An improved straight-line fitting method for analyzing pumping test recovery data

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 (s1), caused by imaginary continuation of the original pumping and the other (s2), 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 s1 and s2. We used the well-known Cooper-Jacob approximation for s1, truncating the expansion of the well function in s2 to its first three terms. For the same level of truncation errors, while the Cooper-Jacob approximation requires the argument u1