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DOE OSTI2023

Evolution of Scenario Generation Capabilities in the ExaSGD Project

High-fidelity renewable energy scenarios and rare-event high-impact contingencies are essential for modeling operations and infrastructure expansion of the next generation power grids using exascale computing resources. As the ExaSGD project progressed, our capabilities for generating scenarios for modeling wind power output at multiple wind farms significantly improved, evolving from the use of independent random perturbations to importance sampling-based techniques capturing representative spatial-temporal relations. Contingency generation also improved, evolving from standard N-1 techniques to probabilistic models of infrastructure damage resulting from extreme weather events. We review the developments in the realistic intermittent-energy scenario forecasting and extreme-event contingency creation as the ExaSGD project progressed and discuss the future work in these areas.

economic dispatch↗

DOE OSTI2024

Techno-economic analysis of renewable energy generation at the South Pole

Transitioning from fossil-fuel power generation to renewable energy generation and energy storage in remote locations has the potential to reduce both carbon emissions and cost. Here, this study presents a techno-economic analysis for implementation of a hybrid renewable energy system at the South Pole in Antarctica, which currently hosts several high-energy physics experiments with nontrivial power needs. A tailored model of resource availability and economics for solar photovoltaics, wind turbine generators, lithium-ion energy storage, and long-duration energy storage at this site is explored in different combinations with and without existing diesel energy generation. The Renewable Energy Integration and Optimization (REopt) platform is used to determine the optimal system component sizing and the associated system economics and environmental benefit. We find that the least-cost system includes all three energy generation sources and lithium-ion energy storage. For an example steady-state load of 170 kW, this hybrid system includes 180 kW-DC of photovoltaic panels, 570 kW of wind turbines, and a 3.4 MWh lithium-ion battery energy storage system. This system reduces diesel consumption by 95% compared to an all -diesel configuration, resulting in approximately 1200 metric tons of carbon footprint avoided annually. Over the course of a 15-year analysis period the reduced diesel usage leads to a net savings of 57 million United States dollars, with a time to payback of approximately two years. All the scenarios modeled show that the transition to renewables is highly cost effective under the unique economics and constraints of this extremely remote site.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Sizing battery energy storage and PV system in an extreme fast charging station considering uncertainties and battery degradation

In this paper, we present mixed integer linear programming (MILP) formulations to obtain optimal sizing for a battery energy storage system (BESS) and solar generation system in an extreme fast charging station (XFCS) to reduce the annualized total cost. The proposed model characterizes a typical year with eight representative scenarios and obtains the optimal energy management for the station and BESS operation to exploit the energy arbitrage for each scenario. Contrasting extant literature, this paper proposes a constant power constant voltage (CPCV) based improved probabilistic approach to model the XFCS charging demand for weekdays and weekends. This paper also accounts for the monthly and annual demand charges based on realistic utility tariffs. Furthermore, BESS life degradation is considered in the model to ensure no replacement is needed during the considered planning horizon. Different from the literature, this paper offers pragmatic MILP formulations to tally BESS charge/discharge cycles using the cumulative charge/discharge energy concept. McCormick relaxations and the Big-M method are utilized to relax the bi-linear terms in the BESS operational constraints. Finally, a robust optimization-based MILP model is proposed and leveraged to account for uncertainties in electricity price, solar generation, and XFCS demand. Case studies were performed to signify the efficacy of the proposed formulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Preventive Power Outage Estimation Based on A Novel Scenario Clustering Strategy: Preprint

The increasing occurrence of extreme weather events is challenging the power grid operation. In front of the extreme weather, the system operator is responsible for estimating the power outage and scheduling the restoration resources. This paper proposes an outage evaluation framework to identify the possible unserved load profiles, vulnerable areas, and mobile energy adequacy. The predicted vulnerable lines of an outage prediction model tool are utilized to generate numerous faulted line scenarios. Next, each scenario's nodal unserved load profile is obtained by solving a three-phase restoration model that considers the schedule of repair crews and mobile energy resources. Then, a novel scenario clustering strategy is developed to cluster the unserved load profiles into multiple representative ones for straightforward analysis. Finally, case studies on a distribution system evaluate the damage level brought by extreme weather and verify the effectiveness of the proposed scenario clustering strategy.

mobile energy resources↗

DOE OSTI2020

Loosely Conditioned Emulation of Global Climate Models With Generative Adversarial Networks

Climate models encapsulate our best understanding of the Earth system, allowing research to be conducted on its future under alternative assumptions of how human-driven climate forces are going to evolve. An important application of climate models is to provide metrics of mean and extreme climate changes, particularly under these alternative future scenarios, as these quantities drive the impacts of climate on society and natural systems. Because of the need to explore a wide range of alternative scenarios and other sources of uncertainties in a computationally efficient manner, climate models can only take us so far, as they require significant computational resources, especially when attempting to characterize extreme events, which are rare and thus demand long and numerous simulations in order to accurately represent their changing statistics. Here we use deep learning in a proof of concept that lays the foundation for emulating global climate model output for different scenarios. We train two "loosely conditioned" Generative Adversarial Networks (GANs) that emulate daily precipitation output from a fully coupled Earth system model: one GAN modeling Fall-Winter behavior and the other Spring-Summer. Our GANs are trained to produce spatiotemporal samples: 32 days of precipitation over a 64x128 regular grid discretizing the globe. We evaluate the generator with a set of related performance metrics based upon KL divergence, and find the generated samples to be nearly as well matched to the test data as the validation data is to test. We also find the generated samples to accurately estimate the mean number of dry days and mean longest dry spell in the 32 day samples. Our trained GANs can rapidly generate numerous realizations at a vastly reduced computational expense, compared to large ensembles of climate models, which greatly aids in estimating the statistics of extreme events.

climate emulation, extreme climate, impacts, machi↗

DOE OSTI2024

Seasonal Cost-Benefit Analysis of Automated Distribution Feeder Upgrades with Advanced Mitigation Technologies

The increasing deployment of distributed solar photovoltaics (DPV) to meet clean energy goals can trigger adverse grid operation issues, such as voltage excursions and the violation of thermal loading constraints of the power delivery elements (e.g., lines and transformers) on the evolving electricity infrastructure. Such integration issues would require distribution upgrades with associated costs to mitigate them and to maintain reliable and resilient grid operating conditions. Traditional distribution network upgrade approaches use a specific single snapshot analysis that is overly conservative. This study considers a multi-time point analysis to capture both moderate (probable bounds) and extreme grid operating conditions using time points such as minimum load with minimum photovoltaics (PV), maximum load with maximum PV, maximum load with minimum PV, and minimum load with maximum PV. Further, this study investigates seasonal variation impacts and associated distribution upgrade costs for a spring season case (March, representing a low load and high PV scenario) and a summer case (July, representing a high load and high PV scenario). Such seasonal analysis will allow system operators to characterize upgrade requirements and associated costs across various periods. Because the spatial distribution of DPV can impact upgrade and associated costs, this study investigates three common DPV deployment scenarios - randomly deployed, close to the substation, and far from the substation - at different penetration levels. Apart from spatial distribution impacts, this project evaluates the techno-economic impacts of the nodal photovoltaic penetration factor (NPPF) for generating the various DPV deployment scenarios at increasing penetration levels. This project investigates the impact of varying nodal PV-to-load ratios using conservative and extreme NPPF values of 3 and 10, respectively. This study investigates the deployment of traditional infrastructure upgrade strategies, such as installing new voltage regulating equipment, transformers and lines replacements, and the activation of advanced inverter functionality (e.g., autonomous volt/VAR) in expanding PV hosting capacity. Existing DPV systems are assumed to operate with the legacy unity power factor, and we considered the possibility of retrofitting such systems with the activation of volt/VAR control as integration standards and regulations continue to evolve to allow such functions. The cost-benefit analysis metrics used in study include distribution upgrade costs, average cost per watt of the upgrade cost, average marginal cost per watt of the upgrade cost, and power losses.

14 SOLAR ENERGY↗

DOE OSTI2022

Optimizing the physical design and layout of a resilient wind, solar, and storage hybrid power plant

We report as wind and solar technologies improve and their costs decrease, the share of power produced by these sources will increase. As the market penetration increases, these power sources will need to provide grid services, such as dispatchability, in addition to providing energy. One way to reduce variability, provide higher quality power to the grid, and address local grid stability issues is through colocating wind and solar power plants. In addition to operating reliably during normal operating conditions, in scenarios with high penetrations of renewable generation, it is important that these hybrid plants can withstand production disruptions and continue to supply power despite prolonged resource reduction, extreme weather events, or other disruptions. In this paper, we present a methodology to optimize a wind-solar-battery hybrid power plant down to the component level that is resilient against production disruptions and that can continually produce some minimum required power. We introduce the models and assumptions we used to simulate a hybrid power plant as well as the design variable parameterization and specific methods we used to optimize the plant. We demonstrate the performance of our method by comparing a plant optimized for different objectives, generation outage durations, minimum power requirements, and power purchase agreements. Although the plant design is sensitive to model parameters and various other assumptions, our results demonstrate some of the optimal designs that occur in different scenarios and what one should expect when designing a hybrid wind-solar-storage power plant.

14 SOLAR ENERGY↗

DOE OSTI2023

Emergency Asset Positioning for Resilient Transmission Grid Operation

In this paper we study a problem of hurricane emergency preparedness via placement of emergency generation assets prior to its strike. We present a two-stage stochastic model for choosing locations and quantities of emergency storage to help support the power grid through a hurricane event. The expectation of losses in our two-stage model is estimated using the sample average approximation. We construct damage scenarios for sample average approximation using WIND Toolkit meteorological data and fragility curves of various electric grid components. We demonstrate the efficacy of our two-stage planning model by simulating operations during Hurricane Dolly on the 2000-bus transmission test system. Our model, coupled with our scenario selection strategy, is effective at mitigating loss of load when compared to a model without emergency generation assets placed prior to an extreme event.

emergency preparedness↗

DOE OSTI2023

Emergency Generation Asset Positioning for Resilient Transmission Grid Operation: Preprint

emergency preparedness↗

DOE OSTI2024

PV Generation and Load Forecasting for Adjuntas PR Community Microgrids

Existing frameworks to forecast time-series photovoltaic (PV) output power and consumer load for microgrid operations and controls assume a near-continuous availability of real-time input features from the field assets such as PV inverters, energy meters, and weather station. These incoming data points are used to periodically retrain models and update forecast snapshots over a moving horizon window, be it one hour-ahead, one-day ahead, or one-week ahead. However, such frameworks are not resilient to disruptions in data availability caused by losses in communications between the field sensors and data loggers. Hence, there is a need for programs that assume no availability of real-time microgrid asset data and still make reliable forecasts that can be used for decision-making. Such programs would be apt to function in extreme weather events such as hurricanes and would use lightweight recursive time-series models to independently forecast solar irradiance and ambient temperature, then compute PV power from those forecasts, as well as independently forecast consumer load. The codebase performs forecasting for the scenario of when the microgrid does not have a reliable access to forecasts or real-time observations of solar irradiance (I) and ambient temperature (AT) and load (Load) to be able to adequately forecast, in real-time, the PV power production or a business' load. In this case, using historical values of PV power and load, a univariate forecasting of generation and consumption are respectively made. The use-case in particular has two sub-scenarios: one, a normal 7-day ahead forecast where the unavailability of real-time data is assumed due to infrastructure issues such as loss of communication or sensor maintenance or service downtimes. Whereas a hurricane-caused unavailability of real-time data requires a second model trained specifically on historical hurricane days to be able to capture the extreme day behavior of generation in particular, and load if applicable. A gradient boosted regression tree comprises an ensemble of additive models that map between the input of historical values (be it irradiance, temperature, or load) and their corresponding output forecasts of a given horizon such that the individual learner predictions are summed up over the total number of such learners in the ensemble to produce an aggregate forecast. A weighting mechanism is applied to the training data in each iteration, where actual and forecast values are compared to penalize incorrect forecasts by increasing the weight and reducing it to reward correct forecasts. The code's benefits are that it: (a) accounts for a contingency where communication loss renders newly measured real-time data unavailable for model tuning and snapshot updates; (b) presents blind forecasting that recursively determines the next time-step value in a horizon using the forecast of the same attribute from a prior step; and (c) employs lightweight models that, once trained, can reliably generalize for different horizons, which make them suitable for enhancing the resilience of field microgrids prone to extreme events that encounter disruptions to data availability.

Sundararajan, Aditya [Oak Ridge National Laborator↗

DOE OSTI2023

Topological Guided Detection of Extreme Wind Phenomena: Implications for Wind Energy

Extreme wind phenomena play a crucial role in the efficient operation of wind farms for renewable energy generation. However, existing detection methods are computationally expensive, limited to specific coordinate. In real-world scenarios, understanding the occurrence of these phenomena over a large area is essential. Therefore, there is a significant demand for a fast and accurate approach to forecast such events. In this paper, we propose a novel method for detecting wind phenomena using topological analysis, leveraging the gradient of wind speed or critical points in a topological framework. By extracting topological features from the wind speed profile within a defined region, we employ topological distance to identify extreme wind phenomena. Our results demonstrate the effectiveness of utilizing topological features derived from regional wind speed profiles. We validate our approach using high-resolution simulations with the Weather Research and Forecasting model (WRF) over a month in the US East Coast.

MATHEMATICS AND COMPUTING,WIND ENERGY↗

DOE OSTI2023

Topological Guided Detection of Extreme Wind Phenomena: Implications for Wind Energy: Preprint

MATHEMATICS AND COMPUTING,WIND ENERGY↗

DOE OSTI2021

Post-extreme-event restoration using linear topological constraints and DER scheduling to enhance distribution system resilience

In this paper, a post-extreme-event restoration (PEER) algorithm is proposed to improve distribution system resilience. Linear topological constraints are proposed to ensure radial topology after N-k contingencies, possibly in multiple islands. The approach is made comprehensive by considering dispatchable distributed energy resources (DERs), non-dispatchable DERs, and demand responses, as well as on-load tap changers (OLTCs) and shunt capacitors. The goal is to minimize the accumulative expense caused by load reduction payment or penalty, as well as DER operation cost. As a result, the overall system will survive longer with higher resilience during an extreme event. To verify the effectiveness of the PEER algorithm, we proposed a resilience evaluation algorithm using Monte Carlo simulation (MCS) with reduced scenarios. This is based on a probabilistic model for generating random scenarios which consider the uncertainty of line faults and solar irradiance. Combined with the proposed PEER algorithm, this reduced-scenario MCS can evaluate the expected energy not served (EENS) which is an essential index for distribution system resilience. Case studies of the IEEE 33-bus and 123-bus test systems validate the proposed algorithm in reducing EENS.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Value of Nuclear Energy to the Reliability of the North American Power System: Results for Western and Eastern Interconnections

This report documents the fulfillment of a milestone for the United States (U.S.) Department of Energy Office of Nuclear Energy Light Water Reactor Sustainability Program: completing a baseline study of regional impact of nuclear power plants and hydrogen production in maintaining grid services and power quality. Models have been comprehensively demonstrated for the Western Interconnection, or Western Electric Coordinating Council area, and in the Eastern Interconnection for scenarios representative of past extreme events (e.g., drought and heat waves). Understanding the impact on the reliability of the bulk electric system of any reduction in generation capacity from nuclear power, for any reason, is the motivation of this work. Factors that might lead to the premature or unplanned closure of nuclear plants, extended outages, or repurposing of nuclear power include: • Aging infrastructure: Many nuclear power plants in the U.S. are nearing the end of their designed operating lives. Upgrading aging infrastructure can be expensive, and some utilities may choose to retire plants rather than invest in costly upgrades. • Low wholesale electricity prices: The deregulation of the electricity market in many states has led to increased competition and driven down wholesale electricity prices, causing nuclear power operators to seek other revenue sources for their heat and power such as clean hydrogen production. • Renewables growth: The rapid growth of renewable energy sources like solar and wind power is posing a challenge to traditional generation sources like nuclear. While many see renewables as a key part of the clean energy transition, their intermittent nature requires additional grid solutions for reliable power supply. • The potential for regulatory decisions to be in conflict: In its 2021 rulemaking, EPA rule (86 FR 880), the Environmental Protection Agency (EPA) set a compliance date for the ban on processing and distribution in commerce of Decabromodiphenyl Ether (DecaBDE). Since DecaBDE is in many components, particularly wiring, of nuclear power plants which are deemed safety-related or important to safety, three plants would not have been able to restart after their 2023 spring outages, and numerous others would have faced issues in the near future. Fortunately, in this case, the EPA provided relief to the nuclear energy industry. The report provides a summary of the significant role nuclear energy plays in the United States’ power generation mix, supplying around 20% of the nation’s electricity generation, spread across 28 U.S. states. Nuclear power is reliable, mostly unaffected by weather and seasonal changes, and provides a consistent source of baseload power. In terms of capacity, nuclear power plants account for as much as 26% of balancing area power generation capacity. Nuclear power also provides a substantial contribution (e.g., 10% of the inertia in the Eastern Interconnection) of the synchronous spinning mass/inertia that buffers the rate at which frequency changes when a load and generation imbalance occurs (e.g., a large plant trips or a load is suddenly shed due to a transmission outage). This contribution is critical for maintaining grid stability during sudden changes in load or generation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Evaluation of Global Climate Models for Use in Energy Analysis

The interplay between energy, climate, and weather is becoming more complex due to increasing contributions of renewable energy generation, energy storage, electrified end uses, and the increasing frequency of extreme weather events. Energy system analyses commonly rely on meteorological inputs to estimate renewable energy generation and energy demand; however, these inputs rarely represent the estimated impacts of future climate change. Climate models and publicly available climate change datasets can be used for this purpose, but the selection of inputs from the myriad of available models and datasets is a nuanced and subjective process. In this work, we assess datasets from various global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6). We present evaluations of their skills with respect to the historical climate and comparisons of their future projections of climate change for two climate change scenarios. We present the results for different climatic and energy system regions and include interactive figures in the accompanying software repository. Previous work has presented similar GCM evaluations, but none have presented variables and metrics specifically intended for comprehensive energy systems analysis including impacts on energy demand, thermal cooling, hydropower, water availability, solar energy generation, and wind energy generation. We focus on GCM output meteorological variables that directly affect these energy system components including the representation of extreme values that can drive grid resilience events. The objective of this work is not to recommend the best climate model and dataset for a given analysis, but instead to provide a reference to facilitate the selection of climate models and scenarios in subsequent work.

14 SOLAR ENERGY↗

DOE OSTI2023

Spatiotemporal Super-Resolution with Generative Machine Learning for Creating Renewable Energy Resource Data Under Climate Change Scenarios

As we plan for a future with higher penetrations of renewables and increasing electrification, it becomes more important to understand how the electricity grid will operate under a variety of weather events. We must also consider that the weather our future grid will experience will be different and possibly more extreme than the historical weather that we have extensive data for. We can use data from global climate models (GCMs) to help understand how our climate may change over the next several decades, but there is often a significant gap between the low-resolution GCM data and the high-resolution weather data required to study power systems under specific weather events. Therefore, our objective in this work is to develop tools that can bridge this gap by using low-resolution GCM data to create realistic high-resolution weather datasets that can be used to study renewable energy generation and electricity demand. To accomplish this objective, we have developed a set of generative machine learning models that can rapidly downscale GCM daily average output data at an approximate grid resolution of 100km to hourly data at an approximate 4 km grid resolution. The models can be used to create high resolution data from nearly any GCM included in the Coupled Model Intercomparison Project (CMIP) Phase 5 or 6. Our methods include all datasets regularly used to study the integration of wind and solar power plants as well as changes in electricity demand due to heating and cooling loads. These models and datasets enable power systems modelers to study climate change-influenced weather events and their impact on the grid. We have downscaled and validated wind, solar, temperature, and humidity data with very promising results. The generative machine learning methods are computationally efficient and produce data that has similar statistical characteristics to current state-of-the-art historical datasets. We have trained initial generative models and produced an initial dataset collectively referred to as Sup3rCC: Super-Resolved Renewable Energy Resource Data with Climate Change Impacts. The data covers a (mostly) historical period from 2015-2025 and a future period from 2050-2059. We have also taken hypothetical high-electrification load data and scaled the heating and cooling loads with respect to the 2050-2059 high-resolution Sup3rCC meteorology. The results show how future levels of renewable energy generation and electrified load may be impacted by climate change, setting the stage for capacity expansion models to consider a dynamic climate through model years.

climate change↗

DOE OSTI2020

Advancement of Commercial Intumescent Expanding Foams for Deactivation and Decommissioning in the Nuclear Sector - 20198

Florida International University (FIU), in collaboration with The Department of Energy's Office of Environmental Management (DOE-EM), Savannah River National Laboratory (SRNL), and sites across the Savannah River complex, have identified an operational requirement for a fixative technology that is intended to immobilize and/or isolate residual contamination within a 3-dimensional space. Fixation of radiological contamination can reduce worker risk and mitigate potentially hazardous conditions, however nearly every marketed contamination fixative has been found to be flammable; a significant concern in radiological facilities. Coupled with this, industry fixatives are normally used as a thin coating which can present problems when attempting to stabilize irregular geometry or areas that are difficult to access whilst ensuring full coverage. The technical evaluation and advancement of commercial-off-the-shelf (COTS) polyurethane foams has yielded a down-selected candidate that shows potential in meeting the requirements to support deactivation and decommissioning activities. Several performance criteria have been established and tested to progress the technology readiness level towards an active field demonstration (TRL-7). Such criteria include: mechanical failure limits, adhesive and cohesive properties, thermal/fire resilience, determining thermal behavior, ability to immobilize contamination, and a means of non-destructive evaluation of applications. The test scenario examined was targeted towards an application for decommissioning nuclear pipework, in which the down-selected polyurethane foam would act as a barrier to segregate pipework and mitigate the potential for release during cutting, packaging, and storage operations. Testing carried out at SRNL included: mechanical evaluation of tensile, compressive, and adhesion strength by dynamic mechanical analysis (DMA), as well as thermogravimetric analysis (TGA). FIU examined the foam's fixative properties by utilizing phosphorescent europium-dysprosium doped strontium aluminate powder to investigating the extent to which contamination can be immobilized. FIU has also exploited previous successes in the field of intumescent technologies to assess the down-selected foam's tolerance to an extreme fire scenario, while maintaining the ability to effectively mitigate a contamination release. Parallel to this, extensive thermal investigations were carried out to determine the upper boundary of anticipated heat generation during the curing process as heat generation has the potential to compromise rubber parts of contaminated enclosures. These investigations subsequently yielded a promising method for a non-destructive application evaluation by means of infrared thermography. Utilizing the high sensitivity of modern IR cameras, coupled with the heat generated during the curing process of the polyurethane foam, FIU has been exploring the concept of monitoring the external pipe surface for indications of an irregular or abnormal application, thus informing operational decision making. The testing carried out utilized several current 'best fit' ASTM standards, which serve as helpful guidelines for testing, however, a precise definition of the operational parameters and requirements is still necessary. With continued collaboration with SRNL, FIU aims refine said definitions and develop new standards by which this, and other decommissioning technologies, can be accredited by relevant standards based testing. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗