Liquid fltEtion 228
Chapter seven
Liquid Filtration
7.I, INTRODUCTION
The separation of solids from a suspension in a tiquid by means of a porous mediurn or screen which retains the solids and aliows the liquid to pass is tcrmed filhation.
ln general, tle pores of ihe medium are larger than the palticles which are to be iemoved, and thc filtcr works cflicicntly only aller an initial deposit has been trapped in fhe medium. ln fte labontory, filtration is oiler canied out using a folnl of Buc}ner funnel, and thc liquid is suckcd tbrough tbc thin laycr of parliclcs using a source of vacLrum. In cven simpler cases the suspension is porred into a conical fLrnncl litted widr a fiiter paper. In the industdal cquivalcnt, dimculties arc encountercd in the mcchanical handling of much larger quantities of suspension and solids. A thickcr layer of solids has to form and, in order to achieve a high rate of passase of liquid throush the solids, higher pressures arc nceded, and a far grcater area has to bc providcd. A rypical filt|ation operation is illustrated iD Figure 7.1, which shows the filter medium, iD this case a cloth, iis support and the layer of solids, or lilter cakc, which has already formed.
Volumes of the suspensions to be handled vary fron the extemely large quantitics involved in water purification and ore handling in ihe mining industry to rclativciy small quantities, as in thc fu1e chemical industry where the variery of solids is considerable. h most industrial applications it is the solids thai are required aM their physical size and properties are of paramount importancc. Thus, the main factors to be considered when selecting equipment and opemting conditions arei
(a) The properties ofthe fluid, particularly its viscosily, density and colrosive Fope ies. (b) The nature of thc solid its padicle size and shape, size distribution, and packing
characteristics.
(c) The concentration of solids in suspcnsion.
(d) The quantity of material to be hardled, and its value. (e) whether ihe valuable product is the so1id, the flujd, or both. (0 Whether it is n€cessary to wash the filtered solids.
(g) Wherher verJ slisht contamination caused by contact of the suspension or filtrate with the various components of the equipment is detimental to the product. (h) Wlether the feed liquor may be heated.
(i) whether any form of pretreaimenr might be he1ptul.
Filtration is essentially a mechanical operation and is less demanding in cncrgy ihan evaporation or drying where the high latent heat ofihe liquid, which is usually water, has to be provided. In the rypical op€ration shown in Figure 7.1, the cake gradually builds up
229 Chemi€l Engineering Processes
Slurry
,1,
lisure 7 L Pimiple ofnlhdon
on the medilun and the resistarce to flow progressively increases. Dudng ihe initial period offlow, particles are deposited in lhe sudace layers of the cloth to form the true filtering medium. This initial deposii may be formcd from a special initial flow of precoat material which is discussed later. The most important factors on which the rate of filtation ihen depeMs will be:
(a) The drop in pressure from the feed to the far side of thc filter medium. (b) The area of the filtering surfacc.
(c) The viscosity of tle filtraie. (d) The resistance of the 6lter cake.
(e) The resistance of the fiIter medium and hitial layers of cakc.
lwo basrc ry?e5 ol filrmrton proce.se( na) be idenlifico. altbougb rbere are cases wbere the two E/pes appear to merye. ln the first, frequently refened to as cake fhrution, the particles from the suspension, which usually has a high proporrior of solids, me deposited on the swface of a porous septum which should ideally ofler only a small resistance to itow. As the solids build up on the septum, the iniiial laycrs folm the effective 6lter medium, preventiry thc particles ftom embedding themselves ir the filtef cloth, and ensuring that a particle-free filtrate is obtained
ln the seco t)?e offilhatlon, depth or deep-bedfltratior, the pariicles penehate into the pores of the filter medium, where impacts between the particles and the surface of the medium are largely responsible for their removal and retention. This configuration is comnonly used for the rcmoval of fine particles ilom very dilute suspensions, where the recovery of the paiticles is not of primary importance. T)?ical examples here include air and water filtation. The filter bed gradually becomes clogged with particles, and ils resistance to flow eventually reaches an unacceptably high level. For continued operatio& it is th€refore necessary to remove the accumulated solids, and it is importart that this can be feadily achiev€d. For this reason, the filter conrmonly consists of a bed of partic-ulate solids, such as sand, which can be cleaned by back-flushing, often accompanied by
fluidisafiol ln this chapter, the emphasis is on cake filhation although deep-bed filtration, which has been discussed in detail by IvES(r.':) is considered in the section or bed filters.
There are two pdDcipal modcs under which decp bed filtmtion may be caded out. Irr he tust, dead-e d fltratian ||hich is illustated in Figure 7.1, the slunl is filtered in such a way that it is fed perpendicularly to the fi1ter medium and there is littl€ flow parallel to the surface of the medium. ln the second, iermed .r'oss-Jla , Jiltration which is discussed in Section 7.3.5. and which is used particularly for very dilute suspensions, the slurry is contiruously recirculated so that it flows essentially across the surface of the filter medium at a rate conslderably in exccss of thc frowratc through the 6lter cake.
7.2. FILTR,{TION THEORY
7.2.1. IntrodLlctionEquations are given in Chapter 4 for the calculation ofthe Iate offlow ofa fluid through a bed of granular material, and ihcsc arc nolv applicd to thc flow of filtrate through a filter cake. Some differences in gcncral behaviour may bc cxpcctcd. however, because the cases so far considered relate to unifom fixed beds, whereas in filtration the bed is steadily growiry in thickness. Thus, if tle filtration pressure is constant, the mte of flow progressively dimjnishes whcrcas. if the flowratc is to bc maintained constant, the pressure must be $adually increased.
The mecha cal details of the equipment, particularly of the flow channel and ihe supporl for the medium, innuence the way th€ cake is built up and the ease with which it may be removed. A uniform structure is v€ry desirable for good washing and cakes formed from paficles ofvery mixed sizes and shapes present special problems. Although iilter cakes arc codplex in their structurc and camot fiuly be regarded as composed of rigid ron-deformable pafiicies, the method of relating the flow parameterc developed in Chapter 4 is useful in describing the flow within the filier cakc. Thc general thcory of f i l t r a r i o n a r d i L s i m p o d a n c e i n d e s i g n h a s b e e n c o ' r . i d e _ e d b i S . | ' r . l l m a ) b e n o l c d that there are nvo quite diferent methods of operating a batch filter. lf thc prcssuro is kept constant then the rate of flow progressively diminishcs, whercas if the flownte is kept constant then the pressurc must be gradually incrcascd. Bccausc thc particles forming the cake are small and the flow through the bed is s1ow, streamline conditions are almost invariably obtained, and, at any instant, the flowrate ofthe filtrate may be represented by the followins forrnula
I e 1 a P
Liqt'id fltration 230
( 7 . r )
where y is the volume offilirate which has passed in time r, ?4 is the total crcss-sectional area ofthe filter cake, r. is the superficial velocity of the filtrate, I is lhe cake thickness, S is the specific surface ofthe palticies, e is the voidage, p is the viscosiry ofthe filtrate, and AP is the applied pressure difference.
ln deriving this equation ii is assumed that the cake is uniform and that the voidage is constant thoughout. ln the d€position of a filter cake this is unljkcly to be the case and the voidage, e will depend on the nature of thc support, including its geometry and
231 Chemical Engineefing Processes
surface sfucture, and on the rate ofdeposition. The idtial stages in the fomation of the cake are therefore of special importance for the ibllowing reaions:
(a) For any filtration pressure, the rate offlow is greatest at the begiDning ofthe plocess since the resistance is then a minimum.
(b) High initial rates offilrration may rcsu1t in pluggtng of the pores ofrhe filter cloth and cause a very high resistance to flow.
(c) The orientation of the particle in the inirial layers may appreciably influerce the sfucture of ihe whoie fitrer cake.
l - i l r e r c a k c s m a y be dividcd L f l o rw o clds.cs incompressible c a l e s . I t r d c o m p r e . s i b l e cakes, In the case ofan incompressible cakc, the resistance ro flow of a given volume of c a l r j r nor ippreciably a f l e c r e d e j r h e r b y he pre.sure d F c r e n c e a " r o s , L ] i cake o r b] rhe m r e otdeposirion o l m d ' e r ; d t . O n r b e o r h c j hcnd. $ i r h a compre\sible c a k e , i n c r e " s c o f the pressure difference or of the rate of flow causes the formation of a denser cake with a higher resistance. For incompressible cakes e in equation 7_l may be taken as constant and th€.quantiry €3lI5(1 - r)2S21 is then a property ofrhe particle; forming the cake and should be constant for a given material.
Thus: (7.2) (7.3) l d v A d t rpl 5 ( 1 - € ) ' z S ' ?
' t
It may be noted thai, when therc is a hydrostatic pressure component such as with a horizontal filter sudace, this should be ircluded ir the calculatio; of _Ap.
. Equation 7.2 is the basic filtration equation and r is termed the specific rcsistance which r s secn r o d e p c n d o n - e _ a D d S . l o f i n c o m o - e s s i b , e c a l e s . r i s t a k c n a 5 con5t t. a,lhough r t d e p c t r d s o n - a l e of depo.iLion. l b e n a n f e of thc panic'er, s n d on rbe lotce. benre;n the particles. r has the dimensions of L : and the units m-2 in the Sl system.
7.2.2. Relation between tlrickness ofcake and volume of ltrate
In equation 7.2, the variables I and y arc connected, and the relatior between them may be obtained by making a material balance betwcen the solids in both the slurry and th€ cake as foliows.
Mass of soiids in filter cak€ : (t - e),41p", where pI is ihe densi, of the solids Mass ofliquid retaircd in the filrer cake = rAlp, where p is the dinsity ofthe fitrrate. If "/ is the mass fraction of solids in the original suspension thenl
t _ a a , , : y l : ! ! ) ! !
1 _ J o r : ( 1 J)(l e ) A l p " : JVp + AeJIp
Liquidiiltralion 232
and:
Q.s)
t
(7.6)
Il D is the volulne of cake deposited by unit volume of filtrate ther
I p " O - e ) ( r - J ) - e p J l A I lA uv u : V o r I : i
d v v
v A , e L P )
t rttvl) t r p x , , v A 2 t L P ) alld iom equahon 7.5:Substituting for , in equatiotr 7.2:
so that:
(7.8)
Equation 7.8 may be regaxded as the basic rclatioll between - AP, y, alrd l. Two important twes of operation are: (i) \'r'here the Fessure diffeleDce is maintained constant alld fi wherc the mte offiltation is rnaintaircd constatrt.
For afltration at constant rate
( r - t ) ( 1 - e ) p " - J f p I dv _ (-aP) A A d! rp l)v dv A'z(-^P) dt TLLL,V
\.
(1.7)
(7.9\ (7.10) ( 7 . 1 1 )Q.r2)
and -AP is directly proportional to V. For a fltration at constant yessure dffercnce
v 2 _ AZ(-LP)i
2 rtt1)
t f|t u
=
2 A r ( _ L P ) ,
Thus for a constant pressure filtration, there is a linear rclatiotr between V' and , or benreen t/Y and V.
Filtration at cofftant pressrre is morc ftequendy adopted in pmctic€, although the Fessure diference is nomally gadualy built up to its ultimate value.
ff this takes a time tr duing which a volume yl of filtrate passes, thetr integatiotr of equation 7.12 gives:
I . ^ A z t - L P l
- ( v . _ v i ) : L l t t t )
233 Chemical Engineenng Processes
f p t . , r . , . . t w v )
2 4 2 ( L P ) A 2 \ L P ) ('7.14) Thus, there where is a linear relatlor berween lz, and r and between (t _ ^)/(V _ Vt) and (y vr), where (r - rr) reFesents rhe time of ihe constant prc""*e ntt otion aoa (y - Vr) the co[esponding volume of filtrate obtained.
Ruru et al(a- 7) have made mcasurements on the flow in a filtcr cake and have concluded t that the resistance is somewhat greater than ihat hdicated by equation 7. I . It was assuned that pmt of the pore space is fendered inefective for the florv of filtrate because of the adsorption of ions on the surface of the paricles. This is not born€ out by cRAcE(s) or by HoFFrNc and LocKrARr(e) who determied the relation between flowrate and oressure d i t r e r c n c e . b o r f b) mean\ o f p e r n e a b r l i $ L e s t . o n a f i \ e d bed a r o by 6lmrion re.r. us.rg suspensions of quartz and diatomaceous earth,
Typical values of thc specific resistance r of filier cakes, taken from the wo* ol CArtIraN(]o), are given in Table 7.1. In the absence of details ofthe physical properties of the particles and of the conditions under which they had been formed, these vilues are approximate although they do provide an indication of the orders of masniruale.
Tabh ?.1. Typical Values of Specific Resislhce, r(roi
1 . 6 x t o r a
3 . 5 x l 0 ' '
1 3 x l 0 ' { 8 x I 0 ' r
2 , 3 x l 0 r 7 7.2.3. Flow ofliquid through the cloth
Expcrimental wo* on the flow of the liquid under streamline conditjons(r0) has shown that the flowrate is directly proportional to the pressure difference. It is the rcsistance of the cloth plus inltial layers of deposited particles that is important since the latter, not only form the true medirm, but also tend to block the pores ofthe cloth thus increasins
cllciu'n cmbonare (pHilnated)
Celadnous magnesiun bydroxide Celatinou aluninium nydroxide Gelatinous feric lydroxidc
7 8 0 l t 0 1 7 0 274 7 8 0 210 780 274 ? 8 0 27Q 780 214 780 210 780 270 650
Liquid fltration 234 its resistarce. Cloths Inay have to be discaded because of high rcsistance well before they are mechanically wom. No true analysis of ihe buildup of rcsistance is possible because the resistance will depend on the way in which the pressure is developed and small vanaiions itr suppot geometry can have an important iniuence. lt is therefore usual to combine the resistance of the cloth with that of ihe fint few layers of parhcles and suppose that this corresponds to a thickness Z of cake as deposited at a later stage. The resistance to flow though the cake aad cloth conbined is now considered.
7.2.4. Flow of ltrate through the cloth and cake combined
Ifthe filter cloth and the hitial layers of cake are together equivaleni to a thickrcss a of cake as deposited ai a later stage in the Focess, and if -AP is the pressure drcp aqoss the cake and cloth combiDed, then:
l dv (-aP) A & r L L ( l + L ) which may be compared with equation 7.2.
dv A(-LP) A 2 ( - L P ) (7.15) (:'7.16) ( 7 .t 1) (7.18) Thus:
This equation Inay be integrated between the limits, : 0, V : 0 and t : tr, v = q for constant rate fi lfation, and t : t1, V : V1 and t : t, V = V for a subsequent const nt pressure filtration.
For the period of coirsldrt rdte fltrationl
dr
Vr
t1 P \ - L P ),r, (v. *
to\
rp,! ,, , fp.L A r ( - A p ) Y F A ( - A r ) . . , L A . . A l l - ^ P ) 1) rtll)For a subsequent corrldr?t pressure fltration:
| . L A A l r A P r - ' V ' - Y ' l + - ( V - V r ) - ( t t t ) 2 r f p u l V - v t + z V t ) \ V V t ) l ' " \ V V ) - ' ' ' ' ' r - r t t - t t r p u . , . , r p ' v t r p L " V V t - 2 A 2 \ - a P ) ' ' 4 ( - a P ) A L - A P )
,,,(,.T)
r t l \ A + L )(7.te)
235 Chemical Engineerifg Pro@sses
Thus there is a linear relation berween (r-rr)/(y yr) and y_yr, as shown in Figurc ?.2, and the slope is propodionat to thc speciflc rcsistance, as in the case of the flow of the filtrate ttuough the filter cake alone given by cquarion 7.14, although the lhe does not now go through the odgin.
V,U (cn3) Figure 7.2. A typicat fill.arion cune
The interccpt on the Q ti)/g - V) a\is shoutd enablc l,, rhe equivatent thickness of the cloth, to be calculated although reproducible results are not obtained because this resistance is ffitically dependent on lhe exact manner in which rhe operation is corlmenced. The time at which measxrement of y and I is commenced does not aflect the slope olthe curve, only the intcrcept. It may be noted that a linear relation between / and yi is no longer obtained when the cloth resistance is aDDreciable.
7.2.5. Compressible Filter cakes
Nearly all iilter cakes arc comFessible to at least some extent althouqh in manv cases r l - e d e g r e e o l c o m p r e s . i b i l i i y i r s o . n a l t loat the cake ndy. tof prac;cdl p u ? o s e s . b e regarded as incompressible. The evidence for compressibilit is that the specific resistancc is a firnction ofthc pressure diflerence across the cakc. Compressibiliy miy be a reversible or an irreversible process. Mosi filter cakes are inelastic and the greater resistance offered r o flo$ ar h,gh o r e s . u r e d i f f e r e n c e s i s caured b y r h c more c o m p a c r p a c t < , n g o t l b e p d n i c l e s fbrming the filter cake. Thus the specific resisrance of the cake corresoonds to that for I )e big'resr p r e s s u r e o i f | e r c n c e r o whrcb r h e c a k e i s . u b j e c r c a . e r e n rh o J g h r b i s m a r m u m pressure dillerence may be maintained for only a short time. lt is therefore important thaf the filtration pressure should not be allowed to excced the normal opemting presswe at
E
t
i l i
Liquid illration 236
any stage. h elastic filter cakes the elasticity is attributable to compression of the panicles themselves. This is less usual, although some forms ofcarboncan give dse to elasiic cakes.
As the filhate flows through the fi1ter cake, it exerts a drag force on the pariicles and this force is iransmitted ltuough successive layers ofpaticles right up to the filter cloth. Tle nagnitude of dis force increases progressively ftom the surface of the fl1ter cake to the filter cloth since at any point it is equal to lhe summation ofthe forces on all the panicles up to that point. lf the cake is compressible, then its voidage will decrease progressively in the direction offlow ofthe filrrate, giving rise to a corresponding increase in the local value ofthe specific resistance, r:, ofthe filter cake. The structure gf the cake is, however, complex and may change during the course ofthe filtration process. lf the feed suspension is flocculated, the flocs may become deformed wiilin ihe cake, and this may give rise to a change in the efective value ofthe specific sudace, s. ln addition, th€ particles themselves may show a degree of comprcssibility. Whcnevcr possiblc, cxpcrimcntal mcasurcments should be made to determine how the specific resistance varies over the mnge ofconditions which wili be enployed in pncticc.
It is usually possible to express the voidage.i: at a depth r as a fuction ofthe dilTerence b€tween the pressure at the ftee surface ofthe cake Pr and the pressure P: ai that depth, that js d: as a function of (4 - P.). Thc nonenclatuc is as defincd in Figure 7.3.
1.1|.v
I lt
v-tu
tv-F " u * " f \ r " 0 ' n .
Figure.7.3 Fow through e conpEssible nlter cake
For a compressible cake, equation 7.1 may be written as:
l d v d l 1 / d P , \
; dr 5(1 - e)'s't \- di / (7.20)
where d. is now a function ofdepth: from the suface of the cake.
In a compressible cake, the volume u of cake deposited per unit area as a result ofihe flow ofunit volune offiltrate will not be constant, but will vary during the filtration cycle. Ifthe particles themselves arc not compressible, however, the volume of panicles (!') will be alnosr independent of the conditions under which the cake is formed assuming a dilute feed suspension. Any small variations in D' arise because the volume of filtrate relahed in the cake is a function of its voidage, alfiough ihe cffect will be very small,
237 Chemical Engineeing Proesses
excQt possibly for tlrc filtration ofvery highly concentrated suspensions. The increase in cake thickrcss, dz rcsulting ftom rhe flow ofa volume of fithate dy is given by:
dz=dvL
(7 2r\
\ r e . l A By comparison with equation ?.6, it may seer that:
. . - t - , . \ 1 . 2 2 )
Substituting Aom equation 7.21 into equarion 7.20 givesj . t d v e l r l - e l A t t d p \ A dt 5(l - e,\252 1,, t1 \ dV ) _ , d v r ' 4 r , d p , \ r t r u s : - l | , r 1 2 t d r 5 r i - ? - ) S r r / u \ d y / A , / d,P"\ (7.24) u . L ' r z \ d , v ./ . 5 ( l - e , ) S l w n e r e : r _ : - 1 7 . 2 5 ) .;
Comparing equations 7.8 and ?.24 shows that for an incomFessible €ake: rtrz = rf
or,
r. =.1
At any instant in a constant pressure filtration, integratiotr of equatiotr 7.24 tbrough the whole depth of the cake gives:
I ' d v . . . A r l F I d p )
I - - i - o v ' -l - 0 . 2 6 1
J 0 o r l t r J P I
At any time t, dy/dr is approximately constant throughout the cake, unless the mte of cha.nge of holdup of liquid withir the cake is compaEble wirh rhe fitrration Iate dyl&, such as is the case with very highly compressitrle cakes and concentaied sluries, and tberefore:
. d v A 2 th t-dp,l-
| t 7 . 2 i )
p t ) V J p l
r. has been showtr to be a firnction of the Fessure difference (pr pz) although it is iDdependent ofthe absolute value of the pressrlle. Experimental studies irequently show that the rclation beh{een r? and (Pr p:) is of the form:
r - r t P - p ) , t : ' . 2 l ) where r' is itrdependert of P. and 0 < r, < I
Thusl Thus: where r// : (i - n/X and:
:I
I
( dP,) Liquid fllralion 238 ('7.30) d! V Ln'r' (t - n')(- LP ),,' A 2 ( - LP) Vl,tr'r'\-LP)trdv
A,(-aP)
dt V LLr'l d P(Pi:E/
= ! ( P r - P)t I r ' l - n ' I l - A P r l ' ' - -""'1- Q 29) r ' l ndv
(7.31)where i is the mean resistance defined by:
(7.32)
Hernr.rns(rr) has studied the effect ofpressure on the porosity ofa filter cake and suggested that, as the pressure is increased above atnospheric, the porosity decreases in proportion to some Dower of the exc
GRAcris) has related the a;ticipated resistance to the physical properties of the feeal slurry. VALLERoY and Mer-or.rEv(i2) have examined the resistance of an incompressible bed of spherical particles when measured in a permeability cel1, a vacuum filter, and a cent ifuge, and emphasised the need for caution in applying laboratory data to units of diflerent geometry.
TrLL!R and HuANa(r3) give futher defails ofthe problem of developing a usable design relationship for filter equipment. Studies by Turn and Smn-qro(ra), Trr-ren and Yls(ts) and RusHroN and HAMEED(Io show thc diffculty h presenthg practical conditions in a way which can be used anallically. It is very impofart to note that tests on sluries must be made with equipment thai is geometrically similar to that proposed. This means that specific resistance is very dimcuit to de6ne in practice, since it is determircd by the nature of {he filtering unit and the way in which the cake is initially formed and then built up.
7.3. FILTRA.TION PRACTICE 7.3.1. The lter medium
The fuction of ihe fi1ter medium is generally to act as a suppo$ for the filter cake, and th€ initial laye6 of cake provide the true filter. The filter medium should be mechanically strong, resistant to the corrosive action ofthe fluid, and offer as little resistance as possible
239 Chemical Eng ineering Proesses
to the flow of filtrate. Woven materials are commonly used, though graDular materials and porous solids are useful fo. filtration of corrosive tiquids in barch;its. An imDortani learure in rbe selection of a $o!en matcnal is $e eare oacake remo\ ai. since Lb;s ii a kev factor ir the operation ofmodem automatic units. Esr_ms(r?) has discussed the selection of woven s)rnthetic materials and Wrorrowsrlr3) that of non-woven materials. Further details ofsome more r€cent materials arc given in the litemtue(re) and a useftl summarv i s p r c s e n r e d i n i . o ' , R ' . i f , r d . . r \ ^ l r , r { ,
7.3.2. Blocking Filhation t
In the previous discussion it is assumed that there is a well-defined boundary between the filter cake aM the 6lter cloth. The iniriai stages in the buitd-up of the filter cake are important, however, because these may have a large effect or the flow resistance and mav seriousl) affecr rhe vseful life of lhe clolb.
The blocking of the pores of the fiiter medium by particles is a complex phenomenon, partly becausc of the complicated natue of the suface structue of the r;ual t'Des of f i h e r m e d i a . a n d p a n l y because r h e tines o f m o l e m e n r of rbe panicles * . # *.ff de6ned. Ar rhe slafl of filrralion. rhe majrtrer in whicb $e cake tonns uill lie berueen two extremes the penet atior ol ihe pores by particies and the shielding of the enh.y to the pores by the particles forming bddges. HEER Ts(rr) considered a number of idealised cases in which suspensions of speciied pore size distdbutions were filtered on a cloth with a rcgular pore distribution. FiNt, it was assumed thai an individual particle was capable on ifs own of blocking a single pore, theD, as filtration Droceeded. successive pores would be blocked. 50 $al rie apparenl \atLre of Lle specrnc iesisonce of tbe filler cake would depeM on the amount of sotids deposired.
The pore and particle size distributions might, however, be such that more thar orc particle couid enter a particular pore. In this case, the rcsistance of the pore inoeases in sragcs as successi\c panicles are rrdpped unlil $e porc is complercl] bloiked. In practice. however, it is much more likely that many of the pores will never become compiet€ly blocked and d cdke of rela'ivet) to$ resislance wi form over rhe enr) ro rbe panialtj blocked porc.
One ofthe most important variables affectitrg the tendency for blockiry is the concen_ hation ofparticles. The greater the conccntration, ihe smaller will be the averaqe distance beiween !}e particles. and rhc smdller wilt be !}e tendeocy lor Lbe partjcle to b-e drawn in ro lbe srreanlines directed rouard. rle opeD pores. loslead, the panicles in lbe concen_ trated suspension tend to distribute themselves fairly evenly over the filter surface ard form bridges. As a result, suspensions of high concenhation generally give rise to cakes
of lower rcsistance than ihose formed from dilute suspensiors.
8.3.3. Efiect of particle sedimentation
on filtration
Th€re are two important effects due to particle sedimentation which may aflect the rate of filtmtion. Fi$t, if the sediment particles are a1l settling at approximately the $rme rate, as is liequently the case in a concentraied suspension itr which the Dadcle s i z e distriburion i s n o r v e r y r r d e . a more rapid burtd-up;f parlictes w i l l occur on an
Liquid fltration 240
8.3.4. Delayed cake liltration
ln ihe filhation of a slurry, the resistaflce of the 6lter cake progressively increases and consequertly, ir a constant pressure operation, the rate of filtation falls. If the build-up ofsolids can tre ieduccd, the cffective cake thickness will be less aM the laie of flow of filhate will be increased.
ltr practice, it is sometimes possible to incoq'orate moving blades in the 61ter equipment so that the thickness of the cake is limited to the clearance between the filter medium and the blades. Filtrate then flows through the cake at an apFoximately constant rate and the solids arc rctained in suspension. Thus the solids concentration in the feed vessel increases until the particles are in permarent physical contact with on€ another. At this stage the boundary between the slurry and the cake becomes i1l-defined, and a signincant resistanee to the flow of liquid develops within the slxrry itself with a consequent reduction in the flowrate of filtate.
By the use of this tecbdque, a much higher mte of filtration can be achieved than is possible in a filter openied in a conventional rnanne.. In addition, the rcsulting cake usually has a lower porosiry because ihe blades effectively break down the bridges or arches which give rise to a structur€ in th€ filter cake, and the final cake is sjgnificantly dder as a result,
If the scmpels are in the form of rotating blades, the outcome differs according to whether they are moving at low or at high speed. At low speeds, the cake thickness is reduc€d to the clearance depth €ach time the sqaper blade passes, although cake then builds up again until the next passage of the scraper. lfthe blade is operated at high speed, there is little time for solids to build up betweetr successive passages ofthe blade and the cake rcaches an approximately constart thickness. Since particles teM to be swept across the surface ofthe cakc by the moving slury, they will be trapped in the cake only if fie drag lorce which the filtrate exerts on them is great enough. As the thickness ofthe cake inffeases the pressure gradient becomes less and therc is a smaller force retaining pallicles ilt the cake surface. Thus the thickness olthe cake tends to reach an eouilibdum value. which can be considerably less than the clearance between the medium a the blades.
Expeimental results for the etrect of stirrer speed on the rate of filtration of a 10 pel cent by mass suspension of clay are shown in Figure 7.4 taken from the work of TrLrR and Cswc@o), in which the fittrate volune collected per unit cross-sectio! of filter is plotted against lime, for several stfrer speeds.
8,3.6, Preliminary
treatment ot slurries before filtration
If a slurry
is dilute
and the solid particles
settle
readily
in the fluid, it may be desirable
to
effect a preliminary concentration in a thickener as disclssed in Chapter 5. The thickened suspension is ihen fed from the ihickener to the filter and the quantiry of materiaj to be handled is thereby reduced.Theoretical treatment has shown that the nature ofthe fr1ter cake has a very pronounced effect on the rate of flow of filtrate and that it is, in general, desirable that ihe particles forming the filt€r cake should have as large a size as possible. More rapid filtration is therefore obtained ifa suitable agent is added io the slurry to cause coagulaiion. Ifthe solid material is formed in a chemical reaction by precipitation, the paticle size can generally
241 Chemic. I Engheer ng processes
be conholled to a certain extent by the actual conditions of lormatior For example, the particle siz€ of ihe resultant pr€cipitate may be conholled by varying the iempemture and co_Dcetrtahon, and sometimes the pH, ofthe reacting solutions. As indicated by Gnacr{s), a flocculated suspension gi!es nse lo a more porous cake al$ough fie compr;ssibijiiy js grearer. ln many cases. cryslat chape mdy be atre,cd by addjDg irace, of mareriat
$hich rs selectlvely adsorbed on Darticular faces
_ Iilter aids are extensiveiy used where the filter cake is relatively impermeable to the 8ow of fil-nare. Tbese are mareridts $ hicb pack to form beds of rery higb voidages and rneretore lhey are capable of Lncreasjog $e poro.iry of $e fiher cake il addcd Lo the slury before filtration. Apart ftom economic consideratjo$, there is an optimum quantity of.fiher ajd which sboutd be added in any given cr,e. lt hcreas rhe pre.ence of rbe filer aid reduces $e specific resrsrance ofr}e filler cake. jl also je.ults in rle formarion oIa thicker cake. The actual quantib, used will rherefore depenal or rhe naturc ofthe matedat. The use of filter aids is rormally restricted to operations in which the filbate is valuable atrd the cake is a wasie producl In some circumstances, howevet fhe filter aid must be readily separable ftom the rest of the filter cake by physical or chemical means. Filter cakes incorporating fi1ter aid arc usually very compressible anal care should therefore be taken to ensure fhat rhe good effect of the filrer aid is not destroyed by emptoying too high a filtration pressure. Kieselgxbr, which is a commonly used 6lter aid, has a"voiaage of about 0.85. Addition ofretatively small quanrities increases the voidage ofmost filtier cakes, and the resr ting porosiry normally lies berween that of rhe filrer aid a.nd thar of the filt€r solids. Sometimes the fitrer medium is ,,precoaied" with filter aid, and a rhin layer of the filter aid is removed with the cake at rhe enal ol each cycte.
ln some cases lbe filnatjon Limc can be redLrced b} diluring tbe.Uspension in order !o reduce the viscosity of the filtlate. This does, of course, increase the bulk to be filtered the temperature may be advantageous in that the viscosity of the filhate is reduceal.
8,3,7.
Washing ol the fitter cake
When the wash liquid is miscibte with rhe filrrare and has similar physical properties, the rate of washing at the same pr€ssure diference wjll be about the same as th; final mte of filhation lf the viscosify of the wash liquid is less, a somewhar grearer rate wil be obtained. Channelli4 somerimes occurs, however, with the resutt thai much of the cake rs rrcompletely washed and rhe fluid passes preferenrially rkough the channels, which are gradualy enlarged by its continued passage. This does not occ; during filtration because channels are self-sealing by virtue of deposition of solids ftom the slurry. Channelling is most narked with comprcssible 6lter cakes and can be minimised by using a smallei pressure differeDce for wasbing tban for 6lE-ation.
. W_ashingmay be regarded as taking place in two stages. Fint, fiIrrare is displaced from the filte. cake by wash liquid dming the period o I displacenent ,ashtug alli in this way up to 90 per cent of the filtrare may be removed. Duftrg the secondltage, (tiff$ionil ,dsr,hg, solvent diffuses into the wash liquid trom the Iess accessible -voids "and the following relation applies:
/ \ o l u m e o f w a s b l i q u i d p a s s e d L ^ ^ - ^ , ^ - , . . , ^ _ / i D i t i a t c o D c e n r J d t i o n o f s o l u r e \ \ cake $ickness / - " "-*" ' '"8 \ coo;;;;oo ur pani.utuJ U-.,/
Liquidnlhaiion 242 Although an immiscible liquid is seldom used for washing, air is often used ro effect partial drying of the filter cake. The rate of iow of air must nomally be determtued experimentally.
7.4. FILTRATION EQUIPMENT 7.4.1. Filter selection
The most suitable filter for any given operation is the one which will fulfrl the rcquirements at minimum overall cost. Since the cost of the equipmert is closely ielated to the filtering arca, it is nomally desimble to obiain a high overaii rate of filtration. This irvolves the use of relatively high pressures although the maximum pressures are often limited by mechadcal design considerations. Although a higher throughput ftom a given filteing surface is obtained from a continuous filter than &om a batch operated filtef it may sometimes be necessary to use a batch filter, pariicularly if the filter cake has a high rcsistance, since most continuous filters operat€ und€r reduced pressure ard the maximum filtration pressure is therefore limited. Other features which are desirable in a filter include ease of discharge of the filter cake in a convenient physical fonn, and a method of observing the qualiry ofthe filtrate obtained from each sectton ofthe plart. These factors are important in considering thc tlT,es of equipment available. Thc most connnon rypes are filter Fesses, leaf filters, and continuous rotary filters. ln additio& there are filters for special purposes, such as bag filt€rs, and the disc type offiiter which is used for the removal of small quantities of soiids ilom a fluid.
The most impodant factors in filter selection are the specific rcsistance of the filter cake, the quandry to be filtered, and the solids concentration. For free-filtering materials, a rctary vacuum filter is generally the most satisfactory since it has a very high capacity for its size and does not require any signmcant manual attentior If the cake has to be washed, the rctary drum is to be prefeded to the rotary leal lf a high degree of washing is required, however, it is usually desirable to repulp the fi1ter cake and to filter For large-scale filtration, there are tlree principal cases where a rotary vacuum filter will not be used. Firstly, if the speciic resistance is high, a positive prcssure filter will be required, and a filter press may well be suitable, particularly if the solid conrelrt is not so high that frequelI dismantling of the press is necessary. Secondly, when efrcient washing is requirc4 a leaf filter is effective, because very thin cakes can be prepared and the risk of chamelling during washing is rcduced to a ntuimum. Finally, where only very small quantities of solids are presert ir the liquid, an edge filter nay be €mployed.
Wlilst it may be possibie to predict qualitatively the effect of the physical properties of the fluid and the solid on the filtration characteristics of a suspension, it is necessary in all cases to carry out a test on a sample before the large-scale plant can be designed. A simple vacuum filter with a filtcr area of 0-0065 m': is used to obtain laboratory data, as illustated in Figure 7.5. The infonnation o! filiration rates and specific resis-tance obtained in this way can be dtecily applied to industrial fi1ters prcvided due account is taken of the compressibiliry of the filt€r cake. It ca lot be stessed too
243 Chemi@l Engineering Processes Slurry.level A C _ A T : ) \ C Otr integration: C /Ca = e-^l
where: C is the voiume concentration of solids in suspension in the filter, Co is the value of C at the surface of the filter,
1 is the depth of the filter and ). is the filter coeficiert.
Figure 7.5. Labohbry resl tilt€.
strongly thal data ftom any laboratory test cell must not be used without practical experience ilr the design of industrial u ts where the geometry of the flow chamel is very difTerent. The laying down ofthe cake iniuences the struchue to a very a marked A "compressibility permeability" rest cetl has be€n developed by RurHo and cRAcBG) for testing the behaviour of slurries under va ous condirions of filtration.
7.4.2. Bed Filters
Bedilters provide an example of the application ofthe pilrciples of deep becl jltration in which the particles penetrate into the interstices of the filter bed where tiey are trapped following impingement on the sxrfaces of fhe material of the bed.
For the purification of water supplies and for wasi,e water treafinent where the solid content is about 10 g/mr or less, as roted by CLr,Asev(23) granular bed filters have larselv rcplaced lbe former ver) slow sand filters. Tbe beds are lormed fiom eronJar mareriaj o f g n i o s;7e 0 . 6 - 1 . 2 mm in beds 0 . 6 - 1 . 8 m d e e p . T h e \ e r y fine paflicles o t s c t i G are removed by mechanical action although the particles fnally adhere as a result of surface elect ic forces or adsoplion. ds lr\r74r poinls out. Ttis opemrion bd5 beeo anatysed b) Iursex 'r) *ho proposes r}e lollou mg equarjon:
('7.36)
L quid lilt|aton 244 If u. js the superficial flowrate of the slurry, then ihe rate of flow of solids tbrough the filter at depth I is ,"C per unit area. Thus the rate of accumulation ofsolids in a disiance dl=-u,(AC/Al)d|.llo is ihe volume ofsolids depositcd per ru t volume of filter at a depth l, the rate of accumulation may also be expressed as (rd/At) dl.
Thus: ( 7 . 3 8 )
The problcm is discussed further by Ivrs(z!) and by SITELMAN and FRr )LANDER{26). The backwashing of lhese beds has presented problems and sevcral techniques hav€ been adopted. These include a backiow of air followcd by water, the flowrate ofwhich may be high enough to give risc to fluidisation, wifh the maximum hydrodynamic shear occuring at a voidage of about 0.7.
8.4,4,
The filter Dress
Thc filter press is oDe of two main types, the p/d/e anti frane ptess and the recessed plate
The plate and frame press
This ryp€ of filter consists ofplates and frames arranged altemaiely and supponed on a pair of nils as shown in Figure 7.6. The platcs have a ribbed surface and the edges stand slightly proud and are carefully rnachlncd. Thc hollow frame is separated from the plate by the filter cloth, and the press is closed either by neans of a hand scrcw or hydraulically, using the minimum pressure in order to reduce wear on the cloths. A cbamber is therefore fbrmed betwccn cach pair of successive plates as shown ir Figure 7-7. Thc slury is introduced tbrough a port in each frame and the flltrate passes through the cloth on each side so that two cakes ar€ fomed simultaneously lJl each chamber, and these join when the fiame is tull. The frames are usually square and may be 100 mm 2.5 m across and l0 mm 75 mrn thick.
The s1urry may bc f.Jd to the press tlfough the contlnuous channel formcd by the holes in the comers ofthe plates and frames, in which case it is recessary to cut coresponding holes in the cloths whjch thcmsclves act as gaskeis. Cutting of the cloth can be avoided by feeding through a channel at the sidc although rubber bushes must then be fitted so that a leaktighi joint is forned.
The filtrate runs down ihe ribbed surlace of the plates and is then discharged ttuough a cock into an open launder so that thc filirate from each plate may be inspected and any plate can be isolated ifit is not giving a clear filtrate. ln some cases the fi1tmte is rcmoved tbrough a closed channel although it is not then possible to observe the discharge ftom each plate separately.
In many filter prcsses, provision is made for siean heating so rhat the viscosity of the filtrate is reduced and a higher rate offiliration obtaincd. Materials, such as wa\es, that solidify at normal temperatures may also be filtered in steam-heated presses. Steam heating also facilitates the production of a dry cake.
Oplimun time cycle. The optimum thickness of cake to bc fonncd in a filter press depends on the resistance offered by the fi1tcr cake and on the time taken to dismantlc
245 ChemicalEnginee ng Proesses
aignre 7.6, A ldg€ nlrsr pies with 2 n by 1.5 n plates
and r€fit the press. Although the production of a thin filter cake results in a high average mte of filhation, it is necessary to disman{le the press more oftea and a greater time is thereforc spent on this operation. For a fiItration ca.rried out entirely at constant pressure, a rcarrangement equation 7. I 9 gives:
t rpx rpL
v 2 A , ( - L P ) , 4 ( _ a P ) : B t V * B z
where Bt and 82 are constants,
Thus the time offiItration, is given by:
t : B r v 2 + B 2 v
w :
W is a maximum when dwldy = 0.
(7.39\ (7.40)
('7.4r'
The time of dismanding and assemblirg the Fess, say //, is substantia.lly hdependent ol th€ thickness of cake Foduced. The total time of a cycle itr which a volume y of filtrate is collected is then (t + r/) and the ovelall rate of filhation is given by:
Liq!idtltrarion 246
Figure7.7. Eate ard flare pless. A-inlei paqa B-f€d ports c-f tfate o!'l d. D- aire F-pat*
Diffsertiating Ir with rq€ct to y and equding to z€ro: B 1 v 2 + B 2 v + { v ( 2 B t V * B z ) : 0
o f , l ' : B t V 2
":l(;)
(7. 42) ( 1 . 4 3 )
If the rei dance of the filter medium is neglected, r = t1y' and thetime during which filtrdion is carried out is e<acily equd to the time the press is out of service. ln pradice, in order to obtain the ma(imum overdl rde of flltrdion, the filhdjon time mud dways be somer,r'hd greder in order to dlow for the rsisalce of the doth, represeted by ihe t€rm B2y. In generd, ihe lovver the pecific rddarce of the cake, the greder will be the economic thickne€s of the fralre
The application of th€se equdions is illu$rd€d later in Exanple ?.5 whidr is based on the work of HARKER(2I.
lj-__-_---i 1
f---:--247 Chemi€l Engineering Proesses
It is $own in Exanple 7.5, whidt appeds lder on the ch4ter, thd, provided the doth rej$arce is vsy low, dopting a filtrdion time equd to the do/vntime will give the rnadmum throrghput. Where the doth r€isance is appreciable, then the term Br(r//Br)ur b€omes dgnificat ad a long€r filtrdion time is d€Firable lt mav be se€n in Figure 7.8, which is b6ed on datia lion Exanple 7.5. thd ndther of ihese vdues represents the minimum co$ condition hower'er, e(@t for the unique dtudion where l - {cod of $utdown)/rcod during filt€ring). and a dec;don has to be mde 6 to whdh€r cod oJ throghput is the overiding consid€rdion. ln practice, operding schedules are prob€bly the dominding fdu.e dthough significdrt sa,r'ings may be mad; by operding d the minimum co$ condition.
4000 3000 2000 1 0 0 0 0 1 5 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 Filt6iion iime, r (ks)
Figure7.8. Opiirnigion of plde at irane pr6 (data fro.n Exand e ?.t en \\6shing
Two methods of washing may be employed, ..simpt€,' washine and ,,through,, or "thorough" washing. With simple washing, rhe wash liquid is fed in rhrough the same cha.nnel as the slulry although, as its velociry near the poinr of enrry is high, erosion of the cake takes place. The channels which are thus formed gmdually enlaxge and weven washing is usually obtained. Simple washing may be used only when the fiame is not completely tull.
In thorough washing, the wash liquid is introduced through a separate channel behind the lter cloth on altemate plates, known as washing plates shown in Figure 7.9, and ows through the whole thickness of the cake, rst in the opposite direction and ther in the same direction as the ltrate. The area during washing is one-half ol that during
Itration and, in addition, the wash liquid has to ow througl tw:ce the thickness, so that the mte of washing should th€refore be about one-quarter ofthe nal rate of ltiation. The wash liquid is usualiy discharged though the same channel as the ltrate thoush s o m e t i m e s a s e p d r a l e o u r l e t i s p r o \ i d e d . I v e n wilh fiorough u a s h i n g s o m e c h a n n e l l i i g occurs and several ir ets are often provided so that the liquid is well distributed. lf the cake is apFeciably compressible, the minimum pressure should be used during washing,
E ! I 6 1 0 i o.2o
e
i o.rs
I E 6 E : 0 . 0 5 0 .9T S
= x3 3
E €
3
t 6 l t 6 |
i : I
Iielre 7.9. Thorough washing
and in no case should the final filtration pressure be excecded. Aftcl washing, the cake may be made easier to handle by removins excess liquid with compressed an.
For case in identification, small buttons are embossed on the sides of the plales and ftames, one on the non-washing plates, two on th€ ftames and three on the washing plaies as shown in Figure 7.10.
E x a m p l e 7 . 1
A sluny is filtered in a plate and ftane press containing 12 ffrmes, each 0.3 m square and 25 nnr ih;ck. During the fiNt 180 s tle pressufe diflefeDce for filtration is slowly ftised to the fiDaL value of400 kN/m: and. dxdng this period, the raie of filtration is maiDtaiDed corstant- After lhe initial perlod, filiration is caried out at constant pressure and the cakes ee compLetely fomed i! a turt}er 900 s. The cakes de theD washed with a pressue ditTerence of 275 kN/nr for 600 s \\slng tharoush ,4rrirg (S.c r! fi!t! an,l ]rni. rLtse nr si.llon i.1.ll. What is the volume ol filn'ate collected pe. cycle dd how nuch wash water is irsed!
A sample of the slu.ry had previously been tested with a leaffihd of0.05 n':filtering su.face usilg a vacuun giving a lressure differerce of71.3 kN/m']. The volume ofnltrate collected in the nnt 300 s, was 250 cm: and, after a tudher 300 s, an additjonal 150 cmr was colLected. Ii may be assumed that the cake is incompressible and that the cloth resistance is the same in the leafas in
249 ChemrcalEnginee ng Processes
ligure 7.10. plares and frades
Solution
In the leaffilter, filtration is at coflsranr presslre from the start. a t - \ a P ) A 2
r l u s :
, t z
- r . r ,
l u "
,
In the filter press, a volume yr offilhate is obiained und€r constant mte and filtration is then cmied ou! at constmr pressure.
vi+lu=tfff,,
(1iom equation 7.18) condjtions in time n,
(from €quation 7.17) Thus:
LiquidliftElion 250
, y , - y , 1 , z A L r v v , t . 2 t n P ' a
-u r - a - I) ( f t o m e q u a l i o o 7 18' When I = 300 s, y : 250cmr : 2.5 x 10 a m3 md when t : 600 s,
y = 400 cn3 = 4 x l0 4 mr, A = 0.05 m! and -AP = 71.3 kN/m, or 7.13 x 10a N/mr. Tlrus: (2.5 x 10-a)z +2(0.05L1u)2.5 x 10-1:20.13 x 104 ' 0.051/tpo)300 and: (4x10 1)z +2(0.05L/v\4 x l0r = 2(7.13 x.104 x 0.05,/.pu)600 That isr 6.25 x l0 s + 2.5 x 10-5! l 0? x 105
a n d : t 6 x l 0 - s + 4 x l 0 5 L - 2 u x l 0 5 H e n c e : L / t = 3 . 5 x 1 0 - t and r p u = ? . 1 3 x 1 0 1 r
A | 2 a 2 0 . l ' 2 . l o m : . A P = 4 0 0 | N / m , 4 ! t 0 r \ / m ' . , . t s O s . T h e v o i u m e offilhate vr collected during ihe constant mte period on th€ filter press is given by:
v i + ( 2 . r 6 x 3 . 5 x 10 3yr) = (4 x 105 x 2 . 1 6 ' ) / ( 7 . 1 3 x r 0 r 1 ) 1 1 8 0 v ? + Q . 5 6 x 1 0 1 v 1 ) ( 4 . 7 ] l x l o - a ) = o
or: 14 = -G.78 x l0-r) +./(1.429 x 10-r +4.7 x l0 4) = 1.825 x t0-, n3 Foi the conslant pressue !€riod:
( r - n ) = 9 o o s
The total volume of fillrate collected is iherefore given by:
( y , - 3 . 3 3 x l 0 - a ) + ( r . 5 1 2 x 1 0 , ) ( V - 1 . 8 2 5 x 1 0 - r ) = 5 . 2 3 5 x l 0 u " 9 0 0 o r : y ' 1 + ( 1 . 5 1 2 x l 0 - , v ) - ( 4 . 7 1 2 x r o ) : 0
T h u s : v : 0 . 7 5 6 x i 0 ' + l\0.572 x 101 +4.712x to-1) = 6.15 x l0 '? or 0.062 m3
The fiml late of filtration is given by:
- A P A 4 ' 1 0 . \ 2 . l o j
r p " i v + A U q i l l ' l 0 ' rol5 ' l0 | ,lo i 7 0 l 0 - ' m ' / s (fton equation 7.16) ff the viscosiry of the filtrate is the same as that of the \rash-water, then:
R a t e o f w a s h i n s a t 4 0 0 k N lnz : I x 3.79 x l0 5 = 9 . 5 x 1 0 6 m 3 / s
Rate ofwashing at 275 kN /nl =9.5 x to4 x (215/400) :6.5 x 10-6 n3/s rhus the amoud of wash-wa'erpasins io 600 s = (60r,::*t:.?r..ln,
251 Chemiel Englieeinq Prc@sses
The recessed plate filter press
The recessed t]?e ofpress is similar to the plate and frame tlpe except that the use of frames is obviated by recessing the ribbed surface of the plates so rhat rhe individual filter chambers arc fomed between successive plates. In this type ofpress thercfore the thickness ofthe cake cannot be varied and it is equal to h{ice the deoth ofthe recess on individual plates.
Fi8ure ?.11. A recessed chanberplate,2 m squre
The feed channel shown in Figure 7.11 usually differs from thai emptoyed on the ptate and ftame press. A11 the chambers are cotrnected by means of a comparatively large hole in the cenhe of each of the plates and the clotls are secured in Dosition by means o f s c r c $ e d unions. s l u r r i e . contaitring r e l a t ; v c l y l a r g e . o l i d p a n i c l i s . 1 r y r.uaity b. halrdled-in fiis O?e ofpress without fear ofblocking ihe feed channcls. As described by CIcRRy0s), developments in filter presses have beer t;wards fhe fabrication oflarger units, made possible by mechanisation and the use of newer lighter materials of constluction. The plates of wood used in earlier times were limitcd in size because of limitations of pressues and large cast-ion plates prcsented difrculty in halrdling. Large plates are now frequently nade of rubber mouldings or of pob?ropylene alrhough distortion may be a problem, particularly if the temperature is high.
The second area of advance is in mechanisation which enables the opening and closillg 1o be done automatically by a ram driven hydraulically or by an electric motor. plate transportation is efTected by fitting triggers to two endtess chains operating the plates, and labour costs have consequently be€n reduced very considenbly. tmproved designs have
(b) (c) ( d ) (el (f) Liquid n[ration 252
given bdter dfajnage whidr h6 led to improved wa$ing. Mud *rorter time cydes are now obtaj ned and the cakes are thjnner, more uniform, and drier. These dvantees har'e b@n father more readily obta;ned with reced pldes where the cloth is $bjeded to less wear.
Advantages of the filter press
(a) BecaJse of its basjc dmpliclty the filter pres is vssatile ard ma/ be usd for a wide rarge of materids unde' varying op€ratjng conditions of cake thickn€ss ad presure
I\,4d ntqance co$ is lor.
I t provi d6 a I age fi lteri ng area on a snd | fl oor spe and foir' additiond Gociated units are nedd.
Mo$ joints ere externd ard le€kage is #ly ddected. High pf#rre opqation is us.tdly posible.
It is equdly s.ritable whdhs the cd(e or the liquid is the majn produd. Disadvantages of the filter press
(a) lt is intermjiiet in operatlon and continud disrna,tling is apt to cause high w@r on the cl oths
(b) Deqite the improvernents mertjon€d prs/ioudy, it is faifly heavy on labour.
Example 7.2
A dufry cont€ining 100 kg of whjting, of dendty 3000 kg/rn3, p€r m3 of wats, a1d, is tittered in a plde dd frane pr6 whi6 td(6 900 s to disnartle, dear, ad reasnbte. tf the cake is incompresjble ard has a voidage of 0.4, whd is the optimlm thickns of ceke for a flltrdio'1 presre ( a P ) of 1000 kN/m'z? The dendty of the whiting is 3000 kg/m3. lf lhe cd(e is wd€d d 500 kN/rn' ad thetotd volumeof wdl wats sndoyd is 25 p6 cet of thd of theilirde, how is the opi rnunr thickns of ihe cd(e dfectd? The rej Sfice ol the filts mdi um may be negt€dd and the viscodty ol wats ls 1 mNsh'?. In an eeedmel, a prsre difference of 165 kN/m, produced a flow of water of 0.02 cnf/s through a catimdre cube of fill€r cd(e
Solution
The bai c fl ltrdion equdion rnay be writtgl as:
1 d v ( - a P ) A d / t p l whse I is ddind 6 the specific rej st€nce of lhe cd(e
Thedurry conleins 100 kg whiting/mr of water Volumeof 100 kg whiting: (100/3000) = 0.0333 m3 Voluneol cake:0.0333/( - 0.4) :0.0556 m3.
253 Chemical Engineenns Pbesses
(825, 10iq x io-a, ois69y - y
Volume of liquid in c*e= (0-0556 x 04) = 0.02 nf. Volume of filtrde: (1 - 0.02):0.978 n3.
Thus volun|e of cd<dvolurne of fttrde u = 0.0569 In lhe eeedmelt:
A = 1 0 . 4 n ? , ( - a p ) : 1.65 x 1 0 5 N i r # , l=0.0f m, : = 2 ^ 1 0 - 3 n l / s , p 1 0 r N g f i l .
Inserting these vdu6 jn equdionT.2 giv6
/ 1 t . . . ^ - a 1 { 1 . 6 5 \ 1 ' ! ' ' [ 1 0 - , 1 , 2 1 0 - , . , r o ; = , ; . a d , = 8 2 s 1 0 ' ] m ': Fron €qudion 7.2: _ _ , 2 A 2 F L P ) t ( € q u d i m 7 . 1 1 ) I tLt)
But I = Mf ftane thi€kness: yulA (equdion 7.6) T h u s L 2 2 A ( - ^ P ) u t
. p
2 x (1 x 1S) x 0.0s60 r. (8.25 x 10€)(1 x 10-3)1
: 1.380 x 10-6t (where t in thefiltrdon time) L : 1 . 1 6 1 " 1 t 1 P
It is $own in Sedion 7.4.4ihd if the reddance of the filts rndium is n€led€d, the optimum c6ke thicknes ocaurs whg| the filtration ii rne is equd to the dorntime,
Thus r = 900 s, l/, = :tt
. . Lod : 34.8 x 10-3 m = 34.8 of 35 mm adi optimum frdne thickns = 70 mm
For tho wdring pro.ess, if the filtrdion pressfe is Mved, the rde of wa*ting is hdved. The wdr wder has twice the thickn€ss to p€ddrde ad hdf the a€ for fld/r/ thd is a/.ildle to lhe liltrde, so thd, condd€ring th6e ftrtorsi the wa$ing rde is oledghth of the ind ithdion rde
d v A 2 t L p l d t I p u v
1x 1$A2 e13 x 1o.aA2)
Liquid filhaton 254
That is:
For dR/dl- = 0, then:
The volune of $ash water = Y/4.
Hence: washins time ,u = 0/4)/(2.66 x t0 'A, lv )
'"=(ffi)(ff):'"'.,'.'
The filtration time t was shown earlier to be: r/ = t,/i.180 x t0-6 = ?.25 x 105t, Thus: total cycle iime = r,(2.90 x 105 + 7.25 x 105) + 900
= 1.015 x t o 6 r , + 900 The Fte ofcake production is t}enl
L : - = R r . 0 2 5 . t 0 6 L r + 9 0 0 1 . 0 2 5 x 1 0 6 4 ' ? + 9 0 0 - 2 . 0 5 0 x t 0 6 I , : 0 "' -
lJ# ,tr and L:2s 6 t r0I n : ze.6 mm
Thus: Frame thickness = 59.2 - 60 mm
7-4.5. Pressure leaf lters
Pressure leaf fiiters are designed for final dischfige ofsolids in either a dry or wet state, under totally enclosed €orditions, with fully automatic operation.
Each type of pressure leaf filter features a pressule vessel in which are located one or more lilter elements ot leaves of circular or rectangular cofftuction. Tte filter media may be in the fonn of a synthetic fibrc or other fabrics, or metallic mesh. SuDDorts and inlermedidle oraiDage members are in €oarse mesh wilh all componenrs beld togerher by edge bhding. Leaf outlets are connected individually to an ourlet manifold which Easses l h r o u g b $ e w a t l oflhe pressure \ e s . c l .
The material io be fitered is fed into the vessel under pressure, and separation takes place with ihe solids being deposited on the leaf surface, and the liquid passing through the drainage system ard out of the filter. Cycle times are detemin€d by pressure, cake capacity or batch quantity. Wlere particularly fiIIe solids must be rcmoved, a layer of precoat material may be deposited on the leaves prior to filtration, using diatomaceous earth, Perlite, or other suitable precoat materials.
Cake washing, for recovery of mother liquor or for removal of solubles, may be caried out beforc dischfige of the solids as a slu.ry or a dry cake.
Presswe leaffilters arc supplied in a wide mnge ofsize and mat€rials of construction. Orc q,pical design is the "Veti-jet" unit wirh a verrical tank alrd vertical leaf fiIter, as shown in Figure 7.12, with rectangr ar leaves mounted individually but connected to a common outlet manifold. For sluice cleaning either a stationary or oscillaiingjet system
255 Chemical Engineeing Processes
Figu€ 7.12. .,Venijet pHsure leafilte.
usiry high efrciency spray nozzles is fitted so as to give complete cake removal. For r€covery of dry solids, vibmtion of the leaves allows automatic dischaEe of the solials througb a bonom drscharge pori pro\ ided wiri a quirk opeoi_og door.
Ir the "Auto jet" design, circular leaves are mormted or a hodzontal shaft which serves as the filbate outlet manifold. The leaves are rotated during the cleaning cycle although, in additioD, extra low speed continuous rotation during operation ensures uniform cake build-up in difrcult applications. The Ieaves are of metallic or plastics construction coveretl with fabdc or wire cloth for direct or precoat operation, and rotation ofthe leaves aludns cleaning promores fasr emcient 5luice discharge wi(b njnrmum power coosumprion. ,A; an altemafi\e. lhe lea\,es ma] be rolated oler knile blades $hich remove fie;ake in a dry state. Units of this type are used for haMling foodstufs and also for the processinq of mineruls atrd eftluents.
For the handliry of edible oils, molten sulphur, efruerrs and foodstufs, a Filrra-Matic unit is used in which either the burdle is retracted from the shell as a unit, or the filter tank is retracted leaviry the frlter leaves and filter cover in position. Such units are available m cylindrical, conical or trough shell coniguratiors, and cleaniry may be either wet or dry, nunual or automatic. In the latter case, for dry discharge, vibBtion systems are used and for wet removal spray jets mouded in an ov€rhead manifold sweep the entire leaf surlace in an oscillating motion. In this design, the heavy duty leaves covereal with cloth oI scr€en are all interchangeable and, whether rcund or rectmgular, are all the same size to give uniform precoat, cake build-up and filtlatior In horizontal tray pressure filten, used in batch processes and interrnittent flows, the trays are momted horizontally with
Liquid iittration 256
connections to a vertical fiitrate ma fold at the rear, and such udts are ideally suited where cake washing and positive cake drying are required. ln many cases, the accumulaied cake may be sluiced otr without removing trays from the filter and a special recovery lcaf is provided wherc heel filtration is requircd in which a thh layer of cake is 1€ft semi-permanently in contact with the filter medium to improve the clarily of the filhate. This system is used in various chrmcaiion processes and is ideal for handling high flows of liquids with a low solids concentration. ln mosi d€signs the tubes are mounted vertically fiom a tube sheet at the top of the iank and cleaning is provided with a self-contained intemal "air-pump" backwash, thus a\roiding the use of lalge volumes of sluichg liquid or separate pumps to provide fast and complete rcmoval ofthe filter cdke. The heary gauge pedorated tube cores are covered with a seanless cloth sle€ve sealed ai either end by a clampirlg device. As an altemative, heavy gauge wire is wound around the centre corc, with cortrolled spacing io give reliable filtration and easy cake release. Tubular element u n i r . 01 tfi. ry?e dre a\iil.ble i1 .tinoaro.izcc u p r o 4 0 n ? .
Carlridge filters
Ore particular design of pressure filter is the flter cartridge. typified by the Metafiltcr which employs a filter bed deposited on a basc of rings mountcd on a fluted rod, ad is exteffively used for claril,ing liquids containing small quantiiies ofvery fine suspcnded solids. The rings are accumtely pressed ftom sheet metal of very uniform thickness and are made in a large nunber of conosion rcsistant lnctals, tbough stainless steels are usually employed. The standard dngs are 22 mm in cxtemal diamcter, 16 nln in inremal diameter and 0.8 mm thick, and are scalloped on ore side, as shown in Figure 7.13, so that the edges of the discs are separated by a distance of 0.025 0.25 mm according to
257 Chemical Engineenng processes
Fjgure ?.14. M€hRIrer ?ack (Stelta Mera)
Tq:nements The pack is fomed by mounting the rings, aI the same way up, on the drainag€ rod and tightening them together by a nut at one enal against a boss at the other as sho$,n in Figure 7.14. The packs are mounted in the body ofthe filter which operates under either positive or reduced pressure.
- The bed is lormed by feeding a dilute suspeffion of material, to the filter usually a l'onn of kjeselgubr. wbich is strained by .he packs ro torm a bed ,U""r : -. rf,i'.1. Nesetgubr rs a\artable n a number of gradec and fonns a bed ot- loose srncrure \hich is
_capable of trapping particles much smaller than the channels. During fittration, the solids build up mainly on the surface and do not genemlly penetrate moie than 0.5 rnm into the bed. The filtrate passes behveen the discs ind leaves through the fluted drainage ro4 and operation is continu€d until the resistance becomes too l;gh. The filter is th-en cleaned by back-flushing, which causes the filter cake to cmck antpeel away. In some cases the cleanitg may be incomplete as a result of channelling. If tor any reason the spaces between the dngs become blocked, the rings may be quickly removed and washed.
,The.\4etafil(er is $idery Jred lor nllering domesric water. beer. orgatric solvents aDd o r r s . . I n e f i r r r a l r o n c h a r a c t e n c l i c s o t ch)_likc materials c a n oRen bc improred b y r h e continuous inE-oductioD of a smdlt quariib ol 6trer aid ro rhe sturrl as ;, .n,"i, ii. nner. Un ue orher band. wben the suspelded solid is relalively coar.e, rhe Mel.afiller wrll operate successfully as a stuainer, without the use ofa filter bed.
Liquid fillrstion 258
The Metafifter is very robust and is economical ir use because there is no filter cloth and the bed is easily replaced and hence labour charges arc low. Mono pumps or diaphmgm pumps are most conrmonly used for feeding the filter.
Example 7.3
The relaiion between flow and head for a certair slury punp may be represented apprcximrely ty a straight lirc, the haximum flow ar zero head beins 0.0015 nl /s md tte maximum head at ^.o flow 760 m or liqurd.
Using this pump to feed a panicular slurry to a pressure leaffilter: (a) How long will it take to produce I mr offlhare?
(b) What will be the pressure across tle flter alier tiris time?
A saople of the slurry was fltered at a consrant rate of 0.00015 mr/s rbroush a leaf fitter cove.ed wiih a similar filter cloth but of one tenth the area of the full-scate unit, and after 625 s tle pressur€ acros tle ilter was 360 n of liquid. Aft€r a firrtner 480 s rhe pressure was 600 m of liquid.
Solution
For constaDt rate filtmtion througl the filter leaf:
v , L 4 , - a'' tcu r e o u a r i o n 7 . t 7 '
L TPT
Ai a constant rate of0.00015 n3/s, then, when the time:625 s: y = 0.094 mr, (-a") = 1530 kN/in, and, a = 1105 si y :0.166 1nr and (-Ap) :5890 kN/n,
Substituting t}ese values into equaiion 7.17 giv€s:
(0.094)? + LA|L x 0.094: lA7/rpx) x3530 x 625
or: 0.0088 + 0.09441lu = 2.21 x 106A1/rpn (t
a n d : ( 0 . 1 6 6 ) ' z + L A / u x 0 . 1 6 6 = ( , 4 , / r p u ) x 5 s 9 0 x l t 0 5
o r i 0 . 0 2 7 6 + 0 . 1 6 6 L A / v = 6 . 5 1 x 1 0 6 A z l r t t v ( i t Equations (i) and (ii) rnay be solved siftultaneously to sive:
L,\ / D = 0.01s4 and A'z / 4tt : 4.64 t l}-e As the tull-size plut is l0 times that of the leaf filre!, tien:
259 Chemical Engineering prccesses
lf the pump develo?s 760 m (7460 kN/m,) ar ze.o flow and has zero head ar O = 0.0015 mr/s, its perfomance may be expresed as:
_AP ='7460 _ ('t460 /0.0015) Q AP : 7460 _ 4.9? x 1060 GN/n ) d v A , ( _ L P )
dr = ;t^(v + LAlf (equation 7 16) Substinrdtg for (-Ap) and the filhatioD consrants giv
dv A'1 i.460 - 4.g1 - to,dv /&, a t r u , , v -ojS4, -s i n c e q = d Y l & , t h e n :
d,v _ 4.6j x 10 117460 _ 4.9j ,t t06(dv /dt)l . . d r . 0 / + 0 1 5 4 )
-i . l . ( y + 0.154)dy = 3.46 x I0-3 -2.3tdv/dt The Lime.ro cotlecr tmr is fien given by:
' . .
1 t . - . - - - .
| ( v + 0 . 1 s 4 + 2 . 3 1 ) d v : / (3_46 x r 0 - r ) d r
J O J
r = 8 5 7 s
. The pressre at this time is fomd by substitutiDg in equation 7. I 7 with y = I m3 dd I = 857 s l , + 0.154 x I = 4.64 x t 0 7 x 8 5 ? ( _ a p )
Ljquid llllral on 260
Tlble 7.2. Clasificalion of vacuum nlte6
(-':)
C D E
Cske Cake lillrare dryness washing cldity
Horizonral lin€ar tipling pan
Rotary drun+tiing disclaree Rotary drm knife discharge Rotary drun rouer discllrge Rohry drm leli discharee
l 3 x x 2 1 2 X X 3 2 5 X X 4 2 0 X X l 2 0 0 x x , 4 1 5 X X 5 8 0 X X 5 8 0 X X 5 8 0 X X 5 8 0 X X X 6 l 0 x x 6 1 0 X 7 I 2 X X 8 l 5 X 9 3 0 0 x x 5 8 I 2 t 2 3 - 4 2-3 2 - 3 8 9 8 9 8 9 7 8 8 9 7 8 6 5 1 L 8 8 7 '1 8 8 8 7 6 5 9 5 . 1 . 8 . 9. t 0 . NOTES
L For small batn production. Has very wide application, is very adaptable and cBn be automBted. 2. Usually 2 ro 4 pans, for nediunr size balch pmduction. Ve.y wide application, very adaprable, can be 3. For free-draining maleriah whcre vcry Cood washing k EquiFd wilh slar? sep{alion between norher
liouor and wsh liouors.
f; fEenFining ;atenab wlEF very good wsline is requirod.
wide ranse of !?s dnd size available. cdenuy suitable for nost slmi* in categories B ard C. Can usually be itted wilh vanous necl8dcal devic* to inprove the {lshing and drying.
Rstjcted to very ftee draining nalerials tut reqliring washing.
Resrlicted io very fiee-draining naleials not requiring wishing, but w]le€ the solids eD be retaiftd by Allows use of high drunr speed ard n capable of very high Row rdtes.
Large thrcughputs for small floor space.
sunable for alnost any clarincaLion and aor hodline natenab whict blind normal6her mcdia. A. Higl solids concentnLion, nomally greater than 20 ler cenl, havine solids whicl a@ free-draining and
f6t settling. givins dimculry in nechanial asilation and civing lish fil1ntlon ra1es.
B. Rlpld cake fomatlor wilh reaonably fat serling solids which can be k€pt ii suspension by nechanical C. Lower solids concenrEtion widr solids giviry slow cake fonnation and thin nlter caks which can be
difrcult lo dischdg€.
D. Low solids concentnlion irith solids giving slow cake fonnation hd ! lilter cake hdving very poor nechanical srrenerh.
E. very low solids conceniration (i.e. chnn@fon duty). or containine solids w]rjcl blind nomal fllter nedia. Fillrale lsually rcquncd.
9 = the highest posible perfonnance. I = very poor or neclicible perfommce.
LIQUID FILTRATION
