Cite this article as: HanYi Wang, Numerical modeling of non-planar hydraulic fracture propagation in permeable medium using XFEM with cohesive zone m e t h o d , Journal of Petroleum Science and Engineering, http://dx. AbstractWith the increasing wide use of hydraulic fracturing in the petroleum industry, it is essential to accurately predict the behavior of fracture propagations based on the understanding of fundamental mechanisms governing the process. For unconventional resources exploration and development, hydraulic fracture pattern, geometry and associated dimensions are critical in determining well stimulation efficiency. In shale formations, non-planar, complex hydraulic fractures are often observed, due to the activation of pre-existing natural fractures. The propagating of turning non-planar fractures due to re-fracturing treatment and unfavorable perforation conditions have also been reported. Current numerical simulation of hydraulic fracturing generally assumes planar crack geometry and weak coupling behaviors, which severely limits the applicability of these methods in predicting fracture propagation under complex subsurface conditions. In addition, the prevailing approach for hydraulic fracture modeling also relies on Linear Elastic Fracture Mechanics (LEFM), which uses stress intensity factor at the fracture tip as fracture propagation criteria. Even though LEFM can predict hard rock hydraulic fracturing processes reasonably, but often fails to give accurate predictions of fracture geometry and propagation pressure in ductile rocks, such as poorly consolidated/unconsolidated sands and ductile shales, even in the form of simple planar geometry. In this study, a fully coupled non-planar hydraulic fracture propagation model in permeable medium based on the Extended Finite Element Method (XFEM) and Cohesive Zone Method (CZM) is developed, which is able to model fracture initiation and propagation in both brittle and ductile formations. To illustrate the capabilities of the presented model, example simulations are presented on both near wellbore and far field scale. The results indicate that the in-elastic deformations induced by propagating hydraulic fracture have significant impact on propagation pressure and fracture geometry, and the prediction of fracture propagation behaviors can be extremely erroneous if ductile formations are simply treated as soft rocks with lower Young's modulus. The method discussed in this article represents a useful step towards the prediction of non-planar, complex hydraulic fractures and can provide us a better guidance of completion design and optimizing hydraulic fracture treatment that will better drain reservoir volume in formations with complex stress conditions and heterogeneous properties.

For unconventional resources exploration and development, hydraulic fracture pattern and associated dimensions are critical in determining well stimulation efficiency and ultimate recovery. When creating arrays of hydraulic fractures along horizontal wells, stress field changes induced by hydraulic fractures themselves can lead to fracture interference and coalescence. The resulting complex fracture geometry may compromise or improve the effectiveness of the stimulation job, depending on the nature of the context. Currently, the prevailing approach for hydraulic fracture modeling also relies on Linear Elastic Fracture Mechanics (LEFM), which uses stress intensity factor at the fracture tip as fracture propagation criteria. Even though LEFM can predict hard rock hydraulic fracturing processes reasonably, but often fails to give accurate predictions of fracture geometry and propagation pressure in quasi-brittle and ductile rocks, such as poorly consolidated sands and clay-rich shales. In this study, a fully coupled hydraulic fracture propagation model based on the Extended Finite Element Method (XFEM), Cohesive Zone Method (CZM) and Mohr-Coulomb theory of plasticity is presented, to investigate the interference and coalescence of fluid-driven hydraulic fractures that initiated from horizontal wells. The results indicate that fracture spacing and the relative timing of fracture initiation control whether the fractures compete against each other to form a divergent pattern or coalesce into a single, primary fracture. Fracture growth can be arrested after fracture tips pass by when simultaneously fracturing adjacent horizontal wells. Even though the in-elastic rock deformation due to shear failure can strongly impact fracture geometry and fracturing pressure, it has limited influence on hydraulic fracture interaction patterns.

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All reservoirs are fractured to some degree. Depending on the density, dimension, orientation and the cementation of natural fractures and the location where the hydraulic fracturing is done, pre-existing natural fractures can impact hydraulic fracture propagation and the associated flow capacity. Understanding the interactions between hydraulic fracture and natural fractures is crucial in estimating fracture complexity, stimulated reservoir volume (SRV), drained reservoir volume (DRV) and completion efficiency. However, what hydraulic fracture looks like in the subsurface, especially in unconventional reservoirs, remain elusive, and many times, field observations contradict our common beliefs. In this study, a global cohesive zone model is presented to investigate hydraulic propagation in naturally fractured reservoirs, along with a comprehensive discussion on hydraulic fracture propagation behaviors in naturally fractured reservoirs. The results indicate that in naturally fractured reservoirs, hydraulic fracture can turn, kink, branch and coalesce, and the fracture propagation path is quite complex, but it does not necessarily mean that fracture networks can be created, even under low horizontal stress difference, because of strong stress shadow effect and flow-resistance dependent fluid distribution. Perhaps, 'complex fracture', rather than 'fracture networks', is the norm in most unconventional reservoirs.

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