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Well response tests: I. The direct problem

Well response tests usually provide a simple and economical method for the estimation of aquifer characteristics such as transmissivity and storability. This study deals particularly with a well-aquifer system response to slug testing. The fluid (oil or water) level in the well responds to piezometric head fluctuations due to disturbances of the aquifer and to the vertical motion of the well-aquifer system. The authors develop a rigorous mathematical formulation of the direct physical problem, i.e. the problem of calculating the piezometric head when the aquifer transmissivity and storativity are known, based upon the theories of fluid flow in continuum and porous media. An analytical treatment of the resulting three problems is also presented. Furthermore, three types of well responses are possible for slug tests depending upon the relation between the inertial forces and viscous effect of water within the well column: namely, over-damped, under-damped and critically damped. The theory is applicable for all such cases.