Dipolic MAR "Bubble" Inside Confined Brine Formation or Floating "Lens" on Top of Unconfined Saline Aquifer.

Abstract

In arid desert environments, MAR sites are often characterized by high salinity of the ambient groundwater and intensive evaporation. We present mathematical modeling of two MAR scenarios: 1) injection-abstraction of fresh water through two horizontal wells with a quasi-vertical sharp interface/transition zone straddling between the caprock and bedrock of a confined aquifer; 2) infiltration from a surface pond into a floating fresh water lens with an interface pinned to two unknown frontal points. Analytical solutions for Darcian, steady, 2-D and axisymmetric flows utilize two types of mathematical dipoles: combination of a line sink and source and superposition of a distributed sink and source. For 2-D dipoles sandwiched between the caprock and bedrock, the theory of holomorphic functions is used (conformal mappings and Keldysh-Sedov's representations of characteristic functions via singular integrals). Numerically, MODFLOW-SEAWAT delineate isoconcentric lines of the MAR "bubble". For axisymmetric floating lenses, U-turn topology of fresh water circulation is modeled by the Dupuit-Forchheimer approximation, which is reduced to a boundary value problem for a nonlinear ordinary differential equation with respect to Strack's potential. The total volume of the lens is evaluated for evaporation rates, which are constant or exponentially decrease with the water table depth.