Catalysis Today 264 (2016) 70-74
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`Contents lists available at ScienceDirect
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`Catalysis Today
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`ELSEVIER
`journal homepage: www.elsevier.com/locate/cattod
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`Catalyst attrition in an ASTM fluidized bed
`
`® CrossMark
`
`Dongfang Wu*, Fanghua Wu, Zhengdong Gu
`Department ofChemical Engineering, School of Chemistry and Chemical Engineering, Southeast University, Jiangning District, Nanjing 211189, China
`
`
`ARTICLE INFO
`ABSTRACT
`
`
`Article history:
`Received 3June 2015
`Received in revised form 21 August 2015
`Accepted 1 September 2015
`Available online 26 September 2015
`
`Catalyst attrition is a major issue for the reliable and efficient performance ofa fluidized-bed reactor.
`In this study, attrition behavior of a commercial FCC catalyst is examined in a laboratory-scale ASTM
`fluidized bed. An attrition rate model that combinesthe jetattrition and bubble-induced attrition is
`derived and confirmed to represent the measured totalattrition rate versus the superficial gas velocity.
`The modelparameters systematically vary with time, since the properties of the attrited particles change
`progressively.It is also shown that the minimum bubbleattrition velocity is far larger than the minimum
`fluidizingvelocity because energyis requiredtoproduceattrition, Furthermore,jetand bubbleattritions
`Foldcatalyticcracking
`are separated and their contributions are discussed. The contribution ofjet attrition increases rapidly
`Fluidized bed
`with increasing the gas velocity, and the fast increase in the jet attrition rate is the major cause of the
`FCCcatalyst
`increasingly serious catalyst attrition with increasing the gas velocity. It is also seen that regression
`Particle attrition
`analysis is an effective tool to the separationof attrition sources.
`Attrition rate
`© 2015 Elsevier B.V, All rights reserved.
`Attrition source
`
`
`1. Introduction
`
`Fluidized beds are widely used in industrial processes such as
`drying, granulation, combustion,and fluid catalytic cracking (FCC),
`because materials mix and contact adequately with each other and
`heat transfers excellently [1,2]. However, particle attrition always
`exists in fluidized beds [3-6]. For example,in a fluidized-bed reac-
`tor, catalyst attrition will result in the generation offines, loss of
`valuable material, degradation ofcatalyst efficiency, environmen-
`tal pollution, etc. Furthermore, new-born small particles brought
`by attrition may damage fluidizing properties and process operat-
`ing conditions [3,6]. Catalyst attrition is, therefore, a majorissue for
`the reliable andefficient performanceofan industrial fluidized-bed
`reactor.
`
`Several methods have been developed to assess and study the
`attrition resistancesof particle materials [7—9]. For powdered cata-
`lysts usedin fluidized-bed reactors, two methods are often used in
`laboratory: ASTM air-jet attrition test [7,8] andjet-cupattrition test
`[9]. They are usually intended to rank different candidate catalysts
`with respect to their attrition resistances. Zhaoet al. [10] reported
`that the jet-cup test needed less catalysts and was as adequate
`as the ASTM standardtest for the prediction of the catalyst attri-
`tion resistance. However,attrition mechanism in an ASTM standard
`fluidized bed is muchcloserto thatin an industrial fluidized bed.
`
`* Corresponding author.
`E-mail address: dfwu@seu.edu.cn (D. Wu).
`
`http://dx.doi.org/10.1016/j.cattod.2015.09.007
`0920-5861/© 2015 Elsevier B.V. All rights reserved.
`
`There are two main typesofattrition: particle fragmentation
`and surface abrasion | 11-18]. Abrasion meansthe loss of edges and
`cornersof particle surfaces, generation of son particles which are
`approximately the samesize to the mother ones anda lot offines,
`while fragmentation refers to a particle breaking into several son
`particles smaller than the motherone. Several sources ofattrition
`can be identified in a fluidized bed system,e.g., grid jet attrition,
`bubble-inducedattrition, and attrition in the cyclones [6,19]. For
`these attrition sources, several correlations have been developed
`to relate the measuredattrition rate to the jet/superficial gas veloc-
`ity, density, orifice diameter,etc. [4,12-15,20-24). Attrition is also
`a time-dependent process and may change systematically with
`time [8,19,25,26]. Many materials show an early nonsteady-state
`attrition behavior, after which attrition decreases to a constant
`value [19,25,26]. Several models have been proposedto describe
`the time-dependence ofattrition behavior,e.g., Gwyn equation [8]
`and exponential decay equation [26]. Moreover,in a fluidized bed,
`attrition is influenced by three categories of factors including parti-
`cle properties (material properties, textural properties, mechanical
`strength, shape,size, and surface roughness, hardness, microcracks,
`etc.), fluidization conditions (gas velocity, pressure, temperature,
`density, humidity, etc.), and fluidized-bed structure parameters
`(most importantly, orifice number and diameter for multi-orifice
`distributor plates) [4,11—15,20-24,27].
`Academicinstitutions active in catalysis research generally con-
`centrate on the chemistry rather than the catalyst mechanical
`properties. Less effort has been madeto investigate the attrition
`behavior and mechanism in fluidized beds, although a reasonable
`
`WRG-1014
`
`1
`
`WRG-1014
`
`

`

`t Elutriated fines
`|
`
`Gravitational
`
`separator
`
`Distributor plate «= Air flow
`
`710
`
`Attrition tube
`
`Fig. 1. Schematic diagram of attrition apparatus (The physical unit of data is mil-
`limeter.).
`
`amountof information is already available concerning the parti-
`cle attrition. To our knowledge,noarticle is available so far in the
`openliterature about the scientific basis for the ASTM air-jet attri-
`tion test; therefore, an interest in studying theattrition behavior
`in an ASTM fluidized bed arises. Moreover, sourcesofattrition in
`fluidized beds should be examined, andthereis a lack of an effi-
`cient and quick methodto separate the total attrition rate into
`contributions of different sources. Therefore, the issues of cata-
`lyst attrition call yet for further elucidation and advancement. In
`this work, dependence ofattrition behavior of a commercial FCC
`catalyst on superficial gas velocity was examined in a Jaboratory-
`scale fluidized bed designed according to ASTM standard. Thetotal
`attrition rate was correlated with a derived attrition rate equation.
`Sourcesofattrition were separated by a simple regression analysis
`method, and their contributions were discussed.
`
`2. Experimental
`
`2.1, Catalyst sample, apparatus, and attrition tests
`
`A commercial FCC catalyst was used in this study. It consists
`mainly of Y-zeolite and kaolin, and is serving in a FCC unit in China
`petroleum industry. Its mean particle diameter, packing density,
`and surface area are about 109 um,0.885 g/cm? and 168.7 m2/g,
`respectively. Other physical properties have been described else-
`where [26]. Prior to attrition tests, the catalyst was sieved by a
`61-micron sieve to eliminate pre-existing fine particles, and then
`dried at 120°C in air for 2 h to remove theeffect of humidity.
`A laboratory-scale fluidized bed, shown in Fig. 1, was employed
`as an attrition test apparatus. It was designed according to ASTM
`D 5757-11 standard [7], consisting of six parts: air supply system,
`gas distribution chamber, three-orifice distributor plate, attrition
`tube, gravitational separator, and fines collector. The distributor
`
`2
`
`D. Wu et al, / Catalysis Today 264 (2016) 70-74
`
`71
`
`plate contains three symmetrically arranged upward-facing holes
`with diameter 0.381 + 0.005 mm, and these holes are 10mm dis-
`tant from the plate center. Other dimensions are markedinFig. 1.
`For more information onthe attrition apparatus, see ASTM standard
`[7] or one of our previous publications [26].
`Attrition tests were carried out at room temperature. After 50g
`of a dried catalyst was charged, an air flow was produced byair
`compressorand fed to the attrition apparatus to fluidize catalyst
`particles. Elutriated fines were collected, dried, and then weighed.
`Detailed operating steps were described in previous article [26].
`It should be mentioned that after fines collector, air flow was
`directly emitted into the atmosphere; therefore, the temperature
`and pressure in the fluidized bed could be approximately regarded
`as normal temperature and pressure (NTP), i.e., 20°C and 101.3 kPa.
`Under the operating condition, seven superficial gas velocities
`(0.0834, 0.0981, 0.1155, 0.1337, 0.1528, 0.1746, and 0.1951 m/s)
`were examinedin this work. For each gas velocity, the mass of the
`elutriated fines was determined as a functionof theattrition time,
`and thenthetotal attrition rate was calculated.
`
`2.2. Data analysis
`
`In theliterature [6,12,19,22,27,28], attrition rate is often defined
`as the massofthe elutriated fines per unit time:
`
`dine
`Ra= >
`
`(1)
`
`whereR, is the attrition rate at attrition time t, and m, the cumu-
`lative mass ofthe elutriated fines at timef. In a fluidized bed, two
`sourcesofattrition,i.e., grid jet attrition and bubble-inducedattri-
`tion, can often be identified; therefore,the total attrition rate in the
`bed is the sum ofthe attrition rates of the two sources[6,19].
`Grid jet attrition has been studied by several authors
`{9,10,23-25,27-31]. Considering the energy utilization of abrasion
`process, Werther and Xi [28] derived a relationship for grid jet
`attrition rate, which can be rewritten as
`
` p&
`5 =G-dpp- pr- >
`d4, .n2,
`Ra,j
`JP
`whereR,j is thejetattrition rate, C; thejet attrition constant, dpp the
`surface mean diameterof bed particles, nor the numberoforifices
`in the distribution plate, dor the diameteroforifices, ps the den-
`sity of jet gas, D, the diameterof fluidized-bed column, and u the
`superficial gas velocity. The mechanisms of bubble-induced attri-
`tion are not quite clear. There are various theoretical and empirical
`approaches[6,14,32] that can be summarized as
`
`(2)
`
`Rap = GQ * m} . (u _ Umin)”
`
`(3)
`
`where R,» is the bubble attrition rate, G, the bubble attrition
`constant, n and m the two powerexponents, u,,j, a threshold
`velocity above which bubble-inducedattrition occurs, and mp the
`decreasing catalyst bed mass duefoattrition (m, =m — Me, where
`Mgis the initial catalyst bed mass,i.e., the catalyst bed massat time
`t=0. mo =50¢g in this study). Combining Eqs. (2) and (3), the total
`attrition rate in a fluidized bed can, therefore, be expressed as
`
`t
`2
`dg, - ner
`
`Ra,tot = Raj + Rab = G - dpb - Pr-
`
`uP +, - me -(u-Umin)™
`(4)
`
`It should be mentionedthatthe catalyst bed mass, mp, decreases
`as the attrition time increases. Nevertheless, for a given attrition
`time, it will also decease probably with increasing the superfi-
`cial gas velocity. Suppose the decreasing catalyst bed mass (or the
`
`2
`
`

`

`72
`
`
`
`Catalystbedmass(g)
`
`50
`
`48
`
`46
`
`42
`
`40
`
`38
`
`36
`
`32
`
`30
`
`D. Wu et al. / Catalysis Today 264 (2016) 70-74
`
`
`
` 0.9
`x@PF@e#e#+OFOO¢
`
`
`
`
`
`Totalattritionrate(g/h)
`
`0.7
`
`0.5
`
`0.3
`
`0.1
`
`0.08
`
`0.10
`
`0.12
`
`0.14
`
`0.16
`
`0.18
`
`0.20
`
` 0.08
`x@rFBe+OPOS 20h
`
`cPop
`
`Myf
`
`2h
`4h
`6h
`Bh
`40h
`42h
`44h
`46h
`48h
`
`0.10
`
`x
`
`#/+/0
`
`.
`
`4
`
`0.16
`0.14
`0.12
`Superficial gas velocity (m/s)
`
`0.18
`
`0.20
`
`Fig. 2. Dependence of catalyst bed mass on air velocity and linear fittings of Eq. (5).
`
`Superficial gas velocity (m/s)
`
`cumulative massofthe elutriated fines, me) has a linear relation
`with the gas velocity,i-e.,
`
`Mp = —ku + b
`
`(5)
`
`Substituting Eq.(5) into Eq. (4), we get
`Ratot = Raj + Rab = G-Co-u? + Cy -(—ku +b)” - (u —Umin)™ (6)
`where
`
`Fig. 3. Dependence oftotal attrition rate on air velocity and nonlinearfittings ofEq.
`(6).
`
`clear from Fig. 1, which shows that the catalyst bed mass linearly
`decreases at a muchfaster speedfora largerattrition time.
`
`3.2. Influence ofgas velocity on thetotalattrition rate
`
`The least-squares nonlinear fittings of Eq. (6) to the total attri-
`Dg
`tion rate data are shown in Fig. 3, and the estimated parameters
`p¢- ——
`Co = dpp
`-
`7
`
`
`0 pb*Pf dt. nz, (7)
`and goodness-of-fit results are given in Table 1. It can be seen that
`the coefficients of determination, R?,are all larger than 0.990,indi-
`For given bedstructure,jet gas and catalystparticles, Cp is acon-
`cating that Eq. (6) gives fairly goodfits to all the data sets. Fig. 3
`stant value; therefore, only seven parameters (k, b, G, Cy, Umin, 1,
`also visualizes that the total attrition rate data follow Eq. (6) well
`for all the attrition times. These reveal that the derived total rate
`and m) exist in Eq. (6), and they can be estimated with regression
`analysis. The massof the elutriated fines is experimentally mea-
`equation presents a suitable description of the total attrition rate
`sured, and the parameters, k and b, are thus obtained directly by
`versus the superficial gas velocity.
`the least-squareslinear fit of the bed mass data to Eq.(5). Then the
`It can be seen from Fig. 3 that for any attrition time the total
`total attrition rate is calculated according to the massofthe elutri-
`attrition rate increases with increasing the gas velocity, reaffirming
`ated fines, and the otherfive parameters can be estimated by the
`that a large gas velocity intensifies the catalyst attrition. Further-
`least-squares nonlinearfit of the total attrition rate data to Eq. (6).
`more,for a largerattrition time,the effect of the gas velocity on the
`total attrition rate is less significant, contrary to the effect of the
`gas velocity on the catalyst bed mass.It results from the fact that a
`larger attrition time leads to a smaller total attrition rate and thus
`weakenstheeffect of the gas velocity on thetotal attrition rate.
`As depicted in Table 1, the estimated parametersin Eq. (6) vary
`with theattrition time.For instance, boththejet attrition constant,
`Cj, and the bubbleattrition constant, Cy, generally decrease with
`increasingtheattrition time.It is quite reasonable, since bothattri-
`tions abate gradually with time,resulting in the decreasein thetotal
`attrition rate. Furthermore,as theattrition time increases, the two
`powerexponents, n and m, both increase in the bubble-induced
`attrition item, showing that the time-dependence of the bubble
`attrition rate is much more complexthan that ofthe jet attrition
`rate. It is also found from Table 1 that the minimum bubbleattri-
`tion velocity, Umin, decreases slightly with time. The variations of
`all these parameters are essentially due to the fact that the prop-
`erties of the attrited particles, particularly shape, size and surface
`characteristics, vary progressively with time.
`As is well known,catalyst particles in a bed will not be fluidized
`unless the pressure drop of the bed is greater than the catalyst
`bed weight per unit cross-sectional area of bed [14,32]. Before
`the beginning offluidization, the pressure drop will increase with
`increasing the gas velocity. As the pressure drop increases to be
`equal to the catalyst bed weight per unit area, catalyst particles
`
`3. Results and discussion
`
`3.1, Influence ofgas velocity on the catalyst bed mass
`
`Fig. 2 depicts the catalyst bed massas a function ofgas velocity
`at different attrition times, where thestraight lines are plotted by
`linearfittings. The estimated parameters, k and b, and the goodness-
`of-fit results are listed in Table 1. Except for the fitting of the 2h
`attrition data set, the otherdata set fittings all give high coefficients
`of determination, R?. Thus it can be seen that a good linear rela-
`tionship exists between the catalyst bed mass and thegas velocity,
`which proves the accuracy of the above-madelinear hypothesis.
`As shownin Fig. 2, for any attrition time, the catalyst bed
`mass always, as expected, decreases as the superficial gas veloc-
`ity increases, indicating that the larger the gas velocity, the more
`seriousthe catalyst attrition will be. It can be seen from Table 1 that
`the k value increases with increasing attrition time, revealing that
`a largerattrition time will lead to a more significant effect of the
`gas velocity on the catalyst bed mass. As mentioned above,attri-
`tion is a time-dependentprocess, and at the early nonsteady-state
`stage ofattrition, fines are elutriated in small quantities, though the
`initial attrition rate is very large [19,25,26], which probably masks
`the effect of the gas velocity on the catalyst bed mass.It is also
`
`3
`
`

`

`Table 1
`Fitting analyses of the catalyst bed mass and total attrition rate data.
`
`D. Wu et al, / Catalysis Today 264 (2016) 70-74
`
`73
`
`Linearfitting of Eq. (5)
`k
`b
`51.28
`52.27
`53.11
`53.87
`54.56
`55.19
`55.75
`56.27
`56.72
`57.13
`
`23.18
`41.50
`57.36
`71.72
`85.01
`97.43
`109.09
`120.04
`130.34
`140.02
`
`Nonlinear fitting of Eq. (6)
`
`R?
`0.914
`0.944
`0.958
`0.965
`0.969
`0.972
`0.973
`0.974
`0.975
`0.976
`
`GG
`138.95
`104.07
`89.41
`84.57
`83.95
`84.04
`83.54
`81.88
`79.23
`75.74
`
`G
`2.47 x 10-2
`7.20 x 10-4
`2.65 x 10-4
`9.26 x 10-5
`1.64 10-5
`2.77 x 10-6
`6.74 10-7
`3.39 x 10-7
`3.46 x 10-7
`6.68 x 10-7
`
`n
`0.805
`1.857
`2,192
`2.506
`2.998
`3,519
`3.962
`4.219
`4.284
`4,162
`
`m
`0.088
`0.269
`0.375
`0.432
`0.482
`0.543
`0.617
`0.693
`0.762
`0.811
`
`Umin (M/S)
`0.0834
`0.0820
`0.0798
`0.0788
`0.0782
`0.0775
`0.0766
`0.0757
`0.0746
`0.0738
`
`R?
`0.990
`0.996
`0.997
`0,998
`0,998
`0,998
`0.998
`0,999
`0,999
`0.999
`
`t(h)
`
`2
`4
`6
`8
`10
`12
`14
`16
`18
`20
`
`
`
`Contributionofgridjetattrition
`
`
`
` 0.08
`
`0.10
`
`0.12
`
`0.14
`
`0.16
`
`0.18
`
`0.20
`
`Superficial gas velocity (m/s)
`
`Fig. 4. Contributionofgrid jet attrition as a function ofair velocity.
`
`—e 0.1746 mis
`
`—#— 0.1528 m/s
`
`—+ 0.1337 m/s
`
`
`
`oa
`= 04 gp
`Cc
`8
`—O 0.1155 m/s
`os} Noae
`
`0.2
`
`0
`
`2
`
`—r- 0.0981 m/s
`
`s
`
`6
`
`8
`
`10
`
`12
`
`14
`
`#16
`
`18
`
`Attrition time (h)
`
`20
`
`
`
`
`
`
`—#- 0.1951 m/s
`
`
`
`
`
`0.8
`
`0.7
`
`0.6
`
`0.5
`
`Cc
`
`3=
`
`ao
`2
`
`3 S
`
`5=
`
`reachacritical state betweenstatic and suspended states. Here,
`the superficial gas velocity is often called minimum (orcritical)
`at first and then increases rapidly with the increaseofthe gas veloc-
`fluidizing velocity, up, [33]. Minimum fluidizing velocity can be
`ity. The slight reduction in the 0.08-0.10 m/s range is probably
`attributed to the somewhat bad randomnessof a small-scale flu-
`accurately measured by experiments, andit can be also determined
`by the method of calculation. In this study, up, was estimated
`by an empirical formula reported in a fluidization textbook [33].
`The obtained upg, is about 0.00347 m/s, far less than all the upin
`(minimum bubbleattrition velocity) values listed in Table 1. This
`reveals that the minimum fluidizing velocity cannot generate bub-
`ble attrition, because energy is required to produceattrition after
`the beginning ofparticle fluidization.
`
`3.3. Contribution ofgridjet attrition
`
`As shown above,thetotal attrition rate in a fluidized bed is the
`sum ofthegrid jet attrition rate and bubble-induced attritionrate.
`The parameters in Eq. (6) are estimated by regression analysis, and
`then thetotal attrition rate can be separated into contributions of
`the two attrition sources. For instance, the contribution ofgrid jet
`attrition, 7, can be expressed as
`— Rai
`~ Ra,tot
`
`(8)
`
`7]
`
`In Fig. 4, the plots of the jet attrition contribution versus the gas
`velocity are illustrated. For the sake of clarity, only three selected
`attrition times are shown inthefigure. Otherattrition times give a
`similar curve behavior. It can be found that in the examined range of
`the gas velocity, the contribution ofjet attrition decreasesslightly
`
`4
`
`Fig. 5. Contribution ofgrid jet attrition as a function ofattrition time.
`
`idized bed used in this study, leading to the uncontrollable variation
`ofthe properties of the catalyst beds used by different experiments,
`and thus to the attrition behavior changes, especially at low gas
`velocities.
`It can be seen from Eq.(3) that the bubble attrition rate is closely
`related to the decreasing catalyst bed mass, and thus a complex
`relationship exists between the bubbleattrition rate and gas veloc-
`ity (see Eq. (6)). However, the jet attrition rate has no connection
`with the catalyst bed mass, and it always increases as the gas
`velocity increases (see Eqs. Eqs. (2) or (6)). These provide strong
`support for the rapidly increasing contribution ofthejet attrition
`with increasing the gas velocity. As shown inFig. 4, for any attri-
`tion time,at low gas velocities, the bubble-inducedattrition is more
`dominant than thejet attrition; however, at high gas velocities,
`the jet attrition plays a dominantrole. Especially, as the gas veloc-
`ity approaches0.2 m/s,the jet attrition contribution reaches about
`70%. These results reveal that the fast increase in thejet attrition
`rate is the major cause of the more and more serious catalyst attri-
`tion occurring as the gas velocity increases.
`Furthermore,Fig. 4 indicates that at higher gas velocities, the
`attrition time has a larger effect on the jet attrition contribution.
`To furtherclarify the effect of the attrition time, the contribution of
`grid jet attrition versus theattrition timeis plotted in Fig. 5. A strik-
`ing feature can be seenthatthejet attrition contribution decreases
`
`4
`
`

`

`74
`
`D. Wu et al. / Catalysis Today 264 (2016) 70-74
`
`at the early nonsteady-state stage of attrition and then increases
`with increasing the attrition time. Nevertheless, compared to the
`effect of the gas velocity, the attrition time has less influence on the
`jet attrition contribution.
`It should be mentionedthatthejet attrition, as its name implies,
`takes place in regions near theorifices in the distributorplate, and
`thereby its rate has no distinct connection with the catalyst bed
`mass. In contrast, the bubble-induced attrition happens forall the
`fluidized particles, andits rate is clearly related to the catalyst bed
`mass. Previous authors [6,14,32] usually neglected the variation of
`the catalyst bed mass, and theinitial catalyst bed mass was thus
`usedin their bubble attrition rate equations. Nevertheless, the cat-
`alyst bed mass always decreases with increasing the superficial
`gas velocity or attrition time, as shown in Fig. 2. In this study, a
`decreasing catalyst bed mass was, therefore, introduced into the
`bubbleattrition rate, and then a more adequatetotalattrition rate
`model,i.e. Eq. (6), was derived, as shown in Table 1 and Fig. 3. More-
`over, in the literature [6,19], a series of preliminary experiments
`must be used to separate thetotal attrition rate into contributions
`of different attrition sources. However,in this study, jet and bubble
`attritions were directly separated by regression analysis. Results
`reveal that it gives a simple, efficient and quick method for the
`separationofattrition sources.
`
`4. Conclusions
`
`The derived attrition rate equation presents a suitable descrip-
`tion of the measured total attrition rate versus the superficial gas
`velocity in a small-scale fluidized bed. The estimated parameters
`in the equation systematically vary with the attrition time, due to
`the fact that the properties of the attrited particles change pro-
`gressively. It is seen that the minimum fluidizing velocity cannot
`generate bubbleattrition and that it is much less than the minimum
`bubble attrition velocity because energy is required to produce
`attrition, Experimental results also indicate that as the gas veloc-
`ity increases, the catalyst bed mass decreaseslinearly and thetotal
`attrition rate increases. For a larger attrition time, the effect of the
`gas velocity on thetotal attrition rate is less significant, while its
`effect on the catalyst bed mass is moresignificant. Furthermore,
`it is found that the contribution ofjet attrition generally increases
`rapidly with the increaseofthe gas velocity. At high gas velocities,
`the jet attrition plays a dominantrole for anyattrition time. Thus
`the fast increase in the jet attrition rate is the major cause of the
`increasingly serious catalystattrition with increasing the gas veloc-
`ity. Finally, regression analysis is shown to be aneffective tool to
`the separationofattrition sources.
`
`Acknowledgments
`
`Financial supports from the National Natural Science Foun-
`dation of China, under Grant Nos. 21176048 and 21376050,are
`gratefully acknowledged.
`
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