# Numerical study of damage mechanism around the fracture tip with irregular overpressure distribution in hydraulic fracturing

• Zhigang Zhang

Student thesis: Master's Thesis

### Abstract

Hydraulic fracturing has been widely used to stimulate unconventional oil and gas reservoir with low permeability. Simulation of hydraulic fracture has become a very important part to successfully develop unconventional gas from tight formations. One of the most pervasive theories used in hydraulic fracture simulation is the Linear Elastic Fracture Mechanics (LEFM). However, when the damaged area around the fracture tip becomes large, the LEFM breaks down. Under this condition, plastic deformation has to be considered. This work dedicates to investigate the damage mechanism around the fracture tip by the study of the fracture process zone and the singularity dominated zone with irregular overpressure distribution inside hydraulic fracture for unconventional reservoir. First, sizes of the fracture process zones and the singularity dominated zones under constant fracture pressure are calculated based on calculations of the full stress field and the singularity dominated stress field around the fracture tip for nine scenarios. Two types of fracture process zones are defined according to different rock failure criteria. Second, the effects of reservoir pressure, faulting condition, fracture pressure and rock properties on the sizes of the fracture process zone and the singularity dominated zone are fully analyzed to investigate the dominating factors. Third, Fourier cosine series, which can represent all functions, is chosen to represent irregular pressure variation inside fracture. Meanwhile, Gauss-Laguerre method is employed to numerically solve the derived full stress equations with infinite integration. Based on the irregular overpressure resulted full stress field and the singularity dominated stress field, sizes of the fracture process zone and the singularity dominated zone are calculated. Finally, the damage mechanism around the fracture tip is studied based on the sizes of the fracture process zone and the singularity dominated zone. In this work, the fracture process zone dominates singularity dominated zone around the fracture tip under all investigated conditions. The inappropriate use of the LEFM is mainly due to the tensile failure of the rock. Based on the sensitive analysis, fracture pressure and minimal principal stress prove to be the dominating factors affecting the applicability of the LEFM. When the irregular overpressure distribution is considered, difference between the fracture process zone and the singularity dominated zone become larger. It means more attention should be paid for the use of the LEFM in hydraulic fracture modelling. According to the damage mechanism around the fracture tip, high tensile strength, high reservoir pressure, low minimal principal stress and low fracture pressure are suggested to achieve better reliability of using the LEFM for hydraulic fracture modelling. A field study for the first Abu Dhabi offshore hydraulic fracturing is also conducted. The result is consistent with the former conclusions. The presented work can be used to understand the damage mechanism around the fracture tip under similar conditions for improved modelling of hydraulic fracturing. The conclusions add to our understanding of the LEFM and assist in the modelling of hydraulic fracturing.
Date of Award 2015 American English MD Rahman (Supervisor)

### Keywords

• Applied sciences
• Fracture mechanics
• Irregular peressure
• Petroleum engineering
• Stress field
• Unconventional reservoir
• 0765:Petroleum engineering

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