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Multi-level modeling of hydraulic stimulation using micromechanics and phase-field models

Hydraulic stimulation is frequently used in geoengineering for the exploitation of deep geothermal reservoirs [1]. It is characterized by the fluid-induced opening (and propagation) of fractures to enhance the transport properties of the reservoir. From a modelling perspective, this constitutes a hydro-thermo-mechanical problem to characterize the geothermal reservoir subject to stimulation taking into account the influence of existing fractures, their topological configuration and their interaction with the diffusing fluid. Moreover, due to the large range of scales typically encountered requires a multi-level modelling strategy. To this end, we propose a synthesis of a phase-field model and a micromechanics model to characterize the hydro-thermo-mechanics of individual fractures and reservoirs characterized by diffuse fractures. At the macroscopic scale within a poromechanics context the crack is represented by a damage field, with the fracture surface energy based on the Griffith's criterion and discretized by the phase-field equation [4]. The transport characteristics in the crack channel is modelled using a microporomechanical approach based on the concept of an REV which provides an up-scaled fluid permeability in the fracture zone depending on the microcrack density, which can be related to the degree of damage [2]. The micromechanics based model provides percolation thresholds that depend on the connectivity of the fissure network and the permeability of the porous rock. The micromechanics predictions for the effective permeability are compared with predictions from a computational homogenization using a GFEM/XFEM model [3] for fluid flow in the presence of discrete fractures within an equivalent numerical REV. The model predictions for the hydraulic fracture-fracture interactions for various fracture/joint configurations, influence of the anisotropy of diffuse fissure distribution on the transport and failure characteristics and the connectivity aspects of diffuse fissures are presented in terms of selected numerical experiments.


REFERENCES
[1] G. Zimmermann, A. Reinicke, Hydraulic stimulation of a deep sandstone reservoir to develop an enhanced geothermal system: Laboratory and field experiments, Geothermics 39, 2010, 70–77
[2] J. J. Timothy and G. Meschke, Diffusion in Fracturing Porous Materials: Characterizing Topological Effects using Cascade Micromechanics and Phase-Field Models. Poromechanics V: pp. 2250-2259. July 2013. doi: 10.1061/9780784412992.264
[3] G. Meschke, D. Leonhart, A Generalized Finite Element Method for hydro-mechanically coupled analysis of hydraulic fracturing problems using space-time variant enrichment functions, submitted for publication.
[4] M.J. Borden “A phase-field description of dynamic brittle fracture”, Comput. Methods Appl. Mech. Engrg. 217-220 (2012) 77-95

Author(s):

Jithender Timothy    
Institute for Structural Mechanics, Ruhr University Bochum
Germany

Ildar Khisamitov    
Institute for Structural Mechanics, Ruhr University Bochum
Germany

Dirk Leonhart    
Institute for Structural Mechanics, Ruhr University Bochum
Germany

Günther Meschke    
Institute for Structural Mechanics, Ruhr University Bochum
Germany