Modeling of core flow in a gas-solids riser

The heterogeneous flow structure in gas-solids riser reactors is typically represented by an upward solids flow in the core region and a back-mixing downward solids flow in the wall region. The hydrodynamic and reaction characteristics in these two regions are highly different, as most reactions with fresh catalyst solids occur in the core region and mostly spent catalyst solids are found in the wall region. Gross understanding on gas-solids riser flow can be conveniently obtained from a cross-section averaged one-dimensional modeling approach, which is probably only valid for the core region. The success of such an approach, however, has to rely on the appropriate modeling of controlling mechanisms of riser flows. Our recent studies show that commonly-employed Richardson-Zaki equation overestimates the hydrodynamic forces in the dense phase and acceleration regimes; there is also a non-negligible effect of solids collision on solids acceleration, and the wall effect should be taken into account in terms of wall boundary and back flow mixing. In this paper we propose a new mechanistic modeling to describe the hydrodynamics of upward flow of solids in a gas-solids riser, with new formula of hydrodynamic phase interactions. The modeling results are validated against published measurements of pressure and solids volume fraction in a wide range of particle property, gas velocity and solid mass flux. Parametric effects of operation conditions such as transport gas velocity and solid mass flux on hydrodynamic characteristics of riser flows are predicted.     

Modeling of drag with the Eulerian approach and EMMS theory for heterogeneous dense gas-solid two-phase flow

Combined with the Eulerian approach, energy minimization multi-scale (EMMS) theory was used to develop a new theoretical model for the drag between the gas and solid phases in dense fluidized systems. The energy minimization was used in the solution procedure as an additional stability condition to close the conservation equations. The model was derived without introducing any empirical factors, so it can be used for more flow conditions in circulating fluidized beds (CFBs) than empirical models, especially for heterogeneous gas-solid two-phase flows that include cluster formation. Non-uniform particle distribution in computational cells, which is usually not described by the differential equations, is also considered in the new drag model. Both the drag values given by the model and simulation results for real systems agree well with experimental data. The results show that the model reasonably describes the interactions between the gas and particle phases in dense flows.     

Computational fluid dynamics for dense gas–solid fluidized beds: a multi-scale modeling strategy

Dense gas–particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic, which can be related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas–particle flows both (effective) fluid–particle and (dissipative) particle–particle interactions need to be accounted for because these phenomena, to a large extent, govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas–solid contact and as a direct consequence thereof strongly affect the performance of the process.Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid–particle and particle–particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid–particle (lattice Boltzmann model (LBM)) and particle–particle (discrete particle model (DPM)) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1) involves the LBM, the DPM, the continuum model based on the kinetic theory of granular flow, and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

Stochastic Modeling of the Particle Residence Time Distribution in an Opposed Multi‐Burner Gasifier

The gasification technology of impinging streams has been extensively applied to chemical production and power generation. Particle residence time distribution (RTD) is an important parameter required for modeling, designing and optimization of an impinging stream gasifier. A stochastic mathematical model based on the Markov chains model is developed for the opposed multi‐burner gasifier (OMBG), which closely describes the behavior of the flow pattern and particle RTD in the gasification system. The model simulates the motion of single particle moving in the gasifier using the Markov chains. The predicted results give a reasonable fit to the experimental data. This shows that the flow process of particles in the gasifier has recirculation eddies, which have a downward flow direction near the downflow core and an upward flow direction near the wall, but no short‐circuit. Finally, the effect of particle flux rate on the RTD is predicted, and the contrast between gas and particles RTDs at a laboratory scale and in an industrial gasifier are presented.     

Flow patterns in high-velocity fluidized beds and pneumatic conveying

Four flow patterns are identified for gas-solids vertical upward flows. Homogeneous dilute phase flow is characterized by the absence of both radial and axial solids segregation. Heterogeneous dilute phase flow (also called core-annulus flow) is characterized by the absence of axial solids segregation, with solids carried upward in the core and travelling downward near the outer wall due to the formation of particle streamers. Collapsed flow with a lower dense region and an upper dilute region is also referred to as the fast fluidization regime. In this case, the flow structure in the upper dilute region is similar to that in heterogeneous dilute phase flow, while the lower dense region resembles that in a turbulent fluidized bed. Dense phase flow can be reached when the riser is completely occupied by a relatively dense suspension with little axial density variation and no net solids downflow near the riser wall. The transition from fast fluidization to dense phase flow is still not clearly defined.     

An Improved LES on Dense Particle‐Liquid Turbulent Flows Using Integrated Boltzmann Equations

An improved large eddy simulation (LES) using a dynamic second‐order subgrid stress (SGS) model has been developed for simulating dense particle‐liquid two‐phase turbulent flows. The governing equations of each phase are obtained from a microscopic point of view, using the kinetic theory of molecular gas. They are derived by multiplying the Boltzmann equation of each phase by property parameters and integrating over the velocity space. An inter‐particle collision term is included in the governing equation of the particle phase. Assuming a Maxwellian distribution of the velocity for particle‐phase, an inter‐particle collision term is derived.     

Gas-particle interactions in dense gas-fluidized beds

The occurrence of heterogeneous flow structures in gas-particle flows seriously affects gas–solid contacting and transport processes in dense gas-fluidized beds. A computational study, using a discrete particle method based on Molecular Dynamics techniques, has been carried out to explore the mechanisms underlying the formation of heterogeneous flow structures. Based on energy budget analyses, the impact of non-linear drag force on the flow structure formation in gas-fluidized beds has been examined for both ideal particles (elastic collision, without inter-particle friction) and non-ideal particles (inelastic collision, with inter-particle friction). Meanwhile, the separate role of inter-particle inelastic collisions, accounted for in the model via the restitution coefficient (e) and friction coefficient (μ), has also been studied.It is demonstrated that heterogeneous flow structures exist in systems with both non-ideal particle-particle interaction and ideal particle-particle interaction. The heterogeneous structure in an ideal system, featured with looser packing, is purely caused by the non-linearity of the gas drag: the stronger the non-linearity of the gas drag force with respect to the voidage, the more heterogeneous flow structures develop. A weak dependence of drag on the voidage produces a homogenous flow structure. Collisional dissipation dramatically intensifies the formation of heterogeneous flow structures after the system equilibrium breaks. Quantitative comparisons of flow structures obtained by using various drag correlations in literature will also be reported.     

基于MP-PIC方法改进EMMS/DP曳力模型

改进了面向离散粒子法的能量最小多尺度曳力模型(EMMS/DP)的颗粒参数生成方式,并将非均匀因子(HD)与固相浓度和滑移速度关联以考虑介尺度结构动态效应的影响,用改进的EMMS/DP模型与多相流质点网格模型(MP-PIC)耦合模拟气固两相流提升管系统,模拟结果与实验值吻合很好,考察了MP-PIC方法的网格无关性和粗粒化模型参数.     

EFFECTS OF PARTICLE CHARACTERISTICS ON THE PERFORMANCE OF A FAST FLUIDIZED BED REACTOR

A heterogeneous model for the fast fluidized bed reactor which carries out a gas-solid non catalytic reaction is presented. The hydrodynamics of the fast fluidized bed is characterized by the model of Kwauk et al. (1985) which assumes the existence of two phases; a dense phase and a dilute pneumatic transport phase. For a given solid flowrate, the length of the reactor occupied by each phase depends on gas velocity, particle diameter and density and average voidage within the reactor. The gas-solid reaction is assumed to follow the shrinking core model. The solids are assumed to be completely backmixed in the dense phase and move in plug How in the dilute pneumatic transport phase. The gas phase is assumed to be in plug flow in both phases

For given gas and solid flowrates, the transition from the dense phase flow to the fast fluidized bed (containing two regions) as functions of particle size and density is determined using the model of Kwauk et al. (1985). The numerical solution of the governing mass balance equations show that for given solid and gas flowrates, (and average voidage) the gas phase conversion shows an unusual behavior with respect to particle diameter and density. Such behavior is resulted from the effects of particle diameter and density on the reactor volume occupied by each phase and the effect of particle diameter on the apparent reaction rate. The numerical results show that a fast fluidized bed gives the best conversion at large particle density and for the particle diameter which results the fast fluidized bed to be operated near the pure dense phase flow.     

Computational fluid dynamics of a circulating fluidized bed under various fluidization conditions

A computational fluid dynamics (CFD) model was developed to simulate the hydrodynamics of gas-solid flow in a circulating fluidized bed (CFB) riser at various fluidization conditions using the Eulerian-Granular multiphase model. The model was evaluated comprehensively by comparing its predictions with experimental results reported for a CFB riser operating at various solid mass fluxes and superficial gas velocities. The model was capable of predicting the main features of the complex gas-solids flow, including the cluster formation of the solid phase along the walls, for different operating conditions. The model also predicted the coexistence of up-flow in the lower regions and downward flow in the upper regions at the wall of the riser for high gas velocity and solid mass flux, as reported in the literature. The predicted solid volume fraction and axial particle velocity were in good agreement with the experimental data within the high density fast fluidization regime. However, the model showed some discrepancy in predicting the gas-solid flow behavior in the riser operating in dense suspension up-flow and low density fast fluidization regimes.     

A second-order-moment–Monte-Carlo model for simulating swirling gas–particle flows

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM–MC two-phase turbulence model. The SOM–MC model was applied to simulate swirling gas–particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle–wall and particle–particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.     

Numerical Simulations of the Effect of Conical Dimension on the Hydrodynamic Behaviour in Spouted Beds

The flow behaviours of gas‐solids were predicted by means of a hydrodynamic model of dense gas‐solid flow in spouted beds. Constitutive equations describing the particulate solids pressure and viscosity were implemented into a hydrodynamic simulation computer program. The effect of operating conditions (inclined angle and gas spouting velocity) on particle velocity and concentration in the spout, annulus and fountain regions were numerical studied. Both vertical and horizontal particle velocities increased with increasing spouting gas velocity. The diameter of the spout increases with decreasing the inclination angle. As the inclination angle is set greater than 60°, the spout cross‐section starts becoming bottlenecked, limiting the upwards flow of solids.     

Correlating gas–liquid co‐current flow hydrodynamics in packed beds using the F‐function concept

A phenomenological model based on the generalization of the single‐phase Forchheimer equation was recently proposed for predicting pressure drop and phase saturations in gas–liquid co‐current horizontal and downward high‐pressure packed beds. Here, we extend the model to packed‐bubble (co‐current upflow) and trickle‐bed operation using phase saturation power laws similar to Corey relative permeabilities. The power‐law exponents were fitted using a wide pressure gradient and liquid saturation databank in co‐current up/downward packed‐bed flows. It was found that this approach, as well as other in the literature developed for down‐flow reactors apply also to upward flows; the prediction accuracy was comparable for both flow directions to existing literature approaches. Copyright © 2004 Society of Chemical Industry     

Computational fluid dynamic simulation of ethylene hydrogenation in a fluidised bed of porous catalyst particles

Computational fluid dynamics (CFD) is used to study the flow behaviour and conversion in a freely bubbling bed of porous cracking catalyst particles fluidised by a mixture of ethylene and hydrogen on the in‐house code FLOTRACS‐MP‐3D. The solid phase viscosity and pressure are modelled on the basis of kinetic theory of granular flows (KTGF). An effective solid density is calculated to account for the inherent porosity of particles. The cohesive inter‐particle forces are incorporated into the CFD model by using an empirical approach proposed in literature. Qualitatively, the CFD model captures the flow behaviour and heat transfer in the bed quite well. On the quantitative front, the variation of conversion with gas velocity is predicted fairly well with the deviation between the predicted and measured conversion remaining within 20%. © 2011 Canadian Society for Chemical Engineering     

Numerical predictions of flow behavior and cluster size of particles in riser with particle rotation model and cluster-based approach

Flow behavior of particles in a circulating fluidized bed (CFB) riser is numerically simulated using a two-fluid model incorporating with the kinetic theory for particle rotation and friction stress models. The particle rotations resulting from slightly friction particle-particle collisions was considered by introducing an effective coefficient of restitution based on the kinetic theory for granular flow derived by Jenkins and Zhang [2002. Kinetic theory for identical, frictional, nearly elastic spheres. Physics of Fluids 14, 1228-1235]. The normal friction stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particles flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] and a modified frictional shear viscosity model proposed by Syamlal et al. [1993. MFIX Documentation and Theory Guide, DOE/METC94/1004, NTIS/DE94000087] were used as the particle frictional stress model. The drag force between gas and particle phases was modified with cluster-based approach (CBA). The flow behavior of particles and the cluster size in a riser of Wei et al. [1998. Profiles of particle velocity and solids fraction in a high-density riser. Powder Technology 100, 183-189] and Issangya et al. [2000. Further measurements of flow dynamics in a high-density circulating fluidized bed riser. Powder Technology 111, 104-113] experiments are predicted. Effects of the rotation and friction stress models on the computed results are analyzed. It is concluded that particle rotations reduce the cluster size and alter the particle flows and distributions through more particle fluctuation energy dissipations. Effects of frictional stress on flow behavior and cluster size are not significant because the particle phase in the CFB riser is not dense enough to take into account for the particle-particle contact interactions.     

On a eulerian and lagrangian combined model in dense particle-laden riser flow

A new numerical model using both Eulerian and Lagrangian coordinates, and taking account of interparticle interactions, has been developed for the study of hydrodynamic aspects of dense particle-laden rise flows. A stochastic particle dispersion model has been incorporated in the original model to describe the gas particle turbulent flows. In addition, the collisional interaction between the particles has been modeled using the kinetic theory of granular flows based on the Chapman-Enskog theory of dense gases. A comparison with the experimental results of Miller and Gidspow (1992) shows reasonably good agreement. The present model may provide a useful approach for predicting the complex hydrodynamic behaviour of fluidized bed systems.     

Computational investigation of the mechanisms of particle separation and “fish‐hook” phenomenon in hydrocyclones

The motion of solid particles and the “fish‐hook” phenomenon in an industrial classifying hydrocyclone of body diameter 355 mm is studied by a computational fluid dynamics model. In the model, the turbulent flow of gas and liquid is modeled using the Reynolds Stress Model, and the interface between the liquid and air core is modeled using the volume of fluid multiphase model. The outcomes are then applied in the simulation of particle flow described by the stochastic Lagrangian model. The results are analyzed in terms of velocity and force field in the cyclone. It is shown that the pressure gradient force plays an important role in particle separation, and it balances the centrifugal force on particles in the radial direction in hydrocyclones. As particle size decreases, the effect of drag force whose direction varies increases sharply. As a result, particles have an apparent fluctuating velocity. Some particles pass the locus of zero vertical velocity (LZVV) and join the upward flow and have a certain moving orbit. The moving orbit of particles in the upward flow becomes wider as their size decreases. When the size is below a critical value, the moving orbit is even beyond the LZVV. Some fine particles would recircuit between the downward and upward flows, resulting in a relatively high separation efficiency and the “fish‐hook” effect. Numerical experiments were also extended to study the effects of cyclone size and liquid viscosity. The results suggest that the mechanisms identified are valid, although they are quantitatively different. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

An improved collision damping time for MP-PIC calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets

This paper describes several improvements to a numerical model introduced by O’Rourke et al. (2009) for collisional exchange and damping in dense particle flows. O’Rourke et al. (2009) use a Bhatnagar, Gross, and Krook (BGK) approximation to the collision terms in a particle distribution function transport equation to model the effects of particle collisions on damping fluctuating particle velocities and, in gas/liquid/solid beds, fluctuating temperatures and compositions of liquid films on particle surfaces. In this paper we focus on particle flows in which the particles have no liquid films and report on an improved expression we have developed for the collision damping time of particle velocity fluctuations used in the BGK approximation. The improved expression includes the effects on the collision damping time of the particle material coefficient of restitution and of non-equilibrium particle velocity distributions. The collision model improvements are incorporated into the general-purpose computational-particle fluid dynamics (CPFD) numerical methodology for dense particle flows. Three computational examples show the benefits of using the new collision time in calculations of particle separation in polydisperse dense particle flows and calculations of colliding particle jets.     

CPFD flow pattern simulation in downer reactors

This study contributes with a computational fluid dynamic simulation based on the numerical solution of continuity and momentum balance equations in a three‐dimensional (3‐D) framework. The proposed down flow gas–solid suspension model includes a unit configuration and C_D drag coefficients recommended for these units. Computational particle fluid dynamics (CPFD) calculations using suitable boundary conditions and a Barracuda (version: 14.5.2) software allow predicting local solid densification and asymmetric “wavy flows.” In addition, this model forecasts for the conditions of this study higher particle velocity than gas velocity, once the flow reaches 1 m from the gas injector. These findings are accompanied with observations about the intrinsic rotational character of the flow. CPFD numerical 3‐D calculations show that both gas and particle velocities involve the following: (a) an axial velocity component, (b) a radial velocity component (about 5% of axial velocity component), and (c) an angular velocity component. The calculated velocity components and the rotational flow pattern are established for a wide range of solid flux/gas flux ratios. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1635–1647, 2013     

Cluster-based drag coefficient model for simulating gas-solid flow in a fast-fluidized bed

Drag coefficient is of essential importance for simulation of heterogeneous gas-solid flows in fast-fluidized beds, which is greatly affected by their clustering nature. In this paper, a cluster-based drag coefficient model is developed using a hydrodynamic equivalent cluster diameter for calculating Reynolds number of the particle phase. Numerical simulation is carried out in a gas-solid fast-fluidized bed with an Eulerian-Lagrangian approach and the gaseous turbulent flow is simulated using large eddy simulation (LES). A Lagrange approach is used to predict the properties of particle phase from the equation of motion. The collisions between particles are taken into account by means of direct simulation Monte Carlo (DSMC) method. Compared with the drag coefficient model proposed by Wen and Yu, results predicted by the cluster-based drag coefficient model are in good agreement with experimental results, indicating that the cluster-based drag coefficient model is suitable to describe various statuses in fast-fluidized beds.