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DOE OSTI2021

Nonequilibrium Physics of Multiphase Flow in Porous Media: Wettability and Disorder

Carbon capture and geologic storage, dissociation of methane hydrates in permafrost, enhanced oil recovery, and water dropout in low-temperature fuel cells, all have something in common: two or more fluids flow simultaneously through a porous medium; and the displacement of one fluid by another is often unstable (either due to gravity or viscous forces). Yet, our ability to model multiphase flow in porous media has remained a challenge. The traditional equations are unable to predict, explain, or even reproduce, the formation of the complex patterns observed in experiments. The overarching goal of the project is to develop new physical understanding of the role of wettability and disorder in multiphase flow through permeable media, and to develop new mathematical and computational models at the pore scale and at the continuum scale.

58 GEOSCIENCES↗

DOE OSTI2017

Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections

This panel presentation focuses on multiphase radial distribution networks with wye and delta connections, and proposes a semidefinite relaxation of the AC optimal power flow (OPF) problem. Two multiphase power flow models are developed to facilitate the integration of delta-connected loads or generation resources in the OPF problem. The first model is referred to as the extended branch flow model (EBFM). The second model leverages a linear relationship between phase-to-ground power injections and delta connections that holds under a balanced voltage approximation (BVA). Based on these models, pertinent OPF problems are formulated and relaxed to semidefinite programs (SDPs). Numerical studies on IEEE test feeders show that the proposed SDP relaxations can be solved efficiently by a generic optimization solver. Numerical evidence also indicates that solving the resultant SDP under BVA is faster than under EBFM. Moreover, both SDP solutions are numerically exact with respect to voltages and branch flows. It is further shown that the SDP solution under BVA has a small optimality gap, and the BVA model is accurate in the sense that it reproduces actual system voltages.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2017

Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint

This paper focuses on multiphase radial distribution networks with mixed wye and delta connections, and proposes a semidefinite relaxation of the AC optimal power flow (OPF) problem. Two multiphase power-flow models are developed to facilitate the integration of delta-connected generation units/loads in the OPF problem. The first model extends traditional branch flow models - and it is referred to as extended branch flow model (EBFM). The second model leverages a linear relationship between per-phase power injections and delta connections, which holds under a balanced voltage approximation (BVA). Based on these models, pertinent OPF problems are formulated and relaxed to semidefinite programs (SDPs). Numerical studies on IEEE test feeders show that SDP relaxations can be solved efficiently by a generic optimization solver. Numerical evidences indicate that solving the resultant SDP under BVA is faster than under EBFM. Moreover, both SDP solutions are numerically exact with respect to voltages and branch flows. It is also shown that the SDP solution under BVA has a small optimality gap, while the BVA model is accurate in the sense that it reflects actual system voltages.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Multiphase Reacting Flow Simulations and Optimization of Commercial-Scale Aerobic Bioreactors

Aerobic bioreactors are widely used in the synthesis of value-added products in pharmaceutical and biotechnology industries, wherein microbial bioreactions aid in the conversion of sugars to macromolecules. These reactors are also being actively investigated as a cost-effective pathway for the production of low-value commodities such as biofuels and animal feed. Reactor scale-up is one of the important challenges when designing these systems. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of commercial-scale (~ 500 m3) aerobic bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for oxygen uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM, to perform these simulations, which has been validated against small-scale reactors in our previous work. This work examines the performance of three different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor oxygen mass-transfer coefficient, gas hold-up, and oxygen distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented.

09 BIOMASS FUELS↗

DOE OSTI2015

Incompressible multiphase flow and encapsulation simulations using the moment-of-fluid method

A moment-of-fluid method is presented for computing solutions to incompressible multiphase flows in which the number of materials can be greater than two. In this work, the multimaterial moment-of-fluid interface representation technique is applied to simulating surface tension effects at points where three materials meet. The advection terms are solved using a directionally split cell integrated semi-Lagrangian algorithm, and the projection method is used to evaluate the pressure gradient force term. The underlying computational grid is a dynamic block-structured adaptive grid. The new method is applied to multiphase problems illustrating contact-line dynamics, triple junctions, and encapsulation in order to demonstrate its capabilities. Examples are given in two-dimensional, three-dimensional axisymmetric (R–Z), and three-dimensional (X–Y–Z) coordinate systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Multiphase lattice Boltzmann simulations for porous media applications

Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this work, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

42 ENGINEERING↗

DOE OSTI2019

TOUGH-UDEC: A simulator for coupled multiphase fluid flows, heat transfers and discontinuous deformations in fractured porous media

A numerical simulator entitled TOUGH-UDEC is presented for the assessment of coupled thermal-hydraulic-mechanical processes in fractured porous media. Two existing well-established codes, TOUGH2 and UDEC, are coupled to model multiphase fluid flows, heat transfers, and discontinuous deformations in fractured porous media by means of discrete fracture representation. TOUGH2 is widely used for the modeling of heat transfers and multiphase multicomponent fluid flows, and UDEC is a well-known distinct element code for rock mechanics. The two codes are solved sequentially, with coupling parameters passed to each equation at specific intervals. After solving thermal-hydraulic equations within the TOUGH2 code, pressure and temperature information is imported into the UDEC model. Upon solving the mechanical equation within the UDEC code the calculated fracture apertures are converted to the equivalent permeability and porosity values for a TOUGH2 flow analysis. The solution is calculated by iteratively following an explicit sequence for numerical efficiency. Verifications are presented to demonstrate the capabilities of the coupled TOUGH-UDEC simulator. Three application examples of (1) shear dilation due to increased pore pressure, (2) thermal stress and (3) CO 2 injection, show that the new simulator can be an effective tool for geoengineering applications involving shear activation of fractures and faults.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Thermodynamically consistent algorithms for models of incompressible multiphase polymer solutions with a variable mobility

Here we present a general strategy for developing structure and property preserving numerical algorithms for thermodynamically consistent models of incompressible multiphase polymer solutions with a variable mobility. We first present a formalism to derive thermodynamically consistent, incompressible, multiphase polymer models. Then, we develop the general strategy, known as the supplementary variable method, to devise thermodynamically consistent numerical approximations to the models. We illustrate the numerical strategy using newly developed models of incompressible diblock copolymer solutions coupled with an electric and a magnetic field, respectively. Mesh refinement is conducted to verify convergence rates of the developed schemes. Some numerical examples are given to exhibit underlying dynamics absent from and driven by the external fields, respectively, highlighting differences between models with the variable and constant mobilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Physics-Constrained Deep Learning Model for Simulating Multiphase Flow in 3D Heterogeneous Porous Media

Physics-based simulators for multiphase flow in porous media emulate nonlinear processes with coupled physics, and usually require extensive computational resources for software development, maintenance and simulation execution. As a result, a huge demand exists for fast modeling of coupled processes in a wide range of subsurface applications including geological sequestration, hydrocarbon recovery and geothermal energy extraction. In this work, an efficient physics-constrained deep learning model is developed for solving multiphase flow in 3-Dimensional (3D) heterogeneous porous media. The model fully leverages the spatial topology predictive capability of convolutional neural networks, specifically U-Net with successive contracting and expansive steps, and is coupled with an efficient continuity-based smoother to predict flow responses that need spatial continuity. Furthermore, the transient regions are penalized to steer the training process such that the model can accurately capture flow in these regions. The model takes inputs including properties of porous media, fluid properties and well controls, and predicts the temporal-spatial evolution of the state variables (pressure and saturation). While maintaining the continuity of fluid flow, the 3D spatial domain is decomposed into 2D images for reducing training cost, and the decomposition results in an increased number of training data samples and better training efficiency. Additionally, a surrogate model is separately constructed as a postprocessor to calculate well flow rate based on the predictions of state variables from the deep learning model. We use the example of CO 2 injection into saline aquifers, and apply the physics-constrained deep learning model that is trained from physics-based simulation data and emulates the physics process. The model performs prediction with a speedup of ~ 1400 times compared to physics-based simulations, and the average temporal errors of predicted pressure and saturation plumes are 0.27% and 0.099% respectively. Furthermore, water production rate is efficiently predicted by a surrogate model for well flow rate, with a mean error less than 5%. Therefore, with its unique scheme to cope with the fidelity in fluid flow in porous media, the physics-constrained deep learning model can become an efficient predictive model for computationally demanding inverse problems or other coupled processes.

58 GEOSCIENCES↗

DOE OSTI2014

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces

Although the Discontinuous Galerkin (dg) method has seen widespread use for compressible flow problems in a single fluid with constant material properties, it has yet to be implemented in a consistent fashion for compressible multiphase flows with shocks and interfaces. Specifically, it is challenging to design a scheme that meets the following requirements: conservation, high-order accuracy in smooth regions and non-oscillatory behavior at discontinuities (in particular, material interfaces). Following the interface-capturing approach of Abgrall [1], we model flows of multiple fluid components or phases using a single equation of state with variable material properties; discontinuities in these properties correspond to interfaces. Here, to represent compressible phenomena in solids, liquids, and gases, we present our analysis for equations of state belonging to the Mie–Grüneisen family. Within the dg framework, we propose a conservative, high-order accurate, and non-oscillatory limiting procedure, verified with simple multifluid and multiphase problems. We show analytically that two key elements are required to prevent spurious pressure oscillations at interfaces and maintain conservation: (i) the transport equation(s) describing the material properties must be solved in a non-conservative weak form, and (ii) the suitable variables must be limited (density, momentum, pressure, and appropriate properties entering the equation of state), coupled with a consistent reconstruction of the energy. Further, we introduce a physics-based discontinuity sensor to apply limiting in a solution-adaptive fashion. We verify this approach with one- and two-dimensional problems with shocks and interfaces, including high pressure and density ratios, for fluids obeying different equations of state to illustrate the robustness and versatility of the method. Lastly, the algorithm is implemented on parallel graphics processing units (gpu) to achieve high speedup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Radiation damage of hollandite in multiphase ceramic waste forms

Radiation damage was simulated in multiphase titanate-based ceramic waste forms using an ion accelerator to generate high energy alpha particles (He + ) and an ion implanter to generate 7 MeV gold (Au 3+ ) particles. X-ray diffraction and transmission electron microscopy were used to characterize the damaged surfaces and nearby regions. Simulated multiphase ceramic waste forms were prepared using two processing methods: spark plasma sintering and melt-processing. Both processing methods produced ceramics with similar phase assemblages consisting of hollandite-, zirconolite/pyrochlore-, and perovskite- type phases. The measured heavy ion (Au 3+ ) penetration depth was less in spark plasma sintered samples than in melt-processed samples. Furthermore, structural breakdown of the hollandite phase occurred under He + irradiation indicated by the presence of x-ray diffraction peaks belonging to TiO 2 , BaTiO 5 , and other hollandite related phases (Ba 2 Ti 9 O 20 ). The composition of the constituent hollandite phase affected the extent of damage induced by Au 3+ ions.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Elaborating the phases and mechanical properties of multiphase alloy: Experimental two-dimensional mapping combined with theoretical calculations

Highlights: • Mechanical modulus and hardness distribution mapping is obtained for the first time by NanoBlitz 3D. • Phases mapping and exact element ratio are characterized for the nano multielement carbides by EPMA. • Carbides types are confirmed by acid etching and XRD refinement. • Young's modulus of multiple carbides is verified by DFT calculations and Voigt-Reuss-Hill model. - Abstract: The relationship between types of phases, microstructure and mechanical properties is always a critical challenge for the research and application of multiphase alloys. We report for the first time that NanoBlitz 3D method implemented in iNano is used to investigate the distribution of micro mechanical modulus and hardness for the entire complex multiphase alloy Fe-6.0W-5.0Mo-4.0Cr-2.0V-0.83C by constructing the two-dimensional mapping. In order to build the correlation between the microstructure and properties, the carbides in this tempering state steel are confirmed to be Fe{sub 3}(W, Mo){sub 3}C, Cr{sub 15.58}Fe{sub 7.42}C{sub 6} and V{sub 8}C{sub 7} by acid etching and XRD refinement. The phases mapping is obtained by electron probe micro-analysis. Exact element ratio is characterized for the nano-scale multielement carbides precipitates. The Young's modulus and hardness of the precipitated carbides are up to 330 GPa and 22 GPa, respectively. The distribution range of Young's modulus and hardness is during 150 to 250 GPa and 2.5 to 7.0 GPa for the matrix phases, respectively. The experimental Young's modulus and hardness results are verified by first-principles calculations combined with Voigt-Reuss-Hill approximation. In fact, this work provides a successful demonstration to three-dimensionally characterize the micro mechanical properties for all the ceramics and alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Clinical analysis of the approximate, 3-dimensional, biological effective dose equation in multiphase treatment plans

A multiphase, approximate biological effective dose (BED{sub A}) equation was introduced because most treatment planning systems (TPS) are incapable of calculating the true BED (BED{sub T}). This work investigates the accuracy and precision of the multiphase BED{sub A} relative to the BED{sub T} in clinical cases. Ten patients with head and neck cancer and 10 patients with prostate cancer were studied using their treatment plans from Pinnacle{sup 3} 9.2 (Philips Medical, Fitchburg, WI). The organs at risk (OARs) that were studied are the normal brain, left and right optic nerves, optic chiasm, spinal cord, brainstem, bladder, and rectum. BED{sub A} and BED{sub T} distributions were calculated using MATLAB 2010b (MathWorks, Natick, MA) and analyzed on a voxel basis for percent error, percent error volume histograms (PEVHs), Pearson correlation coefficient, and Bland-Altman analysis. The maximum BED values that were calculated using the BED{sub A} and BED{sub T} methods were also analyzed. BED{sub A} was found to always underestimate BED{sub T}. The accuracy and precision of BED{sub A} distributions varied between the organs: for optic chiasm and brainstem, 50% of the patients had an overall BED{sub A} percent error of A percent error of A percent error of A distributions had maximum errors ranging from 2% to 11%, with the 11% error occurring for bladder. BED{sub A} produced much more accurate maximum BED values with adjacent organs such as normal brain, bladder, and rectum. This study has shown that BED{sub A} can calculate BED distributions with acceptable accuracy under certain circumstances. However, its consistency and accuracy strongly depend on the dose distributions of the different treatment phases. One should be cautious when using BED{sub A}.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2014

Radiation stability test on multiphase glass ceramic and crystalline ceramic waste forms

A radiation stability study was performed on glass ceramic and crystalline ceramic waste forms. These materials are candidate host materials for immobilizing alkali/alkaline earth (Cs/Sr-CS) + lanthanide (LN) + transition metal (TM) fission product waste streams from nuclear fuel reprocessing. In this study, glass ceramics were fabricated using a borosilicate glass as a matrix in which to incorporate CS/LN/TM combined waste streams. The major phases in these multiphase materials are powellite, oxyaptite, pollucite, celsian, and durable residual glass phases. Al2O3 and TiO2 were combined with these waste components to produce multiphase crystalline ceramics containing hollandite-type phases, perovskites, pyrochlores and other minor metal titanate phases. For the radiation stability test, selected glass ceramic and crystalline ceramic samples were exposed to different irradiation environments including low fluxes of high-energy (~1–5 MeV) protons and alpha particles generated by an ion accelerator, high fluxes of low-energy (hundreds of keV) krypton particles generated by an ion implanter, and in-situ electron irradiations in a transmission electron microscope. These irradiation experiments were performed to simulate self-radiation effects in a waste form. Ion irradiation-induced microstructural modifications were examined using X-ray diffraction and transmission electron microscopy. Our preliminary results reveal different radiation tolerance in different crystalline phases under various radiation damage environments. However, their stability may be rate dependent which may limit the waste loading that can be achieved.

Crystalline ceramic↗

DOE OSTI2018

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability

The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas–liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. To investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been performed. The turbulent dissipation is shown to be highly demanding on mesh resolution compared with other terms in TKE budget. The results obtained with the finest mesh are shown to be close to converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The estimated Kolmogorov scale is found to be similar to the cell size of the finest mesh used here. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.

Mechanics↗

DOE OSTI2018

Multiphase Mechanism for the Production of Sulfuric Acid from SO 2 by Criegee Intermediates Formed During the Heterogeneous Reaction of Ozone with Squalene

Here we report a new multiphase reaction mechanism by which Criegee intermediates (CIs), formed by ozone reactions at an alkene surface, convert SO 2 to SO 3 to produce sulfuric acid, a precursor for new particle formation (NPF). During the heterogeneous ozone reaction, in the presence of 220 ppb SO 2 , an unsaturated aerosol (squalene) undergoes rapid chemical erosion, which is accompanied by NPF. A kinetic model predicts that the mechanism for chemical erosion and NPF originate from a common elementary step (CI + SO 2 ) that produces both gas phase SO 3 and small ketones. At low relative humidity (RH = 5%), 20% of the aerosol mass is lost, with 17% of the ozone-surface reactions producing SO 3 . At RH = 60%, the aerosol shrinks by 30%, and the yield of SO 3 is <5%. In conclusion, this multiphase formation mechanism of H 2 SO 4 by CIs is discussed in the context of indoor air quality and atmospheric chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

High-Speed Quantification of Pore-Scale Multiphase Flow of Water and Supercritical CO 2 in 2-D Heterogeneous Porous Micromodels: Flow Regimes and Interface Dynamics

The pore-scale flow of CO 2 and water in 2-D heterogeneous porous micromodels over a Ca range of nearly three orders of magnitude was explored experimentally. The porous geometry is a close reprint of real sandstone, and the experiments were performed under reservoir-relevant conditions (i.e., 8 MPa and 21°C), thus ensuring relevance to practical CO 2 operations. High-speed fluorescent microscopy and image processing were employed to achieve temporally and spatially resolved data, providing a unique view of the dynamics underlying this multiphase flow scenario. Under conditions relevant to CO 2 sequestration, final CO 2 saturation was found to decrease and increase logarithmically with Ca within the capillary and viscous-fingering regimes, respectively, with a minimum occurring during regime crossover. Specific interfacial length generally scales linearly with CO 2 saturation, with higher slopes noted at high Ca due to stronger viscous and inertial forces, as supported by direct pore-scale observations. Additionally, statistical analysis of the interfacial movements revealed that pore-scale events are controlled by their intrinsic dynamics at low Ca, but overrun by the bulk flow at high Ca. During postfront flow, while permeability is typically correlated with total CO 2 saturation in the porous domain (regardless of its mobility), the saturation of active CO 2 pathways in the current study correlated very well with permeability. This alternate approach to characterize relative permeability could serve to mitigate hysteresis in relative permeability curves. Taken together, these results provide unique insights that address inconsistent observations in the literature and previously unanswered questions about the underlying flow dynamics of this important multiphase flow scenario.

42 ENGINEERING↗

DOE OSTI2019

Mimicking Geologic Depositional Fabrics for Multiphase Flow Experiments

A novel laboratory technique is presented for generating two-dimensional beadpacks with reproducible natural geologic sedimentary bedforms. The heterogeneous beadpacks are deposited in a 0.6 m × 0.6 m × 0.02 m glass slab chamber using a programmable two-axis linear actuator. The method takes advantage of natural mechanical sorting processes, along with the ability to program the motion of the arm, to efficiently build cross-beds and ripple laminae similar to those seen in natural water-lain clastic deposits. By using a mixture of grain sizes (200 to 800 μm diameter), depositional fabrics with multiscale heterogeneity (mm to dm) are generated. Reproducibility tests show very high correlation among multiple fabric realizations produced with similar inputs. After introducing this first-of-a-kind capability to produce depositionally realistic fabrics at scales larger than that of rock cores, a demonstrative study is presented that illustrates gravity unstable multiphase flow which is relevant in the context of CO 2 sequestration. Preliminary results highlight the dramatic impact small scale capillary heterogeneities have on multiphase immiscible displacement and can help bridge understanding between core scale experiments and reservoir scale observations.

54 ENVIRONMENTAL SCIENCES↗