Dense Phase Region Research Articles

A CFD study on the start-up hydrodynamics of fluid catalytic cracking regenerator integrated with chemical looping combustion

ABSTRACT The integration of chemical looping combustion with fluid catalytic cracking (CLC-FCC) is an innovative concept that serves as a cost-effective method for CO2 capture in refineries. This approach has the potential to reduce refinery CO2 emissions by 25–35%, offering a promising solution. As in the conventional FCC unit, it is common for CLC-FCC regenerators to be exposed to an on-off process while they are being maintained and cleaned. The novelty of this research lies in its specific focus on a less-explored phase (start-up) of CLC-FCC regenerators, the application of advanced CFD modeling, and the comprehensive analysis of operational parameters that influence the system’s performance. To validate the CFD simulations of the different drag models for solid-gas granular, bed density profiles under steady-state conditions, collected from industrial processes, were used. For the flow period based on the start-up process of the drag models, the fluidization gas inlet geometry of the regenerator, flow regime (laminar and turbulent), and superficial gas velocity were comprehensively investigated to reveal their effects on hydrodynamic characteristics. The results show that Gidaspow and Syamlal-O’Brien drag models of the solid-gas multiphase granular flow exhibited a better fit with industrial data. The Syamlal-O’Brien and Gidaspow models closely align with industrial data under steady-state conditions, displaying similar bed densities in the dense phase region (230–310 kg/m3 for Syamlal-O’Brien and 235–300 kg/m3 for Gidaspow). During the initial stage (less than 0.2 seconds), both laminar and turbulent models yield comparable bed density profiles, approximately 510 kg/m3 in the dense phase. However, as the process progresses, the dense phase density decreases to about 250–350 kg/m3 at around 0.5 seconds, with laminar flow models showing a slightly better fit with industrial data. Notably, at 0.5 seconds of fluidization time, inlet geometries having better gas distribution achieve a highly diluted phase with bed densities of 10–20 kg/m3. Reaching a steady state, the bed density decreases from around 400 kg/m3 to 260–300 kg/m3, expanding into a higher section of the regenerator where it aligns well with industrial data. The increase in superficial gas velocity would result in the clarification of the difference and well mixing of the solid-gas multiphase flow.

Eulerian investigation of the mechanism of Ultra-low NOx emissions from CFB boilers with finer bed material

Industrial practice has confirmed that decreasing the bed material size substantially diminishes nitrogen oxide (NOx) emissions in coal-fired circulating fluidized bed (CFB) boilers. This reduction allows for compliance with the stringent ultra-low emissions standard (NOx < 50 mg/Nm3@6%O₂, dry) proposed by the Chinese government, all without the need for supplementary denitrification devices. Consequently, it becomes essential to delve into the mechanisms through which particle size, as a gas–solid flow characteristic, directly affects the chemical reaction dynamics within the coal combustion process. Due to the difficulty of field tests, this paper employs the Eulerian-Eulerian numerical method suitable for wide particle size distributions to investigate the impact of bed material particle size on gas–solid flow and NOx concentration. Furthermore, the generalized QC-EMMS drag model is utilized to predict the heterogeneous flow across varying particle size conditions. Industrial test data validated the simulation accuracy, with prediction errors of bed pressure drop, temperature, and NOx emission concentration ranging from 5 % to 8.1 %. The analysis revealed that the particle concentration distribution heterogeneity decreases as the particle size diminishes. The variation trends of NOx with particle size exhibit distinct differences between the lower dense phase region and the upper dilute phase region within the bed. For finer bed material particles, the high NOx concentration generated in the dense phase region experiences a more thorough reduction in the dilute phase region. Through the analysis of material concentration and reaction rate, it is believed that this phenomenon is related to the increased catalytic effect of fine ash particles in the dilute phase region, that is, the reduction in particle size leads to an increase in catalytic specific surface area, enhancing NOx reduction, thus achieving ultra-low emissions at the outlet. These research results provide theoretical support for further development of ultra-low emission coal-fired CFB boilers.

CPFD Simulation of Gas-Solid Flow in Dense Phase Zone of Pant-Leg Fluidized Bed with Secondary Air

Aggregation of fluidization media may appear at the dense phase region of the pant-leg fluidized bed near the incline walls. When the particles flow along the inclined wall, the friction and drag force will cause the particles to accumulate on the inclined wall, resulting in an uneven distribution of particles. The stagnant zones can be minimized by correctly arranging secondary air. Computational particle fluid dynamics (CPFD) method was used to simulate the gas-solid two-phase flow pattern in the dense phase region of pant-leg fluidized bed. Cold tests were performed on a benchtop pant-leg fluidized bed. A high speed imaging technology was used to monitor the flow pattern in the dense phase area, whereas the bubble size and residence time were compared to verify the accuracy of the simulation. The gas-solid flow patterns under various models were simulated. The influence of different secondary air velocities on the reduction of stagnant zone in the dense phase zone of the fluidized bed were predicted. The results indicated that the introduction of secondary air could effectively promote the mixing of particles, and weaken the accumulation of particles on the inclined wall surface. Moreover, secondary air can effectively promote the flow between the gas-solid two-phases and improve the combustion characteristics in the furnace.

Numerical investigation of the Ni-based catalytic methanation process in a bubbling fluidized bed reactor

In this study, the CO methanation process in a three-dimensional bubbling fluidized bed with Ni-based catalyst is simulated with the reactive multiphase-particle-in-cell method, considering the complex gas-catalyst hydrodynamics, chemical reactions, and heat and mass transfer between phases. The consistency between numerical results and experimental data verifies the feasibility and accuracy of the model. The effects of operating parameters on the purity of CH4, the yield of CH4, the CO methanation performance, and gas-catalyst thermophysical properties inside the reactor are explored. The results show that the CO methanation process mainly occurs in the dense phase region. The fresh gas injected has a significant effect on gas and solid flux, and the heat transfer coefficient (HTC) of catalyst particles. A higher inlet gas velocity and operating temperature lead to a larger HTC of catalyst particles. Furthermore, the HTC of catalyst particles close to gas distributor is the largest, and then the dense region. The gas production of CH4 has an inverse relationship with the ratio of CO/H2. Increasing the CO/H2 ratio reduces the yield of CH4. Also, increasing the inlet velocity of gas decreases the reactant gases residence time, which results in the reduction of CH4 production.

Pneumatic feeding characteristics into dense-phase region of a fluidized bed for biomass pyrolysis

That biomass particles are pneumatically fed into the dense-phase region of a fluidized bed is of great significance for the design and operation of pyrolysis equipment. Single factor experiments are adopted in the linkage apparatus to study the effects of the material properties and operating conditions on the pneumatic feeding characteristics of the bed. The results show the feeding rate decreases with the particle size, decreases with the gas velocity, and presents a parabolic and a “M” shape variation with the static bed height and volume flow ratio, respectively. The pneumatic feeding mechanism of the injection gas and the fluidizing gas is different, while the effect of the two gases is complementary in the pneumatic feed. And their reasonable volume flow ratio improves the feeding rate and stability. A regression model is finally developed with R2 = 0.928, which can well predict and guide the pneumatic feed of the bed.

Effect of moisture content on flow behavior and resistance characteristics of dense-phase pneumatic conveying

The flow characteristic of high pressure dense-phase pneumatic conveying of pulverized coal is essential to the safe and stable operation of the gasifier. In this paper, the effects of coal moisture content on conveying behavior and resistance characteristics of dense-phase pneumatic conveying were explored. Meanwhile, a model of the additional pressure drop of particles was proposed and compared with the experimental data. The results show that though the resistance and cohesiveness increase with increasing moisture content, its influence is different in dense and dilute phase. In the dense-phase region, the coal with lower moisture content shows a larger solid mass flow rate and solid concentration; while in the dilute-phase region, the moisture content has minor effect on conveying characteristics. For the coal with lower moisture content in dense-phase region, the solid mass flow rate and solid concentration are larger, and the gas velocity has a small effect on solid friction factor, due to its smaller cohesiveness and resistance, which is showed in our experiments and inferred from our model. The additional pressure drop model was proposed for straight pipes and bends, whose parameters are probably effective than the existing parameters in this kind of model, as the deviation in the vertical rise pipe, horizontal pipe and bend pipe is controlled within ±30%, and the corresponding vertical down pipe are controlled within ±40%.

Heat Transfer Characteristics in the Dense Phase Region of a Pressurized Fluidized Bed

Heat Transfer Characteristics in the Dense Phase Region of a Pressurized Fluidized Bed

Modeling and dynamic characteristics of the dense phase region of a biomass-fired circulating fluidized bed combustion system using Modelica

Using Modelica language, a mathematical model combining static and dynamic contributions of the dense phase region of a 130 t/h biomass circulating fluidized bed boiler combustion system was established on MWorks simulation platform. The mathematical model adopted modular packaging to increase the universality of the model, and it used an implicit, high-order, and multi-step Dassl integration algorithm to conduct the simulation. Under the design condition parameters, the relative error between the bed temperature of the dense phase region obtained by the simulation model and the actual temperature was less than 3.8%, which indicated that the static characteristics of the established simulation model were accurate. The effects of biomass feed and primary air volume step changes on the bed temperature, oxygen content in the flue gas, height of the dense phase region, and the bed pressure difference in the dense phase region were investigated. Both the biomass feeding and the primary wind step of 10% reduced the temperature, and it was obvious that the primary wind had a greater impact on the bed temperature. Meanwhile, the primary wind had a greater impact on the bed pressure difference than the biomass feeding.

Oxidation mechanism of pyrite concentrates (PCs) under typical circulating fluidized bed (CFB) roasting conditions and design principles of PCs’ CFB roaster

The circulating fluidized bed (CFB) roasting process is a promising way to utilize pyrite concentrates (PCs) which are byproducts in nonferrous metal production processes. The oxidation mechanism of PCs was investigated under typical CFB roasting conditions with the temperature of 850 °C and oxygen concentration of 1–21% on a drop tube furnace. The oxidation reaction pathway and products of PCs are strongly coupled with particle morphology evolution, which affects the oxygen diffusion from the particle surface to the core. A reaction path model of PC oxidation coupled with particle morphology evolution under CFB roasting conditions was proposed. The initial relatively slow oxidation of the porous particle structure followed by the relatively fast oxidation for complete oxidation was demonstrated to be the ideal reaction path for the CFB roasting operation of PCs. The critical issue for PCs roasting in the CFB reactor is to inhibit the particle temperature rise in dense phase region to avoid the formation of compact solid spheres. The flow and reaction behaviors of PC particles in CFB reactor naturally follow the ideal reaction path and make the CFB roasting technology feasible. Finally, the design principles of PCs CFB roasting process were suggested.

Two- and three-dimensional hydrodynamic modeling of a pseudo-2D turbulent fluidized bed with Geldart B particle

This study presents a comprehensive comparision between 2D and 3D hydrodynamic modeling of a pseudo-2D turbulent fluidized bed with Geldart B particle. Based on the Euler-Euler approach and the EMMS-based drag model, 2D/3D CFD models are established, their sensitivities to the restitution coefficient and the specularity coefficient are analyzed, and the 2D/3D hydrodynamic simulations are performed and compared. The simulation results show that 3D simulations are more sensitive to the restitution coefficient and the specularity coefficient than 2D simulations. At the beginning of fluidization process, 2D simulation predicts greater bubble size and higher bed expansion than 3D simulation; as a complete fluidization is achieved, 2D model exhibits higher solid concentrations in the middle transition and the upper dilute-phase regions; the fluidization process in the 2D simulation develops more quickly than that in the 3D computation. Both the 2D and 3D models could capture the global flow behavior in the bottom dense-phase region of the turbulent fluidized bed reasonably. In the middle and upper regions, however, the 2D model overestimates the solid concentration and particle velocity while the 3D simulation gives better hydrodynamic prediction. For the present pseudo-2D turbulent fluidized bed with Geldart B particle, the bottom dense-phase region resembles 2D flow and 2D simulations may be adequate; however, the middle and upper regions exhibit 3D flow and full 3D simulations are needed.

On developing improved modelling for particle velocity and solids friction for fluidized dense-phase pneumatic transport systems

Pneumatic transport of fine powders in fluidized dense-phase pneumatic conveying of powders has become popular in several industries because it offers various advantages, such as reduced air flow and gas velocity, reduced pipeline sizing and wear rate, reduced size requirement of gas–solid separator unit etc. For the reliable design of a pneumatic conveying system precise estimation of the solids friction factor through horizontal straight pipes is essential, but it is a challenging task till date because of the highly concentrated, turbulent, and complex nature of the gas–solids mixture. In the present work, power station fly ash (median particle diameter: 22 μm; particle density: 2370 kg/m3; loose-poured bulk density: 660 kg/m3) and cement (median particle diameter: 19 μm; particle density: 2910 kg/m3; loose-poured bulk density: 1080 kg/m3) were conveyed through different pipeline configurations (i.e., 65-mm inner diameter × 254-m-long and 80/105-mm inner diameter × 407-m-long step-up pipeline). For the fluidized dense-phase flow in pneumatic conveying system, governing equations were developed and the same were solved using fourth-fifth-order Runge-Kutta-Fehlberg (RKF45) method. The results revealed that the particle velocity and actual gas velocity and the ratio of the two velocities increases along the direction of flow, while an opposite trend was found for the solids volumetric concentration. The particle velocity and actual gas velocity terms were then included in an existing pure dilute-phase model (for solid friction factor) to modify it, by incorporating sub-models for particle and actual gas velocities and impact and solids friction factor and make it suitable for dense-phase mode. The solids friction-factor model was then validated by comparing the experimental and predicted pneumatic conveying characteristics for different solids flow rates and by using it to predict the total pipeline pressure drops for larger and longer pipelines. The new model has shown reliable predictions in the dense-phase region.

An Experimental Study of Gas Influx in Oil-Based Drilling Fluids for Improved Modeling of High-Pressure, High-Temperature Wells

Summary Oilfield exploration in extreme areas represents additional requirements for drilling-fluid performance and hydraulic models for well control. In general, there is little knowledge about the drilling-fluid properties at high-pressure/high-temperature (HP/HT) conditions, and kick models are based on extrapolation of fluid properties from moderate pressures and temperatures. To verify the validity of extrapolation to downhole HP/HT conditions, increased knowledge about the drilling-fluid behavior under these conditions is required. In this work, we have experimentally determined the effect of gas absorption on saturation pressure, density, and viscosity at temperatures up to 200°C and at 1,000 bar. We provide accurate measurements of methane solubility in two oil-based drilling fluids (OBDFs), which both have the same composition except for the type of base oil (BO). One is based on a refined normal mineral oil, and the other is based on a linear paraffin. For various CH4/OBDF combinations, density and viscosity are measured at pressures and temperatures ranging from standard conditions to HP/HT. The two OBDFs reveal similar flow behavior, but the one that is based on a linear paraffin oil has a stronger gel structure and a stronger shear-thinning effect. This fluid enters the dense-phase region at a lower pressure, and is accordingly able to absorb more gas at a lower pressure than the fluid with a normal mineral oil. Results have been used to validate computational predictions. It is shown that the experimental results form an important basis for tuning the software model to fit the thermodynamic properties of gas-loaded drilling fluid at HP/HT conditions.

Monitoring of particle motions in gas-solid fluidized beds by electrostatic sensors

Gas-solid fluidized beds are widely applied in numerous industrial processes. Particle motions significantly affect the performance of fluidized bed reactors and the characterization of particle movements is therefore important for fluidization quality monitoring and scale-up of reactors. Electrostatic charge signals in the fluidized bed contain much dynamic information on particle motions, which are poorly understood and explored. In this work, correlation velocities of Geldart B and D particles were measured, analyzed and compared by induced electrostatic sensors combined with cross-correlation method in the fluidized bed. The results indicated that the average correlation velocity of particle clouds increased and the normalized probability density distributions of correlation velocities broadened when the superficial gas velocity increased in the dense-phase region. Both upward and downward correlation velocities could be acquired in the dynamic bed level region. Under the same excess gas velocity, the average correlation velocity of Geldart D particles was significantly smaller than that of Geldart B particles, which was caused by the smaller bubble sizes caused by the dominant bubble split over coalescence and less volume of gas forming bubbles for Geldart D particles. The experimental results verified the reliability and repeatability of particle correlation velocity measurement by induced electrostatic sensors in the gas-solid fluidized bed, which provides definite potential in monitoring of particle motions.

An experimental investigation into modeling solids friction for fluidized dense-phase pneumatic transport of powders

Results are presented of an ongoing investigation into modeling friction in fluidized dense-phase pneumatic transport of bulk solids. Many popular modeling methods of the solids friction use the dimensionless solids loading ratio and Froude number. When evaluated under proper scale-up conditions of pipe diameter and length, many of these models have resulted in significant inaccuracy. A technique for modeling solids friction has been developed using a new combination of dimensionless numbers, volumetric loading ratio and the ratio of particle free settling velocity to superficial conveying air velocity, to replace the solids loading ratio and Froude number. The models developed using the new formalism were evaluated for accuracy and stability under significant scale-up conditions for four different products conveyed through four different test rigs (subject to diameter and length scale-up conditions). The new model considerably improves predictions compared with those obtained using the existing model, especially in the dense-phase region. Whereas the latter yields absolute average relative errors varying between 10% and 86%, the former yielded results with errors from 4% to 20% for a wide range of scale-up conditions. This represents a more reliable and narrower range of prediction that is suitable for industrial scale-up requirements.

On improving solid friction factor modeling for fluidized dense-phase pneumatic conveying systems

This paper presents results from an ongoing investigation into the modeling of solid friction factor for fluidized dense-phase pneumatic transport of powders. In spite of having the potential of being an energy economic and a better maintenance free mode of pneumatic transport, reliable design of fluidized dense-phase pneumatic conveying systems is still a difficult task due to the highly turbulent and complex nature of the flow of fine powders under high concentrations, where is it difficult to model particle–wall–air interactions. Several popular/applicable models (developed by other researchers, including one of the co-author of this paper) were evaluated to predict the total pipeline pressure loss for the dense-phase pneumatic conveying of fly ash (median particle diameter: 30μm; particle density: 2300kg/m3; loose-poured bulk density: 700kg/m3) and ESP dust (median particle diameter: 7 μm; particle density: 3637kg/m3, loose-poured bulk density: 610kg/m3) under different diameter and length scale-up conditions (viz. 69mm I.D.×168m; 105mm I.D.×168m and 69mm I.D.×554m pipes). These models are based on solids loading ratio and Froude number). A comparison between the predicted pneumatic conveying characteristics (PCC) and the experimental results showed that the models resulted in significant inaccuracy, especially under scale-up conditions of a new modeling technique has been developed using air velocity and a volumetric loading ratio term by replacing solid loading ratio and Froude number. The volumetric loading ratio term intends to address the product volume occupancy inside the pipeline, which is believed to be a better representation of flow conditions compared to mass ratio. The derived models were examined for scale-up accuracy by predicting pressure drop for different diameter/lengths of pipelines. It is found that the models have generally provided improved predictions in the dense-phase region. Whereas the existing models predicted with relative errors varying between 10 and 127% (depending on product and pipeline conditions), the new developed model resulted in predictions within 24% accuracy for a wide range of scale-up conditions, which provides better reliability and a narrower range of predictions, more suitable for industrial scale up requirements. Future work would require a more fundamental approach to understand the solid friction phenomenon for further accurate modeling.

Flow Characterization of Dense-Phase Pneumatic Conveying System of Pulverized Coal through Electrostatic Sensor Arrays

Experiments are performed in a dense-phase pneumatic conveying system of pulverized coal, and electrostatic signals and coal particle distribution images over cross-section of the pipeline at superficial gas velocities of 5.7 m/s, 6.9 m/s, and 8.1 m/s are obtained through use of electrostatic sensor arrays (ESA) and electrical capacitance tomography (ECT), respectively. In combination with ECT imaging results, the output signals of the ESA are analyzed by FFT and approximate entropy method. Results show that characteristic of particles motion and its change with increasing superficial gas velocity are different in the dense and dilute phase region of the pipe. With increasing the superficial gas velocity, the peak frequency of the electrostatic signal increases linearly in dense-phase region, while that in dilute phase region is nonlinear, implying that the increase of the axial particles velocity is the main dynamic change, while in dilute phase regions, the particles velocity fluctuation in the radial direction cannot be ignored. The ApEn value of the electrostatic signal in dense phase region is larger than that in dilute phase region. When the ApEn value difference of the electrostatic signals is smaller, the pulverized coal particles are better suspended.

Process Simulation of Using Coal Pyrolysis Gas to Control NO and N2O Emissions during Coal Decoupling Combustion in a Circulating Fluidized Bed Combustor Based on Aspen Plus

A process simulation model of CFB coal decoupling combustion process has been developed based on Aspen Plus and verified by comparing with the reported NO and N2O emissions from experiments. The detailed information on formation and decomposition of NO and N2O along the height of CFB riser column can be quantitatively simulated by the developed process simulation model. The simulated results show that about 99.9% of the emitted NO in flue gas is controlled by fuel-N combustion; however, the introduced NH3 in coal pyrolysis gaseous products as an NO precursor can play an important role on NO formation from about 39.7% to 97.6% in the dense phase region at the lower CFB riser column. About 98.9%-99.8% of NO decomposition along the height of CFB riser column is dominated by char particles reduction. About 91.8%-95.8% of the emitted N2O in flue gas is controlled by fuel-N combustion; however, the introduced HCN in coal pyrolysis gaseous products as an N2O precursor has an obvious effect on N2O formation from 74.2% to 94.6% in the dense phase region at the lower CFB riser column. The contribution of char particles reduction on N2O decomposition can be found as 1.8%-3.6% along the height of CFB riser column. A competitive relationship between O-2 oxidization and CO reduction on N2O decomposition along the height of CFB riser column during the CFB coal decoupling combustion process has been revealed.

Hydrodynamic Characteristics of a Novel Annular Spouted Bed with Multiple Air Nozzles

A novel spouted bed, namely, an annular spouted bed with multiple air nozzles, has been proposed for dryness, pyrolysis, and gasification of coal particulates. It consists of two homocentric upright cylinders with some annularly located spouting air nozzles between inner and outer cylinders. Experiments have been performed to study hydrodynamic characteristics of this device. The test materials studied are ash particle, soy bean, and black bean. Three distinct spouting stages have been examined and outlined with the hold-ups increase. In the fully developed spouting stage, three flow behaviors of particles have been observed and delimited. The effects of nozzle mode and spouting velocity on the maximum spouting height of the dense-phase region, spoutable static bed height, and spouting pressure drop in the bed have been investigated experimentally.

Crossover EOS versus classical EOS for pure fluids

A crossover EOS and a classical EOS have been studied and compared. The crossover EOS was a modified Redlich-Kwong EOS with a crossover function implemented, which was taken from literature and modified with one additional parameter. The classical EOS was either a modified Redlich-Kwong cubic EOS (for non-associating fluids) or the same EOS with an association term taken from the chemical theory. The equations of state have been applied to water and to n-alkanes up to n-heptane in the temperature range of 300–900 K and pressure range of 0.1–40 MPa. The modified crossover EOS improves the description in the dense phase region, and gave the following root mean square deviations for the components from a fit to vapor pressure plus a critical volume shift: vapor pressure 0.23–1%, saturated liquid volume 2.4–3.9%, saturated gas volume 0.8–12% and PVT data in the single-phase region 3.8–6.1%. For the classical EOS the root means square deviations were vapor pressure 0.2–0.9%, saturated liquid volume 0.6–3.6%, saturated gas volume 2.7–11.2%, and PVT 10–30%. The modification of the crossover EOS brought an overall improvement compared to the crossover EOS from literature. One advantage of the crossover EOS as modified here is the ability to predict the volumetric properties of both two- and single-phase regions of higher n-alkanes from the vapor pressure fit.

Performance of five equations of state for the prediction of vle and densities of natural gas mixtures in the dense phase region

This paper examines the degree of uncertainty of five Equations of State (EOS) for the prediction of densities in the dense phase region which is beyond the ranges of pressure and temperature originally specified for these equations. Predicted densities were compared with measured values for different hydrocarbon mixtures including a rich mixture. The results show that the GERG equation of state, originally specified for the range of P -8 C, outperforms all other equations in the region up to P=30 MPa and T > -8 C. In this range, its mean deviation from measured values of densities was found to be less than -0.015% and standard deviation ( ) also less than 0.015%. The AGA-8 equation, which identified several regions of pressures and temperatures with different uncertainties, also performed quite well with a mean deviation of -0.2% and less than 0.4% in the region up to P=30 MPa. The other equations showed relatively high deviation: ∼2.7% for BWRS,-5.1% for PR and 2.5% for RKS. Unlike GERG and AGA-8, however, these three equations can also be used to predict the vapour-liquid-equilibrium (VLE). VLE predictions were compared with measured values for eight binary mixtures of methane (C1) and ethane (C2). It is recommended to use PR for VLE prediction, as quite good agreement between measured data and prediction by PR was demonstrated.