Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “recyclable”

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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Calcium Isotope Constraints on Recycled Carbonates in Subduction-related Magmas

Calcium isotope ratios are readily mass-fractionated by low-temperature depositional processes that can be recorded in sedimentary rocks and, therefore, have the potential to track distinct geochemical signatures of recycled materials in mantle-derived igneous rocks. In this study, I report calcium isotopic compositions for well-characterized lavas from the Central American volcanic arc that exhibit a range of trace element and radiogenic isotope signatures that have been used to indicate variable amounts of subducted marine carbonate and hemipelagic sedimentary rocks, fresh carbonatite lavas from Oldoinyo Lengai Volcano, Tanzania, and an intrusive carbonatite clast erupted 12.8 ka from the Laacher See Volcano, Germany. I observed no calcium isotope evidence for recycled sedimentary rocks in the Central American arc magmas or in the Oldoinyo Lengai carbonatite volcanic rocks. They all exhibit isotopic compositions similar to rocks dominated by a primitive, mantle-like, bulk silicate Earth (BSE) composition. The exception in this work is the calcium isotope composition measured in the intrusive Laacher See carbonatite that is resolvable from BSE (δ^44 Ca = 0.0). Although this calcium isotopic signature might be related to ancient carbonate recycling, the magnitude and relatively light calcium isotopic composition (δ^44 Ca = –0.4) of this carbonatite could also reflect an origin that involved partial melting of altered lithospheric mantle, from which isotopically heavy Ca-bearing fluids have been lost. The decoupled signatures between trace elements and their radiogenic isotopes and those recorded by calcium isotope data are important because they likely reflect different sources and processes, and demonstrate that sediment subduction is not a bulk mixing process.

Ca isotopes↗
DOE OSTI2012

Recycler Chromaticities and End Shims for NOvA at Fermilab

In era of NOvA operation, it is planned to slip-stack six on six Booster proton batches in the Recycler ring for a total intensity of 5 x 10{sup 13} protons/cycle. During the slip-stacking, the chromaticities are required to be jumped from (-2,-2) to (-20,-20). However, with the existing 2 families of powered sextupoles in the lattice, the chromaticities can only be adjusted to (-12,-12) from (-2,-2). On the other hand, the presently designed Recycler lattice for Nova replaces the 30 straight section with 8 'D-D half FODO cells'. With the limit of the feasible quad strength, 3 quads in a half-cell were used to obtain the working point under, and the maximum beta-functions in this section cannot be less than 80 m. In this paper, we re-designed the end shims of the permanent magnets in the ring lattice with appropriate quadrupole and sextupole components to meet both chromaticity and tune requirements. We are able to use 2 quads in a half cell in RR30 straight section within feasible quad strength. The maximum beta-functions are also lowered to around 55 m. The dynamic aperture tracking has been done using MAD to simulate the scenario of beam injection into the Recycler ring for Nova.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

Simulations of the Fermilab Recycler for Losses and Collimation

Fermilab has recently completed an upgrade to the com- plex with the goal of delivering 700 kW of beam power as 120 GeV protons to the NuMI target. A major part of boost- ing beam power is to shorten the beam cycle by accumulating up to 12 bunches of 0.5 × 10 11 protons in the Recycler ring through slip-stacking during the Main Injector ramp. This introduces much higher intensities into the Recycler than it has had before. Meeting radiation safety requirements with high intensity operations requires understanding the ef- fects of space charge induced tune spreads and resulting halo formation, and aperture restrictions in the real machine to de- velop a collimation strategy. We report on initial simulations of slip-stacking in the Recycler performed with Synergia.

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

BEAM EXTRACTION FROM THE RECYCLER RING TO P1 LINE AT FERMILAB

The transfer line for beam extraction from the Recycler ring to P1 line provides a way to deliver 8 GeV kinetic energy protons from the Booster to the Delivery ring, via the Recycler, using existing beam transport lines, and without the need for new civil construction. It was designed in 2012. The kicker magnets at RR520 and the lambertson magnet at RR522 in the RR were installed in 2014 Summer Shutdown, the elements of RR to P1 Stub (permanent quads, trim quads, correctors, BPMs, the toroid at 703 and vertical bending dipole at V703 (ADCW) were installed in 2015 Summer Shutdown. On Tuesday, June 21, 2016, beam line from the Recycler Ring to P1 line was commissioned. The detailed results will be presented in this report.

43 PARTICLE ACCELERATORS↗
DOE OSTI2017

Recovering and recycling uranium used for production of molybdenum-99

A processes for recycling uranium that has been used for the production of molybdenum-99 involves irradiating a solution of uranium suitable for forming fission products including molybdenum-99, conditioning the irradiated solution to one suitable for inducing the formation of crystals of uranyl nitrate hydrates, then forming the crystals and a supernatant and then separating the crystals from the supernatant, thus using the crystals as a source of uranium for recycle. Molybdenum-99 is recovered from the supernatant using an adsorbent such as alumina. Another process involves irradiation of a solid target comprising uranium, forming an acidic solution from the irradiated target suitable for inducing the formation of crystals of uranyl nitrate hydrates, then forming the crystals and a supernatant and then separating the crystals from the supernatant, thus using the crystals as a source of uranium for recycle. Molybdenum-99 is recovered from the supernatant using an adsorbent such as alumina.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Method for removal of a foulant from a carrier gas in a single vessel using recycled cold solids

A method for removal of a foulant from a carrier gas is disclosed. A solids conveyance device that spans a vessel and a solids coolant system are provided. A cold solid foulant is provided to the solid inlet of the vessel. The carrier gas containing the foulant is provided to the carrier gas inlet of the vessel. The foulant condenses or desublimates onto the recycled solid foulant, forming a foulant-depleted carrier gas and a solid foulant product. The solids conveyance device passes the solid foulant product out of the vessel. The foulant-depleted carrier gas leaves the vessel. The solid foulant product is split into a final solid foulant product and a recycled solid foulant. The recycled solid foulant is cooled through the coolant system to produce the cold solid foulant. In this manner, the foulant is removed from the carrier gas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Recycling and Life Cycle Issues for Lightweight Vehicles

This chapter addresses recycling and life cycle considerations related to the growing use of lightweight materials in vehicles. This chapter first addresses the benefit of a life cycle perspective in materials choice, and the role that recycling plays in reducing energy inputs and environmental impacts in a vehicle’s life cycle. Some limitations of life cycle analysis and results of several vehicle- and fleet-level assessments are drawn from published studies. With emphasis on lightweight materials such as aluminum, magnesium, and polymer composites, the status of the existing recycling infrastructure and technological challenges being faced by the industry also are discussed.

Das, Sujit↗
DOE OSTI2016

Opportunities to Reuse and Recycle Redundant Radioisotopes - 16023

Sixty plus years of nuclear research and operation in the UK has produced significant quantities of nuclear material. To those involved in decommissioning a site or facility, this material represents a liability that needs to be managed and eventually disposed of. However to those in the wider nuclear industry and supply chain, the radioisotopes represent a potential resource of valuable, and in some cases irreplaceable material for future work. There is therefore an opportunity to create a win-win by identifying material that could be recycled or reused, removing it from being a liability and creating value from what is considered a waste. The UK is currently focused on the clean up of nuclear sites and the safe disposal of legacy nuclear material. Whilst the bulk of legacy material on these sites is mixed wastes in various solid and liquid forms, some of it consists of material produced for research purposes in the form of radioisotopes or exotic fuels. This has resulted in a plethora of unirradiated and irradiated materials in store across the UK including: Depleted and natural Uranium, Enriched Uranium, Mixed U/Pu oxides, Uranium carbide and mixed U/Pu carbides, Thorium as metal and oxides, Research radioisotopes. The material exists in almost every conceivable state from pure metal and oxides to solutions. Some material is well characterised and free from extraneous debris, other material is poorly characterised and contaminated with chemicals, experimental residues and sweepings. In addition, to reduce the risk and potential hazard across the UK there has also been a period of consolidation of obsolete radioactive sources from a wide variety of industrial or medical facilities to secure storage within a licensed site. The waste hierarchy is an established principle for the management of wastes, radioactive or otherwise. Its principles are set out and it gives top priority to prevention in the first place. Where waste is produced, it gives priority to preparation for re-use, then recycling before consideration for disposal as a last resort. The term wastes may only be applicable to the owner of the material where they may view the material as unwanted, unusable, or a by-product. It does not necessarily follow that the material is a waste to all potential owners. Therefore it is important to consider the potential value of material before it is considered for disposal since there is a significant and growing market for radioisotopes across the world. This paper will outline some of the opportunities in the UK for the recycle of surplus radioisotopes and orphan material. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Transport and Treatment of Chapelcross Gas Ducts for Clearance and Recycling - 19662

In the summer of 2018, Cyclife, the EDF group's specialist radioactive waste management and decommissioning company, transported sixteen gas ducts and associated equipment from the shutdown Chapelcross nuclear power plant to treatment facilities in the UK and Sweden. The client requested a full removal, treatment and disposal service for approximately 820 te of low level metallic waste comprising Upper Gas Duct Assemblies (including bellows), Upper Gas Duct elbows, Filter Pots and Convoluted pipework. The complex scope involved heavy lifting, transport by road and sea, processing and recycling on a large scale, thereby necessitating involvement of a wide range of suppliers at different tiers all managed by Cyclife. The purpose of the entire project was to safely handle and treat all of the components for clearance and recycling into the public domain for the manufacture of new steel products. Most of the treatment took place in Cyclife's nuclear licensed metal treatment facility in Sweden. Cyclife has a long and unique experience of arranging safe transport of large contaminated components on road and sea. The metal treatment facility in Sweden can, without special arrangements, receive components up to 30 meters long with a weight of up to 400 tonnes for decontamination, size reduction and melting. The actual treatment of the components consisted of the following steps: a) Separation of a gas duct from the gantry, b) size reduction, radiological verification measurements and clearance of the gantry, c) stepwise segmentation of the gas duct and elbow including removal of asbestos, d) decontamination, e) melting, f) radiological assessment and clearance of the metal ingots, g) management of the secondary waste for return to UK. The result of the project, upon completed treatment of all the material, demonstrates a high recycling rate of the material. 5-10% of the original mass of material will have to disposed as radioactive waste. This number include all residues, untreatable material (asbestos, mineral wool, filters etc.) and two melt batches with a too high activity content for clearance. The paper takes the reader through the entire project from the initial planning to the clearance of the metal and the return of the secondary waste to UK for disposal. It will also present and discuss pros and cons for alternative management approaches in several perspectives. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Oxidation of Glycolate in the Defense Waste Processing Facility (DWPF) Recycle Collection Tank - 20305

The Savannah River Site's Defense Waste Processing Facility (DWPF) operations are being upgraded with the introduction of the Nitric-Glycolic Flowsheet. Glycolic acid has been shown superior to formic acid as the reducing acid used during chemical processing. The new flowsheet improves or maintains necessary parameters such as 1) reduction of mercury, 2) adjustment of feed rheology and 3) adjustment of melter oxidation/reduction potential. Further, the potential for catalytic hydrogen generation in DWPF processing is virtually eliminated. DWPF process condensates are collected and returned to the SRS Concentration, Storage and Transfer Facilities (CSTF). The Recycle Collection Tank (RCT) collects off-gas condensate during chemical processing, vitrification, and other unit operations performed in DWPF and is the singular return vessel delivering recycle effluent back to CSTF. Each batch of recycle may contain a small amount of glycolate from chemical processing and melter off-gas condensates. To avoid potential flammability issues due to thermolysis of glycolate in the CSTF, chemical oxidation within the RCT has been investigated as an option for mitigating the transfer of glycolate. Sodium permanganate has been down-selected as the best option for oxidation of glycolate. Testing was performed using both 2-L and 22-L reactors (16,800:1 and 1,530:1 scale by volume) with non-radioactive waste simulants to approximate the expected RCT compositions. RCT simulants were evaluated at various process pH and temperature conditions. Also, RCT operations, namely the sequence of addition of corrosion inhibitors (NaOH and NaNO{sub 2}) versus a permanganate strike, were evaluated. Glycolate was introduced via a sludge simulant to mimic both expected entrainment and abnormal process foam-over conditions - the range being between 68 and 5100 mg/kg glycolate. Glycolate destruction was monitored by ion chromatography (IC). The corresponding manganese behavior was monitored in real-time using in situ ultraviolet-visible (UV-Vis) spectroscopy. RCT glycolate content can be reduced to below the IC detection limit within 90 minutes for all concentrations investigated. Ion Chromatography analysis revealed that under alkaline conditions, glycolate is primarily oxidized to oxalate with no significant formation of CO{sub 2} or carbonate, and nitrite is not oxidized to nitrate. Initially, complete oxidation of organics species and nitrite was assumed. Determination of the mechanistic chemical reaction has allowed the required amount of permanganate to be more accurately predicted and the total addition to be significantly reduced. UV-Vis measurements reveal that permanganate (Mn{sup 7+}) is reduced to manganate (Mn{sup 6+}) in the RCT. The oxidant stoichiometry is defined by using the initial permanganate to glycolate (P/G) molar ratio. At low initial glycolate concentration (68 and 140 mg/kg), the minimum required initial permanganate to glycolate (P/G) molar ratio was found to be 5-6. With high initial glycolate concentrations (5100 mg/kg) a lower (P/G) molar ratio of ∼2.5 was needed. The final portion of this effort supporting the nitric/glycolic flowsheet will be to test actual (fully radioactive) RCT samples as per the above simulant tests. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Dihydroxyterephthalate—A Trojan Horse PET Counit for Facile Chemical Recycling

Abstract Here, low‐energy poly(ethylene terephthalate) (PET) chemical recycling in water: PET copolymers with diethyl 2,5‐dihydroxyterephthalate (DHTE) undergo selective hydrolysis at DHTE sites, autocatalyzed by neighboring group participation, is demonstrated. Liberated oligomeric subchains further hydrolyze until only small molecules remain. Poly(ethylene terephthalate‐ stat ‐2,5‐dihydroxyterephthalate) copolymers were synthesized via melt polycondensation and then hydrolyzed in 150–200 °C water with 0–1 wt% ZnCl 2 , or alternatively in simulated sea water. Degradation progress follows pseudo‐first order kinetics. With increasing DHTE loading, the rate constant increases monotonically while the thermal activation barrier decreases. The depolymerization products are ethylene glycol, terephthalic acid, 2,5‐dihydroxyterephthalic acid, and bis(2‐hydroxyethyl) terephthalate dimer, which could be used to regenerate virgin polymer. Composition‐optimized copolymers show a decrease of nearly 50% in the Arrhenius activation energy, suggesting a 6‐order reduction in depolymerization time under ambient conditions compared to that of PET homopolymer. This study provides new insight to the design of polymers for end‐of‐life while maintaining key properties like service temperature and mechanical properties. Moreover, this chemical recycling procedure is more environmentally friendly compared to traditional approaches since water is the only needed material, which is green, sustainable, and cheap.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Sustainable Recycling of Rare-Earth Elements from NdFeB Magnet Swarf: Techno-Economic and Environmental Perspectives

Rare-earth elements (REEs) are increasingly susceptible to supply risks due to their limited geographical availability and growing demand in clean energy applications such as neodymium-iron-boron (NdFeB) magnets used in electric vehicles and wind turbines. When NdFeB magnets are produced, 6–73% of swarf is generated during the manufacturing steps. This paper presents an innovative technology that utilizes copper nitrate to dissolve REEs in NdFeB magnet swarf and subsequently recovers ~97% of them as mixed rare-earth oxides (REOs) of purity higher than 99.5%. Techno-economic analysis (TEA) and life cycle assessment (LCA) quantified the economic and environmental impacts of adopting the proposed acid-free dissolution technology, projecting a net profit margin of 12–43% and a global warming impact reduction by up to 73% compared to the prevailing REO production routes in China. As copper nitrate is the single largest contributor to the cost and environmental footprint, recycling of copper nitrate was investigated as well as using alternative copper salts (e.g., copper acetate), revealing significant improvements in TEA and LCA results. Dysprosium was a major revenue source, highlighting the importance of targeting electric vehicle magnets that are rich in dysprosium. As the REO market is volatile, sensitivity analysis was employed to evaluate the profitability of the proposed technology under different REO prices over the last 11 years. Overall, our results confirmed the economic and environmental viability of the proposed technology for sustainable recycling of REEs from the NdFeB magnet swarf.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Recycled Water Reuse Permit Renewal Application for the Central Facilities Area Sewage Treatment Plant

This renewal application for a Recycled Water Reuse Permit is being submitted in accordance with the Idaho Administrative Procedures Act 58.01.17 “Recycled Water Rules” and the Municipal Wastewater Reuse Permit LA-000141-03 for continuing the operation of the Central Facilities Area Sewage Treatment Plant located at the Idaho National Laboratory. The permit expires March 16, 2015. The permit requires a renewal application to be submitted six months prior to the expiration date of the existing permit. For the Central Facilities Area Sewage Treatment Plant, the renewal application must be submitted by September 16, 2014. The information in this application is consistent with the Idaho Department of Environmental Quality’s Guidance for Reclamation and Reuse of Municipal and Industrial Wastewater and discussions with Idaho Department of Environmental Quality personnel.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Optimized purification methods for metallic contaminant removal from directly recycled Li-ion battery cathodes

Metallic contaminants pose a significant challenge to the viability of directly recycling Li-ion batteries. To date, few strategies exist to selectively remove metallic impurities from mixtures of shredded end-of-life material (black mass; BM) without concurrently damaging the structure and electrochemical performance of the target active material. We herein present tailored methods to selectively ionize two major contaminants—Al and Cu—while retaining a representative cathode (LiNi 0.33 Mn 0.33 Co 0.33 O 2 ; NMC-111) intact. This BM purification process is conducted at moderate temperatures in a KOH-based solution matrix. We rationally evaluate approaches to increase both the kinetic corrosion rate and the thermodynamic solubility of Al 0 and Cu 0 , and evaluate the impact of these treatment conditions on the structure, chemistry, and electrochemical performance of NMC. Specifically, we explore the impacts of chloride-based salts, a strong chelating agent, elevated temperature, and sonication on the rate and extent of contaminant corrosion, while concurrently evaluating the effects on NMC. The reported BM purification process is then demonstrated on samples of “simulated BM” containing a practically relevant 1 wt% concentration of Al or Cu. Increasing the kinetic energy of the purifying solution matrix through elevated temperature and sonication accelerates the corrosion of metallic Al and Cu, such that ∼100% corrosion of 75 μm Al and Cu particles is achieved within 2.5 hr. Further, we determine that effective mass transport of ionized species critically impacts the efficacy of Cu corrosion, and that saturated Cl – hinders rather than accelerates Cu corrosion by increasing solution viscosity and introducing competitive pathways for Cu surface passivation. The purification conditions do not induce bulk structural damage to NMC, and electrochemical capacity is maintained in half-cell format. Testing in full cells suggests that a limited quantity of residual surface species are present after treatment, which initially disrupt electrochemical behavior at the graphite anode but are subsequently consumed. Process demonstration on simulated BM suggests that contaminated samples—which prior to treatment show catastrophic electrochemical performance—can be recovered to pristine electrochemical capacity. The reported BM purification method offers a compelling and commercially viable solution to address contamination, particularly in the “fine” fraction of BM where contaminant sizes are on the same order of magnitude as NMC and where traditional separation approaches are unfeasible. Thus, this optimized BM purification technique offers a pathway towards viable direct recycling of BM feedstocks that would otherwise be unusable.

25 ENERGY STORAGE↗
DOE OSTI2026

Polymer Deconstruction and Redesign Strategies for Plastics Recycling

Advancing plastics recycling requires both the selective deconstruction of existing polymers and the design of new materials that enable efficient reuse without loss of performance. This perspective highlights an integrated approach that is rooted in polymer chemistry, catalysis, and process engineering which can enable a circular plastics economy. Here, we outline recent advances in catalytic, solvolytic, and enzymatic pathways for plastic deconstruction, and examine the molecular design principles driving next-generation recyclable-by-design and bio-based polymers. Despite these advances, major knowledge gaps remain in understanding the evolution of polymer morphology and catalyst structure during deconstruction, assessing deconstruction processes with realistic polymers, and offering redesigned polymers with competitive cost and environmental advantage over conventional plastics. United States Department of Energy (U.S. DOE) national laboratories offer unique capabilities to address these challenges through in situ and operando characterization, high-throughput experimentation, environmental studies, technoeconomic and life cycle assessment, scale-up support, and collaboration networks. Advances made in understanding plastic deconstruction mechanisms and structure-property correlations of redesigned polymers inform emerging research directions including autonomous experimentation, real-time feedback-enabled process optimization, and protein engineering for enzymatic depolymerization.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Hybrid Chemo-Mechanical Plastics Recycling: Solvent-free, High-speed Reactive Extrusion of Low-Density Polyethylene

Low-Density Polyethylene (LDPE) is ubiquitous in the packaging industry due to its flexibility, toughness, and low cost. However, it is typically contaminated with other materials, seriously limiting options for mechanical recycling. Interest in chemical recycling techniques such as pyrolysis and hydrothermal liquefaction is growing, but most of these processes face technoeconomic challenges that have limited commercial deployment. We present a hybrid chemo-mechanical approach using reactive twin-screw extrusion (TSE) for tailoring the molecular weight and chain structure of reclaimed LDPE. Two types of zeolite catalysts at several loading levels were evaluated over a range of processing conditions. Structural, thermal, and rheological properties of the extruded samples were investigated and compared to virgin LDPE and LDPE extruded without the catalyst. A nuclear magnetic resonance spectroscopic technique was used to investigate changes in the structure of the polymer. LDPE extruded with microporous y-zeolite showed lower degradation temperature and increased short chain branching. Mesoporous MCM-41 also induced increased branching but had no effect on degradation temperature. The theoretical mechanical energy input for the chemical modification was calculated using process modeling. The demonstrated hybrid reactive extrusion process provides a potential low-cost, simple approach for repurposing LDPE-based flexible packaging as coatings and adhesives.

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

Chemically Recyclable Polyester Thermosets from Activated Adipic Acid and Renewable Polyols

This study outlines a method for producing chemically recyclable crosslinked polyesters using renewable polyols-glycerol and sorbitol-combined with adipic acid (AA), which is transformed/activated into a polyanhydride mixture prior to use. A three-step procedure has been designed: 1) an acid-catalyzed reaction of AA with nontoxic isopropenyl acetate or acetic anhydride to form a crosslinking mixture (CLM) made of adipic-acetic mixed polyanhydrides; 2) a solvent- and additive-free process where glycerol or sorbitol, or a combination thereof, is reacted with the CLM to achieve a prepolymer, and 3) a casting/molding of the liquid viscous prepolymer to yield a thermoset as the end product. Different thermosets (eight examples) are prepared by changing the reagents ratio. These solids are thoroughly characterized by tensile tests, DMA, high-resolution magic angle spinning and solid-state NMR, thermal gravimetric analysis, DSC, and fourier transformed infra red (FT-IR) spectroscopy. The formation of cross-linked polyesters is confirmed in all cases, but mechanical properties varied significantly from one specimen to another. Interestingly, a tensile strength up to 18 MPa-approximately an order of magnitude higher than similar polymers-is achieved when sorbitol and the CLM are used in a 1:1 wt% ratio. The chemical recycle of the resulting polymers is achieved via methanolysis with quantitative recovery of the monomeric units.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗