Multi-scale fracture network simulation and stimulated reservoir volume evaluation of multi-stage fractured horizontal wells in low-permeability coal reservoirs based on physics-enhanced deep operator learning

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Prediction of hydraulic-fracture growth and evaluation of stimulated reservoir volume (SRV) are important for optimising multi-stage fracturing in low-permeability coal reservoirs, where geological heterogeneity and inter-stage interference make repeated numerical analysis expensive. A physics-enhanced deep operator learning (PEDOL) framework is developed to map geological conditions, horizontal-well parameters and staged-fracturing controls to fracture-response fields. Mass conservation, fracture flow, propagation criteria and stress-shadow effects are incorporated into the learning process as physical residual constraints. Five representative cases are examined, including base, low-intensity, high-intensity, dense-stage and roof-communication scenarios. In the base case, the main-fracture half-length ranges from 70 to 93 m, with an average of 80.7 m, and the average fracture height is 5.17 m. The effective SRV of the in-seam horizontal-well case is 3.48 × 10 4 m 3 , compared with 3.02 × 10 4 m 3 for the roof horizontal-well case. The high-intensity case yields the largest geometric SRV, 5.02 × 10 4 m 3 , whereas the dense-stage case reaches an effective SRV of 3.58 × 10 4 m 3 and an SRV efficiency of 74.4%. These results show that a larger geometric fracture envelope does not necessarily translate into a larger effective stimulated volume, because stronger stress interference and uneven proppant support can reduce the useful contribution of newly created fractures. The contribution is an application-specific integration of fracture-physics residuals, operator learning and separate geometric/effective SRV screening for a confined coal seam. The results are simulation-based; independent field validation and controlled accuracy and timing benchmarks remain necessary.