Jacob Method for Transient Flow in a Confined Aquifer

Application: Geotechnics

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Summary

An interactive hydrogeology tool for analysis of transient flow in a confined aquifer, based on the Jacob Method ... with hydrogeology unit conversions.

Notes on Jacob Method for Transient Flow in a Confined Aquifer

  • Select the required output, then set the other parameters to the required values.
  • Transmissivity (T) = K * D

For an explanation of the parameter "u" and to determine the accuracy of Jacob's method see below.

For equations, assumptions and references see below.

Tool Parameters

Values displayed with a may be changed ... click on a value to display an entry form ... or use the arrows right of a value to select from a list.

Tool Behaviour

This tool exhibits spreadsheet-like behaviour ... change a value and related values are re-calculated automatically.

Jacob Method for Transient Flow in a Confined Aquifer1

1Cooper, H.H., and C.E. Jacob,1946, A generalized graphical method for evaluating formation constants and summarizing well field history, Am. Geophys. Union Trans, Vol. 27, pp.526-534.

where:

s = drawdown measured in a monitoring well (m)
Q = discharge from pumping well (constant) (m3/d)
KD = transmissivity of the aquifer (m2/d)
r = distance between the monitoring well and pumping well (m)
S = storativity of the aquifer (dimensionless)
t = time since pumping started (days)

Assumptions2:

  1. The aquifer is confined.
  2. The aquifer has an infinite areal extent.
  3. The aquifer is homogeneous, isotropic and of uniform thickness over the area influenced by the test.
  4. Prior to pumping, the piezometric surface is horizontal over the area that will be influenced by the test.
  5. The aquifer is pumped at a constant discharge rate.
  6. The well is screened over the entire thickness of the aquifer ensuring entirely horizontal flow.
  7. The flow to the well is not at steady-state.
  8. The values of u are small (u<0.01), i.e., r is small and t is sufficiently large.

References:

1Cooper, H.H., and C.E. Jacob,1946, A generalized graphical method for evaluating formation constants and summarizing well field history, Am. Geophys. Union Trans, Vol. 27, pp.526-534.
2Kruseman, G.P. and N.A. de Ridder, Analysis and Evaluation of Pumping Test Data (Second Edition), Publication 47; International Institute for Land Reclamation and Improvement, Wageningen, 1994.

Accuracy of Jacob's Method

The Jacob method is a simplification of the Theis formula, which is as follows:


where:

The terms after ln u become small and can be neglected when measurements are taken near the pumping well after sufficiently long pumping times. The truncated Theis formula becomes:


which is the Jacob approximation. The error associated with the approximation is as follows:

For a u smaller than: The resultant error is less than:
0.03 1%
0.05 2%
0.1 5%
0.15 10%

References:

  1. Cooper, H.H., and C.E. Jacob, 1946, A generalized graphical method for evaluating formation constants and summarizing well field history, Am. Geophys. Union Trans, Vol. 27, pp.526-534.
  2. Theis, C.V., 1935, The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage, Trans. Amer. Geophys. Union, Vol. 16, pp. 519-524.
  3. Kruseman, G.P. and N.A. de Ridder, Analysis and Evaluation of Pumping Test Data (Second Edition), Publication 47; International Institute for Land Reclamation and Improvement, Wageningen, 1994.

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