Toughness-dominated hydraulic fractures in cohesionless particulate materials.

摘要

In this work we argue that toughness (resistance) to fracture propagation is an inherent characteristic of cohesionless particulate materials. This is significant for understanding hydraulic fracturing in geotechnical, geological, and petroleum applications.;We 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, self-propagating, crack-like conduits. By analogy, we call these conduits 'cracks' or 'hydraulic fractures.' The experiments were performed on three particulate materials -- (1) fine sand, (2) silica flour, and (3) their mixtures. Based on the laboratory observations and scale and dimensional analyses, this work offers physical concepts to explain the observed phenomena. The goal of this study is to determine the controlling parameters of fracture behavior and to quantify their affects.;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 the hydraulic fracture) are likely to be in compression. In solid materials (with limited or no leakoff), the fluid lags behind the front of the propagating fracture. However, for fluid-driven fractures in cohesionless materials the lag zone is absent. The compressive stress state and the absence of the fluid lag are important characteristics of hydraulic fracturing in particulate materials with low, or negligible, cohesion. At present, two kinematic mechanisms of fracture initiation and propagation, consistent with both the compressive stress regime and the absence of the fluid lag, can be offered. The first mechanism is based on shear bands propagating ahead of the tip of an open fracture. The second is based on the reduction of the effective stresses and material fluidization within the leakoff zone at the fracture tip.;Our experimental results show that the primary factor affecting peak (initiation) pressure and fracture aperture is the magnitude of the confining stresses. The morphology of the fracture (and fluid leakoff 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-shoots (i.e., small branches, often seen on only one side of the fracture) and the bluntness of the fracture tip. The latter suggests the importance of inelastic deformation in the process of fracture propagation in cohesionless materials. Similar to solid materials, fractures propagate perpendicular to the least compressive stress.;Scaling indicates that, in experiments performed in the regime of limited leakoff (i.e., the thickness of the leakoff zone is much smaller than the fracture length), there is a high-pressure gradient in the leakoff 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.;The main conclusion of our work is that fractures in cohesionless materials can be considered 'thick.' This implies that the pressure drop in the fracture is insignificant. Therefore, the fractures in our tests can be considered toughness-dominated. Further, the primary parameter in determining the peak injection pressure is that of confining stresses. In this work we present a comprehensive experimental development focusing on four main parameters: confining stresses, fluid rheology, injection rate, and permeability. We use dimensional analysis and scaling relationships and compare our experimental results to a toughness-dominated model of hydraulic fracturing in cohesionless saturated materials. Finally, we compare the developed model to field data.