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Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model

This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.

15 GEOTHERMAL ENERGY↗

Synthesis of results for Brine Availability Test in Salt (BATS) DECOVALEX-2023 Task E

In the 2023 phase of the international collaborative DECOVALEX modeling project, Task E focused on understanding thermal, hydrological, and mechanical (THM) processes related to predicting brine migration in the excavation damaged zone around a heated excavation in salt. Salt is attractive as a disposal medium for radioactive waste because it is self-healing and is essentially impermeable and non-porous in the far field. Investigation of the short-term, near-field behavior is important for radioactive waste disposal because this early period strongly controls the amount of inflowing brine. Brine leads to corrosion of waste forms and waste packages, and possible dissolution of radionuclides with brine transport being a potential transport vector to the accessible environment.The Task was divided into steps. Step 0 included matching unheated brine inflow data from boreholes at the Waste Isolation Pilot Plant (WIPP) and matching temperature observations during a Brine Availability Test in Salt (BATS) heater test. Step 1 included validation of models against a thermo-poroelastic analytical solution, and two-phase flow around an excavation. Finally, Step 2 required all the individual components covered in steps 0 and 1 to come together to match observed brine inflow behavior during the same BATS heater test.There were a range of approaches from the teams, from mechanistic to prescriptive. Given the uncertainties in the problem, some teams used one- or two-dimensional models of the processes, while other teams included more geometrical complexity in three-dimensional models. Task E was a learning experience for the teams involved, and feedback from the modeling teams has led to changes in follow-on BATS experiments at WIPP. The primary Task E lessons learned were the impact of hydrologic initialization methods (wetting up vs. drying down), the difference between confined and unconfined thermal expansion, and the large changes in permeability associated with heating and cooling.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Computational Analysis of Coupled Geoscience Processes in Fractured and Deformable Media

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.

58 GEOSCIENCES↗

DECOVALEX-2023: Task E Final Report

This is the Task E final report for DECOVALEX-2023. Task E is focused on understanding thermal, two-phase hydrological, and mechanical (TH2M) processes, especially related to predicting brine migration in the excavation damaged zone around a heated excavation in salt. Salt is attractive as a disposal medium for radioactive waste because it is self-healing and is essentially impermeable and essentially non-porous in the far field (away from excavations). Investigation of the short-term (days to years) near-field (centimeters to tens of meters) behavior of salt is important for radioactive waste disposal because this early period strongly controls the amount of brine in a salt repository. Brine leads to corrosion of waste forms and waste packages, and possible dissolution of radionuclides with brine transport being a potential transport vector to the accessible environment. The main test case used in Task E is the ongoing Brine Availability Test in Salt (BATS) heater test located underground at the Waste Isolation Pilot Plant (WIPP) near Carlsbad, New Mexico, USA. The Task was divided into a series of Steps. Step 0 was an introduction to processes in salt, that included matching historical unheated brine inflow data from boreholes at WIPP and matching temperature observations during BATS heater test 1a. Step 1 included validation of models against a thermo-poroelastic analytical solution relevant to heated boreholes in salt, and two-phase flow around an excavation in salt. Step 2 required all the individual components covered in steps 0 and 1 to come together to match observed brine inflow behavior during the BATS 1a heater test. There were a range of approaches from the teams, from mechanistic to prescriptive. Given the uncertainties in the problem, some teams used one- or two-dimensional models of the processes, while other teams included more geometrical complexity in three-dimensional models. The key learning points from Task E have been: • Heat conduction through salt typically requires non-linear thermal conductivity (as a function of temperature), but most models do a good job matching observations, given appropriate adjustments to the applied power and some thermocouple locations. • Thermal pressurization requires coupled thermal-hydrological-mechanical (THM) responses that consider the thermal expansion of the fluid and solid phases. • Initialization of two-phase flow models around a borehole or excavation in salt are more realistically represented as “wetting up”, rather than “drying down” (i.e., the initial state after excavation is mostly dry, rather than mostly wet). • The BATS 1a heater test includes a significant release of brine after the end of heating, which requires a large increase in permeability to recreate. Task E has been a great learning experience for all the teams involved, and feedback from the modeling teams has led to changes in the design of follow-on BATS experiments, which are now ongoing underground at WIPP. There was a balance throughout the task between freedom to model phenomena how each team saw fit, and prescriptiveness in problem design to bring the modeling teams closer together to allow attribution of smaller differences between models to different modeling choices. The modeling approaches seem to go through two phases: an early phase of discovery or testing, and a later phase of refinement and improvement. In future modeling efforts, different field data could be used (e.g., BATS 2) and more time should be included in the processes for teams to make multiple model refinement or even significant changes to their conceptual model or setup, based on lessons learned from the modeling exercise.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗