In this study, a numerical model for simulating hydraulic fracture propagation in porous media formation with natural fracture based on the phase field method is established. In this model, a new regularized fracture width calculation model and element permeability calculation model is proposed. The coupled fluid flow and stress equilibrium nonlinear equations is solved by the Newton-Raphson(NR) method, and the phase field is solved by Picard iteration method. Based on our numerical model, we investigate the influence of approaching angle between hydraulic fracture and natural fracture on the hydraulic fracture geometry. The results indicate that a small approaching angle is beneficial for hydraulic fracture to divert into the natural fracture and activates natural fracture.

1. Introduction

Hydraulic fracturing is an indispensable technology that is used to enhance the production of shale reservoirs (Li, et al.2017a; Lee, et al.2018). The field and laboratory experiment observations indicated that the hydraulic fracture in shale formation is a complex fracture network because of the influence of nature fracture(Blanton,1982; Beugelsdijk, et al.2000; Fisher, et al.2002; Maxwell, et al.2002). In order to provide advice for hydraulic fracture optimization, a large of numerical models have been proposed to investigate the behavior of the interaction between hydraulic fracture and natural fracture. At present, the most popular numerical methods for stimulating hydraulic fracture intersecting with the natural fracture are the displacement discontinuity method(DDM) (Wu and Olson 2015;Tang, et al.,2018), cohesive zone method (CZM) (Guo, et al.,2015;Cordero, et al.,2019),and the extended finite element method(XFEM) (Dahi-Taleghani and Olson,2011; Shi, et al.,2017; Luo, et al.,2018). In recent years, adopting the phase field method(PFM) to simulate hydraulic fracture propagation has attracted the researcher's attention because this method can flexibly handle fracture nucleation, merging and branching under the action of the multi-physical field (Ambati, et al.2015; Nguyen, et al.2016;Xia, et al.,2017). The phase field value 0 and 1 represent the unbroken state and the fully broken state of the material, respectively(Miehe, et al.2010a; Miehe, et al.2010b). The advantages of using phase field method to simulate hydraulic fracture propagation can be summarized as follows:(1) It is not necessary to re-mesh after the fracture extends;(2) the fracture propagation path are automatically determined because the model is purely based on energy minimization(Wheeler, et al. 2014);(3) This method can easily realize the coupling of fluid flow and rock damage in porous media.

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