Evaluation of near-critical overdamping effects in slug-test response

A slug test behaves as a harmonic oscillator, subject to both inertial effects and viscous damping. When viscous and inertial forces are closely balanced, the system is nearly critically damped, and water-level recovery is affected by inertial effects, but does not exhibit oscillation. These effects were investigated by use of type curves, generated both by modification of Kipp's (1985) computer program and by use of the Butler-Zhan (2004) model. Utility of the type curves was verified by re-analysis of the Regina slug test previously analyzed by Kipp. These type curves indicate that near-critical inertial effects result in early-time delayed water-level response followed by merger with, or more rapid recovery than, response for the fully damped case. Because of this early time response, slug tests in the moderately over-damped range are best analyzed using log-log type curves of (1 - H/H(0)) vs. Tt/r(2c). Failure to recognize inertial effects in slug test data could result in an over-estimate of transmissivity, and a too-small estimate of storage coefficient or too-large estimate of well skin. However, application of the widely used but highly empirical Hvorslev (1951) method to analyze both the Regina slug test and type-curve generated data indicate that such analyses provide T values within a factor of 2 of the true value.