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Kansas Geological Survey, Open-file Report 93-45

Unified Analysis of Slug Tests Including Nonlinearities, Inertial Effects, and Turbulence

by C. D. McElwee and M. Zenner

KGS Open File Report 93-45
Prepared for presentation at The American Geophysical Union Fall Meeting
Dec. 6, 1993


Slug tests are frequently used to characterize the transmissivity of an aquifer. In highly permeable aquifers, however, problems arise when conventional analytical techniques are applied. In an aquifer consisting of coarse sand and gravel overlain by silt and clay, we have consistently seen deviations from the expected response of linear theoretical models. Typically, we see a systematic lack of fit to traditional models and a dramatic dependence of the slug test on the magnitude of the initial displacement. In some wells we have also observed oscillatory behavior. Although there are some theories describing oscillatory behavior in slug tests, until now it has been difficult to analyze tests which are in the so-called "critically damped" region. We have developed a unified model for slug tests that includes the effect of nonlinear terms, inertia, turbulence (spatial velocity distributions), viscosity and differing casing and screen radii. The equation for the borehole can be obtained by either considering the mechanical energy balance equation or by considering the Navier-Stokes equation. This borehole equation is coupled to the aquifer equation by the boundary conditions at the well screen. Generally, the effects of viscosity and changing casing-screen radii are negligible. However, the effects of nonlinearities, inertia, and spatial velocity distributions can be quite important. The nonlinear terms make slug test results dependent on the initial head, inertial effects are important when oscillatory behavior is observed, and spatial velocity distributions cause the effective water column length to be greater than expected. This general model can be reduced to a Hvorslev type model by assuming no storage in the aquifer. We have obtained an iterative numerical solution to this model and have applied it to field data from our research site. The results are quite good both for oscillatory and non-oscillatory situations and give consistent estimates of the physical parameters for various initial displacements.

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Kansas Geological Survey, Geohydrology
Placed online May 8, 2015; originally released Dec. 1993
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