  Particle settling in inclined channels is an important phenomenon that occurs
during hydraulic fracturing of shale gas production. Generally, in order to
accurately simulate the large-scale (field-scale) proppant transport process,
constructing a fast and accurate sub-scale proppant settling model, or
surrogate model, becomes a critical issue, since mapping between physical
parameters and proppant settling velocity is complex. Previously, particle
settling has usually been investigated via high-fidelity experiments and
meso-scale numerical simulations, both of which are time-consuming. In this
work, a new method is proposed and utilized, i.e., the multi-fidelity neural
network (MFNN), to construct a settling surrogate model, which could utilize
both high-fidelity and low-fidelity (thus, less expensive) data. The results
demonstrate that constructing the settling surrogate with the MFNN can reduce
the need for high-fidelity data and thus computational cost by 80%, while the
accuracy lost is less than 5% compared to a high-fidelity surrogate. Moreover,
the investigated particle settling surrogate is applied in macro-scale proppant
transport simulation, which shows that the settling model is significant to
proppant transport and yields accurate results. This opens novel pathways for
rapidly predicting proppant settling velocity in reservoir applications.
