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A model and numerical method for compressible flows with capillary effects
A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.
A numerical study of particle jetting in a dense particle bed driven by an air-blast
In this work, the particle jetting behavior in a blast-driven dense particle bed is studied at early times. Four-way coupled Euler–Lagrange simulations are performed using a high-order discontinuous Galerkin spectral element solver coupled with a high-order Lagrangian particle solver, wherein the inter-particle collisions are resolved using a discrete element method collision model. Following the experiments of Rodriguez et al. [“Formation of particle jetting in a cylindrical shock tube,” Shock Waves 23(6), 619–634 (2013)] and the simulations of Osnes et al. [“Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell,” Shock Waves 28(3), 451–461 (2018)], the simulations are performed in a quasi-two-dimensional cylindrical geometry (Hele-Shaw cell). Parametric studies are carried out to assess the impact of the coefficient of restitution and the strength of the incident shock on the particle jetting behavior. The deposition of vorticity through a multiphase (gas–particle) analog of Richtmyer–Meshkov instability is observed to play a crucial role in channeling the particles into well-defined jets at the outer edge of the particle bed. This is confirmed by the presence of vortex pairs around the outer jets. Furthermore, the effect of the relaxation of the relative velocity between the two phases on the vorticity generation is explored by analyzing the correlation between the radial velocity of particles and the radial velocity of the gas at the particle location.
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.
User's Manual of the TOUGH+ Core Code v1.5: A General-Purpose Simulator of Non-Isothermal Flow and Transport through Porous and Fractured Media
TOUGH+ v1.5 is a numerical code for the simulation of multi-phase, multi-component flow and transport of mass and heat through porous and fractured media, and represents the third update of the code since its first release [Moridis et al., 2008]. TOUGH+ is a successor to the TOUGH2 [Pruess et al., 1991] family of codes for multi-component, multiphase fluid and heat flow developed at the Lawrence Berkeley National Laboratory. It is written in standard FORTRAN 95/2003, and can be run on any computational platform (workstations, PC, Macintosh). TOUGH+ v1.5 employs dynamic memory allocation, thus minimizing storage requirements. It has a completely modular structure, follows the tenets of Object-Oriented Programming (OOP), and involves the advanced features of FORTRAN 95/2003, i.e., modules, derived data types, the use of pointers, lists and trees, data encapsulation, defined operators and assignments, operator extension and overloading, use of generic procedures, and maximum use of the powerful intrinsic vector and matrix processing operations. This report presents the core TOUGH+ v1.5 code, i.e., the part of the code that is common to all its applications. It provides a description of the underlying physics and thermodynamics of non-isothermal flow, of the mathematical and numerical approaches, as well as a detailed explanation of the general (common to all applications) input requirements, options, capabilities and output specifications. The core code cannot run by itself: it needs to be coupled with the code for the specific TOUGH+ application option that describes a particular type of problem. The additional input requirements specific to a particular TOUGH+ application options and related illustrative examples can be found in the corresponding User’s Manual.
Thermo-Hydrological Modeling of Thermal Energy Storage in a Depleted Oil Reservoir
Thermal energy storage in oil and gas reservoirs leverages the existing surface and subsurface infrastructure, which can pave the way for economic production of geothermal energy. Existing studies on geothermal energy storage are focused mostly on the use of aquifers with more homogeneous rock and fluid properties. Coupling of heat and fluid flow in a multiphase-multicomponent system, such as an oil reservoir, is imperative especially if existing oil field assets need to be repurposed as required for a sustainable energy transition. The objective is to model the subsurface thermo-hydrological processes associated with reservoir performance and operational sustainability. The model evaluates formation pressure and temperature within the reservoir and at the injection/production wells during multiple charge and discharge cycles. Hot water (approximately 200 degrees C) heated by Concentrating Solar Power (CSP) at high pressure is injected into the existing oil reservoir for storage and produced as thermal energy for power generation, which will be accompanied by enhanced oil recovery. To demonstrate the coupled fluid and heat flow during the injection/production cycle in the subsurface reservoir, TOUGH3 (developed by Berkeley Lab) is used to simulate the thermo-hydrological (TH) processes in a multiphase, multicomponent system. Two well geometries are considered within the reservoir grid: 1) a single-well huff-n-puff system (same well is used for injection and production), and 2) an isolated injection-production well doublet. Seasonal charge and discharge cycling are implemented based on the scheduling specified in the model input file. The model reports pressure, temperature, enthalpy, liquid fluxes, heat fluxes, pore velocities, and changes in porosity & permeability due to temperature and pressure variations during the cyclic Reservoir Thermal Energy Storage (RTES) operations. The results from the simulations can be used to optimize the operational parameters (such as well spacing and injection/production rates) and round-trip efficiency for surface power-plants coupled with thermal energy storage over time. They can also serve as important inputs for levelized cost of storage estimations. The research will help to design and integrate surface renewable energy sources, such as concentrating solar power (CSP), with RTES to help balance out power supply and demand on the grid.
Active motion of multiphase oil droplets: emergent dynamics of squirmers with evolving internal structure
Synthetic soft matter systems, when driven beyond equilibrium by active processes, offer the potential to achieve dynamical states and functions of a complexity found in living matter. Emulsions offer the basis of a simple yet versatile system for identification of the physicochemical principles underlying active soft matter, but how multiple internal phases within emulsion droplets (e.g., Janus morphologies) organize to impact emergent dynamics is not understood. Here, we create multiphase oil droplets with ultralow interfacial tensions but distinct viscosities, and drive them into motion in aqueous micellar solutions. Preferential solubilization of select components of the oil both drives the droplet motion and yields a progression of internal phase morphological states with distinct symmetries. In this work, we find the active droplets to exhibit five dynamical states during morphogenesis. By quantifying microscopic flow fields, we show that it is possible to map the diverse droplet behaviors to squirmer models of spherical microswimmers in Stokes flow, thus showing that multiphase droplets offer the basis of a versatile platform with which to study and engineer the hydrodynamics of microswimmers.
Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods
Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.
Velocity Profiling of a Gas–Solid Fluidized Bed Using Electrical Capacitance Volume Tomography
In this study, a method of producing velocity profile maps from electrical capacitance volume tomography (ECVT) measurements by reconstructing displacement from measured changes in capacitance is developed and applied to fluidized bed systems. The mapping of the reconstruction leverages the gradient of the sensitivity distribution of the ECVT sensor to circumvent the need for image cross correlation techniques. Experimental data of both bubbling and slugging fluidized beds are collected in a cold flow model. Adaptation of the technique is discussed in detail, and velocity profiles are obtained for a range of gas flow rates. The produced velocity maps are compared against the established methods of cross correlation and against empirical correlations from the literature and are found to agree well in tracking slug and bubble velocity. The exception is when the tracked object is large relative to the ECVT sensor dimensions, a scenario that can be avoided through proper sensor design. The quantities of average velocity, momentum, and solid and gas volume fraction are derived from the image and velocity profiles. The results demonstrate and extend the power of ECVT as a measurement tool for the study and monitoring of gas–solid fluidized beds by providing a computationally cheaper alternative to 3-D cross correlation for deriving velocity profiles.
Uniaxial Creep as a Control on Mercury Intrusion Capillary Pressure in Consolidating Rock Salt
The nature of geologic disposal of nuclear waste in salt formations requires validated and verified two-phase flow models of transport of brine and gas through intact, damaged, and consolidating crushed salt. Such models exist in other realms of subsurface engineering for other lithologic classes (oil and gas, carbon sequestration etc. for clastics and carbonates) but have never been experimentally validated and parameterized for salt repository scenarios or performance assessment. Models for waste release scenarios in salt back-fill require phenomenological expressions for capillary pressure and relative permeability that are expected to change with degree of consolidation, and require experimental measurement to parameterize and validate. This report describes a preliminary assessment of the influence of consolidation (i.e. volume strain or porosity) on capillary entry pressure in two phase systems using mercury injection capillary pressure (MICP). This is to both determine the potential usefulness of the mercury intrusion porosimetry method, but also to enable a better experimental design for these tests. Salt consolidation experiments are performed using novel titanium oedometers, or uniaxial compression cells often used in soil mechanics, using sieved run-of-mine salt from the Waste Isolation Pilot Plant (WIPP) as starting material. Twelve tests are performed with various starting amounts of brine pore saturation, with axial stresses up to 6.2 MPa (~900 psi) and temperatures to 90°C. This corresponds to UFD Work Package 15SN08180211 milestone “FY:15 Transport Properties of Run-of-Mine Salt Backfill – Unconsolidated to Consolidated”. Samples exposed to uniaxial compression undergo time-dependent consolidation, or creep, to various degrees. Creep volume strain-time relations obey simple log-time behavior through the range of porosities (~50 to 2% as measured); creep strain rate increases with temperature and applied stress as expected. Mercury porosimetry is used to determine characteristic capillary pressure curves from a series of consolidation tests and show characteristic saturation-capillary pressure curves that follow the common van Genuchten (1978, 1980) formulation at low stresses. Higher capillary pressure data are suspect due to the large potential for sample damage, including fluid inclusion decrepitation and pore collapse. Data are supportive of use of the Leverett “J” function (Leverett, 1941) to use for scaling characteristic curves at different degrees of consolidation, but better permeability determinations are needed to support this hypothesis. Recommendations for further and refined testing are made with the goal of developing a self- consistent set of constitutive laws for granular salt consolidation and multiphase (brine-air) flow.
Development of a conduction-based model for analyzing frozen startup of alkali-metal heat pipes
One key area of interest in heat pipe modeling/simulation is to analyze the startup behavior of the liquid-metal heat pipes (LMHPs) from a frozen state. This so-called ‘frozen startup’ process involves a complex set of nonlinear mass and heat transport phenomena, including phase transitions from solid to liquid and vapor, multiphase interactions, microporous wick flow, and compressible vapor dynamics. The complexity of these processes makes it challenging to simulate LMHP’s frozen startup using conventional numerical methods or commercial computational fluid dynamics (CFD) software. This paper presents a simplified conduction-based modeling approach that can provide practical insights into the entire LMHP frozen startup process, while alleviating the challenges of modeling its complex physics. The theoretical foundation and physical assumptions of the proposed model are based solely on heat-conduction equation, allowing for a more tractable simulation without sacrificing essential physical accuracy. The proposed model was implemented in a commercial CFD software, and its prediction was compared with the experimental data obtained from sodium heat-pipe startup experiments. The comparison highlights the proposed model's ability to capture the transient thermal behavior of LMHP during frozen startup. This study not only validates the conduction-based frozen startup modeling method but also shows its potential as a practical and efficient tool for understanding the startup performance of the LMHP systems.
Critical analysis of velocimetry methods for particulate flows from synthetic data
Particle tracking methods that extract high-fidelity particle velocity data from high speed video of particle laden flows is a common experimental technique applied to chemical processes. These measurements are used to better understand the motion of particles and fluids in complex systems and create data against which computational models are validated. However, the methods, codes, and experimental setups all have limitations. It is imperative that practitioners verify the methods and their implementation as well as understand the limitations of experimental setups. This work focuses on quantifying the visible depth of field in a high particle concentration fluidized bed. Following a precedent set by the particle imaging velocimetry community, a particle velocity field is manufactured using a computational fluid dynamics and discrete element method simulation. Photo realistic high-speed videos are rendered based on the simulated data using the three-dimensional creation software Blender. Particle velocities are extracted from the synthetic high-speed videos using three variants of Particle Tracking Velocimetry and Optical Flow Velocimetry methodologies. Here, the tracked results are then compared to the known solution, quantifying the error associated with the assumed visible depth. The results indicate that at depth of one particle diameter, all three particle tracking codes give accurate measurements, largely within 5%. However, the error increases when the full bed video measurements are compared to the known solution at one particle diameter, i.e., mimicking a validation study. Finally, for some statistics the constant depth assumption only increases the error slightly, for others significantly.
Coupled thermal–hydrological–mechanical modeling of CO 2 -enhanced coalbed methane recovery
CO 2 -enhanced coalbed methane recovery, also known as CO 2 -ECBM, is a potential win-win approach for enhanced methane production while simultaneously sequestering injected anthropogenic CO 2 to decrease CO 2 emissions into the atmosphere. Here, CO 2 -ECBM is simulated using a coupled thermal–hydrological–mechanical (THM) numerical model that considers multiphase (gas and water) flow and solubility, multicomponent (CO 2 and CH 4 ) diffusion and adsorption, heat transfer and coal deformation. The coupled model is based on the TOUGH-FLAC simulator, which is applied here for the first time to model CO 2 -ECBM. The capacity of the simulator for modeling methane production is verified by a code-to-code comparison with the general-purpose finite-element solver COMSOL. Then, the TOUGH-FLAC simulator is applied in an isothermal simulation to study the variations in permeability evolution during a CO 2 -ECBM operation while considering four different stress-dependent permeability models that have been implemented into the simulator. Finally, the TOUGH-FLAC simulator is applied in non-isothermal simulations to model THM responses during a CO 2 -ECBM operation.Our simulations show that the permeability evolution, mechanical stress, and deformation are all affected by changes in pressure, temperature and adsorption swelling, with adsorption swelling having the largest effect. The calculated stress changes do not induce any mechanical failure in the coal seam, except near the injection well in one case of a very unfavorable stress field.
Insights from high-fidelity modeling of industrial rotary bell atomization
The global automotive industry sprayed over 2.6 billion liters of paint in 2018, much of which through electrostatic rotary bell atomization, a highly complex process involving the fluid mechanics of rapidly rotating thin films tearing apart into micrometer-thin filaments and droplets. Coating operations account for 65% of the energy usage in a typical automotive assembly plant, representing 10,000s of gigawatt-hours each year in the United States alone. Optimization of these processes would allow for improved robustness, reduced material waste, increased throughput, and significantly reduced energy usage. Here, we introduce a high-fidelity mathematical and algorithmic framework to analyze rotary bell atomization dynamics at industrially relevant conditions. Our approach couples laboratory experiment with the development of robust non-Newtonian fluid models; devises high-order accurate numerical methods to compute the coupled bell, paint, and gas dynamics; and efficiently exploits high-performance supercomputing architectures. These advances have yielded insight into key dynamics, including i) parametric trends in film, sheeting, and filament characteristics as a function of fluid rheology, delivery rates, and bell speed; ii) the impact of nonuniform film thicknesses on atomization performance; and iii) an understanding of spray composition via primary and secondary atomization. These findings result in coating design principles that are poised to improve energy- and cost-efficiency in a wide array of industrial and manufacturing settings.
HYDRATE v1.5 OPTION OF TOUGH+ v1.5
HYDRATE v1.5 is a numerical code that for the simulation of the behavior of hydrate-bearing geologic systems, and represents the third update of the code since its first release [Moridis et al., 2008]. It is an option of TOUGH+ v1.5 [Moridis and Pruess, 2014], a successor to the TOUGH2 [Pruess et al., 1999, 2012] family of codes for multi-component, multiphase fluid and heat flow developed at the Lawrence Berkeley National Laboratory. HYDRATE v1.5 needs the TOUGH+ v1.5 core code in order to compile and execute. It is written in standard FORTRAN 95/2003, and can be run on any computational platform (workstation, PC, Macintosh) for which such compilers are available. By solving the coupled equations of mass and heat balance, the fully operational TOUGH+HYDRATE code can model the non-isothermal gas release, phase behavior and flow of fluids and heat under conditions typical of common natural CH4-hydrate deposits (i.e., in the permafrost and in deep ocean sediments) in complex geological media at any scale (from laboratory to reservoir) at which Darcy's law is valid. TOUGH+HYDRATE v1.5 includes both an equilibrium and a kinetic model of hydrate formation and dissociation. The model accounts for heat and up to four mass components, i.e., water, CH4, hydrate, and water-soluble inhibitors such as salts or alcohols. These are partitioned among four possible phases (gas phase, liquid phase, ice phase and hydrate phase). Hydrate dissociation or formation, phase changes and the corresponding thermal effects are fully described, as are the effects of inhibitors. The model can describe all possible hydrate dissociation mechanisms, i.e., depressurization, thermal stimulation, salting-out effects and inhibitor-induced effects.
PFLOTRAN
PFLOTRAN is a GNU LGPL licensed code that simulates single phase water and multiphase (air, co2, water) flow, energy transport, geochemical reaction and biological reaction in the earth's subsurface environment. The problem may be discretized on structured and unstructured grids. The code is designed to run in parallel on supercomputers and leverages the open source PETSc library for solvers and data structures and open source HDF5 for binary file I/O. See www.pflotran.org and/or doc-dev.pflotran.org for further information. SAND2020-12161 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
User's Manual for the Hydrate v1.5 Option of TOUGH+ v1.5: A Code for the Simulation of System Behavior in Hydrate-Bearing Geologic Media
HYDRATE v1.5 is a numerical code that for the simulation of the behavior of hydrate-bearing geologic systems, and represents the third update of the code since its first release [Moridis et al., 2008]. It is an option of TOUGH+ v1.5 [Moridis, 2014], a successor to the TOUGH2 [Pruess et al., 1999] family of codes for multi-component, multiphase fluid and heat flow developed at the Lawrence Berkeley National Laboratory. HYDRATE v1.5 needs the TOUGH+ v1.5 core code in order to compile and execute. It is written in standard FORTRAN 95/2003, and can be run on any computational platform (workstation, PC, Macintosh) for which such compilers are available. By solving the coupled equations of mass and heat balance, the fully operational TOUGH+HYDRATE code can model the non-isothermal gas release, phase behavior and flow of fluids and heat under conditions typical of common natural CH4-hydrate deposits (i.e., in the permafrost and in deep ocean sediments) in complex geological media at any scale (from laboratory to reservoir) at which Darcy’s law is valid. TOUGH+HYDRATE v1.5 includes both an equilibrium and a kinetic model of hydrate formation and dissociation. The model accounts for heat and up to four mass components, i.e., water, CH4, hydrate, and water-soluble inhibitors such as salts or alcohols. These are partitioned among four possible phases (gas phase, liquid phase, ice phase and hydrate phase). Hydrate dissociation or formation, phase changes and the corresponding thermal effects are fully described, as are the effects of inhibitors. The model can describe all possible hydrate dissociation mechanisms, i.e., depressurization, thermal stimulation, salting-out effects and inhibitor-induced effects.
User's Manual for the RealGasBrine v1.0 Option of TOUGH+ v1.5: A Code for the Simulation of System Behavior in Gas-Bearing Geologic Media
REALGASBRINE v1.0 is a numerical code that for the simulation of the behavior of gas-bearing porous and/fractured geologic media. It is an option of TOUGH+ v1.5 [Moridis, 2014], a successor to the TOUGH2 [Pruess et al., 1999] family of codes for multi-component, multiphase fluid and heat flow developed at the Lawrence Berkeley National Laboratory. REALGASBRINE v1.0 needs the TOUGH+ v1.5 core code in order to compile and execute. It is written in standard FORTRAN 95/2003, and can be run on any computational platform (workstation, PC, Macintosh) for which such compilers are available. REALGASBRINE v1.0 describes the non-isothermal two- (for pure water) or three-phase (for brine) flow of an aqueous phase and a real gas mixture in a gas-bearing medium, with a particular focus in ultra-tight (such as tight-sand and shale gas) systems. Up to 12 individual real gases can be tracked, and salt can precipitate as solid halite. The capabilities of the code include coupled flow and thermal effects, real gas behavior, Darcy and non-Darcy flow, several isotherm options of gas sorption onto the grains of the porous media, complex fracture descriptions, gas solubility into water, and geomechanical effects on flow properties. REALGASBRINE v1.0 allows the study of flow and transport of fluids and heat over a wide range of time frames and spatial scales not only in gas reservoirs, but also in any problem involving the flow of gases in geologic media, including the geologic storage of greenhouse gas mixtures, the behavior of geothermal reservoirs with multi-component condensable (H 2 O and CO 2 ) and non-condensable gas mixtures, the transport of water and released H 2 in nuclear waste storage applications, etc.