Analytical solution for determining the critical condition of saltwater upconing in a leaky artesian aquifer

Saltwater upconing that occurs in an aquifer overlain by a leaky confining unit is described by an analytical model that assumes the existence of a sharp interface between the freshwater and saltwater and the occurrence of a critical rise in the interface, above which only an unstable cone can exist. At the critical rise, the pressure on the freshwater side of the interface is equal to the pressure on the saltwater side of the interface. Also, the curve for pressure versus depth on the freshwater side of the interface is tangent to the curve for pressure versus depth on the saltwater side of the interface at the critical condition, and thus the slopes of the freshwater and saltwater pressure distribution curves are equal. These two conditions, equality of pressures and equality of pressure gradients, are used to derive two equations that can be solved simultaneously for the critical interface rise and the associated critical pumping rate. Instead of assuming a fixed value for the critical rise of the interface, its location is calculated using an analytical equation expressed in terms of aquifer and confining unit properties and well geometry. The associated critical pumping rate is calculated as a function of aquifer and confining unit properties, well geometry, and the critical interface rise ratio. For field conditions, the critical rise of the interface and critical pumping rate can be calculated analytically or graphically. In an example calculation, the critical interface rise ratio, which is the ratio of the critical interface rise divided by the distance from the original location of the interface to the bottom of the pumped well, is calculated to be 0.710 and the critical pumping rate is calculated to be 3.72 x 10(4) m(3)/day. (C) 1999 Elsevier Science B.V. All rights reserved.