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DOE OSTI2020

Cesium Removal Performance Comparisons of Crystalline Silicotitanate Media Batches with Savannah River Site Waste Simulant

The Tank Closure Cesium Removal (TCCR) system uses ion exchange columns filled with Crystalline Silicotitanate (CST) media to process radioactive waste solutions for the removal of Cs- 137. The TCCR project is currently focused on dissolving Savannah River Site (SRS) Tank 10H waste (primarily sodium salt cake solids) within the tank followed by at-tank ion exchange column treatment. Plans are underway to prepare and install a second TCCR unit at SRS. Capacity and particle size differences exist between archived (IE-911) and more recently prepared CST media batches (9120-B and 9140-B). Side-by-side comparison testing was performed to evaluate the cesium removal performance of each batch to aid in selecting the preferred CST batch and media characteristics to load into the second TCCR unit. Batch contact equilibrium and flow-through column tests have been conducted with three CST batches using an SRS Average Simulant.

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DOE OSTI2020

Los Alamos National Laboratory Release of Cesium-137 Corrective Action Plan

This Corrective Action Plan (CAP) was developed by a team chartered by John Sarrao, Deputy Director for Science, Technology, and Engineering (DDSTE), to review and respond to the findings of the Joint National Nuclear Security Administration/Triad National Security (NNSA/Triad) Investigation Team (JIT) Joint Investigation Report for the “Sealed Source Recovery at the University of Washington Harborview Training and Research Facility Results in Release of Cesium-137 on May 2, 2019,” dated March 30, 2020. On May 2, 2019, International Isotopes, Inc. (INIS), a subcontractor to Triad National Security, LLC, inadvertently breached a sealed cesium-137 source at the University of Washington (UW), Harborview Medical Center Research and Training (HRT) building in downtown Seattle while attempting to recover the source for the National Nuclear Security Administration (NNSA) Off-Site Source Recovery Program (OSRP). The source breach resulted in contamination of personnel and the HRT building, as well as a release of radioactive material to the environment

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2020

Quantitative Determination of Total Cesium in Savannah River Site (SRS) Tank Waste by Inductively Coupled Plasma Emission Spectroscropy

Utilization of the significant and unique wavelength dynamic range (165 to 1100 nm) available on the Leeman Prodigy Inductively Coupled Plasma Emission Spectroscopy (ICP-ES) allows for quantification of cesium using the emission line 894.347 nm without the potential of Barium interference in nuclear waste samples. Samples are added to a Sodium Peroxide Fusion and Lithium Carbonate buffer in 2% nitric acid solution to increase sensitivity of the easily ionizable (<6 eV) cesium for quantitation to 5 pbb. Through direct comparison of analytical data results, the method is proven to be complementary to the Inductively Coupled Plasma Mass Spectrometry (ICP-MS) analysis (LOQ 100 ppt) in support of the Department of Energy’s (DOE) Nuclear Waste Mission.

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DOE OSTI2020

Functional Ion Pair Receptors Targeting Cesium, Lithium, Sulfate, and Uranyl (Final Technical Report)

The major goal of this project was the synthesis and study of receptors for key ions of interest to the DOE mission, namely cesium, lithium, sulfate, hydroxide, carbon dioxide/bicarbonate, and early actinides. The work, fundamental in nature, had as its objective achieving an increased understanding of how changes in receptor design could be used to optimize binding energies, ion specificity, complex structure, extraction efficiency, and substrate release. Within this broad paradigm, particular emphasis was placed on systems that could be used to sense the cesium cation in mixed aqueous media and act as extractants for the lithium cation and, separately, the carbon dioxide/bicarbonate and hydroxide anions in the form of ion pairs likely to be encountered under conditions of putative use in the field. The development of new nitrogen-rich ligands that act as receptors for early, high-valent actinide cations was also a major point of emphasis. The first in-plane actinide complexes were synthesized using a hexa-aza porphyrin analogue. The complexes exhibited an increase in the ligand–metal bonding covalency on passing from thorium(IV) to uranium(IV) to neptunium(IV) and illustrates how the use of appropriate porphyrinoid-like ligands could be used to modulate the covalency interactions between an f-element metal center and a ligand.

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DOE OSTI2021

CST R9120-B 30x60 Media Pretreatment and Digestion Standard Development to Support Tank Closure Cesium Removal 1A (TCCR-1A) Operations

In support of continued operations of Savannah River Remediation’s (SRR) ion exchange process to remove radioactive cesium from Savannah River Site (SRS) dissolved saltcake, referred to as the Tank Closure Cesium Removal 1A process (TCCR-1A; containing the second set of at-tank ion exchange columns), SRNL was tasked with: 1) validating the field protocol planned for pretreating the crystalline silicotitanate (CST) ion exchange media to be used in the columns, 2) preparing CST media for use in in-tank batch contact testing, and 3) developing a digestion standard to verify complete CST dissolution prior to characterization following each in-tank batch contact test. A procedure (SRNL L29 Manual, ITS-0229) was developed previously in support of the TCCR Demonstration (which contained the first set of ion exchange columns) based on evaluations of a different CST production lot with a larger particle size range to document the protocol for pretreating CST utilizing conditions similar to what will be performed in the field.

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DOE OSTI2021

Maximum Cs-137 Curie Loading onto Crystalline Silicotitanate for the Documented Safety Analysis of the Tank Side Cesium Removal Platform

The Tank Side Cesium Removal (TSCR) system is currently being constructed to process Hanford tank waste supernates for vitrification. TSCR incorporates a filtration system and cesium (Cs) removal system using columns filled with crystalline silicotitanate (CST) ion exchanger, produced by Honeywell UOP, LLC. The documented safety analysis (DSA) developed for TSCR limits a single column curie loading to 141,600 Ci; given a 137 Cs isotopic mass fraction of 20% and the planned CST bed size of a TSCR column, this equates to 0.10 mmole Cs per g CST. Factors that influence 137Cs loading onto the CST include, but are not limited to, CST production lot (different production lots behave differently), contact temperature, contact duration, 137Cs mass fraction, and competitors in the tank waste feed. Seventeen tank waste feeds (compositions) were identified by Washington River Protection Solutions to be processed through TSCR. These feed compositions were used to develop a simulant (referred to herein as Stage 1) that would provide an upper bound to the Cs loading onto CST based on maximizing the Cs/Na activity coefficient ratios in solution while maintaining Na at no less than 5.0 M. Building upon this Stage 1 simulant, a series of four additional simulants were developed based on the cationic/anionic species that impact Cs exchange, with each successive formulation relaxing one or more matrix component concentration constraints as show in Table S.1

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DOE OSTI2021

Temperature Effect of Cesium Exchange onto Crystalline Silicotitanate in AP-107 and AP-105 Hanford Tank Wastes and Two Simulants

Washington River Protection Solutions, LLC (WRPS) is charged with the development of the Tank Side Cesium Removal (TSCR) system to process Hanford tank waste supernates in preparation for vitrification. In addition to a filtration step, TSCR will remove cesium (Cs) using ion exchange columns filled with crystalline silicotitanate (CST) ion exchange media. CST is produced by Honeywell UOP, LLC. The documented safety analysis (DSA) developed for the TSCR system limits a single column loading to 141,600 Ci 137 Cs. Given a 137 Cs isotopic mass fraction of 20% and the planned CST bed size of 596 L (157.5 gal) in a TSCR column, this equates to 0.10 mmole Cs per g CST (Cs distribution coefficient, K d , 1400 mL/g). Factors that influence Cs uptake by CST include (but are not limited to) (1) CST production (lot-to-lot variations), (2) contact temperature, (3) contact duration, (4) competitors in the tank waste feed, (5) anionic composition of the tank waste feed, and (6) the 137 Cs isotopic mass fraction (differs slightly among tank wastes and decreases with time).

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DOE OSTI2021

Reduced Temperature Cesium Removal from AP-107 Using Crystalline Silicotitanate

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DOE OSTI2021

Cesium Exchange onto Crystalline Silicotitanate from Blended Hanford Tank Wastes

The Tank Side Cesium Removal (TSCR) system was developed to filter and remove cesium (Cs and 137 Cs) from Hanford tank waste supernate in preparation for vitrification. The Cs removal will be conducted with crystalline silicotitanate (CST) ion exchange media. Under the planned waste-processing strategy, the tank waste supernate will be queued for TSCR processing in tank 241-AP-107 (AP-107). Once AP-107 tank waste volume is sufficiently depleted, the waste supernate from tank 241-AP-105 (AP-105, the holding tank before transfer to AP-107) will be transferred to tank AP-107. Supernate from another tank will be transferred to the holding tank, AP-105, for eventual transfer to tank AP-107. These supernate streams will undergo blending in tanks AP-107 and AP-105; the volume blend ratios will be driven by how much the tank waste supernate volumes are depleted before the next tank waste is added. The consequence of tank waste blending on Cs uptake by CST was of interest and was tested via batch contacts; results are reported herein.

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DOE OSTI2022

Characterization of Tank 11H Samples from Tank Closure Cesium Removal 1A (TCCR 1A) Batch 1

Savannah River Mission Completion (SRMC) is currently operating the Tank Closure Cesium Removal 1A (TCCR 1A) process to remove 137 Cs from tank waste supernate using an ion exchange process. The TCCR 1A unit processes dissolved salt fed from Tank 10H through a series of ion exchange columns containing crystalline silicotitanate (CST, IONSIV TM R9120-B, 30x60) and the effluent is then discharged to Tank 11H. In support of the TCCR 1A program, SRNL analyzed samples taken from Tank 11H (without tank mixing) before, during, and at the completion of TCCR 1A Batch 1 processing. Tank 11H serves as the receipt tank for the filtered and cesium removed product from the TCCR 1A system. Processing of Batch 1 commenced on January 13, 2022 and completed on February 17, 2022, after processing approximately 70,100 gallons. A pre-production sample was collected from the heel remaining in Tank 11H just before Batch 1 processing began. In addition, five interim surface samples were collected from Tank 11H during processing, and both a surface and a variable depth sample (VDS, ~7” from tank bottom) were collected just after processing completed. Analysis of all samples included density and gamma spectroscopy, in addition to a more comprehensive suite of analytes for the pre- and post-production samples. The density of the pre-production sample was the highest of all samples measured and was then observed to decrease for the first two interim samples, followed by becoming fairly consistent for the remainder of the samples (~1.3 g/mL). The density of 1.3 g/mL is similar to the density measured for one of the three Tank 10H qualification samples (HTF-10-21-126). The 137 Cs activity was found to decrease as additional decontaminated effluent from the TCCR columns was added to Tank 11H during processing; however, an increase in activity was observed during periods of no processing which can be attributed to leaching of 137 Cs from the known solids in Tank 11H. The Cs isotope concentrations in the Tank 11H postproduction surface sample were determined to be 99.7-99.8% lower than the concentrations measured in the Tank 10H feed as measured by mass spectrometry.

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DOE OSTI2022

Reduced Temperature Cesium Removal from AP-101 Using Crystalline Silicotitanate

The Tank Side Cesium Removal (TSCR) system, currently operational under Washington River Protection Solutions LLC (WRPS), sends initial low-activity Hanford waste tank supernate feed to the Hanford Waste Treatment and Immobilization Plant (WTP) Low-Activity Waste (LAW) Facility. In addition to entrained solids removal from the supernate, the primary goal of TSCR is to remove cesium-137 ( 137 Cs) by ion exchange, allowing contact handling of the liquid effluent product at the WTP. Crystalline silicotitanate (CST) ion exchange media, manufactured by Honeywell UOP, LLC (product IONSIV™ R9140-B), was selected as the ion exchange media at TSCR. Laboratory-scale ion exchange processing using TSCR prototypic unit operations continues to contribute toward WRPS establishing accurate process flowsheets for the individual feed campaigns planned for TSCR. This report describes the small-scale ion exchange testing with 14.0 L of diluted and filtered supernate from tank 241-AP-101 (AP-101DF) at 16 °C (62 °F) to demonstrate processing at temperature conditions that are more prototypic of what the TSCR system could experience during colder seasons of the year. Since CST Cs capacity increases with decreasing contact temperature, testing at the lower operating temperature will help to predict the maximum 137 Cs loading onto the CST in the TSCR system. One of the waste acceptance criteria (WAC) for the WTP Low-Activity Waste Facility is that the waste must contain less than 3.18×10 -5 Ci 137 Cs per mole of Na. For the AP-101DF tank waste to meet this criterion, only 0.144% of the influent 137 Cs concentration may be delivered to the WTP; this requires a Cs decontamination factor of 694. Testing with AP-101DF matched TSCR prototypic operations where a lead-lag configuration was used until the lag column reached the WAC limit, then a polish column was brought online for continued processing in a lead-lag-polish column configuration. Feed was processed at 1.9 bed volumes (BVs) per hour; the flowrate, in terms of contact time with the CST bed, matched the expected flowrate at TSCR. The Cs-decontaminated product was retained for vitrification testing (to be reported separately). The lead column reached 62% Cs breakthrough after processing ~1400 BVs of feed; the 50% Cs breakthrough occurred at 1250 BVs. Testing compared to previous AP-107 testing at 16 °C showed ~80 BV increases in volume processed to reach the WAC limit for both lead and lag columns. A similar slope in breakthrough curves for both tests indicates similar kinetic behavior, with variations in feed matrices (Na and Cs concentrations) likely responsible for the deviations in reaching the WAC limit. The Cs effluent from the lag column reached the WAC limit after processing 875 BVs. Anticipating this breakthrough point, the polish column was preemptively installed at 770 BVs. Cs breakthrough from the lag column began at 300 BVs, reaching 5.32×10 0 µCi/mL, or 5.6 % Cs breakthrough, after processing all 1400 BVs of feed. Table S.1 and Figure S.1 summarize the observed column performance and relevant Cs loading characteristics.

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DOE OSTI2023

Cesium Removal from 5.5 and 7.0 M Na AP-105 Using Crystalline Silicotitanate

The Tank Side Cesium Removal (TSCR) system, currently operational by Washington River Protection Solutions LLC (WRPS), prepares initial low-activity Hanford waste tank supernate feeds for the Hanford Waste Treatment and Immobilization Plant (WTP) Low-Activity Waste (LAW) Facility. In addition to entrained solids removal from the supernate, the primary goal of TSCR is to remove cesium-137 ( 137 Cs) by ion exchange, allowing contact handling of the liquid effluent product at the WTP as governed by a waste acceptance criterion (WAC). Specific to 137 Cs, this requirement is < 3.18E-5 Ci 137 Cs/mole of Na. Crystalline silicotitanate (CST) ion exchange media, manufactured by Honeywell UOP, LLC (product IONSIVTM R9140-B), has been selected as the ion exchange media for TSCR. CST is a non-elutable inorganic material that has demonstrated robust chemical, physical, and radiation tolerance while maintaining functionality. However, testing to date on actual tank waste samples has been limited to Na concentrations between 5 and 6 M Na (Fiskum et al. 2019a, 2021b and Westesen et al. 2021a, 2021b, 2022) while actual tank conditions can reach upwards of 9 M Na. Testing with feed from Hanford tank AP-105 incorporated testing at both 5.5 and 7 M Na in order to evaluate the impact of Na concentration on volume of waste processed before reaching the WAC. A 6-L volume of 5.5 M Na AP-105 and an 8-volume of 7 M Na AP-105 was processed through the Radioactive Waste Test Platform system, established at Pacific Northwest National Laboratory to support small-scale waste qualification efforts. The columns consisted of 6- to 9-mL CST beds (CST Lot 2002009604, sieved to screen out >30-mesh particles) placed in 1.5-cm-inner-diameter columns. Feed was processed at 1.9 bed volumes (BV) per hour; the flowrate, in terms of contact time with the CST bed, matched the expected flowrate at TSCR. Table S.1 and Figure S.1 summarize the measured AP-105 Cs load performance for each feed condition.

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DOE OSTI2024

Tank Closure Cesium Removal Ion Exchange Column CST Characterization: SRNL-STI-2024-00072 (Rev.0) pdf

Savannah River Mission Completion (SRMC) recently suspended operation of the Tank Closure Cesium Removal (TCCR) system which utilized an ion exchange (IX) process to remove radioactive cesium from waste supernate. During the demonstration phase, a total of three batches of Tank 10H dissolved salt waste were processed through the original TCCR columns. Subsequently, dissolved salt waste from Tank 9H was processed through TCCR in a phase referred to as TCCR 1A with four new IX columns. All eight columns have now been moved to Interim Safe Storage (ISS). For each batch processed through the TCCR IX columns, SRNL performed a number of analyses on surface and variable depth samples as well as batch equilibrium contact tests (BECT) to determine equilibrium loadings of Cs on the crystalline silicotitanate (CST) IX media. The BECTs were performed by lowering “teabags” containing ~0.1 g of CST each into the tank for a period of at least 10 days. The teabags were then retrieved and sent to SRNL for digestion and analysis.

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DOE OSTI2024

Cesium Removal from AP-106 Tank Waste Using Crystalline Silicotitanate

The Tank Side Cesium Removal (TSCR) system, currently operated by Washington River Protection Solutions, LLC, prepares Hanford waste tank supernate feeds for the Low-Activity Waste Facility at the Hanford Waste Treatment and Immobilization Plant (WTP). In addition to entrained solids removal from the supernate, the primary goal of TSCR is to remove cesium-137 ( 137 Cs) by ion exchange (IX), allowing contact handling of the liquid effluent product at the WTP as governed by a waste acceptance criterion (WAC). Specific to 137 Cs, this requirement is <3.18E-5 Ci 137 Cs/mole of Na. Crystalline silicotitanate (CST), manufactured by Honeywell UOP, LLC (product IONSIV R9140-B), was selected as the ion exchange media for TSCR.

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DOE OSTI2025

Investigating the Role π -Rich Solvents Play in the Growth of Cesium Lead Bromide Nanocrystals

In this report, the role that a high-boiling-point solvent type plays on the nucleation and growth, morphology, and crystal-phase transformation of cesium lead bromide nanocrystals (CsPbBr 3 ) is studied. The CsPbBr 3 products were compared between a one-pot growth mechanism at room temperature (RT) versus a hot-injection mechanism (HI) control using dibenzyl ether (DBE), diphenyl ether (DPE), dioctyl ether (DOE), or 1- octadecene (ODE). The coordination between these solvents and the PbBr 2 salt precursors resulted in different plumbate [PbSBr n ] 2−n precursors being formed. The S-to-Pb 2+ coordination within [PbSBr n ] 2−n was probed by UV−vis and solvent-phase 207 Pb NMR, both of which showed considerable coordination between [PbSBr n ] 2−n and the π-rich DBE and DPE, whose reactivity affected CsPbBr 3 growth. The effect was more pronounced for CsPbBr 3 prepared via RT, where the morphology was tunable, with π-rich solvents producing thin rod-like CsPbB r3 with a blue emission, compared to the green-emitting thicker platelets formed via HI. While XRD showed crystalline products for both RT and HI, with orthorhombic and cubic forms, respectively, the RT products had considerable surface defects, as was indicated by lower quantum yields, and to understand this the photoluminescent lifetimes were measured by time-correlated single photon counting.

207Pb NMR↗

DOE OSTI2020

Potential for Transport of Cesium as Bio-colloids in a High Ionic Strength System

The Waste Isolation Pilot Plant (WIPP) is a deep geologic repository for long-term disposal of transuranic, radioactive waste that is a byproduct from the nation's nuclear defense program. Most likely release scenario → human intrusion (potentially through drilling) (US DOE 1995; 1996). Brine may proceed through the Rustler formation (the most transmissive layer) (Perkins et al., 1999). There is a need to investigate halophilic microbes including their mobility in the Rustler formation and the potential for enhancing transport of cesium as a bio-colloid. Objectives: To quantify the change in mobility of Cs by interaction with microbes (Chromohalobacter) that may be present near Waste Isolation Pilot Plant. What is Chromohalobacter?: a halophilic microbe, isolated from near the WIPP site, able to thrive in the high salt concentrations relevant to the repository. Does the microbe growth phase effect uptake of Cs? Experiments conducted with actively growing and stationary phase Chromohalobacter. Uptake may differ if Cs{sup +} is mistaken for K{sup +} in an actively growing (Log) phase versus stationary phase microbes (not actively reproducing). Materials: 1'' Teflon column packed with 1 gram of dolomite [355-500 μm, CaMg(CO{sub 3}){sub 2}] connected to a syringe pump and fraction collector via Teflon tubing. Chromohalobacter (100 million cells/mL) and dolomite collected near the WIPP. Synthetic brine - 15% NaCl (w/v ∼2.78 M) + 3 mM NaHCO{sub 3}. Methodology: Negative Control 5,000 ppb Cs initially injected into mini-columns with brine. Injection solution was then switched to only brine. Cs Experiments with Stationary Phase Chromo: Set 1: Viable stationary Chromo injected into minicolumns after reaction with 200 ppb Cs. Injection solution was then switched to only brine (without Cs or microbes). Set 2: Stressed stationary Chromo initially injected into mini-columns after reaction with 200 ppb Cs. Then, switched to brine only. Cs Experiments with Log phase Chromo: Set 1: Chromo injected into mini-columns after reaction with 5,000 ppb Cs. Injection then switched to only brine (without Cs or microbes). Set 2: Chromo grown with 5,000 ppb Cs and spiked with additional Cs before injection into columns. Preliminary Conclusions: Cs was not taken up or mobilized by Chromohalobacter in the actively growing or stationary phases or under stressed conditions. Competition may have occurred between Cs and K{sup +} at lower ionic strength, significantly greater concentrations of K{sup +} were present. Results suggest that Chromohalobacter can selectively uptake K{sup +} in the presence of Cs{sup +}. Future Research: K{sup +} and Cs{sup +} uptake will be monitored at high ionic strength in K{sup +} depleted media to consider uptake of Cs in the absence of K.

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DOE OSTI2020

Assessment of the Corrosion Risks to a Double Shell Tank During the Selective Removal of a Cesium-rich Supernate Layer - 20227

The Direct Feed Low Activity Waste (DF-LAW) activity will provide the initial feed to the Waste Treatment and Immobilization Plant at the Hanford Tank Farm facility. Feed preparation for DF-LAW will be carried out in multiple double shell waste tanks (DST) utilizing the Tank Side Cesium Removal (TSCR) process. Tank AP-106 will be an integral part of the TSCR process and hence key to the DFLAW activity. Prior to being utilized for this purpose, the Cs-137 concentration levels in the AP-106 supernate must be reduced significantly. The AP-106 re-purposing process manages normal waste tank addition procedures such that waste acceptance criteria objectives for Cs-137 removal are achieved. As this process was being developed, several concerns regarding tank integrity during and after repurposing of Tank AP-106, and the associated tanks (i.e., AP-102, AN-101, and AP-108), were addressed. The potential corrosion degradation mechanisms identified based on process knowledge included: general and pitting corrosion, caustic stress corrosion cracking, concentration cell corrosion, and microbiologically induced corrosion (MIC). A systematic approach was undertaken to assess the risk of corrosion during the AP-106 re-purposing process. The assessment considered the initial and present condition of the tank, the service history of the tank, the environmental conditions created in each tank during each stage of the process, process timing, and corrosion testing and modeling that approximated tank conditions. Based on this information, recommendations were provided to minimize the exposure of the tank to corrosive conditions. These recommendations included time limits for each stage of the process, staging of corrosion inhibitor solutions should process delays occur, and waste sampling with potential chemistry adjustments at defined steps in the process. Additionally, recommendations for post-process supernate chemistry adjustments and tank inspections were put forth. The greatest risk for this process occurs during the manipulation of large quantities of Columbia River water (i.e., greater than 450,000 gallons) within AP-106, the associated tanks and the supporting infrastructure (i.e., transfer line piping). This risk becomes more pronounced if there is a process upset and the tank walls remain exposed to a corrosive condition longer than intended. As long as the river water is blended into the supernate in a timely fashion, and the waste is adjusted appropriately with corrosion inhibitors, corrosion may be minimized and the final condition of the supernate in AP-106 and the associated tanks is expected to be in compliance with corrosion chemistry requirements. Contingency plans will be made to minimize the impact of a process upset. (authors)

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DOE OSTI2020

Fundamental Study of Migration Behavior of Cesium under the Unsaturated Condition through One-dimensional Column Simulating Soil around the Disposal Site - 20262

Using a packed column simulating unsaturated soil around the disposal site, flow experiments of cesium ions were conducted in order to examine the difference of retardation effect between saturated and unsaturated conditions. The column was packed with silica sand particles of 350 μm in diameter. In this study, it was confirmed that the X-ray CT images of the column showed that the water saturation was mostly uniform within the column under unsaturated conditions. The values of water saturation in the flow experiments of Cs ions were in a range from 0.85 to 0.93. The retardation coefficients(Rd) were estimated by applying the one-dimensional advection-dispersion equation to the experimental results. The comparison of the Rd-values estimated experimentally and theoretically showed that the experimental value was estimated to be larger than the theoretical value. This means that the theoretical value evaluated through a conventional method would bring the conservative value as an apparent retardation coefficient, at least when the flow direction is from top to bottom as shown in this study. (authors)

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