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A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearly degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non-conservative hyperbolic systems. •Inclusion of sub-structure and resolution of intermediate characteristic fields. •Well-balanced for single- and two-layer shallow water equations and multi-phase flows. •Euler equations with real equation of state, MHD equations, nonlinear elasticity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multiphase Transport in Porous Media: Gas-Liquid Separation Using Capillary Pressure Gradients International Space Station (ISS) Flight Experiment Development

Advances in the understanding of multiphase flow characteristics under variable gravity conditions will ultimately lead to improved and as of yet unknown process designs for advanced space missions. Such novel processes will be of paramount importance to the success of future manned space exploration as we venture into our solar system and beyond. In addition, because of the ubiquitous nature and vital importance of biological and environmental processes involving airwater mixtures, knowledge gained about fundamental interactions and the governing properties of these mixtures will clearly benefit the quality of life here on our home planet. The techniques addressed in the current research involving multiphase transport in porous media and gas-liquid phase separation using capillary pressure gradients are also a logical candidate for a future International Space Station (ISS) flight experiment. Importantly, the novel and potentially very accurate Lattice-Boltzmann (LB) modeling of multiphase transport in porous media developed in this work offers significantly improved predictions of real world fluid physics phenomena, thereby promoting advanced process designs for both space and terrestrial applications.This 3-year research effort has culminated in the design and testing of a zero-g demonstration prototype. Both the hydrophilic (glass) and hydrophobic (Teflon) media Capillary Pressure Gradient (CPG) cartridges prepared during the second years work were evaluated. Results obtained from ground testing at 1-g were compared to those obtained at reduced gravities spanning Martian (13-g), Lunar (16-g) and zero-g. These comparisons clearly demonstrate the relative strength of the CPG phenomena and the efficacy of its application to meet NASAs unique gas-liquid separation (GLS) requirements in non-terrestrial environments.LB modeling software, developed concurrently with the zero-g test effort, was shown to accurately reproduce observed CPG driven gas-liquid separation phenomena. The design and fabrication of a micropost plate-lamina Hele-Shaw (HS) cell was performed which served as a computationally attainable geometric structure facilitating direct comparison between physical phenomena observed in our laboratory and the LB software predictions.

Wheeler, Richard R., Jr.↗

From clutter to clarity: Emergent neural operators via questionnaire metrics

Real-world datasets in chemical engineering and bioengineering processes—such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials—can often be unlabeled or disorganized, rendering the training of existing supervised learning models ineffective at learning the underlying dynamics. To salvage these datasets for decision-making, we first seek to obtain clarity from the cluttered data. Here, we present a framework for developing “structural” generative models, discovering emergent equations, and constructing efficient emulators from scrambled datasets by integrating unsupervised organizational learning techniques (Questionnaires) with advanced deep learning architectures (Deep Hidden Physics Models and Deep Operator Networks). Our approach is demonstrated on two illustrative model systems: (a) a 1D advection–diffusion partial differential equation representing a winding underground pipe and (b) an ensemble of Stuart–Landau oscillators, an agent-based system of coupled ordinary differential equations. In both cases, we successfully reconstruct meaningful spatial, temporal, and parameter embeddings from scrambled data, enabling good predictions of system dynamics. As a result, we highlight the framework’s potential for broader applications, enabling data-driven system identification in fields with inherently disorganized or hidden parameter spaces.

42 ENGINEERING↗

Validation of a CFD Model Predicting the Effect of High Level Lateral Acceleration Sloshing on the Heat Transfer and Pressure Drop in a Small-Scale Tank in Normal Gravity

A two-phase CFD model is developed to study the effects of sloshing with high level lateral acceleration on the heat transfer and pressure drop in a small scale tank. Computational results are compared to the data provided by a non-isothermal sloshing experiment without phase change conducted by T. Himeno et al. at the University of Tokyo and JAXA in 2011. The results of the current model are, also, compared to CFD predictions reported by Himeno et al. A step change in lateral acceleration was applied in the experiment. Different levels of lateral acceleration amplitude, varying between 0G and 0.5G, were considered. CFD results for interface movement and tank pressure are presented and compared in this paper to the experimental data for the case in which the value of lateral acceleration was set to 0.5G. The effects of initial and boundary conditions and turbulence modeling approach on the tank pressure change during sloshing are discussed in detail. The effect of conjugate heat transfer in the tank wall is also studied to show its important role in determining the tank pressure evolution. The results of the Reynolds Averaged Navier Stokes (RANS) models are compared to the results of the Large Eddy Simulation model (LES) to underscore the importance of correctly capturing the effects of turbulence for high fidelity predictions.

multiphase flow↗

Validation of A CFD Model Predicting the Effect of High Level Lateral Acceleration Sloshing on the Heat Transfer and Pressure Drop in A Small-Scale Tank in Normal Gravity

A two-phase CFD model is developed to study the effects of sloshing with high level lateral acceleration on the heat transfer and pressure drop in a small scale tank. Computational results are compared to the data provided by a non-isothermal sloshing experiment without phase change conducted by T. Himeno et al. at the University of Tokyo and JAXA in 2011 [1]. The results of the current model are, also, compared to CFD predictions reported by Himeno et al. [2]. A step change in lateral acceleration was applied in the experiment. Different levels of lateral acceleration amplitude, varying between 0G and 0.5G, were considered. CFD results for interface movement and tank pressure are presented and compared in this paper to the experimental data for the case in which the value of lateral acceleration was set to 0.5G. The effects of initial and boundary conditions and turbulence modeling approach on the tank pressure change during sloshing are discussed in detail. The effect of conjugate heat transfer in the tank wall is also studied to show its important role in determining the tank pressure evolution. The results of the Reynolds Averaged Navier Stokes (RANS) models are compared to the results of the Large Eddy Simulation model (LES) to underscore the importance of correctly capturing the effects of turbulence for high fidelity predictions.

multiphase flow↗

Robust Carbon Dioxide Plume Imaging Using Joint Tomographic Inversion of Seismic Onset Time and Distributed Pressure and Temperature Measurements (Final Report)

We develop and demonstrate rapid and cost-effective methodologies for spatiotemporal tracking of CO2 plumes during geologic sequestration using joint inversion of seismic data and distributed pressure and temperature measurements. Key elements of our methodology are: (a) a computationally efficient approach to pressure and temperature propagation, (b) analysis of time lapse seismic data using a novel ‘seismic onset time’ approach to detect fluid front propagation, and (c) data assimilation and uncertainty assessment via joint inversion of pressure, temperature and time lapse seismic data, and (d) validating the numerical tomographic inversion using a CO2 injection demonstration projects, specifically data collected from the from the Petra Nova Parish Holdings CCUS project in the West Ranch Field, Texas and the Chester-16 reef CO2 injection site in Northern Michigan which is part of the DOE Midwestern Carbon Sequestration Project. The research team is led by Texas A&M University and includes Battelle as a subcontractor with support from Shell, Anadarko, Chevron and JX Nippon. A carbon dioxide (CO2) water-alternating-gas (WAG) pilot was conducted to gain insights into tertiary oil recovery potential via CO2 flood in the West Ranch Field as part of the Petra Nova project, the world’s largest post-combustion CO2 capture and utilization initiative. With a fluvial formation geology and large contrasts in permeability, this is a challenging and novel application of CO2 enhanced oil recovery (EOR). We build a predictive dynamic model of the subsurface that incorporates the multiphase and compositional data acquired during the pilot operation. The calibrated model is used for the carbon dioxide plume imaging. The study began with an initialization of the pilot sector model extracted from a calibrated full-field model. The pilot model calibration follows a two-step hierarchical workflow. First, we performed a large-scale update of the permeability distribution by integrating available bottomhole pressure and multiphase production data. In the second step, local permeability field is fine-tuned using a streamline-based method to match CO2 breakthrough times at the producers. The predictive capability of the calibrated model was verified through two blind validation tests: (1) the model showed good agreement with saturation logs acquired at two observation wells; and (2) the model reproduced the CO2 recovery as a fraction of the injected CO2. The use of seismic onset times has shown great promise for integrating near-continuous seismic surveys for updating geologic models. In this study, we analyze the impact of seismic survey frequency on the onset time approach aiming to extend the application of onset time to infrequent seismic surveys. In addition, we quantitatively examine the nonlinearity of the onset time method and compare it to the commonly used amplitude inversion method. We carry out a sensitivity analysis of seismic survey frequency based on the complete seismic survey data (over 175 surveys) of steam injection in a heavy oil reservoir (Peace River Unit) in Canada. Our results show that an adequate onset time map can be obtained from the infrequent seismic surveys by interpolation between seismic surveys as long as there is no change in the dominant underlying physics between the successive surveys. The study also shows that nonlinearity of the onset time method can be -smaller than that of the amplitude inversion method by several orders of magnitude. Application to the Brugge benchmark case shows that the onset time method obtains comparable permeability update as the traditional seismic amplitude inversion method with faster computation and improved convergence characteristics. We extend the streamline-based data integration approach to incorporate distributed temperature sensor (DTS) data using the concept of thermal tracer travel time. Then, a hierarchical workflow composed of evolutionary and streamline methods is employed to jointly history match the DTS and pressure data. Finally, CO2 saturation and streamline maps are used to visualize the CO2 plume movement during the sequestration process. The hierarchical workflow is applied to a carbon sequestration project in a carbonate reef reservoir within the Northern Niagaran Pinnacle Reef Trend in Michigan, USA. The monitoring data set consists of distributed temperature sensing (DTS) data acquired at the injection well and a monitoring well, flowing bottom-hole pressure data at the injection well, and time-lapse pressure measurements at several locations along the monitoring well. The history matching results indicate that the CO2 movement is mostly restricted to the intended zones of injection which is consistent with an independent warm-back analysis of the temperature data. In addition to employing simulation models and inverse methods for CO2 plume imaging, we also initialized a data-driven technology for detecting inter-well connectivity based on production and pressure data. Our machine-learning framework is built on the statistical recurrent unit (SRU) model and interprets well-based injection/production data into inter-well connectivity without relying on a geologic model. We test it on synthetic and field-scale CO2 EOR projects utilizing the water-alternating-gas (WAG) process. The validation of the proposed data-driven inter-well connectivity assessment is performed using synthetic data from simulation models where inter-well connectivity can be easily measured using the streamline-based flux allocation. The SRU model is shown to offer excellent prediction performance on the synthetic case. Despite significant measurement noise and frequent well shut-ins imposed in the field-scale case, the SRU model offers good prediction accuracy, the overall relative error of the phase production rates at most producers ranges from 10% to 30%. It is shown that the dominant connections identified by the data-driven method and streamline method are in close agreement. Texas A&M University, the lead organization in the project, was primarily responsible for the development of tomographic approaches for CO2 plume mapping in conjunction with distributed pressure, temperature and seismic onset time data. Battelle, as a subcontractor, was primarily responsible for the development of analytical and empirical methods for analyzing transient injection rate and pressure data from point/line sources such as injection and monitoring wells. An additional area of emphasis for Battelle was the use of machine learning for such tasks as inferring reservoir connectivity information from injection-production data, and identifying variable importance for machine learning-based proxy models developed from full-physics simulations. The two organizations also collaborated on the application of the tomographic inversion methodology for a field data set.

02 PETROLEUM↗

How does the connectivity of open-framework conglomerates within multi-scale hierarchical fluvial architecture affect oil-sweep efficiency in waterflooding?

Understanding multi-phase fluid flow and transport processes within aquifers, candidate reservoirs for CO 2 sequestration, and petroleum reservoirs requires understanding a diverse set of geologic properties of the aquifer or reservoir, over a wide range of spatial and temporal scales. We focus on multiphase flow dynamics with wetting (e.g., water) and non-wetting (e.g., gas or oil) fluids, with one invading another. This problem is of general interest in a number of fields and is illustrated here by considering the sweep efficiency of oil during a waterflood. Using a relatively fine-resolution grid throughout a relatively large domain in these simulations and probing the results with advanced scientific visualization tools (Reservoir Visualization Analysis [RVA]/ ParaView software) promote a better understanding of how smaller-scale features affect the aggregate behavior at larger scales. We studied the effects on oil-sweep efficiency of the proportion, hierarchical organization, and connectivity of high-permeability open-framework conglomerate (OFC) cross-sets within the multi-scale stratal architecture found in fluvial deposits. We further analyzed oil production rate, water breakthrough time, and spatial and temporal distribution of residual oil saturation. As expected, the effective permeability of the reservoir exhibits large-scale anisotropy created by the organization of OFC cross-sets within unit bars, and the organization of unit bars within compound- bars. As a result, oil-sweep efficiency critically depends on the direction of the pressure gradient. However, contrary to expectations, the total amount of trapped oil due to the effect of capillary trapping does not depend on the magnitude of the pressure gradient within the examined range. Hence the pressure difference between production and injection wells does not affect sweep efficiency; although the spatial distribution of oil remaining in the reservoir depends on this value. Whether or not clusters of connected OFC span the domain affects only the absolute rate of oil production—not sweep efficiency.

58 GEOSCIENCES↗

Final Technical Report: Using Solid Particles as Heat Transfer Fluid for use in Concentrating Solar Power (CSP) Plants

In today’s industrial economy, energy consumption has never been higher. Over the last 15 years the US alone has consumed an average of nearly 100 quadrillion BTUs per year [21]. A need for clean and renewable energy sources has become quite apparent. The SunShot Initiative is an ambitious effort taken on by the United States Department of Energy that targets the development of solar energy that is cost-competitive with other methods for generating electricity. Specifically, this work is concerned with the development of concentrating solar power plants (CSPs) with granular media as the heat transfer fluid (HTF) from the solar receiver. Unfortunately, the prediction of heat transfer in multiphase flows is not well understood. For this reason, our aim is to fundamentally advance the understanding of multiphase heat transfer, particularly in gas-solid flows, while providing quantitative input for the design of a near black body receiver (NBB) that uses solid grains (like sand) as the HTF. Over the course of this three-year project, a wide variety of contributions have been made to advance the state-of-the art description for non-radiative heat transfer in dense, gas-solid systems. Comparisons between a state-of-the-art continuum heat transfer model and discrete element method (DEM) simulations have been drawn. The results of these comparisons brought to light the limitations of the continuum model due to inherent assumptions in its derivation. A new continuum model was then developed for heat transfer at a solid boundary by rigorously accounting for the most dominant non-radiative heat transfer mechanism (particle-fluid-wall conduction). The new model is shown to be in excellent agreement with DEM data and captures the dependence of heat transfer on particle size, a dependency that previous continuum models were not capable of. DEM and the new continuum model were then employed to model heat transfer in a variety of receiver geometries. The results provided crucial feedback on the efficiency and feasibility of various designs. Namely, a prototype design consisting of an array of heated hexagonal tubes was later supplanted by a vertical conduit with internal baffles. Due to low solids heat transfer on the bottom faces of the hexagonal tubes in the prototype, the predicted wall temperature gradients exceeded the design limitations. By contrast, the vertical conduit can be constructed to continually force particle-wall contacts, and thus, result in more desirable solids heat transfer and wall temperature gradients. Finally, a new heat flux boundary condition was developed for DEM simulations to assess the aforementioned wall temperature gradients. The new boundary condition advances current state-of-the-art techniques by allowing the heat fluxes to each phase to vary with space and time while the total flux remains constant. Simulations with the new boundary condition show that the total boundary heat flux is in good agreement with the imposed total boundary heat flux. While the methods we have utilized here are primarily numerical and fundamental by nature, they offer some key advantages of: (i) being robust and valid over a large range of conditions, (ii) able to quickly explore large parameter spaces, and (iii) aid in the construction of experiments. We have ultimately leveraged our computational capabilities to provide feedback on the design of a CSP which possesses great potential to become a cost effective source of clean and renewable electricity. Overall, ensuring that future energy demands are met in a responsible and efficient manner has far reaching impacts that span both ecologic and economic concerns. Regarding logistics, the project was successfully re-negotiated after the go/no-decisions of Years 1 and 2. All milestones were successfully completed.

14 SOLAR ENERGY↗

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗

Insights into mixing of non-isothermal multi-polymer melts for complex plastics recycling

Catalytic recycling or upcycling of plastics is often limited not by catalyst performance, but by transport, arising from highly viscous, non-Newtonian polymer melts. In this work, we develop a reactor-scale framework that integrates rheological measurements, constitutive modeling, computational fluid dynamics (CFD), and experiments to quantify mixing, heat transfer, and dispersion in surrogate hydrocarbon melts representing mixed plastics systems. Temperature- and shear rate-dependent viscosity of low-density polyethylene (LDPE) and high-density polyethylene (HDPE) is measured to create two surrogate polymers (PLD and PHD) that capture the dominant shear-thinning flow behavior while neglecting strong elastic effects, enabling tractable simulation of non-isothermal, polymer-melt mixing using a Carreau-Arrhenius generalized Newtonian framework. Three-dimensional CFD simulations are employed to evaluate impeller performance in PLD using mixing time, cavern volume, thermal uniformity, and interfacial area for regimes in which viscoelastic effects are not dominant. We show that magnetic stir bars commonly used in lab-scale studies produce large thermal gradients (~60 °C) and poor mixing, even under idealized power delivery and polymer flow conditions. In contrast, close-clearance anchor impellers achieve near-isothermal operation, reduce mixing times by up to 5×, and provide >90% active circulation volume. We further demonstrate that, at low pseudo-Deborah number (De*), motor power requirements can be predicted directly from shear rate-dependent rheology using the Carreau-Arrhenius framework, enabling rational selection of operating conditions. Extension to surrogate immiscible multi-polymer systems based on PLD and PHD shows that interfacial area is highly sensitive to operating conditions and impeller design, with coaxial anchor-turbine configurations enhancing dispersion by up to 4 × .

Close-clearance impellers↗

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗

Device-scale CFD modeling of gas-liquid multiphase flow and amine absorption for CO2 capture

In this paper we aim to develop a validated device-scale CFD model that can predict quantitatively both hydrodynamics and CO2 capture efficiency for an amine-based solvent absorber column with random Pall ring packing. A Eulerian porous-media approach and a two-fluid model were employed, in which the momentum and mass transfer equations were closed by literature-based empirical closure models. We proposed a hierarchical approach for calibrating the parameters in the closure models to make them accurate for the packed column. Specifically, a parameter for momentum transfer in the closure was first calibrated based on data from a single experiment. With this calibrated parameter, a parameter in the closure for mass transfer was next calibrated under a single operating condition. Last, the closure of the wetting area was calibrated for each gas velocity at three different liquid flow rates. For each calibration, cross validations were pursued using the experimental data under operating conditions different from those used for calibrations. This hierarchical approach can be generally applied to develop validated device-scale CFD models for different absorption columns.

Pan, Wenxiao↗

Final report of “A Detailed Study of the Physical Mechanisms Controlling CO2-Brine Capillary Trapping in the Subsurface” (University of Arizona, DE-SC0006696)

Carbon capture and storage (CCS) of carbon dioxide emissions generated by production or combustion of fossil fuels is a technologically viable means to reduce the build-up of CO2 in the atmosphere and oceans. Using advantages of scale and location, CCS is particularly suitable for large point sources near ubiquitous deep saline aquifers, depleted gas reservoirs, or at production reservoirs for enhanced oil recovery (EOR). In the BES-funded research project, Oregon State University (OSU) carried out capillary trapping experiments with proxy fluids that mimic the properties of the scCO2/brine system under ambient temperatures and pressures, and successfully developed a unique and novel x-ray compatible, high-pressure, elevated temperature setup to study the scCO2/brine system under challenging reservoir conditions. Both methodologies were applied to a variety of porous media, including synthetic (glass bead) and geologic (Bentheimer sandstone) materials. The University of Arizona (UA) developed pore-scale lattice Boltzmann (LB) models which are able to handle the experimental conditions for proxy fluids, as well as the scCO2/brine system, that are capable of simulating permeability in volumes of tens of millions of fluid elements. We reached the following summary findings (main institute indicated): 1. (OSU/UA) To understand capillary trapping in a multiphase fluid-porous medium system, the system must be analyzed from a pore-scale force balance perspective; trapping can be enhanced by manipulating wetting and nonwetting phase fluid properties. 2. (OSU) Pore-scale fluid connectivity and topology has a clear and direct effect on nonwetting phase capillary trapping efficiency. 3. (OSU) Rock type and flow regime also have a pronounced effects on capillary trapping. 4. (OSU/UA) There is a predictable relationship between NWP connectivity and NWP saturation, which allows for development of injection strategies that optimize trapping. The commonly used Land model (Land, 1968) does not predict amount of trapped NWP accurately. 5. (UA) There are ambiguities regarding the segmentation of large-volume gray-scale CT data into pore-volumes suitable for pore-scale modeling. Simulated permeabilities vary by three orders of magnitude and do not resemble observed values very well. Small-volume synchrotron-based CT data (such as produced by OSU) does not suffer significantly from segmentation ambiguities. 6. (UA) A standard properly parameterized Shan-Chen model LB model is useful for simulating porous media with proxy fluids as well as the scCO2/brine system and produces results that are consistent with tomographic observations. 7. (UA) A LB model with fluid-interactions defined by a (modified) Peng-Robinson Equation of State is able to handle the scCO2/brine system with variable solid phase wettability. This model is numerically stable at temperatures between 0 and 250 °C and pressures between 3 and 50 MPa, and produces appropriate densities above the critical point of CO2 and exhibits three-phase separation below. Based on above findings OSU and UA have proposed continued experimentation and pore-scale modeling of the scCO2/brine system. The reported research has extensively covered capillary trapping using proxy fluids, but due to limited beam-time availability we were unable to apply our high-pressure CO2 setup to sufficient variation in fluid properties, and initial scCO2 connectivity. New data will also allow us to test, calibrate and apply our LB models to reservoir conditions beyond those that are currently feasible experimentally. Such experiments and simulations will also allow us to provide information how suitable proxy fluids are for the scCO2/brine system. We believe it would be worthwhile to pursue the following new research questions: 1. What are the fundamental differences in the physics underlying capillary trapping at ambient vs. supercritical conditions? 2. Do newly developed pore-scale trapping interactions and relationships translate to continuum scales? A motivation for these questions was elaborated in “Capillary Trapping of Super-Critical CO2: Linking Pore and Continuum Scales to Verify new Relationships” that was submitted to DOE-BES in 2015.

20 FOSSIL-FUELED POWER PLANTS↗

Scaling microstructural processes in the sintering of ionic ceramics

A multi-scale framework, combining a multiphase field formulation and large deformation mechanics, was developed as a stepping stone to perform the data analytics of the microstructural level kinetics of a sintering solid. Relevant microstructural information from this framework, such as grain, stress, and porosity statistics, was scaled up to describe the macroscopic level sintering kinetics. Here, the developed formulation was applied to describe the electric field assisted sintering of Y 2 O 3 . Microstructural inhomogeneities in a multi-granular solid result in the formation of a field of compressive stress networks, which interleave with low compression and weakly tensile regions, defining a scaffolding for sintering concentration regions to develop. A Poisson effect-induced lateral stress network is also naturally self-induced as a result of the mechanical constraints imposed by the sintering apparatus. For long sintering times, localized shear stresses enhancing mass flow along grain boundaries and internal surfaces develop. Three-sided pores are removed by either vacancy transport to the surrounding pores, or move towards the external surfaces through grain boundary diffusion. Four- and higher order-sided pores stabilize because an equal amount of vacancies are gained and lost through the connecting grain boundaries. Grain dewetting contributes to pore coalescence, suggesting that pore kinetics and grain growth are coupled and should be analyzed in concert. The combined sintering and grain growth kinetics define six regimes of sintering behavior: (1) T, the transient regime; (2) E$_Υ$, the surface energy dominated, early sintering regime, where the grain growth exponent, p = 1, and the stress concentration factor, $f$ ~ $1/\hat{ρ}^{4.6}$; (3) E S , the stress dominated, early sintering regime, where p = 1 and $f$ ~ $1/\hat{ρ}^{4}$; (4) I$_Υ$, the surface energy dominated, intermediate sintering regime, where p = 2 and $f$ ~ $1/\hat{ρ}^{4.6}$; (5) I S , the stress dominated, intermediate sintering regime, where p = 2 and $f$ ~ $1/\hat{ρ}^{4}$; and (6) L, the late sintering regime, where p = 3 and $f$ ~ 1. At the macroscopic level, the rapid densification and suppression of grain growth observed in the electric field assisted sintering process is a consequence of the compounding effects of the underlying stress-, transport-, and interfacial-energy-induced energy minimization kinetics, as predicted by the multi-scale framework.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Quantitative Characterization of Impacts of Coupled Geomechanics and Flow on Safe and Permanent Geological Storage of CO 2 in Fractured Aquifers

This is the final scientific report for the award DE-FE0023305, entitled “Quantitative Characterization of Impacts of Coupled Geomechanics and Flow on Safe and Permanent Geological Storage of CO 2 in Fractured Aquifers.” The work has been divided into six tasks. In Task 2, we characterized rock properties, which are important when developing a quantitative approach for understanding and predicting geomechanical effects on large-scale CO 2 injection and long-term storage in the subsurface. Rock properties of interest for this characterization include porosity, permeability, elastic constants, strength, and heat capacity. We measured rock properties for three different rock types: concrete, sandstone and shale. These properties were obtained from the acoustic measurement, permeability and porosity measurement, Brazilian test, the uniaxial compressive test, and heat capacity measurement. Then, using the Brazilian technique to fracture samples, we measured their permeability under brine injection for varying effective stresses, followed by similar measurements of permeability under sc-CO 2 injection. Permeability to brine and sc-CO 2 decreased as the effective stress increased. The apparent permeability to sc-CO 2 was an order of magnitude less than that for brine, a consequence of CO 2 being the non-wetting fluid. In Task 3, we developed understandings and correlations for CO 2 injection pressure induced fracturing. We initially fractured four eight inch cubes of concrete with brine to establish a standard test procedure. Then, additional concrete samples were fractured using brine. Confining stresses were exerted on the samples and brine was injected at a constant rate into a borehole that was previously drilled into the concrete cube. The borehole pressure was measured and fracture initiation was identified as a peak in the pressure profile. That was followed by fracture propagation, which was identified as a plateau in the pressure profile, and finally the fracture reached the sample surface. The sample surfaces were photographed before and after fracturing, which enabled determination of where the fracture reached the sample surface. Afterwards, aqueous food dye solution was injected into the fractured concrete samples to color the fracture planes. The borehole was filled with food dye solution in advance, a gas pulse was transmitted to the borehole, and the borehole was then shut in to allow the food dye to be driven into existing fractures. Then, the concrete samples were broken down by high-pressure gas injection to reveal the geometry and morphology of the hydraulic fractures. In addition, acoustic measurements were conducted on multiple locations on each face of the concrete samples before and after injection for comparison. This comparison was used to confirm changes in the internal structure of the concrete sample, namely the formation of fractures. There were six concrete samples fractured with brine. Afterwards, concrete samples were fracture using sc-CO 2 . The main change in experimental procedure was the inclusion of temperature control, since in the field, we mostly encounter temperature and pressure conditions above the supercritical point of CO 2 . The concrete samples were pre-heated in an oven to elevate their temperature, and thermal tape was used to heat the CO 2 to a temperature above its supercritical temperature. Two concrete samples were fractured using liquid CO 2 , four concrete samples were fractured using gaseous CO 2 , and twenty two concrete samples were fractured using sc-CO 2 . For the concrete samples fractured using sc-CO 2 , three had pre-existing hydraulic fractures on the surface near the wellbore, and two were water saturated (as opposed to containing only air). Two concrete samples were composite samples, with a high permeability ball in the center, in order to represent CO 2 injection into a high permeability zone surrounded by a low permeability sealing formation. Later, we fractured five shale samples, obtained from the Niobrara shale outcrop, with sc-CO 2 . The injection rate was constant, confining stresses were applied, the shale samples were pre-heated in an oven to the desired temperature, and the sample was then fractured. An analysis of the failure type was done for many of the concrete samples, based on the predicted break down pressure for tensile and shear failure, and it was found that most samples fractured due to shear failure. Also, the presence of induced fractures has little to no effect on the fracture initiation pressure, but significantly changes the fracture morphology. The CO 2 fracturing in water saturated samples behaved much similar to brine induced fracturing. There was a significant difference of breakdown pressure for injection of CO 2 and brine, where the breakdown pressure for CO 2 induced fracturing is generally around the minimum horizontal stress and that for brine is much higher. Finally, the fracture orientation for most samples with large confining stress differential was perpendicular to the minimum horizontal stress. When the stress differential, especially the difference between the two directions with the smallest stresses was small, the fracture orientation was determined not only by the minimum stress direction, but also the magnitude of the confining stress, the tensile strength of the rock, and the breakdown pressure. In Task 4, we modified our coupled flow-geomechanical models to model fracture growth and propagation in storage formations and caprocks. These flow-geomechanical models are TOUGH2-CSM and TOUGH2-FLAC. The TOUGH2-CSM fluid and heat flow formulation is based on the TOUGH2 formulation of mass and energy conservation equations that govern fluid and heat flow in general multiphase, multicomponent, multi-porosity systems. The TOUGH2-CSM simplified geomechanical formulation is based on the linear theory of elasticity applied to multi-porosity non-isothermal (thermo-multi-poroelastic) media. We previously derived, from the fundamental relations of the linear theory of elasticity, an equation relating mean stress, pore pressures, temperatures, and body force (the Mean Stress equation) that we added to the TOUGH2-CSM fluid and heat flow equations. We extended the TOUGH2-CSM simplified geomechanical formulation to calculate the entire stress tensor by deriving equations for stress tensor components from derivatives of the Cartesian thermo-multi-poroelastic Navier equation components. In addition, we derived equations for stress tensor components in rz-coordinates. We solved these geomechanical equations using the integral finite difference method. This method utilizes momentum fluxes obtained by “factoring” a divergence operator out of each geomechanical equation. In Task 5, we did a literature survey to determine suitable correlations for fracture initiation, growth, and propagation. After surveying numerous papers, we modified TOUGH2-CSM to model stress dependent fracture initiation and growth using the Mohr-Coulomb criterion for shear failure in faults and caprock and the condition of negative minimum effective stress for tensile failure. Tensile failure results in a fracture whose width depends on the difference between fracture pressure and minimum stress and whose propagation is based on the difference between the stress intensity factor at the fracture tip and the rock toughness. The TOUGH-FLAC model is based on the FLAC3D ubiquitous joint model, extended for the modeling of permeability changes induced by changes in effective normal stress across fractures as well permeability changes caused by shearing along fractures. In Task 6, we validated our coupled flow-geomechanical models using analytical solutions and problems from the literature. We validated the TOUGH2-CSM modifications using analytical solutions to the displacement from a uniform load on a semi-infinite elastic medium and the two-dimensional Mandel-Cryer effect. Those were followed by a sample problem to test our stress tensor calculations, which was for injection into a single-phase reservoir with constant properties. Comparisons of our simulator to published results were done on for the depletion of a single-phase reservoir with stress dependent porosity, two examples from the In Salah gas project, an axisymmetric baserock–reservoir–caprock system with a normal faulting stress regime that had thermally induced shear stresses, simulations of CO 2 leakage through caprock in a two-dimensional reservoir in Cartesian coordinates, and predictions of caprock failure from CO 2 injection into an axisymmetric reservoir. Finally, we simulated CO 2 injection pressure-induced fracturing from one of our laboratory studies, Sample 39, and obtained a fracture profile. We also validated the TOUGH2-FLAC model for fluid driven fracture growth against solutions based on the KGD model and a case with an inclined fracture that was loaded from the boundaries to achieve wing-crack propagation. The strain softening tensile behavior and softening of modulus considering a simple damage approach was verified by a simulation representing hydraulic fracturing stress measurement around a vertical well. Finally, the model was validated against deep fracture zone opening and surface uplift at In Salah with inverses analysis used to improve the match of simulation with field data. In Task 7, we developed a scheme based on inverse modeling that can be used to identify caprock leakage. Injection of fluid into a reservoir results in a time varying pressure profile that depends on the properties of the rock and the fluid. The presence of significant caprock leakage would effect this pressure profile and we used inverse modeling, namely the Levenberg-Marquardt method, to determine the leakage location from the pressure profile. A two-dimensional and a three-dimensional example based on published data were presented. The published simulation was run and its results were considered as “field” data. In the two-dimensional example, a simulation of CO 2 injection into a two-dimensional aquifer-caprock system, the caprock had a vertical fault through which leakage could occur. The location of this leakage was obtained from our inverse modeling scheme. In the three-dimensional example, the simulation domain had four geological layers, one of which was the injection zone that contained a horizontal injection well. We simulated fractures as high permeability gridblocks, introduced a fracture that spanned the caprock depth, and ran a simulation to obtain “field” data. Then, using our inverse modeling scheme, we obtained the location of that fracture.

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