Multiple Gravity Wells under Transient States of Flow

Abstract

A method for finding the flow pattern of several wells pumped into an unconfined aquifer under transient conditions is presented. The study of the well group is based on the results of the study of individual wells using the relationships between the hydraulic forces. The method is based in part on some of the available concepts, especially those of Theis, Jacob, and Hantush. A flow equation called the ‘unified well formula’ is developed and written in terms of the areas of the pressure head diagrams across vertical sections. The form of this equation is valid for both artesian and gravity wells. The free surface of an individual gravity well is derived in a general procedure similar to that for steady state cases but introducing time effects. The equation can be solved numerically in one iterative cycle at a given time. The results of the analysis of single wells are used to determine the flow pattern of a multiple well system under transient conditions of flow. The pumping of all wells may not necessarily begin at the same time. The restricted superposition principles used in a previous paper on steady state cases are also used for transient flow. Dupuit's assumptions are eliminated and the circumferential velocities are neglected. The derived equations are further investigated at small radii or at large values of time after the start of pumping. The equation of the free surface reduces to the same form of the corresponding steady state cases. However, the radius of influence, in the transient case, depends on the time and the diffusivity of the flow medium.