Lagrangian approach to analysis and engineering of two generic transport problems in enhanced subsurface flows

Scope is scalar transport in enhanced subsurface flows driven by injection and extraction wells. Two transport problems of great practical relevance, viz. (i) rapid scalar extraction and (ii) contained in situ processing, are investigated in terms of the thermal transport in a two-dimensional circular subsurface reservoir with a well driven Darcy-type flow. Lagrangian (fluid) transport is key to these problems and thus the notion of Lagrangian coherent structures (LCSs) is adopted for analysis and engineering purposes. Analysis by this approach of heat (scalar) extraction reveals that a basic pumping scheme involving a static injector-extractor pair invariably outperforms more elaborate schemes using time-periodic actuation of multiple well pairs due to the formation of "special" LCSs that retard heat release. Such LCSs are, on the other hand, well-suited for contained in situ processing. LCSs namely are fundamentally embedded in the thermal (scalar) transport and, given they admit rapid and accurate control by the pumping scheme, thus naturally emerge as "internal actuators" for the creation of (dynamic) processing zones and reaction fronts. This principle has been developed into an LCS-based in situ processing strategy. To this end the non-trivial link between thermal and Lagrangian transport is rigorously established via methods from dynamical-systems theory so as to enable systematic demarcation and characterisation of confinement zones and their interaction with the wells for the generic case of diffusion. The framework thus developed is demonstrated by way of examples.