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.

Shale reservoirs contain numerous bedding fractures, making the formation of complex fracture networks during fracturing a persistent technical challenge in evaluating shale fracture morphology. Distributed optical fiber sensing technology can effectively capture the process of fracture initiation and propagation, yet the evaluation method for the initiation and propagation of bedding fractures remains immature. This study integrates a distributed optical fiber sensing device based on optical frequency domain reflectometry (OFDR) with a large-scale true tri-axial fracturing physical simulation apparatus to conduct real-time monitoring experiments on shale samples from the Lianggaoshan Formation in the Sichuan Basin, where bedding is well-developed. The experimental results demonstrate that two bedding fractures in the shale sample initiated and propagated. The evolution characteristics of fiber-optic strain in a horizontal adjacent well, induced by the initiation and propagation of bedding fractures, are characterized by the appearance of a tensile strain convergence zone in the middle of the optical fiber, flanked by two compressive strain convergence zones. The initiation and propagation of the distal bedding fracture causes the fiber-optic strain in the horizontal adjacent well to superimpose, with the asymmetric propagation of the bedding fracture leading to an asymmetric tensile strain convergence zone in the optical fiber. Utilizing a finite element method coupled with a cohesive element approach, a forward model of fiber-optic strain in the horizontal adjacent well induced by the initiation and propagation of hydraulic fracturing bedding fractures was constructed. Numerical simulation analyses were conducted to evaluate the evolution of fiber-optic strain in the horizontal adjacent well, confirming the correctness of the observed evolution characteristics. The presence of a "wedge-shaped" tensile strain convergence zone in the fiber-optic strain waterfall plot, accompanied by two compressive strain convergence zones, indicates the initiation and propagation of bedding fractures during the fracturing process. These findings provide valuable insights for interpreting distributed fiber-optic data in shale fracturing field applications.

A method for in-situ stress measurement via fiber optics was proposed. The method utilizes the relationship between rock mass elastic parameters and in-situ stress. The approach offers the advantage of long-term stress measurements with high spatial resolution and frequency, significantly enhancing the ability to measure in-situ stress. The sensing casing, spirally wrapped with fiber optic, is cemented into the formation to establish a formation sensing nerve. Injecting fluid into the casing generates strain disturbance, establishing the relationship between rock mass properties and treatment pressure. Moreover, an optimization algorithm is established to invert the elastic parameters of formation via fiber optic strains. In the first part of this paper series, we established the theoretical basis for the inverse differential strain analysis method for in-situ stress measurement, which was subsequently verified using an analytical model. This paper is the fundamental basis for the inverse differential strain analysis method.