Slug test in confined aquifers, the over-damped case: quasi-steady flow analysis

In the great majority of slug tests performed in wells fully penetrating confined geologic formations, and for over-damped conditions, the response data are evaluated with the transient-flow model of Cooper et al. (1967) when the radial hydraulic conductivity K(r) and the coefficient of specific storage S(s) are to be estimated. That particular analytical solution, however, is computationally involved and awkward to use. Thus, groundwater professionals often use a few pre-prepared type-curves to fit the data by a rough matching procedure, visually or computationally. On the other hand, the method of Hvorslev (1951), which assumes the flow to be quasi-steady, is much simpler but yields only K(r) estimates. In this work, we develop a complete quasi-steady flow model that includes a storage balance inside the aquifer and allows estimating K(r) and S(s) simultaneously, through matching of the well response data to a type-curve. The new model approximates the model of Cooper et al. closely and has the practical advantage that its solution type-curves are generated easily using an electronic spreadsheet, so that the optimal fit of data by a type-curve can be readily automated.