Sinusoidal pumping of groundwater near cylindrical inhomogeneities

Abstract

A new analytic-element solution is presented for a well with a sinusoidal discharge pumping near cylindrical inhomogeneities. Both the transmissivity and the storage coefficient may be different inside each cylinder. The solution consists of separate series solutions inside and outside each cylinder; asymptotic expansions are presented for cases where the sinusoidal period is small and the radius and transmissivity of the cylinder are large. The complex coefficients in the series solutions are determined by requiring continuity of head and normal flow across the boundary of each cylinder resulting in a linear system of complex equations that may be solved with standard methods. The solution represents one of the few analytic solutions for two-dimensional transient groundwater flow in an aquifer with inhomogeneities. Computer implementation requires truncation of the series; machine accuracy may be reached when enough terms are used in the series solutions. The effect of cylindrical inhomogeneities on the amplitude and phase of the head are investigated. The complex behavior suggests it may be difficult to determine location and properties of cylindrical inhomogeneities from pump tests, which confirms reported difficulties of interpreting pump test results from heterogeneous aquifers.

Characterization of Aquifer Poroelastic Response to Impulse and Oscillatory Well Pressure Using Distributed Acoustic Sensing

“…Under these idealized conditions, the radial distance of hydraulic penetration (radius of influence) is a function of the hydraulic diffusivity ($$D$$) and the period ($$P)$$ over which the formation is strained hydraulically. Bakker (2009) defines a characteristic length scale of penetration as λ $$=\sqrt{\mathrm{D}\mathrm{P}/2\pi }$$. The amplitude of the hydraulic signal is expected attenuated by a factor of 10 will be 1.78$$\lambda $$.…”

Pump Hydro Energy Storage systems (PHES) in groundwater flooded quarries

“…Recently, this kind of cyclic stresses has been investigated, through the development of oscillatory pumping tests (Bakhos et al, 2014;Bakker, 2009;Black and Kipp, 1981;Cardiff et al, 2013;Guiltinan and Becker, 2015;Rabinovich et al, 2015;Rasmussen et al, 2003;Renner and Messar, 2006). The approach is to obtain hydraulic parameter estimation, using the amplitude and phase shift of water level oscillations induced in a specific point, and propagated in the porous media.…”

“…Black and Kipp (1981) have estimated the different ranges of hydraulic diffusivity, for which sinusoidal pumping tests can be applied, using the amplitude and phase shift of the measured signal in a homogeneous isotropic confined aquifer. Bakker (2009) studied the effect of aquifer heterogeneities on the response of a sinusoidal pumping sequence, using an analytic-element solution. The possibility to use oscillatory pumping test for hydraulic imaging is investigated by Cardiff et al (2013) with oscillatory pumping tests performed in homogeneous and heterogeneous confined aquifer.…”