The distributions of pore pressure and stresses around a fracture are of interest in conventional hydraulic fracturing operations, fracturing during water-flooding of petroleum reservoirs, shale gas, and injection/extraction operations in a geothermal reservoir. During the operations, the pore pressure will increase with fluid injection into the fracture and leak off to surround the formation. The pore pressure increase will induce the stress variations around the fracture surface. This can cause the slip of weakness planes in the formation and cause the variation of the permeability in the reservoir. Therefore, the investigation on the pore pressure and stress variations around a hydraulic fracture in petroleum and geothermal reservoirs has practical applications. The stress and pore pressure fields around a fracture are affected by: poroelastic, thermoelastic phenomena as well as by fracture opening under the combined action of applied pressure and in-situ stress. In our study, we built up two models. One is a model (WFPSD model) of water-flood induced fracturing from a single well in an infinite reservoir. WFPSD model calculates the length of a water flood fracture and the extent of the cooled and flooded zones. The second model (FracJStim model) calculates the stress and pore pressure distribution around a fracture of a given length under the action of applied internal pressure and in-situ stresses as well as their variation due to cooling and pore pressure changes. In our FracJStim model, the Structural Permeability Diagram is used to estimate the required additional pore pressure to reactivate the joints in the rock formations of the reservoir. By estimating the failed reservoir volume and comparing with the actual stimulated reservoir volume, the enhanced reservoir permeability in the stimulated zone can be estimated. In our research, the traditional two dimensional hydraulic fracturing propagation models are reviewed, the propagation and recession of a poroelastic PKN hydraulic fracturing model are studied, and the pore pressure and stress distributions around a hydraulically induced fracture are calculated and plotted at a specific time. The pore pressure and stress distributions are used to estimate the failure potentials of the joints in rock formations around the hydraulic fracture. The joint slips and rock failure result in permeability change which can be calculated under certain conditions. As a case study and verification step, the failure of rock mass around a hydraulic fracture for the stimulation of Barnett Shale is considered. With the simulations using our models, the pore pressure and poro-induced stresses around a hydraulic fracture are elliptically distributed near the fracture. From the case study on Barnett Shale, the required additional pore pressure is about 0.06 psi/ft. With the given treatment pressure, the enhanced permeability after the stimulation of hydraulic fracture is calculated and plotted. And the results can be verified by previous work by Palmer, Moschovidis and Cameron in 2007.

This work shows that toughness (resistance) to fracture propagation is an inherent characteristic of cohesionless particulate materials, which is significant for understanding hydraulic fracturing in geotechnical, geological, and petroleum applications. We have developed experimental techniques to quantify the initiation and propagation of fluid-driven fractures in saturated particulate materials. The fracturing liquid is injected into particulate materials, where the fluid flow is localized in thin crack-like conduits. By analogy, we call them 'cracks' or 'hydraulic fractures'. Based on the laboratory observations and scale analysis, this work offers physical concepts to explain the observed phenomena. When a fracture propagates in a solid, new surfaces are created by breaking material bonds. Consequently, the material is in tension at the fracture tip. In contrast, all parts of the cohesionless particulate material (including the tip zone of hydraulic fracture) are likely to be in compression. In solid materials, the fluid front lags behind the front of the propagating fracture, while the lag zone is absent for fluid-driven fractures in cohesionless materials. The compressive stress state and the absence of the fluid lag are important characteristics of hydraulic fracturing in particulate materials with low, or no, cohesion. Our experimental results show that the primary factor affecting peak (initiation) pressure is the magnitude of the remote stresses. The morphology of fracture and fluid leak-off zone, however, changes significantly not only with stresses, but also with other parameters such as flow rate, fluid rheology, and permeability. Typical features of the observed fractures are multiple off-shots and the bluntness of the fracture tip. This suggests the importance of inelastic deformation in the process of fracture propagation in cohesionless materials. Similar to solid materials, fractures propagated perpendicular to the least compressive stress. However, peak injection pressures are significantly greater than the maximum principle stresses in the experiments. Further, by incorporating the dominate experimental parameters into dimensionless form; a reasonable power-law fit is achieved between a dimensionless peak injection pressure and dimensionless stress. Scaling indicates that there is a high pressure gradient in the leak-off zone in the direction normal to the fracture. Fluid pressure does not decrease considerably along the fracture, however, due to the relatively wide fracture aperture. This suggests that hydraulic fractures in unconsolidated materials propagate within the toughness-dominated regime. Furthermore, the theoretical model of toughness-dominated hydraulic fracturing can be matched to the experimental pressure-time dependences with only one fitting parameter. Scale analysis shows that large apertures at the fracture tip correspond to relatively large 'effective' fracture (surface) energy, which can be orders of magnitude greater than typical for hard rocks.

[pt] Um dos principais objetivos da engenharia de petróleo é desenvolver e aplicar técnicas capazes de aumentar a produtividade de poços de petróleo, incluindo a estimulação do poço por operações de fraturamento hidráulico. Estudos sobre a propagação de fraturas podem ser feitos analiticamente para algumas situações simplificadas envolvendo homogeneidade, isotropia e condições de contorno simples do meio geológico, ou pela aplicação de métodos numéricos, como o método dos elementos finitos, para casos mais complexos. A presente pesquisa apresenta análise numérica de fraturamento hidráulico utilizando o método estendido dos elementos finitos (XFEM), em conjunto com o modelo constitutivo de dano da Zona Coesiva (MZC). No método estendido dos elementos finitos a geometria da fratura se torna independente da malha, permitindo a propagação da fratura através do domínio, dispensando sucessivas gerações de malha necessárias na aplicação do método convencional dos elementos finitos. Os resultados numéricos obtidos foram comparados com soluções analíticas assintóticas no caso limite em que o regime da propagação é dominado pela rigidez da rocha, obtendo uma boa concordância. Adicionalmente, foram investigados os efeitos de diferentes parâmetros do fluido de injeção e as características de propagação da fratura quando a interface entre diferentes camadas geológicas é inclinada, mostrando dependência do ângulo de inclinação, das propriedades do material e das tensões in-situ. / [en] One of the main objectives of petroleum engineering is to develop and apply techniques capable of increasing the productivity of oil wells, including the stimulation of well by hydraulic fracturing operations. Studies on the propagation of fractures can be done analytically for some simplified situations involving homogeneity, isotropy and simple boundary conditions of the geological medium, or by the application of numerical methods, such as the finite element method, for more complex cases. The present research presents a numerical analysis of hydraulic fracturing using the extended finite element method (XFEM), in conjunction with the damage constitutive model of Cohesive Zone (MZC). In the extended finite element method the fracture geometry becomes independent of the mesh, allowing the propagation of the fracture through the domain without successive mesh generations as necessary in the conventional finite element method. The computed numerical results were compared with asymptotic analytical solutions in the limit case in which the propagation regime is dominated by the rigidity of the rock with good compatibility. In addition, this study investigates the effects of different parameters of the injection fluid and the fracture propagation characteristics when the interface between different geological layers is inclined, shows dependency between the angle of inclination with the properties of the material and the in-situ stresses.