A Critique of the Hvorslev Method for Slug Test Analysis: The Fully Penetrating Well

The Hvorslev (1951) method of slug test analysis addresses a variety of well and aquifer geometries, is easy to apply, and is widely used. Its underlying mathematical model assumes negligible compressive storage (aquifer water and matrix are incompressible, flow is quasi-steady). The consequences of this assumption are explored here for the particular case of a well fully penetrating a confined, radially infinite, homogeneous, isotropic aquifer. The Cooper et al. (1967) model of this setting includes the effect of compressive storage and is otherwise identical to Hvorslev. Therefore, for this setting the performance of the Hvorslev method is gauged against that of the Cooper et al. model. The original Hvorslev model is recast into conventional governing equations to facilitate the comparison with Cooper et al. The Hvorslev estimate of hydraulic conductivity for this setting is accurate only to within an order of magnitude, assuming no knowledge of the aquifer storage coefficient. Accuracy of the Hvorslev estimate depends on the normalized aquifer storage coefficient α, on the matching procedure used to fit the Hvorslev model, and on the analyst's choice for the Hvorslev effective radius re. The Hvorslev model provides no physical basis for selecting re. Some insight is gained by viewing the constant head condition at radius re as an “infinite storage” at re. Flow from this discrete “storage” approximates the distributed storage of a compressible aquifer. By reference to Cooper et al. one can select a value of re, which leads to a correct Hvorslev estimate of hydraulic conductivity, given prior knowledge of the aquifer storage coefficient. For an example aquifer, the Hvorslev and Cooper et al. models yield substantially different distributions of head within the aquifer. Quantitative comparisons here are restricted to a single setting. Hvorslev (1951) also addresses a number of other settings (partial penetration, no lower aquiclude). A companion paper, in preparation, will examine the significance of the incompressibility assumption for these other, more widely applied settings.