Poroelastic Origins of the Noordbergum Effect

The Noordbergum effect refers to temporary rise in hydraulic heads of surrounding observation wells for a short time after starting groundwater withdrawal from a nearby well, before return to the expected declining trend. This effect is herein studied through a poroelastic model of a three-layer aquifer system comprising a middle aquifer layer with dissimilar mechanical properties compared to the adjacent layers of confining rock from the top and bottom. An axisymmetric analytical solution is derived for coupled pore water flow and solid deformation in this aquifer system in response to a vertical line sink representing a producing well within the mid layer. The solution is obtained through the Hankel and Laplace integral transforms of the pore fluid continuity and solid stress equilibrium equations. Results indicate that the occurrence and intensity of the Noordbergum effect are predominantly controlled by the contrast in stiffnesses of the aquifer and confining rocks, with the following distinct characteristics. (a) Typical manifestation of the Noordbergum effect that is usually observed through field measurements occurs when the shear modulus of the aquifer rock is larger; (b) The effect disappears if the two rock layers have the same stiffness; (c) Reverse Noordbergum effect occurs when the shear modulus of the confining rock is larger. This latter case is identified by a faster rate of early decline in the aquifer pore water pressure compared to the prediction made by a decoupled model of the aquifer pore water flow. Occurrence of either effect is not significantly affected by Poisson's ratios of the rock layers, although their intensities do vary with changes in this parameter.