Particle abrasion at high solids concentration in stirred vessels—II

Particle abrasion at high solids concentration in stirred vessels—II

ChemrcaI Engtneemg kmce Perwnon Press Ltd 1980 Vol 35 pp 543-547 Pnnted III Great Etntam PARTICLE ABRASION AT HIGH SOLIDS IN STIRRED VESSELS-II CO...

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ChemrcaI Engtneemg kmce Perwnon Press Ltd 1980

Vol 35 pp 543-547 Pnnted III Great Etntam




R CONTI Istrtuto dl Chlmlca



dl Tormo. Italy

and A W NIENOW Department

of Chemical and Btochemlcal Engmeermg, Umverslty Tomngton Place, London WCIE 7JE, England (Recerued 14 December

1978. accepted

13 Mufch

College London,


Abstract-In the first paper, It was shown that the fragments detached from partrcles undergomg abrasion m sttrred vessels were of approximately constant size and independent of the time over which abrasion had been occurring Thts paper reports data from an expenment conducted to test the accuracy and the effect of the constant fragment size approxlmatton It ts shown to be reasonable tf size and stze dlstnbutlons are determmed on a number basks (as they were in the previous work) but It IS unsatisfactory If an area or volume basis IS used In the latter two cases, the mean size decreases with time By consldermg the underlying theory of partrcle-parMe Impact and abrasion, It IS shown that a different basts should be used for different aspects of the determmahon of E. the “energy” requtred to produce a unit area of fragment surface When this IS done, It IS found that E IS independent of time though the mass abrasion rate IS greatest mltlally when the particle aspentles are being removed The expenmental techmque and model offer a conventent means of assessmg the abrasion reststance of brtttle matenals m stured vessels and of selecting smtable operatmg conditions to enhance or reduce abrasion

The expenmental technique used was described m deli m our previous paper[ l] but m essence It consisted of abrading the carefully-grown homogeneous crystals m non-solvent hqulds In this way, the fragments produced and the changes m the abrading particles from their ortgmai form could only come from abrasion and not from dlssolutlon or growth By samphng at Intervals, approximate size drstnbutions were obtamed for the abrasion fragments usmg nucroscopy These dlstnbutlons mdlcated a narrow size range and a number mean diameter (Da), 0 that was almost constant A dewled size analysis of the final sample, generally taken after more than 30 hr of abrasion, gave an accurate measure of that time and, m the light of the above (ml 0 for observation, this sue was taken as bemg representative of the size of the abrasion fragments throughout the whole run (D,), ,, (D._,), ,, was also used to calculate the abrasion rate and to test the theoretical model The work reported here was camed out to check the assumption that the mean size of abrasion fragments remained constant throughout the run


Many processes are conducted m stu-red vessels m which partlcles are suspended In such systems, particles may impact with the Impeller, with surfaces wlthm the vessel or with each other and as a result of these impacts particle abrasion (or attntlon) may occur Which of these ImpactIon mechanisms IS most important depends mamly on the solids concentration and at high sohds concentrations, our previous paperil] showed that partlcleparticle impacts dominate The abrasion may be undesired e g the breakdown of catalyst particles[Z] or the loss of enzyme activity from sqlid support particles[3], rt may be desired e g the removal of lmpervlous outer layers which slow down reaction rates durmg such operations as the extraction of tungsten[4] or the manufacture of phosphonc acid from phosphate rockE53, or tts magnitude must be known and preferably controllable e g m secondary nucleatlon[6] Most of the work on particle abrasion has been related to either catalyst abrasion m gas fluldlsed beds[7] or to abrasion m slurry transport pipe lines [8,9] Gas flmdised beds clearly represent a different class of problem and m order to simulate slurry pipe lme abrasion, Couette flow devices were employed to gve a well defined shear flow However for stirred vessels, small-scale, geometncallysimilar tanks are preferable and our previouslydeveloped model enabled results from two different scales of operation to be correlated[ll The type of abrasion product LS, of course, dependent on the sohd abraded[S, 91 so m this and our previous work on stu-red vessels [ 11. very carefully-grown homogeneous crystals were used as the abrading solid This choice ensured that the solids being abraded were of consistent quality m al! expenments

l?xpERlMENTAL The abrasion expenments were conducted m a 282 mm dra vessel with a 94 mm dla disc turbme Impeller, both of Rushton dimensions and detruls of which have been given before [ 10.1 l] The solid phase consisted of mckelammomum sulphate hexa-hydrate crystals with a number mean, projected area equivalent dmmeter (0,) of 1 06 mm and the non-solvent hqmd was a 50% by volume methanol-water mixture, presaturated with solute A solid concentration of 88 5 kg/m” of solution and an impeller speed of 7 rev/s were employed and the power mput was measured 543



At mtervals, agrtatlon was stopped and the abrasion fragments were separated from the non-solvent hquld by 0 45 pm pore filter to determine the total amount abraded A4 (see Table 1) and to obtam a size distibution The latter was determined using a Reichert monocular nucroscope, with the sample bemg recorded by an MP-4 Polaroid camera to gvq a total magmficatlon up to x 1750 Finally approximately 1000 particles were counted into 37 equal size ranges between 0 61 pm and 22 42 pm using a Zeiss TGZ-3 particle counter (for further details (see Ref 111)

The thu-ty seven ranges were grouped mto the 5 wider ranges m Table 1 In order to gwe a clearer representation of the changes of size dlstnbutlon with time, particularly tn the larger two ranges From this raw data, the number percent (No) wrthm each of these size ranges was determined From NO.the volume (or mass) per cent (NJ) was calculated assuming a constant shape factor and finally, from A$ and the total mass, the mass m m each of the 5 size ranges All these quantltles are also aven in Table 1

The vanatron of sue drstnbutron and mass abrasron rate with trme Figure 1 shows how the mass m each size range, m, and the total mass of abrasion fragments M vary Hrlth tune, t The shape of each of the curves can be explamed by the sequence m which fragments are removed from the abrading particles Iruhally, abrasion occurs from comers and edges as well as from the faces of the crystals and as a result they become progressively more rounded (see Fw 2 of Ref [l]) It is postulated that the large fragments (few in number but representing approximately 50% by weight) come from the abrasion of edges and comers and these larger fragments are themselves relatively quickly broken down, all having gone within 8 hr of the start of the run after passmg through a maxlmum Subsequently. the mass of the next hugest fragments also increases to a


1 The mass of abrasion fragments m each SE range as a function of tame


Particle abrasron at high sohds concentration m stied maxlmum and then disappears This pattern IS repeated with the third hugest range Once all the comers, edges and large fragments have gone, there IS only a net productlon of fragments mto the two smallest ranges equivalent to those produced from face abrasion at the begmnmg Rather smular effects have been reported for the abrasion of copper sulphate crystals m stured vessels [12] and of coal slumes m a Couette vlscometer [8] The total mass abrasion rate, L e dM/dt decreases quite rapldly at the start of the run but then tends towards a constant value The mass abrasion rate (dmldf) of the


l 2I&),


Implications for the abrasion modd The “energy” E requued to produce a unrt area of new fragment surface was shown to be related to the number abrasion rate r (number of fragments producedlseclabradmg partlcle) and the size of the abrasion fragments produced 0, by the expresslon E&D,‘)-’


when the other parameters m the model were held constant [ll At all samplmg times, the expenmentally determmed value of D, used to test the model was mean projected area eqmvalent (EL cl, the number diameter for the fragments at the end of the run In addltlon the number abrasion rate was calculated from

M r=tNSlr

1 6 P(W?

(2) 0

(Reference [l] 1s mlsleadmg m this respect and the precise defiruhon or r as set out here m eqn (2) was also used for calculations throughout that paper) In eqn (2), N. IS the number of abrading partnzles and remams constant throughout a run so that MD,)


2 65pm





two smallest sizes IS low at first and then mcreases until finally the bulk of the abrasion fragments are bemg produced at an approximately constant rate and m these two size ranges


F& 2 The




Ourattan of run.



of mean p&cle



size with time

these two equations




If (Do)2o or (I&h0 were used, fallmg by 30% and 50% respectrvely dunng the course of the run, the effect 1s more substantial and IS mdlcated m Fig 3 as (I?)*0 and (E)ao Nevertheless the general shape of curve 1s still unaltered However, these substantml vanatlons in (Da)2o and (D,)j0 with time and the different numerical values attibutable to each mean size also makes it necessary to consider from first prmclples which mean 1s the correct one to use m eqn (1) Smce 0,’ mses from consideration of the area of new surface produced, then the mean diameter which keeps the number of pticles, each of the same area, equal to the number of particles and the area of the ongmal datnbutlon seems best, 1 e (D,,)zo Bmdarly, m calculatmg r from eqn (2), the mean diameter should ensure equahty of number and mass (or volume) I e (D,), 0 Thus to obtam a correct value for E from eh 0


Clearly, smce the size dlstibutlon of the abrasion fragments varres with time, so wtll the mean size and the substltutlon of a constant mean size into eqns (l)-(3) IS mcorrect Of course, d the sue vanatlon of (D& ,, mth tnne 1s small and the size range narrow, then the use of (z), ,, may not mtroduce a serious error However, with the present data, the effect of vanations in (D& D can be tested and also the posslb&y that other mean sizes m&t be more smtable can be considered Figure 2 shows the van&on of (D,bo urlth tune where the number mean dmmeter corresponds to n = 1, the area to number mean diameter to n = 2 and the volume (or- mass) to number mean diameter to II = 3 The used[ l] IS also gven It IS value of (Da)l ,, prewously clear that the assumption that (D& ,, IS constant in eqns (1) and (3) does not Introduce a senous error stnce from





I‘ A




2 t&Y





0 corrected OasFtef3 A based on A based on I based on I I I IO 20 30 Duration of run, hrs

_ tD,,B, 0 (D.)20 (D,lao I 40


[email protected] 3 The vanaUon of the “energy” requued to produce a unit area of new surface w& tune the mfluence of dtierent assumptions for mean part~cle size


546 requires

the following


factor -

E fC.rr.xx= (J% 0 wa13 w.A





This Ecorrcct LSalso plotted m Fig 3 and though there IS scatter, a constant value of 3 8150 32 x 10” Jim’ IS obtamed A vartatton of +8% IS well wtthrn expenmental error m such a complex expenment and treatmg the data this way lmphes that the energy required to produce a unit area of new surface remams the same throughout the run The vanatlon of (fiI 0 with time was previously ascribed to the greater ease with which fragments were detached durmg the mIttal stage of abrasion whilst corners and edges were being removed[ll However, the present analysts suggests that a shghtly dtfferent mterpretatlon IS requtred Indeed, abrasion IS easier at the start of a run m that the mass rate of abrasion IS htgher but m addition the stze of fragments produced IS also larger Thus, the previous assumption that they were constant m size led to an excessively high number abrasion rate hemg calculated and, as a result, the energy requirement appeared lower When more logtcal values for particle size are Introduced, the energy requuement to produce new surface IS found to remam constant Provtded the parttcles are homogeneous, thts constancy of the energy requirement m retrospect seems more reasonabl: and may indeed be considered as a substantlon of thev homogeneity Abrasion IS not easier m “an energy/umt area of new surface” sense when corners and edges are being removed but only in the sense of the mass abrasion rate

The use of the abrasion model In our first paper [ 11, the model developed showed that the abraston rate was related to the other system parameters by the relattonshlp ra

pD.dP EP,~‘*SD,’

Expenmental results were obtamed which substantrated the use of the model for two scales of operation, an I-fold range of energy dlsapatton rates, a 3-fold range of sohds concentration and three particle sizes The present work gives further support for the model and for the homogeneity of the crystals used By usmg the model, the susceptablllty of different types of particles to abrasion 111 s&red tanks at high sohds concentration can be easdy obtamed from small scale tests and the determmatlon of E for that particular matenal In addttlon, by calculatmg E m the way recommended here, Its vanatlon wtth ttme eves some mstght mto the homogenetty of the abradmg particles For the assessment of abrasion m stirred tanks such a test and the use of the present model to evaluate the results IS clearly better than the use of smmlation tests m such devices as Couette vlscometers

The above relatIonshIp can also be used to ensure that the best operating conditions for achlevrng or preventrng abrasion m stirred tanks at high sohds concentrations can be selected [ 131 CONCLUSIONS

This work shows that the stze of fragment produced dunng the abraston of mckel-ammonmm sulphate crystals decreases W&I time and so does the size range Abrasion IS easier at the start of a run as corners and edges are removed and this type of abrasion gives nse to the largest fragments which are only present m the early stages and causes a higher mass rate of abrasion at that time However, tf the new surface area of abrasion fragments IS determmed from the surface to number mean diameter (D,,)* Oand the number abrasion rate from the volume to number mean diameter (D.h,,. the “energy” requued to produce a unit area of new surface remams constant This may be consldered as a substantlahon of the homogeneity of the crystals used and offers a simple means of assessmg the abrasive tendency of bnttle mater& agttated at high concentrations m stlrred tanks NOMENCLATURE

D* 0, E


the sue of an abrasion fragment, m the size of an abrading crystal, m a parameter proportional to the energyjumt area requued to produce an abrasion fragment (see Ref [ 1I), J/m* the mass of abrasion fragments m a stze range, kg

A4 the total mass of abrasion fragments, kg NO the number percent of abrasion fragments sue range N3 NS n r t

m a

the volume (or mass) percent of abrasion fragments in a size range the number of abradmg crystals defines a mean diameter (n = 1, 2 or 3-see subscripts)) the number of abrasion fragments per set per abradmg crystal (see eqn (2)), s-’ time smce the begmmng of an expenment, s

Greek symbols S spacmg of abradmg Z cr. p

particles, m mean energy dlsstpatlon rate/umt volume fluld, W m-’ vlscoslty of the suspension, Ns m-* density of the abradmg crystal, kg rn-’


Subscripts 1,0 2,0 34 correct

based based based based

on on on on

a number mean dtameter an area to number mean diameter a volume to number mean duuneter (Da)* 0 and (D.43 ,, (see eqn (6))

Superscnpt based on the number ofarun

mean diameter

at the end



at high sohds


[I] N~wnow A W and Contl R , Chem Engng Scl 1978 33 1077 [2] Forsythe W L , Jr and Hertwlg W R , Ind Engng Chem 1949 41 1200 [3] Regan D L , Dunmll P and Lilly M D , Blocech Broengng 1974 16 333 [4] Derry R , Mm Scr Engng 1972 4 3 [S] Hampton, M G , A Handbook of Phosphonc And Manufacture Scot&h Amcultural Industries, 1974 161 Mulhn J W , Crystuflrzatron, 2nd Edn Butterworths, London 1972


m stured



[7] Bjorklund I S and Dygert J C , A I Ch El 1968 14 553 [8] Karabelas A J , A ICh E I 1976 15 765 [9] GwynJ E.AIChEI 1%91535 [lOI Nlenow A W and Bartlett R , 1st Europeon Conference on mxlrig, 1974 Bl-12 BHRA Fluid Engneenng, 1975 [ 1I) Nlewnow A W , Truns Inst Chem Engng 1976 54 205 [12] Contl RI Attr Accademra Screnze Tonno 1977 111 267 U31 Nlenow A W “The Mixer as a Reactor Solid-Llqmd Systems” In Mlxzng m the Process Industnes I Chem E Post-Experience Course, Umverslty of Bradford 1978