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In this paper, the problem of a hydraulic fracture interacting with a pre-existing natural fracture has been investigated by using a cohesive zone finite element model. The model fully couples fluid flow, fracture propagation and elastic deformation, taking into account the friction between the contacting fracture surfaces and the interaction between the hydraulic fracture and the natural fracture. The effect of the field conditions, such as in-situ stresses, and rock and fracture mechanical and geometrical properties, intersection angle and the treatment parameters (fracturing fluid viscosity and injection rate) on the hydraulic fracture propagation behavior has been analyzed. The finite element modeling results provide detailed quantitative information on the development of various types of hydraulic fracture – natural fracture interaction, fracture geometry evolution and injection pressure history, and allow us to gain an in-depth understanding of the relative roles of various parameters. The value of a parameter calculated as the product of fracturing fluid viscosity and injection rate can be used as an indicator to gauge if crossing or diverting behavior is more likely. In addition, using a finite element approach allows the analysis to be extended to include the effects of fluid leakoff and poroelastic effect, and to study hydraulic fracture height growth through a system of nonhomogeneous layers and their bedding planes.

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With the wide deployment of renewable energies, future power grids become more vulnerable to extreme environments. This paper investigates enhancing the resilience of power systems with high penetrations of renewable energies under emergencies. The resilience enhancement firstly is defined as maintaining as much electric energy to critical loads in a fixed number of post-disaster periods by properly coordinating the available resources. Then, an optimal decision-making method is proposed to maximize the power supply of critical loads and to minimize the instability risks due to the randomness of the output power of renewable energies. The power consumption of loads, charging/discharging power of power storage plants, power generation of generators, and spinning reserve ratios of the renewable energy at each period are taken as decision variables. Constraints include spinning reserve, power flow constraints, and power consumption/generation limits. The interior-point algorithm is used to solve the formulated optimization problem. Numerical simulations verified the effectiveness and superiority of the proposed optimization method in boosting grid resilience after disasters. It is also found that a balance should be sought between decreasing stability risks and increasing the power supply benefit in extreme environments.