Development of a robust numerical simulator for mixed shear and opening modes fluid driven fracture propagation along pre-existing discontinuities
Authors: Lecampion Brice , Sáez Alexis , Fakhretdinova Regina , Gupta Ankit 
Published: February 2023

Hydraulic stimulation of pre-existing fractures is used in deep geothermal development in order to increase reservoir permeability and achieve economical flow rates &#8211; with mixed success [1, 2]. Although the primary idea is to shear dilate these pre-existing discontinuities via injection, in a number of field tests [3], a large increase of permeability is only observed when fracture opening has been reached (sometimes denoted as hydraulic jacking). Shearing of pre-existing discontinuities can also occur during more traditional hydraulic fracturing operations in oil and gas reservoirs, either by direct fluid pressurization or via stress transfer from the main fractures. In this contribution, we discuss the development of a robust numerical solver for the modeling of the fluid-driven growth of a shear crack along frictional discontinuities, accounting for shear-induced dilatancy as well as possible transition to opening hydraulic fracturing. An elasto-plastic constitutive relation with a non-associated flow rule is used to model the frictional and cohesive behavior of the pre-existing discontinuity with or without slip-dependent frictional properties. A fully coupled hydro-mechanical solver is developed for this class of problem. It combines a boundary element discretization of the fracture(s) for the solution of the quasi-static elastic equilibrium of the rock mass with a finite element discretization of the width-averaged fluid mass conservation and momentum in the fractures. Using implicit time-stepping, the resulting non-linear system of coupled equations is solved via a Newton-Raphson procedure using the consistent tangent elasto-plastic operator obtained from the local integration of the interfacial constitutive relation via a predictor-corrector scheme. We present a number of stringent verification problems for strictly frictional as well as strictly hydraulic fracturing conditions. We then investigate the evolution of both the shear and opening front in terms of the properties of the pre-existing discontinuities (friction and dilatancy), the in-situ and injection conditions [4, 5, 6]. We highlight relevant conditions associated with deep geothermal reservoirs, and discuss the occurrence of different propagation regimes from purely frictional to hydraulic fracturing type.References[1] R. Jung. EGS - Goodbye or Back to the Future. In ISRM International Conference for Effective and Sustainable Hydraulic Fracturing. International Society for Rock Mechanics, 2013.[2] M. W. McClure and R. N. Horne. An investigation of stimulation mechanisms in Enhanced Geothermal Systems. Int. J. Rock Mech. Min. Sci., 72:242&#8211;260, 2014.[3] Y. Guglielmi, C. Nussbaum, P. Jeanne, J. Rutqvist, F. Cappa, and J. Birkholzer. Complexity of fault rupture and fluid leakage in shale: Insights from a controlled fault activation experiment. Journal of Geophysical Research: Solid Earth, 2020.[4] K. Hayashi and H. Abe. Opening of a fault and resulting slip due to injection of fluid for the extraction of geothermal heat. Journal of Geophysical Research: Solid Earth, 87(B2):1049&#8211;1054, 1982.[5] A. S&#225;ez, B. Lecampion, P. Bhattacharya, and R. Viesca. Three-dimensional fluid-driven stable frictional ruptures. J. Mech. Phys. Sol., 160:104754, 2022.[6] E. Detournay. Mechanics of hydraulic fractures. Annual Review of Fluid Mechanics, 48:311&#8211;339, 2016.