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DOE OSTI2022

A gradient-based deep neural network model for simulating multiphase flow in porous media

We report simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO 2 storage sites, where CO 2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.

42 ENGINEERING↗

DOE OSTI2020

On the peridynamic effective force state and multiphase constitutive correspondence principle

This article concerns modeling unsaturated deformable porous media as an equivalent single-phase and single-force state peridynamic material through the effective force state. The balance equations of linear momentum and mass of unsaturated porous media are presented by defining relevant peridynamic states. The energy balance of unsaturated porous media is utilized to derive the effective force state for the solid skeleton that is an energy conjugate to the nonlocal deformation state of the solid, and the suction force state. Through an energy equivalence, a multiphase constitutive correspondence principle is built between classical unsaturated poromechanics and peridynamic unsaturated poromechanics. The multiphase correspondence principle provides a means to incorporate advanced constitutive models in classical unsaturated porous theory directly into unsaturated peridynamic poromechanics. Finally, numerical simulations of localized failure in unsaturated porous media under different matric suctions are presented to demonstrate the feasibility of modeling the mechanical behavior of such three-phase materials as an equivalent single-phase peridynamic material through the effective force state concept.

42 ENGINEERING↗

DOE OSTI2023

Integrated low carbon H 2 conversion with in situ carbon mineralization from aqueous biomass oxygenate precursors by tuning reactive multiphase chemical interactions

Meeting our rising demand for clean energy carriers such as H 2 from renewable biomass resources is challenged by the co-emission of CO 2 and CH 4 . To address this challenge, we design novel reactive separation pathways that integrate multiphase chemical reactions by harnessing Ca and Mg bearing minerals as a sorbent to capture CO 2 released during the hydrothermal deconstruction of aqueous biomass oxygenates to produce H 2 and solid carbonates via low temperature aqueous phase reforming and thermodynamically downhill carbon mineralization. Earth abundant catalysts such as Ni/Al 2 O 3 are effective in producing H 2 yields as high as 79% and 74% using ethylene glycol and methanol in the presence of Ca(OH) 2 as an alkaline sorbent, without contaminating or deactivating the catalyst. H 2 yields with in situ carbon mineralization using a Ni or Pt/Al 2 O 3 catalyst are enhanced based on the following order of reactivity: acetate < glycerol < methanol < formate < ethylene glycol. These studies demonstrate that the multiphase chemical interactions can be successfully tuned to enhance H 2 yields through the selective cleavage of C–C bonds using Ni/Al 2 O 3 catalysts to deconstruct biomass oxygenates for producing H 2 and CO 2 , and in situ carbon mineralization by harnessing abundant alkaline materials, as demonstrated using ladle slag. This approach unlocks new scientific possibilities for harnessing multiple emissions including abundant organic-rich wastewater streams and alkaline industrial residues to co-produce low carbon H 2 and carbonate-bearing materials for use in construction by using renewable solar thermal energy resources.

09 BIOMASS FUELS↗

DOE OSTI2015

Multiphase flow modeling based on the hyperbolic thermodynamically compatible systems theory

An application of the theory of thermodynamically compatible hyperbolic systems to design a multiphase compressible flow models is discussed. With the use of such approach the governing equations are derived from the first principles, formulated in a divergent form and can be transformed to a symmetric hyperbolic system in the sense of Friedrichs. A usage of the proposed approach is described for the development of multiphase compressible fluid models, including two-phase flow models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A gas dynamic perspective on particle lifting in electrostatic discharge-like devices using multiphase particle-in-cell approach

Although particle–laden electrostatic discharges are widely used in laboratories as well as in industrial applications, the mechanism of particle lifting for particles initially at rest in such highly unsteady systems is not well understood. A multiphase gas–particle solver is developed using the multiphase particle-in-cell (MP-PIC) approach to emulate the interaction of a compressible shock-dominated gas phase with the dense particle phase. First, the two-way coupled solver is initially used to study the interaction of a planar traveling shock with a vertical curtain of particulates. The gas and particle phase evolution was found to be in good agreement with a similar experimental study in Ling et al. [Phys. Fluids 24, 113301 (2012)]. Second, the MP-PIC code is used to study the interaction of an expanding blast wave with a thick bed of particles. The simulation considered forces such as quasi-steady drag, pressure-gradient, added-mass, Saffman, and Magnus forces. We observe that the vertical liftoff particles close to the shock impingement point in this configuration are associated with the quasi-steady drag, pressure gradient, and added-mass forces. Also, the Saffman lift and Magnus forces contribute to lifting particles located radially farther away from the shock impingement point. In addition, the study finds a decrease in particle lifting efficiency with decreasing plasma kernel length and shock strength.

42 ENGINEERING↗

DOE OSTI2017

Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media

Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to phase pressure. In this study, we develop and study efficient solution algorithms for solving the algebraic systems of equations derived from a fully coupled and time-implicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including “black-box” AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPR-AMG) preconditioning, and a new preconditioner derived using an approximate Schur complement arising from the block factorization of the Jacobian. Finally, we show that the new methods are the most robust with respect to problem character, as determined by varying effects of capillary pressures, and we show that the block factorization preconditioner both is efficient and scales optimally with problem size.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Data supporting the article titled "Heterogeneous Multiphase Flow Properties of Volcanic Rocks and Implications for Noble Gas Transport from Underground Nuclear Explosions"

The submission is a Reproducible Research (RR) data archive that contains the supporting multiphase fluid flow and curve fitting results of the Vadose Zone Journal article titled: "Heterogeneous Multiphase Flow Properties of Volcanic Rocks and Implications for Noble Gas Transport from Underground Nuclear Explosions." The article's DOI number is the following: https://doi.org/10.1002/vzj2.20123. Please see the "Methods and Materials" section of the journal article and the ReadMe.txt in the RR_ARCHIVE folder for further details. 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. SAND Number: SAND2021-3407 O.

mercury injection capillary pressure↗

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↗