Weakly-consolidated sands are dense granular assemblies, held together by a combination of external forces, weak inter-particles cohesion and particle interlocking.

Fluid injected into such media at low pressure can be transported as through any porous solid with a Darcy-like flow. High-pressure fluids, however, displace particles and generate "fractures", through which the flow is enhanced. The geometry of such fractures is complex, often consisting of branched morphologies.

We study the fracture opening and fluid flow during such processes. We assume that a process zone develops in front of the boundary of the fractures. In such a zone, elevated stresses rearrange grains, generating small voids. The opening of such `baby voids’ modifies the local mechanical properties, as well as the local permeability to fluid flow. This, in turn, affects the local pressure field, necessitating a self-consistent modelling.

Here, we present a modified invasion percolation model for this process. The system is characterised by its permeability and the stress distribution in a lattice-based solid. The growth of the connected void clusters modifies the mechanical and flow properties, which combines with the connected cluster geometry to evolve the growth probability distribution at the fracture front. This allows us to gain insight into the effects of the initial distribution of baby voids and the solid stress distribution on the fracture geometry.

We compare the statistics of the fracture surfaces, obtained from this model, with those obtained from numerical models, based on CFDEM open source engine [1], which is a coupled implementation of a computational fluid dynamics (CFD) and discrete element method (DEM).

References:

[1] Goniva, Christoph, et al. "Influence of rolling friction on single spout fluidized bed simulation." Particuology 10.5 (2012): 582-591; DOI 10.1016/j.partic.2012.05.002