Events

Speaker:  Dr. Sanghyun Lee, Research Associate in the Center for Subsurface Modeling,  The Institute for Computational Engineering and Sciences (ICES) at the University of Texas at Austin.

Biography:   Dr. Sanghyun Lee is a Research Associate in the Center for Subsurface Modeling,  The Institute for Computational Engineering and Sciences (ICES), at the University of Texas at Austin. Dr. Lee holds a Ph.D degree in Mathematics from Texas A&M University and  BS degrees in Computer Science and Mathematics from South Korea. He has held postdoctoral position with the Center for Subsurface Modeling at ICES/UT-Austin. His research interests include the mathematics and numerical methods of multi physics and multi scale reservoir simulation including hydraulic fracture propagation with proppant transport.

Abstract: The computational modeling of the formation and growth of the fluid filled fractures in poroelastic media is difficult with complex fracture topologies. Here we study the fracture propagation by approximating lower-dimensional fracture surface employing the phase field function. Using energy minimization for fracture propagation has attracted considerable attention in recent years since the pioneering work of Francfort and Marigo [1998] and Bourdin et al. [2000] by employing Griffith’s model [Griffith,1921] and Ambrosio-Tortorelli elliptic functionals [Ambrosio and Tortorelli, 1990].

The major advantages of using phase-field modeling for crack propagation are:
i) it is a fixed-topology approach in which remeshing is avoided,
ii) crack nucleation, propagation path are automatically determined based on energy minimization, that is, calculating stress intensity factors are embedded in the model. This avoids creating unstable solutions and reduces computational costs when applied to complex fracture networks and models that include fluid flow.

In addition iii) joining and branching of multiple cracks also do not require any additional techniques. 

This work presents recent progress in phase-field-based fracture modeling in heterogeneous porous media. 

We develop robust numerical algorithms that can be used for three-dimensional applications and employ fixed stress iteration to solve Biot system which considers both fluid flow in the porous media and the fracture. Recently, this algorithm is extended to consider proppant transport in the fractures. Several numerical examples considering pressurized fractures in heterogeneous media and fluid-filled fracture propagation in porous media substantiate our developments.

This is a joint work with A. Mikelic, M. F. Wheeler, and T. Wick.