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Predictive Inverse Model for Advective Heat Transfer in a Planar Fracture with Heterogeneous Permeability
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  • Adam Jacob Hawkins,
  • Don Bruce Fox,
  • Donald Koch,
  • Matthew W Becker,
  • Jefferson William Tester
Adam Jacob Hawkins
Cornell University, Cornell University

Corresponding Author:[email protected]

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Don Bruce Fox
Cornell University, Cornell University
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Donald Koch
Cornell, Cornell
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Matthew W Becker
Department of Geological Sciences, California State University Long Beach, Department of Geological Sciences, California State University Long Beach
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Jefferson William Tester
Cornell University, Cornell University
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Abstract

Identifying fluid flow maldistribution in planar geometries is a well-established problem in subsurface science/engineering. Of particular importance to the thermal performance of Engineered (or “Enhanced”) Geothermal Systems (EGS) is identifying the existence of non-uniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a Genetic Algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two-dimensional Hele-Shaw geometry (i.e., parallel-plates). The inverse problem is solved by minimizing the L2-norm between simulated Residence Time Distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C-Dot nanoparticle). Principal Component Analysis (PCA) of spatially-correlated permeability fields enabled reduction of the parameter space by more than a factor of ten and restricted the inverse search to reservoir-scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding-plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. The results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.