Résumé
Hydraulic fracturing has wide engineering applications including exploration ofunconventional resources, Enhanced Geothermal System, storage of radioactive wasteand mining. It is a multi-physics and multi-scale problem which makes it difficult to beevaluated numerically. The multi-physics nature is arisen from coupling of at least threephysical processes – deformation of rock under applied stress, fracture propagation andfluid flow along fracture while the multi-scales nature comes from the presence ofdiscontinuities in different scales in rock mass. Also, fracture growth is highly sensitive toexisting discontinuities which either enhance or suppress the growth. In this paper, asimple discontinuum numerical method – Lattice Element Method (LEM) is proposed tosimulate hydraulic fracturing in large scale three-dimensional model. Rock is modelled aslattice network composed of 1D Hookean’s springs. Fracturing is modelled by removinglattice exceeding a threshold as determined by critical energy release rate of rock. Byintroducing disorder in the model, the heterogeneity of rock is modelled and meshdependency in fracture growth is removed. Disordered network is generated by Delaunaytriangulation of randomly generated nodes and geometries of Voronoi cells are used forscaling of lattice stiffness and breaking threshold to match macroscopic parameters.Complicated fracture evolution like fracture branching and fracture coalescence can bemodelled by LEM. Fluid flow along fractures is simplified as pipe network and cubic lawmodel is used to relate the dependency between fluid transmissivity and aperture offracture. An in-house C++ code using parallel conjugate solver is developed which iscapable to handle large scale three-dimensional models composed of millions of degree offreedom running thousands of steps. LEM simulations of hydraulic fracturing underdifferent pre-existing fractures and different in-situ stress are presented to demonstrate thefeasibility and potential of LEM to model field scale problem in three dimensions withconsideration of heterogeneity of rock and influence of fracture networks.