Partially penetrating multiple-well syste in a confined aquifer with application to a relief well design

Abstract

The present study deals with the derivation of discharge and drawdown expressions in the case of a partially penetrating multiple-well system in a confined aquifer under steady-state conditions. The concept of average pressure around a partially penetrating well along with the theory of images, and the principle of superposition has been employed to derive the needed expressions. Equations have been derived for the discharge in the well and the drawdown at an intermediate point for several well groups with the same drawdown in each individual well for the following cases, viz.: (1) the well being fed from a line source; (2) the well array placed in a semi-infinite strip with both longitudinal sides forming potential boundaries; and (3) a semi-infinite strip with potential boundary along one longitudinal side, and an impermeable boundary along the other. Equations have also been deduced for drawdown factors for a few cases of well groups in special arrays with circular or straight-line recharge boundary under conditions of equal discharge in each individual well. General expressions for the penetration factor, α′, applicable for a well in the presence of an infinite line source have been suggested. The derived results provide an analytical method for fixing the spacing of a partially penetrating relief well system for a desired reduction in the uplift pressure value. They are also useful in investigating the effect of partial penetration on shielding, and analytical determination of constants θ a and θ m which are needed in equivalent ditch approach. Theoretical values of θ a and θ m are found to be in close agreement with experimental results. Results of fully penetrating wells are obtainable as a particular case of penetration ratio unity from the general results of partially penetrating wells presented in this study.