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At least 127 records · Page 7

Geo Thermal Cloud: Cloud Fusion of Big Data and Multi-Physics Models using Machine Learning for Discovery, Exploration, and Development of Hidden Geothermal Resources

The project is motivated by the challenges, risks, and costs associated with geothermal exploration and production. Many processes and parameters impacting geothermal conditions are poorly understood. Diverse datasets are available to help characterize subsurface geothermal conditions (public and proprietary; satellite, airborne surveys, vegetation/water sampling, geological, geophysical, etc.). Yet, it is not clear how to properly leverage these datasets for geothermal exploration due to an incomplete understanding of how physical processes impacting subsurface geothermal conditions are represented in these observations. Recent advancements in machine learning (ML) provide great promise to resolve these issues. The tremendous challenges and risks of geothermal exploration and production bring the demand for novel ML methods and tools that can (1) analyze large field datasets, (2) assimilate model simulations (large inputs and outputs), (3) process sparse datasets, (4) perform transfer learning (between sites with different exploratory levels), (5) extract hidden geothermal signatures in the field and simulation data, (6) label geothermal resources and processes, (7) identify high-value data acquisition targets, and (8) guide geothermal exploration and production by selecting optimal exploration, production, and drilling strategies. Our goals and work under Phases 1 and 2 (as proposed) of this project address all these needs.

15 GEOTHERMAL ENERGY↗

Williston Basin Resource Study for Commercial-Scale Subsurface Hydrogen Storage

The Energy & Environmental Research Center (EERC), in partnership with the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL), the EERC’s State Energy Research Center (SERC), MPLX Operations LLC, and TC Energy Development Holdings Inc. (a subsidiary of TC Energy Corporation), studied the potential for subsurface hydrogen storage and recovery in the Williston Basin of western North Dakota. The project’s goal was to evaluate the feasibility of large-scale, secure geologic H 2 storage to support future hydrogen generation, storage, and use. This work included laboratory testing, H 2 –rock–fluid exposure experiments, literature reviews on H 2 embrittlement, and reservoir modeling and simulations. The study included an assessment of storage potential across three types of storage reservoirs using both reservoir simulation and DOE’s web-based tool SHASTA-HELP (Subsurface Hydrogen Assessment, Storage, and Technology Acceleration – Hydrogen Estimator for Logistical Planning), as well as investigation of potential H 2 production and markets for commercial-scale deployment. Building on prior EERC gas storage research, three storage options were selected for detailed evaluation: the Broom Creek Formation (a clastic saline reservoir), the Dickinson Lodgepole Mounds (DLM) complex (carbonate mud mound structures) of the Lodgepole Formation (an active oil and gas producing reservoir), and the Dunham Salt Interval of the Piper Formation (to be used for engineered salt cavern development). These targets were prioritized based on prior EERC research using datasets related to seal capacity, reservoir quality, mechanical integrity, and injectivity. Exposure tests on Broom Creek and DLM samples showed mineral dissolution and precipitation that increased brine salinity and altered reservoir rock surfaces. Although these results provide useful insight, they are limited by small sample sizes and short-term (30-day) exposure, requiring further study to assess long-term storage integrity. Salt formations were not tested because of their known nonreactivity and established mechanical stability. Results of reservoir simulations performed for a single site demonstrated that the Broom Creek Formation may be capable of receiving up to 42,000 tonnes of injected H 2 over 7 months via one well. H 2 recovery took place over 5 months, resulting in approximately 26,000 tonnes (~62% without cushion gas [CG]). This work suggests water production may be important and subsequent cycles of injection and production may perform more efficiently; however, significant site-specific work in the future is needed to assess actual reservoir performance of injection and withdrawal of H 2 storage. For oil reservoir potential, a multiple-well model was used to simulate injection of approximately 32,000 tonnes of H 2 into a single wellbore while simultaneously producing in place reservoir fluids from four offset wells to maintain reservoir pressure. The simulation results suggested a high recovery (~98%); in addition, cost advantages through existing infrastructure could be realized. Challenges in this reservoir include vi managing gas purity and leakage risks. In both scenarios, production of H 2 takes place in a single-well scenario with 10 cycles (7 months of injection and 5 months of production) over 10 years. Finally, the use of engineered caverns in the Dunhan Salt was evaluated, and the results suggest that while they have a smaller capacity (<1000 tonnes per cavern), they exhibit nearly complete gas recovery (>99%), fast response times, and low purity risk. While caverns in North Dakota may be smaller in capacity, fields can be developed in galleries to accommodate the volumetric needs and rapid turnaround times necessary to meet market demands. Geographic limitations and thin salt intervals in North Dakota may represent less total storage potential than salt domes elsewhere, but significant opportunities exist to expand this market for gas storage in North Dakota. A basinwide assessment was performed to estimate a first-of-its-kind value for H 2 storage on a large scale. DOE’s SHASTA-HELP, combined with EERC simulation work, was used to perform the assessment. Estimated H 2 storage potential varied widely for each formation type. The Broom Creek saline formation was estimated to have a storage potential of approximately 1.7–90.5 million tonnes (MMt). The DLM oil reservoirs were estimated to have 0.07–0.19 MMt of capacity. Notably, each of these estimates relies on significant assumptions regarding reservoir thickness, porosity, permeability, and CG needed for operation. Much research is needed to understand the true site-specific storage resource potential of each formation. Using the Dunham Salt Interval for cavern development may result in as much as 4.79 MMt (up to 2.87 MMt working gas) of H 2 storage potential. An important note for consideration is that the values presented here need significantly more geological characterization and engineering assessments prior to gaining confidence in performance. This will be a focal point for future research and development needs. The basinwide evaluation also indicated that North Dakota has significant H 2 generation potential, with estimates up to a possible 13 MMt annually, suggesting a substantial opportunity for H 2 market development and thus the need for commercial-scale H 2 storage to facilitate growth and resilience. Key Recommendations 1. Conduct detailed site characterization (3D seismic, well logs, core sampling) to reduce geologic uncertainty. 2. Perform techno-economic analyses incorporating market, regulatory, and incentive frameworks. 3. Investigate long-term interactions among H 2 , CGs, well materials, and formations to assess risks. 4. Develop pilot- and field-scale demonstrations to validate models and establish best practices.

03 NATURAL GAS↗

Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration

Geological carbon sequestration (GCS) involves injecting CO2 into subsurface geological formationsfor permanent storage. Numerical simulations could guide decisions in GCS projects by predictingCO 2 migration pathways and the pressure distribution in storage formation. However, these simula-tions are often computationally expensive due to highly coupled physics and large spatial-temporalsimulation domains. Surrogate modelling with data-driven machine learning has become a promis-ing alternative to accelerate physics-based simulations. Among these, the Fourier neural operator(FNO) has been applied to three-dimensional synthetic subsurface models. Despite its good accuracyin simulating CO 2 plume migration, it requires large computational resources in training and alsolacks generalizability. Here, to further improve performance, we have developed a nested Fourier-DeepONet by combining the expressiveness of the FNO with the modularity of a deep operatornetwork (DeepONet). This new framework is twice as efficient as a nested FNO for training and has atleast 80% lower GPU memory requirement due to its flexibility to treat temporal coordinates sepa-rately. These performance improvements are achieved without compromising prediction accuracy.In addition, the generalization and extrapolation ability of nested Fourier-DeepONet beyond thetraining range has been thoroughly evaluated. Nested Fourier-DeepONet outperformed the nestedFNO for extrapolation in time with more than 50% reduced error. It also exhibited good extrapolationaccuracy beyond the training range in terms of reservoir properties, number of wells, and injectionrate.

Lee, Jonathan E. [Department of Chemical and Envir↗

Towards machine-learning a fully-coupled constitutive model for thermal-hydraulic fracture in geothermal systems: phase I (Final Report)

This project, entitled “Towards machine-learning a fully-coupled constitutive model for thermal-hydraulic fracture in geothermal systems: phase I,” addresses challenges in understanding and controlling subsurface fracture networks, which are crucial for applications like deep geothermal heat mining and deep-crustal minerals/metals/hydrogen extraction. The research focuses on advancing the understanding of coupled thermal-hydro-mechanical-chemical (THMC) processes in geologic materials, particularly under the high temperature and pressure conditions found in the deep crust. This seed grant focused specifically on thermal cracking and the development of new constitutive models. Significant progress was made in both experimental and theoretical domains. To study micro-scale fracture formation, the project demonstrated the ability to create thermal cracking under stress in granite samples using a Paterson Gas-medium Deformation Apparatus.

15 GEOTHERMAL ENERGY↗

The DECOVALEX international collaboration on modeling of coupled subsurface processes and its contribution to confidence building in radioactive waste disposal

Abstract The long-lived radiotoxicity of the high-level radioactive waste generated by nuclear power plants requires safe isolation from the biosphere for many hundreds of thousands of years. An international consensus has emerged that such isolation can best be provided by disposal in mined geologic repositories, a strategy that today is pursued by most countries dealing with radioactive waste. However, the need to predict the performance of such repositories over very long time periods generates large uncertainties that have to be accounted for in safety assessments. The findings from such safety assessments need to be conveyed to all stakeholders in a clear way, such that public confidence in geologic disposal solutions can be achieved. It is suggested here that close international collaboration on the technical aspects of geologic waste disposal has helped, and will continue to help, building trust and increasing confidence. This paper discusses a particular international collaboration initiative referred to as DECOVALEX, which brings together multiple teams and disciplines to collectively tackle complex experimental and modeling challenges related to geologic disposal. By describing how DECOVALEX works and by providing joint research examples, a case is made that such international collaboration contributes to knowledge transfer and confidence building in radioactive waste disposal science.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Martian Plains Volcanism in Syria Planum and Tempe Mareotis as Analogs to the Eastern Snake River Plains, Idaho: Similarities and Possible Petrologic Contributions to Topography

Prior to the Mars Global Surveyor (MGS) and Mars Odyssey (MO) missions, The Syria Planum region of Mars was noted for several clusters of small (5-100 km) shield volcanoes and collapse craters, long tube and fissure-fed lava flows, and possible volcanic vents that were thought to be nearly contemporaneous with the volcanism in the Tempe- Mareotis province, which has long been known for volcanic shields and vents analogous to those of the Eastern Snake River Plains (ESRP) in Idaho. Recent MGS-based work on regional and global populations of martian small shields has revealed significant global trends in edifice attributes that are well-explained by eruption models with latitudinal variations in subsurface water/ice abundance, consistent with recent MO evidence for significant amounts of subsurface water that varies in latitude abundance s, and topographic and morphologic evidence for more geologically recent lava-ice relationships. However, while the global trends in small volcano data can be at least partially explained by volatile interactions with volcanism, some global and regional characteristics appear to be perhaps better explained by possible compositional, crystallinity or eruption style variations. This study expands the sampling of shields done in martian initial global studies for the Syria Planum and Tempe-Mareotis regions, which display a newly visible breadth and number of features in image and topography data. We compare these features to a similar range of features visible in the ESRP where both compositional and eruption style variations can quantitatively be shown to contribute to morphologic and topographic differences.

Sakimoto, S. E. H.↗

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↗

Application of machine learning for modeling brønsted-guggenheim-scatchard specific ion interaction theory (SIT) coefficients

Machine learning methodologies can provide insight into Brønsted-Guggenheim-Scatchard specific ion interaction theory (SIT) parameter values where experimental data availability may be limited. This study develops and executes machine learning frameworks to model the SIT interaction coefficient, ε. Key findings include successful estimations of ε via artificial neural networks using clustering and value prediction approaches. Additionally, applicability to other chemical parameters is also assessed briefly. Models developed here provide support for a use-case of machine learning in geologic nuclear waste disposal research applications, namely in predictions of chemical behaviors of high ionic strength solutions (i.e., subsurface brines).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

JAMES BUTTLE REVIEW: Interflow, subsurface stormflow and throughflow: A synthesis of field work and modelling

Interflow, throughflow and subsurface stormflow are interchangeable terms that refer to the lateral subsurface flow above a restricting layer of lower hydraulic conductivity that occurs during and following storm events. Interflow (used here) is a more dominant process in steeper catchments with high infiltration capacity soils overlying a more impermeable soil or geologic layer. Interflow as a runoff process was first recognised in the early 1900s, yet hydrologists still struggle to predict its occurrence, persistence, importance, interaction with other streamflow generation processes, and potential to connect to valleys and streams during and following storms. We review the history of interflow research and address some of the challenges in understanding its role in runoff production. We argue that characterising the controls on interflow initiation and occurrence relies on detailed field observations of subsurface properties, which exist only in limited experimental settings. This data shortcoming contributes to our inability to predict interflow or determine its contribution to streamflow more broadly. There remain many opportunities to advance our understanding of interflow that include both modelling and experimental or observational approaches in hydrology.

hillslope hydrology↗

A Geo‐Structurally Based Correction Factor for Apparent Dissolution Rates in Fractured Media

Abstract Field measurements of apparent geochemical weathering reaction rates in subsurface fractured porous media are known to deviate from laboratory measurements by multiple orders of magnitude. To date, there is no geologically based explanation for this discrepancy that can be used to predict reaction rates in field systems. Proposed correction factors are typically based on ad hoc characterizations related to geochemical kinetic models. Through a series of high‐fidelity reactive transport simulations of mineral dissolution within explicit 3D discrete fracture networks, we are able to link the geo‐structural attributes with reactive transport observations. We develop a correction factor to linear transition state theory for the prediction of the apparent dissolution rate based on measurable geological properties. The modified rate law shows excellent agreement with numerical simulations, indicating that geological structure could be a primary reason for the discrepancy between laboratory and field observations of apparent dissolution rates in fractured media.

58 GEOSCIENCES↗

Application and calibration of the subsurface mapping capability of SIR-B in desert regions

The penetration capability of the shuttle imaging radar (SIR-B) sensor in desert regions is investigated. Refined models to explain this penetration capability in terms of radar physics and regional geologic conditions are devised. The sand-buried radar-rivers discovered in the Western Desert in Egypt and Sudan are defined. Results and procedures developed during previous SIR-A investigation of the same area are extrapolated.

Schaber, G. G.↗

Improving Subsurface Stress Characterization for Carbon Dioxide Storage Projects

Researchers at New Mexico Tech, Los Alamos National Laboratory (LANL), Sandia National Laboratory (SNL), and other collaborators are developing a methodology to improve characterization of stress in the subsurface by means of a model-based inversion of reservoir engineering data, time lapse seismic measurements, and microseismicity. Historically, various geophysical techniques have been used in efforts to understand the state of stress in the subsurface through direct and indirect imaging of stress sensitive features (faults and fractures) and observations of transient stress related observations (time variant elastic moduli and microseismicity). Standard direct and indirect techniques for seismic fault and fracture imaging suffer from detectability limits due to reliance on high data quality and multiplicity. Variations in effective elastic properties from inversion of high quality seismic (Vertical Seismic Profile (VSP)) data may be used to infer stress near the wellbore through integration with independent experimental characterization of the stress-velocity relationship. Given a sufficiently robust observation network, microseismic emissions may be inverted to characterize focal mechanisms which, together with supporting assumptions and constraints, inform estimates of in-situ stress. While each of these techniques contributes in part to the characterization of stress within limited spatial and temporal domains, no one method provides an unambiguous stress measurement or a predictive capability over a site scale spatial extent. Challenges associated with solution non-uniqueness, measurement ambiguity, and irregular sampling may be greatly minimized through combination of one or more of independent measurements within a common framework in which realistic geological, hydrodynamic, geomechanical, and seismological constituent process models may act as constraints.

02 PETROLEUM↗

Technologies Enabling Exploration of Skylights, Lava Tubes and Caves

Robotic exploration of skylights and caves can seek out life, investigate geology and origins, and open the subsurface of other worlds to humankind. However, exploration of these features is a daunting venture. Planetary voids present perilous terrain that requires innovative technologies for access, exploration, and modeling. This research developed technologies for venturing underground and conceived mission architectures for robotic expeditions that explore skylights, lava tubes and caves. The investigation identified effective designs for mobile robot architecture to explore sub-planetary features. Results provide insight into mission architectures, skylight reconnaissance and modeling, robot configuration and operations, and subsurface sensing and modeling. These are developed as key enablers for robotic missions to explore planetary caves. These results are compiled to generate "Spelunker", a prototype mission concept to explore a lunar skylight and cave. The Spelunker mission specifies safe landing on the rim of a skylight, tethered descent of a power and communications hub, and autonomous cave exploration by hybrid driving/hopping robots. A technology roadmap was generated identifying the maturation path for enabling technologies for this and similar missions.

Robot↗

The microwave spectrum and nature of the subsurface of Mars.

Expected microwave spectra of Mars are computed using an improved thermal model and accurate aspect geometry. It is found that when seasonal polar cap effects are included in the calculations, the observable spectrum of Mars is flat from 0.1-21 cm to within the accuracy of present data. The spectra obtained from this model are consistent with all the data and are obtainable from a relatively simple model (homogeneous, dry, smooth dielectric sphere). This result differs from that predicted by the analytical theory in common use which is in apparent conflict with the observed spectra. A range of electrical loss tangents, covering the extreme limits for likely dry particulate geological materials, is employed. The case of a lunar-like subsurface is completely consistent with all present data.

Cuzzi, J. N.↗

Toward more-robust, AI-enabled subsurface seismic imaging for geotechnical applications

Non-invasive seismic imaging has the potential to cost-effectively evaluate large volumes of subsurface material to inform geotechnical site investigation. However, seismic imaging using full waveform inversion (FWI) requires significant computational time and is dependent on an initial starting model. As a result, FWI has not yet been widely adopted into geotechnical practice. Previous efforts, on relatively simple two-layered models, indicate that data-driven artificial intelligence (AI) models may be as effective as FWI at predicting 2D images of shear wave velocity (V s ). Furthermore, the AI model predictions can be made almost instantaneously after data acquisition and do not require an initial starting model. We examine the generality of these findings by developing a new AI model for subsurface seismic imaging, whereby we make several notable contributions. First, we architect a multimodal AI model that combines time- and frequency-domain representations of the seismic wavefield to predict a 50 m by 20 m subsurface image of V s . Second, we developed a new diverse dataset of 100,000 images with their corresponding seismic wavefields to train the AI model. Third, we propose four physics-informed data augmentations for data-driven seismic imaging. Fourth, we develop two prediction consistency tests to evaluate the model’s performance when the true subsurface is unknown. Our final model, which has been made publicly available, is capable of predicting a subsurface V s image from a single seismic wavefield with an average, mean absolute percent error (MAPE) of 24 %. The predictive model is applied to a field dataset and shown to be consistent with local geology and shear-wave refraction measurements from the same location.

Artificial intelligence↗

Geologic hydrogen as an emerging fuel: experimental insights, thermodynamics, kinetics, and reactive transport modeling

Geologic hydrogen (GeoH 2 ) is emerging as a viable clean energy source. It is largely produced through serpentinization, a geological process in which ultramafic rocks react with water under suitable temperature and pressure. Here, this review synthesizes the current understanding of H 2 generation by serpentinization, with an emphasis on reaction mechanisms, kinetics, and thermodynamics, as well as on modeling flow and transport of reacting fluids in geological formations. We describe the role of mineral assemblages, such as olivine and pyroxene, fluid-rock interactions, and catalytic surfaces, in influencing GeoH 2 yield and reaction rates. By integrating models of reaction kinetics, subsurface reactive flow and transport, and the serpentinization process, and by accounting for the thermodynamic state of the system, this review aims to guide future GeoH 2 research and to evaluate the potential of natural hydrogen as a sustainable clean energy source.

Moradi, Rasoul [Univ. of Southern California, Los ↗

Subsurface Characterization and Machine Learning Predictions at Brady Hot Springs: Preprint

Subsurface data analysis, reservoir modeling, and machine learning (ML) techniques have been applied to the Brady Hot Springs (BHS) geothermal field in Nevada, USA to further characterize the subsurface and assist with optimizing reservoir management. Hundreds of reservoir simulations have been conducted in TETRAD-G and CMG STARS to explore different injection and production fluid flow rates and allocations and to develop a training data set for ML. This process included simulating the historical injection and production since 1979 and prediction of future performance through 2040. ML networks were created and trained using TensorFlow based on multilayer perceptron (MLP), long short-term memory (LSTM), and convolutional neural network (CNN) architectures. These networks took as input selected flow rates, injection temperatures, and historical field operation data and produced estimates of future production temperatures. This approach was first successfully tested on a simplified single fracture doublet system, followed by the application to the BHS reservoir. Using an initial BHS dataset with 37 simulated scenarios, the trained and validated network predicted the production temperature for 6 production wells with the mean absolute percentage error of less than 8%. In a complementary analysis effort, the principal component analysis applied to 13 BHS geological parameters revealed that vertical fracture permeability shows the strongest correlation with fault density and fault intersection density. A new BHS reservoir model was developed considering the fault intersection density as proxy for permeability. This new reservoir model helps to explore under-exploited zones in the reservoir. A data gathering plan to obtain additional subsurface data was developed; it includes temperature surveying for three idle injection wells, at which the reservoir simulations indicate high bottom-hole temperatures. The collected data assist with calibrating the reservoir model and may lead to converting these wells to producers to access under-exploited zones in the reservoir. Data gathering activities are planned for the first quarter of 2021.

40 EE - Geothermal Technologies Office (EE-4G)↗

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↗