Crack tip plasticity: a different approach to modelling fracture propagation in soft formations

摘要

Over the last 15 years or so, the numerical simulation of hydraulic fracturing has improved beyond recognition. Considerable time and effort has been spent on the production of these models and on their verification with field trials. In spite of their differences, these models still employ, to a lesser or greater extent, the same basic theory offracture propagation - first put forward in the 1920's and used in the original 2-D fracture models - known as Linear Elastic Fracture Mechanics, or LEFM. Although the various organisations producing fracture propagation models have extensively modified the original LEFM theory, mainly to allow for the effects of non-linearity at the crack tip, the original assumptions of LEFM stil hole true. Failure is by brittle fracture, with no significant plastic deformation of the rock -even at the fracture tip. This assumption is probably valid for most of the formations fractured by the industry today. However, an increasingly important sector of the industry is not stimulating very soft ductile formations, where the assumptions of linear strain and no significant pl;astic deformation are not reliable. Fortunately, LEFM is not the only way to model fracture propagation. The Crack Tip Plasticity (CTP) method assumes a fracture tip of finite radius, with a zone of plastically deformed material around it. This plastic zone acts to absorb extra energy from the fracturing fluid, making it harder to propagate fractures through formations with significant plastic deformation. This in turn means that, for a given ductile material, fractures will be smaller and less conductive than those predicted by LEFM. An understanding of CTP could help predict how much smaller the fracture really is, and could also help explain why LEFM-based fracture simulators cannot adequately model very soft formations.