A Simple Analytical Formula for the Leakage Flux Through a Perforated Aquitard

In this methods note, we present a simple analytical formula to quantify the steady-state leakage flux (Q) over a perforated aquitard. The flux depends on the aquitard thickness (D), the radius of the perforation (R), the hydraulic conductivity of the material inside the perforation (kfill ), the conductivities of the overlying and underlying aquifers (k1 and k2 , respectively), and the head difference between the two aquifers (ΔH): [Formula: see text]. This equation assumes an aquitard separating two homogeneous and infinite aquifers (R ≪ aquifer thickness) in which radial flow to and from the perforation occurs, with no other recharge or discharge boundaries near the perforation. The flux through a perforation in a hypothetical case study with D = 10 m, k1  = 10 m/d, k2  = 20 m/d, R = 0.072 m, and ΔH = 1 m ranges between less than 1 mL/d if the hole is backfilled with bentonite (k(fill ) = 10(-4)  m/d), to several liters per day if the perforation is backfilled with sand from the overlying aquifer (k(fill)  = 10 m/d), to several m(3) /d if the perforation forms an open conduit (k(fill)  = 10(5)  m/d). The leakage fluxes calculated with this model agree well with those calculated using a numerical model (MODFLOW).