Frans R. P. Kalf, B.Sc., Cert. Eng. Hyd., M.App.Sc, PhD.
Principal/Director Kalf and Associates Pty Ltd.
e-mail:frkalf@gmail.com Tel: +61-2-89190272


Keywords: groundwater. optimal yield. wellfield. pumping tests. step tests
well loss. non-linear drawdown.

Click on the following dropbox link for the full report text with figures file on this subject plus FORTRAN programs listings:
 

https://www.dropbox.com/s/1w4otw08bb0ziaj/Determination%20of%20
optimal%20pumping%20rates%20in%20a%20non-linear%20bore%20array%202017%20V10.pdf?dl=0

Abstract

In analysing pumping test data it is sometimes necessary to determine the optimal
pumping rates for a group of bores pumping simultaneously - for a town water supply for
example. The additional drawdown caused by “well losses” in addition to the mutual drawdown interference by other bores in the array, has to be considered in estimating the allowable pumping rate in each bore in order to achieve available drawdown levels. A methodology is presented together with examples to illustrate the procedure that takes into consideration the simultaneous non-linear behaviour of pumping drawdowns when “well losses” are included. 

 

The method of solution does not depend on whether the transmissivity, storativity are uniform, in fact the method does not require that these parameters be determined. Nor is it necessary to develop any type of model or calibration to achieve the outcome or even to know the exact distance between bores. The only requirement is that separate step tests and standard single rate pumping tests are carried out at each bore in turn with corresponding drawdown evident and measured in each of the other bores of the group and that pumping in each bore affects each of the others in the array.

Drawdown rates per log cycle determined from the resulting pumping test measurements of drawdown together with “well-loss” coefficients from step tests are used as input. Because only measured data is included, aquifer heterogeneity and different bore separation distances causing differences in drawdown rates at different times is accommodated. The method involves both Excel graphical and computer method to find the drawdown linear and non-linear parameters from the step pumping test results.

The method of solution used to determine the optimal yield for a user set of maximum drawdowns in each bore is an iterative procedure based on Newton’s method to solve a set of non-linear simultaneous equations. Both Jacob (1950) and Rorabaugh (1953) formulations are covered. Complete FORTRAN programs are included as well as Excel and FORTRAN program for determining linear and well-loss parameters from step-tests.

[1] 'The basis of this text and computer program methodology was recently discovered by the author in his ‘hidden’ archived files. An earlier limited version was written in 1974 whilst the author was a hydrogeologist in the Water Conservation and Irrigation Commission NSW Australia. The material was never published or distributed. The current theory and FORTRAN programs have been extensively updated and extended to include both the Rorabaugh (1953) as well as the Jacob (1950) well-loss methods. It is hoped that it may be of interest to new hydrogeologists in its updated metric units form. After a 42 years wait - better late than never!!

 

[1] 'The basis of this text and computer program methodology was recently discovered by the author in his ‘hidden’ archived files. An earlier limited version was written in 1974 whilst the author was a hydrogeologist in the Water Conservation and Irrigation Commission NSW Australia. The material was never published or distributed. The current theory and FORTRAN programs have been extensively updated and extended to include both the Rorabaugh (1953) as well as the Jacob (1950) well-loss methods. It is hoped that it may be of interest to new hydrogeologists in its updated metric units form. After a 42 years wait - better late than never!!

Determination of practical sustained pumping rates in a non-linear bore field array[1]