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We modeled cross-well strain/strain rate responses of Fiber Optic Sensing, including Distributed Strain Sensing (DSS) and low-frequency Distributed Acoustic Sensing (DAS), to hydraulic stimulation. DSS and low-frequency DAS have been used to measure strain or strain rate to characterize hydraulic fractures. However, the current application of DSS/DAS is limited to acquisition, processing, and qualitative interpretations. The lack of geomechanical models hinders the development of the technology toward quantitative interpretation and inversion. We developed a strategy to use the Displacement Discontinuity Method (DDM) to model the strain field around kinematically propagating fractures. For a horizontal monitoring well, modeling results were able to explain heart-shaped extending pattern before a fracture hit, polarity flip due to fracture interaction during stimulation, and V-shaped pattern when a fracture does not intersect with the monitoring well. For a vertical monitoring well, modeling shows the different characters of strain rate responses when a fracture is near and far away from a vertical monitoring well. We also investigated the effects of fractures with various geometries such as elliptic and layered fractures. We compared and verified the modeling with field data from the Hydraulic Fracturing Test Site 2 (HFTS2), a research experiment performed in the Permian Basin. The modeling work presented by this paper can be used to identify patterns in field observations. They also help to improve acquisition design and lays the groundwork for quantitative interpretation and inversion.

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