Fiber Optic Sensing,including both low-frequency Distributed Acoustic Sensing(DAS)and Distributed Strain Sensing(DSS),can be used to record strain rate or strain for hydraulic fracturing monitoring in an offset well.However,current work focusses on acquisition,processing,and qualitative interpretation.We investigated the modeling of DAS and DSS strain responses to hydraulic fractures during stimulation process.The modeling work provides valuable insights to understand low-frequency DAS and DSS strain measurements during hydraulic stimulation.We used the Displacement Discontinuity Method(DDM)to model the strain/strain rate field around kinematic propagating fractures.This efficient method provides a quick assessment of models with various fracture extents and net pressures.It also allows simulating the strain responses to a network of fractures in consideration of their interactions.During the stimulation stage of hydraulic treatment,the fracture propagation is modeled by prescribing gradually increased fracture size and calculating the displacement discontinuities that representing fractures at each step.After the stimulation stops,we assume the fracture extent will not change but the net pressure within the fracture gradually decreases due to fluid leakoff.We calculate the displacement discontinuities representing fractures using the fracture extent and the stress boundary conditions on fractures.The strain and stress projected along the monitoring well are calculated from these displacement discontinuities at each time step and converted to strain rate by taking their time derivatives.We compared and verified our modeling with field observations from the Hydraulic Fracturing Test Site 2(HFTS2)project,a research experiment performed in the Delaware Basin,West Texas.For a horizontal monitoring well,modeling results explain heart-shaped extending pattern before a fracture hit,polarity flip during stimulation due to fracture interaction,and V-shape patterns when a fracture bypasses the monitoring well from above or below without intersecting.For a vertical monitoring well,modeling shows the different characters of low-frequency DAS and DSS responses when a fracture is near and far away from a vertical monitoring well for both elliptic fractures and layered fractures.Geomechanical modeling lays the groundwork for quantitative interpretation and fracture-geometry estimation.Our modeling approach provides insight into unraveling the patterns observed by far-field low-frequency DAS and DSS during hydraulic fracturing.Synthetic modeling results of various scenarios can also be used to improve fiber-optic acquisition design for stimulation monitoring.Low-frequency DAS and DSS modeling and monitoring integrate information on geomechanics,fluid flow,pressure distribution,earth properties,and fracture propagation.The modeling results and field observations can also be compared and validated with engineering data such as pressure and temperature,with geological data such as cores,and with geophysics data such as microseismic and time-lapse seismic,to provide a comprehensive understanding of hydraulic fractures.
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