Constructing sub-scale surrogate model for proppant settling in inclined fractures from simulation data with multi-fidelity neural network

Particle settling in inclined channels is an important phenomenon that occurs during hydraulic fracturing of shale gas production. 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. However, mapping between physical parameters and proppant settling velocity is complex, which makes the model construction difficult. 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, we propose a new method, i.e., the multi-fidelity neural network (MFNN), to construct a settling surrogate model, which could greatly reduce computational cost while preserving accuracy. 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. The framework opens novel pathways for rapidly predicting proppant settling velocity in reservoir applications. Furthermore, the method can be extended to almost all numerical simulation tasks, especially high-dimensional tasks.