Transmissivity and storage coefficient as obtained from diffusivity in non leaky confined aquifers

Abstract

A specific code based on Theis equation was written which generated a random series of 18,000 theoretical Diffusivities (D) ranging from 0.012 m²/s to 8,914 m²/s in a non-leaky confined homogeneous aquifer. The code also served to provide 200 reaction times t₀ (also called time lags or delay times) for observation wells placed at 15 different distances from the pumping well, for 6 different discharges, achieving eventually 18,000 random pairs (t₀, D). These pairs and its further developments were subjected to power regressions and logarithmic regressions which led to the analytical expression for D as a function of the distance r (m) from the pumping well to an observation well and of the reaction time t₀ (min) of the later. Once D is known, further expressions are proposed which split it into its constituent’s  (s’ = drawdown at a time t’ in min) and storativity ( ). The values obtained for D, T, and S are validated by comparison to 40 values of these parameters obtained from 15 long term aquifer tests performed during the 1980s in the Cabeças Aquifer, Vale do Gurguéia/Piauí/Brazil. This approach is considered as suitable for providing reliable values of D, T, and S which are required for supporting design, construction, and installation of wells and well fields.