- Department of Mathematics
Modeling and Simulation for Physics Couplings and Subsurface Applications
October 24, 2019
Location: 010 Terrace Room (Paige Hall)
Abstract: Mathematical modeling of complex physical phenomena for predictive understanding is challenging because these problems involve multiple, interacting physical and chemical processes. Multiphysics models need to be developed to simultaneously simulate such processes and their interactions. In this presentation we describe two important subsurface applications, carbon storage and multiphase flow in fractured reservoirs. We discuss core technologies needed by these mathematical models based on laboratory experiments and field data sets, coupled with both computational methods for modeling these physical phenomena and statistical analyses of controlling factors.
Phase Field Modeling for Diffusive Networks and Stimulation in Porous Media
October 25, 2019
Location: Bromfield-Pearson Room 101 (Reception: Conference Room)
Abstract: The phase field method has emerged in recent years as a powerful variational approach to model crack propagation in elastic porous media. The most important feature of this method lies in the fact that it can handle fracture nucleation, propagation, merging, branching, kinking and curvilinear paths without any post-processing or additional computations; these complex fracture paths arise naturally as part of the numerical solution of an underlying partial differential equation. Unlike other computational fracture mechanics approaches, the phase field method does not require modeling the discontinuities in the medium or tracking the crack tip Instead, it introduces a diffusive zone that interpolates between the fracture zone and the intact material. This smears out the sharp crack interfaces that typically introduce singularities in the numerical computations.
In this presentation, a novel computational framework is introduced for simulation of multiphase flow, geomechanics, and fracture propagation in porous media based on Biot's model for poroelasticity. Here, state-of-the-art numerical modeling of natural and hydraulic fractures using a diffusive adaptive finite element phase field approach is employed. Since realistic porous media contains many natural fractures, not only is it important to stimulate hydraulic fractures but also to study the interaction between natural and hydraulic fractures. The enriched Galerkin finite element methods (EG) are employed to model multiphase flow with local mass conservation and dynamic mesh adaptivity. Geomechanics approximated by a continuous Galerkin finite element method is coupled to multiphase flow by applying an iteratively coupled scheme. Numerical examples are presented that demonstrate the effectiveness of this framework for different propagation scenarios, by varying the degrees of physics, and the capabilities to perform high-fidelity simulations on complex fracture networks.
The Norbert Wiener Lectures were initially funded by an anonymous gift to the Department of Mathematics. All talks are free and open to the public.