The effect of convergence on entrance losses in pumped wells

Abstract

Data of numerous multiple step drawdown tests performed on selected partially penetrating pumped wells installed in the Punjab Portion of West Pakistan, have been analyzed in detail, to study the variation with time of the formation loss coefficient 'B' and well loss coefficient 'C' which appear in Jacob's (1947) original equation for total drawdown inside a pumped well. In Jacob's equation, sw = BQ + CQ^2, where s represents the total drawdown in the pumped well, and Q its discharge. Assuming the formation coefficient 'B' to be an index of the development of convergence which is associated with partially penetrating wells, a study is made to determine whether this coefficient is invariant or whether it changes with time. It was found that coefficient 'B' increased with time whereas coefficient 'C' remained essentially constant, It is shown that Jacob's equation for drawdown in a pumped well needs modification when applied to partially penetrating wells. To account for the effect of partial penetration Hantush's (1961) relationship for drawdown in a partially penetrating well is utilized. It is compared with Jacob's equation for drawdown to obtain the modified value of coefficient 'B' in dimensionless form. The investigations show that the magnitudes of modified values of 'B' in dimensionless form compare favorably with Hantushs corresponding E factor. The nature of losses that occur in pumping wells have also been described. The coefficients of transmissibility are determined, for various sites, using values of B determined from analysis of the multiple step drawdown tests. These values are utilized in the present study. It should be mentioned that in this thesis the term entrance loss is defined differently than heretofore. Entrance loss includes all head loss over and above the ?formation loss (designated BQ by Jacob) for the case of 100% penetration of aquifer by the pumped well. That is, entrance loss here includes the added formation loss due to partial penetration as well as the well loss due to turbulent flow of water into and inside the well (CQ^2).