Current funding and projects
Simulation of Multiphase Flow and Transport in the Partially Molten Mantle [NSF link]PI: Todd Arbogast (Institute of Computational Engineering and Science, University of Texas at Austin) Project objectives include the development of (1) a mathematical framework for computational simulation of evolving mantle flow which covers the degenerate case of no melt, (2) a numerical method to accurately approximate the transport of temperature and chemical components within the mantle flow, (3) a computer code to implement the flow and transport algorithms, as well as a method for handling simple phase behavior. Furthermore, (4) the code will be applied to study important problems in the geosciences and (5) students will be educated and trained in an interdisciplinary setting. Mathematically speaking, because there are regions with no melt, twophase flow in the mantle is governed by highly degenerate equations. Recent work has established the mathematical foundations of twophase flow when the porosity does not evolve. The key is to scale the solution variables and equations appropriately by the porosity, which is the volume fraction of melt. The evolving case will be treated in this project, with the goal of providing an appropriate computational method for simulating the flow in practical simulations. To model the transport of temperature and the segregation of melt components, appropriate WENO and discontinuous Galerkin methods will be developed for this project, which will respect the possible degeneracies in the porosity. Publications: Hesse & CastilloRogez (2018), 

Bayesian framework for optimal management of waste injection [NSF link]PI: Omar Ghattas (Institute of Computational Engineering and Science, University of Texas at Austin) The focus of the proposed work is on integrating research developments in scientific computing, statistical analysis, and numerical analysis to provide a common platform for waste water storage. Results from this work will be important to energy production in the US, an area of National interest. Geological carbon storage faces two main challenges: the risk of inducing seismicity, and leakage of the injected CO_{2} into potable aquifers. The characterization of the injection site and continued monitoring of the CO_{2} migration as well as stress changes in the region of elevated pressure are therefore particularly important to maximize the amount of CO_{2} that can be stored, while ensuring the long term safety of storage sites. To address these challenges, the overall goal of the proposed research is to (1) integrate well pressure and, where available, surface deformation data into coupled poromechanics models by solving the inverse problem for unknown subsurface properties; (2) to quantify the uncertainty in the inversion for the subsurface properties, and (3) to use the resulting inferred poromechanics models together with their uncertainty to design optimal control strategies for well injection that optimize the amount of stored CO_{2} while controlling the risk of seismicity. It is essential that this poromechanics based inference/prediction/control framework takes into account uncertainties at every stage, since both the observational data and the models are uncertain. However, solving stochastic inverse/optimal control problems for largescale PDE models, such as those of poromechanics, is intractable using current methods, which suffer from the “curse of dimensionality.” Thus, it is proposed to overcome these barriers by developing scalable methods and algorithms that exploit the problem structure to reduce effective dimensionality. While the end application of CO_{2} storage is quite important in itself, the framework to be developed can be applicable to a broader set of science and engineering problems for which largescale uncertain models must be inferred from largescale uncertain data, and then used to solve optimal decisionmaking problems under uncertainty. Publications: Alghamdi et al. (201X) 

Center for Subsurface Energy Security (CFSES II)PI: Larry Lake (Department of Petroleum and Geosystems Engineering, University of Texas at Austin) Grant number: DESC0001114 Description: The Center for Frontiers of Subsurface Energy Security (CFSES) is pursuing scientific understanding of multiscale, multiphysics processes to ensure safe and economically feasible storage of carbon dioxide and other byproducts of energy production without harming the environment. Publications: McNeece and Hesse (2017, 2018), 
Independent funding of graduate students
Injection induced seismicity and coseismic fluid overpressure: Two sides of the same coinGraduate student: Kimberly McCormack Grant type: NSF Graduate Research Fellowship Description: The relation between porous flow, deformation, and seismicity is central to the understanding of natural hazards, and tectonic processes, as well as energy and groundwater resources. The geomechanical coupling is twoway street: One the one hand gradients in fluid pressure can exert forces on the rocks and faults and induce seismic events. On the other hand rock deformation can induce fluid overpressure that can drive largescale flows. Understanding the relation between subsurface fluid flow and induced seismicity is difficult because the interaction of these feedbacks can produce unintuitive results. Advances in satellite geodesy and continuous GPS networks, however, are providing unprecedented information about deformation of the Earth’s surface. Together with advances in seismology these data have the potential to revolutionize our understanding of the coupling between subsurface flow and seismicity. To capitalize on these developments and advance our understanding between subsurface flow and seismicity I propose to integrate geodetic data into geomechanical models using joint and fully coupled inversions. To study the two types of geomechanical coupling I will look at tow phenomena: I) The potential for fluid injection to induce seismic events. II) The potential for large earthquakes to induce flow and fluid. Publications: McCormack et al. (2018, 201X) 
Past funding and projects
Hydrogeochemical dynamics of natural carbon dioxide fields [NSF link]CoPI: David DiCarlo (Department of Petroleum and Geosystems Engineering, University of Texas at Austin) Publications: Sathaye et al. (2016), Ahkbari and Hesse (2016), Liang et al. (2018) 

Trap integrity in salt basins; sub‐salt imaging and seal vs. pore pressure challengesGraduate student: Soheil Ghanbarzadeh 

CSEDI: Constraining the mechanisms of melt transport, storage, and crustal contamination from temporal geochemical variations in monogenetic vents [NSF link]PI: John Lassiter (Department of Geological Sciences, University of Texas at Austin) Publication (with Hesse): Jordan et al. (2018) 

Simulation of Subsurface Geochemical Transport and Carbon SequestrationPI: Mary Wheeler (Department of Mathematics, University of Texas at Austin) Description: This project focuses on the simulation of subsurface transport of geochemical species, especially as applied to carbon sequestration, but also more generally to petroleum reservoirs and water resources, as well as on scientific and engineering computing. We have the following five main objectives:
In addressing the above objectives, we will use the Integrated Parallel Accurate Reservoir Simulator (IPARS), a computational framework developed at UTAustin. It allows us to couple different physical and multiscale models, and it runs efficiently on massively parallel computers. It is ideal for developing and prototyping the new models and algorithms proposed in this project. 

CMG: Robust Numerical Methods for MultiPhase DarcyStokes Flow in Heterogeneous and Anisotropic Partially Molten Materials [NSF link]CoPI: Todd Arbogast (Department of Mathematics, University of Texas at Austin) Publications: Jordan and Hesse (2015), Arbogast and Taicher (2017), Taicher, Arbogast and Hesse (2017), Ghanbarzadeh et al. (2017) 

The interpretation of geochemical patterns through the hyperbolic theory for reactive transport in porous media [ACSlink]Grant number: ACSPRF #51230 DNI8 Publications: 

Characterizing the timedependent flux of CO_{2}saturated brine up a leaky wellGraduate student: Nicolas Huerta Description: The goal of this project is to characterize the fundamental phenomena controlling time dependent leakage of CO_{2} up a leaky well. This work is in collaboration with efforts at NETL and other national laboratories to provide parameters for a higher order risk assessment model to quantify the risk of adverse effects due to geologic carbon storage. This work comprises experiments and numerical modeling to estimate change in leakage rate over time. Specifically, this work looks at the coupling between transport of CO_{2}satuared brine along a cement fracture with the chemical processes of dissolution of some cement phases and precipitation of secondary phases. How the system evolves in time is of critical importance as the coupling determines how the leak will evolve in time, either by selfsealing or selfenhancing. Publications: Huerta et al. (2012), Huerta et al. (2015) 