Hydrodynamics of gas-solid two-phase mixtures flowing upward through packed beds

The work reported here represents part of an effort to address the challenges related to a newly proposed process for hydrogen production through steam-methane reforming, in which a fine adsorbent carried by the gaseous reactants moves through a packed catalyst bed. Comprehensive experimental work was carried out on the hydrodynamic aspects of gas-solid two-phase mixtures flowing upwards through packed beds. The effects of column diameter, packed particle size, and suspended particle size on the pressure drop and solids hold-ups were investigated. It was observed that the pressure drop of gas-solid two-phase flows depended approximately linearly on the solids flux under the conditions of this work, and the dependence was affected by the suspended particle size, packed particle size, packed column diameter, and gas velocity. However, when the data were reprocessed in terms of the Euler number and the solid-to-gas mass flux ratio, they collapsed into a single line for a given packing condition, and the suspended particle size was found to impose little effect. An analysis was conducted on the pressure drop using a modified version of Metha-Hawley equation by taking into account the effects of suspended particles on the viscosity and density. A reasonably good agreement with experimental data was obtained. The experimental results of the solids hold-ups showed that the particle concentration in packed particle interstices was much higher than that at the entrance to the packed column. Effort was also made to relate the solids hold-ups to the operating parameters. It was found that the dynamic hold-up related fairly well to the solid-to-gas velocity ratio as well as the suspended-to-packed particle size ratio for a given packed column, whereas no clear relationship was obtained for the static solids hold-up. Based on the results of this study, recommendations for future work are given.     

Heat transfer of gas-solid two-phase mixtures flowing through a packed bed

This paper reports an experimental study on both transient and steady-state heat transfer behavior of a gas-solid two-phase mixture flowing through a packed bed under constant wall temperature conditions. A logarithmic mean temperature difference (LMTD) method is used to process the temperature data to obtain the overall heat transfer coefficient. The influences of particle loading and gas flow Reynolds number are investigated. The results show that the introduction of suspended particles greatly enhances heat transfer between the flowing gas-solid two-phase mixture and the packed bed, and the enhancement increases approximately linearly with increasing particle loading. The heat transfer coefficient data are processed to give the Nusselt number, which is found to correlate well to the Reynolds number, the Archimedes number and the suspended particle loading ratio. A comparison of the data of this work with the published data reveals large discrepancy. Possible reasons for the discrepancy are discussed.     

Solids behaviour in a gas-solid two-phase mixture flowing through a packed particle bed

This paper reports the solids behaviour in a dilute gas-solid two-phase mixture flowing through a packed bed. The positron emission particle tracking (PEPT) technique was used in the work, which allowed investigation of three-dimensional solids motion at the single suspended particle level. Processing of the data gave solids velocity, the residence time of suspended particles, bed tortuosity in terms of solids motion, as well as solids occupancy in the cross-section of the packed bed. The results suggest that the wall effect on the motion of suspended particles is limited to approximately one packed particle diameter under the conditions of this work. Both the average axial and radial velocities of suspended particles, normalised by the superficial gas velocity, change periodically with radial position, but the periodicity does not correspond exactly to the packed particle diameter. The peak and trough values of the average axial velocity of the suspended particles in the bulk region are, respectively, ∼25% and ∼15% of the superficial gas velocity under the conditions of this work and the superficial gas velocity shows little effect. The peak and trough values of the average radial velocity of the suspended particles in the bulk region are, respectively, +5% (positive) and -5% (negative) of the superficial gas velocity. The results of the residence time and tortuosity of the suspended particles show an approximately Gaussian distribution with the peak residence time and tortuosity increasing with decreasing superficial gas velocity. The occupancy data suggest that particles spend more time in an annular region close to the wall, indicating a non-uniform particle distribution across the packed bed cross-section.     

Flow of a gas-solid two-phase mixture through a packed bed

This paper is concerned with an upward co-current flow of a gas-solid two-phase mixture through a packed bed, a system employed in a number of industrial processes. Experimental work was carried out by using glass balls for packed bed, and both glass beads and FCC as suspended particles. The effects of solids loading and gas velocity on the pressure drop as well as the static and dynamic solid hold-ups within packed bed were examined. Experimental results showed different behaviour of the FCC from glass beads. At a given gas velocity, pressure drop increased approximately linearly with solids loading with a slope for FCC much higher than that for glass beads. The static hold-up of glass beads was much lower than corresponding dynamic hold-up at a given gas velocity, and it did not seem to change much with solids loading under the conditions of this work. At a given gas velocity, the static hold-up of FCC, however, was found to be comparable with the corresponding dynamic hold-up. An analysis was conducted on the pressure drop using a modified version of the Ergun equation by taking into account the effects of suspended particles on the viscosity and density, as well as the gravitational force. It was found that the modified Ergun equation agreed well with the experimental results of both this work and those reported in the literature. Effort was also made to develop relationships for the dynamic hold-up and the interaction coefficient between the suspended and the packed particles, the so-called solid-phase friction factor in the literature. The dynamic hold-up was found to increase with an increase in the product of velocity ratio of the solid to gas phases and the square root of the diameter ratio of the suspended to packed particles, whereas the interaction coefficient increased in general with increasing Froude number but with significant scattering.     

Vertical upward flow of gas-solid two-phase mixtures through monolith channels

This paper reports some recent experimental observations of both gas and gas-solid two-phase flows through small monolith channels. For gas flows, the laminar-to-turbulent transition in monolith channels was observed to occur at a Reynolds number of ∼620, much lower than the conventional transition criterion of 2200 for large pipes. Surface roughness of and non-uniform distribution of gas in monolith channels were proposed to be possible reasons. For gas-solid two-phase flows, both pressure drop and solids hold-up were measured. It was found that the pressure drop of gas-solid two-phase flows through monolith channels was significantly lower than that through packed particle beds with even lower surface area per unit bed volume. Reprocessing of the pressure drop data in terms of the dimensionless groups showed that the Euler number depended approximately linearly on the solids-to-gas mass flux ratio for a given superficial gas velocity, and suspended particle size imposed little effect under the conditions of this study. Measurements of the solids hold-up showed that the hold-up in monolith channels increased with a decrease in both the gas velocity and the suspended particle size. The pressure drop results were also compared with semi-theories developed for pneumatic conveying. An overprediction was observed, an indication of the need for more controlled experiments for fundamental understanding of the hydrodynamics in monolith channels.The work reported here on gas-solid two-phase flows through monolith channels represents the first attempt in this area as no previously studies have been found in the literature.     

Solids behaviour in a dilute gas-solid two-phase mixture flowing through monolith channels

This paper reports, for the first time, the solids behaviour in a dilute gas-solid two-phase mixture flowing through monolith channels. The non-intrusive positron emission particle tracking (PEPT) technique was used in the work, which allowed investigation of three-dimensional solids motion at the single suspended particle level. Processing of the PEPT data gave solids velocity and occupancy in the monolith channels. The results showed a non-uniform radial distribution of both the solids velocity and concentration. The highest axial solids velocity occurred in monolith channels located in the central part of the column, whereas the highest solids concentration took place at a position approximately 0.7 times the column radius. The axial distribution of the axial solids velocity showed an entrance region with a length of approximately 33 times the hydrodynamic diameter of a monolith channel under the conditions of this work. Analysis of the PEPT data also gave distributions of particle residence time and tortuosity in terms of solids motion. The distributions were approximately Gaussian-type with the tortuosity distribution more skewed toward the right hand side. The peak residence time and tortuosity decreased with increasing superficial gas velocity and the distributions were broadened at lower superficial gas velocities. The results of this work also provided a possible explanation to our previously observed early laminar-to-turbulent flow transition in monolith channels.     

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.     

Oscillatory flow and axial dispersion in packed beds of spheres

The effect of oscillations in the bulk flow on the axial dispersion coefficient in packed beds of spherical particles has been studied using the imperfect pulse tracer method with two probes located within the bed. Three bed sizes with diameters in the range 25-47.3 mm have been used with oscillation frequencies and amplitudes in the range 0-2.4 Hz and 0-3.5 mm, respectively. In the absence of oscillations, the axial dispersion coefficient increases linearly with interstitial velocity. For a given bulk velocity and oscillation frequency, the axial dispersion coefficient-amplitude relationship shows a minimum. Over the ranges of conditions studied, the best reduction (up to 50%) in the axial dispersion coefficient from the non-oscillation base case occurred at the highest frequency studied and when the wall effect was the greatest, i.e. when the column-to-particle size was the smallest. The axial dispersion coefficient was fitted to a mathematical model, which takes into account the diameters of both the column and the packing, the fluid velocity, and the oscillation intensity (frequency and amplitude). The model was adapted from those developed by Göebel et al. (1986) and Mak et al. (1991) so as to need no a priori assumptions about the relationship between oscillation parameters and the axial dispersion coefficient. The model provides near-perfect fits to the experimental data for the higher frequencies studied.     

Modelling the liquid-phase adsorption in packed beds at low Reynolds numbers: An improved hydrodynamic model

A hydrodynamic model including only one parameter (λ_O) for the prediction of both axial dispersion and external mass transfer in fixed-bed adsorbers at low Reynolds numbers (creeping flow regime) has been developed. The theoretical analysis is based on the application of the (two-dimensional) uniform dispersion model originally proposed by Bischoff and Levenspiel [1962a. Fluid dispersion—generalization and comparison of mathematical models—I. Generalization of models. Chemical Engineering Science 17, 245-255] to the representative capillary of a tube bundle model for describing the flow and mixing behaviour in packed beds. The combination of this model with the relationship between longitudinal and radial dispersion leads to the definition of the sole hydrodynamic parameter λ_O (one-parameter hydrodynamic model). Furthermore, the detailed investigation reveals that the one-parameter concept may be utilized for the application of the (one-dimensional) axial dispersed plug flow model as well. The functional dependence of the parameter λ_O on the flow conditions is elaborated from axial dispersion measurements. Both the new (one-parameter) hydrodynamic model and the classical model including axial dispersion and external mass transfer coefficients (two-parameter model) are utilized to simulate the breakthrough curves for the adsorption of naphthalene onto silica gel. This simulation study reveals that only the one-parameter hydrodynamic model is able to predict the adsorber dynamics over a large range of flow rates.     

Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model

Using an illustrative sphere packing assembly, it is demonstrated that flow structure and wall heat transfer patterns in low aspect ratio fixed bed reactors are more realistically modelled by properly accounting for the discrete void fraction variations. A 3D network-of-voids (NoV) model has been devised to characterise and examine the discrete flow and heat transfer phenomena in a low aspect ratio packed bed with d_t/d_p = 1.93. The model as formulated is deliberately designed to be not too complicated so as not to place severe demands on computational resources. Hence, the model can potentially easily be applied to simulate the typically large sets of tubes (often comprising more than 10,000) in the case of industrial multi-tubular reactors, where every tube is different due to the random insertion of the packing particles. Because of its simplicity, the model offers an opportunity of coupling the individual catalyst pellet level transport with the complex interstitial flows at the reactor scale. Illustrative studies of this NoV model on a random packed bed of spheres predict large variations of discrete in-void angular velocities and consequently wall heat transfer coefficients within a single tube. The wide variations of wall heat transfer coefficients imply that the different angular sections of the tube will transfer heat at radically different rates resulting in potentially large temperature differences in different segments of the tube. This may possibly result in local temperature runaway and/or hot spot development leading to several potentially unanticipated consequences for safety and integrity of the tube and hence the reactor. The NoV model predictions of the overall pressure drop behaviour are shown to be consistent with the quantitative and qualitative features of correlations available in the literature.     

Integration of ECT measurements with hydrodynamic modelling of conventional gas-solid bubbling bed

The electrical capacitance tomography (ECT) provides fast images of the cross-sectional concentration distribution of solid-gas flow in a confined volume. This information can be integrated with numerical simulation to estimate some of the most important hydrodynamic quantities in solid-gas flow, such as the particles velocity, interstitial gas velocity and particle-particle contact forces.In this study, using the two-fluid approach, momentum and energy balance equations, along with the appropriate boundary conditions, have been solved by integrating the numerical procedure with the experimental data of the fluidised bed pressure drop and pixel distribution of particle concentration available from the ECT measurements. Preliminary results of time-dependent hydrodynamic features of the bed are presented. These results were analysed and assessed using the available experimental literature data on conventional bubbling fluidised bed. In general, it is demonstrated that the integration of ECT measurements with numerical modelling offers a unique and promising technique for comprehensive non-intrusive information on gas-solid flow systems.     

Modelling and measurements of the velocity gradient and local flow direction at the pore scale of a packed bed

In a packed bed with single phase liquid flow, velocity gradient and local flow direction are measured at the pore scale using tri-segmented microelectrodes flush mounted at the surface of a sphere equator area. The experimental measurements are compared to numerical predictions deduced from the solution of a 3D model based on continuity and momentum balance equations.     

Flow of two-phase oil/water mixtures through sudden expansions and contractions

Pressure loss data in a sudden expansion and a sudden contraction were obtained for two-phase oil/water mixtures, covering a wide range of oil concentration: 0 to 97.3 vol.% oil. The emulsions were of oil-in-water type up to an oil concentration of 64 vol.%. Above this concentration, the emulsions were water-in-oil type. An on-line conductance cell was used to monitor the inversion point and the type of emulsion. The pressure loss was determined from the measured pressure profiles upstream and downstream of the fitting. From the pressure-loss/velocity data, the loss coefficients were obtained. The loss coefficients for the emulsions are found to be independent of the concentration and type of emulsions. Furthermore, there is no observable difference between the loss coefficients for emulsions and single-phase water.     

Critical fluidization velocities and maximum bed pressure drops of homogeneous binary mixture of irregular particles in gas-solid tapered fluidized beds

Recently, tapered fluidized bed has become more attractive because of the problems associated with conventional (cylindrical) beds like fluidization of widely distributed particles, entrainment of particles and limitation of fluidization velocity. There have been some investigations on hydrodynamics of uniform single size particles but there have been no detailed studies of homogeneous binary mixture of particles of different sizes and different particles in tapered beds. In the present work, an attempt has been made to study the hydrodynamic characteristics of homogeneous binary mixture of irregular particles in tapered beds having different tapered angles. Correlations have been developed for important characteristics, especially critical fluidization velocities and maximum bed pressure drops of homogeneous binary mixture of irregular particles in gas-solid tapered fluidized beds. Experimental values of critical fluidization velocities and maximum bed pressure drops have been compared with the developed correlations.     

Computer simulations of gas-solid flow in spouted beds using kinetic-frictional stress model of granular flow

A gas-solid two-fluid flow model is presented. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated in the simulations of spouted beds. This model treats the kinetic and frictional stresses of particles additively. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson et al. (J. Fluid Mech. 210 (1990) 501) and the modified frictional shear viscosity model proposed by Syamlal et al. (MFIX documentation. US Department of Energy, Federal Energy Technology Center, Morgantown, 1993). The body-fitted coordination is used to make the computational grids best fit the shape of conical contour of the base in the spouted beds. The effects of inclined angle of conical base on the distributions of particle velocities and concentrations in the spout, annulus and fountain zones were numerical studied. Calculated particle velocities and concentrations in spouted beds were in agreement with experimental data obtained by He et al. (Can. J. Chem. Eng. 72 (1994a) 229; (1994b) 561) and San Jose et al. (Chem. Eng. Sci. 53 (1998) 3561).     

Slow-mode gas/liquid-induced periodic hydrodynamics in trickling packed beds derived from direct measurement of cross-sectional distributed local capacitances

Hydrodynamics of a periodically operated trickling packed bed was studied with a high-speed wire-mesh sensor technique based on direct measurement of cross-sectional distributed local capacitances. Liquid cycles in the alumina packing were generated by periodic induction of gas and/or liquid phase in distinctive slow-mode. Hydrodynamics were characterized with respect to liquid saturation and liquid saturation distribution varying period length, split and time-averaged superficial gas and liquid velocities. The sensors technique allows direct access to local phenomena during liquid pulse breakthrough, to distribution patterns and their reproducibility at different cycle positions that were studied based on transient liquid saturation distribution data of different periodicity variables. Due to simultaneous measurement at four different axial reactor positions, pulse attenuation along the reactor and pulse velocity could be analyzed. Furthermore, hydrodynamics of different modes of gas-induced periodic cycling, e.g. gas cycling only, asynchronous and synchronous cycling of gas and liquid flow rate and alternating gas–liquid cycling, were studied.     

CFD studies of solids hold-up distribution and circulation patterns in gas-solid fluidized beds

Numerical results for a gas-fluidized bed using a 2D Eulerian model including the kinetic theory for the particulate phase were provided. The circulation patterns for various operating conditions were discussed. Modeling parameters of drag function, algebraic and transport equations of granular temperature, frictional stress model, turbulent model and discretization scheme were investigated for a bed with different gas distributors and a slotted draft tube. CFD results showed that the drag model is an important hydrodynamics parameter for gas-fluidized beds with various gas distributors. Transport and algebraic equations for granular temperature should be utilized, respectively, for beds including partial and complete sparging at U_g = 2.18 m/s. Frictional stresses play an important role for the beds containing partial sparging with and without draft tube. Discretization schemes should be examined to achieve better results. The Simonin and k-ε turbulent models can improve the CFD results at high gas velocities. Considering perforated plate distributor improves the results.     

Numerical investigation of gas-solid heat transfer in rotating fluidized beds in a static geometry

Gas-solid heat transfer in rotating fluidized beds in a static geometry is theoretically and numerically investigated. Computational fluid dynamics (CFD) simulations of the particle bed temperature response to a step change in the fluidization gas temperature are presented to illustrate the gas-solid heat transfer characteristics. A comparison with conventional fluidized beds is made. Rotating fluidized beds in a static geometry can operate at centrifugal forces multiple times gravity, allowing increased gas-solid slip velocities and resulting gas-solid heat transfer coefficients. The high ratio of the cylindrically shaped particle bed “width” to “height” allows a further increase of the specific fluidization gas flow rates. The higher specific fluidization gas flow rates and increased gas-solid slip velocities drastically increase the rate of gas-solid heat transfer in rotating fluidized beds in a static geometry. Furthermore, both the centrifugal force and the counteracting radial gas-solid drag force being influenced by the fluidization gas flow rate in a similar way, rotating fluidized beds in a static geometry offer extreme flexibility with respect to the fluidization gas flow rate and the related cooling or heating. Finally, the uniformity of the particle bed temperature is improved by the tangential fluidization and resulting rotational motion of the particle bed.     

Investigation of fine granular material flow through a packed bed

Three different methods cut-off, time-of-flight, and Pulsed Field Gradient Nuclear Magnetic Resonance were used to study downstream flow of fine granular material through the fixed bed reactor. For describing the transport of solid particles within a fixed granular bed, a model has been developed. In time-of-flight and cut-off techniques the highest average velocity of filtration is observed at the lowest mass flow rate in all experimental traces, while upon the flow rate increase it tends to an asymptotic value. Experimental results obtained by pulsed field gradient nuclear magnetic resonance technique have revealed the bimodal character of particles velocities distribution. The average filtration velocity has a maximum at an intermediate mass flow rate close to the bed flooding, in contrast to the results obtained by cut-off and time-of-flight methods. The velocities measured using all three techniques were compared by converting them into dimensionless values. From the experimental results, the values of model parameters have been evaluated which allowed us to describe particle velocities within a bed.     

Slow non-newtonian flow through packed beds: Effect of zero shear viscosity

The slow non-Newtonian (inelastic) flow through packed beds of mono-size spherical particles has been simulated by solving the equations of motion numerically. The inter-particle interactions have been modelled by using a simple cell model. Theoretical estimates of pressure, friction and total drag coefficients as function of the pertinent physical (l≥n≥ 0.2; 0.3 ≤ e ≤ 0.5) and kinematic parameters (0.01 ≤ '≤ 100) for a fixed value of Reynolds number {Re = 0.001) have been obtained. The theoretical predictions reported herein have been validated using the suitable experimental results available in the literature, and the importance of including the zero shear viscosity in analyses for the creeping flow problems is convincingly demonstrated.