# title
Investigation of Strain Fields Generated by Hydraulic Fracturing with Analytical and Numerical Modeling of Fiber Optic Response

# abstract
<jats:title>Summary</jats:title>                <jats:p>The use of fiber optics in reservoir surveillance is bringing valuable insights into fracture geometry and fracture-hit identification, stage communication, and perforation cluster fluid distribution in many hydraulic fracturing processes. However, given the complexity associated with field data, its interpretation is a major challenge faced by engineers and geoscientists. In this work, we propose to generate distributed strain sensing (DSS)/distributed acoustic sensing (DAS) synthetic data of a crosswell fiber deployment that incorporates the physics governing hydraulic fracturing treatments. Our forward modeling can be used to add value to the interpretation task.</jats:p>                <jats:p>The forward modeling is based on analytical and numerical solutions. The analytical solution is developed integrating two models: 2D fracture (e.g., Khristianovic-Geertsma-de Klerk known as KGD) and Sneddons induced stress. DSS is estimated using the plane strain approach that combines calculated stresses and rock properties (e.g., Youngs modulus and Poissons ratio). On the other hand, the numerical solution is implemented using the displacement discontinuity method (DDM), a type of boundary element method, with net pressure and/or shear stress as the boundary condition. In this case, the fiber gauge length concept is incorporated deriving displacement (i.e., DDM output) in space to obtain DSS values. In both methods, DAS is estimated by the differentiation of DSS in time.</jats:p>                <jats:p>The analytical technique considers a single fracture opening and is used in a sensitivity analysis to evaluate the impact that rock/fluid parameters can promote on strain time histories. Moreover, advanced cases including multiple fractures failing in tensile or shear mode are simulated applying the numerical technique. Results indicate that our models are able to capture typical characteristics present in field data: heart-shaped pattern from a fracture approaching the fiber, stress shadow, and fracture hits. In particular, the numerical methodology captures relevant phenomenon associated with hydraulic and natural fractures interaction, which is often interpreted purely in terms of opening fractures.</jats:p>                <jats:p>We can anticipate that the developed forward modeling, when embedded in a classification or regression artificial intelligence framework, will be an important tool adding substantial insights related to field fracture systems that ultimately can lead to production optimization. Also, the development of specific packages (commercial or otherwise) that explicitly model both DSS and DAS, incorporating the impact of fracture opening and slippage on strain and strain rate is still in its infancy. This paper is novel in this regard and opens up new avenues of research and applications of synthetic DAS/DSS in hydraulic fracturing processes.</jats:p>

# authors[].organizations[].label
Texas A&M Engineering Experiment Station (TEES)

# keywords[]
4019 Resources Engineering And Extractive Metallurgy

# authorList[]
Gurjao, K., Gildin, E., Gibson, R., & Everett, M.