1 Mary F. Wheeler 1, Sanghyun Lee 1 With Nicholas Hayman 2, Jacqueline Reber 3, Thomas Wick 4 1 Center for Subsurface Modeling, University of Texas at Austin 2 UTIG, University of Texas at Austin 3 Iowa State University, 4 RICAM, Austria March 3, 2016

Challenge 1: Sustaining Large Storage Rates Challenge 2: Using pore space with unprecedented efficiency Challenge 3: Controlling undesired or unexpected behavior Theme 1 Fluid-Assisted Geomechanics Chemo-mechanical coupling during fracture propagation Chemo-mechanical effects on reservoir rock weakening --- Coupled chemo- mechanical processes in shale caprock Pressure and Fluid-Driven Fracture Propagation in Porous Media Using an Adaptive Finite Element Phase Field Model 2 Hayman – theoretical fracture mechanics Wheeler – continuum and fracture modeling Lee – phase field fracture network modeling Reber – experimental fracture, rheology Senior Personnel Post-Docs

3 Control fracture propagation in the reservoir. Activity Objectives Improve Storage Efficiency Predict solubility trapping Predict mineral trapping Enhance capillary (ganglion) trapping Control Emergence Prevent unexpected migration of CO 2 Sustain Injectivity Enhance permeability/avoid precipitation during injection CHALLENGES Control pathway development Guide injection limits Control wellbore failure Improve sweep efficiency Prevent unwanted fracturing

Phase Field Model 4 Variational methods based on energy minimization. Diffusive crack zones for free discontinuity problems. Γ-Convergent approximation. [Ambrosio-Tortorelli 1992] Classical theory of crack propagation. [Griffith 1921] Variational methods based on energy minimization. [Francfort-Marigo 2003], [Miehe et al 2010] [Real fractures] [Interface approach] [Diffusive approach using Phase field]

Advantages of Phase Field Model 5 Before JoiningAfter JoiningBranching Fixed-topology approach avoids re-meshing Determine crack nucleation, propagation, and the path automatically Simple to handle joining and branching of (multiple) cracks Promising findings for future ideas as an indicator function based on theory and numerical simulations Heterogeneous Media Initial Fractures

Verification 6 Sneddon’s test [Sneddon-Lowengrub 1969] Crack opening displacement

Validation 7 Experimental Validation using gelatin [L.-Reber-Wheeler-Hayman] Great Lakes gelatin, USA Mixed at 3 wt% with DI H 2 O E = 10 5, = 0.48 = 1.96 α = 0.3, 0.6, 0.9 m α m

Numerical Examples 8 3 parallel fractures in 3D domain Not all fractures are growing because of the stress-shadowed effect. Fractures Horizontal well

Numerical Examples 9 Multiple cracks in 3D heterogeneous media Dynamic mesh adaptivity: predictor-corrector method [Heister-Wheeler-Wick, 2014] Heterogeneous Young’s Modulus Adaptive Mesh Fractures

Numerical Examples 10 A fracture in layered media with different fracture toughness values = 100 Pa m Fracture = 1 Pa m Injection well

Coupling with a probability map [L.-Wheeler-Wick-Srinivasan] Further Related Extensions 11 Probability map InSAR (Surface Deformation Map) Initialize hydraulic fractures. Interactions with natural fractures.

12 Activity Achievement Improve Storage Efficiency Predict solubility trapping Predict mineral trapping Enhance capillary (ganglion) trapping Control Emergence Prevent unexpected migration of CO 2 Sustain Injectivity Enhance permeability/avoid precipitation during injection CHALLENGES Control pathway development Guide injection limits Control wellbore failure Improve sweep efficiency Prevent unwanted fracturing Scientific Achievement 3D non planar fracture propagation. Joining and branching in heterogeneous media. Coupling pressure diffraction equation to a fully-coupled displacement- phase field. Significance Impact and future work Interactions between hydraulic fractures and natural fractures. Couple phase field fracture with reservoir simulator to do realistic scenarios (well failures, CO 2 sequestrations). Chemicals, thermal, etc. Related Publications partially supported by CFSES Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model. [L.-Wheeler-Wick], CMAME 2016 Initialization of phase-field fracture propagation in porous media using probability maps of fracture networks. [L.-Wheeler-Wick-Srinivasan], in revision A Locally Conservative Enriched Galerkin Approximation and User-Friendly Efficient Solver for the Parabolic Problems. [L.-Lee-Wheeler], in revision Experimental validation of a phase field method for fracture propagation using gelatin [L.Reber-Wheeler-Hayman], in preparation

Thank You for Your Attention. 13

Numerical Examples 14 Multiple fractures propagating near the well bore. Pressure Fractures

Numerical Examples 15 Experimental validation using gelatin [L.-Reber-Wheeler-Hayman] α = 0.3 m α = 0.6 m α = 0.9 m Force (N) Displacement [mm] Force (N)

Phase Field Modeling (Back Up Slides) 16 A fluid filled fracture with maximum pressure values Governing System: Biot’s System Pressure Diffraction System Mechanics and Phase Field Poro-elasticity Newton Iteration Primal-dual Active Set Method a) Phase Field b) Pressure The pressure drops when the fracture starts to propagate.

Phase Field Modeling (Back Up Slides) 17 Energy Functional [Ambrosio-Tortorelli 1992] [Francfort-Marigo, 1998] Variables

Phase Field Modeling (Back Up Slides) 18 Energy Functional [Ambrosio-Tortorelli 1992] [Francfort-Marigo, 1998] Global Constitutive Dissipation Functional [Miehe et al. 2013] [Mikelić-Wheeler-Wick, 2014]

Phase Field Modeling (Back Up Slides) 19 Pressure Diffraction Problem [Mikelić-W.-Wick, 2015] Variables ρ : fluid density ϕ ⋆ : fluid volume fraction v : velocity K : permeability η : fluid viscosity M : Biot modulus q : source/sink term corresponding to injection/production well (Peaceman, 1978)