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DOE OSTI2022

Dissociation-induced depletion of high-energy reactant molecules as a mechanism for pressure-dependent rate constants for bimolecular reactions

In 1922, Lindemann proposed the now-well-known mechanism for pressure-dependent rate constants for unimolecular reactions: reactant molecules with sufficiently high energies dissociate more quickly than collisions can reestablish the Boltzmann distribution of the internal energies of the molecule during its dissociation at low pressures – yielding pressure-dependent rate constants for unimolecular reactions due to the preferential depletion of the high energy states capable of dissociation. In the last century, incredible progress has been made in achieving a far greater understanding of and quantitative predictions for unimolecular and association reactions. In the modern era, pressure-dependent phenomenological rate constants are now nearly universally used to describe the rates of unimolecular and associative reactions in phenomenological kinetic modeling. However, there is a second, more indirect, implication of Lindemann’s mechanism that relates to how these dissociation-induced non-equilibrium distributions impact bimolecular reactions, including non-associative bimolecular reactions – which are generally not considered to have pressure-dependent rate constants. Yet, as we show herein, the same high energy states depleted due to dissociation would otherwise react most rapidly in high-activation-energy bimolecular reactions – yielding a mechanism for pressure-dependent rate constants for bimolecular reactions (including non-associative reactions). Here, we present results from a case study for CH 2 O dissociation, isomerization, and bimolecular reaction with O2 to explore this question. Results from our master equation calculations indicate that the effect of dissociation-induced non-equilibrium distributions on bimolecular reactions can be substantial – even when chemical timescales are well separated from internal energy relaxational timescales (i.e. when the traditional rate constant description would be thought to apply). This effect is found to be more pronounced – and more complex – for bimolecular reactions involving molecular entities whose chemical timescales are merged with the internal energy relaxational timescales. Lastly, we present some ideas for discussion regarding what should be considered as “chemical species” in phenomenological kinetic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Different structural behavior of MgSiO 3 and CaSiO 3 glasses at high pressures

Knowledge of the structural behavior of silicate melts and/or glasses at high pressures provides fundamental information for discussing the nature and properties of silicate magmas in the Earth’s interior. The behavior of Si-O structures under high-pressure conditions has been widely studied, while the effect of cation atoms on the high-pressure structural behavior of silicate melts or glasses has not been well investigated. Here, in this study, we investigated the structures of MgSiO 3 and CaSiO 3 glasses up to 5.4 GPa by in situ X-ray pair distribution function measurements to understand the effect of different cations (Mg 2+ and Ca 2+ ) on high-pressure structural behavior of silicate glasses. We found that the structural behavior of MgSiO 3 and CaSiO 3 glasses are different at high pressures. The structure of MgSiO 3 glass changes by shrinking of Si-O-Si angle with increasing pressures, which is consistent with previous studies for SiO 2 and MgSiO 3 glasses. On the other hand, CaSiO 3 glass shows almost no change in Si-Si distance at high pressures, while the intensities of two peaks at ~3.0 and ~3.5 Å change with increasing pressure. The structural change in CaSiO 3 glass at high pressure is interpreted as the change in the fraction of the edge-shared and corner-shared CaO 6 -SiO 4 structures. The different high-pressure structural behavior observed in MgSiO 3 and CaSiO 3 glasses may be the origin of differences in properties, such as viscosity between MgSiO 3 and CaSiO 3 melts at high pressures. This signifies the importance of different structural behaviors due to different cations in investigations of the nature and properties of silicate magmas in Earth’s interior.

36 MATERIALS SCIENCE↗

DOE OSTI2023

The colliding planar shocks platform to study warm dense matter at the National Ignition Facility

We have developed an experimental platform at the National Ignition Facility that employs colliding planar shocks to produce warm dense matter with uniform conditions and enable high-precision equation of state measurements. The platform uses simultaneous x-ray Thomson scattering and x-ray radiography to measure the density, electron temperature, and ionization state in warm dense matter. The experimental platform is designed to create a large volume of uniform plasma (approximately 700×700×150μm 3 ) at pressures approaching 100 Mbar and minimize the distribution of plasma conditions in the x-ray scattering volume, significantly improving the precision of the measurements. Here, in this study, we present the experimental design of the platform and compare hydrodynamic simulations to x-ray radiography data from initial experiments studying hydrocarbons, producing uniform densities within ±25% of the average probed condition. We show that the platform creates a homogeneous plasma that can be characterized using x-ray Thomson scattering. Thus, the new platform enables accurate measurements of plasma conditions necessary to test models for the equation of state and ionization potential depression in the warm dense matter regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Design and Analysis of 10” Parallel Plate Relief Device

All Cryomodule (CM) and Cryogenic Distribution System (CDS) relieving into Helium Low Pressure (LP) return header, which is connected to compressor suction so, helium can be preserved during small flow relieving event and recirculated to system. However, during worst case scenario, Helium LP header requires a parallel plate relief device to relieve excess pressure from header. To complete the CDS Warm piping header, a new design for a 10 parallel plate relief device is necessary to relieve outside of the tunnel into atmosphere.

Chicas, Kelly↗

DOE OSTI2026

Additional Data Focused on Phase 1 Geared Toward Computational Fluid Dynamics (CFD) validation

A new validation campaign was developed within the Offshore Code Comparison Collaboration, Continued, with Correlation and unCertainty (OC6) to better understand the complex interactions between components of a floating wind system (e.g., columns, pontoons, etc.) in a more generic sense, and to validate modeling approaches for a variety of floating designs. A set of cylinders based on the Offshore Code Comparison Collaboration Continuation (OC4)-DeepCwind semidesign were tested under wave loading, both individually and in different combinations (including the attachment of heave plates of different sizes). The cylinders were held rigid, and pressure sensors were used to measure the distributed loading on the structures, while load cells measured the total integrated hydrodynamic loads.

17 WIND ENERGY↗

DOE OSTI2025

Comparing XRISM Cluster Velocity Dispersions with Predictions from Cosmological Simulations: Are Feedback Models Too Ejective?

The dynamics of the intracluster medium (ICM), the hot plasma that fills galaxy clusters, are shaped by gravity-driven cluster mergers and feedback from supermassive black holes (SMBHs) in the cluster cores. XRISM measurements of ICM velocities in several clusters offer insights into these processes. We compare XRISM measurements for nine galaxy clusters (Virgo, Perseus, Centaurus, Hydra-A, PKS 0745–19, A2029, Coma, A2319, and Ophiuchus) with predictions from three state-of-the-art cosmological simulation suites, TNG-Cluster, the Three Hundred Project GADGET-X, and GIZMO-SIMBA, that employ different models of feedback. In cool cores, XRISM reveals systematically lower velocity dispersions than the simulations predict, with all 10 measurements below the median simulated values by a factor of 1.5–1.7 on average and all falling within the bottom 10% of the predicted distributions. The observed kinetic-to-total pressure ratio is also lower, with a median value of 2.2%, compared to the predicted 5.0%–6.5% for the three simulations. Outside the cool cores and in non-cool-core (NCC) clusters, simulations show better agreement with XRISM measurements, except for the outskirts of the relaxed, cool-core cluster A2029, which exhibits an exceptionally low kinetic pressure support (<1%), with none of the simulated systems in either of the three suites reaching such low levels. The NCC Coma and A2319 exhibit dispersions at the lower end but within the simulated spread. Our comparison suggests that the three numerical models may overestimate the kinetic effects of SMBH feedback in cluster cores. Additional XRISM observations of NCC clusters will clarify if there is a systematic tension in the gravity-dominated regime as well.

galaxy clusters↗

DOE OSTI2025

Computationally efficient subglacial drainage modelling using Gaussian process emulators: GlaDS-GP v1.0

Subglacial drainage models represent water flow at the ice–bed interface through coupled distributed and channelized systems to determine water pressure, discharge, and drainage system geometry. While they are used to understand processes such as the relationship between surface melt and ice flow, the number of uncertain model parameters and the computational cost of running models makes it difficult to adequately explore the high-dimensional parameter space and evaluate uncertainty in model predictions. Here, we develop Gaussian process (GP) emulators that make fast predictions with associated uncertainty of subglacial drainage model outputs. Using a truncated principal component (PC) basis representation, we construct a GP emulator for diurnally averaged subglacial water pressure. We also explore emulation of scalar variables describing drainage efficiency and configuration. We train the emulators using ensembles of up to 512 simulations varying eight parameters of the Glacier Drainage System (GlaDS) model on a synthetic domain intended to represent an ice-sheet margin. The emulators make predictions ∼ 1000 times faster than GlaDS simulations, with errors <3 % for the water pressure field and ∼ 5 %–9 % for drainage efficiency and configuration. We apply the emulators to explore the eight-dimensional parameter space by computing variance-based parameter sensitivity indices, finding that three parameters (ice flow coefficient, bed bump aspect ratio, and the subglacial cavity system conductivity) explain 90 % of the variance in modelled water pressure in response to parameter changes. The GP emulator approach described here is well suited to integrating observational data with models to make calibrated, credible predictions of subglacial drainage.

58 GEOSCIENCES↗

DOE OSTI2022

Electron Density Changes across the Pressure-Induced Iron Spin Transition

High-pressure single-crystal x-ray diffraction is used to experimentally map the electron-density distribution changes in (Fe,Mg)O as ferrous iron undergoes a pressure-induced transition from high- to low-spin states. As the bulk density and elasticity of magnesiowustite—one of the dominant mineral phases of Earth’s mantle—are affected by this electronic transition, our results have applications to geophysics as well as to validating first-principles calculations. Furthermore, the observed changes in diffraction intensities indicate a spin-transition-induced change in orbital occupancies of the Fe ion in general accord with crystal-field theory, illustrating the use of electron density measurements for characterizing high-pressure d-block chemistry and motivating further studies characterizing chemical bonding under pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Development of a Turbulent Liquid Spray Atomization Model for Diesel Engine Simulations (Final Technical Report)

This project addresses the systematic lack of predictive capabilities by spray models within engine CFD codes. We develop a new modeling approach to predict the breakup of diesel sprays based on recent literature showing that liquid turbulence plays a fundamental role in spray atomization. A new body of quantitative validation data is also developed as a critical element of the project, leveraging the joint capabilities of Georgia Tech’s high-pressure continuous-flow spray chamber and Argonne National Lab’s near-nozzle x-ray diagnostics at the Advanced Photon Source. This project contributes spatially-resolved measurements of drop size distribution within well-characterized diesel injectors, Spray A and D, from the Engine Combustion Network (ECN) to the engine combustion community for the first time. Utilizing this new body of measurements, we validate and demonstrate a new spray model for diesel sprays, termed the KH-Faeth model, that predicts global and local spray characteristic more accurately than the widely adopted and employed KH model. Predicted drop size distributions are seen to predict measured drops sizes both quantitatively and predictively, with accurate response in droplet size distributions over a wide range of ambient density, injection pressure, and injector nozzle size (Spray A and D) without model tuning. The KH-Faeth model can reduce error in the predicted centerline droplet size profile by up to 80% for ECN Spray D simulations when compared to use of the widely employed KH model.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Heterogeneous multiphase flow properties of volcanic rocks and implications for noble gas transport from underground nuclear explosions

Of interest to the Underground Nuclear Explosion Signatures Experiment are patterns and timing of explosion-generated noble gases that reach the land surface. The impact of potentially simultaneous flow of water and gas on noble gas transport in heterogeneous fractured rock is a current scientific knowledge gap. This article presents field and laboratory data to constrain and justify a triple continua conceptual model with multimodal multiphase fluid flow constitutive equations that represents host rock matrix, natural fractures, and induced fractures from past underground nuclear explosions (UNEs) at Aqueduct and Pahute Mesas, Nevada National Security Site, Nevada, USA. Capillary pressure from mercury intrusion and direct air–water measurements on volcanic tuff core samples exhibit extreme spatial heterogeneity (i.e., variation over multiple orders of magnitude). Petrographic observations indicate that heterogeneity derives from multimodal pore structures in ash-flow tuff components and post-depositional alteration processes. Comparisons of pre- and post-UNE samples reveal different pore size distributions that are due in part to microfractures. Capillary pressure relationships require a multimodal van Genuchten (VG) constitutive model to best fit the data. Relative permeability estimations based on unimodal VG fits to capillary pressure can be different from those based on bimodal VG fits, implying the choice of unimodal vs. bimodal fits may greatly affect flow and transport predictions of noble gas signatures. The range in measured capillary pressure and predicted relative permeability curves for a given lithology and between lithologies highlights the need for future modeling to consider spatially distributed properties.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2026

DEM Modeling and Validation of Pebble Bed Packing Using Chrono::GPU

Accurate prediction of pebble packing structure is important for pebble bed reactors because the spatial distribution of void fraction directly affects coolant flow, pressure drop, heat transfer, and neutronic behavior. However, experimentally validated DEM studies that directly evaluate local void-fraction structure in reactor-relevant pebble beds remain limited. In this work, the pebble bed experiment conducted at Missouri University of Science and Technology is simulated using the graphics processing unit (GPU)-based discrete element method (DEM) code Chrono::GPU. The study focuses on evaluating the ability of Chrono::GPU to reproduce the packing arrangement and void-fraction distribution of a randomly packed spherical pebble bed. The DEM results are first verified against established radial void-fraction correlations, including the Mueller and Vortmeyer-Schuster models, to assess the predicted bulk porosity, near-wall behavior, and oscillatory packing structure. The simulation is then verified against reference DEM data and validated against gamma-ray computed tomography (CT) experimental data at three axial locations. The Chrono::GPU results reproduce the main features of the experimental packing, including the high void fraction near the wall, the first near-wall trough, and the damped oscillatory radial profile caused by wall-induced ordering. Quantitative comparison with DEM data and the CT-based radial profiles shows good agreement, with mean absolute errors on the order of 0.07 and root-mean-square errors below 0.09 for the averaged profiles. These results demonstrate that Chrono::GPU can accurately capture the void-fraction structure of spherical pebble beds and provides a reliable DEM framework for future pebble bed reactor packing, recycling, and thermal-hydraulic studies.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A novel lung-inspired 3D-printed desiccant-coated heat exchanger for high-performance humidity management in buildings

Offering an independent humidity management method for buildings, desiccant-coated heat exchangers (DCHXs) are deemed a promising approach to improve the overall energy efficiency of air conditioning (AC) systems. State-of-the-art DCHXs, however, are bound with conventional HX topologies either providing limited desiccant-air interfacial areas or introducing excessive pressure drop penalties. In this paper a novel 3D-printed DCHX concept inspired by the bronchi arrangement of a human lung is introduced to address the shortcomings inherent in existing DCHX designs. The proposed lung-inspired DCHX utilizes two intertwined bicontinuous flow networks enabling highly efficient heat and mass transfer characteristics for augmented adsorption and regeneration processes at low pressure drop penalties. While the first network evenly distributes an incoming air stream through the entire volume of the lung-inspired DCHX, the second network volumetrically splits a cooling water stream within and through the first network. Effects of various parameters including air flow rate, outdoor air humidity ratio, and regeneration temperature on dehumidification performance and energy efficiency of the proposed lung-inspired DCHX were investigated. Experimental results indicated the proposed lung-inspired 3D-printed DCHX outperforms existing DCHX systems by demonstrating an excellent balance between a high volumetric adsorption rate and a low pressure drop penalty. The volumetric adsorption rate of the proposed lung-inspired DCHX technology is 54.8 g/m 3 -s, a more than two-fold improvement compared with state-of-the-art DCHX systems. Additionally, the lung-inspired DCHX offers high thermal energy efficiency of 56% at a low regeneration temperature of 40 °C. Therefore, the proposed lung-inspired 3D-printed DCHX offers a new solid-desiccant-based air dehumidification pathway for next-generation high-performance AC systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

A Bayesian Approach for In-Situ Stress Prediction and Uncertainty Quantification for Subsurface Engineering

Many subsurface engineering applications require accurate knowledge of the in-situ state of stress for their safe design and operation. Existing methods to meet this need primarily include field measurements for estimating one or more of the principal stresses from a borehole, or optimization methods for constructing a 3D geomechanical model in terms of geophysical measurements. These methods, however, often contain considerable uncertainty in estimating the state of stress. Here, in this paper, we build on a Bayesian approach to quantify uncertainty in stress estimations for subsurface engineering applications. This approach can provide an estimate of the 3D distribution of stress throughout the volume of interest and provide an estimate of the uncertainty arising from the stress measurement, the rheology parameters, and a paucity of measurements. The value of this approach is demonstrated using stress measurements from the In Salah carbon storage site, which was one of the world’s first industrial carbon capture and storage projects. This demonstration shows the application of this Bayesian approach for estimating the initial state of stress for In Salah and quantifying the uncertainty in the estimated stress. Also, an assessment of a maximum injection pressure to prevent geomechanical risks from CO 2 injection pressures is provided in terms of the probability distribution of the minimum principal stress quantified by the approach. With the In Salah case study, this paper demonstrates that using the Bayesian approach can provide additional insights for site explorations and/or project operations to make informed-site decisions for subsurface engineering applications.

58 GEOSCIENCES↗

DOE OSTI2022

Coupled diffusion-deformation-damage model for polymers used in hydrogen infrastructure

The soft materials used in the infrastructure of hydrogen storage and distribution systems are vulnerable because exposure to high-pressure hydrogen can lead to mechanical damage and property degradation. Some materials, such as polymers, can undergo mechanical failure due to a phenomenon wherein hydrogen gas diffuses through the polymer chains and occupies preexisting cavities or voids inside the polymer material. If the hydrogen gas pressure is reduced more quickly than hydrogen can diffuse back out of the polymer which is necessary for some applications, the trapped hydrogen gas instead escapes by rupturing the material, causing surface blistering or permanent damage. In this study, a continuum mechanics-based fully coupled diffusion-deformation model with damage is developed to predict the stress distribution and damage propagation while the polymer undergoes rapid decompression failure. The hyperelastic material model, along with the maximum principal strain failure theory, was chosen for this study as it represents the nonlinear material response with brittle failure observed in uniaxial tensile tests perfectly. EPDM polymer was chosen for this study because of its commercial availability and common use in hydrogen storage and distribution system. It has superior mechanical properties, high and low temperature resistance, and certain compounds work well in hydrogen gas. This work is useful for design engineers to alter the parameters while manufacturing polymer composites to increase their performance in a high-pressure hydrogen environment.

Kulkarni, Shank S.↗

DOE OSTI2024

Leveraging Existing Assets for Long Duration Energy Storage

Increased renewables penetration to electrical grid is necessary to reduce overall emissions from the electrical power generation sector. Nonetheless, its integration creates challenges to grid operators who must match the power being generated by intermittent renewables and other traditional energy sources with the demand from consumers, while ensuring the reliability and power quality for the entire system. Energy storage has been proposed as an alternative to natural gas peaking plants and a form to deliver excess renewable energy generation at times of peak demand. For energy storage to provide benefits to end customers (energy consumers), it must be reliable, efficient, and cost effective. The Illinois Sustainable Technology Center (ISTC), one of the surveys that integrate the Prairie Research Institute (PRI), aims to develop a Center for Energy Storage at Existing Assets (CESEA) at UIUC with the participation of Waste Pressure Corp and Ecotek Engineering USA LLC. CESEA will focus on LDES systems that can integrate to existing infrastructure in a manner that reduces the initial capital expenditure and demonstrates the ability to repurpose fossil assets that would otherwise become stranded, to serve the energy transition. CESEA aims to leverage UIUC’s unique facilities to validate LDES systems performance at a relevant operating environment. UIUC’s facilities include a 85-MW combined heat and power (CHP) power plant, two (2) solar PV plants totaling over 18 MWdc of installed capacity, an electrical grid along with a substation at transmission and distribution voltages, a 22-mile gas pipeline network operating at two pressure levels, along with steam and chilled water distribution networks. The new LDES systems will connect to the existing UIUC grid through a new test electrical station, which will have the capacity to accommodate additional connections to test new devices and technologies as part of future CESEA R&D activities. The test electrical station will contain meters, instrumentation, and controls to accurately capture data and allow optimization of control algorithms. CESEA will initially focus on technologies that: i) utilize existing equipment or facilities to perform at least one of the process steps in LDES (charging, storage, or discharging), ii) leverage mature or commercially available components or controls, iii) show potential for cost-leadership in 10+ hour storage at a commercial scale. Initial technologies that were identified to meet these criteria include Compressed Gas Energy Storage (CGES), and TES. CGES stores electricity by raising the pressure of a compressible gas inside a control volume and converting the stored energy to electricity via expansion-generation. CGES is a generalization of CAES that covers any working gas (not just air). A successful CGES demo will help to circumvent many challenges faced by CAES (long development times due to site prospecting, high cost of compression and storage, heat recovery management, etc.) by: 1) utilizing existing infrastructure (compressors, pipelines, underground storage or pressure vessels) used in the transportation and storage of industrial gases for LDES charging and storage; 2) deploying over sites already-developed for industrial applications with minor additional work; 3) leveraging the price structure of commercial industrial gas to cover the costs of electricity used during charging. A previous DOE-sponsored conceptual study (DE-FE-0032018) estimated the levelized cost of energy of a 1.1 MW / 17 MWh CGES system at $0.08/kWh, with a commercial 10x scale system cost estimated at <$0.04/kWh (Giardinella, 2022). The pilot-sized system was estimated to avoid up to 2693 tons of CO2/year.

25 ENERGY STORAGE↗

DOE OSTI2025

Experimental and Computational Characterization of a Modified Sioutas Cascade Impactor for Respirable Radioactive Aerosols

Oak Ridge National Laboratory is collecting and characterizing aerosols released when spent nuclear fuel (SNF) rods are fractured in bending. An aerosol collection system was designed and tested to collect respirable sized (<10 μm aerodynamic diameter [AED]) particulates inside a hot cell facility. The setup is a modified version of the commercially available Sioutas cascade impactor, to which additional stages were added to expand the aerosol collection range from 2.5 to ~15 μm AED. To accommodate the additional stages and specific test conditions, the operating flow rate for aerosol collection was reduced, and testing was conducted by using pressure drop measurements, surrogate dust collection, and particle size characterization. The fluid flow distribution within the cascade and its stages was simulated in STAR-CCM+, and the stage-wise pressure drops obtained using the computational fluid dynamics model were then compared to experimental data. Lagrangian particle simulations were also performed, and stage-wise collection statistics were obtained from the simulation for comparison with the experimental data obtained using SNF-surrogate dust particles. The results provide valuable insights into the stage-wise particle collection characteristics of the modified cascade impactor and can also be used to improve the prediction accuracy of the manufacturer-determined analytical correlations.

aerosol modeling↗

DOE OSTI2021

Noble gas incorporation into silicate glasses: implications for planetary volatile storage

Incorporation of small molecules in silicate melts may provide an important mechanism for storing noble gases in the deep Earth, yet the means by which chemically inert noble gases enter and are retained in silica-based materials is not understood. High pressure, room temperature sound velocity measurements on silica and natural basalt glasses in different pressure-transmitting media reveal that neon enters the structure of silicate glasses and enhances their elastic strengths, whereas an ethanol-methanol mixture does not. Combined with literature data, we found the incorporation of small molecules into silica and basalt glasses is controlled by the void size distribution of the glass and size of the molecules. Pressure primarily reduces the size of noble gases, thereby increasing their solubilities in silicate melts and glasses.

58 GEOSCIENCES↗

DOE OSTI2025

Investigating the Performance of SF6 Replacement Gases to Enable the Next Generation of Pulsed Power

High voltage switches are essential components in pulsed power systems, where consistent and reliable performance is crucial—particularly as the field explores alternatives to SF 6 as an insulating gas. This project examines the self-break voltage distributions of various gases, with a focus on the low-voltage discharges observed in the lower tail of these distributions. Experimental results revealed that the specific housing design influenced the self-break behavior. Among the tested gases, air demonstrated a more favorable overall distribution compared to SF 6 , albeit requiring higher operating pressures. However, air also exhibited a greater likelihood of extremely low-voltage dropouts, raising concerns about its suitability as a direct replacement for SF 6 . Notably, all gases tested showed a higher-than-expected probability of low-voltage events when considering the tail of the distribution rather than the bulk behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗