An Improved Straight-Line Fitting Method for Analyzing Pumping Test Recovery Data

摘要

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.