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Vertical profiles of local pressure, horizontal profiles of net vertical solid mass flux, and residence time distributions (RTD) of the solid phase are experimentally assessed in the riser of a small scale cold circulating fluidized bed of 9 m high having a square cross section of 11 cm × 11 cm. Air (density 1.2 kg/m3, dynamic viscosity 1.8 × 10−5 Pa s) and typical FCC particles (density 1400 kg/m3, mean diameter 70 μm) are used. The superficial gas velocity is kept constant at 7 m/s while the solid mass flux ranges from 46 to 133 kg/m2 s. The axial dispersion of the solid phase is found to decrease when increasing the solid mass flux. Simultaneously, 3D transient CFD simulations are performed to conclude on the usability of the eulerian–eulerian approach for the prediction of the solid phase mixing in the riser. The numerical investigation of the solid mixing is deferred until later since the near-wall region where the solid phase downflow and mixing are predominant is not well predicted in spite of well-predicted vertical profiles of pressure.

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... The crucial factors of determining the RTD will be thoroughly discussed, especially in terms of the specific flow behavior of solids, the diffusion coefficient of particles, and the tracer injection time. To test the numerical model, experimental study of Andreux et al. (2008) was investigated here for comparison, in which the riser of a labscale cold CFB was 9 m high and having a square cross-section of 0.11 m Â 0.11 m. The predicted hydrodynamics of gas and solids were firstly compared with the available experimental data, including radial profiles of solids mass flux, axial profiles of solids volume fraction, and some observations from the experiments. ...

... According to the description of experimental set-up in Andreux et al. (2008), the calculation of the riser section was performed in a 3D domain, which was 9-m long with a square cross-section of 0.11 m Â 0.11 m. In the experiments, to obtain a stable and horizontal solids injection at the bottom of the riser, a 0.1 m-diameter L-valve was modified to be a square cross-section of 0.025 m Â 0.025 m through a diaphragm. ...

... These factors which may affect the model predictions will be further investigated in the near future. Andreux et al. (2008) have performed a 3D hydrodynamic simulation for the above same system. The grid number was 31,000 (10 grids in both two radial directions and 310 grids in the axial direction). ...

Solids residence time distribution (RTD) in circulating fluidized bed risers is a critical parameter for evaluating reactor performances, however, it is still very difficult to be predicted via computational fluid dynamics (CFD) simulation due to the complexity of particle clustering phenomenon. This paper tries to establish an effective CFD model to reasonably predict solids RTD of gas-solids riser flows by means of properly addressing the paramount role of particle clusters in determining solids RTD. The gas-solids hydrodynamic characteristics were solved by Eulerian-Eulerian model, where an energy minimization multi-scale (EMMS) drag model was applied to modify the gas-solids drag force to account for the influence of particle clusters. The motion of tracer particles was calculated using species transport equation, where the diffusion coefficient of particles, a vital parameter indicating particle diffusion capacity, was investigated thoroughly. The established CFD model was validated against the available experimental data in the literature. It was shown that axial profiles of solids volume fraction and radial profiles of solids mass flux can be well predicted with EMMS drag model, but not with homogeneous drag model. The proper prediction of bed hydrodynamics is also very crucial to the success of solids RTD simulation. On the other hand, the effect of the diffusion coefficient of particles, the magnitude of which can span a range from 10-5m2/s to 10m2/s, is minor when compared with the convective transport mechanism, at least for the specific cases we studied. In addition, the importance of the sampling time resolution and tracer injection time for a RTD curve was addressed. The simulation results showed that a low time resolution often results in the loss of some micro-scale information, i.e. drastically smoothing the fluctuations of the RTD curve, and an inappropriate assessment of the tracer injection time can lead to a significant change of the RTD curve.

... (Bi and Grace, 1995). The CFB riser of Andreux et al., (2008) was simulated and operated in the core-annular dilute transport regime. Figure 12 shows the effect of grid resolution on the global voidage prediction. ...

... Note that the integral of the radial solids flux of the experimental data was 163.1 kg/m 2 s, which is higher than the measured solid mass flux G s = 133kg/m 2 s. This is because, in the experiment, Andreux et al. (2008) pointed out that solid downward flow in the near wall region could be visually observed, while a probe could not detect it. As shown in Figure 16, solid mass fluxes were higher and almost flat in the core regime, while they greatly decreased in the near wall regime. ...

... Heterogeneity index (normalized drag force) of various drag models as a function of voidage at different Re (=Re p /α g ): (a-b) bubbling fluidized bed ofDubrawski et al. (2013) at Re=1 and 8; (c-d) turbulent fluidized bed of Venderbosch (1998) at Re=2 and 12; (e-f) fast fluidized bed ofWei et al. (1988) at Re=4 and 20; (g-h) dilute phase transport fluidized bed ofAndreux et al., (2008) at Re=10 and 40. The parameters listed in ...

Coarse-grid two-fluid simulation of gas-solid fluidized bed reactors based on the kinetic theory of granular flow exhibits a significant dependence on drag models, especially for Geldart A particles. Many drag models are available in the literature, which have been reported to work for different systems. This study focused on the evaluation of an enhanced filtered drag model along with other different drag models derived from different methods for three-dimensional two-fluid model simulations of gas-solid fluidized beds of Geldart A particles covering a broad range of fluidization regimes, including bubbling fluidization, turbulent fluidization, fast fluidization, and dilute phase transport regimes. Eight drag models were selected, which included five heterogeneous drag models and three homogeneous drag models. Comparison with the available experimental data demonstrates the need for modification of homogeneous drag models to account for the effect of mesoscale structures (i.e., bubbles and clusters). The enhanced filtered drag model and energy-minimization multi-scale (EMMS) drag models were found to achieve superior predictions in all fluidization regimes, while the other drag models were only capable of predicting certain fluidization regimes. The results of this work provide a guideline for choosing appropriate drag models for simulating Geldart A particles and suggestions on developing more reliable and general drag models applicable in all flow regimes.

... For solids RTD in CFB risers, some significant discrepancies arose among numerous publications, and even seemingly contradictory conclusions were drawn by various researchers. First of all for the shape of RTD, some researchers observed the occurrence of a double-peak (Ambler et al., 1990;Bhusarapu et al., 2004a;Kojima et al., 1989;Lin et al., 1999;Patience et al., 1991;Wei et al., 1998;Weinell et al., 1997) or even multi-peak (Bhusarapu, 2005;Wang et al., 1996), whereas more researchers only measured a typical single-peak curve (Andreux et al., 2008;Bader et al., 1988;Harris et al., 2003c;Rhodes et al., 1991;Smolders and Baeyens, 2000;Viitanen, 1993;Zheng et al., 1992). Secondly, as the two widely used parameters to quantitatively measure solids RTD, solids dispersion coefficient, D, and Peclet number, Pe, have a huge discrepancy in magnitude for the tests measured in risers. ...

... For example, the estimated axial or radial solids dispersion coefficients can differ by more than 4 orders of magnitude (Breault, 2006). And axial solids Peclet number can span from 1 to 100 (Andreux et al., 2008;Rhodes et al., 1991;Smolders and Baeyens, 2000;Wei et al., 1998Wei et al., , 1995Yan et al., 2009). Thirdly, the reported effects of operating conditions, like superficial gas velocity, U g , and solids mass flux, G s , on D and Pe are totally different. ...

... In their proposed correlation, Pe a is the function of G s to the power of 0.33. This trend had also been observed by Andreux et al. (2008). Contrary to this report, Bi (2004) found that Pe a decreases with increasing G s when G s is not very high, based on the analysis of experimental data from the open literature. ...

Solids Residence Time Distribution (RTD) in Circulating Fluidized Bed (CFB) risers has received increasing attention due to its vital role in determining the operating condition, particle property, and reactor geometry in industrial CFB applications. In recent years, various solids RTD experimental techniques and theoretical models have been utilized and proposed to study CFB risers. Some controversial issues, however, also arose in the open publications. By means of exploring the advantages and disadvantages of each available RTD experimental technique and model when they are applied to particles in CFB risers, this study discussed the primary causes leading to the huge discrepancy in magnitude of solids dispersion coefficient and Peclet number, which can achieve 4 orders or span from 1 to 100. On the basis of the massive experiment data collected from the literature, the variations of average residence time, Peclet number and dispersion coefficient of solids with superficial gas velocity, solids mass flux and solids concentration were presented. By applying the transition of flow regime in CFB mode, we provided a helpful way to explain some existing contradictions in the reported effects of operating conditions on solids RTD. The possible reasons were also summarized to clarify why some researchers measured a double- or multi-peak solids RTD curve and the others could not in a similar situation.

... [1][2][3][4] For liquid phase applications, NaCl and KCl solutions are good tracers particularly with conductivity detectors. [5][6][7][8][9][10][11] A second option is a colourful dye like blue indigo carmine that UV-vis spectrophotometers and high speed cameras detect. [12][13][14] Irradiating solids and detecting the gamma ray emission or bremsstrahlung radiation with scintillating NaI detectors is the most effective method for the solids phase. ...

... The spread of the residence time, S, is a function of the time to recover 10% (t 0.1 ), 50% (t 0.5 ), and 90% (t 0.9 ) of the injected tracer [11] : ...

... Several assumptions limit the validity of the axial dispersion model [2,11,27,35] : ...

Reactor performance, solids‐(gas)‐mixing, flow through porous media, distillation columns, or through granulators improve as the fluid dynamics approach ideal plug flow. The residence time distribution is a diagnostic measure of how close fluid flow approaches ideal conditions. The technique introduces a step change to the inlet concentration—a Dirac‐δ function, Heaviside step function, or a rectangular pulse (bolus)—while high frequency detectors monitor the concentration along the vessel and/or at the exit. The effluent concentration profile spreads due to the variance in the process lines leading to the vessel and at the exit, the detector response, and the system. We quantify how much each of these contributes to the overall variance in a fluidized bed with 9 g of fluid cracking catalyst in 8 mm diameter quartz tubes. The injection variance is lowest for a GC sample loop configuration, compared to a 3‐way valve or 4‐way valve geometry. RTD measurements detect bypassing due to dead zones in vessels and the axial‐dispersion model and continuous stirred‐tank model to characterize deviation from plug flow. However, when the contribution to variance from the ancillary lines and detector is large compared to the system, the uncertainty in the model parameters is high. Research on RTD fundamentals concentrate on boundary conditions while, here, we focus on experimental errors: mechanical, physicochemical mathematical, and instrumental. This article is protected by copyright. All rights reserved.

... Andreux et al. [12] Riser of cold fluidized bed NaCl crystals injected in the connecting point between L-valve and the riser Cui et al. [13] Stripper of fluidized bed FCC particles were impregnated with a saturated solution of table salt and then dried to remove all moisture Rhodes et al. [14] Riser of CFB NaCl as tracer; Tracer sampling was performed in three locations in the riser ...

... Therefore, they must be chosen and applied with great care. 11 The chemically different tracers technique have been used extensively for fluidized bed and CFB studies [12]- [15], [51]. Bader et al. [52] obtained the solid residence time distribution in a fluidized bed cracking catalyst (FCC) riser from pulse injection of sodium chloride (NaCl) tracer. ...

... Figure 1.4 shows the sampling probe. Andreux et al. [12] investigated solid motion and particle RTD inside the riser of a CFB. NaCl was injected as a tracer in the connecting point between the L-valve and the riser and then sampled at the top of the riser. ...

The aim of the present thesis is to develop a novel experimental technique for determining the residence time distribution (RTD) of solid particles in solid unit operations as well as model development. Initially, a novel optical method was developed to measure the particle RTD. Experiments are carried out with Silicon Carbide (SiC) and the pigment phosphorescent (Lumilux® Green SN-F50 WS) as tracer particle. A preliminary experimental study was conducted in a simple bubbling fluidized bed in order to validate the proposed RTD measurement methodology. In the second step, the developed technique of the concentration measurement was applied to measure the RTD of a deep fluidized bed. The particle RTD curves are determined experimentally in different operating conditions. Finally, a model consisting of the combination of the ideal reactors is proposed to predict the particle residence time distribution in the studied fluidized bed. The predicted output values are then compared with the experimental data to establish a good model fitting data

... However, complex non-uniform flow patterns were found in the fluidized bed reactors [6][7][8], especially for Geldart A particle, which makes it challenging to accurately detect the tracer particle concentration that directly affects the accuracy of RTD measurement. Various types of tracers have been proposed to improve the accuracy of J o u r n a l P r e -p r o o f Journal Pre-proof RTD measurements, such as chemical tracer [9], radioactive tracer [10,11], magnetic tracer [12], colored tracer [13], thermal tracer [14,15] and fluorescent tracer. [15] To reduce errors in the experimental measurement of solid RTD, the injection duration of pulse tracer should be controlled as short as possible when compared with the particle mean residence time. ...

... The solid species transport equation was solved to calculate the solid residence time. The governing equations and constitutive relations are summarized in Table 1 9 10 ...

... The flow hydrodynamics and solid RTD measurement experiments conducted by Andreux et al. [9] in a pilot-scale CFB riser with FCC Geldart A particles were selected as a test case. Figure 2 shows the 3D geometries of the riser, which is 9m long with a square cross-section of 0.11m ×0.11m. ...

Computational fluid dynamics (CFD) is a powerful tool for prediction and analysis of complex multiphase flow hydrodynamics and residence time distribution (RTD) in chemical reactors. This study presented the validation and application of a filtered drag model for solid RTD prediction in a pilot-scale fluid catalytic cracking (FCC) circulating fluidized bed (CFB) riser with Geldart A particles. First, the filtered drag model implemented in the open-source MFiX-TFM solver was validated for flow hydrodynamics simulation in a FCC CFB riser. After that, the model was further employed to validate its ability for solid RTD prediction in the same riser by comparing the simulation results with the experimental data. The simulation with the filtered drag model well reproduced the tracer response experiment which is more accurate than that with the Gidaspow drag model. Simulations with both pulse and step tracer injection methods were compared, which reveals the limitation of solid RTD measurement using a pulse tracer injection method in the experiment.

... To improve the measurement of the RTD of the solid, various tracer particles have been used since 1980, including ferromagnetic particles [23,24] , radioactive sand [25] , sodium chloride [26][27][28] , and phosphorescent particles [29][30][31] . These studies mainly focused on the effect of the operating conditions; i.e. , the superficial velocity, solid circulation rate, and the diameter of the riser [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] . ...

... With the growth of computational power, CFD simulations have become powerful tools with which to investigate the complex gassolid flows in CFB risers, and in recent years, investigations of the RTD of solid particles have been carried out using CFD simulations. Broadly speaking, these can be divided into two schemes: Eulerian-Lagrangian approaches, in which the motion of each particle motion is tracked [35,36] ; and Eulerian-Eulerian approaches, whereby the effective stresses of the solid phase are modeled using the kinetic theory of granular flow [37][38][39] . Hua et al. [37] successfully validated the results of simulations of the RTD of solids using the Eulerian-Eulerian model against experimental data. ...

The authors investigate the effects of the direction of the gas jet on the solid residence time distribution in a CFB riser. Tracer technique was employed to calculate the RTD of solids. A Eulerian–Eulerian model with kinetic theory of granular flow and species transport was used to simulate the motion of tracer particles in a CFB riser. For a comparative analysis of the direction of the gas jet, simulations of vertical, horizontal and hybrid jets were carried out. The direction of the gas jet significantly influenced the axial and radial structure of bed, and hence affected the RTD for solid particles. The mean residence time of solids was changed, and the results showed that 16.3 s, 14.8 s, and 11.4 s with vertical, horizontal and hybrid jets nozzles, respectively.

... On the other hand, CFD is often used to describe electrochemical reactor performance, in which the hydrodynamics can be analyzed in detail [11]. Residence time distribution (RTD) has been obtained in different kinds of reactors using CFD, either by the particle tracking method or by the stimulus-response simulation method using different mathematical models [12][13][14]. Under practical operating conditions, the electrochemical reaction performance is directly related to the reactor hydrodynamics [15]. ...

... To simulate the tracer pulse injection, normally a short time concentration pulse in the form of triangle, square, delta Dirac or Gaussian functions are used. Numerically it is complicated to find a correct function that represents exactly the experimental pulse, causing variations in the RTD prediction [12][13][14]. In this paper, we employed a Gaussian function: y t ð Þ ¼ 1 ...

... The numerical simulation of the RTD obtained in different kind of reactor [17][18][19] with CFD, either by particle tracking method or by stimulus-response simulation method using different models (standard k-ε, RNG k-ε and Reynolds stress model), can lead to variations in the RTD prediction. Therefore, to ensure acceptable accuracy of the RTD prediction by CFD, comparison with experimental RTD is essential before they are applied in practice for prediction of flow behavior of the industrial systems. ...

... In the case of the stimulus-response simulation method, normally a short time concentration pulse in the form of triangle, square, Dirac delta or Gaussian functions are used, numerically is complicate to find a correct function that represent in precise way the experimental pulse causing variations in the RTD prediction. On the other hand, different aspect of the numerical method, such as computational mesh and the turbulence model choose influence in the prediction of the RTD experimental curves [17][18][19]. ...

... Instead of gas back-mixing, the core-annulus structure was assumed to dominate solid radial dispersion [24]. Besides, experiments by Andreux et al. [25] indicated that the solid axial dispersion decreased as the solid mass flux increased. Based on the abovementioned studies on solid mixing and dispersion via experimental measurements and semi-empirical correlations, motivation of the current work is to study the solid mixing and dispersion at particlescale level using the CFD-DEM approach. ...

... In contrast, particles in the annulus region moved downward with a lower velocity. In the radial direction, particles went back and forth between core and annulus regions, which benefited the solid mixing [25,36,49,50]. In the axial direction, solid concentration showed a nonuniform distribution. ...

The effect of superficial gas velocity (Uf) on solid behaviors in a full-loop circulating fluidized bed is numerically studied using computational fluid dynamics-discrete element method (CFD-DEM). Specifically, the solid mixing and dispersion, solid residence time, solid force and velocity, and particle granular temperature are comprehensively explored. The results show that increasing Uf slows the solid mixing. The solid axial dispersion in the riser is dominated among that in the three regions. Besides, increasing Uf decreases the solid cycle time and leads to a more uniform solid residence time (SRT) distribution in the riser and dipleg. The fluid force is an order of magnitude smaller than the collision force. Increasing Uf shows distinctive influences on the rotational speed and translational velocity in the three regions. Moreover, increasing Uf suppresses the particle granular temperature. The average particle granular temperatures in the riser at four superficial gas velocities (i.e., 5.5 m/s, 6.0 m/s, 6.5 m/s, and 7.0 m/s) are 0.09326 m²/s², 0.08040 m²/s², 0.06531 m²/s², and 0.05047 m²/s², respectively.

... Here, Huilin-Gidaspow drag model is adopted [33,34]. For the gas-solid interphase fluctuating energy, a modified Simonin model is developed in this work [35][36][37]. In this model, the fluctuating energy transfer between the SGS turbulent kinetic energy of gas and the second-order moment of particles is considered, and the term of gas-solid interphase fluctuating energy P gs can be expressed as: ...

The second-order moment (SOM) method is developed to describe the fluctuating anisotropy of particles in coal combustion process. Large-eddy simulation (LES) is employed for turbulence of gas phase. The LES-SOM model is coupled with chemical kinetics for coal combustion simulations and the anisotropy characteristic of particles is analyzed in circulating fluidized bed (CFB). The simulation results reveal that the molar fractions of gas species with the SOM model considering fluctuating anisotropy of particles are in better agreement with experimental data than those with the KTGF model. The distribution of the SOM of particles is evaluated. It is found that the SOM of particles is enhanced towards the wall. With the increasing particles concentration, the SOM of particles is sharply increased at first, reaches the maximum, and then gradually decreases. The SOM for coal particles is relatively lower compared to desulfurizer particles, while the fluctuating anisotropy for coal particles is larger. The Reynolds stresses of particles are also investigated. It is found that the Reynolds stresses of particles are one order of magnitude greater than the second-order moment of particles.

... For instance, Parmentier et al. [14] shows that neglecting the small structures in dense fluidized bed simulation leads to an overestimation of the bed height. According to Ozel et al. [13] and Andreux et al. [1] the insufficient mesh refinement leads to underestimate the vertical solid mixing and residence time in circulating fluidized bed. In addition, in bi-solid circulating fluidized bed, Batrak et al. [3] show that the "coarse mesh" simulation leads to underestimate the momentum coupling between particle species with large density ratio and, consequently, the entrainment rate of the coarse particles by the small ones. ...

Detailed sensitivity numerical studies have shown that the mesh cell-size may have a drastic effect on the modelling of circulating fluidized bed. Typically the cell-size must be of the order of few particle diameters to predict accurately the dynamical behaviour of a fluidized bed. Then the Euler-Euler numerical simulations of industrial processes are generally performed with grids too coarse to allow the prediction of the local segregation effects. A filtered approach is developed where the unknown terms, called sub-grid contributions, have to be modelled. Highly resolved simulations are used to develop the model. They consist of Euler-Euler simulations with grid refinement up to reach a mesh independent solution. Then spatial filters can be applied in order to measure each sub-grid contribution appearing in the theoretical filtered approach. Such kind of numerical simulation is very expensive and is restricted to very simple configurations. In the present study, highly resolved simulations are performed to investigate the sub-grid contributions in case of a binary particle mixture in a periodic circulating gas-solid fluidized bed. A budget analysis is carried out in order to understand and model the effect of sub-grid contribution on the hydrodynamic of polydisperse gas-solid circulating fluidized bed.

... As a result, the diffusion coefficient of particles was investigated based on the kinetic theory of granular flow and the empirical correlations [17]. Many experts [18][19][20] studied on the motion and residence time distribution of spherical particles in a number of fluidized beds. A small number of research on flexible filamentous particle was reported due to the complexity of agglomeration. ...

The mean residence time of granular particles is one of the most crucial indexes in drying processes. In this paper, a new formula for correction of the mean residence time(MRT) is proposed, which includes the correlation among the MRT and the slope, number of flights and moisture content of particle. As a consequence, the results obtained by the new corrected formula agree well with the experimental. Then, a series of experiments is presented to describe the mean residence time and motion performance of flexible filamentous granular particles under different operating conditions. In order to meet the requirements of description properly on the residence time of granular particles, slope and rotational speed of drum, moisture content of particle at the inlet, mass flow rate of particles, and velocity of air flow are taken into account. Experimental results on flexible filamentous particles demonstrate that the mean residence time is significantly influenced by those parameters mentioned above. Moreover, the decrease of drum slope makes the mean residence time rise, and the increase of rotational speed results in the dropping of mean residence time. The reduction of mean residence time becomes slower with the faster increase of rotational speed. Moreover, the mean residence time climbs following the increase of moisture content and mass flow rate of particles at the inlet while experiences a slightly drop with the increase of air flow velocity.

... Based on the background summarized above, we hypothesize that it should be possible to combine a simplified reactor modeling approach such as that proposed by Liden et al (1988) with appropriate global reaction kinetics (modified for particle size and moisture) and low-order particle RTD functions to simulate the expected trends for fast pyrolysis in both bubbling bed and circulating bed reactors. To increase our confidence in the reliability of the RTD functions, we evaluated the ability of each function above to fit the experimental RTD results for Group B particles in both bubbling and circulating fluidized beds reported by the following investigators: Helmrich et al (1986), Berruti et al (1988), Ambler et al (1990), Smolders and Baeyens (2000), Harris et al (2003a&b), Bhusarapu et al (2004), and Andreaux et al (2008). We observed that all of the above RTD functions can give reasonably close agreement to the reported RTDs using appropriate parameter values, especially considering the significant measurement errors that were explicitly reported or implied. ...

... uações gonvernantes, equações de conservação da massa, momento e constutivas, que serão resolvidas numericamente. As equações utilizadas neste trabalho estão fundamentadas na teoria cinética do escoamento granular, desenvolvido por Gidaspow (1994). Outros pesquisadores comprovaram a validade desta teoria (Neri e Gidaspow, 2000;Sun e Gidaspow, 1999;Andreux et. al., 2007). Mais tarde Yang et. al., (2003) e Yang et. al., (2004 desenvolveram coeficientes de arrasto com base na abordagem da Minimização Multi-Escala (EMMS). Neste trabalho, o modelo de arraste de Gidaspow foi aplicado, tendo nestas condições de fluidização rápida este coeficiente tem apresentado desempenho satisfatório. ...

... Computational fluid dynamics (CFD) is a promising tool to support the investigation of the complex phenomena occurring between the gas and particle phases in fluidized and spouted beds as demonstrated by several research groups [6][7][8][9][10][11][12][13][14][15]. For many years, contributions to the analysis of multiphase flows in fluidized beds could be done based on the research of Kinetic Theory of Dense Gases summarized by Chapman and Cowling [16]. ...

Fluidized bed reactors can be used for fast pyrolysis of polyethylene-aluminum composite (LDPE/Al) to achieve good gas-solid mixing together with high rates of heat and mass transfer in bed columns. Pyrolysis of waste from post-consumer carton package (i.e., polyethylene-aluminum composite) reduces the manufacturing costs of new packages as it permits to produce them using the recovered aluminum and polyethylene in the process. Therefore, this research aims at modelling and analyzing the gas-solid flow in fluidized beds composed of sand and LDPE/Al mixtures. For all mixtures used, results show that gas-solid flow can be well described by the Eulerian-Eulerian Granular model coupled with the usage of parameterized Syamlal-O’Brien’s model for momentum transfer between phases. For bed mixtures with up to 20% LDPE/Al composite, the bed pressure drop can be predicted by the model with an error of less than 18%. In addition, for bed mixtures operating at air velocities higher than 50% minimum fluidization, significant segregation of LDPE/Al was not observed. This result indicates that bed mixtures can achieve a good gas-solid contact in the bubble fluidization regime and can be used as a fluidized bed reactor for pyrolysis of wastes from post-consumer carton packages.

... The gas-solid interphase force is mainly drag force, which is the embodiment of the first-order interaction and closed by Huilin-Gidaspow drag model . The gas-solid interphase fluctuating energy is the embodiment of the second-order interaction and the revised Simonin model is used Andreux et al., 2008;Fotovat et al., 2015). The detailed descriptions are expressed in Table 3. ...

... Since computational assets have expanded significantly at forcefully diminishing costs, specified computational data about the flow can these day be acquired even at small amount of the expense relating to experimental (Xia & Sun, 2002). The transient CFD simulations are performed to suggest on the usability of the multiphase approach for the prediction of the solid phase mixing and residence time distribution in the riser (Andreux, et al., 2008). ...

In this study, numerical simulations of a gas-solid fluidized bed reactor involving a two-fluid Eulerian multi phase model and incorporating the Kinetic Theory of Granular Flow (KTGF) for the solids phase have been performed using a commercial Computational Fluid Dynamics (CFD) software. The fluidized bed setup consists of 1.5 m height and 0.2 m diameter in which a series of experiments were performed using Helium tracer to determine the Residence Time Distribution (RTD) at various normalized velocities i.e. with different degrees of gas-solids mixing. Both 2D and 3D simulations of the fluidized bed reactor are performed. The main purpose of this study is to understand the hydrodynamic behavior of a gas-solid fluidized bed reactor through a framework of Eulerian multi phase model and to analyze hydrodynamic behavior of the gas-solids mixing. As a first approach, the CFD model is validated using the experimental results of the residence time study. The numerical results of RTD corresponded well with the experimental findings indicating that the CFD model can be used to predict the performance of the fluidized bed reactor.

... The humps and trailing on the particle RTD curves suggest a complex micro-mixing behavior in liquid-solid systems originating from particle-scale behavior. Andreuxa et al. [21] Hydrodynamic and solids residence time distribution in a circulating fluidized bed: Experimental and 3D computational study CFB The numerical investigation of the solid mixing is deferred until later since the near-wall region where the solid phase down flow and mixing are predominant is not well predicted in spite of well-predicted vertical profiles of pressure. Zhang et al. [22] CFD simulation and experiment of residence time distribution in short-contact cyclone reactors ...

The present work focuses on a numerical investigation of the solids residence time distribution (RTD) and the fluidized structure of a multi-compartment fluidized bed, in which the flow pattern is proved to be close to plug flow by using computational fluid dynamics (CFD) simulations. With the fluidizing gas velocity or the bed outlet height rising, the solids flow out of bed more quickly with a wider spread of residence time and a larger RTD variance (σ²). It is just the heterogeneous fluidized structure that being more prominent with the bed height increasing induces the widely non-uniform RTD. The division of the individual internal circulation into double ones improves the flow pattern to be close to plug flow.

... Since the inventories are stabilized after 10 s, the following time averaged results are based on the post-simulation analysis of results with a frequency of 20 Hz from time 20 s to 40 s. Also, the tracer particles are added into the riser from 20 to 23 s and detected at riser height of 8.5 m in accordance with experimental measurements 54 . ...

For a long time, salt tracers have been used to measure the residence time distribution (RTD) of FCC particles. However, and due to limitations in experimental measurements and simulation methods, the ability of salt tracers to faithfully represent RTD’s has never been directly investigated. Our current simulation results using coarse grained CFD-DEM with filtered drag models show that the residence time of salt tracers with the same terminal velocity as FCC particles is slightly larger than that of FCC particles. This research also demonstrates the ability of filtered drag models to predict the correct RTD curve for FCC particles while the homogeneous drag model may only be used in the dilute riser flow of Geldart type B particles. Thus, the RTD of large scale reactors can be efficiently investigated with our proposed numerical method as well as by using the old-fashioned salt tracer technology.

... Since computational assets have expanded significantly at forcefully diminishing costs, specified computational data about the flow can these day be acquired even at small amount of the expense relating to experimental (Xia & Sun, 2002). The transient CFD simulations are performed to suggest on the usability of the multiphase approach for the prediction of the solid phase mixing and residence time distribution in the riser (Andreux, et al., 2008). ...

ABSTRACT
In this study, numerical simulations of a gas-solid fluidized bed reactor involving a two-fluid Eulerian multiphase model and incorporating the Kinetic Theory of Granular Flow (KTGF) for the solids phase have been performed using a commercial Computational Fluid Dynamics (CFD) software. The fluidized bed setup consists of 1.5 m height and 0.2 m diameter in which a series of experiments were performed using Helium tracer to determine the Residence Time Distribution (RTD) at various normalized velocities i.e. with different degrees of gas-solids mixing. Both 2D and 3D simulations of the fluidized bed reactor are performed. The main purpose of this study is to understand the hydrodynamic behavior of a gas-solid fluidized bed reactor through a framework of Eulerian multiphase model and to analyze hydrodynamic behavior of the gas-solids mixing. As a first approach, the CFD model is validated using the experimental results of the residence time study. The numerical results of RTD corresponded well with the experimental findings indicating that the CFD model can be used to predict the performance of the fluidized bed reactor.
Keywords
Computational Fluid Dynamics, fluidized bed, residence time distribution, gas-solids mixing, turbulence

... In general, there are two common CFD approaches to calculate RTD, the Pe is then calculated by the axial diffusion model (Hua and Wang, 2018). In Eulerian-Eulerian approach, investigators choose the species transport equation to calculate the flow of tracers and further obtain the global RTD curve (Andreux et al., 2008;Chen et al., 2019;Foust et al., 2017;Geng et al., 2017;Hua and Wang, 2018;Hua et al., 2014;Hua et al., 2019;Khongprom et al., 2012;Liu et al., 2012;Wadaugsorn et al., 2016;Zou et al., 2017). On the other hand, the Eulerian-Lagrangian approach does not use tracers, global RTD curve is obtained directly from the motion of particles. ...

Solids velocimetry based on cross-correlation algorithm has been widely used in multiphase systems. Recent studies have revealed that its measurement qualities depend critically on fluidization regimes, and the underlying mechanism was supposed to be the competition between solids convection and mixing. In this study, a method was proposed to analyze the local solids residence time distribution (RTD) from the results of Eulerian-Lagrangian simulations. Systematic simulations were then conducted to acquire the local solids RTDs in various gas-solids fluidization regimes. Afterward, the local Péclet numbers were quantified. It was found that the measurement qualities are intimately related to the local Péclet numbers and the solids convection-mixing competing mechanism. Present study revealed the underlying mechanism of the success and failure of cross-correlation based solids velocimetry, and proved that the cross-correlation algorithm is ideal for solids convection-dominated systems or regions in a system, but caution is needed when solids mixing is important.

... The gas-solid interphase fluctuating energy reflects the transfer between SGS-TKE of gas and SOM of particles for the LES-SOM model. Here, a modified Simonin model is used in this simulation [15,34,35]. ...

... Researchers have used theoretical, experimental and numerical methods to study the RTD of particles during the past several decades (Hua and Wang, 2018). Eulerian-Eulerian simulations have been extensively carried out to study the RTD of particles, the effects of such as operation conditions (solid flow rate and gas velocity), bed geometry, tracer injection time, and sampling frequency on the RTD of particles have been explored (Andreux et al., 2008;Khongprom et al., 2012;Hua et al., 2014;Geng et al., 2017;Zou et al., 2017a,b;Hua et al., 2019;Gao et al., 2020;Yu et al., 2021). However, Eulerian-Eulerian method normally faced the difficulty of using realistic particle size distribution in numerical simulations. ...

A GPU-based, massively parallel coarse-grained CFD-DEM method was adapted to study the scale-up effect of residence time distribution of particles in continuously operated multiple-chamber fluidized beds, where the bed is scaled up either by keeping a constant length of each chamber and increasing the number of chambers (Scaling method I) or by maintaining the number unchanged but increasing the length of each chamber (Scaling method II). It was shown that (i) the pressure drop and the residence time distribution of particles in a laboratory scale fluidized bed can be predicted reasonably well; (ii) when the solids feed rate is a constant (Operation I), the mean residence time of each type of particles scaled linearly as the bed length in both of Scaling methods I and II; (iii) when the solids feed rate is linearly increased with increasing bed length (Operation II), Scaling method I results in a continuously reduced ratio of mean residence time between coarse (medium) particles and fine particles, and the ratios level off with increasing bed length in Scaling method II; (iv) the mean residence time of particles can be inferred from the mean solids holdup obtained from CFD simulations and the mass fraction of particles at the inlet, thus offering a much faster way to estimate the mean residence time of particles; and (v) the equivalent number of perfect mixing tanks that corresponds to the mixing characteristics of real fluidized beds is linearly scaled as the bed length in Operation II, irrespective of Scaling methods.

... Many of reported studies have used continuum model, in which tracers have to be added into the system to collect the necessary data for analyzing RTD. There are generally two methods: one is using a two-fluid model to simulate the hydrodynamics of gas-solid flow and using a species transport equation to track the motion of solid tracers (Andreux et al., 2008;Liu et al., 2012;Hua et al., 2014;Wadaugsorn et al., 2016;Foust et al., 2017;Geng et al., 2017;Zou et al., 2017b;Chen et al., 2019;Hua et al., 2019). In this method, how to properly determine the diffusion coefficient in the species transport equation is always an issue that needs to be addressed (Hua et al., 2014;Chen et al., 2019). ...

Residence time distribution of particles is a critical parameter for proper design of gas-solid fluidized beds, especially in many non-catalytic solid conversion processes where it is highly desirable to match the residence time of a particle and its complete conversion time to achieve the synchronized conversion of particles of different sizes. However, the requisite of considering particle polydispersity and the long residence time of particles required by reaction kinetics together pose a great challenge to the computational fluid dynamics study of such systems. To this end, a GPU-based, massively parallel coarse-grained CFD-DEM method-the EMMS-DPM method (Lu et al., 2014) was extended to simulate the residence time distribution of polydisperse particles in a continuously operated multiple-chamber fluidized bed with a calculation of physical time of up to one hour. It was shown that the experimentally measured pressure drop of the bed or the solid holdup can be predicted reasonably well by the ad hoc drag models of non-spherical and polydisperse particles proposed in present study; the residence time distribution of particles of whole system can also be predicted correctly; and finally, the ratio of the mean residence time of coarse particles to that of fine particles is about three, which is insufficient to achieve the synchronized conversion of particles of different sizes according to an ideally theoretical analysis, great effort is needed to get a better match between the residence time and the compete conversion time of particles.

... In the current work, we propose to use the equations based on the Kinetic Theory of Granular Flow (KTGF) developed by Gidaspow [13] and available in the commercial software package Ansys Fluent. This theory's validity has been proven by many researchers [14][15][16][17][18] and was founded on the application used of the kinetic theory of dense gases to the particulate assemblies. This approach gives more perspicacity in terms of interactions between particles by assuming that binary collisions between hard spheres take ...

As most classical fluidization technologies, Circulating Fluidized Beds (CFB) are widely employed in chemical and physical operations. However, CFB Reactors still have some disadvantages such as the non-uniform solid particles distribution and the backflow of the solid particles near the wall, which deteriorate the system mixing, and lead to low system conversion/heat and mass transfer rate. To improve the CFB performance, we propose in the current work to study the effect of the ring baffle configuration on the fluidization system hydrodynamics using a multifluid Eulerian CFD model, incorporating the Kinetic Theory of Granular Flow. In this approach, two different types of ring baffles, circular and trapezoidal, were considered and the corresponding results were compared. The results revealed that the incorporation of ring baffles improved the system mixing and reduced the backflow near the wall. Nevertheless, the shape of baffles had a limited impact on the system hydrodynamics.

... In the current work, we propose to use the equations based on the Kinetic Theory of Granular Flow (KTGF) developed by Gidaspow [13] and available in the commercial software package Ansys Fluent. This theory's validity has been proven by many researchers [14][15][16][17][18] and was founded on the application used of the kinetic theory of dense gases to the particulate assemblies. This approach gives more perspicacity in terms of interactions between particles by assuming that binary collisions between hard spheres take ...

As most classical fluidization technologies, Circulating Fluidized Beds (CFB) are widely employed in chemical and physical operations. However, CFB Reactors still have some disadvantages such as the non-uniform solid particles distribution and the backflow of the solid particles near the wall, which deteriorate the system mixing, and lead to low system conversion/heat and mass transfer rate. To improve the CFB performance, we propose in the current work to study the effect of the ring baffle configuration on the fluidization system hydrodynamics using a multifluid Eulerian CFD model, incorporating the Kinetic Theory of Granular Flow. In this approach, two different types of ring baffles, circular and trapezoidal, were considered and the corresponding results were compared. The results revealed that the incorporation of ring baffles improved the system mixing and reduced the backflow near the wall. Nevertheless, the shape of baffles had a limited impact on the system hydrodynamics.

... In the dilute transport regime, the CFB riser of Andreux et al. 81 was selected as the test ...

This study focused on assessing the effect of mesoscale solid stress in the coarse grid TFM simulation of gas‐solid fluidized beds of Geldart Group A particles over a broad range of flow regimes, including bubbling, turbulent, fast, and pneumatic transport fluidization regimes. Particularly, the impact of mesoscale solid pressure, mesoscale solid viscosity, and mesoscale solid stress anisotropy were investigated by comparing six different coarse grid TFM settings. Compared with the available experimental data, it is found that both the kinetic theory based TFM with only drag correction and the filtered TFM can predict the flow behavior in all fluidization regimes. Mesoscale solid pressure and viscosity have the opposite impact on flow hydrodynamics; they compete and offset each other, which confirms the assumption employed in many previous studies that the mesoscale solid stress could be neglected in coarse grid TFM simulation.
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Olive oil production urges the energy companies to exploit the potential of the residues as biomass fuels for clean energy production. Circulating fluidized bed (CFB) gasifier gains global interest within these several years due to its promising solution for converting biomass material to renewable energy. However, the multi-physics processes and multiscale structures inside the gasifier impede the experimental measurements. As an alternative, a reactive multiphase particle-in-cell approach is developed in this work to simulate the gasification process of olive oil waste in a pilot-scale full-loop CFB gasifier. After the model validation, the heat transfer properties of solid phase and the effect of size-induced segregation on solid thermochemical properties are explored. The results show that the low-temperature biomass particles injected highly influence the spatial distribution of solid temperature and solid heat transfer coefficient (HTC). A larger particle size gives rise to a higher HTC. Moreover, the temperature and HTC of biomass are larger than that of sand. A wide and narrow residence time distribution of sand in the riser and cyclone can be observed. The scale of the biomass dispersion is respectively larger and the same as that of sand in horizontal and vertical directions. Particles in the dense region have a smaller HTC, Reynolds number, and temperature. Superficial gas velocity improves the uniformity of solid distribution. Elevating the gas velocity and initial bed temperature enhances solid dispersion intensity.

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The Eulerian multi-fluid approach is a powerful numerical tool to investigate high-velocity gas-solid flows in vertical risers. The overall hydrodynamic behaviors of gas-solid flows are significantly modified by the existence of mesoscales, such as streamers and clusters in dilute flows. Clusters and streamers continuously occur in risers by a reason of local instabilities, such as damping of fluctuating motion of particles by the interstitial fluid, inelastic collisions, the non-linear drag between phases (Agrawal et al., 2001). The typical length scale of mesoscales is in the order of particle diameters and the time scale varies between and (De Wilde, 2005). Although formations and breakage of mesoscales structures can be captured by multi-fluid formalism and transport equations developed in the frame of the kinetic theory of granular media on a small domain, large ranges of spatial and temporal variations of these structures restrict the resolution of calculations for large industrial units due to computational cost. To account for the effect of mesoscales on the macroscopic behavior in coarse grid simulations, the analogy can be constructed with large eddy simulation of single phase turbulent flow. These effects can be taken into account by subgrid scales through additional closure relations. The key feature in the present study is the proposition of the subgrid model for monodisperse gas-solid flow which takes into account the effects of mesoscales and validation of this model by experimental data.
In this paper, the modelling approach is based on the multi-fluid model formalism that involves mean separate transport equations of mass, momentum and energy for each phases. Interactions between phases are coupled through interphase transfers. Two transport equations, developed in the frame of kinetic theory of granular media supplemented by the interstitial fluid (Balzer et al., 1996), were solved to model the effects of velocity fluctuations and inter-particle collisions on the dispersed phase hydrodynamic. The gas phase is predicted using Large Eddy Simulation. Concerning the transfers between the phases with non-reactive isothermal flow, the drag and Archimede forces are accounting for the momentum transfer. Three-dimensional simulations are performed by the numerical code - - of a french industrial consortium comprised of EDF / CEA / AREVA_NP / IRSN, which has been extended by Institut de Mécanique des Fluides de Toulouse (IMFT). The point has to be stated that this study does not discuss the multi-fluid model, only proposes a different closure equation for an effective drag coefficient for the interfacial momentum transfer which is explicitly filtered by the grid size.
The effects of the mesoscale structures have been investigated by several authors. The pioneer work done by Agrawal et al. (2001) and it is remarked that coarse grid simulations overestimate the drag force. Wang (2006) proposed a structured dependent drag force by the energy-minimization multi-scale model. Addition to these works, Heynderick (2004) has taken into account the clusters effect by the concept of effective drag with considering the solid particles to be a part of a cluster and also to be present as individual particles. Igci (2007) proposes filter size dependent closures for the effective drag.
In the present modelling approach, we propose the following decomposition of the filtered interfacial momentum transfer:
(1)
where is the filtered solid volume fraction (the "overline" defines the filtered quantity),
(2)
In (), is the particle relaxation time scale. The velocity is the subgrid contribution that we propose to model as:
(3)
where the non-dimensional grid size, , is defined as follows:
(4)
where is the control volume of cell. The subgrid model construction has been done by "a priori" tests. High-resolution numerical predictions have been computed with fine computational grid ensuring results without dependency on the grid resolution. These high-resolution data are filtered by several filter widths based on explicit grid sizes. Then, the subgrid drift velocity has been constructed by difference between filtered and high-resolution data.
The results obtained by the subgrid model are validated with experimental data of Andreux (2008) and Andreux (2001). The riser is a scaled cold circulating fluidized bed of high having a square cross section of . Typical FCC particles (A-type) with density and mean diameter were conducted. The density of air is set to and dynamic viscosity is equal to . Averaged volume fractions of solid and pressure gradients obtained with and without subgrid model are compared in Fig.. The unphysical accumulation at the bottom of the riser vanishes and the pressure gradient obtained by fine mesh is in a good agreement with the one obtained by subgrid model.
Figure: (a) Averaged volume fraction solid distribution and (b) pressure gradient along streamwise direction.
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A Computational Particle Fluid Dynamics (CPFD) approach was applied to investigate the solids residence time distribution (RTD) and back-mixing behavior in a circulating fluidized bed (CFB) riser. The comparison between the simulation results and the experimental data indicates that the CPFD method was capable to predict the hydrodynamics and solids mean residence time. It was found that the solids residence time exhibited a non-uniform distribution both in the axial and in the radial directions of the riser. Even in the dilute phase transport (DPT) regime, the predicted solids RTD curves had the feature of an early peak and an extended tail, indicating that the solids flow deviates from plug flow and exhibits back-mixing. The solids back-mixing mainly occurred in the lower part of the riser, which provided significant implications for the industrial applications of the CFB reactors since most of the chemical reactions and heat/mass transport processes occur at the lower part of the riser. It is important to minimize the solids back-mixing at the lower part of the riser for the industrial CFB applications like the FCC.

The gasification characteristics of herb residue for producing syngas in a pilot-scale circulating fluidized bed were investigated experimentally in this paper. The results indicated that the gas composition and tar yield were affected by the parameters including the equivalence ratio (ER), biomass feeding rate (FR), and steam-to-biomass mass ratio (S/B). The concentrations of combustible gases (H-2, CO, CH4, and CnHm) showed a decreasing trend with increasing ER, while the lower heating value (LHV) exceeded 4.0 MJ/N.m(3) in all cases when the ER was lower than 0.4. An increase in the ER can improve the reaction temperature, facilitate carbon conversion, and decrease the tar yield. The LHV increased gradually from 4.2 to 5.7 MJ/N.m(3) with an increase in the FR from 210 to 352 kg/h. The cold gas efficiency and carbon conversion efficiency reached their maximum values of approximately 68% and 93% at a feeding rate of 352 kg/h, whereas both of them decreased with a further increase in the feeding rate. The supplement of steam into the gasifier improved the LHV of the product gas, which reached a maximum value of about 6.0 MJ/N.m(3) when S/B was 0.23-0.43 and the cold gas efficiency and carbon conversion efficiency were within 62-73% and 87-94%, respectively.

With the Computational Particle Fluid Dynamic (CPFD), which is based on the scheme of Multi-Phase Particle-In-Cell (MP-PIC), the present work studied the flow hydrodynamics and solids back-mixing behaviors in the riser with smooth and abrupt exit geometries. It was found that the flow hydrodynamics and solids back-mixing behaviors are quite different in the riser with different exit geometries. While particles can uniformly flow out of the riser with smooth exits with relatively lower residence time, part of the particles tend to be reflected back into the riser with abrupt exits. Different mechanisms were proposed to explain the distinct solids back-mixing behaviors in the riser with smooth and abrupt exit geometries. The moderate solids back-mixing in the riser with smooth exits is mainly due to the dynamic formation and dissolution of particle meso-scale structures/particle-clusters at the bottom part of the riser, while the intense solids back-mixing in the riser with abrupt exit geometries is the combined results of the particle downward flow from the riser top and the dynamic formation and dissolution of particle meso-scale structures at the riser bottom. The present work implied that the riser exit geometry should be carefully specified in the modeling study of the CFB riser.

Flow behaviors in the V-baffled, Disk-donut and two-stage annular industrial resid fluid catalytic cracking (RFCC) strippers were investigated by using computational fluid dynamics (CFD) method. The volume fraction distribution and the residence time distributions (RTD) of catalysts were obtained at the outlet in the way of coupling the tracer technology. The parameters indicating mixing characteristics, i.e., mean residence time t m, dimensionless variance σθ 2, and Peclet number were analyzed, and the fractions of dead, plug and well-mixed volumes were obtained. The results show that the density difference between the outer and inner loop in the annular stripper is the driving force for catalysts' annular flow. The V-baffled stripper possesses the smallest t m and Pe, and the biggest σθ 2. Meanwhile, the dead volume fraction in the V-baffled stripper is about 40% while the plug volume fraction is only 15.8%. All above demonstrate the serious back-mixing and low stripping efficiency in the V-baffled stripper. Compared to the disk-donut stripper, the two-stage annular stripper exhibits bigger σθ 2 and smaller Pe, standing for stronger overall back-mixing. In terms of the dead volume model, however, the plug and the dead volumes are respectively 26.8% and 32.3% in the two-stage annular stripper, higher than that in the disk-donut stripper and causing a higher stripping efficiency.

Based on the renormalization group (RNG) K-ε turbulence model, the model coefficient and near-wall treatment were modified. The modified RNG K-ε turbulence model was applied to the numerical simulation of single-phase strongly rotational flow in a cyclone separator. And the simulation results of RNG K-ε model, the advanced RNG K-ε model and Reynolds stress model (RSM) were compared with the experimental data. Then, numerical simulation of the gas and solid phase flows in cyclone separator was carried out by applying Eulerian-Lagrangian model (Turbulence flow model of RSM) and Eulerian-Eulerian model (Turbulence flow model of the advanced RNG K-ε model) respectively. The effects of different two-phase models on the flow behaviour and solid distribution in cyclone separator were studied. It was shown that the agreement between the results of the advanced RNG K-ε model and RSM and those of experiments were obtained. The advanced RNG K-ε model can be more useful in practical engineering calculation due to its time-consuming dramatically decreased. The Eulerian-Eulerian model (Turbulence flow model of the advanced RNG K-ε model) also can preferably reappear the flow characteristics in cyclone separator, which can be useful for design optimization of cyclone separators.

The characteristics of residence time distribution (RTD) of solid particles (Geldart B) with the pulse particle tracer approach in two cold rectangular bubbling fluidized beds (BFB) with continuous particle flow were experimentally investigated. The parameters tested were superficial gas velocity (U), feeding rate of particles (G s), particle bed height (H) and particle size (d p), and the used tracer was coal particles. The results showed that G s, H and dp were the major influential factors, while U affected little. The particle flow pattern in BFB reactor lied between those of the ideal plug flow reactor and completely stirred reactor (CSTR), it was close to the plug flow when the particle bed height was lower and G s, larger, whereas the flow was much closer to the full mixing flow of the CSTR at the higher particle bed height and smaller G s. The averaged residence time of particles was calculated as the value of 9%~18% below of the plug flow for the design of BFB based on the present experimental data.

Solid mixing process plays a crucial role in evaluating the reaction performance of multiphase reactor. However, there still lacks the systematic research on solid mixing for the multistage circulating fluidized bed with enlarged sections. Solid mixing mechanism in a multistage riser is investigated numerically in this study. Some individual characteristics of solid mixing are found. It is shown by analyzing residence time distributions that solid mean residence time and the degree of solid dispersion increase with the increasing solid flux or the decreasing superficial gas velocity. Nevertheless, particle diffusion coefficient increases as solid flux decreases or superficial gas velocity increases. Moreover, the diffusion coefficient in enlarged sections decreases with the increasing height, which is contrary to the variations in traditional risers. Compared with the traditional riser, particle diffusion is weak, but overall solid mixing is enhanced in the multistage riser. Furthermore, two mixing patterns that gas-solid flow develops towards the plug-type flow in the center region of riser and the mixed-type flow in the enlarged section are identified. In addition, the dominant recirculation time of solids in the enlarged section is predicted as 1.5 s under examined cases.

Traditional methods for measuring the residence time distribution (RTD) of particles in a fluidized bed are complex and time-consuming. To this regard, the present work proposes a new measurement method with remarkable efficiency based on digital image analysis. The dyed tracers are recognized in the images of the samples due to the difference of colors from bed materials. The HSV and the well-known RGB color space were employed to distinguish the tracers. By enhancing the Saturation and the Value in HSV and adjusting the gray range of images, the recognition error is effectively reduced. Then the pixels representing the tracers are distinguished, based on which the concentration of the tracers and RTD are measured. The efficiency, accuracy and repeatability of the method were validated by RTD measurements experiments. The method is also fit for distinguishing the target particles from multi-component systems consisting of particles of different colors.

This work presents a novel technique with fast response for Residence Time Distribution (RTD) measurements in gas-solid unit operations (e.g., fluidized bed reactors). This technique is based on an optical method which eliminates the requirement of knowing the velocity and concentration profiles at the exit section of the system. Experiments were carried out with SiC particles and a phosphorescent pigment used as a tracer. A concentration measurement system was developed to measure the tracer concentration in SiC/pigment mixtures. The corresponding pigment concentrations were evaluated at the bottom of this system using a photomultiplier. The pigment concentration was derived from the integral of the signal intensity received by the photomultiplier. Then, a calibration curve was established which provided the empirical relationship between the integral and pigment concentration. In order to validate this RTD measurement technique, a series of experiments was performed in a bubbling fluidized bed and the effect of the bed height was studied. It was shown that the experimental RTD curves were in good agreement with the theoretical RTD of bubbling fluidized beds. This solids RTD measurement technique can be used to provide a better understanding of the hydrodynamics of complex solids unit operations.

Fluid dynamic characterization for a set of three serial rectangular based spouted beds (RBSB) using sawdust or turnip seeds, were made. In batch experiences, the minimum spouting velocity (Ums) and the maximum pressure drop (ΔPmax) were determined based on the bed height and moisture content. With respect to the continuous solid feed experiences, initially the conditions that allowed the stationary operation for 1, 2 and 3 beds connected in series, were determined. Following, injecting colored particles and with an image analysis it was possible to determine the residence time distribution (RTD). When compared with expressions from literature, good agreement was found for Ums, whereas for ΔPmax an expression is proposed that includes the sphericity of the particles. The RTDs were adjusted with the tank in series model, finding that the effects of solids feed rate, air flow and moisture content are significant for each solid RTD.

Particle clusters are well acknowledged to affect the hydrodynamics and overall performance of gas-solid fluidized beds. Since one of the first reports on the clustering phenomenon in 1948, the understanding of particle clustering has been rigorously attempted via both modeling and experimental efforts, with significant traction gained especially in the last few decades. Accordingly, the current review targets at providing a comprehensive landscape of the experimental cluster trends to summarize the findings, in particular on circulating fluidized bed (CFB) risers, to date. More questions than answers seem to have sprouted from the abundant experimental data available, which impedes model development. The quantitative comparison of cluster characteristics across studies must be treated with caution, because of (i) different riser configurations, instruments and analysis methods, which can lead to discrepancies of an order-of-magnitude; (ii) the impact on cluster characteristics by an interplay of a host of factors, hence the influence of a single parameter is not straightforward, even within the same study; (iii) the irregularity in the form of clusters, hence the definition and/or measurement of the various cluster characteristics differ; and (iv) the general lack in the reporting of the actual particle size distribution. What is remarkable is that the trends of the cluster characteristics are relatively consistent despite different experimentalists and units.

Fluidised bed technology is a very common industrial process and has a wide range of applications in process engineering. Though indirectly, a common way to infer the end product uniformity is through investigating the solid residence time distribution (RTD) in the system. A good understanding of the particle RTD is crucial for the proper design, optimisation, and scale-up of a fluidisation process. Flexible ribbon particles have a very different flow behaviour in a fluidised bed compared to that of spheres which in turn influences the RTD of the particles. However, this issue is still not very well addressed to date. In this paper, a double chain model is adopted to model cut tobacco strips in a fluidised bed riser. The spring constants of this chain model are calibrated, and the model is validated against experimental datum. Finally, the particle RTD as a function of different process parameters is investigated.

In this computational study, we model the mixing of biomass pyrolysis vapor with solid catalyst in circulating riser reactors with a focus on the determination of solid catalyst residence time distributions (RTDs). A comprehensive set of 2D and 3D simulations were conducted for a pilot-scale riser using the Eulerian-Eulerian two-fluid modeling framework with and without sub-grid-scale models for the gas-solids interaction. A validation test case was also simulated and compared to experiments, showing agreement in the pressure gradient and RTD mean and spread. For simulation cases, it was found that for accurate RTD prediction, the Johnson and Jackson partial slip solids boundary condition was required for all models and a sub-grid model is useful so that ultra high resolutions grids which are very computationally intensive are not required.. We discovered a 2/3 scaling relation for the RTD mean and spread when comparing resolved 2D simulations to validated unresolved 3D sub-grid-scale model simulations.

Maleic Anhydride (MA) production by selective oxidation of n-butane in a Multi-Tubular Fixed Bed reactor is constrained by the flammability limits. The use of Fluidized Bed circumvents this constraint but suffers from high back mixing. The Circulating Fluidized Bed (CFB) reduces the back mixing of the catalyst and enhances the catalyst activity by reactivating the catalyst. A simple reactor model with suitable hydrodynamic and kinetic models at the operating conditions of both the pilot and commercial MA CFB reactors is proposed. A dispersion model with variable gas density is used for modeling the hydrodynamics of these reactors. The reactors' configurational complexities are also accounted for in the model. The data fitting exercise of the proposed reactor model is performed. The proposed method simultaneously minimizes the total bias based on the individual biases for each component of the multi component reactor system and the total error in a multi-objective framework.

Using the validated simulation model developed in part one of this study for biomass catalytic fast pyrolysis (CFP), we assess the functional utility of using this validated model to assist in the development of CFP processes in fluidized catalytic cracking (FCC) reactors to a commercially viable state. Specifically, we examine the effects of mass flow rates, boundary conditions (BCs), pyrolysis vapor molecular weight variation, and the impact of the chemical cracking kinetics on the catalyst residence times. The factors that had the largest impact on the catalyst residence time included the feed stock molecular weight and the degree of chemical cracking as controlled by the catalyst activity. Because FCC reactors have primarily been developed and utilized for petroleum cracking, we perform a comparison analysis of CFP with petroleum and show that the operating regimes are fundamentally different.

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.

The raise of environmental concerns in the past decades consequently increased the need of obtaining cleaner sources of energy. Among the studied alternatives, second generation biofuels (produced from non-food resources) are one of the most promising solutions and nearly reached industrialization. The production of cellulosic bioethanol is one of the possibilities of second generation biofuels, and the studies involving the use of cellulosic compounds to produce bioethanol recently increased. Its production involves four dependent steps: pretreatment, enzymatic hydrolysis, fermentation and distillation. This work considered the pretreatment stage, aiming at modifying the structure of the lignocellulosic biomass so that cellulose becomes more accessible to enzymatic hydrolysis step.
This work particularly focused on the biomass flow characterization in the transport and compression screws involved in the pretreatment step of an industrial-scale process. The main challenge was firstly to perform measurements on an industrial-scale device working under harsh conditions. Residence time distribution (RTD) experiments were thus performed using a novel methodology adapted to these working conditions. Sodium carbonate was selected as a tracer. Due to the reaction with the acidified biomass, both electrical conductivity and pH were monitored at the exit of the screws. A chemical model was developed, allowing the determination of tracer concentrations from the measured data. The measurements obtained were compared with three optimized models: a combination of plug flow and continuous stirred tank reactor in series (PFR-CSTR), plug flow with axial dispersion (AD) and a model based on the Zusatz function. The results of this work pointed out the non-plug flow behavior of these screws in their standard working conditions. In accordance with the physical motion of the tracer inside the screws, the use of the PF-CSTR is recommended for representing RTD inside screws in conditions in which backflow is likely to occur.

Bubbles rising through fluidized beds at velocities several times superficial velocities contribute to solids backmixing. In micro‐fluidized beds, the walls constrain bubble sizes and velocities. To evaluate gas‐phase hydrodynamics and identify diffusional contributions to longitudinal dispersion, we injected a mixture of H2, CH4, CO, and CO2 (syngas) as a bolus into a fluidized bed of porous fluid catalytic cracking catalyst while a mass‐spectrometer monitored the effluent gas concentrations at 2 Hz. The CH4, C0, and CO2 trailing RTD traces were elongated versus H2 demonstrating a chromatographic effect. An axial dispersion model accounted for 92% of the variance but including diffusional resistance between the bulk gas and catalyst pores and adsorption explained 98.6% of the variability. At 300 °C, the CO2 tailing disappeared consistent with expectations in chromatography (no adsorption). H2 and He are poor gas‐phase tracers at ambient temperature. We recommend measuring RTD at operating conditions. This article is protected by copyright. All rights reserved.

Electrostatic effects are commonly found in gas-solid fluidized beds. With an electrical field applied in a gas-solid fluidized bed, the charged particles there would be separated according to the opposite charge polarity. A charge-to-mass ratio test showed that quartz can easily be given a negative charge when tribo-charging with coal. A binary particle mixture was employed to explore the enrichment effect in an electrical-field fluidized bed unit. The results showed that the mass fraction of quartz in the products decrease gradually from negative plate to positive plate. The increase of fluidization time, plate voltage and gas velocity, along with low bed height, were beneficial to the improvement of the enrichment effect. The mass fraction of quartz close to the positive plate was >40%, while that of negative was around 10%. This work demonstrates the possibility of separating fine coal using a fluidized bed with applied electrical field.

Cross-flow bubbling fluidized beds (BFBs) have been widely used in dual fluidized bed systems such as chemical and heat looping. Understanding the residence characteristics of solids in such system is important for better design and optimization of reactors. Previously we experimentally measured the residence time distributions (RTDs) of sands in a cross-flow rectangular BFB by using coal particles as tracer. A computational investigation of solids RTD using multi-fluid Eulerian method combined with the species transport equation showed that the RTD of sands could be correctly represented by that of coal particles, and the simulation results well agreed with experimental data. Parametric studies demonstrated that, under the considered operation conditions, the influence of tracer injection time period on the predicted solid residence times was nearly ignorable. Simulation results revealed that in the investigated cross-flow BFB the solids RTD is closely related to solids inventory and solids flux. Through proper data processing, it was found that the descending part of solids RTD profile can be uniquely fitted by an empirical exponential function. A semi-empirical approach was thus developed and further validated, for the first time in the literature, to predict the entire profile of solids RTD, in which the ascending part of solids RTD profile is obtained through CFD simulation whereas the descending part is given by the fitted empirical exponential function.

Recent theories for rapid deformations of granular materials have attempted to exploit the similarities between the grains of deforming granular mass and the molecules of a disequilibrated gas. Methods from the kinetic theory may then be used to determine, for example, the form of the balance laws for the means of density, velocity, and energy and to calculate specific forms for the mean fluxes of momentum and energy and, in these dissipative systems, the mean rate at which energy is lost in collisions.

An approximate equation governing the turbulent fluid velocity encountered along discrete particle path is used to derive the fluid/particle turbulent moments required for dispersed two-phase flows modelling. Then, closure model predictions are compared with results obtained from large-eddy simulation of particle fluctuating motion in forced isotropic fluid turbulence.

A horizontal rapid gas-particle separator dedicated to the Fluid Catalytic Cracking process was tested on a small scale cold Circulating Fluidized Bed. Air (density 1.2 kg/m3, dynamic viscosity 1.8×10-5 Pa.s) and typical FCC particles (density 1400 kg/m3, mean diameter 70 mm) are used. The inlet gas velocity is kept constant at 7.3 m/s while the inlet solid loading and the separator dipleg back pressure range from 0 to 16 kg/kg and 100 to 500 Pa, respectively. Solid collection efficiency and pressure drop are studied. A model based on cyclone concepts is proposed. The solid collection efficiency increases with the inlet solid loading and reaches an asymptotic value close to 95 % when the inlet loading is above 5 kg/kg. Two flow regimes are observed in the separator dipleg through the range of inlet solid loadings, related to the available flow section modification and the interstitial gas entrainment. At constant gas collection efficiency, the separator pressure drop is maximum under single-phase flow conditions and reaches a minimum when the inlet solid loading is close to 2.5. The pressure drop increases again for higher inlet solid loading. The final modeling allows good prediction of the separator operation for all inlet solid loading conditions when the gas collection efficiency is at 100 %.

In the last decade considerable progress has been made in the area of hydrodynamic modeling and numerical simulation of gas-solid fluidized beds. Broadly speaking, two different approaches can be distinguished based on the treatment of the particulate phase, continuum (Eulerian) and discrete particle (Lagrangian) models. Discrete particle models solve the Newton equation of motion for each individual particle, taking into account the effects of particle collisions and forces acting on the particle by the gas. The gas flow is calculated from volume-averaged Navier-Stokes equations accounting for the porosity of the bed and for the force acting on the gas by the particles in the frame of the PIC method. The two-fluid model is based on the continuum approach for the dispersed phase leading to compute separate Eulerian equations (averaged Navier-Stokes equations) for interacting media. Owing the continuum representation of the particulate phase, two-fluid models require additional closure laws to describe the transport properties of the particulate phase. This paper presents a detailed comparison of the results obtained by using the two different approaches for the prediction of a pseudo two-dimensional gas-solid fluidized bed. Time averaged fields from both model simulations of the mean and fluctuating velocities, gaseous pressure and solid concentration are compared. The effect of grid refinement, particle-wall interaction and particle-particle collision model are studied.

This paper presents a multi-fluid modeling approach, developed in the EDF 3D code Saturne_Polyphasique@Tlse, with separate transport equations for the mean velocity and fluctuant kinetic energy for each particulate phase. The collisions between unlike particles lead to additional source terms accounting for the mean and fluctuant momentum transfer between classes and modification of the effective transport property (viscosity, diffusivity) modeling. Simulation results for a cold Circulating Fluidized Bed (CFB) pilot (square section of 0.96 m2, total height 10.4 m) with three particle size classes are presented. The polydispersed modeling approach allows to improve the 3D unsteady prediction of gas-solid circulating fluidized bed hydrodynamic, especially in regards of the circulation of the largest particles.

A two-equation turbulence model has been developed for predicting two-phase flows. The two equations describe the conservation of turbulence kinetic energy and dissipation rate of that energy for the carrier fluid in a two-phase flow. They have been derived rigorously from the momentum equations of the carrier fluid. Closure of the time-mean equations is achieved by modeling the turbulent correlations up to third order. The new model eliminates the need to simulate in an ad hoc manner the effects of the dispersed phase on turbulence structure. Preliminary testing indicates that the model is successful in predicting the main features of a round gaseous jet laden with uniform-size solid particles.

Compared to mechanical valves, nonmechanical solids feed and recycle devices can improve process reliability and simplify operation when transferring solids, especially at high temperatures and/or high pressures. The non-mechanical devices use only aeration and piping geometry to control the flow rate of solids, have no moving parts, are inexpensive, and can be manufactured “in-house”. However, like mechanical devices, they must be designed properly. The principles of operation of these nonmechanical devices and where they can be used in circulating fluidized bed systems is discussed. Information on the design and operation of nonmechanical feed and recycle devices is presented.

Tests were conducted in a 30.5-cm-diameter riser with 76 μm FCC catalyst to determine the degree of gas/solid contacting in the “fast-fluid bed” regime. Data were obtained at superficial gas velocities of 3.7 to 6.1 m/s and solid fluxes of 98 to 195 kg/s-m². The conveying gas was air at ambient temperature and 103 kPa. Data were obtained on axial pressure profiles, particle velocity and mass flux as a function of radial and axial position, radial and axial gas dispersion, and solids residence time distributions. Density and voidage profiles were calculated from these data.

A new type of probe for sampling from relatively dense flowing gaseous suspensions of particulate solids in ducts is described. The probe is non-isokin

Catalytic cracking units are present in most refineries to convert a large fraction of heavy oils. Over the last 50 years, catalyst development and improvement of the technology in the reaction zone lead to a continuous evolution, that is still going on, of this process. In this paper, R&D tools for technology are discussed through the development of riser separation systems and catalyst coolers. Catalyst circulation aspects in the reaction zone are also discussed.

The residence time distribution (RTD) of solids is essential for the design of CFB reactors where conversion proceeds with time. The residence time distribution for the solids is measured at different working conditions. The resulting average residence times are correlated as function of gas velocity and solids circulation rate and are compared with literature data. In order to predict the RTD of the solids, the solids/gas flow is firstly described by a plug flow with dispersion. A fitting procedure gave experimental Péclet numbers, which were correlated as function of gas velocity and solids circulation rate. A more fundamental approach based on the core/annulus flow structure is thereafter used to predict the residence time. The riser is divided in a dilute core with particles flowing upward and a denser film moving slowly downward along the wall. Particle interchange between the two regions is described by a convective interchange flow. The model is used to predict experimental RTD-curves. The interchange flux between core and annulus corresponds well with radial fluxes reported in literature. Although the RTD is qualitatively well described, experimental curves show a higher dispersion than the calculated ones. To improve the core/annulus approach, further research is necessary.

Attention is given to a new approach for the modeling of the statistical characteristics of heavy particle clouds in turbulent two-phase flows, which is proposed taking into account the dragging by the fluid
turbulence and the interparticle collisions. This model is based on separate transport equations for the dispersed phase Reynolds stress tensor components and the fluid-particle velocity correlation. The
proposed closure assumptions make it possible to compute dispersed dilute two-phase flows and lead to classical results derived by applying kinetic theory when interparticle collision is the dominating
phenomenon. The model is used to predict axisymmetric dilute particle-laden jets and a confined swirling gas-particle flow. The numerical results compare favorably with available experiment results. The model accounts for, among other phenomena, the influence of the radial rms velocity measured at the nozzle exit on particle dispersion and the high anisotropy of the particle fluctuation motion observed in
the main flow.

Longitudinal solids mixing was studied experimentally in circulating fluidized bed risers of internal diameter 0.152 m and 0.305 m. Superficial gas velocity and mean solids flux used were 2.8–5.0 m/s and 5.0–80 kg/m2·s, respectively, and the bed solids had a surface volume mean diameter of 71 μm and a particle density of 2,456 kg/m3. A sodium chloride tracer was used in impulse injection experiments. A simple, one-dimensional dispersion model describes measured solids mixing satisfactorily. Peclet numbers (UoL/Dz) found, in the range 1.0–9.0, were correlated with the riser diameter and mean solids flux. The modeling approach described here permits residence time distribution curves to be calculated directly from the knowledge of superficial gas velocity, mean solids flux, and riser diameter. Longitudinal solids mixing in the riser decreased with increasing riser diameter. The results are consistent with recent hydrodynamic studies.

This article presents preliminary fluid dynamic simulation results of ethylene polymerization dense fluidized bed using the two-phase flow numerical code ESTET-ASTRID developed by Electricité de France for CFB boilers and based on the two-fluid modelling approach. The continuous phase consists of gas and the dispersed phase consists of catalyst particles. The particle fluctuating motion is modelled using two-separate transport equations, on the particle kinetic energy and the fluid–particle covariance, developed in the frame of kinetic theory of granular medium accounting for particle–particle and fluid–particle interactions. Time-dependent 2D and 3D simulations have been performed for industrial and pilot reactor operating conditions. The numerical predictions are in good qualitative agreement with the observed behaviour in terms of bed height, pressure drop and mean flow organization, such as the down falling of the PE particle layer along the walls. Moreover, these simulations help to provide information about instantaneous and time-averaged solid concentration and velocity fields. Characteristic mechanisms and influence of model closure assumptions on flow predictions are also investigated. Finally, such numerical simulations look very powerful, when validated on exhaustive data collection, to improve design and performance of industrial facilities and to provide insight into the complex physical mechanisms involved. Copyright © 2003 John Wiley & Sons, Ltd.

Numerical simulations, based on an Eulerian approach, of a freely bubbling fluidized bed (BFB) are performed where emphasis is put on the importance of the inlet boundary conditions (influence of the pressure drop of the air distributor on the state of fluidization). The numerical results are compared with local instantaneous pressure measurements and time-averaged measurements (bed height, mean particle concentration). The closure of the Eulerian model is treated as follows: the drift velocity is modelled with a binary dispersion coefficient, gas-phase (continuous phase) fluctuations are modelled with a modified two-equation k1–ϵ1 model, and particle-phase (discrete phase) fluctuations are also described by a two-equation k2–k12 model derived from the kinetic theory of granular flow (modified to account for the interstitial gas) and a Langevin equation. The numerical computations (of a bubbling fluidized bed) predict qualitatively the experimental values, which shows that there is a coupling between the bed and the air supply system.

Non-mechanical valves, especially the L-valves, have been used extensively in fluidized beds and circulating fluidized beds for solids recycling or to serve as a pressure seal. Despite their widespread use, reliable characterization equations for L-valves are still not available, though design principles have been proposed by Knowlton of the Institute of Gas Technology. This paper presents a set of L-valve equations which relate the solids flow rate to the L-valve design, aeration rate, and pressure drop across the L-valve. The equations were developed by visualizing a L-valve as a pneumatically-operated pseudo-mechanical valve. The valve opening is activated pneumatically by L-valve aeration. The physical interpretation of the L-valve operation corresponds to that observed by Knowlton and other researchers, and the proposed equations correlate well with the extensive data base. The data base covers L-valve diameter from 38 mm to 152 mm for particles ranging from 175 μm to 509 μm, particle density ranging from 1230 kg m−1 to 4150 kg m−3, and shape factor ranging from 0.56 to 0.915.

Improvement of operating conditions of existing circulating fluidised bed combustor units, as well as attempts to scale up present units to larger ones, are mainly based on empirical correlation or simplified scaling laws. Moreover, it is known that the details of the unit geometry (entry and exit design, horizontal cross-section shape, secondary air location and configuration) have a great importance in the overall plant performance. Improvement of our understanding of the complex hydrodynamic behaviours involved in these processes requires refined and local physical models. The approach retained at the Laboratoire National d'Hydraulique of EDF for the prediction of the two-phase flows in complex geometries is based on the two-fluid model formalism, where both phases are characterised by their first velocity moments (volumetric concentration, mean velocity and second order fluctuating velocity correlation tensors). Separate transport equations are written for each moment with appropriate closure assumptions for unknown terms such as the momentum exchange between the two phases and the effective stress tensors of both phases.

A general classification of two-phase flows and a number of possible ways to formulate two-fluid models are discussed. The two-fluid model is adopted, and a general procedure to develop such a model is presented. The local instantaneous equations of mass and momentum are derived together with the corresponding jump conditions. Volume, time and ensemble averaging procedures are discussed, and averaged equations and jump conditions are derived using a general averaging operator. A Reynolds decomposition and weighting procedure is applied to obtain the final equations. The equations necessary to close the system, so-called closure laws, are discussed. The mechanisms contributing to the viscosity of both phases and mixture viscosity models are presented. The particle pressure is discussed, and some simple models based on the modulus of elasticity concept are given. The interfacial momentum transfer term is discussed in detail, and a study of common models of the drag function is presented. A discussion of turbulence models for the gas and particulate phases is included. A summary and critical assessment of published work on simulations of hydrodynamics in bubbling and circulating fluidized beds are also presented.

Numerical simulations of a stationary bubbling fluidized bed (BFB), based on an Eulerian approach, are performed. The closure of the Eulerian model is treated with two-equation models. Emphasis is put on the importance of three dimensionality in the simulations. The numerical results are compared to local instantaneous pressure measurements and time-averaged measurements (bed height and probability density function (pdf) of the spatial distribution of particles). The results of the simulations show that two-dimensional simulations should be used with caution and only for sensitivity analysis, whereas three-dimensional simulations are able to reproduce both the statics (bed height and pdf of the spatial distribution of particles) and the dynamics (power spectrum of pressure fluctuations) of the bed. The non-sphericity of the particles is accounted for in the models and its influence on the results is presented.

This work deals with the experimental and computational study of the co-current gas-solid flow behaviour in a riser of a FCC process. The FCC particles belong to the group A of Geldart's classification and are inclined to form ephemeral agglomerates. Thus, such agglomeration process may constitute an important phenomenon in the fast fluidization of FCC particles because it modifies the structure of the flow and reduces the effectiveness of the gas-solid contact. As first approach for taking the phenomenon of agglomeration into account, we confronted experimental results and predictions of two series of unsteady three-dimensional calculations using the CFD code Saturne_Polyphasique@Tlse. In the first series, the size and density of the particles are those of the FCC particles (70 µm and 1400 kg/m3) whereas in the second ones, they correspond to an equivalent particle (350 µm and 950 kg/m3). The computational results allow to obtain good predictions for the axial pressure gradients profiles for the FCC particles whereas the solid average mass flux profiles are not very well predicted for the two types of particles. The discrepancy between predictions for the two types of particles relies for the increase of inertia effect for the equivalent particles characterize by a larger value of the particle relaxation characteristic time. These results should enable us to direct our works for the understanding of the Group A particles behaviour

Eulerian Gas–Solid Modelling of Dense Fluidized Bed

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Contribution a l'´ etude de la dé du carbonate de sodium monohydrate en lit fluidise dense et mise en oeuvre en lit fluidise circulant: ´ etude expé et modé

- S Diguet

S. Diguet, Contribution a l'´ etude de la dé du carbonate de sodium monohydrate en lit fluidise dense et mise en oeuvre en lit fluidise circulant: ´ etude expé et modé, Ph.D. Dissertation, INP Toulouse, France, 1996.

An efficient FCC riser separation system: from R&D to industrial practice

- R Andreux
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- R Roux

R. Andreux, J. Verstraete, T. Gauthier, R. Roux, J.-L. Ross, An efficient FCC riser separation system: from R&D to industrial practice, in: A. Luckos, P. Smit (Eds.), IFSA—Industrial Fluidization South Africa, Proceedings, Johannesburg, November 16–17, 2005, South Africa Institute of Mining and Metallurgy, 2005, pp. 225–244.

Statistical and Continuum Modelling of Turbulent Reactive Particulate Flows. Part 1. Theoretical and Experimental Modelling of Par-ticulate Flows, Lecture Series

- O Simonin

O. Simonin, Statistical and Continuum Modelling of Turbulent Reactive Particulate Flows. Part 1. Theoretical and Experimental Modelling of Par-ticulate Flows, Lecture Series 2000–2006, von Karman Institute for Fluid Dynamics, Rhode St Gené, Belgium, 2000.

Experimental and numerical study of a gas–solid separator

- R Andreux

R. Andreux, Experimental and numerical study of a gas–solid separator

Bi- and three- dimensional numerical simulation of a CFB: application to fluidizing regime diagram establishment

- J Begis
- G Balzer

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L-valve equations, Powder Techn

- W C Yang
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FCC : Fluidization phenomena and technologies, Oil & Gas Science and Technology, Revue de l'IFP

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Mechanics of fluidization, Chemical engineering symposium series

- C Y Wen
- Y H Yu

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Experimental and numerical study of a gas-solid separator of a cold FCC moke-up

- R Andreux

Contribution à l’étude de la déshydratation du carbonate de sodium monohydrate en lit fluidise dense et mise en oeuvre en lit fluidise circulant: étude expérimentale et modélisation

- S Diguet

An efficient FCC riser separation system: from R&D to industrial practice

- Andreux