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Partitioning of rare earths in multiphase nuclear waste glass-ceramics
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A proximity‐based image‐processing algorithm for colloid assignment in segmented multiphase flow datasets
Summary Colloidal transport and deposition are of both environmental and engineering importance. Easier access to x‐ray microtomography (XMT) coupled with improved imaging resolution has made XMT a unique and viable tool for visualizing and quantifying these processes. Currently, there is scant information in the literature addressing colloid segmentation and analysis in saturated and unsaturated porous media, in particular related to spatial partitioning of colloids. To support this need, an approach to assign segmented colloidal particles and aggregates to different partitioning classes based on their proximity to different phases is presented here. The method uses different markers for each attachment site (e.g. wetting‐nonwetting phase interfaces). An example XMT dataset from a drainage experiment is used to demonstrate the efficacy of the image processing algorithms. Flow conditions, and fluid and colloid properties, can thus be compared to the behaviour of colloids within the porous medium. This algorithm can help elucidate colloidal deposition mechanisms and the importance of different attachment sites, explore the importance of fluid properties, as well as the arrangement and shape of the colloids.
A consistent and conservative volume distribution algorithm and its applications to multiphase flows using Phase-Field models
In the present study, the multiphase volume distribution problem, where there can be an arbitrary number of phases, is addressed using a consistent and conservative volume distribution algorithm. The proposed algorithm satisfies the summation constraint, the conservation constraint, and the consistency of reduction. The first application of the volume distribution algorithm is to determine the Lagrange multipliers in multiphase Phase-Field models that enforce the mass conservation, and a multiphase conservative Allen-Cahn model that satisfies the consistency of reduction is developed. A corresponding consistent and conservative numerical scheme is developed for the model. The multiphase conservative Allen-Cahn model has a better ability than the multiphase Cahn-Hilliard model to preserve under-resolved structures. The second application is to develop a numerical procedure, called the boundedness mapping, to map the order parameters, obtained numerically from a multiphase model, into their physical interval, and at the same time to preserve the physical properties of the order parameters. Along with the consistent and conservative schemes for the multiphase Phase-Field models, the numerical solutions of the order parameters are reduction consistent, conservative, and bounded, which are theoretically analyzed and numerically validated. Then, the multiphase Phase-Field models are coupled with the momentum equation by satisfying the consistency of mass conservation and the consistency of mass and momentum transport, thanks to the consistent formulation. Finally, it is demonstrated that the proposed model and scheme converge to the sharp-interface solution and are capable of capturing the complicated multiphase dynamics even when there is a large density and/or viscosity ratio.
Simulation of Multiphase Flow and Poromechanical Effects Around Injection Wells in CO 2 Storage Sites
In geological CO 2 storage operations, wellbore deformations and leakage pathways formations can occur around injection and abandoned wells subjected to high rates and long-term CO 2 injection. To guide engineering design and prevent CO 2 leakage risks, a full understanding of the underlying physics and robust numerical models is necessary to evaluate the response of underground formations in the near wellbore region and in the reservoir. In this study, a multi-scale and multi-physics open-source simulator (GEOS) is used to simulate multiphase flow and poromechanical deformations over time in three dimensions. The governing equations for mechanical deformations of the rock body and multiphase compositional fluid flow within the rock matrix are solved with a fully coupled finite element and finite volume approach. The Drucker–Prager model with friction hardening is applied to simulate elastoplastic deformation and a multiphase fluid model with power-law correlations for relative permeability is used to model the migration of CO 2 plume, which are coupled with numerical implicit scheme. Simulation results are verified against multiple analytical solutions for multiphase flow and wellbore problems, thus demonstrating the accuracy of this advanced simulator. In two engineering applications, here we highlight the impact of elastoplastic deformation and coupled modeling for assessing induced displacements and stress perturbations, which are more pronounced in the near wellbore regions. This work focuses on short-term processes in the vicinity of injection wells where stress evolutions, rock deformations and multiphase compositional flow and transport are simulated jointly to ensure wellbore stability and prevent damage. This fully coupled geomechanical model can simulate multiphase flow and any associated poromechanical effects within the CO 2 storage site and in the surrounding formations. Such a large-scale, long-term, multi-physics simulation model is useful in many ways: it can guide operational decisions for CO 2 injection, assess the containment potential and risks of a site, and analyze the wellbore stability and integrity during and after CO 2 injection.
A consistent and conservative Phase-Field method for multiphase incompressible flows
In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.
Semi-implicit method to solve compressible multiphase fluid flows without acoustic time step restrictions
A new 3D multiphase numerical capability is presented here for simulating multiphase flow regimes at all Mach numbers (M). The new method is a semi-implicit extension of the finite volume discrete equation method (DEM) of Chinnaya et al. (2004), which originally used explicit time-stepping. The capability is also developed to work with another extension of the DEM to moving grids for arbitrary Lagrangian-Eularian (ALE) methods detailed in Dunn (2011). Rather than solving all phase equations simultaneously, the DEM reduces the equations to a system of single-phase Riemann solves, where each phase has its own velocity and thermodynamic state. Exchanges between the phases are modeled through source terms accounting for the phase interactions. Furthermore, since the original multiphase scheme uses an explicit time-advancement scheme, it has time step restrictions dictated by the speed of sound, which limits the model's ability to simulate weakly compressible flows which typically need to be integrated for longer time periods. Here, we extend the current multiphase formulation by implementing a pressure-correcting step to enable implicit calculations and remove acoustic time step limitations. The new semi-implicit algorithm allows use of relatively large time steps compared to an explicit method. Validation and benefits of the new implicit time-step method are illustrated using several examples including weakly compressible flows and strong shock waves. The scheme presented here is general and may be used for a variety of applications which require capabilities for handling multiphase flow at a wide range of Mach numbers. However, the goal of this research is to simulate all stages of high energy explosions, including the shock formation (high Mach numbers) and evolution of the buoyant cloud (low Mach numbers).
A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media
Simulation of multiphase poromechanics involves solving a multiphysics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also known as monolithic approaches, are usually preferred. The main bottleneck of a monolithic approach is that it requires solution of large linear systems that result from the discretization and linearization of the governing balance equations. Because such systems are nonsymmetric, indefinite, and highly ill-conditioned, preconditioning is critical for fast convergence. Recently, most efforts in designing efficient preconditioners for multiphase poromechanics have been dominated by physics-based strategies. Current state-of-the-art “black-box” solvers such as algebraic multigrid (AMG) are ineffective because they cannot effectively capture the strong coupling between the mechanics and the flow subproblems, as well as the coupling inherent in the multiphase flow and transport process. In this work, we develop an algebraic framework based on multigrid reduction (MGR) that is suited for tightly coupled systems of PDEs. Using this framework, the decoupling between the equations is done algebraically through defining appropriate interpolation and restriction operators. One can then employ existing solvers for each of the decoupled blocks or design a new solver based on knowledge of the physics. We demonstrate the applicability of our framework when used as a “black-box” solver for multiphase poromechanics. Here, we show that the framework is flexible to accommodate a wide range of scenarios, as well as efficient and scalable for large problems.
A large deformation multiphase continuum mechanics model for shock loading of soft porous materials
A large deformation, coupled finite-element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain-rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one-dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed-form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain-rate, and (iii) showing differences in deformations between a single-phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain-rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single-phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain-rate loading of soft porous materials. It was discovered that explicit, adaptive time-stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time-stepping schemes for shock-like loadings. Here, shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.
Asymmetric oligomerization state and sequence patterning can tune multiphase condensate miscibility
Endogenous biomolecular condensates, composed of a multitude of proteins and RNAs, can organize into multiphasic structures with compositionally distinct phases. This multiphasic organization is generally understood to be critical for facilitating their proper biological function. However, the biophysical principles driving multiphase formation are not completely understood. Here we use in vivo condensate reconstitution experiments and coarse-grained molecular simulations to investigate how oligomerization and sequence interactions modulate multiphase organization in biomolecular condensates. We demonstrate that increasing the oligomerization state of an intrinsically disordered protein results in enhanced immiscibility and multiphase formation. Interestingly, we find that oligomerization tunes the miscibility of intrinsically disordered proteins in an asymmetric manner, with the effect being more pronounced when the intrinsically disordered protein, exhibiting stronger homotypic interactions, is oligomerized. Our findings suggest that oligomerization is a flexible biophysical mechanism that cells can exploit to tune the internal organization of biomolecular condensates and their associated biological functions.
Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management
Accurate subsurface reservoir pressure control is extremely challenging due to geological heterogeneity and multiphase fluid-flow dynamics. Predicting behavior in this setting relies on high-fidelity physics-based simulations that are computationally expensive. Yet, the uncertain, heterogeneous properties that control these flows make it necessary to perform many of these expensive simulations, which is often prohibitive. To address these challenges, we introduce a physics-informed machine learning workflow that couples a fully differentiable multiphase flow simulator, which is implemented in the DPFEHM framework with a convolutional neural network (CNN). The CNN learns to predict fluid extraction rates from heterogeneous permeability fields to enforce pressure limits at critical reservoir locations. By incorporating transient multiphase flow physics into the training process, our method enables more practical and accurate predictions for realistic injection-extraction scenarios compared to previous works. To speed up training, we pretrain the model on single-phase, steady-state simulations and then finetune it on full multiphase scenarios, which dramatically reduces the computational cost. We demonstrate that high-accuracy training can be achieved with fewer than three thousand full-physics multiphase flow simulations – compared to previous estimates requiring up to ten million. This drastic reduction in the number of simulations is achieved by leveraging transfer learning from much less expensive single phase simulations.
Toward Water Volume Fraction Calculation in Multiphase Flows Using Electrical Capacitance Tomography Sensors
Real-time monitoring of water volume fraction in multiphase flows is an important problem for a number of industrial applications. The water phase in the multiphase flows may correspond to either the dispersed phase or the continuous phase. In the past, several lowcost and nonintrusive techniques based on the electrical capacitance tomography (ECT) has been developed to image and monitor in real-time multiphase flows containing water. Furthermore, such monitoring becomes increasingly challenging for high salinity levels, and no reliable ECTbased method is presently available which could work for obtaining water volume fraction in multiphase flows for all water salinity levels. In this paper, we propose a new approach based on the Hanai’s formula for complex dielectric constant and taking advantage of the Maxwell- Wagner-Sillars effect to obtain, to a good approximation, water volume fractions in multiphase flows containing water as either dispersed or continuous phase.
Multiscale modeling of microwave-heated multiphase systems
Modeling of microwave heating of multiphase systems requires resolving the electromagnetic field from the single particle to the entire cavity. We introduce a multiscale methodology for computationally affordable simulations of microwave heating of multiphase systems consisting of one phase dispersed in a continuum phase. The methodology homogenizes the original multiphase system, by taking advantage of the large separation of length scales, to calculate the effective permittivity, effective thermal conductivity, and volumetric power absorbed in each phase. The methodology is rigorously assessed against particle-resolved detailed numerical simulations of model systems. We demonstrate a significant reduction in computational cost while retaining the accuracy of detailed simulations. Lastly, the present methodology enables high throughput exploration of novel multiphase system designs utilizing microwave heating.
A review of microwave-assisted process intensified multiphase reactors
Microwaves provide alternative heating and allow process intensification due to their rapid, volumetric, and selective nature. Recognizing the central role of multiphase reactors in chemical industry, a recent surge in employing microwaves is observed. We review the recent experimental and modeling investigations of microwave heating of multiphase reactors with emphasis on chemical engineering applications. Here we demonstrate that there is accumulated evidence for improved performance via microwave heating and a clear opportunity for further process intensification. In most of the cases, this improved performance stems from a temperature gradient between two phases. We discuss the ongoing debate on the mechanism by which microwaves affect chemical processes exacerbated by the inability of measuring the temperature distribution in a microwave cavity. We outline recent progress in this direction in monolith reactors and needs for future work. We underscore the lack of detailed modeling and simulation tools even for single-phase systems and emphasize the imperative for multiscale predictive modeling to bridge the experimental-modeling gap. Promising results are shown by a few recently published modeling studies that can predict the experimental measurements in complex multiphase reactors. A combination of experimental and modeling tools can provide a comprehensive picture of the microwave multiphase reactors as well as a means toward scale-up and optimization.
Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration
Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the amount of carbon dioxide in the atmosphere, which also places high demands on reliability. Multiphase flow in porous media is essential to understand CO 2 migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory (<15%) and GPU memory (<35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. Furthermore, we observed that Fourier-MIONet can maintain good accuracy when predicting out-of-distribution (OOD) data. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time. Furthermore, the developed Fourier-MIONet makes it possible to solve the long-time evolution of geological carbon sequestration in a large-scale three-dimensional space accurately and efficiently.
Transforming layered 2D mats into multiphasic 3D nanofiber scaffolds with tailored gradient features for tissue regeneration
Abstract Multiphasic scaffolds with tailored gradient features hold significant promise for tissue regeneration applications. Herein, this work reports the transformation of two‐dimensional (2D) layered fiber mats into three‐dimensional (3D) multiphasic scaffolds using a ‘solids‐of‐revolution’ inspired gas‐foaming expansion technology. These scaffolds feature precise control over fiber alignment, pore size, and regional structure. Manipulating nanofiber mat layers and Pluronic F127 concentrations allows further customization of pore size and fiber alignment within different scaffold regions. The cellular response to multiphasic scaffolds demonstrates that the number of cells migrated and proliferated onto the scaffolds is mainly dependent on the pore size rather than fiber alignment. In vivo subcutaneous implantation of multiphasic scaffolds to rats reveals substantial cell infiltration, neo tissue formation, collagen deposition, and new vessel formation within scaffolds, greatly surpassing the capabilities of traditional nanofiber mats. Histological examination indicates the importance of optimizing pore size and fiber alignment for the promotion of cell infiltration and tissue regeneration. Overall, these scaffolds have potential applications in tissue modeling, studying tissue‐tissue interactions, interface tissue engineering, and high‐throughput screening for optimized tissue regeneration.
Liver metastases of neuroendocrine tumors: is it possible to diagnose different histologic subtypes depending on multiphasic CT features?
Purpose: To assess and compare the multiphasic computed tomography (CT) features of neuroendocrine tumor (NET) liver metastases and to investigate the possibility to predict the histologic subtype of the primary tumor. Materials and methods: Between January 2013 and December 2017 patients with biopsy proven NET with at least one liver metastasis who underwent multiphasic CT were enrolled in this study. All cases were acquired using a standardized multiphasic liver CT protocol, arterial, portal, and hepatic venous phases were obtained. Images were retrospectively analyzed in consensus by two abdominal radiologists blinded to clinical data and histologic subtype. The size, number, and location of lesions were noted. Enhancement patterns of each lesion on arterial, portal, and hepatic venous phases were assessed. For quantitative analysis, CT attenuation of tumors, liver parenchyma, and aorta were measured using a circular region of interest (ROI) on arterial, portal, and hepatic venous phases for reflecting the blood supply of the tumor. Tumor-to-aorta and tumor-to-liver ratio were calculated in all three phases. Differences between subtypes of NET liver metastases were studied using ROC analysis of clustered data. Results: A total of 255 neuroendocrine tumor liver metastases divided into 101 (39.6%) pancreatic, 60 (23.5%) gastroenteric and 94 (36.8%) lung NET liver metastases were analyzed. Contrast enhancement of lesions was homogeneous in 78% of patients (n = 199), which was significantly more frequent in patients with pancreatic group than in those with gastroenteric origin (n = 90, 89.1% vs. n = 28, 46.7%; p < 0.001). Gastroenteric NET metastases frequently showed heterogeneous enhancement, which was significantly higher than in the other two groups (50% vs. 3% and 2%). With respect to the location of the primary tumor, the difference in enhancement patterns of the liver lesions was statistically significant (p < 0.001). Pancreatic NET metastases were mostly hyperdense on arterial images and isodense on portal and hepatic venous phase images (79.2%, n = 80). Gastroenteric NET metastases were mostly hyperdense on arterial phase images and hypodense on portal and hepatic venous phase images (n = 28, 46.7%). The most frequent pattern for lung NET metastases was hypoattenuation on all three phase images (n = 44, 46.8%). ROC analysis of clustered data revealed statistically significant differences between pancreatic NET liver metastases, gastroenteric NET liver metastases, and lung NET liver metastases in terms of tumor-to-aorta (T–A) ratio and tumor-to-liver (T–L) ratio (p < 0.001). Conclusion: We observed statistically significant differences in multiphasic CT features (enhancement pattern, T–A ratio, and T–L ratio) between histologic subtypes of NET liver metastases. As the difference in histological subtypes of NET liver metastases results in a different prognosis and different management strategy, these CT features might help to identify the primary tumor when it is not known to ensure accurate tumor staging and to provide optimal treatment.
Preparation and characterization of multiphase ceramic designer waste forms
Abstract The long-term performance, or resistance to elemental release, is the defining characteristic of a nuclear waste form. In the case of multiphase ceramic waste forms, correlating the long-term performance of multiphase ceramic waste forms in the environment to accelerated chemical durability testing in the laboratory is non-trivial owing to their complex microstructures. The fabrication method, which in turn affects the microstructure, is further compounding when comparing multiphase ceramic waste forms. In this work, we propose a “designer waste form” prepared via spark plasma sintering to limit interaction between phases and grain growth during consolidation, leading to monolithic high-density waste forms, which can be used as reference materials for comparing the chemical durability of multiphase waste forms. Designer waste forms containing varying amounts of hollandite in the presence of zirconolite and pyrochlore in a fixed ratio were synthesized. The product consistency test (PCT) and vapor hydration test (VHT) were used to assess the leaching behavior. Samples were unaffected by the VHT after 1500 h. As measured by the PCT, the fractional Cs release decreased as the amount of hollandite increased. Elemental release from the zirconolite and pyrochlore phases did not appear to significantly contribute to the elemental release from the hollandite phase in the designer waste forms.