Search NASA⌕ Search

SEARCH · Search NASA

Results for “optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

Machine learning-enhanced model-based scenario optimization for DIII-D

Abstract Scenario development in tokamaks is an open area of investigation that can be approached in a variety of different ways. Experimental trial and error has been the traditional method, but this required a massive amount of experimental time and resources. As high fidelity predictive models have become available, offline development and testing of proposed scenarios has become an option to reduce the required experimental resources. The use of predictive models also offers the possibility of using a numerical optimization process to find the controllable inputs that most closely achieve the desired plasma state. However, this type of optimization can require as many as hundreds or thousands of predictive simulation cases to converge to a solution; many of the commonly used high fidelity models have high computational burdens, so it is only reasonable to run a handful of predictive simulations. In order to make use of numerical optimization approaches, a compromise needs to be found between model fidelity and computational burden. This compromise can be achieved using neural networks surrogates of high fidelity models that retain nearly the same level of accuracy as the models they are trained to replicate while reducing the computation time by orders of magnitude. In this work, a model-based numerical optimization tool for scenario development is described. The predictive model used by the optimizer includes neural network surrogate models integrated into the fast Control-Oriented Transport simulation framework. This optimization scheme is able to converge to the optimal values of the controllable inputs that produce the target plasma scenario by running thousands of predictive simulations in under an hour without sacrificing too much prediction accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints. Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

17 WIND ENERGY↗

Online Optimization for Networked Distributed Energy Resources With Time-Coupling Constraints

This paper proposes a Lyapunov optimization-based online distributed (LOOD) algorithmic framework for active distribution networks (ADNs) with numerous photovoltaic inverters and inverter air conditionings (IACs). In the proposed scheme, ADNs can track an active power setpoint reference at the substation in response to transmission-level requests while concurrently minimizing the social utility loss and ensuring the security of voltages. Conventional distributed optimization methods are rarely feasible to track the optimal solutions in fast variable environments using a fine-grained sampling interval where the underlying optimization problem evolves with the iterations of the algorithms. In contrast, based on the framework of online convex optimization (OCO), the developed approach uses a distributed algebraic update to compute the next round decisions relying on the current feedback of measurements. Notably, the time-coupling constraints of IACs are decoupled for online implementation with Lyapunov optimization technique. An incentive scheme is tailored to coordinate the customer-owned assets in lieu of the direct control from network operators. Optimality and convergency are characterized analytically. Finally, we corroborate the proposed method on a modified version of 33-node test feeder. Benchmark tests show that the proposed method is computationally and economically efficient, and outperforming existing algorithms.

active distribution networks↗

Engine Combustion System Optimization Using Computational Fluid Dynamics and Machine Learning: A Methodological Approach

Gasoline compression ignition (GCI) engines are considered an attractive alternative to traditional spark-ignition and diesel engines. Here, a Machine Learning-Grid Gradient Ascent (ML-GGA) approach was developed to optimize the performance of internal combustion engines. ML offers a pathway to transform complex physical processes that occur in a combustion engine into compact informational processes. The developed ML-GGA model was compared with a recently developed Machine Learning-Genetic Algorithm (ML-GA). Detailed investigations of optimization solver parameters and variable limit extension were performed in the present ML-GGA model to improve the accuracy and robustness of the optimization process. Detailed descriptions of the different procedures, optimization tools, and criteria that must be followed for a successful output are provided here. The developed ML-GGA approach was used to optimize the operating conditions (case 1) and the piston bowl design (case 2) of a heavy-duty diesel engine running on a gasoline fuel with a research octane number (RON) of 80. The ML-GGA approach yielded >2% improvements in the merit function, compared with the optimum obtained from a thorough computational fluid dynamics (CFD) guided system optimization. The predictions from the ML-GGA approach were validated with engine CFD simulations. This study demonstrates the potential of ML-GGA to significantly reduce the time needed for optimization problems, without loss in accuracy compared with traditional approaches.

33 ADVANCED PROPULSION SYSTEMS↗

ENGINE COMBUSTION SYSTEM OPTIMIZATION USING CFD AND MACHINE LEARNING: A METHODOLOGICAL APPROACH

Gasoline compression ignition (GCI) engines are considered an attractive alternative to traditional spark-ignition and diesel engines. In this work, a Machine Learning-Grid Gradient Algorithm (ML-GGA) approach was developed to optimize the performance of internal combustion engines. Machine learning (ML) offers a pathway to transform complex physical processes that occur in a combustion engine into compact informational processes. The developed ML-GGA model was compared with a recently developed Machine learning Genetic Algorithm (ML-GA). Detailed investigations of optimization solver parameters and variables limits extension were performed in the present ML-GGA model to improve the accuracy and robustness of the optimization process. Detailed descriptions of the different procedures, optimization tools and criteria that must be followed for a successful output are provided here. The developed ML-GGA approach was used to optimize the operating conditions (case 1) and the piston bowl design (case 2) of a heavy-duty diesel engine running on a gasoline fuel with a Research Octane Number (RON) of 80. The ML-GGA approach yielded > 2% improvements in the merit function, compared to the optimum obtained from a thorough computational fluid dynamics (CFD) guided system optimization. The predictions from the ML-GGA approach were validated with engine CFD simulations. This study demonstrates the potential of ML-GGA to significantly reduce the time needed for optimization problems, without loss in accuracy compared to traditional approaches.

engine optimization↗

Machine learning enhanced characterization and optimization of photonic cured MAPbI 3 for efficient perovskite solar cells

Photonic curing (PC) can facilitate high-speed perovskite solar cell (PSC) manufacturing because it uses high-intensity light pulses to crystallize perovskite films in milliseconds. However, optimizing PC conditions is challenging due to its many variables, and using power conversion efficiency (PCE) as the optimization metric is both time-consuming and labor-intensive. This work presents a machine learning (ML) approach to optimize PC conditions for fabricating methylammonium lead iodide (MAPbI 3 ) films by quantitatively comparing their ultraviolet-visible (UV-vis) absorbance spectra to thermal annealed (TA) films using four similarity metrics. We perform Bayesian optimization coupled with Gaussian process regression (BO-GP) to minimize the similarity metrics. Refining PC conditions using active learning based on BO-GP models, we achieve a PC MAPbI3 film with an absorbance spectrum closely matching a TA reference film, which is further verified by its crystalline and morphological properties. Thus, we demonstrate that the UV-vis absorption spectrum can accurately proxy film quality. Additionally, we use an AI-based segmentation model for a more efficient grain size analysis. However, when we use the optimized PC condition to fabricate PSCs, we find that interaction between MAPbI 3 and the hole transport layer (HTL) during PC critically degrades the PSC performance. By adding a buffer layer between the HTL and MAPbI 3 , the optimized PC PSCs produce a champion PCE of 11.8%, comparable to the TA reference of 11.7%. Using UV-vis similarity metrics instead of device PCE as the objective in our BO-GP method accelerates the optimization of PC processing conditions for MAPbI 3 films.

14 SOLAR ENERGY↗

A large-scale benchmarking of deterministic and stochastic derivative-free optimization algorithms

This presentation summarizes our work in the PrOMMiS project on benchmarking of data-driven optimization algorithms and their applications in self-driving laboratories. This work supports the broader project goal of accelerating the identification of promising separation methods and operating conditions for critical minerals separation processes. We present a systematic benchmarking study of 42 data-driven optimization algorithms on a broad collection of 502 test problems. The results identify BAM, GLCCLUSTER, and MULTIMIN as the most effective optimization solvers, with BAM showing the highest overall performance and solving more than 80% of the benchmark problems. The study also shows that no single solver consistently outperforms the others across all problem types, indicating that our future laboratory applications may benefit from using a small set of strong solvers rather than relying on a single method. The presentation also illustrates an in-silico chemical reactor case study showing that data-driven optimization methods can guide autonomous experimentation in a self-driving laboratory and identify optimal operating conditions within a small number of experiments. Overall, the results provide a basis for selecting efficient optimization methods and demonstrate the practical use of data-driven optimization in self-driving laboratory workflows.

36 MATERIALS SCIENCE↗

Insights into Methodologies and Stochastic Optimization of Thermal Energy Storage-Coupled Advanced Reactor Systems: A Comparison of Methods for Accessing Long-Term Sub-System Sizing Adequacy

This paper investigates the potential of coupling Thermal Energy Storage (TES) with Advanced Reactors (ARs) to address uncertainties posed by climate change in deep decarbonized power systems. The TES Use-case Team at Idaho National Laboratory (INL) has examined the potential of storing thermal energy from ARs during low demand periods and optimizing discharge during peak-priced hours, in both steady-state and transient conditions. Building on this groundwork, this study bridges the gaps in optimal sizing of the sub-system of TES-coupled AR systems using Risk Analysis Virtual Environment (RAVEN) and Holistic Energy Resource Optimization Network (HERON), INL?s framework for grid optimization. By applying this framework, we present statistically-robust optimal charge, discharge including balance of plant (BOP), and storage sizing for the High-Temperature Gas-Cooled Reactor (HTGR) with 203 MWth output. To this end, we generated synthetic price samples for 30 years using 2018 ? 2021 real-time market data from ERCOT, PJM and MISO. Our results reveals that the TES-coupled HTGR system is highly effective in maximizing revenue from electricity sales. We observed a substantial increase of 40 % in ERCOT and a noteworthy 15 % increase in PJM and MISO when compared to the conventional BOP without TES. This improvement is achieved through regionally-tailored sub-system sizing, which ranges from 398 to 416 MWth for the discharge system and 610 to 1029 MWth for the TES. We find that the average electricity price directly impacts the overall economics, while price volatility influences storage size. Additional sensitivity analyses were performed to access the impact of key assumptions on system economics and sizing, differentiating the optimization window (i.e., 24 ? 219 hours of chronological observations) and by imposing storage continuity condition in tracking TES cycles. We observed that at the 120-hour of the optimization window, a reasonable balance between computation time and accuracy was achieved. Our analysis also highlights the significance of conducting multi-day cycle analysis (> 120-hour) for TES to capture interaction between electricity prices and storage dynamics, providing a comprehensive understanding of TES behavior that AR developers should integrate into their plant designs.

25 ENERGY STORAGE↗

A Novel Method for Controlling Crud Deposition in Nuclear Reactors Using Optimization Algorithms and Deep Neural Network Based Surrogate Models

This work presents the use of a high-fidelity neural network surrogate model within a Modular Optimization Framework for treatment of crud deposition as a constraint within light-water reactor core loading pattern optimization. The neural network was utilized for the treatment of crud constraints within the context of an advanced genetic algorithm applied to the core design problem. This proof-of-concept study shows that loading pattern optimization aided by a neural network surrogate model can optimize the manner in which crud distributes within a nuclear reactor without impacting operational parameters such as enrichment or cycle length. Several analysis methods were investigated. Analysis found that the surrogate model and genetic algorithm successfully minimized the deviation from a uniform crud distribution against a population of solutions from a reference optimization in which the crud distribution was not optimized. Strong evidence is presented that shows boron deposition in crud can be optimized through the loading pattern. This proof-of-concept study shows that the methods employed provide a powerful tool for mitigating the effects of crud deposition in nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Digital Twin for Optimizing Real-time Economy of the Integrated Energy Systems

Economic and safe operation of integrated energy systems (IES) requires real-time optimization (RTO) of the control and actions conducted on each system component. In this regard, digital twins (DTs), which consist of a physical system, a virtual system, and the data communication that occurs between the two, are essential for effective RTO. Through the data warehouse, the virtual system is constantly updated with real-time data from the physical system, and functions as the model in the optimization framework. The reduced-order model of the dynamic process model in the virtual system is used in the optimization framework. The optimization results are then returned, via the data warehouse, as control actions to the physical system. This work demonstrates the software capabilities of DT assets for an IES in the context of preparing a DT for an experimental system comprised of Idaho National Laboratory (INL)’s Thermal Energy Delivery System and battery system. For the virtual demonstration, the DTs encompass (1) a physical system, including the Modelica models of the Thermal Energy Delivery System and the battery system; (2) virtual optimization via the Optimization of Real-Time Capacity Allocation (ORCA) platform; and (3) the open-source data warehouse software DeepLynx. This work assesses the performance of ORCA, which utilizes a reduced-order model built using the Risk Analysis Virtual Environment (RAVEN) and trained on the Modelica models and real-time data pipeline through the graph database hosted in DeepLynx. The proposed optimization workflow will be an RTO model based on DTs and the data they generate.

25 ENERGY STORAGE↗

Particle Swarm Optimisation for group structure optimization for radiotherapy shielding

Neutron transport simulations are ubiquitous in nuclear engineering because they allow one to model experimental systems and render a model platform for easy perturbation of experimental designs. In addition, simulations allow one to gain experimental insight without actually having to go through the trouble of building a physical experiment. Neutron transport simulations can be stochastic or deterministic based. Stochastic neutron transport simulations are typically simulated using the Monte Carlo method and yield very accurate solutions but are computationally expensive, while deterministic methods are typically faster but can be less accurate. Here we focus on optimizing the accuracy of deterministic neutron transport simulations for radiotherapy simulations. Deterministic neutron transport requires discretization of angle, energy, and space to appropriately analyze the system one is trying to model. Discretization of energy is challenging because of the highly variable neutron flux at certain neutron energies. Improper discretization of energy in the transport model can lead to erroneous results and therefore inaccurate interpretations of the solution. In this study, we evaluate Particle Swarm Optimization (PSO) as a mechanism for selecting optimal group structures for radiotherapy shielding. We tested the particle swarm optimization algorithm on radiotherapy shielding problems using Los Alamos National Laboratory's (LANL) main deterministic transport code PARTISN. Results show that the optimized energy group structures generated from the optimization algorithm outperformed LANL's standard energy group structures, and therefore demonstrate utility in using PSO to expedite computation times due to the increased accuracy obtained with a smaller but optimized group structure. (authors)

43 PARTICLE ACCELERATORS↗

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗

Nonlinear Multiobjective MPC-Based Optimal Operation of a High Consistency Refining System in Papermaking

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. Here in this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refining system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. In conclusion, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of set-point tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗

HOPP - Hybrid Optimization and Performance Platform

The Hybrid Optimization and Performance Platform, HOPP, is a wind + solar + battery + X design software for optimizing co-located, utility-scale hybrid plants down to the component level for different markets and technoeconomic objectives. Key technology and financial inputs to the HOPP model that inform the objective to be optimized are presented. The layout and performance integration is combined with optimal dispatch and full financial modeling within an optimization framework. With an example scenario, optimal sizing and layout results are shown in a sensitivity analysis of prices for two hybrid configurations.

batteries↗

Analysis of Hydrocyclone Geometry via Rapid Optimization Based on Computational Fluid Dynamics

Abstract Hydrocyclones exploit density gradients for the centrifugal separation of dispersions in a continuous liquid. Selection of the geometrics for optimal separation is case specific, like the media characteristics. The existing optimization method based on computational fluid dynamics (CFD) provides a powerful analytical tool but requires long computational times. The most common praxis for CFD optimization is via the single‐factor optimization method (SFOM). In this study, a novel approach is presented as an improved rapid optimization method that implements a dynamic‐mesh and user‐defined function optimization method (DUOM). The DUOM adapts the dynamic‐mesh approach from other applications to the optimization analysis of hydrocyclones. The DUOM reduced the computational time by 31.1 %, compared to the SFOM.

Liu, Lin↗

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

25 ENERGY STORAGE↗

Optimized thermodynamic properties of REE aqueous species (REE 3+ and REEOH 2+ ) and experimental database for modeling the solubility of REE phosphate minerals (monazite, xenotime, and rhabdophane) from 25 to 300 °C

Rare earth elements (REE) are critical elements found in monazite, xenotime, and hydrated REE phosphates which typically form in hydrothermal mineral deposits. Accurate predictions of the solubility of these REE phosphates and the speciation of REE in aqueous fluids are both key to understanding the controls on the transport, fractionation, and deposition of REE in natural systems. Previous monazite and xenotime solubility experiments indicate the presence of large discrepancies between experimentally derived solubility constants versus calculated solubilities by combining different data sources for the thermodynamic properties of minerals and aqueous species at hydrothermal conditions. In this study, these discrepancies were resolved by using the program GEMSFITS to optimize the standard partial molal Gibbs energy of formation (Δ f G° 298 ) of REE aqueous species (REE 3+ and REE hydroxyl complexes) at 298.15 K and 1 bar while keeping the thermodynamic properties fixed for the REE phosphates. A comprehensive experimental database was compiled using solubility data available between 25 and 300 °C. The latter permits conducting thermodynamic parameter optimization of Δ f G° 298 for REE aqueous species. Optimal matching of the rhabdophane solubility data between 25 and 100 °C requires modifying the Δ f G° 298 values of REE 3+ by 1–6 kJ/mol, whereas matching of the monazite solubility data between 100 and 300 °C requires modifying the Δ f G° 298 values of both REE 3+ and REEOH 2+ by ~15–31 kJ/mol and ~2–10 kJ/mol, respectively. For xenotime, adjustments of Δ f G° 298 values by 1–26 kJ/mol are only necessary for the REE 3+ species. The optimizations indicate that the solubility of monazite in acidic solutions is controlled by the light (L)REE 3+ species at <150 °C and the LREEOH 2+ species at >150 °C, whereas the solubility of xenotime is controlled by the heavy (H)REE 3+ species between 25 and 300 °C. Based on the optimization results, we conclude that the revised Helgeson-Kirkham-Flowers equation of state does not reliably predict the thermodynamic properties of REE 3+ , REEOH 2+ , and likely other REE hydroxyl species at hydrothermal conditions. We therefore provide an experimental database (ThermoExp_REE) as a basic framework for future updates, extensions with other ligands, and optimizations as new experimental REE data become available. As a result, the optimized thermodynamic properties of aqueous species and minerals are available open access to accurately predict the solubility of REE phosphates in fluid-rock systems.

58 GEOSCIENCES↗