Stochastic models for individual particle behavior in straight
and zig zag classifiers
Citation for published version (APA):
Senden, M. M. G. (1979). Stochastic models for individual particle behavior in straight and zig zag classifiers. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR144750
DOI:
10.6100/IR144750
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STOCHASTIC MODELS FOR INDIVIDUAL PARTICLE BEHAVIOR IN STRAIGHT AND ZIG ZAG AIR CLASSIFIERS
STOCHASTIC MODELS FOR INDIVIDUAL PARTICLE BEHAVIOR IN STRAIGHT AND ZIGZAG AIR CLASSIFIERS
STOCHASTIC MODELS FOR INDIVIDUAL PARTICLE BEHAVIOR IN STRAIGHT AND ZIG ZAG AIR CLASSIFIERS
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. DR. P. VAN DER LEEDEN, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAR TE VERDEDIGEN OP
VRIJDAG 30 MAART 1979 TE 16.00 UUR
DOOR
MATHIJS MARIA GERARDUS SENDEN
Dit proefschrift is goedgekeurd door
de pronotoren: prof. ir .M. Tels
Aan mijn ouders, aan Marianne
Het in dit proefschrift beschreven onderzoek is verricht in de vak-groep Fysische Technologie en alle leden die direct of indirect een bijdrage aan het tot stand kalen van dit proefschrift hebben geleverd, ben ik dank verschuldigd.
De opstellingen zijn voor het grootste gedeelte gebouwd door Henk de Goeij en Piet van F.eten. De voortreffelijke en snelle wijze waarop dit is gebeurd, is door mij zeer gewaardeerd. De overige leden van de technische staf dank ik ook voor hun assistentie bij de technische 'Wel:kzaamhede:n.
De prettige sairenwerking mat Pierre Otten en Albert Bieze heeft veel bijgedragen tot het goed verlopen van het onderzoek. Met dank heb ik gebruik gemaakt van hun bijdrage aan het onderzoek op het gebied van luchtclassificatie.
Van zeer groot belang is het -.,.,erk geweest van de studenten die op dit onderzoek zijn afgestudeerd. Zij hebben zov.iel experimanteel als theoretisch een wezenlijke bijdrage geleverd aan het onderzoek dat in dit proefschrift ~rdt beschreven. Mijn erkentelijkheid hiervoor gaat dan ook uit naar Joost Mostert, Rafael Nioolaas, John Thimister, Hans van Nistelrooij, John Hopnans, Anne.mie Savelsberg, Henk Jacobs, Kees van Ginneken en Jenk de Jong.
Bij de visualisatie van de luchtstraning is de hulp van W.J .A. van de Ven zeer gewaardeerd. De experilrenten op de watertafel zijn uitgevoerd mat de enthousiaste medewerking van A.L. van Wezel.
In het bijzonder zou ik Anniek van Bern:relen willen bedanken, die het proefschrift mat grote zorg heeft getypt. Mijn broer André heeft mat veel toewijding de· tekeningen gemaakt en het proefschrift "gerronteerd", waarvoor mijn allergrootste dank.
Tenslotte wil ik iedereen uit mijn naaste om:JeVing bedanken voor hun norele steun en het uit handen naren van allerlei werkzaamheden.
Curriculum Vitae
The author was born on May 21, 1948, In Eindhoven, The Netherlands. Following his secondary education at the "Gymnasium Augustinianum" in Eindhoven, he began hls studies at the Departnent of Chem:ical Engineering of the Eindhoven University of Technology in 1966. Graduate 'WOrk, leading to the title of "Scheikundig Ingenieur" in 1971, was perforrred under the guidance of prof.dr.ir.H.A.C.Thijssen. For one year the author was research co-worker at the "Centraal Technisch Instituut T.N.O." in Rijswijk. In 1972 he joined the Departnent of Chemica! Engineering of the Eindhoven University of Technology as "wetenschappelijk Iredewerker", where he naw 'WOrks under the guidance of prof.ir.M.Tels.
CONTENTS
vi
S1\MENVATI'ING ix
CHAPTER 1: IN.l'Ra:>UCTICN 1
CHAPI'ER 2: ClIARACTERIZATICN OF THE DESIRED SEJ?ARATION
2.0 Abstract 8
2 .1 Introduction 8
2.2 Description of the separation results with respect to the 12
fall velocity of the particles
2.3 Cctrp::>nent separation efficiency and its relation to the 21
separation function ~ (w)
2. 4 caribination of separation techniques for a canplete 25
conp:nent separation
2.5 Conclusions 29
References 30
List of symbols 31
CHAPI'ER 3: A S'I'OCHASTIC MJDEL FOR THE SEPARATICN PROCESS IN A S'l'Rl\IGHT VERTICAL GBAVITATIONAL AIR CUSSIFIER
3. 0 Abstract 34
3.1 Introduction 35
3. 2 Description of the stochastic nodel 38
3. 3 Mathematical fonnulation of the one dinensional particle 40
transport
3. 4 Calculation of the separation function ~ (w) 45 3. 5 calculation of the i:rean and variance of the residence 50
tine distribution of the particles
3. 6 Experinental verification of the mixing concept for the 60
straight vertical air classifier
3.7 Discussion of the numerical results 71
3.8 consequences for the design of vertical air classifiers 78
based on this rrodel study
3. 9 Conclusions 82
References 83
CHAPTER 4: STCX:HASTIC MODEI.S FOR THE INTERACTION BETWEEN THE STAGES OF THE STANDARD 90° AND 120° ZIG
ZAG AIR CIASSIFIER
4. O Abstract 90
4 .1 Introduction 91
4.2 The experiments to record the single stage behavior 94 of the particles
4.3 Description of the interaction between the stages 106 by a Markovian random walk m:::rlel
4.4 Description of the interaction between the stages 121 by the one step m=rro:cy m::xlel
4.5 Experi.nental verification of the one step :me.rro:cy m::xlel 141 for the standard 90° and 12D0 zig zag air classifier ·
4.6 Conclusions 150
References 151
List of syrnbols 151
CHAPl'ER 5: SINGLE STAGE BEHAVIOR OF INDIVIDUAL PARI'ICLES IN THE STANDARD 90° AND 120° ZIG ZAG AIR CLASSIFIER
5.0 Abstract 155
5 .1 Introduction 155
5.2 Visualization of the air flow pattern with helium 159 filled soap bubbles
5.3 Local air velocities in a stage of the standard 90° 163 and 120° zig zag air classifier
5.4 Analysis of the trajectories of the m:::rlel particles A2 172 in the standard 90° and 120° zig zag air classifier
5.5 Particle trajecto:cy calculations in the standard 90° 182 and 120° zig zag air classifier
5.6 Conclusions 213
References 215
List of syrobols 215
CHAPTER 6: THE INFllJENCE OF. THE STAGE GEOOETRY ON THE PERFORM-ANCE OF ZIG ZAG AIR CLASSIFIERS Nr IJ:M PARI'ICLE CONCENrRATIONS
6.0 Abstract 219
6.1 Introduction 219
6.2 CaTiparison of the separation results of the 90° and 120° 220 zig zag air classifier with standard depths
6.3 Variations in gearretry: the standard 150° zig zag air classifier and different channel depths
dt for
the 900 and 1200 zig zag air classifier
6.4 Alternative design variations 6.5 Conclusions
References List of syrnbols
APPmDICE.S
3.1 calculation of the particle concentration profiles in.a straight vertical air classifier for steady state conditions
3. 2 Calculation of the separation function il> (w) by sol ving the
transport equation for the one-dinensional straight vertical air classifier
3. 3 calculation of the mean residence tine -r for the particles in the one dinensional vertical air classifier
3.4 calculation of the variance cr2 of the residence tine distribution of the particles
3.5 separation function <t>(vf) and mean residence tine T(v.f) of the various nodel particles in the straight vertical a i r classifier.
4.1 -F.quiprent specification of the experinental set up for the zig zag air classif iers
-EKperirrental data on single stage particle behavior in
the standard 900 and 120 zig zag air classifier -Experinental data on <PR(vf~ f?r the 90° and 120° zig
zag air classifier of stanäard depth
4. 2 The Markovian random walk nodel
4. 3 The one-step-marory nodel: saoo mathematical deri vations
5.1 Nunerical data of the neasurenents of the local air velocities by hot film anenaretry
5.2 catparison of the :rceasured local air velocities and the predicted local air velocities on the basis of the apprax:imated local air velocity pattern
6.1 Separ~tion fW::~ions <t>R(vf/vf50> for the various zig zag a i r class1f1ers. 229 244 249 250 250 A.1 A.2 A.7 A.18 A.23 A.24 A.25 A.28 A.31 A.36 A.41 A.43 A.46
Sum:nary
In the last decade a nunber of processes have been developed for the recovery of usable carponents or fractions from mixed rrn.micipal wastes. In these processes the separation is usually brought about by a canbination of different techniques such as sieving and air clas-sification.
This thesis starts wi th a discussion of the relation between the characteristic separator perforrrance and the efficiency of the
com-ponent separation obtained in it. In every separation technique the particles are classified according to a characteristic property of the particles. The efficiency in component separation depends on both the characteristic separation perfonnance of the separator and the distribution of the characteristic particle property within the
various carponents. The relation between the characteristic separation performance of the·apparatus and the efficiency of the ccmponent separation has been quantified for the air classification process.
The thesis deals with air classification. Air classification is a separation technique in which solid particles are classified accord-ing to their fallaccord-ing behavior in an air flCM. The classification of relatively large particles has been studied at very low particle con-centration. The particles were suanitted individually to the drag of an upwards flowing air stream in a vertical channel. This channel was either straight or had a zig zag shape. The result of the classific-ation process is not fully deterrnined by the force balance between gravity and the rrean air dragon the particles because of a large nunber of disturbing effects. Important disturbances are the turbul-ence of the air flow, air entrance and exit effects as well as particle-wall interactions. The efficiency of separation of the air
classif ier is deterrnined by these effects that exhibit a stochastic character.
In the straight vertical air classif ier the process has been describ-ed by a canbination of convecti ve and mixing transport teJ::mS. The
mix-ing disadvantageously influenees the separation efficiency. The
sinple rate equations that are anenable to e:xperirrental verification. The no:lel was verified by recording and analyzing the separation process for individual particles. The m:xlel describes the relation between separation efficiency and nean residence tine of the part-icles. The I!Dst favorable relation between separation efficiehcy and maan residence line of the particles is obtained by a fast reI!DVal of the particles frcm the apparatus exits and by reducing the mixing in the classification zone as far as possible. The influence of the rem:>val rates of the particles on the separation efficiencyhas been
quantified.
In a zig zag shaped channel the classif ication process takes place at
every junction of tVlO channel sections. A series of junctions leads to nultistage classification. The separation performance is
determ:i.n-ed by the separation characteristic of the single stages on the one hand and by the interaction between the stages on the other hand. The interaction between stages has been described as a stochastic pnxess with discrete transitions. In general the particle transition fran a stage depends not only on process conditions, particle
proper-ties and stage gearetry but also on the di.rection fran which the
particle had entered the stage.
The separation process at a single stage has been studied experinent-all y for an angle of 90° and 120° between the sections. The st.andard depth of the classifier has been chosen such that the edges protrud-ing into the channel are vertically in line. The separation efficien-cy of a single stage in the st.andard 120° zig zag air classifier is superior to that in the st.andard 90° zig zag air classifier. This fact has been explained by an analysis of the individual particle behavior at a single stage, visualization and measurement of the local air velocity pattem and calculation of the particle traject-ories fran these data.
The relation between miltistage performance and single stage particle behavior has been derived and verified experinentally. The interact-ion between the stages of the standard 90° zig zag air classifier is greater than that in the st.andard 120° zig zag air classifier. The
zig zag air classifier that results from it does not suffice to obtain a separation efficiency that is as good as that reached in the stan-dard 120° zig zag air classifier. Moreover the mean residence time of the particles is relatively high in the standard 90° zig zag air clasisifier because the particles pass nnst stages repeatedly.
The understanding of the relation between separation perfonnance and stage georretry in zig zag air classifiers has been widened by measure-ments in clasSi:lfiers wi tb. channel depths different from the standard depths and in the standard 150° zig zag air classifier. The separat-ion process in the standard 150° zig zag air classifier does not
clearly take place at discrete stages. The process therefore rese.mbles tb.at in the straight vertical air classifier rather tb.an the process in the zig zag air classifier with an angle of 120°.
Sanenvatting
In het laatste decennium zijn een aantal processen ontwikkeld voor de terugwinning van bruikbare corrp:menten of fracties uit stadsafval. In deze processen 'WOrdt de scheiding van de corrp:menten vaak langs mechanisch/fysische weg gerealiseerd. ~re scheidingstechnieken,
waaronder veelal het windziften, worden hierbij gecanbineerd toege-past.
Dit proefschrift begint net een beschouwing omtrent de samenhang tus-sen de scheidingskarakteristiek van scheidingsapparaten en de effi-ciëntie van de daarin bereikte ca:nponentscheiding •. Iedere scheidings-techniek classificeert deeltjes naar een karakteristieke eigenschap.
De efficiëntie van een caip::>nentscheiding is· steeds een functie van Z<Mel de scheidingskarakteristiek van het apparaat als van de verde-ling van de karakteristieke deeltjeseigenschap binnen de verschillen-de cai:ponenten. Aan de hand van het windziften is de relatie tussen de scheidingskarakteristiek van het apparaat en de efficiëntie van de corrp:mentscheiding gekwantificeerd.
Het onderzoek heeft betrekking op windziften, ook wel luchtclassifi-catie genoenrl. Luchtclassifiluchtclassifi-catie is een scheidingstechniek, waarbij deeltjes op hun valgedrag in een luchtstroom worden geclassificeerd.
De classificatie van relatief grote deeltjes in zeer lage concentra-tie is bestudeerd. De deeltjes zijn daartoe in een vertikaal kanaal, dat recht is dan wel een zig zag vonn bezit, individueel onderworpen aan de neesleepkracht van~ straiende lucht. Door allerlei storende effecten, zoals de turbulentie van de luchtstroom, in- en uitstro::imaffecten van de luchtstraning en deeltjes-wand interacties, is het verloop van het ziftproces niet volledig bepaald door de balans tussen de zwaartekracht en de gemiddelde m=esleepkracht van de lucht-stroam op het deeltje. Het zijn deze effecten net een stochastisch karakter, die de scheidingsefficiëntie van de zifter bepalen.
In het rechte kanaal wordt het ziftproces hier beschol.:i\-.d als een convectief deeltjestransport, waarop een nengproces is gesuperponeerd dat storend wex:kt op de scheiding. De afvoer van de uit de zifter is beschreven net. eenvoudige kinetische relaties, die zodanig
zijn gekozen dat het ll'Odel experirrenteel kan >«>rden getoetst. Door het vastleggen en analyseren van het procesverloop voor individuele deeltjes is het transportmxlel geverifieerd. Het m::idel toont de be-trekking tussen de scheidingsscherpte van de zifter en de daarvoor
benodigde verblijftijd van de deeltjes. Voor vaste stof concentraties die de beschouwingswijze van indiv~duele deeltjes rechtvaardigen, leidt deze betrekking tot conclusies aangaande het zifterontwerp. De
gunstigste verhouding tussen scheidingsscherpte en de daarvoor beno-digde verblijftijd van de deeltjes wordt bereikt wanneer de deeltjes bij de apparaatuitgangen snel worden afgevoerd en de menging in de classificatiezone zoveel nogelijk wordt onderdrukt. De invloed van de afvoersnelheden van de deeltjes op de scheidingsscherpte van het apparaat is gekwantificeerd.
In een zig zag kanaal vindt de classificatie in het algemeen plaats ter hoogte van iedere afzonderlijke knik. De aaneenschakeling van knikken maakt herhaalde classificatie nogelijk. De ziftprestatie >«>rdt bepaald door de scheidingskarakteristiek van een enkele knik en de deeltjesuitwisseling tussen de knikken. De interactie tussen de knikken wordt als een stochastisch proces m:!t discrete overgangen beschreven. In het algerreen is de afloop van de deeltjesbewegingen op
een knik niet alleen afhankelijk van de procescondities, deeltjes-eigenschappen en knikgeanetrie, maar ook van de richting waarin de deeltjes de knik naderen.
De scheidingskarakteristiek van een enkele knik is experirrenteel bepaald voor een knikhoek van 90° en 120°. De standaard kanaaldiepte is daarbij zo gekozen dat knik.hoeken recht boven elkaar liggen. De
scheidingsscherpte van een enkele knik in de standaard 120° zig zag zifter overtreft die in de standaard 90° zig zag zifter. Een verkla-ring hiervoor wordt gegeven op grond van een analyse van het deeltjes-gedrag op een enkele knik, het gevisualiseerde en gen:eten luchtsnel-heidsprofiel en op grmd daarvan uitgevoerde berekeningen van deel-tjesbanen.
De betrekking tussen de totale zifterprestatie en het procesverloop op
een enkele knik is uitge'Ylerkt. De interactie tussen de knikken is in de starrlaard 90° zig zag zifter sterker dan in de standaard 120° zig
zag zifter. De gunstige verhouding van neertraps- tot eentraps-scheidingsprestatie in de standaard 90° zig zag zifter, die hiervan het gevolg is, is niet voldoen:je cm even goede scheidingsresultaten te behalen als in de standaard 120° zig zag zifter. Bovendien is de gemiddelde verblijftijd van de deeltjes in de standaard 90° zig zag zifter relatief groot doordat de deeltjes de knikken veelvuldig
door-lopen.
Het verkregen inzicht cmtrent de sarre:nhang tussen scheiding5prestatie en gearetrie van de knik werd tenslotte verruinrl door netingen aan zifters net andere dan bovengenoem:le standaard diepte en aan een zif-ter net een knik.hoek van 1500. Het scheidingsproces in een zifter net
knik.hoek van 150° en standaard diepte blijkt niet duidelijk in neer-dere gescheiden trappen te verlopen, zodat dit toestel eerder gelij-kenis vertoont net een rechte stijgzifter dan net een zig zag zifter net een knik.hoek van 120°.
CHAPTER
1
INTRODUCTIONGravitational air classification is a separation process in which solid particles are classified accordi.ng to their falling behavior in a classification zone where they are subjected -in the gravity force field- to the drag force of an air ~low. The separation is based on the differences in the trajectories of non-identical particles within the classification zone.
OUr interest in gravitational air classification originates fran its potential applicability to m.m.icipal waste separation processes. In these processes m.m.icipal waste is shredded and subsequenUy.
separat-ed into useful caaponents [1.1-1.15]. The products may consist of isolated single waste carp:ments, such as paper and plastic, or of useful waste mixtures such as organic garbage. In the last decade a rn:nnber of these processes [1.1-1.15] have been developed., of which there are nr::M several CCllllm'cially available Il • 9-1. ll
J •
The fast developi:ent of these separation processes to their present camièrcial status is due to the general interest taken in reducing the "throwEMay" character of our. society, the possible relief of overburdened
tipping facilities and the capability of separation processes to be
integrated into existing waste disposal plants. The separation of the
shredded m.m.icipal waste in these processes is usually realized by a canbination of separation techniques such as sieving apd air classif-ication. In Europe gravitational air classification is often use:êl in m.m.icipal waste separation processes to isolate the paper and plastic fraction fran the waste mixture. Cllaracteristic for this application is the fact that the separation is carried out with particles which are relatively large with regard to the characteristic dirrensions of the classifier.
The separation in an air classifier is disadvantageously influenced
by stochastic disturbances. The main stochastic disturbances are due to the turbulence of the air streain, particle-wall interactions and
particle-particle interactions. These disturbances cause an
ineffic-iency in the separation process, as particles may be displaced into
another particle product stream than was to be expected on the basis of the canbined actian of gravity and air drag alone. The questian is
whether canplex separations such as the isolation of paper and plas-tic foil fran shredded m.micipal waste can be carried out in a single stage classifier with a sufficient degree of efficiency. Although the single stage classifiers that have been proposed in sane separation processes [1. 5, 1.13-1. 14
J
may be sufficient for a pr:i.rnary rO\lghseparation, nultistage air classifiers have been chosen in sane of the llDSt important and best developed waste separation processes
Il
.1-1. 4, 1.9-1.10]. In these processes nultistage zig zag air classifiersfl.16] have been chosen as this type of classifier provides sane fa-vorable characteristics in addition to its nultistage operation: -the process is carried out in a single colurm
-the same air is used f or all stages
-both the upflO';iing stream of light particles and the descending flOW' of heavy particles are subjected to a repeated classification -the particle streams are repeatedly broken up inside the classifier. Infonnation on the gecmetcy of the classifier, the air flOW' pattern and the daninant f lows of solid particles inSide the classif ier is given in figure 1.1.
GEOMETRY OF THE ZIG ZAG AIR CLASSIFIER cross sectio
D
AA' ~ t AIR FLOW Feed of Separation. region of tur-bulent airAIR FLOW PATTERN
solid particles tary valve
,
...
~
d.·
o ••°tl
'', .~ DOMINANT PARTICLE STREAMS • \ \ o Descending particles
'• • Rising particles
tt
AIR FLOW
Figure 1.1 Geometry of the standard 120° zigzag air classifier: the air flow pattern and the dominant particle streams
The classifier is constructed by joining a number of sections together at a fixed angle in order to create a zig zag channel. Nornally this angle is 120°. The channel has a rectangular cross section. Its par-ticular gecmetry and the air flow pattern induced by it cause two distinct particle streams:
-a stream of "light" particles carried upwards by the upflowing air current, and
-a stream of "heavy" particles nDVing dawnwards along the lower wall of each section.
At each junction of two sections, i.e. at each stage, the particles of both streams are subjected to a renewed classification after which they may either continue their movemant in the original stream or be transported to the stream noving into the opposite direction. The
per-fornance of the classifier is detenni.ned by the particle behavior at a single stage on the one hand and by ·the interaction between the stages on the other hand. This interaction causes the overall separation efficiency of the entire apparatus to differ from that which can be obtained in a single stage.
The zig zag air classifier takes up an .important place in this thesis. This st.udy will provide the information for a better understanding of 1
the processes that take place in the zig zag air classifier and
the role of the gearetry of the classifier in them.
Scope of this thesis
In the introductory chapter 2 methods of characterizing the separat-ion results are discussed. The relatseparat-ion between the degree of isol-ation of one specific component fran a mixture on the one hand and
the separation efficiency with respect to the fall velocity of the particles on the other hand is shown. This will lead to an explanat-ion of the positive effect of the ccmbinatexplanat-ion of different separatian techniques on the overall efficiency in the isolation of a specific canponent. Canbinations of different separation techniques, such as sieving and air classification, are camon practice in the design of municipal waste separation systems.
In this thesis the study of gravitational air classification concerns the description of the separation process for pärticles that are
1
rcl.atively large with respect to the characteristic dimansions of the classifier. 'l'his object is inspired by the actual situation inside
the classifier in which paper and plastic foil are isolated fran
sbredded numicipal waste and by our interest in the behavior of coarse solids-gas dispersions in genera!. Pieces of paper are used a.S m:x1el particles in order to s:inulate the actual situation in the classifier
in which paper and plastic foil are separated fran shredded mixed
numicipal waste.
In the first analysis of this problempresented in this thesis the influences of particle-particle interactians have been eliminated by carrying out the experim:mts at low particle concentrations in the classifier. The . results of this research program are a basis frcm which a future systenatic extension towards higher particle conoen-trations may well be possible. Fran the experim:mtal point of view it is an advantage that at lowparticle ooncentrations the registration of the particle behavior inside the classifier can be carried out by · nethods such as film and video recording.
The air classification process will be described by stochastic m:xlels.
The stochastic approach makes it possible to describe the separation results inclusive of the efficiency of separation. It further allows
an
esd.ma.te to be 1llé'!de .of the potentia1 throughput capacity of the classifier. The latter aspect is in:lissolubly oonnected with the separ-ation results. No fonw.lation and/or explanation of this aspect havebeen presented.in literature so far.
In chapter 3 the stochastic approach is first worked out for the straight vertical classifier. Dur interest in this classifier origin-ated fran the need of a better understand.ing of the werk on stochastic m:xlelling of air classification processes published in literature
[1.17-1.20]. 'lhe question to be a:nswered here is whether this w:xk is
va1id without m:xlification for relatively large particles. It then turned out that. the practical application of the theory was han:pered
by a lack of knowledge about the exit velocities of the particles out of the classifier. A solution for this problem, that is supported by
systenatic experim:mts especially dedicated to this theory, is pre-sented in chapter 3. 'l'his results in a set of approximative equations
capacity of the classifier which can be translated into qualitative consequences for the design.
The remainder of this thesis is entirely devoted to the zig zag air classifier. The study involves an explanation l:x:>th of the single stage behavior of the particles and of the interaction between the stages. The only existing mathematica! node! for the classification process in a zig ~ag air classifier is given by Kaiser [1.21] whose work irrplies without exact derivation the concept of a Markovian rand.cm walk. The validity of his node! had not been proven up to now. In chapter 4 a generalization of his node! wil! be given. The relation between the separation efficiency and the potential throughput capacity is derived. Systematic experiments wil! show the lirnits of applicability of the Markovian rand.cm walk node!. Furtherirore, the requirements that a nore realistic node! should fulfil wil! be indicated. This results in a stochastic one-step-m:m:>ry node! that is based on knowledge of the single stage behavior of the particles. This node! together with the experimental verification of its tenabi1ity for two characteristic classifier geatetries ccrcpletes chapter 4.
The explanation of the single stage behavior of the particles, that was experimentally detennined and thoroughly analysed in a lirnited number of laborieus experiments, is based on approximative calculat-ions of the particle trajectories at the single stage concerned. The approximative solution is based upon an analysis of the local air flow pattern by flow visualization techniques and hot fiJ.nl.anem:::rretry to-gether with an analysis of the eJq?erimental particle trajectories. Chapter 5 deals with the results of this part of the study.
Finally, the gearetry of the classifier has been varied. In this introductory study the angle between the sections of the classifier which is undoubtedly one of the main geometrie pararreters has been chosen as a starting point. In chapter 6 the experimental results are evaluated with respect to the total perfonnance of the classifier. Air classifiers with an angle of 90°, 120° and 150° between the sections are studied. The results of these experiments indicate lirnits ih-gearetric variations above which the multistage character of the air classifier dirninishes or even disappears. It is selfevident that
thê
sane limi:ts apply to the validity of the one-step-maoory m:::idel. In chapter 6 the influence of the cha:nnel depth on the separation perfoi:mance of the 90° and 120° zig zag air classifier will be dis-cussed on the basis of preliminary el!peri.nents. The influence of the geaoetric variations that have been studied will be caipared to thescarce results that were presented on th1s subject in literature.
References
l.l Colon F
.J.,
De Ingenieur 86 (1974), no. 7, p.131-1331. 2 Colon F .J. , Kruydenberg H., Proc. First Vbrld Recycling Cong.ress p.3.15.i-3.15.ix, March 6-8 1978, Basel
1.3 Hoberg H., Schulz E., MÜll und Abfall (1974), no.8, p.263-268. 1.4 Hoberg H., Schulz E., Aufbereitungstechnik (1977), no.l, p.l-5. 1.5 Douglas E., B.i.rch P.R., Resource Recovery and Conservation
!
(1976), p.319-344.
1.6 Ni.edner P., Hillekanp K., Ul.l:Melt (1974), no.6, p.37-39. 1. 7 Orth H., MÜll und Abfall (1976), no.l, p. 7-17.
1.8 Arella O.G., U.S. E.P.A. report no. SW-47d, (1974). 1.9 F.smi.l/Envirotech Technica! Information Bulletin
h:'ldress: Stationstraat 48, Amersfoort, The Netherlands
1.10 Fl.äkt I.uchttechniek Technica! Infrn:ma.tion Bulletin: RRR-system Address: Amersfoort, The Netherlands
'1.11 Krauss Maffei Technical InfÓrmation Bulletin: System RBO Address: Krauss Maffeistrasse 2, München,
GeJ::m.3ny.
1.12 Morey B., Proc. 4th Mineral waste Utilization Symposium, p.85-94, Chicago, Illinois, May 7-8, 1974.
1.13 Sullivan P.M., Makar H.V., Proc. 4th Min.era! waste Utilization Symposium, p.129-141, Chicago, Illinois, May 7-8, 1974.
1.14 cavanna M., Riano E., Proc. 4th Mi.neral waste Utilization Symposium, p.143-149, Chicago, Illinois, May 7-8, 1974. 1.15 Shannon L.J., National Environlrental Research Center, Publ.
PB-243-634, May, 1975.
1.16 I:np::>l:tant infonna.tion can be found in the following patents: U.S.Patent 1,650, 727, A.H.Stebbins, Septeniler 28, 1926. U.S.Patent 11861,248, A~H.Stebbins, May 31, 1932.
Elritish Patent Specification 1,014, 723, Alpine A.G., December 31, 1965.
B.R.D,Auslegeschrift 1482424,Alpine A.G., May 27, 1971. Elritish Patent Specification 468,2121F.Carey et al., June 28, 1937.
1.17 Molerus
o.,
Chem.Ing.Techn. 38 (1966), no.2, p.137-145. l.18 Moleruso.,
Hoffmann H., Chem.Ing.Techn. 41 (1969), no.5+6,p.340-344.
l.19 Molerus
o.,
Chem.Ing.Techn. 39 (1967), no. 13, p.792-796. 1.20 Rumpf H. et al., Verfahrenstechnik .§. (1974), no.9, p.261-263. l.21 Kaiser F., Chern.Ing.Techn. 35 (1963), no.4, p.273-282.CHAPTER
2
CHARACTERIZATION OF Tl-E DESIRED SEPARATION2. 0 Abstract
In this chapter methods of characterizing the results of a separation
obtained are discussed. The separation results with respect
tO
thefall behavior of the particles are described by the separation funct-ion il\ (w) • il\ (w) represen'ts the fraction of the particles in the feed stream with a fall velocity w between w and w+dw that leaves the classifier in the heavy product stream. It is shown that in this
thesis il\ (w) may well be characterized by the separation cut point w
50, i.e. the fall velocity for which t(w) = 0.5, and by the
derivat-ive of il\ with respect_ to wat any suitable value of w within the1
interval 0 <
«w>
< 1.In an operation aimed at the separation of bo different oc:mponents
the degree of oc:mponent isolation is of first concern. It will be shown quantitatively hcM the efficiency in oc:mponent isolation is the canbined effect of classif ier perf o:rmance and the particle fall velo-city distributions of the individual oc:mponents in the feed. Th1s
discussion leads to the explanation of the advantage of canbining
different separation techniques, such as sieving and air classificat-ion, in oc:mponent isolation processes.
2.1 Introduction
In figure 2.1 the classification process is illustrated for the
straight vertical air classifier. The particles are fed into the
classification zone at a feedpoint -fixed S<m:!Where along the oolumn height. The particles shou1d be w'li.formly spread over the classifier cross section. During the feeding of the particles forma.tien of con-glanerates of particles should be avoided or conglcm::irates should be
breken up as nuch as possible. The actual separation process tak.es
place inside the vertical oolumn, i.e. the classification zone, in which an air stream flows upwards. Particles with a fall velocity
smaller than the average air velocity tend to be carried upwards by the upflawing air strearn. Consequentiy, a light product stream to the top of the column is created in which the particles with a small fall velocity are preferentially taken up. Particles with a fall velocity larger than the average air val.ocity tend to fall to the bottan of
the column in spite of the upflowing air stream. This results in a heavy product stream falling towards the bottan of the column in 'Nhich the particles with a large fall velocity are preferentially taken up. In the last step of the classification process the partic-les leave the product exits of the column and are thereup:m rerooved fran the air stream. The ren:oval of the pa:rticles may be realized in a s.imple open reception vessel for the bottan product and in a cyclone for the top product.
~ fall veloc:ty, distribution function a.c lne feedstream
îlAl
G
W-tl> d of solid rticles .0 O'cj, ";J>. ' ' ""'o : '" ç:i.' ' 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Upward flowing air stream
'
w --+
~ weighed fall velocity distribution function of the light top product
'f:
I I 1 1 w -+ ~ weighed fall velocitydistribution function of the heavy bottom product
t·iyurc 2.1 Reprcsentation of the air classification pr0:.::css
for a straiqbt vcrtical air classifier by weighed fall velocity distributions
The tenninal fall velocity of a particle in infinite, stationary air can be expresse:i by:
w
=
"'
Z'lr;f
(pp-pf)'1,
A.L Pf (2.1)in which w..,
=
the tenninal fall velocity of a particle in infinitestationary air m/s
V p = the vol'lll'OO of the particle ~ m3
A .L
=
the cross sectional area of the particle perpendi-cular to the directio:n of the relative air velooity m2q,
= the drag ooefficientpp = the density of the particle Pf = the density of the air
g = the gravity acceleration
kg/m
3
kg/m3 m/s2In cases
where
the orientatiOn of a particle and/or where particle rotation plays a roleq,
and A J. represent the average values during the fall of the particle. w.., has theoretica! significance because the tenninal fall velocity of a particle must necessarily be determi.nedin a finite piece of apparatus. It is therefore unavoidable that the fall velooi ty of a particle w as rreasured in actual practice will be
influenced to soms extent by the geanetry of that apparatus and by
the relationship of the geai:etry of the apparatus to that of the
particle.
The separation prooess will be desc:ribed on the basis of the fall velooity distribution functions ni(w) of the various process streams. n1
Cw)
for any process stream i is defined by:ni (w)dw s the weight fraction of the particles within the prooess stream i with a fall velocity w between wand w+dw
and
f n1 (w)dw = 1 0
(2 .2)
The corresponding cunulative distribution function is defined by:
w
N
1 (w) = f n1 (w)dw = the weight fraction of the particles within the 0
In figure 2.1 this is illustrated by a graphical display of the fall velocity distribution functions of the various process streams. The product functions are weighed by the :i.ntegral factors f and g to indicate the weight ratio of OOth product strearns to the feed stream. f and g are defined by:
Q
f::
~
in which:m
and g :: ..Jl. for batch classification mF
Q
and g ::: iJ;: for cont:i.nuous classification
m f
=
the weight of the light top product mg = the weight of the heavy l:x:lttan product mF=
the weight of the feedQf
=
the light top product fl()!d rate ~=
the heavy l:x:lttan product flow rate ~=
the feed flow ratef = the weight ratio top product to feed g = the weight ratio l:x:lttan product to feed and the subscripts:
F = feed; f
=
light; g =heavykg kg kg kg/s kg/s kg/s
The weighing of the distribution functions of the process streams enables a direct visualization of the split of the particles with a fall velocity between w and w+dw over the two product streams. Since the weighed distribution functions fully describe the separation re-sults with respect to the particle fall velocities, any characterizat-ion parameter or function may be derived fran them. Evidently, such a Characterization relates the classification results to the particle fall velocities. This is in agreement with the actual mechanism of separation, but in an operation aimed at separating two different co:rponents the first :interest of the operator concerns the degree of co:rponent isolation rather than the efficiency with regard to the fall velocity. This causes an ambiguous :i.nterpretation of the concept of separation efficiency, as the efficiency with regard to the fall velocity looses its direct significance for the operators logic :i.nterpretation of the results with respect to the efficiency of the co:rponent isolation. Unfortunately, ccnp:ment separation is the
can-bined effect of the classifier perfomence with respect to the par-ticle fall velocity and the existing overlap of 'the fall velocity distributions of the various oarponents in the feed stream. Any
com-ponent separation efficiency definition, therefore, mixes feed proper-ties and actual classifier perfonnance that only discr:l.minates between fall velocities of the particles.
2.2 Description of the separation results with respect to the fall velocity of the particles
The nost pclW'erfu1 tool for a quantitative description of the separat-ion results is the separation or "Tranp" function [2.24] IP(w), which is defined by
n (w)
IP(w)
=
g·n;(w) (2.3)For particles with fall velocities bet.ween w and w+dw, ~(w) thus re-presents the fraction of those particles in the feed stream that leave
the air classifier in the bottan (heavy product) stream. The con-struction of ~(w) fran n
9(w) and IT(w) is illustrated in figure 2.2a. In practice the distributions are often obtained as cumulative funct-ions. It is possible to construct IP(w) directly fran these cunulative functions [ 2. 2] • <P (w) has a value between o and 1 for particles with a fall velocity w*) that may errl up either in the light top product or in the heavy bottan product. An ideal separation is
char-acterized by a step function at the separation cut point wcut (figure 2.3).
Like any separation technique, air classification is afflicted by an inevitable degree of inefficiency due to all kinds of disturbances of which particle-particle and particle-v.iall interactions, the tur-bulence of the air stream as -well as the air velocity profile in the
classifier are the nnst important. This inefficiency expresses itself in the presence of a fall velocity region for which 0 < @(w) < l
(fig. 2.3). The width of this fall velocity region is directly relat-ed to the degree of inefficiency of the separation,
1.0 t(w) = g ng(W)
y(:
0î
Il 1 ---1 wso w ,__. w w -a @ -Construction of ~(wl from g n 9{w) and nF(w) -Illustration of the definitions of w 50 and wa@ Illustration of the definition of wu
Illustration of the definition of
w
f'igure 2. 2 Illustration of the definitions of the variousseparation cut points (table 2.1)
1
t
t(w) no separation at _all 2 normal separation 3 ideal separation w-+Figure 2.3 Separation function t(w) for various degrees of separation efficiency
2. 2 .1 '.PJ.e ~ation cu;!: E2in~
The separation cut point is the first characteristic separation para-neter that can be defined on the basis of the separation function
lb(w) • In principle any value of w can be chosen as the separation cut point, as long as the definition is suitable for the specific applic-ation [2.3]. Table 2.1 gives a ocnpilation of definitions encountered in literature. The preparative separation cut point w50 will be used in this study, as it follON'S straightforwardlv and unan'biguously fran <l>(w}. It represents the fall velocity of which 50 wt.% of the parti-cles will end up in the heavy prcxluct stream, as expressed by t (w)
=
0.5.For w50 the follawing equation holds: f nf(w50>
=
g n9cw50> (2.4)
which shows that w
50 can also be interpreted as the value of w at the point of intersection of the weighed distri.bution functions of both process streams. The preparative separation cut point w50 is prefer-ed here alx:we the analytica! separation cut pointwa and the overlap separation cut point wu as these last two paraneters, in contrast to w50, are not uniquely dependent on t(w), but also on n_e.(w) as can be seen fran equation 2.5.c and 2.6 (table 2.1).
Significant differences between the.values of w50 and wa occur in situations in which t(w) clearly deviates fran a sym:ietric s-shaped curve. The definition of wu is nme vague than that of wa' as it does not even take into acoount the relative weight of the product dis-tri.bution functions expressed by f and g. The definitions of wu and wa are of interest in practical situations. wu can be calculated even if g and f are unknown, for instance in technica! applications. wa is used for analytica! purposes. ~(wal can be determined fran the
ex-perine:ltal f-value that is obtained in an analytica! air classifier working at a cût poi.Ilt Wa· The equality Óf ~(wa) and f is given in equation 2.5.b (table 2.1).
Representation of the separation cut point by
was
defined by eq. 2.8 requires sane explanation. The air classification process is con.-sidered to be a separation technique in which the separation condit-ions inside the classificati<?11 zone ~ for the individual particlesdue to stochastic disturbances. This itrplies that the effective va1ue
~(w) can be interpreted as being the cumtl.ative distribution function
of the separation cut point: w
<t> (w)
=
f <p(w)dw (2.7)0
\>fuere <p(w) is the distribution density functian of the separation cut point. w(w) then rep:resents the probability that particles with a fall velocity
w
are perfectly separated according to a separation cutpoint value that is smaller tl1an their fall velocity, and consequent-ly will end up in the heavy bottan prcx1uct stream. As a logic
con.se-quence of this interpretation the mean value of the separation cut point is defined by:
..,.
w
= f w <p(w)dw (2.8)0
'lbe fundamental weakness in this interpretation of ~(w) is that it
cannot be assumed a priori t)l.at <p =
;i! ;:;,
9
for all values of w which is an essential condition för a distribution density function. In fact, ancmalities mayoccUr
in the separation p:rocess [2.5, 2.6] that cause a negative valueof~·
The sticking of small particles tolarge particles is an illustrative example. Stochastic nodels for air
classification p:rocesses, however, oftèn pass over these ancmalities
too and this leads to mathanatical expressions for «i(w) that could fit the way of expression used by Rullpf [loc.cit.].
2.2.2 ~izatiog_of the ~tion e!Ë:94:~-2Y-~_the basis
gL«i~wl
In this section criteria wi1l be discussed that characterize the
degree of separationwith respect to the fall velocity of the parti-cles in the region 0 < w (w) < 1. The various criteria give an
im-p:ression of either the separation efficiency (~l Tl) or t;he . separation inefficiency (symbol iT1) • The general teDl:ls "efficiency"
and "inefficiency" are used for the follCMing three categories: A: parameters that express the difference or ratio of tfflo fall
veloc-ities at which ~(w) bas a distinct value
B: parameters that are related to partial areas be1ow the weighed
fall velocity distribution functians of the prooess streaJllS C: parameters that describe the steepness of \\>(w) in a differential
1
!--'
O'I
Table 2.1 Oef initions of the separation cut point for air classification processe,s
Symbol Name Lit. Description equation no. Mathematical formulati-::>n
W5Q Preparative [2.1] 1. value of w for which •(w)=0.5 t(wso> = 0.5
separation 2. value of w at the point of inter- 2.4
g ng<wso> = f nf(wso> cut point section of the weighed
distribut-ion density functdistribut-ions ni·(w) for" both product streams
wa Analytica! [2. l] Value of w for which the fraction 2.5.a 9 Ng(wa) = f[l-Nf(Wa)J or separation of light particles in the heavy
cut point product equals the fraction of heavy wa
m particles in the light product
I g n
9(w)dw = I f n (w)dw(•) or
stream. The weight ratios f and g are 0 f
taken into account. wa
w a
2.5.b f = ! nF(W)dw = NF(Wa)
0
w
u Overlap separation (2. 4] Value of w light ,particles in the heavy f or which the f raction of 1-Nf (wul = Ng(WU) or
cut point product equals the fraction of heavy wu wu
particles in the light product
2.6 1 - f nf(w)dw = ! n (w)dw(u)
stream. The weight ratios f and g are
0 0 9
not taken into account.
;:; Mean value for [2.1] Expectation for w. • (w) is interpret- m ~
the separation ed as the cumulative distribution
-= J w d•(w) dw ;:; 1 wip(w)dw =
w + =
function of the separation cut point.
0 dw 0
1 1 wd$(w)
0
-Illustratien and explanation of the symbols is given in fig. 2.1 and 2.2
~a wa m ~ ® m
(*) eq.2.Sa; g n
9(w)dw = f t(w)nF(w)dw = I f nf(w)dw = f nF(w) [1-~(w)]dw. Thus: f nF(w) t (w) dw = f nF(w)dw " 1-NF(wa)
0 0 wa wa 0 wa
(2.Sc) (*.) Eq. 2.6 can be elaborated in the same manner to show the dependence of wu on •(w) and nF(wl.
'""' -...)
Table 2.2.a: Criteria for the inefficiency of separation
1n1 2 l (W75 - W25] [2. 7] w90 - wlO [2.B] inl/wso (2.9] wcut in4 g Ng (wout) = g J n 9(w)dw 0 in 5 f[l-!if(w0utl l = f I nf(w)dw wcut [2.3] in6 f[l-Nf(wcut)] + g Ng (wcut) in 6 in4 + in5 wcut g J n 9(w)dw g N9'(wcut) in7 NF(wcut) 0 nF(w)dw f I nf(w)dw in 8 J wout nF(w)dw - 2. l 2 (w-w) IJl(w)dw = I (w-w) d$ (w) [2.1,
Half of the difference of the w-values Dimensional quantity for which 9(w) = 75% and ;."';%
The difference of the w-values for Dimensional quantity which 9(w) = 90% and 10%
Relative uécart terra" or nécart Dimensionless quantity probable"
The "lights" in the heavy product stream
The "heavies" in the light product stream
Summation of the fractions of misclassified particles
Misclassif ied heavy particles Total heavy particles in the feed stream
Variance of the distribution density
corresponding definitions can be for the "lights" in the product stream
and for 11heavies 11 in the
heavy product stream (effi-· ciencies) [lit.2.3]
This has a minimum value w w [lit.2.11 l cut 50 A A A B B B B B c
wso ! •(w)dw + f [1-o(W)}:lw o w50 w f • (wl [w-w]dw + 0
n1-.
(w) J [w-w]dw w [ 2 .16] [2.17 2.18]sum of the area below ~(w) for W<w50 and the area below 1-o(w) for w>w50
The moment of separation errors
Criteria for the efficiency of separation
of the Lit. Description
also is used:
g J
[2 .9] and
Ratio of the fall velocities for which $(W) 25% and 75% or
[ 2 .10] for which • (w) 35% and 65%
Light fraction yield
[2.3 J
Heavy fraction yield
[2.19] Characterization of the separat-ion functseparat-ion steepness at w=wx
Remarks
Dimensionless numbers
For processes -in which only one product stream is of interest- combinations of the following criteria may be used: characterization of the heavy product: n6:n4-10 7 (2.12] characterization of the light product: n7:n
3-in8 [2.13 2 .14]
This criterion may be calcul-ated at any point of the separation function c Category (section 2.2.2) A A B c
Table 2.3 Dependence of the (in)efficiency numhers belonging to the 'Category Bon o(w) and nF(w)
Definition Mathematical reformulation
wcut w cut w cut
in 4 = g f ng(w)dw in 4 J g ng(w}dw f •(w) .nF(w)dw
0 0 0
f f nf(w)dw in 5 = J f nf{w)dw = [nF(w)-g ng(w)]dw =
wcut wcut wcut
nF(w) (l-4>(W) ]dw w cut w cut w cut g J ng(w)dw f nF(w) •:wJdw 0 in7 wcut f 0 nF{w)dw J 0 nF{w)dw f J nf(w)dw J nF(w) (l-4>(w)]dw
ins in8 wcut
I nF{w)dw I nF(w)dw wcut w cut wout wcut f I nf(w)dw I 0 nF(w) [l-•(w) ]dw n3 n3 wcut I nF(w)dw I nF(w)dw 0 0 g J ng(w)dw I • (w) nF(w)dw w cut n4 n4 J wcut nF(w)dw f wcut nF(w)dw (see table 2. 2)
The following equations are used: ó(w) nF(w) = g ng(wî and nF(w) = f nf (w) + g ng(w)
form and parameters that descr:ibe the deviation of • (w) fran the
ideal step function in an integral fo:rm.
The various definitions and renarks ooncerning their actual meaning
are given in table 2.2: table 2.2.a gives criteria for the ineffic-iency of the separation, table 2.2.b gives criteria for the effic-iency of separation.
For this study -we have no exclusive interest in only one of the
prOOuct streams which excludes the definitions belonging to the cat-egory B with exception of in6• The criterion will be selected such that it does not depend on the fall velocity distribution of the feed stream beyond its relation to • (w) • 'Ibis is the case for all criteria belonging to the category B, as can be seen fran their def-initions and the mathematica! reformulations given in table 2.3. These criteria are of course of practical interest for a given specific problem and consequently for a given
°:F
(w) function. The criteria of category A and C 1.llliquely depend on t (w) • The variance defined byRunpf [2.1] and the criteria in
10 and in11 by Mayez [2.16, 2.11] yield an integral value of the separation inefficiency. The integrat-ive character of these parameters guarantees a reasonable evaluation of the total deviation of Hw) fran the 1deal step function. It
pro-hibits, hOileVer, the possibility to generate nore than one character-ization number within the regian 0 < t(w) < l. 'Ibis ~d be advan-tageous in order to discriminate between the efficiencies at various values of the fall velocity.
Nevertheless, these integral parameters are preferable to the arbi-trarily chosen differences and ratios of. fall velocities at pre-selected ~ (w) values belonging to the category A. These definitions lack. the integral character that is necessary for an acceptable
re-presentation of the total t(w) funÓtion. They also laak the flexibil-ity to represent the steepness of ~ (w) at arbitrary points within the.
0 < w (w) < 1 region. The derivative of w (w) with respect to w is a
direct rreasure for the steepness of w(w) at the location wand thus for the local efficiency obtained. N:> constraints have to be :pit for-Ward to the shape of w (w) , although any ananality in the separation
function will require nDre than one value of : to descr:ibe the cur-vature of Hw) sufficiently. In nany situations, lnvever, the steep-ness of w(w) at the separatian cut point gives sufficient infon:nation
for a e<::Irparison of different classification e.xperiments. In this thesis
d~!;w
)~x
wil! be used as efficiency criterion for the des-cription of the separation results with respect to the particle fallvelocity. The derivative of dl with respect to w is ma.de dimensionless with the help of the fall velocity wx at which the derivative is calculated.
2.3 canponent separation efficiency and its relation to the
separation function dl (w)
Sofar the discussion bas concentrated on the characterization of the
separation according to the fall behavior of the particles. It bas been said beföre, however, that in component separations the result of the process is rooasured on the basis of the degree of isolation of
the camponents. In this section a criterion suitable for describing the efficiency of the camponent isolatian will be introduced and its relation to t::le actual process of separatian with respect to the
particle fall velocity will thereup:n be discussed.
The criterioo wil! be introduced for a blo camponent mixture. The application cf the criterion may also be used for multicamponent mix-tures, provided that the main interest concerns the isolation of one
particular cmq:;.ionent which enables a pseudo-binary interpretation of the mixture. The separation is schematically given in figure 2.4.
Rieterna et al. [2.20] give an extensive review of the various definit-ions for separation efficiency criteria that might be used for the
description of the efficiency in canponent isolation.
On the basis of a set of requiremants that should be satisf ied by any efficiency definition Riete.na proposes the following criterion for
efficiency that wil! be used here to characterize the degree in can-ponent isolation:
E- lg - g 1 = lf - f 1 =
13 -
:=a1
=
IAf -Bfl
J: A B A B ~B.F ~B.F
in which gA = the weight ratio bottan product A
9 to· feed ~ gB = the weight ratio bottan product Bg to feed ~ fA = the weight ratio tcp product ~ to feed ~ fB = the weight ratio top product Bf to feed ~
_ _ _ _ _..Af+ Bf AIR nAf (w) + nBf (w) nAF (wl + nBF(w) CLASSIFIER Ag + Bg nAg(W) + nBg(w)
AF weight (flow ra te) of component A in the feed kg, (kg/s) BF weight (flow ra te) of cornponen t B in the feed kg, (kg/s) Af weight (flow ra te) of component A in the top product kg, (kg/s) Bf = weight (flow ra te) of component B in the top product kg, (kg/s)
= weight (flow ra te) of component A in the bottom
product kg, (kg/s)
Bg weight (flow ratel of component B in the bottom
product kg, (kg/s)
nAF(w), nAf(w), nAg(w) are the fall velocity distribution functions of component A in the feed, the top product and the bottom product respectively.
n8F(w), nBf(w), n
89(w) are the fall velocity distribution functions of component B in the feed, the top product and the bottom product respectively.
Figure 2.4 Air classification of a binary mixture of components A and B
Equa.tion 2. 9 may be refoowlated
t.O
achieve the ma:thematical relation between Ef and t (w) • tA (w) represents the weight fraction of the particles A in the feed stream with a fall velocity between w and w+dw that leaves the air classifier .til. the heavy product stream, ~(w) and ~g(w) are the fall velocity distribution functions of carp:ment A in respectively the feed stream and the heavy product stream. It then fellows for the carp:ment A:(2.10)
which yields after integration:
(2.11)
The same relations hold for carp:ment B. Eli.mi:nation of gA and g 8 out of equation 2.9 with the help of eq:. 2.11 for A and the corresponding equation for B leads to:
Ef
=
17
[il>A (w)~(w)
- il>B (w) rw(w)]dwl 0(2.12)
It is further assUl'lk:d that the particle fall V!Slocities unambiguously determine the separation results. This maans that il>A(w)
=
il>8(w)=
il>(w), as both canponents are separated in the sarre classifier under the sarre process conditions. This leads to:Ef
=
1 7[il>(w)(~(w)
- 113F(w))]dwl0
(2.13) In figute 2.5 eq. 2.13 is graphically illustrated. Ef is an integral characterization pararreter. An analogous differential efficiency
num-ber for particles with fall velocities between w and w+dw does not have any significance, as for these particles no enrichment wi th regard to one of the canponents can be achieved. The reason for this is that the apparatus cannot discr:i.m:i.nate between particles of
can-t
. 1 (nAF (w) -nBF (w)]-• (w)lt=Ot
1 1 t=l 1 1 w-(w) Of--~....,--'-"~~~~77777-7"7777-_.L Ef=]1-III
! , I I are the positive areas Figure :t.5 Graphical repres-entation of the relation between Ef' t (w) and nAF (w) , n 8F (w)1 ~ (w)
t
Af + Bf...----·
nAf (W) + nBf (W) AIR A., + B"-111>---1 - CLASSIFIER nAF (w) '+ n5F(w) Perfect w-A + B---1"
9 g nAg(w) + n6g(w) m Ef = !HM( nlll"(w)"""'BF(w)Jdw! 0 (eq.2_.13)Figure 2.6 Extremes of the relation between Ef. and •(w), nAF(w) and nBF(wl for the separation of a binary mixture ~ + BF
. . .. .
ponents A and B with the same fall velocity. B:l· 2.13 clearly shCMS that the efficiency in acmponent isolation Ef only parily depends on the separation functian ~ (w) which represên:ts the actual tool with
which the separation process itself can be influenced. The outccme of the process also depends on the location of the fall velocity distrib-utions of bath carp:>nents with regard to each other, as expressed by
[~(w) - 1l!F(w)]. Nc:M ~(w) and 1l!F(w) result fran material proper-ties and the previous proèeSsing of the materials. The distribution functions of both acmponents in the feed stream are a fixed starting point that cannot be influenced by the separation process itself. Ef is therefore only of direct interest wi thin a specific application in acmponent separation. It lacks the unambiguousness required for the
description of the actual separation. A:ny other feed mixture 'WOU.ld prabably yield a different value of Ef under the sane process oondit-ions in the same classifier. Nevertheless, fran a point of view of catp)nent separation it is a sensible definition of efficiency ..mich allows an a priori insight into the capability of the air classificat-ion technique to achieve the desired separation. In the case of poor
efficiency it reveals whether the reason for it has to be sought in
bad operation of the classifier (\ll(w)) or in unsuitable feed proper-ties that e.xclude the use of this tecbnique. Figure 2.6 illustrates
the extrares of this oanbined effect.
It is sb.cMn that even in a perfect classifier, characterized by a step fwiction for ili (w) , Ef ma.y vary fran zero to one depend:ing on the
relative location of IJ\:F(w) and
ry<w).
In fact eq. 2.13 is thema:t:hanatical fonnulation of the dilerma that exists where a carponent
separation is desired ..mile the actual separation process discrimin-ates on the fall behavior of the particles only. tl1ere a discrepancy
between goal and achievanent is caused by the feed properties, the
operator should shift his.efforts fran optimizing the air classificat-ion process to influencing the feed properties.
2. 4 CC!nbination of separation techniques for a carplete
ca:nponent .
separationVhen insufficient separation results are caused by the feed properties · a solution for the problem can be found in the application of nore
than one separation tecbniqua and, if possible, in the use of select-ive size reductian. This leads to a oc:m:p::ment separation process in
..mich vari01.1s separation techniques are integratèd. In tb.is section
tb.is subject will be elaborated to SCl!iEl extent as it reveals the technological rationale of many process scheires for the separation of dalestic waste. The elimination of unfavorahle feed prq:ierties by a oanbination of separation techniques will be illustrated .on the basis of a oanbination of sieving and air classification. Both techniques are supposed to produce two product streaI!lS. In the first instance it will be assumed that both techniques achl.eve a per>f ect separation with respect to their separation criterion x. For the sieving process
the separation criterion is the characteristic particle size
