Magnetically assisted gas-solid fluidization in a tapered vessel: Part Ⅰ. Magnetization-LAST mode

Available online at www. sciencedirect.comScienceDirectPARTICUOLOGYELSEVIER .Particuology 7 (009) 26-34www. clsevie.com/locate/particMagnetically assisted gas- solid fuidization in a tapered vessel:Part I. Magnetization-LAST modeJordan HristovDepartment. of Chemical Eninering. University of Chemical Technology and Mtallurgy, 1756 Sofia, 8 KL Ohridsky Blvd, BulgariaRcceived s August 2008; accepled 28 October 2008AbstractThis article presents further experimental results of the Magnetization-LAST mode in magnetically assisted gas-fuidized tapered beds, includingextemal transverse magnetic field control of solid phase movement, central channel formation, spout depth and the pressure drop across the bed.Phase diagrams similar to those recently reported for the Magnetization-FIRST mode were alsodeveloped. Dimensional analysis based on "pressuretransform" of the initial set of variables and involving the magnetic granular Bond number pertinent to particle aggregate formation was appliedto develop the scaling relationships.◎2009 Chinese Society of Paricuology and Istiute of Process Engneing, Chinese Academy of Sciences. Published by Elsevier B.V. Allrights reserved.Keynwords: Fluidization; Magnetization-LAST; Tapered bed; Dimensional analysi; Pressure transform of variables; Magnetic granular Bond number1. Introduction(2002, 2003a, 2003b, 2004, 2006, 2007a). Recently, promisingresults on magnetically assisted nano-fluidization were reportedOriginally conceived by Mathur and Epstein (1974) for gas-by Hao et al. (Hao, Zhu, Lei, & Li, 2008a; Hao, Zhu, Jiang, &fuidization of Geldart D particles (Geldar, 1973), the use of Li, 2008b) on mass ransfer pertinent to CH4-CO2 reforming.tapered vessels has been extended to the fuidization of cohesiveThe present article addresses magnetically assisted spoutedparticles (Venkatesh, Chaouki, & Klvana, 1996; Erbil, 1998),beds with the Magnetization-LAST mode as a continuation ofe.g.. the drying of agriculture by-products (Wachiraphansakul the recent report (Hristov, 2008) on the Magnetization-FIRST& Devahastin, 2007) and pasty materials (Bacelos, Passos, &mode. For such Magneically Assisted Tapered Bed (MATB)weFreire, 2007; Bacelos & Freire, 2008). Such sticky solids withshall demonstrate how the extemnal magnetic field controls thehigh liquid content and interparticle caillary forces cause easy bed behaviour through induced inerpaticle forces and aggre-particle aggregation and afet adversely the fluid-bed hydrody-gate formation. The microscopic phenomena at the particlenamics (Bacelos et al., 2007; Bacelos & Freire, 2008).diameter scale finally affect the gross bed behaviour in termsIn magnetically asisted fAuidization a magnetic field con- of pressure drop, bed depth, etc.trols, remotely and outside the fuidized bed, interparticle forcesIn this work, we used a single tapered vessel with a fixedbetween solid particles that are magnetic while fuidized by cone angle in the Magnetization-LAST mode (Hristov, 1998,either a liquid (Hristov, 2006), a gas (Hristov, 2002, 2003a)1999, 2002). The magnetic field was generated by saddle coilsor gas -liquid fow (Hristov, 2008), in either of two basicoriented normally to the fuid flow and the vessel axis as detailedmagnetization modes, FIRST (magnetizaion of a fixed bed by Hristov (2008). The fllowingg basic features pertinent to thebefore fuidizaion) and LAST (magnetization of a preliminarily effets of magnetic field are to be adressed to:fuidized bed). The bydrodynamic behaviour of magnetic fu-idization of coarse Geldart B particles was reviewed by Hristov●Bed behaviour, pressure drop histories, bed collapse (poros-ity), variations and the related phvsics due to variation in theAbbreriations: MSB, manetically sabilid bed; FrB, frozen bed.nte |中国煤化工eld.E-mail addres: jordan.hristov@ mail.bg.s of regimes as afectedyL1HURL: h:/:ritov.com/jordan.167420015- see isite back cover。200 Chicse Sociey of Pricuology and losiute ofProcs Eaiecig Chincec Acalcmy ofScieacs. Pubibiedby Eleriar B.V. AU righs rseveddoi:1.010fj_arci.200.10.000J. Hristov/ Paricuology 7(2009) 26-342:NomenclatureQmyO volumetric gas flow rate at the minimum fuidiza-Ao, Apo dimensionless coefficients defined by Eq. (7a)tion point in absence of a field (m2/s)Apdimensionless cofficient defined by Eq. (4d)Qmsvolumetric gas flow rate at the minimum spoutingBOg- -c= PclPg =Pc/psgdp Bond number of granular mate-point in absence of a field (m'/s)rials with a natural cohesionsuperficial gas velocity (denoted also as Ut orBog- m=(uoMsH)(Ps8dp) magnetic Bond number forUo- see the text) (m/s)Vp =Mp/Ps volume occupied by the solids (m3):odimensionless coefficient in Eq. (7a)Voed = (rtho0/12)(D吃+ DLDb+吲(m')Cp =△Po/2pfU} tapered bed friction factor before themagnetic field application (-)Greek lettersD。diameter of the flow entrance (m)cone angle (9)DLtube diameter (diameter of the cylindrical sectionporosity (-)above the cone) (m)initial bed porosity (-)ODbLdimensionless ratio of bed geometric characteris-e(Qo)porosity of the preliminary fuidized bed intics defined by Eq. (2c)(H)absence of a field (-)dpparticle diameter (m)annular bed porosity (-)E1, Er dimensionless functions defined by Eqs.(11a) andmagnetic permeability (Wb/A m) or (H/m)(11b)(-)uomagnetic permeability of the space (Wb/A m)e1,e2, e3,e4 dimensionless exponents in Eqs. (11a) andnffluid dynamic viscosity (denoted also as η forsimplicity of the expressions) (Pas)fi.f2dimensionless functions defined by Eqs. (4a) andPffuid density (kg/m3)(4b)Pggas density (kg/m3)fio=GaODbL dimensionless function (Eqs. (7a) and(7b))D%solid particle density (kg/m3)fhsfh1/f62 dimensionless functions defined by Eqs. (10a)and (10b)SubscriptsfluidGmass of particle bed (kg)particleGa = (dpgpj2)/ng Galileo numbersolidsgravity acceleration, 9.81 m/s2magnetic field intensity (A/m)Hgcmagnetic field intensity at which the particle●Dimensional analysis of both the effect of the conical shapeaggregation begins (A/m)of vessel and the presence of the magnetic field, includingHf-1minimum freezing magnetic field intensity atdata correlation.onset of top frozen bed (A/m)Hfr- -2 minimum freezing magnetic field intensityrequired for complete bed freezing (A/m)2. Experimentalhbbed height (m)hooinitial bed height (m)The experimental set-up, described in detail elsewherebed length at the wall (see Fig. 1) (m)(Hristov, 2008), consists of a conical vessel (15° opening angle,hoinitial bed length at the wall (see Fig. 1) (m)30-mm-ID bottom diameter and 190-mm-_ID top diameter)hubed depth before the magnetic field application(see Eq. (10a)) (m)Field LinesMsmagnetization at saturation (A/m)Mpmass of particles charged into the vessel (kg)dimensionless exponent in Eq. (10b) (-)np,npl,np2 dimensionless exponents (H)cohesion (Pa),SaddlePg= Psgdp gravity pressure peer unit surface of interpar-CoilsOPticle contacts (Pa)hppressure drop (Pa)△Popressure drop across the preliminary fuidizedbed中国煤化工prior to magnetization (Pa)Qvolumetric gas flow rate (m'/s)fYHCNMHG2ovolumetric gas flow rate at which the bed is fu-2幼Jidized before the magnetic field application (m3/s)Fig 1. Experinental setup.281. Hrisov 1 Particuology 7(2009) 26 -34FROZEN BEDsurrounded by 200-mm-ID and 400-mm-high saddle coils(Hristov, 2002, 2008). The field lines were oriented trans-Freezingversely to the cone axis and fluid flow, as shown in Fig. 1.The magnetic field was steady with maximum intensity ofabout 40kA/m. Magnetite sand(315-400 pum, Ps = 5100kg/m',Ms= 477.37 kA/m) was fuidized by air in the experiments. ASPOUTED BEDmechanical valve and a calibrated rotameter were used to con-en Hstrtrol and measure the gas flow rate. Pressure drop was measuredby an U-tube water manometer connected between the gas inletand a fine-tube pressure probe placed above the bed top surface.FLUIDIZED BED3. Results.5 1.0 1.5 202.5 3.0 3.5 4.03.I. Phase diagramsQ/Qmto ()Fig.2 describes the flow regimes in a typical phase diagramFig. 2. Phase diagam of magneite (315- 400 pum) in Magnetization-LASTin Q -H coordinates (Hristov, 2008), showing that with increas-mode with G=2kg and huo = 250 mm.ing intensity H the originally fuidized bed passes through threebasic states as described in Fig. 3: (a) a fuidized bed with minoreffects of the magnetic field on smooth fuidization with wave-FluidizationStablo spoutingat the bottom3[A]Zero-fieldconditionsQ> QmsQ < Qmf0Qmf0< Q HstrFrozen bed withfrozen voids ( bubbles,这B1 sP.B2B3B5,p[B]bed(FrB)-Moderate9gas flowratesFrozen bedFluidization at the bottom andfluidizationwith slitsBubbling fluidization F旧 aboveH> Hr-2H> Hr.1H field conditions. (B) Bedbehaviour with increasing field intensity. Initial conditions: low gas fow rates with bubbling in absence of a field; (C) bed bchaviour with increasing field intensity.lnitial condions: high gas fow rales enough lo create stable spouted beds in absence of a field.3C1. Hristov 1 Pricuology 7 (2009) 26 -34(A) Fe30(315 o0u)60000 |(B- 95 % conldence limitQ= 4.99 m3s- linear ftof data M=f(H)nbo*245 mm40000.4G-2g300022 r.0 K2000ClapinbedQ(m3s)x10-3:1.666 ;●2.77;▲4.16;▼4.99850 t1000.0.43025 30754H(kA/m)FoenbedHnglI 7 160.010;of500Cllptinog04.181, 10~3 m21sithatoen bedQ=27M710-m31$350++H (kA/m)(C) 0r 4499.103m3/s .°r-2-777x 10-3 m31s0tCollapsing bedwith intermal spout( bubbies and lt )and frouen bed at the top\.60吗230 FEoBONDNUMBER,BoOgm HBOND NUMBER,Bogm ()Fig. 4. Pressure drop cllapse curves - experimental data and crelations. (A) Original data of pressure drop cllapse - main figure with low pressurefuidization regime. Inset: high-pressure drop curve at Q=4.99x 10-3 m/s. (B) Pressure drop collapse data ftting hrough Eq. (8) as Mo ={(H), wbereMo=[1 -(SPIOPo)(Qm/0/10.055490) since for the material usced BOg m =0.055490H. (C) Pessusre drop cllps data fiting through Eq (7a).The above physical phenomena led to the fuidization regimesare required to stop the motion of the solids (aggregates) and todemarcated in Figs. 4 and 5. The behaviours of the solids asfreee the bed. The frozen bed consists of field aligned aggre-described above are easily detected by the pressure drop curvesgates that repel each other with forces balanced by fuid drag andrather then by the collapsing (porosity evolution) curves. Evengravity since the bed has a fixed structure. However, the frozenat gas fow rate slightly beyond the onset of fuidization, thebed structure is not homogeneous depending on the fuidizationpressure drop tends to decrease with increasing magnetic fieldregime developed before applying the magnetic field. At lowintensity, while the collapsing curves exhibit detectable changes中国煤化工voids occur as slis, thatat suficiently high gas flow rates. At gas flow rate correspondingis, frFrated by horizontal voidsto bbling fuidization, application of magnetic field results inas shHC N M H Gan originally spouted bedfast bed collapse without excessive formation of aggregates andresults in a fixed bed with a clean central void (see Fig. 3C) asthe bed“freezes" easily with moderate magnetic feld intensities.the trace of the prior spout channel is surrounded by an almostAt sfficiently high gas flow rates high magnetic field intensitieshomogenously arranged annular section.J. Hrisov/ Paricuology 7(2009) 26 -34310.80Hubeyond minimum fluidization, the particles move intensivelybut bed expansion is restricted to allow formation of freely mov-C 0.78Qx 10~(m31s)ing aggregates and the particle rearrangement is manifested byw 0.781.68the bed expansion shown as section C, followed by a plateau.完0.74277.Bed collapse does not occur, since the particle aggregation isG 0.72enhanced by the high particle concentration just beyond mini-mum fluidization, which finally shifts the bed behaviour to the0._fsbsd01 Frozen bedsituation with repulsion between aggregates. However, the gasflow is not sufficient to create expanded bed to the extent for0.66(high gas flow rates such as for setions B.s 0.84Frozen bed>iFroxmn bd5 0.824. Dimensional analysis and data correlationfield Insty0.eThis section develops dimensionless groups describing mag-H(kA/m)netically assisted tapered gas-fluidized beds employing thegeneral expressions developed by Hristov (2008) for theFig. 5. Bed cllpse curves (bed depbh reduction) due 1o increasing magneticmagnetization-LAST mode. Dimensionless scaling of pressurefield intensity expressed through tbe overal porosity evolution.drop evolution with increase in magnetic field intensity is toFig. 5 and its inset show ranges of magnetic field intensitybe correlated with experimental data. Porosity scaling is to bedeveloped only theoretically.yielding the following different bed behaviours:●Nearly linear bed collapse withincreasing magnetic field4.1. General considerations and pressure drop scalingintensity for relatively weak field intensities- Section A.Dimensional analysis based on the“pressure transform"●Increasing bed porosity after the initial collapse, with increas-approach (Hristov, 2008) generates the following dimensionlessing magnetic field intensity, followed eventually by finalgroups relevant to magnetically controlled spouted beds:frozen bed- Section B.●Monotonously increasing porosity with increasing magneticFluid- particle interaction Ga =nd(2a)field intensity- Section C.Psgdp'All these trends much depend on the original bed structurebefore application ofthe magnetic field, implying that free move-Solids ineariclcnacts)Boa-=.(2b)ment of particles in the bed leads to bed collapse and aggregateDr- Dbformation, as shown by the initial linear section A of the col-Vessel geometry simplex SDol =2hbo=g(号). (20)lapse curves. The consequent aggregate -aggregate interactionand the aggregate formation parallel to the field lines but trans-These dimensionless numbers are independent variablesverse to fuid flow result in bed expansion due to repulsiveexcept for OP/psgdp. Generally, pressure drop varies as a func-aggregate- aggregate force, as shown by section B. This fact istion of magnetic field intensity as follows:△PuoMsH. 0rU呢:cPsgdp=fi ' Ga=Bog-m :Psgdp’Pngdp'ODbL(3)not new in magnetically assisted fuidization, as has beenwhere Bog- m is the magnetic Bond number (Hristov, 2006,well documented by plots and physical explanations (Hristov,2007b, 2008). In Eq. (3) Ga characterizes the fuid-particle sys-1998, 199, 2002). For both cylindrical and tapered beds,tem, while 0DbL represents the inital bed geometry, both notparticle particle and aggregate- aggregate interactions are con-varying for conditions imposed by a given experiment. The ratiotrolled by common physical mechanisms but only vessel shapepfU}/psgdp represents the initial bed conditions where the fieldaffects the gross bed depth (expansion or collapse). Section C ofis applied and is the initial condition of the dependent variablethe bed collapse curve resembles to some extent the behaviourSP/psgdp. In both dimensionless ratios the granular pressurecorresponding to section B, that is, both start with unrestrictedat particle level Psgdp (Hristov, 2006, 2007b, 2008) is usedfluidization but with different degrees of solids mixing intensity.as a pressure scale. The independent variable is the magneticThe higher the bed expansion, the easier the particle movementBond ny中国煤化工Hence, we may reduceand aggregation, to finally yield more distinct arrangement ofthe presensionless numbers bythe aggregates along the magnetic field lines in the loose frozencreatingYHCNMHGbed. The ltter consequently expands due to simultaneous fuiddrag and aggregate-aggregate repulsion parallel to gas flow,( OF(4a)to result in section B of the collapse curve. In this case, just\Psgdp,Psgdp )pfU}32J. Hristov/ Paricuology 7 (2009) 26 -34which is a reasonable way to minimize the number of variables(see Hristov, 2008). Inasmuch as△Po and 0Po/pjU} are inter-in Eq. (3) and to include the effect of the initial conditionsrelated through the hydrodynamics of the non magnetized bed,with Magnetization-LAST mode (in fact Fluidization FIRST)the literature provides many relationships that might be used.represented by (pjU}) as an initial condition (nor variable).Hence, either experimental or predicted values of OPo can beFurther, the basic phenomena such as particle aggregationused to develop correlation such as Eq. (5). The ratio (Q0Qm)and string- string interaction occur at the paricle level scale sorepresenting fow Qo prior to bed magnetization needs to bethe paricle diamer dp is the characeristic length scale of ihe introduced. This step was avoided in Eq. (2a), since fisty,. theprocess. In this context the Bond number B0g-m represents theuse of OPo violates the rule to use a common pressure scalestability of interparticle contact in the aggregates due to magnetichaving a natural basis, and the granular gravity pressure Psgdp,cohesion. With the above clarifications, Eq. (3) becomesin contrast to OPo, is a natural pressure scale independent ofexperiment, and secondly, Qo depends on experiment and theOP( Ga='Bog-m=μoMsH.ODbLflow rate scale cannot be defined prior to experiment. Therefore,ρjU}PEgdpEq. (5) is a compromise between the basic rules in data scaling(4b)and the existing practice in spouted bed data presentation. Withthis compromise, Eq. (5) could be simplified toIn the above equation the RHS could be re- arranged in terms(6)of two sub-functions, namelyP= fiAp(Om )(Bog-mYo.sD(B0-- HoMHA(4c) 4.2. Practical correlations of the pressure drop evolutionojU}形)o(ePagdpwith magnetic field intensityThe initial conditions are defned by fi which plays therole of a pre-factor of the power-law relationship (Kline, 1965;Under the initial conditions, neither OP/pjUj nor OP/SPoBrrenblat, 1996, and functionfh is then reenede by is 2ero and it fllowls from Eqs. (5) and (6) that at H=0 wea power-law of the Bond oumber, Bog -m. Hence, Eq. (4c)have BOg- m =0 and no particle aggregation exists (see limitsbecomesBog-m→0 and Bog-m→∞in (Hristov, 2008)). Because ofthat, the function could be modified as follows:uoMsH\PjU}= fiAp(o-m=Psgdp(4d)= Ao+ Ap0 exp(-coB0g- m),(7a)The use of (jUB) in the above relationships is a compromisewith the uradition in spouted bed data correlations where theOP_superficial fuid velocity at the gas inlet orifice is often used; evenSP=1-fio A0(2) (Bo_-mYm.(7b)though this is generally incorrect since the tapered vessel has nonalully deind velociy scale (Hiso, 20080. The pesse where Ao + Apo = 2CD = AP:/prUB in Eq. (78) is he dou.drop in abene ofa feld APo (at a given gas fow rate at which bled fiction factor of the bed in absence of a magnetic feld andthe' bed is prelimninarily fuidized)can also be used as a reference could be calculated independently, depending on initial condi-scale. Hence, the ratio (0P/OPo) is correlated astions. The parameters of Eq. (7a), estimated through non-linearregression analysis and using Origin 6.0, are summarized inAPTable l.This ftting yields scattering results, as shown in Fig. 4C,; 0DoLcoming mainly from the fact that the LHS of Eq. (7a) does notmatch I under the initial conditions as a dimensionless variable.This approach avoids the use of (AjU}/psgdp) as an initialMore successful results were obtained with Eq. (7b) wherecondition since the tapered beds have no definitive velocity scale in any case under the initial conditions of OP/OPo= 1, the dataTable 1Versions of Eq. (72) prinent to beds of magnetite paricles wihin tbe range0≤BOg- m≤1665.Q(m's)x 10-3U (m/s) (eined by theQ/Qm(-)Equation 0 =Ao+ Ap exp(-coBoqm)gas inlet cross-section)1.66662.3572.727品=83.03 +34.5 expl-(ogm)8.1 x 10-'1R2=0.8096; x = 12.46; 26 data poins2.7773.9294.5450=179+8.9+01;2=102; 26 data poins中国煤化工4.165.8946.818品=797+15501; x2= 1022; 24 da pointsYHCNMHG4.9997.0738.182=11.75+ 56.6 exp[-(BOqgm)9 x 10~']R4 =0.9505; 2 = 10.29: 26 dato pointsNotes: (1) Numerical values of co in equations are located at end of the oumerical expressions. (2) Second rows beneath the equations contain data on accuracy ofcorelation.J. Hrisov/ Particuology 7 (2009)26 -3433can well be approximated by a linear descending equation:a new pre-factor and exponents in Eq. (11a):OP△Po=1-(1x10-))(品)Bog-m.(8)50where fro=GaODbL =9.05，Ga=68.781， ODoL =0.1316,(11b)np2=1 and 0≤Bog-m≤1665. For all the 104 data points col-lected from Fig.4A (main figure and inset) Eq. (8) fits within anaccuracy of less than 10-4 , scattering within the range of -0.2In both cases, O81 and O&2 are decreasing functions when ato +0.3.bed collapses bomogenously down to the frozen state. The pre-Alternately, the "L-shaped" pressure drop curve can befactors Et and E2 as well as the exponents e1,e2, e3 and e4 haveexpressed by the following exponential relationship within theto be determined through ftting to experimental data.range of0≤Bog- -m≤1665 as shown by the inset of Fig.4A (26For what we saw of the trends of data correlation on bed col-data points):lapsing, the data available were yet not sufficient to test thescaling equations, particularly because only one single coneSP.=0.245 +0.753 exp[- (Bog -m)] (S.5x 10-). (9) angle was used with a narow size fraction of magnetile as thefwidized material. More data are needed in broader ranges of par-Eq (9), in fact, confirms Eq. (7a) and fits the data with anticle size and cone angles, though the principal dimensionlessaccuracy of about 10 -3 in the descending section of the curve.groups controling the process have been tested to demonstrateThe term 0.245 in Eq. (9) underestimates the pressure drop atthe coberence of the present analysis.high field intensities (i.e. across the“frozen bed"), which is about0.375 of the initial value of OPo≈4000Pa.5. Conclusions4.3. Bed collapse- - general considerations about theInitial information about magnetically assisted gas fuidizedscaling equationstapered beds with the Magnetization-LAST mode has beenreported in this work, The main issue was to show the gen-This case addresses the relative bed depth ratio as functioneral bed behaviour represented by phase diagrams with relevantof applied field intensity:changes in pressure drop and overall bed porosity. In this contextit was clearly demonstrated that:(品)== f(.qy.H)=fn((号0;Ga: Bog-m: sDu), Magnetic field intensity increase allows change of the fuid-(10a)bed behaviour from that of a freely fuidized or spouting bedtowards that of a magnetically controlled system consistingwhere hu and 2o represent the initial conditions prior to bedof a spouted bed topped by a progressively increasing frozenmagnetization. The bed collapse function fh could be expressedbed., Magnetic field intensity alws cortolling both pressure dropand bed porosity thus creating conditions for suitable processfs(U.o I)=1(G; Du)(a-=0(=) (0b)performance utilizing the top located frozen bed or the internalspouted bed below.where the functionfhi and the ratio sQ=Qv/2ms are, in fact,● Dimensionless analysis draws the basic rules of the methodofparameters since they do not vary as the bed undergoes vol-“pressure transforms". Correlations of data pertinent to pres-ume shrinkage with increasing magnetic field intensity. Thesure drop collapse with increase in magnetic field intensityonly independent variable is the Bond number. Actually,fhi isshow adequate applications of the general scaling rules, withidentical tofi in Eq. (4b).limited deviations, to the classic correlations in the spoutedEven though Eqs. (10a) and (10b) are generally correet, bedbed technology.depth is nota clearly representative measure for conical bed col-lapse. If the function fh(U,dp, H) is represented by the porosityReferencesratio Oe = e/E(Qo), Eq. (7b) can be expressed asAe1=_Bacelos, M. s. Passos, M. L, & Freire,J.T. (2007). Efect of iteparicle forcese(Qo)on the conical spouted bed bebaviour of wet particles wiub size disribution.Powder Technology, 174(1), 114 126.Bacelos, M. s.. & Freir, J. T. (2008). Flow regimes in wet conical spouted beds= EI[fn(Ga; ODb)*'[fn2(BOg -)]'1(2)”.(11a)Barentsin |中国煤化工cand intermediate asymptotics:1, 72-80.where 0< Oε1 =e/e(Qo)S 1 and Qo denotes the gas flow rateMHCNMHgtotics. Cambridge: Carnbridgeprior to bed magnetization.Erbil, A. C. (1998). Predictiono of the fountain heights in fine particle spoutedAlternately, the ratio OE can be expressed in terms of thebed systems. Turkish Journal of Engineering and Environmental Sciences,initial fixed bed porosity, i.e. O82 = eleo (O82≥1), thus defining22(1),47-54.34J. Hrisov 1 Particuology 7(2009) 26 -34Geidan, D. (1973). Types of gas fudization. Powder Teclnology, 7(5), 285-Hristov, J. Y. (2004). Magnetic field asisted fuidization- A unified approach.Part 4. Moving gas fuidized beds. Reviews in Chemical Engineering,Hao, Z. Zhu, Q.. Lei, z. & Li, H. (2008). CH4-CO2 refoming over Ni/Al2O320(5- 6), 377- -50.aerogel catalysts in a fuidized bed reactor. Powder Technology, 182(3),Hristov,J. Y. (2006). Magnetic feld asisted fuidizatio- A unifed approach.Part 5. A hydrodynamic treatise on liquid- solid fuidized bed. Reviews inHao, z, Zhu, Q., Jiang, z, & Li, H. (2008). 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Heat ransfer- -a critical re-evaluation of the results. Reviews inTechnology, 40, 207-219.Chemical Engiering, 19(3), 229 -355.5中国煤化工MYHCNMHG