Diagnostic analysis of pumping tests using derivative of dlgs/dlgt with case study

Diagnostic derivative interpretation of drawdown data from pumping tests is discussed in this paper. An emphasis is placed on the conceptualization of derivative term of dlgs/dlgt. Use of a combined plot of dlgs/dlgt and ds/dlgt is made to identify various flow patterns from variable discharge tests with infinite conditions, constant rate tests in bounded aquifers, and tests involving double porosity, which can be used to further characterize the aquifer. Compared with the standard derivative method (ds/dlgt), the combined derivative analysis of dlgs/dlgt and ds/dlgt of drawdown behaviours possesses certain advantages identified as follows: (1) the plot of dlgs/dlgt is strikingly sensitive for use in unveiling differences between pumping and recovery periods in a variable discharge test; (2) storativity (S) of pumped aquifers can be accurately evaluated by the combined plot; and (3) a quantitative assessment of double porosity behaviour can also be achieved. Based on applied case studies, Lagrange Interpolation Regression (LIR) is recommended for numerical derivative calculation. Advantages and disadvantages of LIR and traditional methods are demonstrated via a selected case study. The result of the case study confirms that LIR is a preferred method for numerical derivative calculation as it can be used to effectively minimise noisy effect during derivative processes. The proposed derivative approach provides the hydrologists with an additional tool for characterizing pumped aquifers.