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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

High-pressure Cr 3+ luminescence and Raman spectroscopy of a natural MgAl 2 O 4 spinel to ∼60 GPa

Cr 3+ luminescence and Raman spectroscopy of a natural spinel were collected up to ∼60 GPa at ambient temperature using a Ne or a 4:1 methanol-ethanol mixture as the pressure transmitting media. Here, in the Ne experiments above ∼40 GPa, and in the 4:1 methanol–ethanol experiments above ∼20 GPa, all luminescence emission lines shift non-linearly, and by 59 GPa the spectra are broadened and are significantly changed. The Raman modes shift smoothly to higher frequencies with pressure, with a slight change in slope above 40 GPa, with no kinks or discontinuities. By ∼60 GPa, only the most intense Eg mode remains resolvable, appearing broadened and reduced in intensity. The change in slope in the Raman modes and luminescence bands may be due to a change in the compression mechanism of spinel. When spinel was decompressed from 40 GPa all changes were fully reversible; however, when the samples were decompressed from 54 to 60 GPa in Ne and 59 GPa in 4:1 methanol-ethanol the spectra were irreversibly changed. The change in the luminescence spectra and the Raman spectra are likely due to a pressure induced disorder of the anions or partial amorphization between 40 and 60 GPa.

Cr3+↗
DOE OSTI2025

Spectral Properties of Globally Distributed ENA Fluxes across Diverse Regions of the Heliosphere

This study analyzes energetic neutral atom (ENA) spectral properties across distinct regions of globally distributed flux (GDF) sky maps, using Interstellar Boundary Explorer data from a full solar cycle, corrected for time dispersion. By time-shifting the data to the heliosheath using GDF source distances from D. B. Reisenfeld et al., we achieve a more accurate representation of heliosheath GDF energy spectra. We quantify ENA spectral characteristics, heliosheath line-of-sight-integrated proton pressure, and heliosheath proton temperature, comparing these to solar wind properties at 1 au and interplanetary scintillation-derived solar wind data. Our findings show that the spectral index is generally anticorrelated with heliosheath proton temperature and pressure, except in the central tail, where a partial positive correlation is observed. The lowest spectral index values occur when high-latitude heliosheath regions are dominated by fast solar wind from polar coronal holes. The south pole exhibits the flattest energy spectra due to plasma heating from both fast solar wind and a late-2014 pressure pulse. The central tail shows shorter variability (5–6 yr) for spectral index and heliosheath proton temperature, while proton pressure follows the 11 yr solar cycle. Most spectral shapes exhibit a “knee” distribution, peaking during solar maximum, with an “ankle” shape observed only at the south pole during solar cycle transitions. Asymmetry in proton pressure in the lobes is driven by the draping effect of the local interstellar magnetic field. This study provides insights into the energetic properties of GDF across the heliosphere, enhancing our understanding of the heliospheric environment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Non-equilibrium simulations of hydraulic permeation: Role of mechanical boundary conditions in dense membranes

Understanding the mechanisms of water transport in reverse osmosis membranes is critical for improving membrane performance and guiding material design. While classical models describe transport as either solution-diffusion (SD)—involving concentration-driven diffusion through a homogeneous medium—or pore-flow (PF)—involving pressure-driven convection through percolated water channels—their applicability to crosslinked polyamide membranes remains debated. Here, using non-equilibrium molecular dynamics simulations, we investigate the impact of mechanical support conditions on pressure-driven water transport in polyamide membranes across varying crosslink densities and pressure differentials (1000–5000 bar). Two support conditions are considered: graphene-restrained, representing experimentally relevant supported membranes, and freeze-restrained, mimicking a self-supported structure. In graphene-restrained systems, water concentration gradients and constant pressure profiles emerge, consistent with SD theory and incompatible with PF assumptions due to the absence of percolated pores and sub-nanometer voids. In contrast, freeze-restrained systems display uniform water concentration and linearly decreasing pressure at 1000 bar, and exhibit compressibility-induced water gradients and partial percolation at 5000 bar, resembling PF-like behavior. However, the underlying assumptions of PF theory—continuous solvent pathways and pressure transmission through water-filled pores—are not met under most conditions. Our results demonstrate that accurate modeling of reverse osmosis membranes must incorporate realistic mechanical boundary conditions to distinguish between transport mechanisms. For dense polyamide membranes supported by porous substrates, graphene-restrained simulations best reflect experimental setups and support the SD model as the dominant mechanism of water permeation.

molecular dynamics↗
DOE OSTI2025

Symmetry progression and band vs Mott character of CdPS 3 under pressure

Complex chalcogenides are renowned for their tunable electronic, magnetic, and optical properties under external stimuli. The MPX 3 family (M = Mn, Ni, Co, V; X = S, Se) is a platform for many exciting discoveries—especially under compression—although CdPS3 is thought to be different because the Cd center possesses a filled 4d shell, which precludes Mottness. Here, we combine synchrotron-based infrared absorbance and Raman scattering spectroscopies with diamond anvil cell techniques, complementary lattice dynamics calculations, and an analysis of the energy landscape to reveal a series of structural phase transitions in CdPS 3 . We find four distinct pressure-driven transitions, with low frequency modes detectable over the full 35 GPa range of our investigation. A group–subgroup analysis along with our first-principles calculations allows us to partially unravel the space group sequence. For instance, the first critical pressure is a monoclinic C2/m to trigonal $\overline{R}$3 transition at 10 GPa. Despite the softness and overall sensitivity to pressure, we do not locate an insulator-to-metal transition in this pressure range, indicating that the energy scale for gap closure is significantly higher than expected. We discuss these findings in terms of force-induced color change and Mott vs band character in this system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Structural transition and uranium valence change in UTe 2 at high pressure revealed by x-ray diffraction and spectroscopy

High-pressure x-ray diffraction up to 30 GPa, in conjunction with resonant emission x-ray spectroscopy and partial fluorescence yield x-ray absorption spectroscopy up to 52 GPa, were used to study how the structural and electronic properties of UTe2 evolve with pressure at room temperature. An orthorhombic-to-tetragonal phase transition was observed to occur between 5 and 7 GPa, with a large volume collapse of nearly 10% and a nearest U-U distance increase by about 4%. This lower-to-higher symmetry transition suggests less 5⁢f electron participation in bonding when the weakly correlated superconducting phase in the tetragonal structure of UTe 2 appears. Beyond 7 GPa, no new structural transitions were found up to 30 GPa. The resonant x-ray emission spectra clearly demonstrate an intermediate valence of U, nearly +3.74 at 1.8 GPa and room temperature, and reveal that the U valence shifts towards 4+, passes through a peak at 2.8 GPa, then decreases towards 3+ and settles down to a nearly constant value above 15 GPa. These experiments reveal that some fundamental structural and valence changes occur in UTe 2 at relatively low pressures, which could be responsible for the interplay between unconventional superconductivity, magnetic ordering, and weakly correlated superconductivity that is manifested in the temperature-pressure phase diagram of UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Poromechanical cohesive interface element with combined Mode I-II cohesive zone elastoplasticity for simulating fracture in fluid-saturated porous media

A combined Mode I-II cohesive zone (CZ) elasto-plastic constitutive model, and a two-dimensional (2D) cohesive interface element (CIE) are formulated and implemented at small strain within an ABAQUS User Element (UEL) for simulating 2D crack nucleation and propagation in fluid-saturated porous media. Here, the CZ model mitigates problems of convergence for the global Newton-Raphson solver within ABAQUS, which when combined with a viscous stabilization procedure allows for simulation of post-peak response under load control for coupled poromechanical finite element analysis, such as concrete gravity dam stability analysis. Verification examples are presented, along with a more complex ambient limestone-concrete wedge fracture experiment, water-pressurized concrete wedge experiment, and concrete gravity dam stability analyses. A calibration procedure for estimating the CZ parameters is demonstrated with the limestone-concrete wedge fracture process. For the water-pressurized concrete wedge fracture experiment it is shown that the inherent time-dependence of the poromechanical CIE analysis provides a good match with experimental force versus displacement results at various crack mouth opening rates, yet misses the pore water pressure evolution ahead of the crack tip propagation. This is likely a result of the concrete being partially-saturated in the experiment, whereas the finite element analysis assumes fully water saturated concrete. For the concrete gravity dam analysis, it is shown that base crack opening and associated water uplift pressure leads to a reduced Factor of Safety, which is confirmed by separate analytical calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

Here, in this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

early-time solution↗
DOE OSTI2024

Analysis and Optimization of the Recompression Cycle with High Temperature Recuperator Bypass for Concentrating Solar Power Applications

This work analyzes the sCO2 recompression with high temperature recuperator (HTR) bypass power cycle for use in concentrating solar power (CSP) systems. CSP operation differs from other thermal power plants in that CSP must balance between maximizing the heat transfer fluid (HTF) temperature difference and maximizing the cycle thermal efficiency, which typically are inversely related. Large HTF temperature differences reduce the size and cost of thermal energy storage (TES), improve the solar receiver efficiency, and require lower mass flow rates that reduce pumping power required to elevate the HTF to the receiver. The recompression cycle with HTR bypass potentially offers improved thermal efficiency with larger HTF temperature differences as compared to the recompression cycle, and it has fewer turbomachinery components than the partial cooling cycle. The recompression with HTR bypass cycle adds a second lower temperature primary heat exchanger which transfers heat from the HTF to the fraction of sCO2 flow that bypasses the HTR. We developed a model to compare the recompression with HTR bypass cycle to the recompression and partial cooling cycles. A sweep of design parameters including bypass fraction, recompression fraction, recuperator conductance, and pressure ratio is used to form a pareto-optimal front with the cycle thermal efficiency and HTF temperature difference as objectives. An optimization routine has also been developed to find optimal design point parameters for a target HTF temperature difference. The performance of the recompression with HTR bypass cycle is compared with recompression and partial cooling cycles.

concentrating solar power↗
DOE OSTI2026

A Boundary Element Model for Assessing Large‐Scale Pressurization in Faulted Geological Storage Systems

Assessing large-scale pressurization at the regional scale—a possible outcome of large subsurface storage applications such as wastewater injection and geological carbon sequestration—presents significant computational challenges. These challenges are particularly pronounced when accounting for complex geologic structures with multiple reservoir and caprock layers, fault zones, and wells. This study introduces a computationally efficient model that integrates single-phase semi-analytical solutions with a boundary element (BE) approach. The model simulates pressure propagation in multilayered 3D systems, including vertical faults, caprock, basement, and confining units. We apply this new model to a representative scenario involving CO 2 injection near a partially sealing fault with verification against an independent two-phase flow model. Results demonstrate that our model accurately captures far-field pressure responses and that, outside the CO 2 plume zone, pressure predictions from single-phase and two-phase models are nearly identical. This supports the use of single-phase models like ours for efficient estimation of far-field pressure changes. Additionally, we demonstrate its effectiveness at a large scale, incorporating multiple wells and faults. With its ability to represent multiple wells, fault zones, and geological heterogeneity, our model is well suited for assessments of basin-scale pressurization. Its computational efficiency also makes it a promising tool for integration with optimization frameworks aimed at designing and managing injection strategies in faulted storage systems.

Cihan, A. [Lawrence Berkeley National Laboratory (↗
DOE OSTI2024

Redox dynamics and surface structures of an active palladium catalyst during methane oxidation

Catalysts based on palladium are among the most effective in the complete oxidation of methane. Despite extensive studies and notable advances, the nature of their catalytically active species and conceivable structural dynamics remains only partially understood. Here, we combine operando transmission electron microscopy (TEM) with near-ambient pressure X-ray photoelectron spectroscopy (NAP-XPS) and density functional theory (DFT) calculations to investigate the active state and catalytic function of Pd nanoparticles (NPs) under methane oxidation conditions. We show that the particle size, phase composition and dynamics respond appreciably to changes in the gas-phase chemical potential. In combination with mass spectrometry (MS) conducted simultaneously with in situ observations, we uncover that the catalytically active state exhibits phase coexistence and oscillatory phase transitions between Pd and PdO. Aided by DFT calculations, we provide a rationale for the observed redox dynamics and demonstrate that the emergence of catalytic activity is related to the dynamic interplay between coexisting phases, with the resulting strained PdO having more favorable energetics for methane oxidation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

The solubility and speciation of REE phosphate endmembers (CePO 4 and YPO 4 ) in Cl-rich aqueous fluids from 350 to 450 °C and implications for natural systems

The rare earth elements (REE) are important metals used increasingly in advanced technologies. Within the crust, the elements Ce and Y are commonly more abundant compared to other lanthanides and comprise important end-member constituents of REE-bearing minerals. Specifically, Ce is part of the light (L) REE which have larger ionic radii than the heavy (H) REE, which are grouped together with Y. These differences in ionic radius can lead to important physico-chemical trends within the lanthanide group. Despite a recent increase in experimental and thermodynamic data for the REE at high temperature and pressure, there is still a significant lack of these data at supercritical conditions. In this study we conducted batch-type experiments to measure the solubility of REE phosphates (CePO 4 and YPO 4 ) at varying starting pH (1.5–10), and salinity (0.01–1.4 mol/kg NaCl) at 350 and P sat , and from 400 to 450 °C at 700 bar. Results show that the solubility of Ce (33–0.14 ppb) is generally higher than Y (13–0.13 ppb) and that Ce complexes more strongly with both chloride and hydroxyl ligands compared to Y. The solubilities of both REE phosphates are highly pH-dependent and, to a lesser extent, depend on salinity at the studied conditions. The solubility data from this study were implemented into the GEMSFITS program to optimize the thermodynamic properties of Ce and Y hydroxyl and chloride species. The updated standard partial molal Gibbs energies of formation (Δ f G 0 T,P ) are used within the experimental temperature and pressure range to accurately predict the CePO 4 and YPO 4 solubility and Ce and Y speciation behavior. Based on the updated thermodynamic properties we also provide formation constants (log β n Cl,OH ) for Ce and Y hydroxyl and chloride species. Updated thermodynamic properties are applied to model REE-apatite dissolution and REE mobility based on the Pea Ridge iron oxide apatite deposit in Missouri, USA. The apatite dissolution model replicates natural observations including the replacement of monazite and xenotime after apatite and is an example of the utility of the new thermodynamic constants applied to supercritical crustal fluids. Furthermore, the findings of this study advance the predictive capabilities of geochemical models, our understanding of the behavior of individual REE, and permit modeling the overarching fractionation trends between LREE and HREE in supercritical crustal fluids.

58 GEOSCIENCES↗
DOE OSTI2025

Symmetry Determining Equations of the Euler Equations

This purpose of this document is to provide a clear derivation of the symmetry determining equations (SDEs) of the Euler equations to supplement the lecture document. The Euler equations are a coupled system of three first-order quasilinear hyperbolic partial differential equations (PDEs). The Euler equations are a system of partial differential equations (PDEs) for fluid velocity v(t, r), fluid density ρ(t, r), and fluid pressure P(t, r), where t is time and r is the spatial coordinate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Operation at Reduced Atmospheric Pressure and Concept of Reliability Redundancy for Optimized Design of Insulation Systems

Electrified transportation is calling for insulation design criteria that is adequate to provide elevated levels of power density, power dynamics and reliability. Increasing voltage levels are expected to cause accelerated intrinsic and extrinsic aging effects which will not be easily predictable at the design stage due to a lack of suitable modeling. Designing reliable insulation systems would require finding solutions able to control accelerated aging due to an unpredictable increase of intrinsic stresses and the onset of extrinsic stresses as partial discharges. This paper proposes the concept of reliability redundancy for the insulation design of aerospace electrical asset components, which is also validated at lower-than-standard atmospheric pressure. The principle is that extrinsic-aging-free design might be achieved upon determining the aging stress or abnormal service stresses distribution and being sure that aging will not generate conditions that can incept extrinsic aging (partial discharges) during operation life. However, such information is never, in practice, fully available to insulation system designers. Hence, especially in critical applications such as electrified aircraft, aerospace, and combat ships a further level of reliability should be added to a partial-discharge-free design, which can consist of the use of corona-resistant materials and/or of life models able to consider the accelerated aging effect of partial discharges (or any other type of extrinsic-accelerated aging factor). Innovative life modeling considering both extrinsic and intrinsic aging stresses, insulating material testing to estimate model parameters, and a metric for quantifying the extent of corona (or partial discharge) resistance can lead to establishing feasibility and limit conditions for optimized or fully reliability-redundant design. It is shown in the paper that if an extrinsic-aging-free design is not feasible, and it is therefore replaced by a redundant design, a further level of reliability redundancy can be provided by effective condition monitoring plans.

Montanari, Gian Carlo↗
DOE OSTI2026

A wide-range thermodynamically consistent constitutive model for dynamic loading of partially saturated porous media

SUMMARY This paper presents a novel thermodynamically consistent constitutive model for partially saturated porous rocks across a wide range of conditions. The material states generated behind the shock wave from an explosive source can vary significantly, ranging from crushed and melted rock near the source to a poroelastic medium in the far field. In the model, rock strength is determined by the effective pressure, which is calculated using two independent equations of state: one for the solid rock and another for the pore fluid. The model accounts for shock-induced liquefaction resulting from fluid pressure buildup in the pore spaces near the explosive source. Simultaneously, it describes the increase in wave propagation speed due to elastic pore contraction in both dry and partially saturated rocks. This model is applied to investigate how fluid saturation affects the amplitude and shape of the generated waves, as well as the residual stress surrounding the cavity formed by spherical explosions.

Vorobiev, Oleg [Lawrence Livermore National Labora↗
DOE OSTI2024

Effect of Pressure on Crystal Structure and Phonon Density of States of FeSi

The strongly correlated material FeSi displays several unusual thermal, magnetic, and structural properties under varying pressure-temperature (P-T) conditions. It is a potential thermoelectric alloy and a material with several geochemical implications as a possible constituent at the Earth's core-mantle boundary (CMB). Previous theoretical studies predicted a pressure-induced B20-B2 transition at ambient temperature below 40 GPa; however, experimentally, the structural transition is observed only at high P-T conditions. In this study, we have performed high-pressure powder X-ray diffraction (XRD) up to 90 GPa and Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements up to 120 GPa to understand the phase stability and lattice dynamics. Our study provides evidence for a non-hydrostatic stress-induced B20-B2 transition in FeSi at around 36 GPa. We deduced the Fe partial phonon density of states (PDOS) and thermal parameters from NRIXS measurements up to 120 GPa and compared them with density functional theory (DFT) calculations. Furthermore, the computations show pressure-induced metallization and the band gap closing around 12 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Low Temperature CO 2 Hydrogenation on Unsupported Mo 2 C Catalysts

CO 2 hydrogenation to methanol, a key reaction for decarbonizing the fuel and chemical industries, requires catalyst formulations that hydrogenate CO 2 selectively to methanol at temperatures where methanol conversion is not significantly equilibrium limited (<423 K). Herein we report continuous CO 2 hydrogenation at low temperatures (348-408 K, H 2 /CO 2 = 0.1-50, 5-35 bar) with high selectivity to methanol (up to ca. 80%) over unsupported β-Mo 2 C catalysts. Active site density quantification via titration with trifluoroacetic acid at reaction temperatures enables an assessment of site-specific rates. Methanation and reverse water gas shift (RWGS) occur concurrently with methanol synthesis during CO 2 hydrogenation over Mo 2 C. Reaction pathway analysis, product cofeeds, and reversibility formalisms show that all products form through primary reaction pathways from CO 2 , but secondary reactions of CO contribute significantly to rates of methanation. Dependences of forward rates on reactant and product concentration determined by independently varying the CO 2 , H 2 , CO, H 2 O, CH 3 OH, and CH 4 pressure in conjunction with reversibility formalisms reveal that all products form through H-assisted CO 2 activation and involve partially hydrogenated CO 2 -derived intermediates. Here, these inferences were verified by quantitative agreement between measured site-time yields and site-time yields predicted by closed form kinetic rate expressions in an integral reactor model over widely varying conditions (85-2000 kPa H 2 , 80-1500 kPa CO 2 , 0-45 kPa H 2 O, 0-21 kPa CO, 0-25 kPa CH 3 OH, 0-75 kPa CH 4 , 5-87 mol Mo s s mol CO 2 -1 ). Coverages calculated based on the kinetic model reveal that the Mo 2 C surface is covered with bidentate CO- and CO 2 -derived intermediates of the stoichiometry H 2 CO 2 and H 2 CO, indicating that H 2 and CO x do not compete for surface occupancy but instead adsorb cooperatively to form partially hydrogenated intermediates. Hydrogenation of the CO-derived H 2 CO** intermediate favors methanation, while hydrogenation of CO 2 -derived H 2 CO 2 ** favors methanol synthesis. Together, these findings demonstrate the ability of unsupported Mo 2 C to catalyze the hydrogenation of CO 2 to methanol at low temperatures and provide insight into the reaction network and mechanisms involved in its formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Pure-Water-Fed Forward-Bias Bipolar Membrane CO 2 Electrolyzer

Coupling renewable electricity to reduce carbon dioxide (CO 2 ) electrochemically into carbon feedstocks offers a promising pathway to produce chemical fuels sustainably. While there has been success in developing materials and theory for CO 2 reduction, the widespread deployment of CO 2 electrolyzers has been hindered by challenges in the reactor design and operational stability due to CO 2 crossover and (bi)carbonate salt precipitation. Herein, we design asymmetrical bipolar membranes assembled into a zero-gap CO 2 electrolyzer fed with pure water, solving both challenges. By investigating and optimizing the anion-exchangelayer thickness, cathode differential pressure, and cell temperature, the forward-bias bipolar membrane CO 2 electrolyzer achieves a CO faradic efficiency over 80% with a partial current density over 200 mA cm –2 at less than 3.0 V with negligible CO 2 crossover. In addition, this electrolyzer achieves 0.61 and 2.1 mV h –1 decay rates at 150 and 300 mA cm –2 for 200 and 100 h, respectively. Postmortem analysis indicates that the deterioration of catalyst/polymer– electrolyte interfaces resulted from catalyst structural change, and ionomer degradation at reductive potential shows the decay mechanism. Furthermore, all these results point to the future research direction and show a promising pathway to deploy CO 2 electrolyzers at scale for industrial applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

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.

97 MATHEMATICS AND COMPUTING↗