We present numerical simulations using a flow-coupled discrete element model, developed by authors, to study the lateral growth and interaction of fluid driven fractures in unconsolidated formations. This new approach accounts for the development of anisotropy in micro-structure that is typical of sands and fractured media. The model is a departure from continuum mechanics approaches and provides a deeper insight into the processes which take place in a particulate system. The paper describes the main features of the flow-coupled discrete element model and presents the simulations of two fractures initiating and propagating in a dense cohesionless granular medium under hydrostatic and non-hydrostatic stress fields.
In order to increase the permeable communication between injection and production wells for enhanced petroleum recovery, it may be desirable to have multiple fractures. Among several different techniques, simultaneous hydraulic fracturing from two neighboring wells has been used to establish communication between wells. The interaction of two fractures passing through dense sands is of interest to the petroleum industry, particularly in relation to poorly consolidated sandstones such as oil sand deposits. Mechanically, poorly consolidated sandstones are dense, low cohesion, granular media (Dusseault and Morgenstern, 1979). A review of crack interactions indicates that most of the published studies are based on conventional continuum mechanics principles and in which few have considered crack interactions in compressive stresses which would be of interest for rock and granular media. The continuum models are phenomenological and are primarily concerned with mathematical modelling of observed phenomenon with- out detailed attention to their fundamental physical significance. However, a realistic behavioral law for poorly consolidated sandstones and dense sands requires descriptions of induced anisotropy, stress path dependency, dilatancy, and confining pressure dependent modulus. Most current models lack one or more of these aspects, hence they cannot explore the physical processes which take place due to the particulate nature of the medium; they can only simulate macroscopic response in cases where granular material behaviour is reasonably emulated by the continuum constitutive law chosen. It is to be expected that interactions within granular media will generally be more complex and varied because the internal stresses are not uniformly applied and the material is anisotropic. Hence, most models cannot cope fully with stress rotations, stress history, and dilation effects. In rock mechanics and petroleum geomechanics, researchers have used glass, photo-elastic and plaster of Paris models to investigate the effects of nearby fractures on both micro-fracture initiation and its subsequent propagation. These tests do produce results which mimic reality, with certain qualifications, but still one may question the relevance of using homogeneous model materials and uniform boundary conditions to model geomaterials. Little information is available concerning the nature of crack-crack interaction in stressed granular media. It is a complicated problem which involves inhomogeneous local stress fields and often an anisotropic medium. In materials dominated by granular behaviour, it is advantageous to treat the medium as an assemblage of particles, rather than as a continuum, as this permits exploration of the actual mechanisms involved.
