Estimation of transmissivity and storage coefficient by means of a derivative method using the early-time drawdown

A novel methodology is proposed to calculate transmissivity (T) and storage coefficient (S) in a confined aquifer, based on the Theis (1935) solution and using only the first derivative of the drawdown with respect to time. By analyzing the behavior of the third derivative of the drawdown with respect to the logarithm of time, it is apparent that the third derivative vanishes when the first derivative attains its peak value. Since the third log-derivative is zero if, and only if, the argument, u, of the Theis well function is equal to unity, this condition can be used to estimate T and S, knowing the time at which the first derivative reaches its peak, and so overcoming the problem of actually computing the third log-derivative, which is very unstable. The main characteristic of the proposed method is that it does not require long pumping tests, since T and S are calculated using only the early-time drawdown. The proposed method was verified with a synthetic, an experimental and a field pumping test showing its validity when applied to homogeneous media. Theis CV (1935) The relation between lowering the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Trans Am Geophys Union 16(2):519–524