Countercurrent Backmixing Model Research Articles

Experimental and simulated solids mixing and bubbling behavior in a scaled two-section two-zone fluidized bed reactor

Digital Image Analysis techniques, a phenomenological Counter-Current Back-Mixing model (CCBM) and Two-Fluid Model (TFM) simulations were employed to evaluate the effect of scale on the Two-Section Two-Zone Fluidized Bed Reactors (TS-TZFBR) fluid dynamics, i.e. bubble characteristics, axial mixing of solids and defluidization phenomena. The reactor scaling did not affect the quality of the TFM bubble size predictions. A bubble size correlation previously proposed by the authors for TS-TZFBR units was able to predict the experimental axial bubble size evolution at the different reactor scales and gas velocities (ugas/umf=1.5–3.0) with a relative error under 17%. The TFM simulated axial solid mass fluxes were same order as these obtained by Particle Image Velocimetry for every reactor size. However, the classical CCBM model was unable to predict the effect of scale on the solids axial mixing in a TS-TZFBR. The inclination angle of the defluidized bed regions found within the TS-TZFBR tapered zone, β, increased by (ugas/umf)0.25 when duplicating the reactor size. Nevertheless, it did not exceed the prescribed upper limit of β=80° for any of the conditions tested.

Particle Mixing in a Two-Section Two-Zone Fluidized Bed Reactor. Experimental Technique and Counter-Current Back-Mixing Model Validation

Effective particle circulation between the two zones is a prerequisite for ensuring the simultaneous reaction and catalyst regeneration inside a two-zone fluidized bed reactor (TZFBR). An appropriate degree of particle mixing provides a steady state catalytic operation, whereas poor solid circulation between the bed zones leads to unhampered catalyst deactivation. To achieve effective control of the fluid dynamic regime within the two bed regions, a new design has been proposed with a different cross sectional area in each zone. The transition angle (α) between these zones represents the most characteristic feature of the so-called two-section TZFBR (TS-TZFBR). In the present study, the influence of operational variables (α, gas velocities, gas distributor location) on the particle circulation has been determined. Phosphorescent particles have been used as optical tracers to measure the solid axial mixing between the zones in a cold pseudo-2D TS-TZFBR facility. Additionally, a modified counter-current back-mixing model (CCBM) without adjustable parameters has been developed to explain and predict the solid mixing rate for different TS-TZFBR geometries. The experimental mixing results show a reasonably good agreement with the suggested mixing model predictions in a wide range of operational conditions: ugas–umf = [5–20] cm3/(cm2 s), α = [0°–85°].

Effect of Temperature on Solids Mixing in a Bubbling Fluidized Bed Reactor

Solid mixing in fluidized bed reactors has a great impact on the transport phenomena in the reactor. Most studies, concerning solid behavior and hydrodynamic correlations of fluidized bed reactors, have been done at ambient temperature. Industrially, however, fluidized bed reactors operate at high temperatures. The lack of studies at higher temperatures is due to difficulties associated with measuring techniques under these conditions. In extrapolating hydrodynamic parameters derived at ambient temperature to higher temperatures, only the physical property changes of gas and solid phases, such as density and viscosity are taken into consideration. On a microscopic scale, however, change of temperature strongly affects the interaction between particles, which in turn has a substantial impact on the hydrodynamics of a fluidized bed.In this study and for the first time, the Radioactive Particle Tracking (RPT) is used to investigate the effect of temperature on the fluidization of silica sand particles (Geldat-B) in a bubbling fluidized bed reactor. Experiments have been carried out at different temperatures (25-400oC) and superficial gas velocities (0.17-0.75 m/s). The effect of temperature on the global mixing is studied in conjunction with the changes found in the dynamic of the ascending and descending phases. A two-phase countercurrent back-mixing model (CCBM) was used to investigate global solid mixing at different temperatures. The wake exchange coefficient, in the CCBM model, is calculated and compared with the values obtained from different correlations. For various experiments, the exchange coefficient is found to be in the range of 0.6-1.7 sec-1. The correlations can predict the trend of the wake exchange coefficient change with temperature, but they all overestimate it. The correlations developed by Hoffmann et al. (1993) and Lim et al. (1993) were found to give a better agreement with the results at high temperatures.

An extended version of the countercurrent back-mixing model suitable for solid mixing in two dimensional fluidized beds

An extended version of the countercurrent back-mixing model suitable for solid mixing in two dimensional fluidized beds

The use of two different models to describe the axial mixing of solids in fluidised beds

Two widely used models to describe axial solid mixing in fluidised beds (the dispersion model and the countercurrent backmixing (CCBM) model) are evaluated against identical sets of experimental data. Experimental work has been obtained at different conditions (gas velocity, particle properties and two column diameters) using an image analysis technique. Previously published data by other authors are also compiled to enlarge the experimental database for model development and validation. It is shown that both models are capable to fit the majority of experiments well, in agreement with a well-known relation between the models in some extreme conditions. This relation is further explored by incorporating independent measurements of the tracer rise velocities during the mixing experiments. It is concluded that, although a simple correlation for the solid dispersion coefficients compiled in this work is useful, the CCBM model is a much more reliable idealisation in describing and scaling up axial solid mixing in fluidised beds.

Modeling the Axial and Lateral Mixing of Solids in Fluidized Beds

The solid flow patterns in fluidized beds are often depicted as a number of convective currents induced by rising bubbles. This description is revisited in this work to develop a mathematical model for both the axial and the lateral mixing of solids in fluidized beds. The model uses concepts similar to those used in the countercurrent backmixing model, which is widely used for axial mixing only. Mixing experiments using coal and PVC (as a white tracer) were carried out to obtain experimental concentration maps for model validation. The model reproduces well the general features observed during the mixing experiments, as well as the effects of gas velocity, particle size, and the presence of internals. The selection of most model parameters can be justified with observations of bed and bubble properties. The choice of the exchange rate of solids between countercurrent phases is discussed in light of the new data derived in this work, previously published data, and a sensitivity analysis of the model predictions for this parameter.

An extended version of the countercurrent backmixing model suitable for solid mixing in two-dimensional fluidised beds

In this work, a new mathematical model to describe axial and lateral mixing in fluidised beds is presented. The model is an extension of previous versions of the countercurrent backmixing model (CCBM) that were restricted to axial mixing only. The fluidised bed is divided into parallel ‘mixing columns’, which are convective currents induced by the bubbles. Each mixing column has a central upflowing stream of solids and two adjacent moving downwards. The practical application of the model requires a minimum knowledge of the bubble properties and the definition of one empirical parameter: the exchange coefficient between countercurrent phases, K w. The model can be rapidly solved with the proposed algorithm and reproduces semi-quantitatively the main features observed in mixing experiments carried out in a bidimensional fluidised bed of coal and PVC as tracer.

Influence of horizontal tube banks on the behavior of bubbling fluidized beds: 2. Mixing of solids

Video image analysis techniques were used to investigate the solids mixing behavior in a two-dimensional (thin) fluidized bed containing “simulated” horizontal tube banks. Colored glass beads were used as the tracer, and the image intensity was used to deduce the variation of axial concentration profiles with time. A three-phase counter-current back-mixing model was developed for data interpretation. The model accounted for the axial variations in bubble properties and in flow (of gas and solids) in the presence of tubes. These variations induce cross-flow of material between phases (for volume conservation). Mathematical form for the cross-flow term for inclusion in the conservation equations was deduced. The model equations were solved using finite difference techniques; bubble parameters for use in the model have been described in a previous paper, part 1 in this series. Calculations compare favorably with experimental data. The results also show that both tube position and tracer feed location have significant effects on the mixing time. Tubes located in the top and the bottom of the bed lead to smaller mixing times; tracer fed in the middle of the bed provides the fastest mixing rate.

Solids mixing in gas-liquid-solid fluidized beds: Experiments and modelling

Mixing in monosized particles and binary mixtures of solids in three-phase fluidized beds is investigated by means of a non-invasive Radioactive Particle Tracking technique (RPT). Pulses of particles at different column heights are constructed from the trajectory of a single radioactive tracer whose motion is tracked for several hours. For each pulse released, number distributions of particles in the axial direction are thus obtained for each instant of time from injections at different axial positions in the reactor. Using this information, axial mixing times for the solids are measured for the experimental conditions studied. A one-dimensional two-zone model based on the three-phase counter-current backmixing model used for gas-solid fluidization (Gwyn et al., 1970) is proposed and solved for these conditions to calculate solids axial number distributions and mixing times. Agreement between experimental and predicted results is satisfactory.

Reaction engineering simulations of a fluidized‐bed reactor for selective oxidation of fluorene to 9‐fluorenone

AbstractThe catalytic oxidation of fluorene to 9‐fluorenone in a fluidized‐bed reactor was investigated by modeling of the reactor and simulation of its performance. The “Bubble Assemblage Model” of Kato and Wen, the “Bubbling Bed Model” of Kunii and Levenspiel and the “Countercurrent Backmixing Model” of Potter were applied. From a comparison of simulation results obtained by the various fluidized‐bed models and a fixed‐bed model conclusions were drawn about the influence of interphase mass transfer and gas backmixing on the conversion of fluorene and slectivity of 9‐fluorenone formation. Furthermore, the dependence of conversion and selectivity on temperature and hydrodynamic conditions was investigated. In particular, the implications of a change of hydrodynamic conditions for scale‐up were analysed. The highest yield of 9‐fluorenone predicted for a bench‐scale fluidized bed amounted to 88% (XF = 97%, SNON = 91%). This yield was lower than in a fixed‐bed reactor (YNON = 92%, XF = 99%, SNON = 93%). A further drop of the yield was predicted when scaling‐up from a bench‐scale reactor to a commercial size unit (YNON = 54%, XF = 86%, SNON = 63%).

Mixing of homogeneous solids in bubbling fluidized beds: Theoretical modelling and experimental investigation using digital image analysis

An automated non-intrusive image analysis method has been developed for following the course of solids mixing in two-dimensional bubbling fluidized beds. In this investigation, experimental data have been obtained on the axial mixing of uniform solids. Oscillations in the concentration response, resulting from the gross circulation of the solids, have been observed experimentally. These oscillations become increasingly more prominent as the bed particle size increases. These measurements have been used to evaluate the three-phase counter-current back-mixing model (Gwyn et al.). The bubble parameters required for the model were obtained from independent experiments conducted as a part of this investigation; the exchange coefficient however, was found by parameter estimation using the solids mixing data. With this choice of parameters, the counter-current flow model has been found to predict the experimental trends reasonably well. The estimated values for the exchange coefficient do not compare favourably with the predictions of the models available in the literature (Yoshida and Kunii, and Chiba and Kobayashi). These models predict that the wake exchange coefficient should increase with increase in the minimum fluidization of the bed particles. Our results, on the other hand, show that the wake exchange coefficient increases with U O/ U mf for U O/U mf < 3 and the values, in this region are independent of the particle size. In line with these results, the experimental measurements of Chiba and Kobayashi, for injected bubbles in a two-dimensional fluidized bed of particles smaller than those used in this investigation, are found to be in excellent agreement with the lower bound of our estimations.

The counter-current backmixing model for fluid bed reactors — computational aspects and model modifications

Numerical solution of differential equations describing the counter-current backmixing model of Fryer and Potter is very difficult due to the boundary value nature of the problem. Several numerical methods (shooting, superposition and finite difference) have been described and tested on a problem with a single first-order reaction in an isothermal fluid bed reactor. It was found that the finite difference method is the most stable method and provides accurate solution over the entire range of parameters that were investigated, while the shooting and the superposition methods could not produce accurate solutions for some parameter values. Also, some modifications of the Fryer and Potter model such as: compartment models and conversion to an initial value type of problem (Jayraman-Kulkarni-Doraiswamy model), have been described. Results obtained from compartment models are in close agreement with predictions obtained from the original Fryer and Potter model.

The countercurrent backmixing model for fluid bed reactors—effect of cross flow and boundary conditions

En tenant compte de la variation de la taille des bulles avec la hauteur dans le reacteur du titre, on aboutit a une modification de la distribution du gaz dans les trois phases le long de la hauteur du lit. Ceci a peu d'effet sur les previsions du modele. L'utilisation des conditions limites proposees par Peters (1982) et al. donnent en general de plus grandes valeurs de conversion que pour les conditions limites de Fryer et Potter (1972)

Experimental and theoretical study of a multistage fluidized-bed reactor

The performance of a multistage fluidized-bed reactor was investigated. The system was studied using the ozone decomposition reaction over alumina catalyst. A 7.8 cm ID PVC fluidized-bed reactor was designed and constructed. Bubble frequency measurements were made using a differential pressure probe in conventional (unbaffled) and baffled fluidized beds with or without a downcomer with no reaction. The longitudinal concentration profile was measured in each of the systems. The results showed the occurrence of a unique minimum, which provided evidence of gas backmixing in the bed. The overall conversion in the baffled fluidized bed was higher than that in the conventional bed. Within the operating conditions used in this study, it was found that the number and location of baffles significantly affect the overall conversion. In contrast, the use of a 1.1 cm ID downcomer did not affect the conversion level in the baffled fluidized beds. A modified countercurrent backmixing model was used to predict the overall conversion and concentration profiles in the fluidized beds. The model included three-regimes: bubble, transition, and slugging; and three-phases: bubble or slug, wake, and emulsion. The model accounted for the effect of reversed flow of emulsion gas. The bubble diameter in the fluidized bed was calculated using the experimentally measured bubble frequency. The model showed the potential of predicting the experimentally observed overall conversion and concentration profile of the ozone gas in both the conventional and baffled fluidized bed with or without downcomer.

CHARACTERIZATION OF FLUIDIZED BED REACTORS WITH GAS TRACER MEASUREMENTS

In a steady state bench scale fluidized bed the decomposition reaction of NaHCO3 was carried out. The residence times distributions, DRT, of carbon dioxide (the gaseous product) and non adsorbing argon (the reference tracer) were mass spectroscopically measured as a function of the bed temperature. By means of single-, two- and three-phase dispersion models as well as by a cell model, the DRT's were evaluated on line by a computer. The steady state transverse and longitudinal concentration profiles of these tracers upstream from the plane source were also measured and evaluated by a dispersion model as well as by a counter current back mixing model. Comparison of the steady state and nonsteady state dispersion coefficient measurements indicate that the longitudinal gas mixing is only partially due to backmixing. The experimentally determined wake fractions agree well with those published in the literature. Since the adsorption rate of CO2 on the pore surface area of the particles in the dense phase is hig...

Countercurrent backmixing model for slugging fluidized‐bed reactors

AbstractA model is developed for slugging fluidized bed catalytic reaction which improves on the model of Hovmand and Davidson by incorporating the solids mixing. The model parallels the countercurrent backmixing model of Fryer and Potter. Solids mixing is accounted for by the model of Thiel and Potter which assumes the rising slug is followed by a well‐mixed wake into and out of which solids flow at a rate determined by the rise velocity of the slug. Comparison is made with experimental data reported by Hovmand and Davidson with good results.

Experimental investigation of models for fluidized bed catalytic reactors

AbstractThe countercurrent backmixing model of a fluidized bed reactor predicts axial concentration profiles quite different from those suggested by simple two‐phase models. The models can also be distinguished in terms of the dependence of conversion on operating variables.An experimental study of ozone decomposition in a reactor of 22.9 cm diameter has provided extensive data for comparison with backmixing and two‐phase models which incorporate bubble size variation. The measured profiles show a minimum concentration within the bed at gas velocities above a critical value, as predicted only by the backmixing model. The effect of operating variables on the shape of the profiles is also well accounted for by this model. The backmixing model is further supported by good agreement between predicted and measured reactant conversion. In particular, the variation of conversion with rate constant and gas velocity is fitted more accurately by the backmixing model than by two‐phase models.

Countercurrent Backmixing Model for Fluidized Bed Catalytic Reactors. Applicability of Simplified Solutions

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTCountercurrent Backmixing Model for Fluidized Bed Catalytic Reactors. Applicability of Simplified SolutionsColin Fryer and Owen E. PotterCite this: Ind. Eng. Chem. Fundamen. 1972, 11, 3, 338–344Publication Date (Print):August 1, 1972Publication History Published online1 May 2002Published inissue 1 August 1972https://doi.org/10.1021/i160043a009RIGHTS & PERMISSIONSArticle Views278Altmetric-Citations52LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (629 KB) Get e-Alerts

Particle tracking in a Two-Section Two-Zone Fluidized Bed Reactor (TS-TZFBR). Experimental technique and CCBM model validation

The Two Zone Fluidized Bed Reactor (TZFBR) provides a high level of process integration, allowing reaction and, in situ, continuous catalyst regeneration, in a single fluidized bed. Reactive and regenerative atmospheres are induced simultaneously inside the single vessel due to a separated gas inlet and particles fluidization provides reactor continuous operation. Therefore, the fluid dynamic key factor in a TZFBR is the mixing rate between solids inside the two bed zones (a good mixture provides continuous catalyst regeneration, while bad contact between bed zones leads to deactivation and loss of catalytic surface). In the present study, phosphorescent particles have been used as optical tracers to measure solids axial mixing between reactor zones in a catalytic TZFBR. Additionally, a different cross-sectional area between zones has been studied to get a certain fluidization regime, allowing small flowrates in the regeneration zone. This geometry implied a transition angle α between zones to be implemented (Two-Section TZFBR). In line with it, a modified counter-current backmixing model (CCBM) without fitting parameters was developed to predict mixture rates inside the bed for different TS-TZFBR geometries. Modifications carried out in the CCBM basis model involved reactor geometry and the presence of two simultaneous gas feed points along the bed. Model parameters related to bubble/solid fraction and wake-emulsion mass transfer were fully correlated to operational conditions (gas velocity, feed point location and section change). The adapted CCBM model predictions were further validated with optical tracers experimental fluid dynamic data, resulting in a high agreement.

Back-mixing of gas in a 6-in diameter fluidised bed

The counter-current back-mixing model of fluidised-bed behaviour is applied to experimental back-mixing data obtained in a 6-in diameter column, with beds consisting of glass spheres, of mean diameter 75μ, 97μ and 125μ respectively. With still larger particles, the gas velocity required to produce back-mixing is such that slugging is produced in the 6-in diameter column. While the data have been expressed as axial diffusion coefficients, primarily they have been interpreted in terms of the counter-current back-mixing model to determine 1. (i) the critical velocity, U cr, at which back-mixing commences; U cr/U o ⋍ 3; 2. (ii) f w, the volume of dense phase, set in motion per unit volume of bubble; f w ⋍ 1·0. 3. (iii) the rate of gas-exchange between ascending and descending material. The rate calculated from the experimental data in terms of the back-mixing model is of the same order of magnitude as the theoretical estimate of the exchange rate given by Davidson and Harrison, but the dependence on bubble diameter is different.