Predictive Inverse Model for Advective Heat Transfer in a Planar
Fracture with Heterogeneous Permeability
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.