The heat generated by high-level radioactive waste can pose numerical and physical challenges to subsurface flow and transport simulators if the liquid water content in a region near the waste package approaches residual saturation due to evaporation. Here, residual saturation is the fraction of the pore space occupied by liquid water when the hydraulic connectivity through a porous medium is lost, preventing the flow of liquid water. While conventional capillary pressure models represent residual saturation using asymptotically large values of capillary pressure, here, residual saturation is effectively modeled as a tortuosity effect alone. Treating the residual fluid as primarily dead-end pores and adsorbed films, relative permeability is independent of capillary pressure below residual saturation. To test this approach, PFLOTRAN is then used to simulate thermal-hydrological conditions resulting from direct disposal of a dual-purpose canister in unsaturated alluvium using both conventional asymptotic and revised, smooth models. Importantly, while the two models have comparable results over 100 000 years, the number of flow steps required is reduced by approximately 94%.
This report describes research and development (R&D) activities conducted during Fiscal Year 2023 (FY23) in the Advanced Fuels and Advanced Reactor Waste Streams Strategies work package in the Spent Fuel Waste Science and Technology (SFWST) Campaign supported by the United States (U.S.) Department of Energy (DOE). This report is focused on evaluating and cataloguing Advanced Reactor Spent Nuclear Fuel (AR SNF) and Advanced Reactor Waste Streams (ARWS) and creating Back-end Nuclear Fuel Cycle (BENFC) strategies for their disposition. The R&D team for this report is comprised of researchers from Sandia National Laboratories and Enviro Nuclear Services, LLC.
Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region. We use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton's method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. We show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Furthermore, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.
The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for evaluating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2022 accomplishments by the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2022, the PFLOTRAN development team made several advancements to our software infrastructure, code performance, and process modeling capabilities.
As presented above, because similar existing DOE-managed SNF (DSNF) from previous reactors have been evaluated for disposal pathways, we use this knowledge/experience as a broad reference point for initial technical bases for preliminary dispositioning of potential AR SNF. The strategy for developing fully-formed gap analyses for AR SNF entails the primary step of first obtaining all the defining characteristics of the AR SNF waste stream from the AR developers. Utilizing specific and accurate information/data for developing the potential disposal inventory to be evaluated is a key principle start for success. Once the AR SNF waste streams are defined, the initial assessments would be based on comparison to appropriate existing SNF/waste forms previously analyzed (prior experience) to make a determination on feasibility of direct disposal, or the need to further evaluate due to differences specific to the AR SNF. Assessments of criticality potential and controls would also be performed to assess any R&D gaps to be addressed in that regard as well. Although some AR SNF may need additional treatment for waste form development, these aspects may also be constrained and evaluated within the context of disposal options, including detailed gap analysis to identify further R&D activities to close the gaps.
As presented above, because similar existing DOE-managed SNF (DSNF) from previous reactors have been evaluated for disposal pathways, we use this knowledge/experience as a broad reference point for initial technical bases for preliminary dispositioning of potential AR SNF. The strategy for developing fully-formed gap analyses for AR SNF entails the primary step of first obtaining all the defining characteristics of the AR SNF waste stream from the AR developers. Utilizing specific and accurate information/data for developing the potential disposal inventory to be evaluated is a key principle start for success. Once the AR SNF waste streams are defined, the initial assessments would be based on comparison to appropriate existing SNF/waste forms previously analyzed (prior experience) to make a determination on feasibility of direct disposal, or the need to further evaluate due to differences specific to the AR SNF. Assessments of criticality potential and controls would also be performed to assess any R&D gaps to be addressed in that regard as well. Although some AR SNF may need additional treatment for waste form development, these aspects may also be constrained and evaluated within the context of disposal options, including detailed gap analysis to identify further R&D activities to close the gaps.
Multiphase flow simulation is well-known to be computationally demanding, and modeling large-scale engineered subsurface systems entails significant additional numerical challenges. These challenges arise from: (a) the presence of small-scale discrete features like shafts, tunnels, waste packages, and barriers; (b) the need to accurately represent both the waste form processes at the small spatial scale of the repository and the large-scale transport processes throughout heterogeneous geological formations; (c) the strong contrast in material properties such as porosity and permeability, as well as the nonlinear constitutive relations for multiphase flow. Numerical solution entails discretization of the coupled system of nonlinear governing equations and solving a linear system of equations at each Newton–Raphson iteration. Practical problems require a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. The unique challenges noted above can lead to an ill-conditioned Jacobian matrix and non-convergence with Newton's method due to discontinuous nonlinearity in constitutive models. Moreover, practical applications can require numerous Monte-Carlo simulations to explore uncertainly in material properties, geological heterogeneity, failure scenarios, or other factors; governmental regulatory agencies can mandate these as part of Performance Assessments. Hence there is a need for flexible, robust, and computationally efficient methods for multiphase flow in large-scale engineered subsurface systems. We apply the open-source simulator PFLOTRAN to the practical problem of performance assessment of the US DOE Waste Isolation Pilot Plant (WIPP) site. The simulator employs a finite volume discretization and uses the PETSc parallel framework. We evaluate the performance of several preconditioners for the iterative solution of the linearized Jacobian system; these range from stabilized-biconjugate-gradient with block-Jacobi preconditioning (BCGS) to methods adopted from reservoir modeling, such as the constrained pressure residual (CPR) two-stage preconditioner and flexible generalized residual solver (FGMRES). We also implement within PETSc the general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), which truncates the Newton update or modifies the update with a Cauchy solution that is within the quadratic model trust-region of the objective function. We demonstrate the effectiveness of each method for a series of test problems with increasing difficulty. We find that the NTRDC and FGMRES-CPR-ABF (FCA) preconditioners generally perform best for the test problem having the extreme nonlinear processes, achieving a 50x speed-up compared with BCGS. The most ill-conditioned and extreme nonlinear simulations do not converge with BCGS (as one may expect), but they do complete the simulation with NTRDC and FCA. We also investigate the strong scalability of each method and demonstrate the impact of node-packing upon parallel performance on modern processor architectures.
The Spent Fuel and Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and highlevel nuclear waste (HLW). A high priority for SFWST disposal R&D is disposal system modeling (DOE 2012, Table 6; Sevougian et al. 2019). The SFWST Geologic Disposal Safety Assessment (GDSA) work package is charged with developing a disposal system modeling and analysis capability for evaluating generic disposal system performance for nuclear waste in geologic media.
The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for evaluating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2021 advances of the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2021, development proceeded along three main thrusts: software infrastructure, code performance, and process model advancement. Software infrastructure improvements included implementing an Agile software development framework and making improvements to the QA Test Suite. Code performance improvements included development of advanced linear and nonlinear solvers as well as design of flexible smoothing algorithms for capillary pressure functions. Process modeling advancements included the addition of flexible thermal conductivity function definitions and refinement of multi-continuum reactive transport to support Sandia’s participation in DECOVALEX