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Development of Enabling Technologies for Chemical Looping Combustion and Chemical Looping with Oxygen Uncoupling (Final Report)

This report summarizes results from the project, “Development of Enabling Technologies for Chemical Looping Combustion and Chemical Looping with Oxygen Uncoupling,” which evaluated several aspects of dual fluidized bed chemical looping combustion and chemical looping with oxygen uncoupling (CLOU). The objective was to provide tools and enabling technologies to help advance fluidized bed chemical looping technology to pilot, demonstration and commercial scale. One focus area is oxygen carriers, which are key to chemical looping combustion. The copper oxygen carrier-coal ash system was systematically evaluated through a combination of thermodynamic modeling and lab-scale experiments, taking into consideration different oxygen carrier support materials and coal types. A method of mapping “safe” and “risk” zones for different combinations was established, and recommendations for target conditions are provided. In addition, a simple solution for limiting negative influence of some coal ashes, namely adding small amounts of calcium to the system, is proposed. In addition, a novel process for recovering and recycling copper from spent oxygen carriers is proposed. A new approach for design and operation of loop seals in a CLOU system was developed, and involves distinct gas injection points and a short horizontal section to help control the fate of the fluidizing gases. For the air-to-fuel reactor loop seal, the upstream side is fluidized with air, ideally input into the side rather than into the bottom, which prevents uncoupling (reduction) of the oxygen carrier before entering the fuel reactor. Also, alternative for separating oxygen carrier particles and gas in circulating fluidized bed-based chemical looping system is proposed. A new reduced reaction scheme for conversion of coal in copper-based CLOU was developed and implemented into CPFD Software’s Barracuda VR package. The resulting model provides higher fidelity than the baseline, especially when it comes to minor reactions that are part of the overall combustion environment. For in-reactor heat extraction, it was determined in this project that the best way to do that in a dual circulating fluidized-bed system is through heat exchange low in the air reactor. The air reactor is the hotter of the two and for a fast-fluidized circulating bed, the lower, more dense section has a higher heat transfer coefficient and offers more consistent particle-wall contact since it doesn’t have the splashing behavior the top of the bed does. It was determined that just the wall surface area in the lower quarter to third of the air reactor is sufficient to control temperatures in both reactors. Finally, consideration was given to a new concept for CLC, which involves a staged fuel reactor with a different type of oxygen carrier in each stage.

01 COAL, LIGNITE, AND PEAT↗

Sensitivity Analysis of MFiX-PIC Parameters Using Nodeworks, PSUADE, and DAKOTA

The study presented in this report was aimed to demonstrate UQ analysis performed not only with Nodeworks, but also two other well-established UQ software tools from the U.S. DOE’s National Laboratories (PSUADE from Lawrence Livermore National Laboratory and DAKOTA from Sandia National Laboratory). It is important to emphasize that the motivation of this study was not to determine the best UQ software, but to verify if the global sensitivity analyses from the end-to-end workflow in Nodeworks are consistent with the results of other two UQ software. The components of Nodeworks from Python’s ecosystem have been tested as standalone libraries. However, an assessment study for the complete workflow targeting a specific UQ analysis has not been performed for Nodeworks. Hence, this study is expected to serve as an equivalent of solution verification for Nodeworks using other established UQ tools as reference solution. For this purpose, three distinct flow configurations (i.e., settling bed, bubbling fluidized, and circulating fluidized bed) have been used as representative multiphase flow problems of interest. The results of the systematic simulation campaigns performed in an earlier study using the particle-in-cell (PIC) approach in the Multiphase Flow with Interphase eXchanges (MFIX) suite of solvers (i.e., MFiX-PIC) was utilized. The same set of tabulated results was provided as input to the different UQ software for global sensitivity analysis. Results for the three cases indicate that based on the Sobol’ Sensitivity Indices method the order of importance ranking determined by Nodeworks for the Sobol’ Total Sensitivity Indices is consistent with PSUADE and DAKOTA in each case for the five model parameters considered. The input files for Nodeworks for the three cases are also shared through NETL’s Gitlab repository for the reader interested in reproducibility and further analysis (See Section 1.2).

97 MATHEMATICS AND COMPUTING↗

Experimental and Simulation Analysis of Binary Mixtures of Biomass and Inert Material

A literature review was conducted to identify experiments on various scales of biomass combustion specific to circulating fluidized bed (CFB) combustors. Typical feedstock and inert bed material characteristics for biomass combustion in a CFB were gathered. This information was used to design laboratory-scale, non-reacting experiments on biomass-inert bed material mixtures in a 1-in. cylindrical test rig in the Multiphase Flow Analysis Laboratory (MFAL) in Morgantown, WV. The biomass chosen was a hardwood. Pellets from the hardwood were milled and sieved to obtain three size ranges—small, medium, and large. Three mass loadings of each of the biomass samples were fluidized with glass beads as the inert bed material to study the mixing characteristics under varying fluidizing gas velocities. Hydrodynamic data including pressure drop measurements at select vertical locations and video recordings of the mixture behavior were generated in this effort.

09 BIOMASS FUELS↗

Scaling CFB risers: Maintaining microstructure dynamics

Over the years there have been numerous approaches to develop a scaleup methodology for circulating fluidized beds. Many of these past approaches have relied on macroscopic definitions of similitude to define dimensionless groups such as Reynolds number, Froude number, density ratios, and dimensional ratios involving different length scales. These approaches have demonstrated various levels of success, but often fail when used outside the bounds of experimental datasets. The issue with these methods is that they rely on macroscopic similitude with the hopes that those conditions would provide microscopic similitude as it does in single phase systems where the Buckingham Pi techniques have given reasonable success. Two of the main reasons for failure are 1) changing fluidization regimes and 2) changing material properties that result in the material falling into a different Geldart group. Both are certain to change the microstructure (local instantaneous volume solids fraction) and changes to the microstructure affect the interphase transport properties of the reactor system, namely the mass transfer and heat transfer. Here, this work presents a new approach towards scaling based upon maintaining similitude at the microscale. It reviews a novel dimensionless flow regime map developed from analysis of the deterministic chaos parameters and higher order moments to ensure microstructure similitude. The work then examines four cases from the literature to assess the scaling approach used: (1) same particle-different scale risers for Geldart Group B particles, (2) Glicksman scaling of atmospheric circulating fluidized bed combustor, (3) same particle-different scale risers for Geldart Group A particles and (4) Glicksman scaling for pressurized gasification. General findings are that none of the scaling approaches produced directly applicable microstructure similar behavior based upon the chaotic and higher moment analysis. The positive take away is that the approach can define scale conditions that will provide similar microstructure that can be us to predict transport behavior.

42 ENGINEERING↗

Design, scaling and cost evaluations of circulating fluidized-bed systems for biomass pyrolysis

To generate updated and transparent capital cost estimates for biomass fast pyrolysis equipment, refinery fluidized catalytic cracking design and sizing principles are examined and extended to pyrolysis of woody biomass. Capital costs for the sized equipment are estimated with process-industry software. A one-dimensional flow simulation with pyrolysis kinetics is leveraged to validate the fluidization conditions and thermal energy balance. After successful sizing and a system cost estimate of $\$$2.8 M (in 2016 US$\$$) at the biorefinery scale of 1000 metric tons per day (MTD), these methods were exercised for even smaller equipment at the distributed pyrolysis scale with modifications to the process design constraints, and not directly comparable with the 1000 MTD case, arriving at capital cost estimates of $\$$1.2 M for a 500 ton/day system and $\$$0.9 M for a 200 ton/day system. Here in this work, It is noted that this work only estimates purchased equipment costs at the ±50% accuracy level; there are significant other custom factors applicable to each installation based on location, maturity, scale, complexities during installation, engineering and licensing costs, etc. that need to be added on to these estimates to derive investment costs.

09 BIOMASS FUELS↗

Calculating the Effects of Solids Input and Removal as a Temperature Control in the Advanced Scale Up Reactor Experiment (ASURE) Facility at NETL Using Aspen

The Advanced Scale Up Reactor Experiment (ASURE) facility at NETL is being designed to be a fuel-flexible multi-purpose reactor that can be used for pyrolysis/gasification or evaluation of other high pressure “circulating fluidized bed” (CFB) chemical processes. The initial system design calculations for pyrolysis/gasification are presented in this work showing the expected performance of the ASURE facility when used as a biomass conversion reactor. Several other areas of application include gasification of any carbonaceous fuel including biomass, coal, plastics, and other waste materials. The reactor can therefore be used to produce SYNGAS of various compositions and hydrogen as well as other high value chemicals resulting from a typical tuned gasification process. This paper discusses an ASPEN model of the facility, focusing on the riser of the CFB reactor and the solids recirculation loop. The ASPEN model divides the riser into two sections. A bottom section which receives ash, char and sand which have been recirculated from a return loop. In this section an inert fluidization gas, (N2 or CO2), is introduced which acts as the primary mover of the solids through the system. The bottom section is equipped with a restricted air feed so that the recirculated char can be partially oxidized. This oxidation process along with the inventory of recirculating sand are used to effectively control the temperature in the following two chemical conversion sections of the reactor which are the pyrolysis zone followed by a tar cracking zone. Fresh fuel is added to the pyrolysis zone and undergoes drying and devolatilization. The products ash, char, volatile matter, and water vapor exit the pyrolysis zone and enter the reaction block for tar cracking. Steam and CO2 gasification reactions will be incorporated into the tar cracking zone, however at the design operating temperature, conversion from these reactions is expected to be essentially zero. The unit when completed in 2026 will test mixtures of biomass, plastics, and waste coal. This presentation discusses the basic ASPEN engineering design model for this project and provides preliminary sensitivity studies to determine how the various parts of the reactor will perform.

ASSURE↗

Calculating the Effects of Solids Input and Removal as a Temperature Control in the Advanced Scale Up Reactor Experiment (ASURE) Facility at NETL Using Aspen

The Advanced Scale Up Reactor Experiment (ASURE) facility at NETL is being designed to be a fuel-flexible multi-purpose reactor that can be used for pyrolysis/gasification or evaluation of other high pressure “circulating fluidized bed” (CFB) chemical processes. The initial system design calculations for pyrolysis/gasification are presented in this work showing the expected performance of the ASURE facility when used as a biomass conversion reactor. Several other areas of application include gasification of any carbonaceous fuel including biomass, coal, plastics, and other waste materials. The reactor can therefore be used to produce SYNGAS of various compositions and hydrogen as well as other high value chemicals resulting from a typical tuned gasification process. This paper discusses an ASPEN model of the facility, focusing on the riser of the CFB reactor and the solids recirculation loop. The ASPEN model divides the riser into two sections. A bottom section which receives ash, char and sand which have been recirculated from a return loop. In this section an inert fluidization gas, (N2 or CO2), is introduced which acts as the primary mover of the solids through the system. The bottom section is equipped with a restricted air feed so that the recirculated char can be partially oxidized. This oxidation process along with the inventory of recirculating sand are used to effectively control the temperature in the following two chemical conversion sections of the reactor which are the pyrolysis zone followed by a tar cracking zone. Fresh fuel is added to the pyrolysis zone and undergoes drying and devolatilization. The products ash, char, volatile matter, and water vapor exit the pyrolysis zone and enter the reaction block for tar cracking. Steam and CO2 gasification reactions will be incorporated into the tar cracking zone, however at the design operating temperature, conversion from these reactions is expected to be essentially zero. The unit when completed in 2026 will test mixtures of biomass, plastics, and waste coal. This paper presents the basic ASPEN engineering design model for this project and provides preliminary sensitivity studies to determine how the various parts of the reactor will perform.

ASSURE↗

Validation and application of a multiphase CFD model for hydrodynamics, temperature field and RTD simulation in a pilot-scale biomass pyrolysis vapor phase upgrading reactor

Accurate prediction of transport phenomena is critical for VPU reactor design, optimization, and scale-up. The current study focused on the validation and application of a multiphase CFD model within an open-source code MFiX for hydrodynamics, temperature field, and residence time distribution (RTD) simulation in a non-reacting circulating fluidized bed riser for biomass pyrolysis vapor phase upgrading (VPU). First, an Eulerian-Eulerian approach three-dimensional CFD model was employed to simulate the pilot-scale VPU riser on the supercomputer Joule. Excellent quantitative agreement between experimental and simulated results was achieved for pressure drops and temperature field in a range of operating conditions. Then the validated multiphase CFD model was applied to predict gas and solid residence time distributions (RTDs) since prediction and analysis of RTD is an important tool to study the complex multiphase flow behavior and mixing inside chemical reactors. The predictions show that solid mean residence time is 3.5 times the gas residence time; the solid RTD is more sensitive to the process gas flow rate than the solids circulation rate.

09 BIOMASS FUELS↗

Electrical Capacitance Volume Tomography for the Packed Bed Reactor ISS Flight Experiment

Fixed packed bed reactors are compact, require minimum power and maintenance to operate, and are highly reliable. These features make this technology a highly desirable unit operation for long duration life support systems in space. NASA is developing an ISS experiment to address this technology with particular focus on water reclamation and air revitalization. Earlier research and development efforts funded by NASA have resulted in two hydrodynamic models which require validation with appropriate instrumentation in an extended microgravity environment. To validate these models, the instantaneous distribution of the gas and liquid phases must be measured.Electrical Capacitance Volume Tomography (ECVT) is a non-invasive imaging technology recently developed for multi-phase flow applications. It is based on distributing flexible capacitance plates on the peripheral of a flow column and collecting real-time measurements of inter-electrode capacitances. Capacitance measurements here are directly related to dielectric constant distribution, a physical property that is also related to material distribution in the imaging domain. Reconstruction algorithms are employed to map volume images of dielectric distribution in the imaging domain, which is in turn related to phase distribution. ECVT is suitable for imaging interacting materials of different dielectric constants, typical in multi-phase flow systems. ECVT is being used extensively for measuring flow variables in various gas-liquid and gas-solid flow systems. Recent application of ECVT include flows in risers and exit regions of circulating fluidized beds, gas-liquid and gas-solid bubble columns, trickle beds, and slurry bubble columns. ECVT is also used to validate flow models and CFD simulations. The technology is uniquely qualified for imaging phase concentrations in packed bed reactors for the ISS flight experiments as it exhibits favorable features of compact size, low profile sensors, high imaging speed, and flexibility to fit around columns of various shapes and sizes. ECVT is also safer than other commonly used imaging modalities as it operates in the range of low frequencies (1 MHz) and does not radiate radioactive energy. In this effort, ECVT is being used to image flow parameters in a packed bed reactor for an ISS flight experiment.

Tomography↗

The Development of a Generalized Riser Flow Regime Map Based Upon Higher Moment and Chaotic Statistics Using Electrical Capacitance Volume Tomography (ECVT)

Dynamic analyses have been applied to the temporal signals from an Electro Capacitance Volume Tomography instrument located near mid-height on the riser of an industrial-scale cold-flow circulating fluidized bed to characterize gas-solids flow behavior in the riser. Twelve capacitance electrodes surround the cylindrical riser over a height of 1.3 m. The instrument used a neural network deconvolution algorithm to determine the spatially resolved solids fraction recorded at 52 Hz. Experiments were carried out over a range of gas and solids flows in the transport regime using a Geldart Group B bed material, high density polyethylene with mean particle size of 880 μm. The radial solids distribution was found to vary from one-time step to the next between profiles typical of laminar and turbulent flow. The duration of time spent in each of these flow profiles depended upon the operating regime – dilute, core-annular, or fast fluidized bed. The chaotic structure of the temporal data was characterized using the three conventional approaches: the first 4 moments from the distribution of signal in time, system memory parameters from the autocorrelation function and the Hurst exponent, and analysis of the correlationentropy and correlation dimension of the attractor. These signal analysis techniques were used to clearly distinguish differences between different transport operating regimes. Specifically, it was experimentally observed that a riser transitions from core annular flow profile to dilute and dense regimes via increasing the frequency of short term transients to either dilute or dense flow profiles, respectively. A regime map was generated based upon these dynamics using solids flux and gas velocity axes. Fast fluidized, core annular, and dilute each exhibited different degree of dynamic characteristics typical of fluid dominated or particle compromising behavior. It should be noted that the magnitude for the different statistics was in the same range regardless of the regime, it was the radial profile for the statistic that changed and subsequently identified that there was a change in the regime. Finally, a reduced regime map was developed consisting of plotting the gas velocity normalized by the upper transport velocity versus the solids flux normalized by the saturation carrying capacity. The use of this reduced plot allowed the data from widely different conditions to be plotted and compared on the same<p>graph. Note that in many instances, some of the statistics identified the operating point as being in one regime while others indicated that it was in another indicating a transition region between dilute or core annular regimes and between the core annular and fast fluidization regimes. This now provides a tool that can be used to optimize process performance, identify changes in operating states, or replicate process dynamics during process scaling or changing operating parameters. </p>

Breault, Ronald↗

Scaling CFB risers: Beyond the data using microstructure similarity

Scaling circulating fluidized bed risers has been a point of contention for nearly a century. There have been numerous attempts to define various methodologies. These have all fallen short of providing a robust approach, primarily due to a lack of maintaining microstructure dynamics – a key factor in maintaining interphase heat and mass transfer. Recent work by the author put forward an approach based upon preserving dynamic similarity at different scales by ensuring that the microstructure remained similar by maintaining statistical and chaotic parameters across the scale. That work relied on a dimensionless regime map in which the x-axis was defined by the ratio of the solids flux to the saturation carrying capacity. This latter property was only good within the range of the data, and it became evident that extrapolation beyond the limits of the data could induce unrealistic conditions. Therefore, literature was reviewed to develop a better correlation for the saturation carrying capacity. In doing so, a critical riser diameter concept was developed and applied to the correlations for both Geldart Group A and B materials. The critical diameter for Geldart Group A and B materials is 0.2 m and 0.3 m, respectively. Here the paper then gives three examples on how to use the scaling approach to maintain dynamic similarity across the scales.

02 PETROLEUM↗

Verification and Validation of MFiX-PIC

This work is aimed at verification and validation (V&V) of particle-in-cell (PIC) approach in the National Energy Technology Laboratory’s (NETL) Multiphase Flow with Interphase eXchanges (MFiX-PIC) which was officially released in April 2019. Under verification, the results from MFiX-PIC are compared with exact or analytical solutions, while experimental results are used for benchmarking under validation. The test suite consists of the following cases: Terminal velocity. Particle advection in time-varying flow field. Particle settling in a dense medium. Evaporation. Rayleigh-Taylor instability. Minimum fluidization. Mini-circulating fluidized bed. The cases reported in a format consistent with the existing Verification and Validation Manual (Musser et al., 2018) explore a wide range of flow velocities and concentration regimes. Only one case considered in this work verifies the implementation of heat and mass transfer routines in MFiX-PIC, while a few other studies are currently underway to further expand the validation space in reacting flows. This study highlights the need for a rigorous analysis to objectively quantify the effect of model parameters. In addition, there is a scarcity of high-quality experimental data in the literature suitable for validating PIC methodology. Future efforts would include performing experiments which provide results for a valuable database. While designing such experiments, particle count should be significant to have sufficient particles per parcel while maintaining an optimal parcel to cell volume ratio. Also, datasets should have objectively assessed experimental uncertainty whereby confidence interval in those measurements become more explicit.

42 ENGINEERING↗

Optimized Performance and Cost Potential for Exemplar Indirect SCO 2 Coal Plants

This NETL report presents the techno-economic analysis (TEA) optimization results of coal-fired utility-scale power plants based on the indirect supercritical carbon dioxide (sCO 2 ) power cycles both with and without carbon capture and storage (CCS). For the plants without CCS, the heat source is an air-fired circulating fluidized bed (CFB). For plants with CCS, the heat source is an oxy-fired CFB. Four power cycle configurations were examined for this study: recompression cycle (RC) without and with reheat turbine (“RC without reheat” and “RC with reheat”), and partial cooling cycle (PCC) without and with reheat turbine (“PCC without reheat” and “PCC with reheat”).

01 COAL, LIGNITE, AND PEAT↗

Cost and Performance Baseline for Fossil Energy Plants Volume 3: Low Rank Coal and Natural Gas to Electricity

This report presents an independent assessment of the cost and performance of select fossil energy power systems—pulverized coal (PC), circulating fluidized bed (CFB), and natural gas combined cycle (NGCC) plants—using a systematic, transparent technical and economic approach. This is Volume 3 of a five-volume series, which comprise the following reports: Volume 1: Bituminous Coal and Natural Gas to Electricity; Volume 2: Coal to Synthetic Natural Gas and Ammonia (Various Coal Ranks); Volume 3: Low Rank Coal and Natural Gas to Electricity; Volume 4: Bituminous Coal to Liquid Fuels; and Volume 5: Natural Gas Electricity Generating Units for Flexible Operation. The cost and performance of fossil fuel-based generation technologies represented in this report (and the series at large) are important inputs to assessments and determinations of technology combinations to be utilized to meet the projected demands of future power markets. In addition to informing technology comparisons, the reference plant configurations found in this report provide perspective for regulators and policy makers. From a research and development perspective, this report is used to assess goals and metrics and to provide a consistent basis for comparing developing technologies.

20 FOSSIL-FUELED POWER PLANTS↗

The Co-Firing of Pine Biomass and Waste Coal in 100 and 600 MW Power Plants: A Sustainable Approach to Reduce GHG Emissions

Climate change is a global issue that has gained much attention recently. Co-firing biomass with coal/waste coal reduces the electricity sector’s GHG emissions sustainably. This study uses commercial software to model waste coal and biomass co-firing in 100 MW and 600 MW power plants. The objective is to assess the effects of fluid types (subcritical and supercritical), plant capacities (100 MW and 600 MW), boiler types (pulverized coal and circulating fluidized bed boilers), biomass and waste coal co-firing ratios (0:100, 20:80, 40:60, 60:40, 80:20, and 100:0), and carbon capture and storage efficiencies (0%, 90%, 95%, and 97%) on performance parameters such as net plant efficiency, heat rate, net plant CO2 and SO2, and particulate matter emissions. The feedstocks selected for this investigation include anthracite waste coal and loblolly pine biomass. As the biomass fraction increases from 0% to 100%, co-fired power plants net efficiency increases by 3–8%. Supercritical plants had a 6% higher net plant efficiency than the subcritical plants. The study found that the biomass’s high heating value decreased the fuel flow rate and reduced plant CO2 emissions by 10–16%. With 100% biomass power plant feed and 90% carbon capture and storage efficiency, CO2 emissions drop by 83% and SO2 and PM emissions drop to zero.

Bhoi, Prakashbhai R. (ORCID:0000000333104888)↗

Particle Flow Distribution in a Fluidized-Particles Multitube Solar Receiver

A fluidized-particles two-tube solar receiver was tested at ambient temperature at PROMES Laboratory to investigate the influence of an inhomogeneous solar flux density on the particle mass flow rate between the tubes. The principle of this 3rd generation solar receiver is to fluidize the particles in a container, called dispenser, in which the tubes’ bottom are immersed. The fluidized particles are flowing upward the tubes by applying an overpressure in the dispenser. Air velocities are changed inside the tubes, thanks to air mass flow controllers, to represent temperature heterogeneity between the tubes. Air velocities from 0.05 up to 0.52 m/s were tested, both in homogeneous and heterogeneous conditions. In the heterogeneous ones, the differences in air velocity between the tubes aim to mimic a difference in temperature from 20 to 100 % with homogeneous air flow rates injected. The following conclusions were drawn. First, the particle mass flux in the tubes are the same with homogeneous air velocities, each one following a calibration map previously obtained. Second, different air velocities lead to different particle mass flux. Third, the rise of the total particle mass flux diminishes the pressure in the dispenser. Four, this diminution of pressure leads to a decrease of the particle mass flow rate of the tube with the lower air velocity. This influence can lead in some cases to the stop of the fluidized bed circulation in the affected tube.

Sahuquet, Guillaume (ORCID:0000000302752890)↗

Process for generating high purity synthesis gas hydrogen from heavy oil or hydrocarbons

The present invention provides a steam reforming process for heavy oil or hydrocarbons using a circulating fluidized bed reactor, the process having a reforming step and a regeneration step, wherein the reforming step and the regeneration step comprise a fluidized reactor containing a fluidizable nickel-containing reforming catalyst and produce hydrogen as a product of the reforming bed. The invention produces high purity hydrogen in the synthesis gas product stream and avoids irreversible fouling on the catalyst.

Srinivas, Girish↗

Maintaining Microstructure – The Path to Successful Technology Maturation in Fluidized Systems

Scaling circulating fluidized bed risers has been a point of contention for nearly a century. There have been numerous attempts to define various methodologies. These have all fallen short of providing a robust approach, primarily due to a lack of maintaining microstructure dynamics – a key factor in maintain interphase heat and mass transfer. Recent work by the author put forward an approach based up maintaining dynamic similarity at different scales by ensuring that the microstructure remained similar by maintaining statistical and chaotic parameters across the scale. That work relied on a dimensionless regime map in which the x-axis was defined by the ratio of the solids flux to the saturation carrying capacity. This latter property was only good within the range of the data and it became evident that extrapolation beyond the limits of the data could induce unrealistic conditions. Therefore, literature was reviewed to develop a better correlation for the saturation carrying capacity. In doing so, a critical diameter concept was developed and applied to the correlations for both Geldart Group A and B materials. The critical diameter for Geldart Group A and B materials is 0.2 m and 0.3 m, respectively. The paper then gives examples on how to use the scaling approach to maintain dynamic similarity across the scales.<br>

Breault, Ronald↗