A Model of Attrition In the Jetting Region of Fluidised Beds t

Attrition causes material Joss and environmental hazards in powder processing. In fluidised beds, the jetting region is the main contributor to attrition. The present paper reviews the recent investigations of the effects of the interaction between single particle properties and jet hydrodynamics. A model of attrition in the jetting region of fluidised beds is presented, based on the impact attrition propensity of single particles and on modelling of the particle flow patterns in the jetting region. The experimental work, carried out for the purpose of evaluation of the model, focused especially on the effects of orifice gas velocity and diameter. The experiments involve measurements of impact attrition of single particles and measurements of particle velocities and solids concentrations in fluidised bed jets. The test materials are fluid cracking catalyst and common salt, both representatives of widely used classes of composite and crystalline materials, respectively. Significant effects of orifice gas velocity and diameter were predicted, which corroborated the experimental data. Hence, the model successfully establishes a link between single particle properties and bulk behaviour in a fluidised jet.


Introduction
Attrition, the unintentional breakage of particulate solids during processing, handling and storage, causes material loss and environmental hazards. Fluidised bed operations have become increasingly popular in industrial particle processing, for the ease of solids handling, mixing and high rates of heat and mass transfer. These features are desirable for a number of processes, such as drying and reactor systems, e.g. fluid catalytic cracking and combustion. Unfortunately, the intensive particle motion in fluidised beds causes attrition at the same time. For example, material loss in fluidised catalytic cracking units can amount to several tonnes per day! Zenz and Kelleher [1] have identified the distributor region and the cyclone as important sites for attrition due to the presence of high local velocity gradients. The distributor region provides by far the largest contribution to attrition in fluidised beds, when compared to the bubbling bed and the freeboard above it. Several studies have been undertaken in the past to characterise the attrition propensity of particles in fluidised beds [2], but few take account of the material * Guildford-Gl'2 5XH CC'K) t Recei\'ed: 3 June 1996 KONA No.l4 (1996) properties of particles, or attempt to decouple the interacting hydrodynamic parameters. The dependence of the attrition rate in the jet region on the design and operating parameters, such as the distributor orifice size and gas velocity, and particle size and properties has so far not been established satisfactorily.
A number of empirical correlations for the rate of attrition in fluidised beds, R 3 , have been reported in the literature. These are summarised in Table 1.
Focusing on two main design and operation parameters, the orifice size, d 0 ro and the gas velocity, u, the correlations are generally written in the form of a power law: (1) where u can be the orifice gas velocity (u 0 ), or the superficial (u 5 ) or excess gas velocity (u 5 -umf), with values of n ranging from 0.66 to 5.8 and of h from 0 to 1.11, as reported by different authors. The exponential correlation of Lin et al. [6] appears to be an exception to this general form, but replotting their data shows that there is no need for an exponential correlation, and that a good fit is also achieved with a linear regression. Notwithstanding this basic similarity, each of these correlations has been obtained for different materials, experimental set-up and ope- In this work, the attrition of common salt and fluid cracking catalyst (FCC) is considered, focusing in particular on the link between single particle properties and bulk attrition behaviour. These two material types, in addition to their own significance, may be considered as representatives of large classes of widely used materials, i.e. crystalline and composite structures. In this paper, the modelling approach will first be described. The experimental work supporting the development of the model is then presented.

Modelling Approach
In the present modelling approach, the impact breakage of single particles is coupled with a hydrodynamic model to predict the rate of attrition. The structure of the approach is represented schematically in Figure 1.
For impact attrition, Zhang and Ghadiri [16] have proposed the following correlation for the extent of attrition upon impact, Ri, based on the fracture mechanics of lateral crack formation: where PP is the particle density, ui the impact velocity, H the hardness, Kc the fracture toughness, d a linear dimension of the particle, and a is a proportionality constant to be determined experimentally. In practice, the value of the power index of ui may differ slightly from 2, depending on the complexity of the particle structure. It is therefore more general to consider: KONA No.l4 (1996) where the power index m may be obtained from particle impact tests. In a fluidised bed with a jetting distributor region, the contribution of the bubbling zone to the attrition rate is usually very small compared to that of the jetting region [13]. The attrition mechanism in a fluidised bed jet involves the entrainment of particles into a dilute jet core, followed by the acceleration of the particles, whereafter they impact on the dense phase on top of the jet. Intense interparticle collisions are considered to cause attrition, at a rate that can be estimated from impacts of single particles on a rigid target, at an impact velocity, u i, corresponding to the particle velocity, uP' in the jet.
The number of particles engaged in the attrition process scales with the rate at which solids become entrained from the bulk into the dilute jet core. A hydrodynamic model may be used to obtain the dependence of W 5 , and uP on the orifice gas velocity. This can be done by power-law correlations [12]: Ghadiri et al. [12] proposed that the attrition rate in the jetting region is linearly related to the single particle impact attrition and the solids entrainment rate. Thus, substituting Eq. (4) into Eq. (3), and multiplying by the solids entrainment rate, W 5 , the attrition rate in a single jet may be given as: (6) In this way, a descriptive and predictive model is established, which incorporates the single particle attrition characteristics. The results of this approach will be presented in section 4.
The dependence of the attrition rate Ra on the orifice size, as reported in the literature, is inconsistent. The power index h in Eq. 1 given by Kono [8] and Ghadiri et al. [15] is of order unity, between 0.44 and 1.11. For comparison with other correlations that are expressed in different dimensions, e.g. those of Werther and Xi [11], and Zenz and Kelleher [1], it is necessary to normalise the correlations, e.g. by dividing the rate of attrition by the mass flow rate of fluidising gas. Following this approach, the correlations of Werther and Xi [11] and Zenz and Kelleher [1] indicate that the attrition rate does not depend on the orifice size.
For the analysis of the effect of the orifice size on the attntlon rate Ra, Ghadiri et al. [15] have employed a similar approach as described above for the effect of orifice gas velocity. Normalising the solids entrainment rate with respect to the gas flow rate, Wg, its dependence on the orifice diameter, dor• can be expressed in a power law [15]: (7) and similarly for the dependence of the particle velocity: Following the same approach as for the effect of velocity (Eq. 6), the attrition rate in the jet can expressed as: Thus, the dependence of the attrition rate on the orifice size can be established by quantifying the power indices. This is described in section 4.
Independent studies of the hydrodynamics of fluidised bed jets by Massimilla and co-workers, firstly introduced by De Michele et al. [17], have provided comprehensive models of particle flow patterns in the jetting region [18]. With these hydrodynamic models, particle velocities and solids entrainment rates can be readily obtained for different orifice velocities and sizes. However, the application of these models requires knowledge of the relevant input parameters, describing the jet geometry, such as the jet penetration length, the jet divergent angle, and the solids concentration in the jet. These have to be obtained from separate experiments, which are described in sections 3.2 and 3.3.

Experimental
Several tests have been employed in the evaluation of the jet attrition model. The experiments involve firstly single particle impact tests for the determination of the impact attrition of single particles as a function of the impact velocity, as shown in Eq. 2. This is described in section 3.1. Secondly, the attrition rate in a fluidised bed with several gas distributors has been measured in order to compare these results with predictions from the attrition model. This is described in section 3.2. In order to quantify the power indices given in equations (6) and (9), it is first necessary to specify a number of hydrodynamic parameters, such as the jet angle.
8 This is described in section 3.3.

Single particle impact test
Single particle impact tests have been carried out in an impact test rig developed previously [19] and shown in Figure 2. It consists of a funnel-shaped inlet section guiding the particles into an eductor tube, which ends in a collection chamber, where particles impact on a rigid horizontal target plate made of sapphire. The particle velocity before impact is measured with dual light diodes or with a laser Doppler velocimeter.
The impact product is analysed gravimetrically. As a criterion for attrition, the mass of debris passing through a sieve, with a size of two BS410 sieve sizes below the lower limit of the original size, is chosen. In the low range of impact velocities, where mainly surface damage (chipping) occurs, the fines produced will be far smaller than the original mother particles.
Cleaver et al. [20] have shown that the attrition results are in this case insensitive to the specific criterion applied, as long as the sieve size, used for the separation of debris from the mother particles, lies in between the particle size distributions of the Fine Product and Coarse Product, as shown schematically in Figure 3. The attrition rate is then simply defined as the ratio of the mass of fine product to the initial sample mass of mother particles:

Fluidised bed attrition test
Fluidised bed attrition tests have been carried out for the determination of the variation of attrition with orifice gas velocity and size.
Two materials have been investigated, Pure Dried Vacuum (PDV) NaCl salt, produced by ICI pic, mean particle size dp = 418 flm, with a density of 2180 kg m· 3 , and FCC, dp = 106 flm, with a density of 1500 kg m· 3 . For FCC, the data of Werther and Xi [11] were used. The experimental set-up used for fluidised bed attrition tests of salt is shown in Figure  4. A detailed description can be found elsewhere [13]. Three different perforated plate distributors were used, with 73, 110, and 175 holes of 1 mm diameter, i.e. each with a different free area. This enabled the decoupling of the effect of superficial and orifice gas velocity on the attrition rate, since the bed could be operated at the same superficial velocity for three different orifice gas velocities. According to the correlation of Fakhimi [21], all grid holes were active in all conditions, so that good distribution of air across the distributor was ensured.
The contributions of the jetting region and of the bubbling part of the bed to the attrition rate have been decoupled by operating the bed at different loading, yielding different bed heights. By plotting the attrition rate against bed height and extrapolating to a height equal to the jet height, the contribution of the jetting region to attrition has been quantified.
The effect of distributor orifice diameter on the attrition rate has been investigated by Ghadiri et al. [15] using salt as the test material in a 58 mm diameter cylindrical Perspex bed of 0.9 m height, otherwise similar to the set-up shown in Figure 4.
The results are presented in section 4.

Measurement of jet parameters
In the hydrodynamic jet model of De Michele et al. [17], which is employed here, the particle flow patterns in the jet are calculated on the basis of Schlichting similarity profiles, following the turbulent jet theory of Abramovich [22]. These profiles scale with the actual geometry of the jet, as it extends axially and expands radially into the bulk of the bed. To establish these profiles for a given orifice size and velocity, several parameters, such as the jet angle and height, and the initial solids concentration at the jet exit need to be specified.All these parameters are difficult to measure, especially in a threedimensional bed. A number of measurements have been carried out in two-dimensional and three-dimensional (cylindrical) fluidised beds, using various measurement techniques [12][13][14][15][23][24][25]. The measurements with two-dimensional beds are only used for input in the two-dimensional version of the hydrodynamic model. However, comparison of the model predictions with the experimental data from twodimensional configurations can be used to check the validity of the current approach. Measurements of jet angles in the cylindrical fluidised bed, described in section 3.2, have been carried out using an X-ray facility using salt, dp = 418 flm, and alumina particles, dp = 107 llm [25].
Digital analysis of video images taken from a twodimensional fluidised bed, shown in Figure 5, has been used for measurements of jet half angles with FCC catalyst, dp = 90 flm. In this apparatus, the gas jet is produced by slots, sandwiched between two porous plates for background fluidisation [23].
In this two-dimensional set-up, a strong dependence of the jet angle on orifice gas velocity has .... been found, even with a narrow orifice of 0.5 mm, where the jet half angle decreases in a linear fashion from 11.5° (u 0 = 9.4 ms-1 ) to 7° (u 0 = 54 ms-1 ).
The trends for different orifices behave like tangents to a single hyperbolical curve, as shown in Figure 6. There is, however, a certain overlap in the gas velocity range, where the trendlines for neighbouring jet sizes cross over each other, indicating a distinct effect of the orifice size, rather than just a velocity effect. Similar effects, but to a different extent, were observed in the three-dimensional set-up [25]. Measurements of the initial solids concentration in the jet have been made using the two-dimensional fluidised bed, shown in Figure 5, which was equipped with optical glass walls for the specific purpose of video recordings with a high resolution camera [23]. Results of these measurements are shown in Figure 7. The solids concentration at the nozzle exit appears to increase with decreasing orifice size. This is supported by our visual observations [24] that with wide orifices, the jet core is clear of solids, 10 whereas with narrow orifices the jet core is occupied by a significant amount of solids, even at high u 0 • In order to compare the hydrodynamic model predictions with the actual solids flow patterns, measurements of particle velocities have been carried out in the two-dimensional bed equipped with optical glass walls, for the FCC and the NaCl salt. The results are shown in Figure 8 and 9 [23,24]. These measurements have been obtained, using digital image analysis of video images of the particle flow, recorded with a Kodak high speed video camera at frame rates up to 40500 frames per second.
For FCC (Figure 9), a good agreement is shown between experimental data and predictions from the hydrodynamic model. For NaCI (Figure 8), the agreement is fair, but the data are more closely matched for large orifice diameters. Considering the observation that NaCl particles do not accelerate significantly along the jet height for narrow orifices, because of the increased solids concentration, this feature suggests that there is a distinct effect of the ratio of particle-to-orifice diameter on the flow pattern, which is currently not accounted for in the model.

Attrition model application and evaluation
4.1 Effect of velocity on single particle impact attrition The first step in the application of the attrition model is the establishment of the power index m in Eq. (3). The single particle impact tests show a slight variation from the theoretical value of 2 for some materials. Table 2 shows measured values of m for melt-grown and solution grown NaCl crystals, and for FCC. The solution grown NaCl crystals contain poly crystals and crevasses, which contribute to the deviation of m from 2. The index m is sensitive to internal and surface defects and structure, the presence of polycrystals, work-hardening and fatigue [13,14,16,26].

Effect of distributor orifice size and velocity on fluidised jet attrition
The measurement of the fluidised bed jet attrition as a function of orifice velocity and size involved decoupling of a number of concurrent processes, such as the attrition in the jetting region and in the bubbling part of the bed. As described in section 3.2, experiments with different bed heights have been carried out to enable the establishment of a correlation between the bed height and the attrition rate, from which the attrition in the jetting region may be inferred. The result of this operation is shown in Figure 10, where the data points are accompanied by a trendline of a best fit with a power index yielding a value of n in Eq. (6), as reported in Table 3.
The entrainment rate and particle velocity in the jet, as predicted by the hydrodynamic jet model, are shown in Figures 11 and 12 for NaCl for a 1.0 mm orifice diameter. From the curve fits, values of the power indices k and 1, for the particle velocity and the solids entrainment rate, respectively, as given in Eqs (4) and (5), may be obtained. These are given in Table 3, together with the value of m, from Eq. (3), for the NaCI particles. The overall attrition index n (Eq. 6) is then calculated and is given in Table 3.
The predicted results compare favourably with experimental data for NaCl and FCC, also shown in Table 3. The experimental value of n for FCC is that given by Werther and Xi [11]. Zenz and Kelleher   by Werther and Xi [11] and m has been obtained by single particle impact testing [1] using the same material as used by Werther and Xi [11]. The predicted dependence of the attrition rate on the orifice diameter is shown in Table 4, where the values of s, t and h have been given (see Eqs (7)- (9)).
The values of h compare reasonably well with the experimental values of Kono [8] and Ghadiri et al. [15], but contradict with the absence of any effect of the orifice size, as indicated by Werther and Xi [11] and Zenz and Kelleher [1]. Variations in the level of background fluidisation may be responsible for this difference (see Table 1).

Discussion
The model of jet attntwn combines a model of particle breakage with a hydrodynamic model of particle flow in a jet in order to predict the rate of attrition. The experimental observations of particle velocity and concentration profiles suggest that there is an influence of the orifice-to-particle size ratio. and this is currently not taken into account in the hydrodynamic model.
For orifices much larger than the particle size, the core of the jet is almost entirely clear of particles, whereas for orifices of size comparable to or smaller than the particle size the solids concentration in the jet was observed to be high. This strongly influences the particle-particle interactions. For the latter, at high orifice velocities, the particles will shear against each other, causing abrasion, whereas for the former, particles may accelerate freely, causing more integral damage, thus increasing the probability of fragmentation. Further refinement of the model is necessary to incorporate the effect of the ratio of orifice diameter to particle size.
There are several simplifying assumptions in the attrition model, whose validity may have to be assessed for particles of interest. These are as follows. i) It is assumed that the dependence of interparticle impact damage on impact velocity follows the same trend as the impact of a particle on a rigid target. The latter may provide a more extensive damage as the target is rigid. However, the effect of impact velocity is not expected to be different from interparticle collisions.
Generally, the collision frequency in a fluidised bed is very high. The high speed video recordings of NaCl particles showed that particles in fact accelerate along the jet axis, which is almost clear of particles, and subsequently impact on the dense phase on top of the jet. The particles often scour the jet boundary as if they had been launched into a pin ball machine. However, most of the momentum is dissipated during the first impact, and the subsequent collisions take place at a velocity similar to the recirculation velocity of particles in the bulk. Therefore, the actual process of attrition will be contained in the first particle-bulk collision, and the similarity between the single impact and the jet impact is preserved.
ii) The influence of time is shown in Figure 13 for NaCl particles. This effect has not been considered in several investigations, where tests have been performed for one hour only [3,27], or even shorter periods [10]. Cairati et al. [28] have shown that KONA No.14 (1996) molybdate catalyst particles do not reach steady state equilibrium within one hour in the Forsythe-and-Hertwig test [27], and the present NaCl particles reach steady state only after five hours. iii) Impact breakage studies have shown that repeated impacts at the same velocity may progressively either weaken or strengthen the particles, causing the attrition rate to vary with the number of impacts [29]. Plastic deformation of semi-brittle particles may cause work-hardening, which eventually leads to an increase in the attrition rate. On the other hand, the first few impacts may cause weaker particles to break, whence the remainder would appear to be more resistant to attrition. iv) In the analysis of attrition, Ghadiri et al. [12][13][14][15] have carried out a complete analysis of the bed inventory, accounting for the debris in the bed. In a number of previous investigations, the attrition rate is quantified by the amount of fines elutriated from the bed. This process ignores the quantity of the debris [30] which is in dynamic equilibrium in the bed [31]. This may be a source for discrepancies in the trends reported in the literature.
The power index m for single particle impact damage does not vary widely from its theoretical value of 2 for FCC and different types of NaCI. However, the overall attrition index varies from 3 to about 5 ~ It is interesting to note that the present approach is capable of identifying the relevant hydrodynamic parameters to predict the actual power index for attrition in the processing environment.

Conclusions
The model of attrition in fluidised bed jets provides a realistic prediction of the effect of a number of important design and operating parameters such as orifice size and gas velocity. The model takes account of the particle properties and hydrodynamic conditions of the jet. The procedure established to estimate the attrition rate in the jetting region of fluidised beds is to obtain a measure of the attrition propensity of single particles by impact testing and to couple this process with the rate of solids entrainment into the jetting region by the use of hydrodynamic modelling. The model has been successfully applied to two very different types of material, FCC powder and NaCl crystals. Further testing with materials such as weakly-bonded agglomerates and resins would be useful to establish the range of the applicability of the model.

Acknowledgement
Financial support from the University of Surrey and Shell Research B. V. is gratefully acknowledged. The authors are grateful to EPSRC and Mr Peter Goodyer for providing quick access to the high speed video and photography facilities from EPSRC' s equipment pool. Dr W. Duo is thanked for his valuable comments on the manuscript.

Professor Mojtaba Ghadiri
Mojtaba Ghadiri graduated in Chemical Engineering from the University of Tehran, and subsequently obtained an MSc from Imperial College and a PhD from the University of Cambridge. He then worked for Unilever Research as a scientist for two years before joining the University of Surrey in 1983. Mojtaba Ghadiri holds the Chair of Particle Technology at the University of Surrey. His current research activities are on attrition and comminution of particulate solids, fluidisation, and electrical effects in bulk particulate systems. He has developed a specialised facility for mechanical testing of fine particulate solids and has worked extensively on linking the material properties with particle behaviour KONA No. 14 (1996) in attrition and comminution processes.

Ir Renee Boerefijn
Renee Boerefijn graduated in Mechanical Engineering from the University of Twente in 1994. For his Diploma Thesis, he spent a year at the University of Naples, where he worked on the hydrodynamics of fluidised beds and developed a special probe for measurement of voidage waves. His current research activities are focused on the interactions between the hydrodynamics of fluidised bed jets and attrition in fluidised beds, using stateof-the-art digital image processing and high-speed video techniques, as well as laser doppler anemometry, as part of his PhD dissertation. Additionally, his recent work includes the impact fracture behaviour of various types of particulate solids.