A Closed Form Slug Test Theory for High Permeability Aquifers

Abstract

We incorporate a linear estimate of casing friction into the analytical slug test theory of Springer and Gelhar (1991) for high permeability aquifers. The modified theory elucidates the influence of inertia and casing friction on consistent, closed form equations for the free surface, pressure, and velocity fluctuations for overdamped and underdamped conditions. A consistent, but small, correction for kinetic energy is included as well. A characteristic velocity linearizes the turbulent casing shear stress so that an analytical solution for attenuated, phase shifted pressure fluctuations fits a single parameter (damping frequency) to transducer data from any depth in the casing. Underdamped slug tests of 0.3, 0.6, and 1 m amplitudes at five transducer depths in a 5.1 cm diameter PVC well 21 m deep in the Plymouth-Carver Aquifer yield a consistent hydraulic conductivity of 1.5 x 10(-3) m/s. The Springer and Gelhar (1991) model underestimates the hydraulic conductivity for these tests by as much as 25% by improperly ascribing smooth turbulent casing friction to the aquifer. The match point normalization of Butler (1998) agrees with our fitted hydraulic conductivity, however, when friction is included in the damping frequency. Zurbuchen et al. (2002) use a numerical model to establish a similar sensitivity of hydraulic conductivity to nonlinear casing friction.

An Analytic Data Analysis Method for Oscillatory Slug Tests

“…In this regard, the sampling frequency of the test response should be no less than 5 Hz. In addition, it is noted that the earlytime fluctuations, as presented by Zurbuchen et al (2002, figure 2), Ostendorf et al (2005, figure 3), or Butler (1998, figure 8.1), are absent in the two field examples. This early-time noise is a direct consequence of the pneumatic method of initiating the slug test (Zurbuchen et al 2002), and its presence in the test data could obscure the occurrence time of the first extremity, thereby hindering the application of this analytic method.…”

“…Thus, the analysis of oscillatory pressure heads measured by a submerged pressure transducer requires a theoretical conversion of w(t) to the depth-dependent dynamic pressure (Zurbuchen et al 2002;Ostendorf et al 2005;Chen and Wu 2005). The water pressure under an oscillatory w(t) pertains to dynamic pressure, which nonlinearly varies with water depth.…”

“…The water pressure under an oscillatory w(t) pertains to dynamic pressure, which nonlinearly varies with water depth. Thus, the analysis of oscillatory pressure heads measured by a submerged pressure transducer requires a theoretical conversion of w(t) to the depth-dependent dynamic pressure (Zurbuchen et al 2002;Ostendorf et al 2005;Chen and Wu 2005). Also, due to the acceleration of the rapid water movement in cyclic rise and fall, the relationship between the damping frequency and the hydraulic conductivity is complicated by the inertial forces, casing friction, and minor losses of the water motion (McElwee and Zenner 1998;Zurbuchen et al 2002;Ostendorf et al 2005).…”

Unconfined aquifer response to infiltration basins and shallow pump tests

“…2), as presented by Ostendorf et al (2005). These latter suggest a permeability ranging from 7 · 10 À11 -2 · 10 À10 m 2 , based on a rapid (10 s) recovery of the piezometric surface from a pneumatically induced slug.…”

“…The data of Fig. 4 extend over hours and tens of meters, while the slug tests have a 1 m radius of influence, two orders of magnitude smaller than r. The pneumatic slug tests, as analyzed by Ostendorf et al (2005), do not estimate storage. Thus, the transient pump test provides new information.…”