Dynamic groundwater management using Lagrangian coherent structures

Abstract

<p>Scope is scalar transport in enhanced subsurface flows driven via injection and extraction wells. An important application of this concept is found in groundwater treatment by containment and remediation of polluted groundwater via so-called “permeable reactive treatment zones” (PRTZs) and “permeable reactive barriers” (PRBs). Climate change introduces new challenges to clean and safe water as intrusion of seawater or contaminants into water catchment areas by rising sea levels or changing subsurface flow patterns. This necessitates groundwater management that enables shielding and containment of subsurface water bodies under dynamic conditions. However, this is beyond the above conventional water-treatment technologies; PRTZs and PRBs are namely created through a “screen” of injected reactants, construction of infiltration trenches or establishment of subsurface “ice walls” and thus static and inflexible to unforeseen or changing circumstances.</p><p> </p><p>This study explores an in situ processing strategy that relies on the existence of so-called “Lagrangian coherent structures” (LCSs) forming in the fluid trajectories and governing the advective transport in the reservoir. Such LCSs emerge naturally in (subsurface) flow systems and admit rapid and accurate control by the pumping scheme for the wells. Moreover, LCSs are fundamentally embedded in the transport of scalar quantities (e.g. reactants or heat) even in case of significant diffusion and/or chemical reactivity. Thus LCSs act as “internal actuators” for scalar transport and can be utilized for the creation of dynamic processing zones, reaction fronts and transport barriers in a wide range of operating conditions. LCS-based in situ processing may offer a promising alternative to conventional methods for groundwater management by enabling dynamic shielding and containment of subsurface water bodies without the need for physical (and static) boundaries as in PRTZs and PRBs.</p><p> </p><p>The concept of dynamic in situ processing using LCSs is demonstrated by the advective-diffusive scalar transport in a two-dimensional (2D) unsteady Darcy flow in a circular reservoir driven by an array of injection/extraction wells. To this end the non-trivial link between scalar and Lagrangian transport is rigorously established via methods from dynamical-systems theory. This enables systematic demarcation and characterization of confinement zones and transport barriers as a function of (dynamic) operating conditions for the generic case of scalar transport subject to diffusion.</p>