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 geothermal
reservoirs 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. The inverse problem is solved by
minimizing the -norm between measured and simulated fluid Residence Time
Distribution (RTD). 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 large-scale permeability variations. Thermal experiments and
tracer tests conducted at a meso-scale field laboratory in Altona, New
York demonstrate that the method accurately predicts the effects of
extreme flow channeling on heat transfer in a 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 measurement, 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.