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.