It was found necessary to account for effects of gradual drainage from the unsaturated zone in order to obtain satisfactory agreement between measured and simulated drawdown, particularly in piezometers located near the water table. The commonly used assumption of instantaneous drainage from the unsaturated zone gives rise to large discrepancies between measured and predicted drawdown in the intermediate-time range and can result in inaccurate estimates of aquifer parameters especially when automatic parameter estimation procedures are used.

The values of the estimated hydraulic parameters are consistent with estimates from prior studies and from what is known about the aquifer at the site. Effects of heterogeneity at the site were small as measured drawdowns in all piezometers and wells were very close to the simulated values for a homogeneous porous medium. The estimated values are: specific yield, 0.26; saturated thickness, 170 feet; horizontal hydraulic conductivity, 0.23 feet per minute; vertical hydraulic conductivity, 0.14 feet per minute; and specific storage, 1.3x10-5 per foot.

It was found that drawdown in only a few piezometers strategically located at depth near the pumped well yielded parameter estimates close to the estimates obtained for the entire data set analyzed simultaneously. If the influence of gradual drainage from the unsaturated zone is not taken into account, specific yield is significantly underestimated even in these deep-seated piezometers. This helps to explain the low values of specific yield often reported for granular aquifers in the literature. If either the entire data set or only the drawdown in selected deep-seated piezometers was used, it was found unnecessary to conduct the test for the full 72-hours to obtain accurate estimates of the hydraulic parameters. For some piezometer groups, practically identical results would be obtained for an aquifer test conducted for only 8-hours. Drawdowns measured in the pumped well and piezometers at distant locations were diagnostic only of aquifer transmissivity.







Purpose and Scope

Response of an Idealized Unconfined Aquifer to Pumping

Hydrogeology of the Aquifer-Test Site


Mathematical Model


Boundary-Value Problem

Dimensionless Boundary-Value Problem

Laplace Transform Solution

Aquifer-Test Design and Operation


Preliminary Analysis

Analysis by Nonlinear Least Squares

Evaluation of Sy, Kr, Kz Using Late-Time Data (Step 1)

Evaluation of Sy, b, Kr, Kz Using Late-Time Data (Step 2)

Evaluation of Sw Using Late-Time Pumped-Well Data (Step 3)

Evaluation of Ss Using Early-Time Data (Step 4)

Evaluation of Sy, b, Kr, Kz, and am Using Data for Entire Time Range (Step 5)


Effect of Heterogeneity of Aquifer Test Results

Parameter-Estimation Experiments with Measured Drawdown

Experiments with Pumped-Well Data

Experiments with Limited Piezometer Distribution

Experiments with Reduced Length of Test




Appendix I–Derivation of the Laplace Transform Solution

Appendix II–Drawdown Data Plots for Well Test and Data Selected for Parameter Estimation





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Errata Sheet

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