Abstract
In this paper, we apply the enhanced local pressure (ELP) model to study crack interaction in hydraulic fracturing. The method is based on the extended finite element method (X-FEM) where the pressure and the displacement fields are assumed to be discontinuous over the fracture exploiting the partition of unity property of finite element shape functions. The material is fully saturated and Darcy’s law describes the fluid flow in the material. The fracture process is described by a cohesive traction-separation law, whereas the pressure in the fracture is included by an additional degree of freedom. Interaction of a hydraulic fracture with a natural fracture is considered by assuming multiple discontinuities in the domain. The model is able to capture several processes, such as fracture arrest on the natural fracture, or hydraulic fractures that cross the natural fracture. Fluid is able to flow from the hydraulic fracture into the natural fracture. Two numerical criteria are implemented to determine whether or not the fracture is crossing or if fluid diversion occurs. Computational results showing the performance of the model and the effectiveness of the two criteria are presented. The influence of the angle between a hydraulic fracture and a natural fracture on the interaction behaviour is compared with experimental results and theoretical data.
Highlights
The technique of hydraulic fracturing can be used to stimulate low permeable gas and oil reservoirs
Tectonic stress rotations tilt the natural fracture network at the time of the fracture formation which may result in tilt fractures that are not aligned with the maximum horizontal stress
Based on the enhanced local pressure model, we present a numerical model to investigate the interaction of multiple cracks in hydraulic fracturing
Summary
The technique of hydraulic fracturing can be used to stimulate low permeable gas and oil reservoirs. The criterion has been validated and extended by means of experiments for non-orthogonal angles by Gu et al [8] by solving the criterion numerically Another mechanism that causes crack tip branching occurs when the fracture propagation speed exceeds the Rayleigh wave speed of the material [9, 10]. Other methods that considered hydraulic fracturing in porous media are, e.g. based on interface elements with a cohesive zone [24], remeshing techniques [25] and phase field approaches [26]. We extend the ELP model to account for multiple, interacting fractures These fractures are included by adding a set of additional degrees of freedom for each fracture. We demonstrate the performance of the model by investigating four numerical examples
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