Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “multi-stage 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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Multi-stage charging and discharging of electric vehicle fleets

Fleets of electric vehicles will likely shift electricity demand, and the effect of upstream charging emissions will come from generation sources that are dispatched in response. This study proposes a multi-stage charging and discharging problem to translate low-cost energy transactions into vehicle dispatch decisions. A day-ahead charging optimization problem minimizes electricity purchases and marginal emissions damages, with energy transactions becoming targets in an optimization-based dispatch strategy for an on-demand shared autonomous electric vehicle (SAEV) fleet. The framework was tested for Austin, Texas, using an agent-based simulator. Fleets can schedule charging to lower daily power costs (averaging 15.5% or $\$0.79$/day/SAEV) while reducing health damages from generation-related pollution (2.8% or $\$0.43$/day/SAEV). Finally, fleet managers can increase profits ($\$8$ per SAEV per day) by adopting a multi-stage charging and discharging strategy that can serve more passengers per day than price-agnostic dispatch strategies.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Surrogate Neural Architecture Codesign Package (SNAC-Pack)

Neural Architecture Search is a powerful approach for automating model design, but existing methods struggle to accurately optimize for real hardware performance, often relying on proxy metrics such as bit operations. We present Surrogate Neural Architecture Codesign Package (SNAC-Pack), an integrated framework that automates the discovery and optimization of neural networks focusing on FPGA deployment. SNAC-Pack combines Neural Architecture Codesign's multi-stage search capabilities with the Resource Utilization and Latency Estimator, enabling multi-objective optimization across accuracy, FPGA resource utilization, and latency without requiring time-intensive synthesis for each candidate model. We demonstrate SNAC-Pack on a high energy physics jet classification task, achieving 63.84% accuracy with resource estimation. When synthesized on a Xilinx Virtex UltraScale+ VU13P FPGA, the SNAC-Pack model matches baseline accuracy while maintaining comparable resource utilization to models optimized using traditional BOPs metrics. This work demonstrates the potential of hardware-aware neural architecture search for resource-constrained deployments and provides an open-source framework for automating the design of efficient FPGA-accelerated models.

Weitz, Jason [UC, San Diego] (ORCID:00090004631535↗
DOE OSTI2023

High-gradient magnetic separation of colloidal uranium oxide particles from soil components in aqueous suspensions

The separation of uranium oxide (UO 2 ) particles from soil-surrogate particles in aqueous suspensions was achieved using filtration enhanced by a magnetic field. Enhanced attraction of paramagnetic UO 2 colloids to a ferromagnetic stainless-steel filter placed in a strong magnetic field arises because of the positive magnetic susceptibility of the particles and the high-gradient field generated near ferromagnetic fibers. Enhanced uptake of smaller particles over larger ones occurs through Brownian motion that promotes the collision of particles with the ferromagnetic fibers of the filter. Hence, this work focused on UO 2 particles in the colloidal size range. Experiments used a water-cooled electromagnet and an array of permanent magnets. Chemical analysis showed that the magnetic field increased the capture efficiency of uranium particles from a range of 27–53% with the magnet off up to 98% with the magnet on after a single pass of the suspension through the filter. Further, the recovery of the UO 2 particles from the filter, however, was more difficult to achieve. Small amounts of UO 2 , together with significant amounts of background SiO 2 particles, were removed from the filter during a first flush with the magnetic field on. A much larger recovery of UO 2 was not observed until a second out-of-field flush was performed, which also released some SiO 2 . The degree to which particle separation was enhanced through the use of multi-stage filtration compared to single pass-through filtration was also examined. A design was suggested that could be used to optimize the separation efficiency for a continuous process.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

Bayesian optimal experimental design for constitutive model calibration

Computational simulation is increasingly relied upon for high/consequence engineering decisions, which necessitates a high confidence in the calibration of and predictions from complex material models. However, the calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure—Interlaced Characterization and Calibration (ICC)—is introduced and demonstrated. Further, this framework leverages Bayesian optimal experimental design (BOED), which creates a line of communication between model calibration needs and data collection capabilities in order to optimize the information content gathered from the experiments for model calibration. Eventually, the ICC framework will be used in quasi real-time to actively control experiments of complex specimens for the calibration of a high-fidelity material model. This work presents the critical first piece of algorithm development and a demonstration in determining the optimal load path of a cruciform specimen with simulated data. Calibration results, obtained via Bayesian inference, from the integrated ICC approach are compared to calibrations performed by choosing the load path a priori based on human intuition, as is traditionally done. The calibration results are communicated through parameter uncertainties which are propagated to the model output space (i.e. stress–strain). In these exemplar problems, data generated within the ICC framework resulted in calibrated model parameters with reduced measures of uncertainty compared to the traditional approaches.

42 ENGINEERING↗
DOE OSTI2026

Interregional Transmission Operational Coordination (IRTOC)

This report presents a modeling and evaluation framework developed through the Inter-Regional Transmission Operational Coordination (IRTOC) project to study market-to-market (M2M) congestion management across day-ahead and real-time markets. The framework extends the Sienna platform through Sienna Decomposition, a multi-stage evaluation architecture that enables flexible representation of multiple regions and systematic assessment of alternative market coordination designs. Additional modeling capabilities include reserve deliverability constraints, High-Voltage Direct Current (HVDC) optimization for Alternating Current (AC) congestion management, and several real-time distributed coordination algorithms. Case studies using the RTS-GMLC test system and a large-scale Eastern Interconnection model demonstrate that the framework can evaluate alternative coordination structures and quantify their economic and operational impacts. The proposed framework provides a scalable platform for analyzing inter-regional coordination strategies in large-scale electricity markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Process Systems Engineering-Informed Design and Scale-Up of Multi-stage Diafiltration Cascades for Lithium and Cobalt Recovery from Spent Lithium-Ion Batteries

These slides present work jointly completed by Tasks in PrOMMiS. The first half of the presentation motivates the importance of critical materials for national security and how the recovery of critical minerals via membrane separations can be more cost effective than currently used technology. The second half of the presentation presents cost-optimal results for the custom cost model for diafiltration using the superstructure flowsheet developed by CMU. These results highlight how PSE can inform process targets (i.e., product purity targets) and suitable design strategies for scaled-up membrane cascades.

critical materials↗
DOE OSTI2025

Fuel cells for single-aisle regional aircraft: System configuration, performance and cost

A hydrogen fuel cell propelled electric aircraft can compete with incumbent turbofan technologies for single-aisle regional aircraft by coupling design of stack, air handling, thermal management, propulsion, and airframe to optimize performance. The stack operates at 95°C to facilitate heat rejection during take-off and below 75°C during cruise to extend lifetime and is oversized to satisfy power requirements at end of life. A multi-stage turbocompressor with a compression ratio >10 is selected to reach high stack power density at 11,300-m cruise altitude. The propulsion system is configured to accommodate air handling within the core duct, an inclined heat exchanger in the outer duct to limit the nacelle size, and variable area nozzles to independently control mass flows through the core and bypass ducts. The airframe is modified for maximum lift coefficient and longer balanced field length for dramatically reduced thrust during take-off, and the fuselage is stretched by 20% to store liquid hydrogen (LH 2 ). Modularization of power systems promotes safety in one engine inoperative scenarios and allows reaching specific power metrics for stack, balance-of-plant and fuel cell system (FCS), necessary for acceptable take-off weight. In conclusion, cost parity requires increase in FCS lifetime, LH 2 cost reduction, and improved FCS specific power.

Catalyst durability↗
DOE OSTI2024

Interregional Transmission Operational Coordination

This presentation will discuss challenges and opportunities on interregional coordination in the areas of interchange transaction, congestion management, reserve sharing and deliverability across multi-stage operational processes. It will then provide an overview of the interregional transmission operational coordination (IRTOC) project that currently focuses on congestion management, including Inter-regional transmission coordination in real time operations and operational planning, HVDC optimization (intra- and interregional), ancillary service deliverability (intra- and interregional). In addition, it will discuss the Sienna-Decomposition tool development to systematically study interregional coordination methods.

congestion management↗
DOE OSTI2022

Concurrent Enhancement of Acetylene Uptake Capacity and Selectivity by Progressive Core Expansion and Extra–Framework Anions in Pore–Space–Partitioned Metal–Organic Frameworks

A multi-stage core-expansion method is proposed here as one component of the integrative binding-site/extender/core-expansion (BEC) strategy. The conceptual deconstruction of the partitioning ligand into three editable parts draws our focus onto progressive core expansion and allows the optimization of both acetylene uptake and selectivity. Herein the effectiveness of this strategy is shown through a family of eight cationic pore-partitioned materials containing three different partitioning ligands and various counter anions. The optimized structure, Co 3 -cpt-tph-Cl (Hcpt=4-(p-carboxyphenyl)-1,2,4-triazole, H-tph=(2,5,8-tri-(4-pyridyl)-1,3,4,6,7,9-hexaazaphenalene) with the largest surface area and highest C 2 H 2 uptake capacity (200 cm 3 /g at 298 K), also exhibits (desirably) the lowest CO 2 uptake and hence the highest C 2 H 2 /CO 2 selectivity. The successful boost in both C 2 H 2 capacity and IAST selectivity allows Co 3 -cpt-tph-Cl to rank among the best crystalline porous materials, ionic MOFs in particular, for C 2 H 2 uptake and C 2 H 2 /CO 2 experimental breakthrough separation.

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

Practical Implementation of GPU-based Computing at the Grid Edge for Resilience Scenarios

This paper presents a practical implementation of GPU-accelerated computing at the grid edge to enhance power system resilience through next-generation smart meters. Advanced Metering Infrastructure (AMI) systems rely predominantly on centralized processing architectures, which limit real-time response capabilities during grid disturbances. This work proposes the integration of GPU-enabled computational platforms directly within smart meter to enable local execution support for power system analytics, fault detection algorithms, and optimization routines. The proposed framework uses the Julia programming language to leverage highperformance parallel computing capabilities while maintaining code portability and development efficiency. We use two experimental scenarios to benchmark the computational feasibility of this approach: sparse linear system solutions representative of power flow analyses, and multi-stage production cost simulations incorporating unit commitment and economic dispatch operations. Results demonstrate that computationally intensive power system algorithms, such as those supporting resilience scenario calculations, can be effectively executed at the distribution edge using commercially available embedded GPU hardware. Keywords—GPU acceleration, edge computing, smart meters, grid resilience, AMI, resilience.

De Souza, Reubun [School of Electrical Engineering↗
DOE OSTI2023

Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy

This paper presents a multi-stage model with recourse decisions for solving complementarity problems in a competitive electricity market under uncertainty, while also considering renewable energy technologies and battery storage utilization. The model is based on a Nash-Cournot formulation of imperfect competition among power producers. We analyze the value of variable renewable energy (VRE) and battery storage under different uncertainties, such as demand level and VRE availability. To illustrate the proposed model, we apply it to three- bus five-player model and analyze different cases varying costs, including a user-optimal perspective (with market power) and a system-optimal perspective (with central planning). We also consider the potential for congestion in the system by restricting the transmission capacity between a single interface that connects two buses. Our findings show that increasing the battery storage capacity results in a decrease in the need for perfect information about future uncertainties. Additionally, as the model allows for more uncertainty, it becomes more apparent that the stochastic mixed complementarity problem (MCP) has an advantage over a deterministic equivalent. We propose the use of the Value of the Stochastic Equilibrium Solution (VSES) as a quality metric to compare the stochastic MCP with its deterministic equivalent. Overall, expanding battery storage capacity can lower the maximum, mean, and variance values of delivered prices, but there are diminishing returns to this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Lossy Compression: An Online Multi-Stage Technology for High-Fidelity Synchro- Waveform Measurements

Effective real-time monitoring and analysis of distributed grids necessitate the use of synchro-waveform measurements, which capture almost all high-frequency disturbances and transient phenomena. However, due to limitations in high-speed measurements and network bandwidth, it is challenging to transfer all high-fidelity synchro-waveforms losslessly and successfully. To cope with these challenges, a hybrid-based online multi-stage compression algorithm is proposed to significantly improve the compression efficiency for synchro-waveform measurements. Initially, the multiple discrete Wavelet transformation is deployed to deconstruct the waveform components. The delta encoding is further developed to decrease the magnitude. In conjunction with the Lempel-Ziv-Markov chain, the hybrid compression algorithm is implemented to achieve real-time compression for the synchro-waveform measurements. Moreover, an innovative error index that synergizes the time and frequency domain error and correlation is formulated to evaluate the waveform distortion. By integrating compression ratio, suitable parameters can be optimally selected. Finally, the simulation, laboratory experiments, as well as field tests across a spectrum of sampling frequencies and time intervals are conducted to substantiate the efficacy of the proposed method. Here, the outcomes demonstrated that a compression ratio of approximately 15.5 and 17.83 can be reached for 0.5 s and 1 s data under both offline and online scenarios, which equates to a substantial 93.5% to 94.39% reduction in data storage requirements.

High-fidelity synchro-waveform measurements↗
DOE OSTI2024

Low-Cost Heliostat for High-Flux Small-Area Receivers (Final Technical Report)

This project analyzed a two-stage heliostat concept consisting of a tracking stage and a concentrating stage. The tracking stage uses mirrors mounted on a common drive that move to track the sun. The concentrating stage consists of stationary mirrors that each have a unique angle to direct rays towards a small-area, high-flux, point-focused receiver. By splitting the collection and concentrating process into two stages, multiple small, inexpensive mirrors can share a structure and be controlled by a single drive in the tracking stage. The project effort developed modeling techniques that were specifically relevant to this two-stage heliostat concept. Both field-level and unit-level models were developed. The field-level model does not explicitly consider unit-level losses which are predicted by the unit-level model and then integrated into the field-level model through a correlation referred to as an efficiency modifier. This approach is referred to as the two-model approach; the development and demonstration of this two-model approach for a multi-stage heliostat technology is a key outcome of this work. The field-level model is used to design a field that hits a specific design day power given a set of heliostat design parameters. An oversized field is simulated and then heliostat units are removed based on their annual energy production in order to generate the highest performing field. The field reduction procedure fits a smooth curve fit to annual energy production as a function of position in the field which has the effect of reducing the noise that is otherwise caused by the Monte Carlo ray tracing technique. This approach is referred to as the annual energy fit method and substantially reduces computational run time for a given field level modeling accuracy. The annual energy fit approach enables the selection of a properly sized, high-performing field using orders of magnitude fewer rays than would otherwise be possible and the development of this approach is a second key outcome of this work. These models are used within a genetic optimization algorithm in order to optimize the geometric parameters associated with a heliostat in order to achieve the lowest cost per unit of collected design day power. The cost modeling that underlies the optimization is a simple, scaling type analysis backed up by a much more detailed Design for Manufacture and Assembly (DFMA) analysis. Although the figure of merit used for optimization was not cost per mirror area, this metric is reasonable to use as a means of comparison. The optimally designed 500 kW design has a tracking mirror specific cost of $181.85/m 2 , which is significantly larger than the target value and also larger than the current state of the art. The cost of the torque-tube type linkages contributed substantially to the overall cost. Based on this observation, potentially attractive alternative design configuration utilizing a capstan type actuation system should be investigated. Finally, NREL compared the performance of the two-stage heliostat to the performance of a focused and different sized flat conventional heliostats and showed that, as expected, additional losses versus the convention heliostat caused by a worse cosine efficiency, two stages of reflection, and interstage interactions. The two-stage heliostat requires around 75% more reflective area than a flat 1x1 meter conventional heliostat (similar to a focused heliostat) and 40% more than a flat 2x2 meter conventional heliostat.

14 SOLAR ENERGY↗
DOE OSTI2022

Energy and exergy analysis of multi-stage vacuum membrane distillation integrated with mechanical vapor compression

Membrane distillation (MD) is a promising candidate for desalinating hypersaline brine, but its poor energy efficiency has remained a major barrier for widespread application. One possible solution to this issue is to recover the latent heat in the process. In this work, a multi-stage vacuum MD (MSVMD) was integrated with a mechanical vapor compressor (MVC) to enhance the latent heat recovery, and the energetic and exergetic performance of this integrated process was examined. A comprehensive energy and exergy analysis is provided to compare MSVMD and MSVMD-MVC processes for desalination of hypersaline brine. This analysis was conducted by examining the effect of the compression ratio on the energetic and exergetic performance, and the findings are reported in terms of specific thermal energy consumption (STEC), specific electricity consumption (SEC), and exergetic efficiency. The energy analysis shows that thermal energy consumption can be reduced as the compression ratio increases, due to the enhancement of latent heat recovery. The MSVMD-MVC process can be operated in a steady-state condition, without the need for thermal heat input; with STEC and SEC of 0 and 49 kWh/m 3 at the feed temperature of 50 °C and MVC compression ratio of 2.14. Moreover, exergy analysis demonstrates the efficacy of the eNRTL model in exergy calculation. Exergy destruction can be greatly reduced by increasing the compression ratio to an optimal value. For high salinity brine (124 g/L), MSVMD-MVC achieved a higher exergetic efficiency of 6.85%, compared to 2.42% in MSVMD. Furthermore, the result suggests that the application of MVC can intensify the energy efficiency and exergetic efficiency of the MSVMD system, although this process cannot outperform the current desalination technologies from the standard primary energy point of view.

42 ENGINEERING↗
DOE OSTI2024

Development and field demonstration of residential air source integrated heat pump using a three-stage compressor

To promote decarbonization and all electrification at residential sectors, it is necessary to use air source heat pumps (ASHPs) to replace natural gas for space heating and water heating. ASHPs are widely utilized for residential space cooling, heating, and water heating due to their simplicity and cost-effectiveness. However, their performance can be compromised in cold climates, where they may experience reduced heating capacity. A multi-functional heat pump, using a single compressor, to meet all home space conditioning and water heating demands, is an emerging technology. To address this limitation, we have developed and demonstrated an air source integrated heat pump to fulfill comprehensive home comfort requirements. This system employs a three-stage compressor and a single set of heat exchangers and valves, optimizing functionality while minimizing costs. The performance of the developed system was rigorously evaluated in both laboratory and field settings. In laboratory conditions, the system achieved a Seasonal Energy Efficiency Ratio of 17.0 (average COP of 4.98) and a Heating Seasonal Performance Factor of 11.0 (3.22). Additionally, in its most efficient operational mode—combining space cooling and water heating—the unit attained a total energy efficiency exceeding 7.0 seasonal COP in the field and could heat a 189-liter tank of water in just 25 min. The field study corroborated the laboratory findings, validating the system’s performance in real-world conditions. Here, this integrated heat pump represents an ideal solution for decarbonizing homes in northern climates by providing efficient space heating and water heating, thereby replacing the need for natural gas.

Integrated heat pump↗
DOE OSTI2023

HFTS-1 (Final Report)

Despite the long history of hydraulic fracturing, the optimal number of fracturing stages during multi-stage fracture stimulation in horizontal wells can be a complex subject. In addition to the increased expense of multistage fracturing in horizontal wells, increasing the number of fracturing stages does not always correlate with a commensurate increase in production. The problem is the application of a uniform fracture stimulation design to all stages with no consideration for geological variations along the wellbore. The result is an inefficient use and costly waste of energy and water. Optimization of the fracturing process requires an understanding of the cause-and-effect relationship between fracturing parameters and local geological properties at a given location along the wellbore. Realizing that the generalized rock mechanics theories and hypotheses are not truly applicable to fractured and laminated shales, quantifiable impacts of a shale’s geomechanical and depositional features are a prerequisite for design and implementation of optimized hydraulic fractures. The overarching goal of this project is to understand and define the relationships of shale geology and fracture dynamics using detailed field data that includes coring of the fracture domain. Finally, resource recovery from shale formations is estimated to be less than fifteen percent. Research proposed in this project will establish the foundations for investigating enhanced recovery techniques for increased resource recovery in existing fracture treated wells. Natural gas as an EOR fluid is in the initial stages of being used broadly in the oil and gas industry and as such, many aspects of the process need to be researched and addressed prior to widespread acceptance. In addition, re-fracturing techniques, particularly using cemented liners also need to be further investigated. This project explores several of these EOR techniques in greater detail, not just at the theoretical level, but through actual field test sites. This report delves into the research program, identified tasks, several studies, observations, results, and conclusions under the Hydraulic Fracturing Test Site (HFTS) project. This test project is subdivided into three distinct phases and each phase is discussed in detail under separate sections. The original test site for Phase 1 as well as the Phase 2 site are in Midland Basin in Texas and operated by Laredo Petroleum. In the first two phases, the program targeted the Wolfcamp formation in Midland Basin. Phase 3 of the study targeted the EagleFord play in South Texas with Devon Energy as the operator. Significant conclusions from this study include: 1) lateral and vertical fracture growth mapping as well as proppant transport behavior, 2) Use of field gas and its applicability for huff n puff EOR injection in the Midland Basin, 3) Development and validation of proppant log, both at core scale as well as in-fill well implementation by analyzing drilling mud return samples, 4) Applicability of liner refracturing including best practices for enhanced unit level productivity. This report will detail all these studies as well as technical results and conclusions from said studies. These include general subsurface characterization work, completion designs as implemented, studies looking at fracture geometry, high resolution microseismic study, advanced crosswell strain mapping studies including drainage characterization, core characterization results, proppant analysis (core and observation wells), geochemistry, etc. to name a few.

02 PETROLEUM↗
DOE OSTI2025

Artificial Intelligence for Data Center Operations (AIOps): Cooperative Research and Development (Final Report)

High performance computing data centers will increasingly need to rely on automation to keep pace with exascale growth in compute capability and to manage and optimize the data center environment and facility resources. Artificial intelligence and machine learning approaches provide the means to improve HPC data center operational efficiency, by learning historical trends and training models to operate on real-time data collected from both IT and facilities sources. NREL has developed methods of real-time collection, aggregation and streaming of these data in the ESIF HPC Data Center and has collected a significant dataset of relevant metrics across computer systems, racks, environmental, building and utility sources for research into various predictive analytics problems. HPE's Advanced Technology Group (ATG) is doing comprehensive research into exascale monitoring and management for High Performance Computing (HPC) systems (hereinafter HPE's Data Monitoring/ Management Technology). NREL and HPE will collaborate to add Artificial Intelligence (AI) to NREL's real-time data collection/ aggregation/ streaming system and HPE's Data Monitoring/ Management System, with the goal of improving the operational efficiency of NREL's Energy Systems Integration Facility (ESIF) HPC Data Center through data analytics on both historical and real-time data from IT systems and facilities operations. This collaboration will consist of efforts in Data Management, Data Analytics, and AI/ML Optimization for both manual and autonomous intervention in data center operations. This will be a multi-year, multi-staged effort with a goal towards building capabilities for an Advanced Smart Facility, and demonstration of these techniques in the NREL ESIF HPC Data Center.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Design of Multi-Stage Solvent Extraction Process for Separation of Rare Earth Elements

Flowsheet design and stage determination for the separation of rare earth elements (REEs) using solvent extraction (SX) is a challenging task because of the chemical similarity of the REEs. Low separation factors between the elements and complex equilibrium chemistry provide unique challenges to designing an efficient flowsheet for the separation of elements. The multi-stage nature of the SX process adds further complexity, making the assessment of products for a proposed design and stage combination difficult. Therefore, to develop a SX flowsheet, it is essential to quantify the performance for various design and separation conditions. This paper attempts to address the challenge by utilizing an equilibrium and process modeling approach. Results from a bench-scale study performed on a 10 g/L rare earth salt mixture were used in studying the extraction/stripping behavior and developing equilibrium models. DEHPA with TBP as a phase modifier was used as an extractant, while hydrochloric acid was utilized as a stripping agent. The results obtained were used in developing extraction/stripping models, which were integrated into a process framework of a SX train in a Matlab/Simulink environment. The models were programmed as a function block routine and used for developing a flowsheet, which was simulated for differing separation and design conditions. To identify optimum stage combinations, a particle swarm optimization (PSO) routine was developed and implemented for each SX train. Recovery and purity of elements of interest were used as objective function criteria. The stage combination leading to the minimization of the objective function was used to identify the optimum stage combination for a series of SX trains to attempt a balance of purity and recovery. The models and optimization method were implemented to separate a feed mixture containing REEs, which indicated that 99.52 and 85.41 percent purity is achievable for Yttrium and Lanthanum separation using 8-12-3 and 10-3-5 stage combination for loading, scrubbing, and striping. The model also indicated difficult separability between neodymium, praseodymium, and cerium.

Srivastava, Vaibhav (ORCID:0000000212645987)↗