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An Improved Straight‐Line Fitting Method for Analyzing Pumping Test Recovery Data
Author(s) -
Zheng Li,
Guo JianQing,
Lei Yuping
Publication year - 2005
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.2005.00094.x
Subject(s) - drawdown (hydrology) , truncation (statistics) , moment (physics) , residual , mathematics , line (geometry) , function (biology) , simple (philosophy) , test data , constant (computer programming) , dimension (graph theory) , mathematical analysis , computer science , algorithm , statistics , physics , geology , geotechnical engineering , geometry , philosophy , epistemology , classical mechanics , evolutionary biology , aquifer , groundwater , biology , programming language , pure mathematics
Abstract Theis (1935) derived an exact solution for the residual drawdown in a well after the cessation of a pumping test by summing two drawdowns: one ( s 1 ), caused by imaginary continuation of the original pumping and the other ( s 2 ), due to an imaginary injection at the same constant rate. We approximated the Theis solution to obtain a simple linear relation for determining the transmissivity and storage coefficient from recovery data. Unlike other existing straight‐line fitting methods, in our method, we applied different approximations to the well functions in the solutions of s 1 and s 2 . We used the well‐known Cooper‐Jacob approximation for s 1 , truncating the expansion of the well function in s 2 to its first three terms. For the same level of truncation errors, while the Cooper‐Jacob approximation requires the argument u 1 ≤ 0.01, the second approximation requires the argument u 2 ≤ 0.2, thus dramatically improving the utility of short‐term recovery data. Application of our method requires only recovery data from a single observation well and no knowledge of the drawdown at the moment of pumping cessation.