Semi-analytical forward model for hydraulic fracture propagation monitoring using distributed fiber optics in adjacent wells

Distributed fiber optic monitoring in adjacent wells has increasingly become an essential technique for fracture surveillance during hydraulic fracturing of unconventional oil and gas reservoirs. Developing forward models for distributed fiber optic strain response in adjacent wells is of significant importance for understanding the mechanism of fiber response and for the inversion of fracture geometries. However, existing forward interpretation models face limitations from insufficient flexibility in the selection of fracture propagation models, and by computational inefficiency caused by grid-based discretization, especially when high precision is required. To address these limitations, this study presents a semi-analytical stress-displacement field model for simulating fracture propagation with arbitrary aperture and geometric shape. Based on this, a forward modeling framework for adjacent well distributed fiber optic strain response is established. Using a penny-shaped fracture as a representative example, the stress field around the fracture is calculated and benchmarked against the classical Sneddon analytical solution. A forward simulation of fiber optic strain response for a scenario where a horizontal adjacent well monitors a vertically oriented elliptical fracture is conducted. The results are compared with the forward-modeled strain response from the Displacement Discontinuity Method (DDM). The results reveal strong consistency between the semi-analytical model and both the analytical and DDM solutions in classical benchmark cases, confirming the model’s validity and applicability. The model is further coupled with various fracture propagation models and applied to the interpretation of real field data. In particular, distributed fiber optic monitoring results from Stage 19 of Well B1H and Stage 20 of Well B2H in the Hydraulic Fracturing Test Site 2 (HFTS-2) project in the United States are analyzed. The modeling results show that the proposed approach accurately reproduces the characteristic patterns observed in field fiber data. For Stage 20 of Well B2H, which exhibits higher-complexity response characteristics, the model provides a closer match to observed details and temporal evolution compared with the DDM-based approach. In conclusion, this study establishes a semi-analytical forward modeling approach for fiber optic strain in adjacent wells under arbitrary fracture aperture and geometry, significantly reducing computational cost and improving efficiency. The model’s flexibility enables seamless integration with a variety of fracture propagation models, enhancing its capacity to accurately capture complex fracture behaviors observed in field monitoring. This provides a powerful tool for detailed interpretation and analysis of distributed fiber optic data in adjacent well applications.