Prediction of flow, transport, and deformation in fractured and porous media is critical to improving our scientific understanding of coupled thermal-hydrological-mechanical processes related to subsurface energy storage and recovery, nonproliferation, and nuclear waste storage. Especially, earth rock response to changes in pressure and stress has remained a critically challenging task. In this work, we advance computational capabilities for coupled processes in fractured and porous media using Sandia Sierra Multiphysics software through verification and validation problems such as poro-elasticity, elasto-plasticity and thermo-poroelasticity. We apply Sierra software for geologic carbon storage, fluid injection/extraction, and enhanced geothermal systems. We also significantly improve machine learning approaches through latent space and self-supervised learning. Additionally, we develop new experimental technique for evaluating dynamics of compacted soils at an intermediate scale. Overall, this project will enable us to systematically measure and control the earth system response to changes in stress and pressure due to subsurface energy activities.
Accurate modeling of subsurface flow and transport processes is vital as the prevalence of subsurface activities such as carbon sequestration, geothermal recovery, and nuclear waste disposal increases. Computational modeling of these problems leverages poroelasticity theory, which describes coupled fluid flow and mechanical deformation. Although fully coupled monolithic schemes are accurate for coupled problems, they can demand significant computational resources for large problems. In this work, a fixed stress scheme is implemented into the Sandia Sierra Multiphysics toolkit. Two implementation methods, along with the fully coupled method, are verified with one-dimensional (1D) Terzaghi, 2D Mandel, and 3D Cryer sphere benchmark problems. The impact of a range of material parameters and convergence tolerances on numerical accuracy and efficiency was evaluated. Overall the fixed stress schemes achieved acceptable numerical accuracy and efficiency compared to the fully coupled scheme. However, the accuracy of the fixed stress scheme tends to decrease with low permeable cases, requiring the finer tolerance to achieve a desired numerical accuracy. For the fully coupled scheme, high numerical accuracy was observed in most of cases except a low permeability case where an order of magnitude finer tolerance was required for accurate results. Finally, a two-layer Terzaghi problem and an injection–production well system were used to demonstrate the applicability of findings from the benchmark problems for more realistic conditions over a range of permeability. Simulation results suggest that the fixed stress scheme provides accurate solutions for all cases considered with the proper adjustment of the tolerance. This work clearly demonstrates the robustness of the fixed stress scheme for coupled poroelastic problems, while a cautious selection of numerical tolerance may be required under certain conditions with low permeable materials.
To mitigate adverse effects from molten corium following a reactor pressure vessel failure (RPVF), some new reactor designs employ a core catcher and a sacrificial material (SM), such as ceramic or concrete, to stabilize the molten corium and avoid containment breach. Existing reactors cannot easily be modified to include these SMs but could be modified to allow injectable cooling materials. Current reactor designs are limited to using water to stabilize the corium, but this can create other issues such as reaction of water with the concrete forming hydrogen gas. The novel SM proposed here is a granular carbonate mineral that can be used in existing light water reactor plants. The granular carbonate will decompose when exposed to heat, inducing an endothermic reaction to quickly solidify the corium in place and producing a mineral oxide and carbon dioxide. Corium spreading is a complex process strongly influenced by coupled chemical reactions, including decay heat from the corium, phase change, and reactions between the concrete containment and available water. A recently completed Sandia National Laboratories laboratory directed research and development (LDRD) project focused on two research areas: experiments to demonstrate the feasibility of the novel SM concept, and modeling activities to determine the potential applications of the concept to actual nuclear plants. Small-scale experiments using lead oxide (PbO) as a surrogate for molten corium demonstrate that the reaction of the SM with molten PbO results in a fast solidification of the melt due to the endothermic carbonate decomposition reaction and the formation of open pore structures in the solidified PbO from CO2 released during the decomposition. A simplified carbonate decomposition model was developed to predict thermal decomposition of carbonate mineral in contact with corium. This model was incorporated into MELCOR, a severe accident nuclear reactor code. A full-plant MELCOR simulation suggests that by the introduction of SM to the reactor cavity prior to RPVF ex-vessel accident progression, e.g., core-concrete interaction and core spreading on the containment floor, could be delayed by at least 15 h; this may be enough for additional accident management to be implemented to alleviate the situation.
Recent advances in drilling technology, especially horizontal drilling, have prompted a renewed interest in the use of closed loop geothermal energy extraction systems. Deeply placed closed loops in hot wet or dry rock reservoirs offer the potential to exploit the vast thermal energy in the subsurface. To better understand the potential and limitations for recovering thermal and mechanical energy from closed-loop geothermal systems (CLGS), a collaborative study is underway to investigate an array of system configurations, working fluids, geothermal reservoir characteristics, operational periods, and heat transfer enhancements (Parisi et al., 2021; White et al., 2021). This paper presents numerical results for the heat exchange between a closed loop system (single U-tube) circulating water as the working fluid in a hot rock reservoir. The characteristics of the reservoir are based on the Frontier Observatory for Research in Geothermal Energy (FORGE) site, near Milford Utah. To determine optimal system configurations, a mechanical (electrical) objective function is defined for a bounded optimization study over a specified design space. The objective function includes a surface plant thermal to mechanical energy conversion factor, pump work, and an energy drilling capital cost. To complement the optimization results, detailed parametric studies are also performed. The numerical model is built using the Sandia National Laboratories (SNL) massively parallel Sierra computational framework, while the optimization and parametric studies are driven using the SNL Dakota software package. Together, the optimization and parametric studies presented in this paper will help assess the impact of CLGS parameters (e.g., flow rate, tubing length and diameter, insulation length, etc.) on CLGS performance and optimal energy recovery.
The catastrophic nuclear reactor accident at Fukushima damaged public confidence in nuclear energy and a demand for new engineered safety features that could mitigate or prevent radiation releases to the environment in the future. We have developed a novel use of sacrificial material (SM) to prevent the molten corium from breaching containment during accidents as well as a validated, novel, high-fidelity modeling capability to design and optimize the proposed concept. Some new reactor designs employ a core catcher and a SM, such as ceramic or concrete, to slow the molten corium and avoid the breach of the containment. However, existing reactors cannot easily be modified to include these SMs but could be modified to allow injectable cooling materials (current designs are limited to water). The SM proposed in this Laboratory Development Research and Development (LDRD) project is based on granular carbonate minerals that can be used in existing light water reactor plants. This new SM will induce an endothermic reaction to quickly freeze the corium in place, with minimal hydrogen explosion and maximum radionuclide retention. Because corium spreading is a complex process strongly influenced by coupled chemical reactions (with underlying containment material and especially with the proposed SM), decay heat and phase change. No existing tool is available for modeling such a complex process. This LDRD project focused on two research areas: experiments to demonstrate the feasibility of the novel SM concept, and modeling activities to determine the potential applications of the concept to actual nuclear plants. We have demonstrated small-scale to large-scaled experiments using lead oxide (Pb0) as surrogate for molten corium, which showed that the reaction of the SM with molten Pb0 results in a fast solidification of the melt and the formation of open pore structures in the solidified Pb0 because of CO 2 released from the carbonate decomposition. Our modeling simulations show that Sierra Mechanics/Aria code can be used to model a molten corium spreading experiment and the PbO/carbonate experiment. A simplified carbonate decomposition model has been developed to predict thermal decomposition of carbonate mineral in contact with corium. This model has been incorporated into an input model for MELCOR, a severe accident nuclear reactor code developed by Sandia National Laboratories for the U.S. Nuclear Regulatory Commission. A full-plant MELCOR simulation suggests that the ex-vessel accident progression, e.g., core-concrete interaction and core spreading on the containment floor, could be significantly delayed by the introduction of SM to the reactor cavity prior to the reactor pressure vessel failure. Delays of one and half day are suggested with limited SM. Filling the cavity with SM might delay progression by days. Additionally, the modeling suggests that the relative concentration (molar fraction) of hydrogen in containment could be substantially reduced by the non-condensable gas (CO 2 ) generation associated with the SM reaction effectively making the hydrogen concentration below its flammable limit. ACKNOWLEDGEMENTS This research was supported by the Laboratory Directed Research and Development Program of Sandia National Laboratories (Sandia). The authors would like to express thanks to all Sandia staff who helped with this research, including Ms. Denise Bencoe for assisting with the performance of the small-scaled experiments at Advanced Material Laboratories, Ms. Amanda Sanchez and Ms. Lydia Boisvert for grinding all natural carbonate materials and sieving, Dr. Anne Grillet for measuring the microstructure of the samples using X-ray micro CT Scan (SKYSCAN 1272), Dr. Clay Payne for the XRD measurement, Dr. Eric Lindgren for assisting the selection of crucible materials, Dr. Larry Humphries for review this report and Dr. Randall O. Gauntt for reviewing this research, who has retired from Sandia at the time of this publication. The authors like to thank Ms. Laura Sowko for editing this report. Additionally, the authors appreciated the use of the FARO L-26S data information described in Section 4.2.2.1 of this report downloaded from STRESA, Joint Research Centre, European Commission (c) Euratom, 2019.
When the core is breached during a severe nuclear accident, a molten mixture of nuclear fuel, cladding, and structural supports is discharged from the reactor vessel. This molten mixture of ceramic and metal is often referred to as “corium”. Predicting the flow and solidification of corium poses challenges for numerical models due to the presence of large Peclet numbers when convective transport dominates the physics. Here, we utilize a control volume finite-element method (CVEM) discretization to stabilize the advection dominated flow and heat transport. This CVFEM approach is coupled with the conformal decomposition finite-element method (CDFEM), which tracks the corium/air interface on an existing background mesh. CDFEM is a sharp-interface method, allowing the direct discretization of the corium front. This CVFEM-CDFEM approach is used to model the spreading of molten corium in both two- and three-dimensions. The CVFEM approach is briefly motivated in a comparison with a streamwise upwind/Petrov-Galerkin (SUPG) stabilized finite-element method, which was not able to suppress spurious temperature oscillations in the simulations. Our model is compared directly with the FARO L26 corium spreading experiments and with previous numerical simulations, showing both quantitative and qualitative agreement with those studies.