Professor Mary Wheeler
CSEE Webinar
Tuesday, June 14, Noon Central
Dynamic Adaptivity for Coupled Flow and Geomechanics in Unconventional Reservoirs


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Coupled multiphase flow, geochemistry,  and geomechanics models are  receiving growing research interests for applications in unconventional reservoirs that include  geological CO2 sequestration,  geothermal and recently  hydrogen storage.  These multiphysics and multiscale  simulations are computationally expensive and  require preservation of physics, chemistry and biology across spatial and temporal scales.  In  addition, these algorithms must be able to handle efficiently  high performance computing, adaptive mesh refinement and highly nonlinear algebraic systems with rough coefficients..  Additional computational issues include data extraction, optimization, uncertainty quantification and machine learning.  In this presentation we discuss two high fidelity approaches that have been introduced for unconventional reservoirs that show promise for modeling reservoir energy production:  a posteriori error estimation for coupling of multiphase and geomechanics and space time modeling for multiphase flow.

A posteriori error estimates are derived for the Biot’s system solved with a fixed-stress split, the Enriched Galerkin (EG) approximation for the flow equation, and the conforming Galerkin (CG) approximation for the mechanics equation. An upper bound is derived for the error equation, distinguishing different error components, namely the fixed-stress algorithmic error, the time error, the flow error, the penalty jump, and the errors arising from the mechanics equation.

Based on  a posteriori error estimates, a hybrid discretization technique using CG and EG is developed for the flow equation, namely, EG degrees of freedom are only added to  a subset of the computational domain where the pressure jump indicators are large. Furthermore, the computational mesh is adaptively and dynamically modified using the error estimators. An improved three-way coupling algorithm is adopted where new convergence criteria are designed using a posteriori error estimators.

Numerical examples demonstrate the efficiency and effectiveness of the estimators, specifically for unconventional scenarios: The hybridization of EG shows significant improvement of accuracy. The dynamical mesh adaptivity achieves higher solution accuracy with the same degree-of-freedom compared to the non-adaptive case. The new three-way coupling achieves significant speedup while maintaining accuracy compared to fixed-stress split, even in unconventional scenarios.

In this presentation  we also discuss a fully implicit space-time multiscale scheme to improve computational efficiency in solving nonlinear multiphase flow in porous media. Here, error estimators are used for adaptively changing the spatial-temporal mesh. Error estimators are introduced to determine subdomains of the reservoir in which high nonlinearity hinders Newtonian convergence. This is followed by applying local fine timesteps to these marked regions, whereas the remaining regions retain the coarse time scale. Once a temporal discretization is determined for different parts of the reservoir, the spatial mesh is refined for treating saturation fronts. The nonmatching interfaces arising from different temporal and spatial scales are resolved by the enhanced velocity method, The efficiency of this approach is demonstrated for black oil systems.


Mary Fanett Wheeler is an expert in computational science. She has been a member of the faculty at The University of Texas at Austin since 1995 and holds the Ernest and Virginia Cockrell Chair in the departments of Aerospace Engineering and Engineering Mechanics, and Petroleum and Geosystems Engineering. She is also director of the Center for Subsurface Modeling (CSM) at the Oden Institute for Computational Engineering and Sciences . Before joining the faculty at UT Austin, Dr. Wheeler was the Noah Harding Professor in engineering at Rice University in Houston, Texas, and was  the first tenured female associate and full professor in engineering at Rice.

Dr. Wheeler’s research group employs computer simulations to model the behavior of fluids in geological formations. Her particular research interests include numerical solution of partial differential systems with application to the modeling of subsurface flows and parallel computation. Applications of her research include multiphase flow and geomechanics in fractured reservoirs, contaminant transport in groundwater, sequestration of carbon in geological formations.  Dr. Wheeler has published more than 300 technical papers and edited seven books; she is currently an editor of five technical journals.

 Dr. Wheeler is a member of the Society of Industrial and Applied Mathematics and the Society of Petroleum Engineers. She is a Fellow of the International Association for Computational Mechanics and is a certified Professional Engineer in the State of Texas. She was co-organizer of the SIAM Activity Group in the Geosciences, and alongside Dr. Hans van Duijn, started the Journal on Computational Geosciences.

 Dr. Wheeler has served on numerous NSF. DOE. And DOD committees.  For seven years she was the university lead in the DOD User Productivity Enhancement and Technology Transfer Program (PET) in environmental quality modeling.  Dr. Wheeler has served on the Board of Governors for Argonne National Laboratory and   advisory committees for Argonne, Oak Ridge and Pacific National  Laboratories . In 1998, Dr. Wheeler was elected to the National Academy of Engineering. In 2006, she received an honorary doctorate from Technische Universiteit Eindhoven in the Netherlands. In 2008, she received an honorary doctorate from the Colorado School of Mines. In 2009, Dr. Wheeler was honored with the SIAM Geosciences Career Prize, as well as her third IBM Faculty Award. That same year, she was awarded the Theodore von Kármán prize at the SIAM national meeting, recognizing her seminal research in numerical methods for partial differential equations, her leadership in the field of scientific computation and service to the scientific community, and for her pioneering work in the application of computational methods to the engineering sciences. In 2010, she was elected to the American Academy of Arts and Sciences. In 2011, she received a Humboldt award. In February 2013, Dr. Wheeler was selected to receive the Lifetime Achievement Award of the International Society for Porous Media, InterPore. The award is given in recognition of her achievements in the area of subsurface flow and in recognition of her great contribution in increasing the visibility, credibility and prestige of porous media research. In May 2013, Dr. Wheeler received the John von Neumann Medal award from the Unites States Association for Computational Mechanics (USACM). It is the highest award given by USACM to honor individuals who have made outstanding, sustained contributions in the field of computational mechanics over substantial portions of their professional careers. In 2014 she was awarded Honorary Member by the Society of Petroleum Engineers, the highest award bestowed by this society. In 2016, she received the ICES Moncrief Award and in 2017 the University Co-Op Hamilton Book Award. In 2020, she received the Billy & Claude R. Hocott Distinguished Centennial Engineering Research Award.