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Lattice modeling of hydraulic fracture

Characterizing the path of the hydraulic fracture in a heterogeneous medium and the change of the transport properties of this medium is one of the challenges of current research on hydraulic fracturing.
A 2D lattice hydro-mechanical model is used to describe hydraulic fracturing. Natural joints are represented introducing elements with a Mohr-Coulomb behavior. The action of fluid pressure on skeleton is represented using Biot’s theory. The interactions of cracks on fluid flow are represented considering a Couette flow between two parallel plates. Coupling is achieved with a staggered coupling scheme. It has been previously demonstrated that the 2D lattice meso-scale model can capture the failure process at the scale of the heterogeneities with a level of detail that continuum based models cannot provide [1].
In a first part, we present the propagation of fracture restricted to the mechanical case. The influence of a natural joint crossed by the fracture is analyzed with the help of a parametric study. The evolution of the FPZ is also studied using Ripley functions [2]. Ripley’s function provides a tool to extract the evolution of the FPZ upon localization of damage during the fracture process. It provides information concerning the spatial correlations involved during the fracture process. The evolution of these correlations nearby the joint is reported.
In a second part, the hydro mechanical coupling is introduced. We compare the computations performed on the lattices with a mechanical stimulation and a hydraulic stimulation: results concerning characteristic length and hydraulic fracture behavior are discussed. The size of the area concerned by the change of transport properties, the stimulated reservoir volume, with respect to permeability, is analyzed. This parameter is important in order to evaluate the efficiency of the stimulation by hydraulic fracture in the context of tight hydrocarbon reservoirs.

Acknowledgments :
TOTAL Exploration & Production

References
[1] Peter Grassl, David Grégoire, Laura Rojas Solano, and Gilles Pijaudier-Cabot. Meso-scale modelling of the size effect on the fracture process zone of concrete. International Journal of Solids and Structures, 49(13):1818–1827, 2012.
[2] B.D. Ripley, Modelling Spatial Pattern. Journal of the Royal Statistical Society. Series B 39(2):172, 1977.

Author(s):

Gilles Pijaudier-Cabot    
Université de Pau et des Pays de l'Adour
France

Vincent Lefort    
Université de Pau et des Pays de l'Adour
France

David Gregoire    
Université de Pau et des Pays de l'Adour
France