Saturation Carrying Capacity Research Articles

Investigating choking phenomena in CFB risers under different operating parameters

Choking phenomena in circulating fluidized bed (CFB) risers pose a significant challenge to industrial operations. To tackle this concern, multiphase particle-in-cell (MP-PIC) simulations are employed to investigate the impact of varying solids flux, bed height, and riser size on solids transport in CFB risers. The research sheds light on the complex interplay of operating parameters in CFB systems. The transition of solids holdup profiles from exponential to S-shaped curves with increasing solids inventory is observed, accurately predicting the choking point. By adjusting geometric dimensions, the choking point distance from the outlet at a fixed length-to-diameter ratio can be efficiently shifted. The findings provide a deeper understanding of saturation carrying capacity (SCC) in CFB risers, which can be leveraged to optimize industrial performance. This research is instrumental in mitigating choking effects and enhancing the design and operation of CFB systems.

Saturation Carrying Capacity for Group A Particles in a Circulating Fluidized Bed

Empirical models continue to play a significant role in the design process of multiphase chemical reactors, particularly riser reactors in circulating fluidized bed (CFB) processes. It is imperative that accurate, industrial relevant correlations are developed to aid these design efforts. Using poor correlations could result in startup issues and significant redesign work. In this work, a new correlation is proposed to predict the saturation carrying capacity of Geldart Group A particles. This new correlation improves upon the currently available correlations for these materials and covers a broad range of Geldart Group A particles (particle diameters from 52 to 70 µm, and Archimedes numbers ranging from 5 to 20), superficial gas velocities (1 to 4 m/s), and riser diameters (0.066 to 0.3048 m). The new correlation has an Absolute Average Percent Deviation of only 17.6%, making it the most accurate correlation for Geldart Group A particles in the current literature.

Saturation carrying capacity Group B particles in a circulating fluidized bed

The saturation carrying capacity of risers in a circulating fluidized beds (CFB) is a critical design parameter that sets an upper limit on the solids flux with respect to riser gas velocity for operation in the fast fluidization regime. It is imperative that well developed correlations, spanning multiple riser diameters, particle properties, and gas velocities be developed to aid in the design of risers. This work adds four new data sets and subsequently proposes a new correlation for Geldart group B particles. It was discovered that the functionality for the saturation carrying capacity differed greatly for small and large group B particles, but this behavior could be explained with the gas velocity raised to the square root of the particle size. A new correlation is formulated, including literature data and the new data presented in this work. The correlation for Geldart Group B particles has a correlation coefficient exceeding 95%.

A revisit to saturation carrying capacity and saturated solid fraction in gas-solid upward flow

Flow regime transition between dilute pneumatic conveying and fast fluidization is identified for two Geldart A particles and four Geldart B particles in a novel gas-solid fluidization system configuration without exit restrictions. The results indicate that both saturation carrying capacity Gs⁎ and saturated solid fraction εs, ch strongly depend on superficial gas velocity and particle properties. Based on data from this study and literature, improved correlations for estimating Gs⁎ and εs, ch were developed. The correlations predictions agreed much better with experimental data than previously reported correlations.

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 correlation entropy 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 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.

Predicting the fast transition conditions by the correlation of particle entrainment rate

A model for predicting the fast transition condition in a riser of a circulating fluidized bed was proposed using the correlation of particle entrainment rate. The saturation carrying capacity of Bai and Kato could be regarded as the particle entrainment rate at the fast transition condition. The correlation of Choi et al. on particle entrainment rate could be used as a tool to predict the fast transition condition. The effect of interparticle forces seemed to be negligible at the fast transition condition. The model was in fair agreement with the measured values at the fast transition condition.

A hydrodynamic model for circulating fluidized beds with low riser and tall riser

Based on different flow regimes classified by the saturation carrying capacity in the riser, a comprehensive hydrodynamic model for circulating fluidized beds was proposed and validated with experimental data. The model can describe the different axial solids distributions or regimes in previous literatures, especially the boundaries among them. The calculation of model shows good agreement with experiments not just for gas solids behavior in riser, but also for that in standpipe.The influences of the riser height on the axial solids distribution in riser were discussed. With the increase of the distance between the upper end of dense phase and the bottom of riser, the axial solids distribution in low riser appears as the exponential profile, the quasi exponential profile and the quasi S-shaped profile continuously. For the tall riser, the quasi exponential profile is replaced by the S-shaped profile due to the dilute phase in the upper. In addition, the saturation carrying capacity prevails in the tall riser, and with greater inventory solids circulation rate would exceed the saturation carrying capacity to form the quasi S-shape profile.

Experimental investigation on flow asymmetry in solid entrance region of a square circulating fluidized bed

To study the influence of back feeding particles on gas–solid flow in the riser, this paper investigated the flow asymmetry in the solid entrance region of a fluidized bed by particle concentration/velocity measurements in a cold square circulating fluidized beds (CFB). The pressure drop distribution along the riser and the saturation carrying capacity of gas for Geldart-B type particles were first analyzed. Under the condition of u 0 = 4 m/s and G s = 21 kg/(m 2 s), the back feeding particles were found to penetrate the lean gas–solid flow near the entrance (rear) wall before reaching the opposite (front) wall, thus leading to a relatively denser region near the front wall in the bottom bed. Higher solid circulation rate ( u 0 = 4 m/s, G s = 33 kg/(m 2 s)) resulted in a higher particle concentration in the riser. However the back feeding particles with higher momentum increased the asymmetry of the particle concentration/velocity profile in the solid entrance region. Lower air velocity ( u 0 = 3.2 m/s) and G s = 21 kg/(m 2 s), beyond the saturation carrying capacity of gas, induced an S-shaped axial solid distribution with a denser bottom zone. This limited the penetration of the back feeding particles and forced the fluidizing air to flow in the central region, thus leading to a higher solid holdup near the rear wall. Under the conditions of u 0 = 4 m/s and G s = 21 kg/(m 2 s), addition of coarse particles ( d p = 1145 μm) into the bed made the radial distribution of solids more symmetrical.

Effects of riser height and total solids inventory on the gas–solids in an ultra-tall CFB riser

More and more CFB boilers with large capacity and ultra-tall furnaces are used for power generation. Understanding the fluid dynamics in the ultra-tall furnace is important. However, existing studies on fluid dynamics in the CFB furnace are limited to the risers with rather short height. An experimental study was conducted with a cold CFB test rig of 240 mm in I.D. and 38 m and 54 m in height respectively. The influences of total solid inventory I v, and fluidizing gas velocity U g on the axial voidage profile along the riser and solid circulation rate G s were investigated. Experimental results showed that when U g exceeded the transport velocity, an S-shaped voidage profile characterized by fast fluidization was established in the riser. In such circumstance, the voidage at top dilute section kept constant and G s reached saturation carrying capacity ( G s = G s ⁎) and inappreciably change with riser height and I v. Moreover, G s ⁎ increased from 40 kg to 50 kg when the riser height increased from 38 m to 54 m. The results indicated that even for the 600 MWe supercritical CFB boiler with a 54 m tall furnace, only a modest increase of I v and power of forced draft fans is needed to obtain high enough G s to meet the requirements of heating surfaces arrangement in furnace and the circulation loop. The necessary conditions to form the S-shaped profile of voidage in the riser were also discussed.

Simplified modeling of circulating flow of solids between a fluidized bed and a vertical pneumatic transport tube reactor connected by orifices

Interconnected and dual fluidized bed (FB) systems with various regimes of gas-solids flow are commonly studied with the aim to find and ensure suitable circulation of solids and control of flow between two chambers/reactors with different reacting gases. Dual separated fluidized beds or fluidized and transporting bed systems are convenient for cleaning of gases with regeneration of a solid sorbent or for gasification of solid fuels and production of fuel gas practically free of nitrogen. The paper concentrates on the development, comparison and checking of three simplified models for solid particle velocity, pressure drop and mass flux in a pneumatic transport reactor (riser). The simplified models have been used in a more general model for flow of solids via orifices between a FB near the incipient fluidization and a tube with vertical pneumatic transport (PT) of solids and recirculation to the FB. The model predictions have been compared with experimental data and validated in a limited range of operating conditions: for lower solids fluxes of sand particles ( d p = 0.3 mm, mass fluxes below 40 kg/m 2/s) at gas velocities higher than the terminal velocity U T of solids and for relatively high solid fluxes (over 160 kg/m 2/s) and gas velocities higher and lower than U T. Predictions from the models were used to estimate effects of particle size, gas velocity in the pneumatic transport column and height of the FB on circulating mass flux of solids. Comparison of the model-computed and experimental mass fluxes of solids with a theoretical forecast for the saturation carrying capacity of gas in pneumatic transport and a forecast of “choking” as computed by use of the Yang correlation has indicated possible problems and instabilities of solids flow in regimes with higher solids mass fluxes and/or lower gas velocities in the riser (PT-column). To control the circulation rate of a given particulate material in the dual FB-PT systems three main, practically important parameters should be considered: the superficial gas velocity in the riser (PT-column), height of the FB and cross sectional area of the orifices.

Multi‐scale CFD simulation of operating diagram for gas–solid risers

AbstractOur recently presented multi‐scale computational fluid dynamics (CFD) approach has proven to be able to capture the choking phenomena in a circulating fluidized bed (CFB). However, how to transfer this capability to assist industrial operation remains to be explored. To this end, this paper presents further simulation results over the intrinsic flow regime diagram and the operating diagram for gas–solid risers, showing the variation of flow regimes with gas velocity and solids flux as well as riser height. It is confirmed that the choking in CFB risers, characterized by the saturation carrying capacity and the coexistence of both dense and dilute flows, holds clear‐cut definition in hydrodynamics. In physics, both the choking, non‐choking transitions, and the critical point in‐between are intrinsic nature of gas–solid riser flows; they initiate as functions of gas velocity and solids flux. In engineering operation, however, their appearances vary with the riser height used. As a result, the intrinsic flow regime diagram can be defined by the combination of gas velocity and solids flux, although it is hard to obtain in practice owing to the limitation of riser height. The operating diagram of a CFB should be, accordingly, height‐dependent in practice, demanding the riser height as a parameter besides commonly believed gas velocity and solids flux.

Choking and flow regime transitions: Simulation by a multi-scale CFD approach

The so-called “choking” phenomenon in fluidized systems lacks understanding from micro-scale hydrodynamics and hence always causes disputes. To solve this problem, a newly established multi-scale CFD (computational fluid dynamics) approach, which is based on drag correction from the EMMS (energy-minimization multi-scale) model, is used to simulate our experiments about choking and relevant flow-regime transitions. The computed flow-regime diagram is described with the functional relation between the imposed pressure drop and the solids flux at given gas flow rates. A bell-shaped area with an abrupt plateau, within which the solids flux equals the saturation carrying capacity and the dense upflow coexists with the dilute pneumatic transport, marks the choking transition in this diagram. The non-choking transition, however, is characterized by a smooth shift from the dilute flow to the dense flow, without an area for coexistence of flow regimes. The critical point, the summit of the bell-shaped area, demarcates between the choking and the non-choking transitions, near which the fluctuation of solids volume fraction reaches a maximum. In general, this CFD simulation of flow regime transitions suggests a good perspective of the EMMS based multi-scale approach.

Saturation carrying capacity at high archimedes number of vertical concurrent gas–particle flow

The existing literature data on the saturation carrying capacity G s * for vertical concurrent gas–particle flow are limited to Archimedes numbers Ar below 1000. By experimental measurement and dimensionless analysis the present article extended Ar to 2500 to demonstrate how G s * varies with gas velocity under these high Ar values. The obtained result revealed that G s * is subject to the same kind of correlation with gas velocity irrespective of Ar. The degree that G s * depends on gas velocity, however, generally decreases with raising Ar and it tends to be a constant when Ar becomes higher than 530. This shows in fact that the flows with heavy/large particles or dense/viscous gas possess a low increase in particle-carrying capability with increasing gas velocity until a steady specific capability per m/s is reached at Ar of 530. The article also reanalyzed the influence of column diameter on G s * , demonstrating that the column diameter influence exists only in small columns and for flows with heavy/large particles. The influence is negligible in commercial conveying columns and differs according to Ar in those small columns employed in laboratory studies. All of these findings resulted in an upgraded correlation for G s * , which manifested not only wide applicability to flows in differently sized columns and with Ar of up to 2500 but also better accuracy in the mentioned flow conditions when comparing with several other literature correlations.

A transient method for determination of saturation carrying capacity

Clear definition of smooth and stable operating regimes is necessary if circulating fluid bed reactors are going to be adopted commercially for process applications that require load following capabilities. One significant source of instability or long-term transient occurs when traversing the transition from transporting in a lean phase fluidization regime to transporting in a turbulent or fast-fluidized bed regime. The gas saturation carrying capacity (SCC) is the key functional parameter required to define this transition. A simple method is presented to accurately determine the SCC in which the solids flux was abruptly halted and the loss in pressure signal monitored over time. The SCC was measured for PVC under a variety of conditions. Upon drawing from the analogous liquid–vapor to vapor phase transition, a predictive relationship is also presented to estimate SCC for various gas–solid flow systems, knowing the gas velocity and solids' terminal velocity in that gas.

More fundamentals of dilute suspension collapse and choking for vertical conveying systems

AbstractUsing gas‐solid flows in circulating fluidized‐bed risers to analogize vertical pneumatic conveying systems, the collapse of dilute suspension, that is, the choking of accumulative type, was studied in three different risers with respect to different particles. The collapse of dilute suspension was dominated by an identical differential pressure drop over the measuring section. This differential pressure drop was independent of gas velocity and riser diameter, but varied with particle properties. The saturation carrying capacity, the solid flow rate at the dilute suspension collapse, was closely related to particle characteristics and riser diameter. With an increase in the riser diameter, it increased for lighter and smaller particles, but decreased for heavier and larger particles. Based on these experimental measurements, as well as the related literature reports, a correlation was developed for the saturation carrying capacity by analyzing its dependencies on gas velocity and riser diameter. More than 150 experimental data of the saturation carrying capacity available in the literature were compiled to evaluate the accuracy of the proposed correlation by comparing with 13 other literature correlations, demonstrating that this new method has the highest accuracy.

The EMMS model — its application, development and updated concepts

Circulating fluidized beds (CFB) operate with a heterogeneous structure consisting of a solid-rich dense phase and a gas-rich dilute phase, the variational criterion and the critical condition of which are indispensable for CFB quantification. With such a strategy, a comprehensive model is developed on the basis of the energy-minimization multi-scale (EMMS) approach. The model is capable of predicting the saturation carrying capacity and the steady states at both the top and the bottom of an S-shaped axial profile. Comparison between the model prediction and available experimental data shows reasonable agreement. In addition, the overall strategy adopted in the EMMS approach is also discussed with updated concepts. It is concluded that the variational criterion (or something equivalent) in analyzing heterogeneous two-phase systems is indispensable unless the observation scale can be sufficiently small.

Quantitative estimation of solids holdups at dense and dilute regions of circulating fluidized beds

This paper focuses on developing correlations for better prediction of solids holdups at the dense and dilute regions of circulating fluidized bed risers based on experimental data from the literature and our laboratory. Analysis of the experimental axial profile of solids holdup and the data on ε sd and ε s* has identified a critical solid circulation rate: saturation carrying capacity of gas, G s*, which distinguishes two different variations of ε sd and ε s* with solid circulation rate. In the case of G s< G s*, ε sd and ε s* increase with increasing solid circulation rate and may vary with other system properties, whereas ε sd and ε s* are only the functions of gas velocity and gas-solid properties and change little with the solid circulation rate, the riser diameter, the solids inventory as well as the solid feeding system in the case of G s≥ G s*. Based on these facts, more generalized empirical correlations for estimation of ε sd and ε s* are obtained. Comparisons with experimental data and the existing literature correlations confirmed the validity of the present correlations.

Analytical solution of the energy-minimization multi-scale model for gas–solid two-phase flow

To avoid complicated computation, analytical solution of the energy-minimization multi-scale (EMMS) model for heterogeneous particle–fluid two-phase flow has been derived through analyzing the suspension properties of clusters, thus allowing local hydrodynamics, choking velocity and saturation carrying capacity to be conveniently calculated without recourse to complex mathematical algorithm. It not only greatly simplifies the formulation of the EMMS model but also makes the computation of the model converge more easily to its solution, and therefore greatly facilitates the application of the EMMS model. In addition, some confusion on extremum energy in fluid–particle two-phase flow is also clarified by recapitulating the EMMS model.

Saturation carrying capacity of gas and flow regimes in CFB.

This paper presents a generalized approach to the saturation carrying capacity of gas, Gs*, in high-velocity fluidized beds. Starting from discussion of the variation of solid holdup in the dense region of circulating fluidized beds (CFBs) with the solid circulation rate, we defined the saturation carrying capacity of gas, Gs*, as the solid circulation rate at which a maximum achievable or saturation solids concentration at the dense region of the CFB starts to be reached. It has been experimentally demonstrated that above Gs*, solid concentrations in the dense region are really independent of changes in the solid circulation rate, the riser diameter, solids feeding system and the solids inventory, and a characteristic S-shaped axial solid holdup distribution would be observed. Based on this physical phenomenon, the saturation carrying capacity of gas was determined as functions of gas velocity and gas-solid properties, and a generalized correlation was therefore proposed on the basis of collected literature data. Finally, a flow diagram in which the flow conditions for occurring of S-shaped and exponential profiles of solids holdup was presented.

On the entrainment of solid particles from a fluidized bed

This paper presents a generalized approach to the phenomenon of entrainment of solids from a fluidized bed. Starting with the discussion of the transport disengaging height (TDH) and of the elutriation of particles above the TDH, one arrives finally at the relationship between the elutriation rate constant, saturation carrying capacity and choking parameters of pneumatic transport.