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79 records · Page 5

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗

Data-Centric Approach to Capture Non-Polynomial Nonlinear Dynamics

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of observable functions is fundamental for applying EDMD to nonlinear problems arising in systems and control. Existing methods either start from a set of dictionary functions and look for the subset that best fits the underlying nonlinear dynamics or rely on machine learning algorithms to “learn” observable functions. Conversely, in this paper, we start from the dynamical system model and lift it through the Lie derivatives, rendering it into a polynomial form. This proposed transformation into a polynomial form is exact and provides an adequate set of observable functions. The strength of the proposed approach is its applicability to a broader class of nonlinear dynamical systems, particularly those with nonpolynomial functions and compositions thereof. Moreover, it retains the physical interpretability of the underlying dynamical system and can be readily integrated into existing numerical libraries. We demonstrate the proposed approach with an application to electric power systems. The modeled system consists of a single generator connected to an infinite bus, where nonlinear terms include sine and cosine functions. The results demonstrate the effectiveness of the proposed procedure in off-attractor nonlinear dynamics for estimation and prediction; the observable functions obtained from the proposed construction outperform methods that use dictionary functions comprising monomials or radial basis functions.

extended dynamic mode decomposition↗

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

Here, we demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 38 cases from the PGLib-OPF library, showing that the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 6.2% and 17.5% respectively. The NF relaxation is strengthened in 46.2% of test cases, with average and maximum differences in the optimality gaps of 1.3% and 17.3% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality improvement due to these LNC.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Supply Chain Road Map for Offshore Wind Energy in the United States

"A Supply Chain Road Map for Offshore Wind Energy in the United States" identifies pathways to developing a domestic offshore wind supply chain that can manufacture and deploy the major components needed to set the United States on a pathway to installing 30 GW of offshore wind by 2030 and 110 GW by 2050. The report estimates that this supply chain could require an investment of at least $\$$22.7 billion this decade to meet an annual demand for components, ports, and vessels in 2030. Although this is a considerable investment, it could allow the industry to install around $\$$100 billion worth of offshore wind this decade by reducing risk of delays due to global supply chain bottlenecks and creating a robust network of assets that will continue to be effective well beyond 2030. The United States would need at least 34 manufacturing facilities employing 10,000 workers, 39,000 jobs in the supporting supply chain, 10 marshaling ports, 4-6 dedicated wind turbine installation vessels, 4-6 dedicated heavy-lift vessels, and 4-8 U.S.-flagged specialized feeder barges to come online this decade to support an average annual deployment of 4-6 gigawatts offshore wind capacity per year. This supply chain could be developed in 6-9 years, but would require near-term decision making and efficient permitting and planning to strategically develop these resources by 2030. Additional investment and expansion would be required in the 2030s as the sector expands into new regions (such as the Gulf of Mexico) and new technologies (such as larger wind turbines and floating wind energy projects). Furthermore, the planning process needs to meaningfully engage with communities that will be impacted by supply chain expansion to achieve just outcomes and maximize benefits to these stakeholders, which will result in a more equitable and sustainable supply chain. While U.S. offshore wind has made significant progress in recent years, remaining supply chain challenges include uncertainty surrounding deployment and procurement timelines; a lack of port and vessel infrastructure; and limitations in the available workforce, supporting supplier networks, and energy justice best practices. However, many of these problems can be addressed through improved communication between key stakeholder groups, support from federal and state governments, and forward-thinking designs of supply chain assets to accommodate future technology changes for fixed-bottom and floating offshore wind. Although it is a significant task, developing these domestic capabilities represents a once-in-a-generation opportunity to contribute to a decarbonized energy future and also create massive economic benefits that are distributed throughout the country.

17 WIND ENERGY↗

Macro-physical Properties of Shallow Cumulus from Integrated ARM Observations (Final Report)

Fair-weather shallow cumuli (ShCu) play an important role in many climate-related processes. Irregular geometry of ShCu and their strong temporal and spatial variability make it challenging to observe ShCu holistically and to represent them correctly in climate models. To improve ShCu parameterizations, information on both vertically and horizontally resolved cloud properties is required. Commonly, the vertically resolved cloud properties are provided by zenith pointing lidar-radar observations with a very narrow field of view (FOV). Thus, these “pencil-beam” properties may not be representative of a larger surrounding area. Limited number of areal-averaged cloud properties, such as fractional sky cover (FSC), are offered typically by wide-FOV observations. The main goal of our project was to integrate advantages of the narrow-FOV (vertical structure of clouds) and wide-FOV (spatial arrangement of clouds) observations for an improved characterization of single-layer ShCu observed at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site for an 18-yr period (2000-2017). There are four major accomplishments of our project, First, an updated operational cloud classification for days with ShCu has been suggested and evaluated through a detailed comparison with the manually curated records. Our classification extends successfully the latest ARM cloud type Value Added Product (VAP) based on the Active Remote Sensing of Clouds (ARSCL) cloud product by incorporating both cloud fraction (CF) provided by narrow-FOV ceilometer data and FSC from wide-FOV images offered by a Total Sky Imager (TSI). Moreover, our classification allows one to identify impact of instrumentation changes at the SGP site, namely the transition to KAZRARSCL with the updated cloud radar, on the identification of periods with single-layer ShCu. Second, a new approach that resolves cloud area distributions for a given region (up to 4x4 km 2 ) has been suggested and cloud equivalent diameters (CEDs) have been estimated for the first time. These estimations have been performed over a wide range of cloud sizes (about 0.01–3.5 km) with high temporal resolution (30s) using wide-FOV TSI images and cloud base height (CBH) provided by complementary narrow-FOV lidar measurements. Our simple and computationally inexpensive approach offers a previously unavailable dataset for process studies in the convective boundary layer and evaluation of ShCu parameterizations in cloud-resolving models. Third, a long-term integrated record of ShCu macrophysical properties has been developed. The developed record represents the longest available compilation of events with ShCu and includes (i) a novel visualization of the spatial variability in cloud cover both along- and across-wind directions, (ii) updated estimates of narrow-FOV CF and wide-FOV FSC, (iii) updated narrow-FOV CBH, and (iv) complementary data, such as wind speed and direction from the 915-MHz Radar Wind Profiler (RWP) data. The developed record has been used successfully to assess conventional observational estimates of cloud cover and their sensitivity to the following two factors: (i) instrument-dependent cloud detection and data merging criteria and (ii) FOV configuration. Fourth, co-variability of the ShCu macrophysical properties and environmental parameters has been analyzed for a 3-yr period (2016-2018). Our initial analysis includes diurnal changes of FSCs obtained for clouds with small, moderate and large CEDs and several environmental parameters, such as lifted condensation level (LCL) and mixed layer height (zi). Preliminary results of our analysis suggest that the horizontal extent of ShCu is controlled substantially by the sign and magnitude of difference between these two parameters (zi-LCL): the CED tends to grow with increase of this difference (zi exceeds LCL). We have initiated relationships between the ShCu and key atmospheric parameters that control both the development and evolution of ShCu using our new data product, which combines effectively the advantages of narrow-FOV data offered by zenith pointing cloud radars and lidars and wide-FOV TSI images. While the latest instrumentation at the ARM sites may address these challenging relationships in the future, we believe that the historical ARM data at the SGP site has not yet been fully utilized. Overall, our data product can be used by researchers working on a wide range of climate-related projects. These projects may include (i) a comprehensive evaluation of outputs from the Large-Eddy Simulation (LES) and single-column models for their future improvement, (ii) the representativeness of “short-period” results obtained from the previous model and observational studies and (iii) the planning of future field campaigns with focus on improved understanding of the diurnal cycle of cumulus convection.

54 ENVIRONMENTAL SCIENCES↗

Are Marine Low Cloud Droplet Concentrations Buffered by Entrained Aitken‐Mode Aerosol (Final Technical Report)

During the summertime, the high-latitude oceans come to life with green phytoplankton, which gain their energy from sunlight and are food for sea creatures small and large. When the phytoplankton are eaten or die, sulfur-rich gases are released under the ocean surface and mix into the air. Observations suggest that, over the Southern Ocean, frequent storms lift this air high into the atmosphere while raining out particulates like salt. As a result, the sulfur-rich air then spawns high concentrations of small ‘Aitken-mode’ aerosol particles. We hypothesize that these particles work their way down into the marine boundary layer, where they can replenish the supply of cloud-condensation nuclei scavenged by frequent precipitation. Further, this process maintains high concentrations of liquid cloud droplets in austral summer, promoting more sunlight to be reflected to space. We call this ‘Aitken buffering’. The primary objective of this project has been to document and test what role Aitken-mode aerosols play in clouds over the Southern Ocean and elsewhere. This effort has included three main components: 1) developing a computer model that realistically simulates the aerosol processes and the small-scale turbulent air motions that move aerosols around and create the clouds, 2) using that model to interpret and extend these observations for process understanding, by allowing different factors that contribute to the aerosol budget, such as surface wind speed, precipitation, surface gas exchange, etc. to be separated, and 3) studying Aitken-mode aerosol and its variability with a focus over the Southern Ocean and Antarctica, using data from Atmospheric Radiation Measurement (ARM) sites and other available observations. Initial computer studies in more idealized conditions found that elevated concentrations of Aitken-mode aerosols above the clouds could help prevent the breakup of those clouds by acting as cloud-condensation nuclei after they were entrained into the cloudy boundary layer. Simulations of a day during the ACE-ENA field campaign showed that Aitken-mode aerosols could also prevent cloud breakup under more realistic conditions. A new method that extracts information about Aitken-mode aerosols from measurements of aerosols onto which cloud droplets can form finds that Aitken-mode aerosols do vary seasonally over the Southern Ocean, with a peak in summertime, as described above. Other work during this project has focused on understanding how patterns of water vapor, clouds and precipitation are coupled within low-lying clouds over the oceans, and also on how cloud droplets cluster within clouds and how the distribution of cloud droplet sizes change as dry air is mixed into clouds, with the latter studies also using observations from ACE-ENA.

54 ENVIRONMENTAL SCIENCES↗

ELECTRIFICATION OF A HEAVY-DUTY OFF-ROAD MATERIAL HANDLER: ENERGY SAVINGS AND EMISSION REDUCTIONS

Federal regulations are driving the adoption of electrification technologies to reduce carbon dioxide equivalent (CO2e) emissions, a metric that quantifies the global warming potential of various greenhouse gases in terms of carbon dioxide (CO2). Although no specific CO2 regulations exist for heavy-duty off-road machines, future reductions are likely, given stricter emissions standards for on-road vehicles. The heavy-duty off-road sector offers significant fuel-saving potential, as its focus has traditionally been on reliability and performance rather than fuel efficiency. This dissertation examines fuel and CO2e savings opportunities on a heavy-duty off-road material handler, the Pettibone Cary-Lift 204i, from stock configuration to simple modifications to a complete teardown and reconfiguration of the machine with a plug-in series hybrid architecture using electrified hydraulics. The study begins by modeling the baseline machine’s fuel and energy consumption, calibrating with experimental data from custom operating cycles. An energy analysis identifies key areas for fuel savings. Two simple powertrain modifications result in a combined 16.2% fuel savings. Next, a Pugh-style analysis narrows a list of electrified architectures, leading to high-fidelity models that evaluate total lifetime CO2e and costs. Higher electrification levels reduce CO2e emissions but increase costs, and electricity grid emissions significantly impact CO2e for plug-in architectures. A plug-in series hybrid is chosen for the project. In its base control form, 49% fuel and 29% CO2e savings are expected from the plug-in series hybrid compared to the baseline machine. Further savings are pursued through regenerative braking (6.3%) and load-following hydraulic control (17.8%), totaling 24.1% fuel savings, and leading to a total of 61% fuel and 41% CO2e savings compared to the baseline. Battery chemistries and charging strategies are also analyzed for cost and CO2e impacts, finding LFP batteries as superior due to longevity, and overnight level 2 charging usually at a lower cost but resulting in higher emissions than opportunity DC fast-charging (DCFC). DCFC emissions are highly dependent on grid emissions, and DCFC cost is highly dependent on grid demand charges. Finally, artificial intelligence is applied to operating cycle recognition. Neural network accuracy ranges from 81% to 99%, with applications to worksite efficiency and safety improvements.

24 POWER TRANSMISSION AND DISTRIBUTION↗