Predictive Inverse Model for Advective Heat Transfer in a Short‐Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration

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 enhanced (or "engineered") geothermal systems is identifying the existence of nonuniform (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 L 2 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 10 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.

Influence of Extreme Flow Channeling on the Thermal Performance of Open-Loop Geothermal Systems at Commercial Scale

“…Alternatively, Neuville et al (2010) and Fox et al (2015) discuss the influence of fluid flow short circuits on the thermal behavior of single-fracture geothermal reservoirs using randomly generated, self-affine aperture fields. However, a recent meso-scale field demonstration presented in Hawkins et al (2020) suggests that field-scale "realistic" fractures may suffer from flow channeling more acutely than suggested by previous studies that adopted core-scale aperture statistics at the reservoir-scale. This, in addition to other issues like limited availability and sparsity of permeability data at reservoir scale, often make going from theoretical studies to site-specific predictive models a challenging endeavor (Smith, 2019).…”

“…In this work, we test the effects of the extreme short-circuiting effects identified at meso-scale by Hawkins et al (2020) at the commercial-scale, where project lifetimes of 10 to 30 years are desired.…”

“…For this, we simulate heat extraction in a single fracture within a large-scale geothermal reservoir and utilize a fully coupled thermal-hydraulic model with an empirically-derived, up-scaled permeability distribution. Using the best-fit aperture distribution from Hawkins et al (2020), 13 different well-pair configurations are considered to determine the thermal performance variability at commercial scale using field-measured trends in the spatial distribution of fracture aperture. In our simulations, we consider variations in: (1) separation distance between wells; (2) mass flow rates; and (3) relative well locations within the non-uniform fracture aperture plane.…”

Predicting Thermal Performance of an Enhanced Geothermal System From Tracer Tests in a Data Assimilation Framework

“…The well configuration and geological condition of the testbed has been reported in the literature (Hawkins, Fox, et al, 2017;Hawkins et al, 2018Hawkins et al, , 2020 and therefore not repeated here. In what follows, we first briefly describe relevant field measurements, and then use the proposed framework to infer the aperture distribution in the sub-horizontal fracture and predict production temperature during the thermal test.…”

“…The arrival times of peak concentration are almost identical for iodide and cesium, but the normalized peak magnitude is smaller for cesium. The second peaks at ∼40 min were mainly caused by the continuous reinjection of produced fluids during the tracer tests (Hawkins et al, 2020). To determine the adsorption reaction parameters of cesium, Hawkins et al (2018) performed two batch reactor experiments in which cesium dissolved in water were adsorbed onto two rock samples collected at roughly 17 m below the testbed surface.…”