Study on the compressibility of filtercakes

STUDY ON THE COMPRESSIBILITY

OF FILTERCAKES

P R O E F S C H R I F T

TER VERKRIJGINC; VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAP AAN DE TECHNISCHE HOOGESCHOOL TE DELFT, KRACHTENS ARTIKEL 2 VAN HET KONINKLIJK BESLUIT VAN ló SEPTEMBER 1927, STAATSBLAD Nr. 310 EN OP GEZAG VAN DE RECTOR MAGNIFICUS Dr. O. BOT-TEMA, HOOGLERAAR IN DE AFDELING DER ALGEMENE WETENSCHAPPEN, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDE-DIGEN OP WOENSDAG 10 DECEMBER 1952,

DES NAMIDDAG TE 2 UUR

DOOR

KORNiXIS RIETEMA GEBOREN TE GRONINGEN

UITGEVERIJ EXCELSIOR - s-GRAVENHAGE

-J

DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR: PROF. DR IR P.M. HEERTJES

Han mijn Ouders Ran mijn Vrouw

Acknowledgement

The work presented i n l:his t h e s i s was c a r r i e d out a t The Royal D u t c h / S h e l l Laboratories, Amsterdam.

My sincere thanks are due t o the management of these l a b o r a t o -r i e s fo-r t h e i -r consent to publish t h i s wo-rk.

C O N T E N T S

Chapter I. Theoretical considerations § 1. Introduction

§ 2. Survey of the l i t e r a t u r e

§ 3. nerivation of f i l t r a t i o n equations used Notations

9 10 18 24 Chapter I I . Preliminary investigations

§ 1. Description of apparatus and method of

a n a l y s i s 25 § 2. Undesirable effects which influence normal

cake f i l t r a t i o n 27 § 3. Experiments 28

Chapter I I I . An apparatus for the measurement of filter cake

characteristics

§ 1. Description of the apparatus 35 § 2. The measurtaient of the e l e c t r i c a l cake r e

-sistance 3'^ § 3. The r e l a t i o n between e l e c t r i c a l r e s i s t a n c e

and p o r o s i t y 38 § 4. The technical performance of the manometers 40

§ 5, Calculation of the manometer lag 40 § 6. lïie manometer and gauge pin indications 42

Chapter IV. Retarded packing compressibility

§ 1. Description of the phenomenon 47 § 2. Constant r a t e f i l t r a t i o n 52 § 3. Measurements with s l u r r i e s of mixtures of

limestone and f i l t e r a i d 53 § 4. Possible explanations 53 § 5. Influence of solute in suspension l i q u i d 60

§ 6. Streaming p o t e n t i a l 63 § 7. Streaming p o t e n t i a l measurements 66 Notations 68 Summary Literature references 69 71 Graphs

C h a p t e r I

T H E O R E T I C A L C O N S I D E R A T I O N S

§ 1. Introduction

F i l t r a t i o n i s the s e p a r a t i o n of a f l u i d from a s o l i d p r e s e n t i n i t by means of a porous substance, which has the property of l e t t i n g through the f l u i d and r e t a i n i n g the s o l i d , the d r i v i n g force being a d i f f e r e n c e in l i q u i d head *) through the porous substance, and the cake formed on i t . Sometimes, emulsion separa-tion by means of a porous substance i s also referred to as filtra-tion.

In the present t h e s i s the author will confine himself to the study of f i l t r a t i o n of s o l i d s suspended i n l i q u i d s . Further r e -s t r i c t i o n -s will emerge in the cour-se of t h i -s c h ^ t e r .

F i l t r a t i o n , as thus defined, i s a known physical method of separation, applied in almost every chemical process. I t i s t h e r e -fore by no means s u r p r i s i n g t h a t ample a t t e n t i o n has been devoted to t h i s s e p a r a t i o n by t h e o r i s t s since the r i s e of the chemical industry round about 190C. This a t t e n t i o n i s r e f l e c t e d in an ex-tensive l i t e r a t u r e on the subject.

About 1925 i t came to be r e a l i s e d t h a t c o n p l i c a t i o n s occurred due t o clogging in cake f i l t r a t i o n . '•'>. Since Hermans and Bred^e, a d i s t i n c t i o n has been made between blocking f i l t r a t i o n and cake f i l t r a t i o n , as these forms of f i l t r a t i o n occur under d i f f e r e n t circumstances and obey d i f f e r e n t f i l t r a t i o n laws. Though in both cases the r a t e of f i l t r a t i o n decreases with time, the causes of t h i s decrease d i f f e r .

In blocking f i l t r a t i o n the decrease in the r a t e of f i l t r a t i o n i s due to increasing flow r e s i s t a n c e of the f i l t e r medium, which i s caused by p a r t i a l or complete clogging of the p o r e s of t h e f i l t e r medium by the f i n e p a r t i c l e s of s o l i d matter p r e s e n t in the suspension f i l t e r e d . "Hiis form of f i l t r a t i o n i s the more com-mon when l i q u i d s with few contaminations and l i t t l e t u r b i d i t y oc-c u r r i n g in a very finely d i s p e r s e of oc-c o l l o i d a l form, have to be c l a r i f i e d . Blocking f i l t r a t i o n has received a t t e n t i o n from Her-mans and Bredée ^>, B r i e g h e l - M ü l l e r ^'>, H e e r t j e s and h i s co-workers *'> and Gonsalves * \

When the c o n c e n t r a t i o n of s o l i d matter i n the suspension i s h i g h e r than in t h e case j u s t r e f e r r e d t o , c l o g g i n g may indeed s t i l l occur, but i t i s e a s i l y avoided or only makes I t s e l f f e l t

a t the beginning of f i l t r a t i o n . We then l..^ve cake f i l t r a t i o n , and a f i l t e r cake i s formed over the f i l t e r medium. I t i s only at the beginning of f i l t r a t i o n t h a t the f i l t e r medium has the task of e f f e c t i n g s e p a r a t i o n between the s o l i d and the l i q u i d , Once the cake has been formed, tliis task i s taken over by the top layer of the cake, which continues to i n c r e a s e in t h i c k n e s s . I t i s t h i s form of f i l t r a t i o n t h a t i s p a r t i c u l a r l y common in the chemical i n d u s t r y , the form of the f i l t e r s varying from f i l t e r p r e s s e s , f i l t e r drums, trough and bag f i l t e r s , to r o t a t i o n f i l t e r s , e t c , In „Theory and P r a c t i c e of F i l t r a t i o n " by Dickey and Bryden ®^ an e x c e l l e n t record of t h e p r a c t i c a l side of f i l t r a t i o n i s given, The present t h e s i s i s confined to the study of cake f i l t r a t i o n , where Darcy's law i s v a l i d . The experiments to be discussed were c a r r i e d out a t Reynolds* numbers <1, the Reynolds' number being taken as

v,p.d Re =

•n

( v i s l i n e a r s u p e r f i c i a l v e l o c i t y , p density and r\ the v i s c o s i t y of the l i q u i d and d the average p a r t i c l e s i z e ) ,

No new developments i n the theory of t h i s subject have appear-ed since 1935. In 1935 Hermans and Brappear-edee observappear-ed: „Die Theorie dieses F i l t r a t i o n s t y p u s i s t durch die in l e t z t e r Zeit erschienen Arbeiten von Ruth, Montillon und Montanna, besonders aber durch d i e Arbeit von Carman weitgehend aufgeklart worden und kann nun-mehr a l s ziemlich abgeschlossen b e t r a c h t e t werden",

The a r t i c l e s t h a t appeared since then have accordingly all been concerned with the p r a c t i c a l s i d e of the problem, a f f o r d i n g no e s s e n t i a l l y fresh p o i n t s of view as regards compressible f i l t e r cakes.

I t i s hoped, however, by applying new measuring methods, t o a r r i v e a t a b e t t e r understanding of cake c o n s t r u c t i o n and cake s t r u c t u r e , of which l i t t l e i s as y e t known and which i s responsi-ble for t h i s i n v e s t i g a t i o n .

§ 2. Survey of the l i t e r a t u r e

Theoretical d i s c u s s i o n s of f i l t r a t i o n are g e n e r a l l y based on Darcy's law ' \ which can be taken to be a m o d i f i c a t i o n of the law of Hagen-Poiseuille ^ \ which only a p p l i e s to one pore. Dar-cy' s law i s a g e n e r a l i z a t i o n of t h i s , v a l i d for every porous me-dium. Darcy found h i s law by e}5)erimental means. He i n t r o d u c e s the permeability and then finds for a porous medium of thickness

I that the l i n e a r flow v e l o c i t y v = permeability , - ^ where Ap i s 10

the pressure difference applied. This law was later on modified, so that nowadays allowance is also made for the viscosity T^ of the flowing liquid. Thus, permeability is now defined as K = (Darcy's permeability).-n. In the following, accordingly, the per-meability will be denoted by K. The specific resistance r is al-so introduced, which by definition is taken to be equal to -^r

(r =-^). Sometimes it will be found that this specific resistance is a function of the pressure and is taken to be equal to rocp(P), where P stands for the pressure on the particles of the porous medium. As the resistance of the filter cake is also frequently referred to, the resistance R of a porous medium will also be de-fined, viz. as - ^ , where A is the surface of the medium.

In the early days only the time dependence of the filtration rate was recorded, this being

4^-- constant. i£*i_ according to Lewis and Almy ' \ but after-wards Sperry ^"^ and others pointed out that the resistance of the filter cake should also be taken into account. It was then con-sidered that the filtrate-time curve might be represented by a part of a parabola, the axis of the parabola being parallel to the time axis. That the top of the parabola was lacking was due to the resistance of the filter croth. Sperry and Ruth ^'^ ex-pressed this later on as '/2(V + V^) ^ = constant. (9 + 9o), where VQ stands for the quantity of filtrate that would effect the same resistance as the filter sloth resistance and which on an unre-sisting medium would be filtered in a time of G Q at a pressure difference of Ap.

As experiments had also shown that the thickness of the cake is proportionate to the quantity of filtrate, it was concluded that resistance R of the cake is proportionate to its thickness, for then the above-mentioned parabolic relation between the quan-tity of filtrate and filtration time follows, after integration, from Darcy's law: dV 1 A

d e " n R+a

where a i s the resistance of the f i l t e r cloth. R is proportijonate to the cake thickness and therefore to the quantity of f i l t r a t e . The mean specific resistance r therefore proved to be a constant during f i l t r a t i o n at cons:ant pressure. In the case of most f i l -t e r cakes, however, -t h i s cons-tan-t was dependen-t on f i l -t r a -t i o n pressure, the mean specific resistance increasing as f i l t r a t i o n pressure increases. F i l t e r cakes complying with this were called conpressible f i l t e r cakes.

•Hie f i r s t investigators of the f i l t r a t i o n process ^^' ^^' ^*' **• '*^ concluded from the above that also in the case of

p r e s s i b l e f i l t e r cakes the specific resistiuice was equal through-out the cake during f i l t r a t i o n a t constant p r e s s u r e . Considering t h e dependence on f i l t r a t i o n p r e s s u r e , the p r e s s u r e had t o be equal everywhere and i t was taken for granted t h a t t h i s doforming pressure, or p a r t i c l e p r e s s u r e as most i n v e s t i g a t o r s c a l l i t * ) , was equal t o the f i l t r a t i o n p r e s s u r e . A suspended p a r t i c l e t h a t came to the top of the cake was therefore, according to these inv e s t i g a t o r s , pressed on to the cake with the full filtration p r e s -sure.

\Wien the actual physical occurrence i s considered more closely, however, t h i s theory i s no longer t e n a b l e . For, in the case of highly compressible cakes, the lower l a y e r s of the cake are found t o be much l e s s porous than the upper, in other words, deforming / pressure near the bottom i s much higher than near the top.

Bloomfield ^^^ was the f i r s t to draw a t t e n t i o n to t h i s and to r e a l i z e that the p i c t u r e was untrue. According to Bloomfield part i c l e p r e s s u r e o r i g i n a part e s i n parthe flow of l i q u i d along parthe s part a -tionary p a r t i c l e . The force exerted on the p a r t i c l e i s therefore a purely viscous one ( a t l e a s t i f Darcy's law i s v a l i d , which i s a l l we are concerned with h e r e ) . Consequently, a p a r t i c l e a t the top of the cake only exerts s l i g h t pressure on the cake, the p r e s -sure on the l i q u i d being reduced by the same quantity, A p a r t i c l e lower down in the cake a l s o undergoes t h i s v i s c o u s f o r c e , and there too the pressure on the l i q u i d i s reduced by a similar quant i quant y , The p a r quant i c l e concerned, however, feels in addiquantion quanthe p r e s -sure of a l l the other p a r t i c l e s over i t . Therefore, the deeper we go down i n t o the cake, the p a r t i c l e pressure becomes g r e a t e r and the liquid pressure smaller. So, according to Bloomfield, the sum of the two remains constant throughout the cake and i s equal t o the t o t a l f i l t r a t i o n pressure,

• The s p e c i f i c r e s i s t a n c e of the cake i s t h e r e f o r e higher low down in the cake than near the top. The course of specific r e s i s t

-ance through the r e l a t i v e h e i g h t in the cake **) i s i n v a r i a b l e , however, which means t h a t i f we consider a cake a t two d i f f e r e n t times of f i l t r a t i o n , the thicknesses being ?i and IQ, r e s p e c t i v e -l y , the s p e c i f i c r e s i s t a n c e r a t -l e v e -l h^ has in the f i r s t case the same value as t h a t a t l e v e l hQ in the second case i f h i / i i = hs/Zs.

In t h i s conception, the mean s p e c i f i c r e s i s t a n c e i s constant as well ( a t constant f i l t r a t i o n p r e s s u r e ) .

Ruth, Montillon and Montonna ^'^ confirmed t h i s conception.

*) Afterwards it will be explained why this name is misleading, for which reason another name is used by the author.

**) The relative height will be defined as the height divided by the cake thickness.

Carman '^'' contributes another view of the origin of deforming pressure, and is supported by Brleghel-Miiller ^^\ Carman diffe-rentiates between particle! pressure, deforming pressure and the pressure on the liquid. According to him, the first of these is constant throughout and equal to the pressure of the liquid over the cake. The last decreases from top to bottom and the deforming pressure is the difference between the two. In his calculations he finds, therefore, the same result as Ruth, Montillon and Mon-tonna, as his deforming pressure is numerically equal to the par-ticle pressure as specified by these authors.

If this theory were correct* however, it would follow that though the porosity near the bottom of the cake is lower than near the top, the cohesion near the top is just as strong as near the bottom, for the particles are everywhere pressed together with equal force. This is found not to be the case in practice. Also, according to Carman, the deformation makes itself felt in all directions where the particles do not touch. Prom the

strati-fied structure of filter cakes it is evident, however, that com-pressive pressure is exerted in the direction of flow of the li-quid.

In view of the above arj^ments and considering the unaccepta-bility of the starting point: equal particle pressure throughout

the cake. Carman's opinion must be rejected.

The term particle pressure needs some explanation. In the fore-going this term was taken from the literature. Since, however, this name is not correct in the sense meant in the theory of fil-tration, the name cake pressure will be used in the following. To avoid all confusion on this point, a description will now be given of what cake pressure must be taken to mean.

Considering that the particles consist of rigid material it is not sufficient simply to refer to particle pressure, as this

par-ticle pressure need not necessarily be equal in all directions (as it is in the case of fluids). In a filter cake the particle pressure is actually dependent on the direction in which this is exerted. For, in a direction perpendicular to the direction of flow, particle pressure is equal to the liquid pressure, whereas in the direction of flow the particle pressure is equal to the liquid pressure plus the frictional pressure, of the liquid along the other particles over the particle in question, ignoring dif-ferences in gravity in the cake. The particle pressure determines the decrease in volume of the solid particle. In practice this is quite negligible. The di::ferences in particle pressure for the various directions determine the deformation of the particle. As a rule this is also negligible, but occasionally it may have some effect. If the solid is easily deformable, as is paraffin wax for

instance, the cake may become much l e s s porous and sometimes i t may even become almost completely plugged at the bottom. Deform-ation of the p a r t i c l e will, moreover, lead to equalizDeform-ation of the p a r t i c l e pressure in the various d i r e c t i o n s . This i s in agreement with Carman' s theory.

P a r t i c l e p r e s s u r e in a given d i r e c t i o n w i l l here be taken t o mean: t h e l i q u i d p r e s s u r e p l u s t h e sum of a l l f o r c e s of o t h e r origin operating in the same d i r e c t i o n and divided by the average cross section of the p a r t i c l e perpendicular to t h i s d i r e c t i o n .

Cake pressure will also be defined. This pressure makes i t s e l f f e l t only i n the d i r e c t i o n of flow and v a r i e s from top to bottom in the cake from zero to the full f i l t r a t i o n pressure difference. I f we c o n s i d e r a s u r f a c e of u n i t area a t a given p o i n t in the cake, p e r p e n d i c u l a r to the d i r e c t i o n of flow, we understand by the cake p r e s s u r e a t t h a t p o i n t the t o t a l of the forces exerted within t h i s area and passed on by the p a r t i c l e s of the cake.

I t i s t h i s cake p r e s s u r e t h a t determines p o r o s i t y and cake permeability a t a given s p o t . At the top of the cake i t i s equal to zero, and a t the bottom equal to the difference in l i q u i d p r e s -sure through the cake (if the p a r t i c l e s have the same density as the l i q u i d ) . The sum of the l i q u i d pressure and the cake p r e s s u r e , though they are of a d i f f e r e n t nature and therefore cannot be ad-ded up p h y s i c a l l y , i s constant throughout the cake and equal t o t h e l i q u i d p r e s s u r e over t h e f i l t e r . I t i s t h i s cake p r e s s u r e t h a t Bloomfield, Ruth, Montonna and Montillon mean when they r e f e r to p a r t i c l e pressure.

If we take the p a r t i c l e p r e s s u r e i n t h e d i r e c t i o n of flow t o be P j , the l i q u i d p r e s s u r e a t an a r b i t r a r y spot in thé cake t o be p and over the f i l t e r cake Pi and f i n a l l y the cake -pressure P, we find the following r e l a t i o n s .

At a given place in the cake: p + P e.p + ( l - e ) Pj

and Pj where e = porosity at that spot.

As „cake pressure" is the easier term to handle, and it deter-mines porosity and permeability, it will be exclusively used in the following.

Carman '^^ has derived a filtration equation based on the as-sumption that the deforming pressure on particles varies from 0 to the full pressure difference, passing from the top of the cake to the bottom. 14 Pi Pi 1 P + p l-e

An analogous view i s e n t e r t a i n e d by Ruth, Montillon and Mon-tonna. Tti^ take a thin l a j e r of f i l t e r cake containing a quantity of s o l i d matter equal to dW with a p r e s s u r e d i f f e r e n c e of dp, They use a s l i g h t l y modified d e f i n i t i o n of the s p e c i f i c r e s i s t -ance, taking t h i s to be r e s i s t a n c e a of 1 g of s o l i d matter on a surface area of 1 cm^, Darcy's law, applied to t h i s l a y e r , then gives;

J dV _ _A_ _dp_ A d6 TYX ' dW

dV

Throughout the cake, a t a given moment — i s constant and we may then i n t e g r a t e as follows: o r 1 dV . , dW A d ê o A T) dV - - -— , W = A 2 d e 1 dV _ 1 A 2 cië ncV o T]a ^ " d p o a o a and a s W = cV

Carman also includes the filter cloth in his derivation, assuming that it also has resistance that changes with the pressure. When the compressibility of the cloth has the same pressure dependence as the filter cake he finds:

J_ dV _ 1 ^P dp A 2 d9 ncCVo + V) o a

where VQ again stands for a quantity of f i l t r a t e forming a f i l t e r cake whose r e s i s t a n c e i s equivalent to t h a t of the f i l t e r cloth, and where c i s the c o n c e n t r a t i o n of s o l i d matter in the suspen-sion f i l t e r e d ,

As r e g a r d s t h e dependence of a on the f i l t r a t i o n p r e s s u r e , d i f f e r e n t i n v e s t i g a t o r s hold d i f f e r e n t views, a l s , of course a constant for non-compressible f i l t e r cakes,

Lewis and Almy ' \ who were not y e t acquainted with the above derivation, found from t h e i r experiments on a suspension of chro-mium hydroxide for the mean siieciflc r e s i s t a n c e per gram of solid,

t h a t t h i s depends on the p r e s s u r e d i f f e r e n c e through cake and cloth in accordance with a = C'.Q(/^) ' where (XQ and s are constants > 0.

Now, according to the above theory, Ap ^ ^ " J p

a o a

from which i t follows that, according to the experiments of Lewis and Almy, function a has the form

«oCAp)'

(1-s)

Van G i l s e , Van Ginneken and Waterman ^ ^ \ who c a r r i e d o u t a f i l t r a t i o n i n v e s t i g a t i o n on a suspension of finely d i s t r i b u t e d a c t i v a t e d carbon found for the average s p e c i f i c r e s i s t a n c e a = «1(1 + 3Ap) and claimed t h a t t h i s was a b e t t e r approximation than

that of Lewis and Almy.

According to Carman, however, the formula developed by Van Gilse, Van Ginneken and Waterman i s not generally applicable, but only obtains in a special case. Moreover, t h e i r measurements were c a r r i e d out i n a comparatively small range, in which case i t i s always p o s s i b l e to find by approximation a p r a c t i c a l l y l i n e a r r e -l a t i o n between mean s p e c i f i c r e s i s t a n c e and f i -l t r a t i o n p r e s s u r e .

As a general expression for the s p e c i f i c r e s i s t a n c e a i t s e l f Carman gives a = ao(l + 3 ^ ) ' , where, therefore, there are three constants to be adapted to the suspension filtered. For s = 2, the equation for mean s p e c i f i c r e s i s t a n c e given by Van G i l s e . Van Ginneken and Waterman can be derived after i n t e g r a t i o n .

Compressibility of f i l t e r cakes may be due to various f a c t o r s . At f i r s t , only a reduction of the volume of the p a r t i c l e s under the influence of cake p r e s s u r e was thought of (Underwood ^*^). Later on, deformation of the p a r t i c l e s was considered, by which

the pores would be more e a s i l y f i l l e d up. Most suspensions, how-ever, only c o n t a i n p a r t i c l e s which are hardly deformable at the comparatively s l i g h t pressures applied in filtration. All the same, these cakes too may very well be compressible, by what i s known a s packing compressibility, by which i s understood compressibili-t y compressibili-t h a compressibili-t makes i compressibili-t s e l f f e l compressibili-t i n c l o s e r packing of compressibili-t h e p a r compressibili-t i c l e s , which also makes the pores smaller. This, too, may occur in sever-al forms. One of them was pointed out by Carman ^"^ I t occurs in suspensions whose p a r t i c l e s are not e n t i r e l y dispersed, but com-bined e n t i r e l y or p a r t i a l l y in conglomerations. Cohesion in such a conglomeration i s only s l i g h t , so t h a t any force exerted on i t e a s i l y deforms i t . When such a suspension i s f i l t e r e d , the f i l t e r cake i s a t first b u i l t up. of these conglomerations. When the p r e s -sure difference increases, however, the conglomerations are strong-ly deformed, r e s u l t i n g in denser packing of the lower s t r a t a of the cake and higher s p e c i f i c r e s i s t a n c e .

Other forms of packing c o m p r e s s i b i l i t y are also p o s s i b l e , as will be seen l a t e r on.

In view of the above i t i s f e l t t h a t there i s not much p o i n t in giving one generally applicable formula for a l l these forms of 16

compressibility. I t can have a different form for each f i l t e r cake and has to be determined i n d i v i d u a l l y .

In what now follows some phenomena t h a t occasionally occur in f i l t r a t i o n will be discussed. F i r s t of a l l the scouring effect, already referred to by Baker and t r e a t e d t h e o r e t i c a l l y by Lewis, Donald and Hunneman, Underv/ood; Brieghel-Müller and o t h e r s . This phenomenon i s t h e c a r r y i n g along of the f i n e s t p a r t i c l e s of the suspension by the flow of Liquid through the pores of the cake.

The theory on t h i s s u b j s e t has never passed beyond the stage of hypotheses. I t i s not Imown whether anyone has ever demon-s t r a t e d t h a t , demon-should t h i demon-s rhenomenon occur, there are f i n e r par-t i c l e s i n par-the lower s par-t r a par-t a of par-the cake par-than in par-the h i g h e r . The l i t e r a t u r e i s not very clea.r on t h i s point e i t h e r . Normally, when 4 ^ i s p l o t t e d a g a i n s t V, f i l t r a t i o n a t a constant p r e s s u r e

dif-ference produces a s t r a i g h t l i n e . Any deviation from the s t r a i g h t l i n e i s by some authors put down to the scouring effect,

Weber and Hershey ^U d e r i v e d a formula for f i l t r a t i o n , in which they make allowance far scouring effect and assume t h a t few-e r finfew-e p a r t i c l few-e s arfew-e c a r r i few-e d along by thfew-e l i q u i d whfew-en thfew-e r a t few-e of flow in t h e cake becomes s m a l l e r . The degree in which t h i s c a n n i n g along decreases i s expressed by the scouring coefficient, I t makes i t s e l f f e l t i n the bend of the ( j ^ - V) curve, which tends towards the V a x i s , a s the clogging in the lower s t r a t a of the cake by fine p a r t i c l e s then becomes r e l a t i v e l y l e s s , so t h a t the mean specific r e s i s t a n c e i s reduced. However, in some f i l t r a -tion e}5)eriments i t i s found t h a t the (4S-- V) curve bends in the opposite d i r e c t i o n . To account for t h i s Weber and Hershey i n t r o -duce a negative scouring c o e f f i c i e n t , without explaining the phy-sical background of t h i s phenomenon.

Brieghel-Müller only gives a mathematical formulation of the scouring e f f e c t , without any p h y s i c a l b a s i s . According to him scouring i s demonstrated by a bend towards the - ^ a x i s .

The f i l t e r e f f e c t occurs; when pure water i s f i l t e r e d through a cloth or f i l t e r paper, and c o n s i s t s in a lowering of the f i l -t r a -t i o n veloci-ty i n s p i -t e of -the fac-t -t h a -t no cake i s formed. Va-rious causes are mentioned in the l i t e r a t u r e , such as swelling of the c l o t h d u r i n g f i l t r a t i o n , which i n c r e a s e s the r e s i s t a n c e of the cloth, and e l e c t r o - c a p i l l a r y a c t i o n . The pore w a l l s are then supposed to adsorb ions, which r e s u l t s i n an e l e c t r i c double lay-e r t h a t rlay-educlay-es thlay-e porlay-e diamlay-etlay-er. As somlay-e timlay-e i s rlay-equirlay-ed for the adsorption equilibrium to be e s t a b l i s h e d , t h i s might indeed account for the e f f e c t observed. Ruth gives a survey ^2) of the p o s s i b i l i t i e s t h a t may c o n t r i b u t e to the f i l t e r effect, BrleghelMiiller and Heertjes, however, s t a t e t h a t in most cases, the p r o -17

blem is only an apparent one and that in reality even ,jpure" water still contains a sufficient amount of contaminations - though very small and finely dispersed - to clog a filter medium in the long run.

A study of this effect has recently been undertaken by Zaghloul and is described in his thesis 2^).

Lewis and Almy '^ suggested filtration at constant velocity so as to ensure less trouble from the scouring effect, Donald and Hunneman '^^ carried out measurements on this type of filtration, and so did Ruth ^'\ who found a phenomenon that he puts down to what he calls ,,tardy compressibility", which is compressibility that takes some time to take full effect. Undoubtedly this does exist, for upon conpression porosity is reduced and therefore li-quid must flow from the cake, which cannot happen at once owing to the resistance of the cake,

§ 3. Derivation of filtration equations used

In the preceding section it was noted that there are still many gaps in our theoretical knowledge of filtration, most of which are due to the fact that in drawing up their theories many inves-tigators have been guided only by measurements of filtration ve-locity, filtration pressure and filtrate volume, and correlation between these quantities. Hitherto, filtration has been regarded too much as a statistical science.

The actual problem of filtration lies in the filter cake, how-ever, and in the structure and building up of the cake. The pro-blems still open will therefore have to be solved by carrying out measurements on the filter cake itself. In Chapter III an appara-tus will be described by means of \rtiich these measurements can be carried out,

In this section the mathematical forraul-ations applied will be dealt with, using as far as possible the same symbols as in the preceding section.

Use is made of the specific resistance r = roCP(P) according to the customary definition, in which the function symbol cp stands for the dependence of v on the cake pressure P, as well as of the concept adhered to by many investigators, viz. the resistance a

of 1 g of solid matter on an area of 1 cm^. This a also depends on cake pressure. Of course, there is a relationship between r and a; for, 1 g of solid matter occupies an absolute volume of 1/p ml when p stands for the density of the solid. The correspon-ding cake volume is J-, _ 1 _ ml, where e stands for the porosity

p 1-E

of the cake layer concerned ( e l s also a function of cake pressure P ) . We t h e r e f o r e now f i n e t h a t the r e l a t i o n between r and a i s given by

r = p ( l - e)a (1) I f p i s known, t h i s r e l a t i o n enables us to c a l c u l a t e one of the

three q u a n t i t i e s , r, e or ï, provided the other two are measured. If we now know r, e and a throughout the cake, we have l a i d the foundation on which we can build up the s o l u t i o n of f i l t r a t i o n problems,

Take a t h i n layer of f i l t e r cake with a thickness of dh, over which the pressure difference dp p r e v a i l s and where the cake p r e s -sure i s P, then, according to Darcy's law, the following applies:

- 1 dp 1 dP

V , = , (2) rir dh Tiro^CP) dh

Here p i s the l i q u i d p r e s s u r e and P the cake p r e s s u r e . This can be integrated through the whole cake, giving

„P1-P2 dP

r o . n . v . Z = ƒ (3) cp(P)

Pi i s the l i q u i d pressure over the cake and P2 the l i q u i d pressure under the cake. Through the cloth the pressure difference i s P2-P3. During the experiment Pi-Ps i s c o n s t a n t , but Ps depends on the thickness of the cake. If i t i s assumed t h a t a l s o the r e s i s t a n c e of the f i l t e r c l o t h depends on p r e s s u r e , we can draw up an ex-pression similar to the above and find:

rP.-P, dP

r i . r i . v . Zi = ƒ ' ' (4)

P 1 - P 2 % ( P )

Here Zi i s the thickness of the f i l t e r cloth and ricpi(P) the spec i f i spec r e s i s t e n spec e of the spec l o t h under the i n f l u e n spec e of specake p r e s -sure P, which now changes from P1-P2 to pj-Pg. When the f i l t e r cloth has the same compressibility as the cake we find:

- p . - p , dP

n . v . (ToZ + r i Z i ) ^= J — = constant = rok (5) q)(P)

By t h i s equation the filtration coefficient k i s defined. Even when the filter cloth has not the same compressibility as the cake, the above equation i s approximately valid for thick filter cakes *).

*) This can be seen at once: from the equation;

^\ <!' (Pi(P) cp(P)'

when (p(P) = CPi(P), dk = 0 ^^j ^^^^ d ^ approaches zero. the case for thick cakes, then 4 ^ approaches zero also.

As v = - i - , . ^ w e f i n a l l y find: A dB A.k d9 r i Z = . - l i ^ - (6) r\ dV ro Therefore, if I i s p l o t t e d a g a i n s t -^, we find a s t r a i g h t l i n e Ak

with a gradient of -jr. As A and r\ are known, we can c a l c u l a t e k. I f f i l t r a t i p n experiments are then c a r r i e d out a t various p r e s -sures and k calculated a t each pressure, k can be p l o t t e d against t h e f i l t r a t i o n p r e s s u r e ( P i - P s ) . By d i f f e r e n t a t i n g t h i s curve, which i s a s t r a i g h t l i n e through the p o i n t of o r i g i n for non-com-p r e s s i b l e cakes, we find from the exnon-com-periments:

dk 1

(7) d ( P i - P 3 ) roCp(P)

Similarly, we may derive when a = «Q^IKP)

V r P l ' P l d P

ao.c.ri. X (V* + VÏ) = J ^ = constant = «of* (8)

A o \v(r)

Again, by t h i s equation the filtration coefficient f* i s defined. In t h i s formula c i s the concentration of the suspension to be f i l t e r e d and VJ a q u a n t i t y of suspension t h a t , a f t e r being f i l -t e r e d on an u n r e s i s -t i n g medium of -t h e same a r e a as -t h e f i l -t e r cloth, produces a cake with r e s i s t a n c e equal to t h a t of the f i l -t e r c l o -t h .

Now V* i s not the amount of filtrate, but the amount of filtered suspension. At high p o r o s i t y of the cake and high c o n c e n t r a t i o n of the suspension V* can d i f f e r considerably from the quantity of

f i l t r a t e V (the difference being the cake volume),

If we consider a thin layer in the cake with a thickness of dZ, the amount of jsolid matter in the layer i s equal to:

cdV*

= (1 - e) A,dZ (9)

P

i f dV* i s the amount of suspension responsible for the formation of the l a y e r . We find for the r e l a t i o n between V* and V:

dV = dV* - A dZ = dV* {l } (10) P ( l - e ) Therefore ^y ^ = 1 -dV* p ( l - e ) After i n t e g r a t i o n we find t h a t P ( l - e ) 20 ( V + V i ) = / ' ^ 4 ( 1 }dP = f (11) A o * P ( l - e )

- ^ - = J - ( 1 - - ^ } (12)

(a and e both a t cake pressure Pi-Pa)

By combining (1), (7) and (12) we f i n a l l y find df r ^ dk

— = {p(l-e) - c} (13) dP dP

from which the porosity e in the various s t r a t a can be c a l c u l a t e d , The phenomena r e f e r r e d to in section 2, viz, scouring e f f e c t , f i l t e r effect, clogging, sedim:;ntation and o t h e r s , are to be r e -garded as disturbances of „ideal f i l t r a t i o n " , where only the dif-ference in pressure exerted i s the driving froce and none of these phenomena occur. Ideal f i l t r a t i o n therefore expresses i t s e l f as a purely parabolic progress of f i l t r a t i o n with time. Any deviation from t h i s may therefore be taken to be a disturbance of ideal fil-t r a fil-t i o n .

Several of these disturbances can be mathematically expressed and t h e i r influence on the course of ideal f i l t r a t i o n can t h e r e -fore be ascertained. This i s important because then any deviations from ideal f i l t r a t i o n can a t once be recognized as a consequence of a p a r t i c u l a r d i s t u r b a n c e . If necessary, steps can then be t a -ken t o remove the disturbance.

One form of disturbance may be t h a t a c e r t a i n part of the cake becomes thinner than the o t h e r . I t i s often assumed t h a t if t h i s disturbance i s removed the; cake recovers automatically, because, i t i s argued, the r a t e of f i l t r a t i o n through the thinner p a r t i s then higher and the growth of t h a t p a r t i s more rapid u n t i l the whole cake i s again homogenous in thickness,

But les us now think of the cake as being not of uniform thick-ness, The thin p a r t can be supposed to have been formed by filtra-t i o n during filtra-time G^, - when no disfiltra-turbance occurred - filtra-the filtra-t h i c k p a r t during a time Gj > Gi.If f i l t r a t i o n i s continued undisturbed for a time GQ, a c o n d i t i o n a r i s e s in which the 'Originally t h i n part has a thickness corresponding to a time BQ + Gj. and the other part a thickness corresponding to time 9o + 92, which i s l a r g e r than 9o + Gi, so t h a t the t h i n part cannot possibly have acquired the same thickness as the thick p a r t . Admittedly, the difference g e t s smaller and smaller, owing to the q u a d r a t i c course of f i l -t r a -t i o n , bu-t will never disappear,

Sedimentation and i t s influence on filtration u n t i l the coarsest p a r t i c l e s have s e t t l e d will be t r e a t e d mathematically; during t h a t period the amount of sediinentating material i s p r o p o r t i o n a t e t o

time. I t i s assumed t h a t the f i l t e r surface i s h o r i z o n t a l and 21

t h a t f i l t r a t i o n proceeds from top to bottom. The cake then i n -creases by

1) a q u a n t i t y due to f i l t r a t i o n , which i s p r o p o r t i o n a t e to the amount of f i l t r a t e , and

2) by a quantity due to sedimentation, which i s p r o p o r t i o n a t e to time.

The same applies t o the r e s i s t a n c e of the cake. The differential equation showing the r e l a t i o n between f i l t r a t e and time i s found by extending (11):

1 dV f

V = = — r (14) A dG n{c(V + Vi)/A + bG}

where b stands for the amount'of s o l i d matter s e t t l i n g per s e c . on an area of 1 cm^. The solution, of t h i s differential equation i s :

n e b nb^G ,TTcbVi 2M. (V + Vi) + c + = ( — f T ^ + c) e fA (15) f A f ^^ ^ " ^ dG - c n c v i c -^i-v + ( + ) p f A dV bA fA^ bA

We t h e r e f o r e do not find a s t r a i g h t l i n e for the d9/dV v e r s u s V curve, but an increase of d0/dV t h a t i s more than p r o p o r t i o n a t e t o the amount of f i l t r a t e V. Vtien Zir^ i s small, however, and the p r e s s u r e d i f f e r e n c e r e l a t i v e l y high, we find t h a t t h e slope of the dG/dV versus V curve for V = 0 i s almost equal to the slope of t h i s curve when there i s no sedimentation.

Other disturbances, too, such as the wearing down of the cake owing to vigorous s t i r r i n g in the f i l t e r v e s s e l , might be t r e a t e d in t h i s manner; i t would then also appear t h a t a t small cloth r e -s i -s t a n c e and high f i l t r a t i o n p r e -s -s u r e , the i n i t i a l trend of the d9/dV versus V curve i s a measure of the slope of the dG/dV ver-sus V curve when there i s no disturbance.

Some remarks may be added on f i l t r a t i o n a t constant f i l t r a t i o n v e l o c i t y . This type of f i l t r a t i o n may heln to o b t a i n more know-ledge of f i l t r a t i o n a t c o n s t a n t p r e s s u r e and more g e n e r a l l y of t h e growth and s t r u c t u r e of the f i l t e r cake.

In f i l t r a t i o n a t c o n s t a n t v e l o c i t y p r e s s u r e c o n t i n u a l l y i n -c r e a s e s i n obedien-ce to Dar-cy's law. When the -cake i s non--com- non-com-p r e s s i b l e the t o t a l non-com-p r e s s u r e difference i s non-com-p r o non-com-p o r t i o n a t e to the

t h i c k n e s s of the cake and t h e r e f o r e to the time of f i l t r a t i o n . When the cake i s compressible t h i s r e l a t i o n i s l e s s simple,

Owing to the constant r a t e of filtration the top layer i n v a r i a -bly o r i g i n a t e s in the same manner (except perhaps a t f i r s t , when the f i l t e r c l o t h may t o a c e r t a i n extent influence the formation of t h i s l a y e r , because the pore density in the cloth may be dif-22

ferent from t h a t of the cake); therefore the top layer always has the same s t r u c t u r e and t h e r e f o r e the p r e s s u r e g r a d i e n t through t h i s l a y e r i s a l s o c o n s t a n t . The sajne a p p l i e s in the case of a deeper layer a t a c e r t a i n level of the cake, from the moment t h a t t h i s l a y e r i s f i r s t formed. Therefore the p r e s s u r e d i s t r i b u t i o n measured from the top of the cake remains the same during f i l t r a -t i o n . This means -t h a -t -the l i q u i d p r e s s u r e a -t a h e i g h -t h &l-t; Zabove the f i l t e r medium i s indicated by

A.h d(Ap)

(Ap)h, =Ap- ƒ 7 f • di

rl d(Ap) = J . d Z

With the aid of t h i s formula, the i n t e r p r e t a t i o n of data on con-s t a n t r a t e f i l t r a t i o n will be much con-simplified.

N O T A T I O N S

V = l i n e a r r a t e of flow K = permeability

T\ - v i s c o s i t y

Ap = difference in pressure through a porous medium or f i l t r a t i o n pressure

Z = thickness of porous medium

r = roCP(P) = specific r e s i s t a n c e of porous medium P = cake pressure in porous medium

P j = p a r t i c l e pressure i n porous medium A = surface area of porous medium

V = t o t a l quantity of l i q u i d passing through porous medium

h = height in porous medium 9 = time W = quantity of s o l i d i n f i l t e r cake a = r e s i s t a n c e of 1 g s o l i d matter on 1 cm"^ in f i l t e r cake c = concentration of s o l i d s in suspension to be f i l t e r e d p = density of solid

volume of pores in porous medium porosity =

apparent volume of porous medium Pi = liquid pressure over cake, in the suspension P2 = liquid pressure over cloth

Ps = liquid pressure under cloth, in filtrate b = quantity of solid matter settling per sec on

1 cm2

k = filtration coefficient based on thickness of cake

f = filtration coefficient, based on filtrate

dimensions cm cm cm*\ cm**, cm cm" 2 cm* *. cm* * cm 2 cm^ cm sec g cm.g" cm*^. cm*^. cm**. cm**. cm**, cm* 2. sec" 2 sec" sec' sec' sec' 1 g g s e c ' sec* s e c ' sec* cm. s e c " 2, cm* 2, s e c ' 1 1 2 2 2 2 2 2 1 • K 2 • g g g g g g g g g 24

C h a p t e r II

P R E L I M I N A R Y I N V E S T I G A T I O N S

§ 1. Description of apparatus and method of a n a l y s i s

When t h i s r e s e a r c h on compressible f i l t e r cakes was s t a r t e d preliminary i n v e s t i g a t i o n s were c a r r i e d out with a small f i l t r a -t i o n appara-tus. Some i n -t e r e s -t i n g phenomena were encoun-tered, which will be described in t h i s chapter.

The apparatus c o n s i s t s of a f i l t e r head I and a r e -versed U-tube I I (see f i g . 1),. One leg of t h i s U-tube i s c a l i b r a t e d up to 25 cm . The filter head i s connected v i a a g l a s s cock C with the other l e g , which i s f i l l e d with the mother l i q u i d of the s l u r r y , as i s also the f i l t e r head. The c a l i b r a t e d l e g can be emptied by a

9 g l a s s cock A. The f i l t e r a r e a amounts t o 5.0 cm and when necessary can be diminished with the help of f i t -t i n g i n l a i d r i n g s . Cons-tan-t reduced pressure can be ap-p l i e d through a g l a s s cock B, The l i q u i d column in the

f i l l e d leg i s of constant length, as during f i l t r a t i o n the l i q u i d flows over in the c a l i b r a t e d tube, whei'e the amount of f i l t r a t e can be meajsured. So the f i l t r a t i o n p r e s s u r e does not change during f i l t r a t i o n . The f i l t e r

head i s immersed in a vessel with f i l t e r s l u r r y , which can be s t i r r e d when necessary, for which purpose a mag-n e t i c s t i r r e r i s very s u i t a b l e . By opemag-nimag-ng t h e g l a s s cock C f i l t r a t i o n i s s t a r t e d , the amount of f i l t r a t e i s measured in the c a l i b r a t e d leg as well as the filtration time by means of a stop watch. For good readings i t i s necessary to clean the apparatus regularly with a

solu-tion of chromic acid,

As the f i l t r a t i o n sometimes proceeds very r a p i d l y , e s p e c i a l l y in the beginning, the stop watch i s photo-graphed a t each cm^ of f i l t r a t e by means of a film camera, on which i s mounted a b o l t so t h a t only one photograph i s made every

time the bolt i s unlocked. Moreover, t h i s method has the advantage t h a t when more magnitudes a r e measured ( e . g . the e l e c t r i c a l r e -s i -s t a n c e of the cake) during f i l t r a t i o n t h i -s mea-surement can be

photographed a t the same time, ^ Prom the measurements the reversed f i l t r a t i o n r a t e ^ i s c a l

-c u l a t e d and p l o t t e d in a graph v e r s u s the amount of f i l t r a t e V, As follows from the f i l t r a t i o n equation:

cMr

J_ dV

A dG

fA nc(V + Vi)

(see chapter I (11)) t h i s should give a s t r a i g h t l i n e (see fig.2). The slope of t h i s l i n e i s , / 2 tg P dWdV^ fA"

nc

We now define a factor F = tg a expressed i n c m v s e c , which can be d e r i v e d a t once from the experiments, depending on the f i l -t e r area as well as on -the v i s c o s i -t y of -the l i q u i d and the concentration of the s l u r r y . The f i l t r a t i o n c o e f f i c i e n t f only depends on the solid substances and on the s t a b i l i -t y of -the suspension. Bo-th F and f depend on t h e f i l t r a t i o n pressure,

When the l i n e which gives the r e l a t i o n between V and dO/dV i s not a s t r a i g h t one, t h i s must be caused by some d i s t u r b a n c e , e , g . clogging of the f i l t e r , s e t t l i n g or s t i r r i n g e f f e c t . Every d e f l e c t i o n from the s t r a i g h t w i l l t h e r e f o r e i n d i c a t e t h a t t h e conditions for ideal f i l t r a t i o n are not quite s a t i s f i e d .

The time necessary for the f i l t r a t i o n of V' era of f i l t r a t e i s i n d i c a t e d by the hatched surface i n f i g . 2. This i s a l s o v a l i d when the curve i n the graph shoiüd not be a s t r a i g h t l i n e , since t h e hatched surface i s equal t o :

nt.a

Y—

o dV

dV Gj. - Go

The ratio of line segments OA and 08 is equal to the ratio of the cloth and cake resistance, when V^ cm of filtrate has been collected. So from this ratio it can be concluded whether the cloth resistance may be neglected or not.

When partial clogging has occurred this can also be seen from the discussed graph, By this clogging the original active filter area is diminished. When, however, a cake has been formed no more clogging occurs. The rate of increase of the filter cake re-sistance with the amount of filtrate con-tinuously decreases and at last approximates a constant value. Since also the active fil-ter area (viz. the top of the filfil-ter cake) has been restored, the clogging at the out-set is then only indicated by the apparent-26

ly higher c l o t h r e s i s t a n c e , as i n d i c a t e d by the l i n e segment OA (see f i g . 3 ) , and the 4y-versus V curve approximates to a s t r a i g h t l i n e , which has the same d i r e c t i o n as the curve would have i f no clogging had occurred.

§ 2. Undesirable effects which influence normal cake flltration We invariably succeeded in avoiding clogging by using a s u i t a -ble f i l t e r medium and when necessary by removing the f i n e s t par-t i c l e s from par-the suspension before f i l par-t e r i n g . Of course par-the l a par-t par-t e r measure will be of only s l i g h t importance in p r a c t i c e as t h i s r e -moval of finest p a r t i c l e s (e.g. by s e t t l i n g ) takes too much time.

As already pointed out in the i n t r o d u c t i o n , however, we confined ourselves to cake f i l t r a t i o n and any form of blocking f i l -t r a -t i o n was for -t h a -t reason undesirable.

Other disturbances t h a t could be avoided from the beginning are s w e l l i n g of the f i l t e r c l o t h (by t r e a t i n g the c l o t h in b o i l i n g water before f i l t r a t i o n was s t a r t e d ) and s e t t l i n g of the s l u r r y (by s u f f i c i e n t s t i r r i n g in the f i l t e r vessel and by designing the f i l t r a t i o n apparatus to f i l t e r upwards).

Deterioration of the s l u r r y by growth of micro organisms (mi-crobes, algae and b a c t e r i a ) i s not d e s i r a b l e e i t h e r , since these might clog the f i l t e r c l o t h . Vhen no precautions are taken, t h e i r influence i s f e l t already a f t e r 24 hours. Poisoning of the s l u r r y by, e.g., '/2% phenol i s already s u f f i c i e n t to prevent t h i s effect. When the suspension lic;uid i s water, e l e c t r o l y t e s p r e s e n t in the suspension cause a higher f i l t r a t i o n r a t e . An e l e c t r i c double la;yer e x i s t s along the w a l l s of t h e cake c a p i l l a r i e s owing t o adsorption of n e g a t i v e i o a s a t the wall. This double l a y e r d i minishes the effective cross section of the c a p i l l a r i e s and t h e r e -fore reduces permeability. Presence of metal ions and e s p e c i a l l y of p o l y v a l e n t metal ions reduces the t h i c k n e s s of t h i s double l a y e r , '.'hen these ions are p r e s e n t to a s u f f i c i e n t degree, the double layer becomes so t h i n t h a t any further decrease has no more effect on the f i l t r a t i o n r a t e . Of course, t h i s degree of ion con-c e n t r a t i o n i s dependent on the con-c a p i l l a r y diameter. When the dia-meter becomes smaller t h i s c r i t i c a l concentration i n c r e a s e s . When the cake p a r t i c l e s are about 5 p., tap water has mostly enough me-t a l ions for me-t h i s c o n d i me-t i o n me-to be r e a l i z e d . The f i l me-t r a me-t i o n r a me-t e i s then increased by about 20% (as compared with d i s t i l l e d water). Vihen i n s u f f i c i e n t ions are present t h i s effect causes an apparent increase in v i s c o s i t y and i s therefore called e l e c t r o v i s c o s i t y ^*\ The influence of the temperature on v i s c o s i t y n e c e s s i t a t e s a constant temperature during f i l t r a t i o n .

Finally, the stirring effect must be mentioned. Vigorous stir-ring in the filter vessel might cause deformation of the cake. This deformation can be of different kinds and hence also the in-fluence on the filtration rate may differ. Fvidently, the stir-ring effect is greater at lower filtration pressure (see graph I),

Stirring can have a threefold influence on the cake viz.: 1) Grinding off the cake, resulting in a higher filtration rate. 2) Deformation of the cake, e.g., grinding off the cake at one side and accretion at the other side, also resulting in a high-er filtration rate.

3) Shearing of the upper layer of the cake with regard to lower layers (or in the case of the apparatus described here shear-ing of the lower layer in relation to higher layers). This causes a denser packing, a lower porosity and hence a decreas-ing permeability, and a lower filtration rate.

The effects mentioned under 1 and 2 permit quantitative cal-culations to be made when this grinding off or accretion of the cake is proportional to the time. These calculations are similar to that one of the disturbance by settling as done in the first chapter.

rtG

In graph I are p l o t t e d (V—iiS.) curves for a quartz suspension: 1) without stirring, "•

2) with slow stirring,

3) with rapid s t i r r i n g and also for a limestone s l u r r y with s t i r -ring 4)

and for a PVC s l u r r y with s t i r r i n g 5 ) .

From t h i s graph i t can be seen t h a t for a q u a r t z suspension the t h i r d s t i r r i n g e f f e c t dominates and for a limestone s l u r r y and a PVC s l u r r y the f i r s t and the second effect.

Fortunately in most cases i t i s s t i l l p o s s i b l e to draw conclusions from these disturbed f i l t r a t i o n experiments, i f the o r i g i -nal slope of the (V - " ^ curve i s taken for the c a l c u l a t i o n of t h e filtration coefficient.

§ 3. Experiments

To determine the pro; e r t i e s of a c e r t a i n slurry some filtration experiments must be made with t h i s s l u r r y a t different filtration pressures (but a t the same concentration and a t the same tempera-t u r e ) . From each experimentempera-t tempera-the f a c tempera-t o r F i s detempera-termined and tempera-then F i s p l o t t e d versus the filtration pressure difference Ap. Some char-a c t e r i s t i c (F-Ap) curves w i l l now be discussed. Unless otherwise s t a t e d the concentration of the s l u r r i e s i s 3.5%(wt) and the tem-p e r a t u r e 18°C.

The (P-Ap) curve of a quartz suspension always proved to be a s t r a i g h t l i n e through the o r i g i n . This means t h a t the cake of these suspensions i s not compressible. In chapter I i t was already shown that for a non-compressible cake the filtration coefficient f should be p r o p o r t i o n a l to the f i l t r a t i o n p r e s s u r e , so t h i s must also be the case with the factor F, which i s equal to

fA^ TIC

There are only a few s l u r r i e s t h a t show t h i s property. S l u r r i e s of a c t i v a t e d kieselguhr, such as C e l l t e or Hyflo supercel in wa-t e r give an incompressible cake a wa-t low pressure differences up wa-to 1 atm. At higher pressure differences such a cake i s s l i g h t l y com-p r e s s i b l e , At low com-pressure differences and a t a temcom-perature below

30°C a l s o the cake of a PVO suspension with 0.1% deflocculant i s not conpressible. This wil] be shown further on.

When a s l u r r y of limestone in pure water i s filtered the (F-Ap) curve shows some resemblance to a parabola (see graph I I and table I ) . The cake of t h i s s l u r r y i s compressible. When the f a c t o r F divided by the pressure difference Ap i s p l o t t e d versus Ap a curve i s found which approximates t a n g e n t i a l l y t o t h e Ap a x i s . For a quartz cake, P//!p i s a constant. I t i s i n t e r e s t i n g to compare F/Ap (which i s a measure of the average cake p e r m e a b i l i t y ) with the cake p o r o s i t y in dependence on t h e p r e s s u r e d i f f e r e n c e , (graph I I I ) . The p o r o s i t y of the cake was determined by taking off the cake, weighing, drying and weighing i t again. I t seems p o s s i b l e (and also probable) t h a t the cake expands more or l e s s e l a s t i c a l -ly a f t e r the f i l t r a t i o n pressure difference i s removed, hence the p o r o s i t y during f i l t r a t i o n should not be determined in t h i s way.

Ap cm Hg 5 . 0 10.0 2 0 . 0 3 5 . 0 4 5 , 0 5 2 . 5 Quart F cm V s e c 1.8 3 . 5 7 . 0 12.3 1 5 . 1 1 8 . 3 z - s l u r r y A p cm Hg 4 . 5 1 1 . 5 2 0 . 0 2 9 . 5 4 0 . 0 5 1 . 0 5 8 . 0 F cm ^ ' s e c 0,57 1.12 1.47 1.90 2 . 3 2 2 . 5 5 2 . 7 5 Liniesto F / A p c m ' ' , s e c / g 9 . 5 , 1 0 " * 7 . 3 5 . 5 4 . 8 4 . 3 3 . 8 3 . 6 e 0.530 0 . 5 1 0 0 . 4 8 4 0 . 4 8 1 0 . 4 7 1 0 . 4 6 6 0 . 4 6 4 n e - s l u r r y Ap cm Hg 2 . 0 5 . 0 15.5 2 9 . 5 6 0 . 0 Wax-F c m V s e c 3 . 4 5 . 1 6 . 1 6 . 9 6 . 7 s l u r r y Table 1

F i l t r a t i o n f a c t o r F and p o r o s i t y 6 as a function of filtration pressure ^ ( f i l t e r area = 5 cm^)

However, from graph I I I the s i m i l a r course of F/Ap and the poro-s i t y a poro-s meaporo-sured can be c l e a r l y poro-seen.

When a deflocculant (e.g. gum arabic, soap, or an alkyl sulphate) i s added to the limestone suspension, the f i l t r a t i o n r a t e becomes very small. The d i s c r e t e p a r t i c l e s of the limestone used were very small, approximately 1 to 2 [i, by which the low f i l t r a t i o n r a t e i s explained. When no deflocculant i s used the suspension coagula-t e s and coagula-t h i s causes a looser s coagula-t r u c coagula-t u r e of coagula-the filcoagula-ter cake in ques-t i o n (see chapques-ter I, page 16).

Already by visual observation i t can be seen how a defiocculant i n f l u e n c e s t h e s l u r r y . The f l o c c u l a t e s of s l u r r y p a r t i c l e s may sometimes have dimensions of the order of 1 mm (dependent on the r a t e of s t i r r i n g in the suspension). These f l o c c u l a t e s a r e very porous formations with a r a t h e r loose binding. A coagulated s u s -pension s e t t l e s very quickly, because the flocculates are so much l a r g e r than the o r i g i n a l p a r t i c l e s , although the apparent density of these f l o c c u l a t e s i s smaller. The cake which forms by s e t t l i n g of t h i s suspension has a large volume and a high p o r o s i t y .

A deflocculant has the function of s t a b i l i z i n g the suspension. Round each p a r t i c l e an e l e c t r i c double l a y e r i s formed, which causes a repulsion between the p a r t i c l e s . IVhen t h i s repulsion i s

greater than the a t t r a c t i o n due to the v.d.Waals forces no coagu-l a t i o n o c c u r s . Then no f coagu-l o c c u coagu-l a t e s a r e observed, the suspension s e t t l e s very slowly and the sedimentary volume i s much smaller ^9 When a f l o c c u l a t e d s l u r r y of p a r t i c l e s which a r e themselves not deformable i s f i l t e r e d a t a low pressure difference the cake i s b u i l t up of f l o c c u l a t e s of p a r t i c l e s and because of t h i s low pressure difference the cake pressure i s low throughout the cake and unable to disrupt these f l o c c u l a t e s . Therefore the filter cake has a high porosity and a high permeability.

Vlhen the same s l u r r y i s f i l t e r e d a t a high pressure difference the cake pressure a t the bottom i s high and may be high enough to s h a t t e r the flocculates and then the porosity i s decreased a t t h a t place. The average permeability of the cake i s now a l s o decreased, When the cake p r e s s u r e has a c e r t a i n c r i Lical value P^., an i n -crease i n t h i s p r e s s u r e does not de-crease the p o r o s i t y any more, because t h i s value of the cake pressure i s so high t h a t a l l bind-ings between the p a r t i c ' ' e s b u r s t . The p a r t i c l e s rearrange them-s e l v e them-s u n t i l t h i them-s cake p r e them-s them-s u r e P^ i them-s reached; a t h i g h e r cake p r e s s u r e the cake i s b u i l t up as if f l o c c u l a t e s had never been

there and the packing has reached i t s highest density,

So when the pressure difference through the cake i s l a r g e r than P^ only the upper p a r t of the cake shows a d e c r e a s i n g p o r o s i t y from the top downwards. When the p r e s s u r e d i f f e r e n c e i n c r e a s e s further, t h a t p a r t of the cake where the cake pressure i s smaller 30

than P^ and which shows a higher porosity decreases more and more and at very high pressure difference i t may seem as if t h i s layer of higher p o r o s i t y i s not p r e s e n t at a l l . Therefore the average p o r o s i t y and a l s o the average p e r m e a b i l i t y of the cake show a lower l i m i t .

The same s l u r r y - but now with enough d e f l o c c u l a n t added to s t a b i l i z e the suspension - when f i l t e r e d gives a t any p r e s s u r e difference a cake which i s b u i l t w of the d i s c r e t e p a r t i c l e s and when these p a r t i c l e s a r e not deformable a t the applied p r e s s u r e s the cake has throughout the same p o r o s i t y and does not show any compressibility. The permeability of t h i s cake i s the same through-out and equal to the lower l i m i t of the above-mentioned case.

The given theory i s i l l u s t r a t e d very well by f i l t r a t i n g PVC s l u r r i e s ( t a b l e I I I ) . The experiments were c a r r i e d out on a s l u r r y of 3.5% wt PVC fines ( p a r t i c l e s i z e about 10 li) in water. In graph IV, F i s p l o t t e d v e r s u s Ap f o r d i f f e r e n t c o n c e n t r a t i o n s of de-f l o c c u l a n t (Na dodecyl s u l p h a t e ) , which was varied de-from 0.25 t o 4 m i l l i e q u i v a l e n t / l i t r e . The (P-Ap) curve for a PVC slurry with-out or with a small amount of deflocculant c o n s i s t s of two p a r t s ; one p a r t for Ap > c r i t i c a l cake p r e s s u r e P^, which i s a s t r a i g h t l i n e p a r a l l e l to the (P-Ap) curve obtained for a PVC s l u r r y with 4.0 m i l l i e q / 1 . or more deflocculant, and one p a r t t h a t connects the other p a r t with the o r i g i n . By d i f f e r e n t i a t i n g the f i l t r a t i o n c o e f f i c i e n t

Pnc

' • —

versus Ap i t follows a t once t h a t the s p e c i f i c i-esistance i s a constant for cake pressures higher than the c r i t i c a l cake pressure

(see chapter I, page 16).

The same r e s u l t i s p l o t t e d in another way in graph V, where P/Ap i s p l o t t e d versus the deflocculant concentration for d i f f e r -ent p r e s s u r e differences. Prom t h i s figure i t i s c l e a r t h a t F/Ap i s p r a c t i c a l l y the same for each pressure difference a t a defloc-culant c o n c e n t r a t i o n > 3. 5 m i l l i e q / 1 . So a t t h i s d e f l o c c u l a n t concentration F i s p r o p o r t i o n a l to the f i l t r a t i o n p r e s s u r e dif-ference and so the cake i s incompressible. Also the ajuount of de-flocculant adsorbed on the PVC i s p l o t t e d an graph V as a func-tion of the deflocculant concentrafunc-tion. (When the deflocculant i s an a n i o n - a c t i v e agent i t can be t i t r a t e d with a c a t i o n - a c t i v e agent and methylene blue as an I n d i c a t o r ) .

As mentioned before, f i l t e r cakes are sometimes more or l e s s e l a s t i c , as a r e s u l t of which t h e cake expands when f i l t r a t i o n pressure i s diminished. V/e measured t h i s phenomenon, a l s o on PVC cakes, as follows:

CO to Deflocculant concentration in f i l t r a t e m i l l i e q . / l i t r e 0.25 0.47 0.7Ó 0.93 1.14 l.-,3 2.50 3.94 Concentration of adsorbed def] occulant in per cents of PVC (% wt) 0.11 0.21 0.31 0.41 0.48 0.56 0.67 0.75 F i l t r a t i o n pressure = 10 cm Hg F cm / s e c 3.6 3.5 3.2 2.5 1.85 1.5 1.25 1.00 F//5p cm . s e c / g 27.10"^ 26 24 18.8 13.9 11.3 9 . 4 7.5 F i l t r a t i o n pressure = 30 cm Hg F 6/ cm / s e c 7.8 7.2 6.9 5.0 4.6 3.3 3.1 3.0 F / ^ cm . s e c / g 19.5.10-^ 18.0 17.2 12.5 11.5 8.3 7.8 7.5 F i l t r a t i o n pressure = 50 cm Hg 1 F cm / s e c 10.3 6.8 5.0 F/ZSp cm . s e c / g 15.5.10"^ 9.8 7.5 Table II

Influence of deflocculant concentration on filtration factor F at filtration of PVC slurries (filter area = 5 cm'') Ratio of f i l t r a t i o n pressures (Ap)i/(/!p)2 2.0 10.3 Ratio of f i l t r a t i o n r a t e s 1.7 6.0 E l a s t i c i t y of PVC cake without deflocculant Ratio of f i l t r a t i o n pressures ( ^ ) l / ( Z ^ ) 2 2.5 4.1 7.7 Ratio of f i l t r a t i o n r a t e s 2.3 3.8 7.0 E l a s t i c i t y of PVC cake with defiocculant Table III

At a pressure difference l^^ the s l u r r y was f i l t e r e d and the f i l t r a t i o n r a t e measured as a function of f i l t r a t e volume. Half-way f i l t r a t i o n the pressure difference was diminished to Apjj and again the f i l t r a t i o n r a t e measured as a function of f i l t r a t e . 4 ^ was p l o t t e d versus V. At the moment when the pressure was changed, • ^ a l s o changed. By extrapolating, the f i l t r a t i o n r a t e (gn) j and

' M ^ I I ^^ ^^^- pressure differences / ^ j and / ^ j j and at the moment t h e p r e s s u r e was changed, can be a c c u r a t e l y determined. If the cake does not expand the r a t i o ^ j / A p j j must be equal to the r a t i o

However, when the cake expands the f i l t r a t i o n r a t e r a t i o i s smal-l e r than the pressure difference r a t i o , for when the cake expands i t s r e s i s t a n c e decreases. In graph VI both r a t i o s have been p l o t -ted against each other, once for a PVC slurry without defiocculant and once for a PVC s l u r r y with 3.5 m i l l i eq/1 deflocculant ( / ^ j always being 50 cm Hg, see t a b l e I I I ) . From t h i s p i c t u r e i t can be c l e a r l y seen t h a t the cake of t h e f i r s t s l u r r y i s r a t h e r e l a s t i c , while that of the other s l u r r y i s not e l a s t i c (the s l i g h t d e f l e c t i o n from the s t r a i g h t l i n e i s probably due to some com-p r e s s i b i l i t y of the f i l t e r c l o t h ) . That a non-comcom-pressible cake i s not e l a s t i c i s of course not s u r p r i s i n g .

The l a s t c h a r a c t e r i s t i c (P-Ap) curve t h a t w i l l be discussed here i s t h a t of a suspension of wax c r y s t a l s . These c r y s t a l s are so highly deformable, e s p e c i a l l y when the suspension temperature i s near the melting tempeiuture of the wax, t h a t above a c e r t a i n c r i t i c a l f i l t r a t i o n p r e s s u r e d i f f e r e n c e the f i l t r a t i o n f a c t o r F becomes independent on the p r e s s u r e difference. The (F-Ap) curve becomes a s t r a i g h t l i n e p a r a l l e l to the Ap axis (see graph I I ) .

D i f f e r e n t i a t i o n of the (F-Ap) curve gives, as already pointed out i n chapter I, the r e s i s t a n c e otp per g s o l i d s on 1 cm as a function of the cake p r e s s u r e P. As can be seen from graph VII, oip, increases very r a p i d l j a t a c r i t i c a l cake p r e s s u r e P[, equal to the above mentioned c r i t i c a l f i l t r a t i o n pressure difference *). This r e s u l t s in p r a c t i c a l l y t o t a l blocking of the lowest cake lay-e r . Howlay-evlay-er, thlay-erlay-e always rlay-emains a filtration r a t lay-e . This apparlay-ent paradox can be solved by supposing t h a t t h i s lowest layer i s very thin. Througli t h i s t h i n layer there i s then a pressure difference equal to the f i l t r a t i o n pressure difference Ap minus the c r i t i c a l

*) The a c c e n t in P'(. i s used h e r e t o d i s t i n g u i s h between t h i s c r i t -i c a l cake p r e s s u r e and t h a t for PVC cakes w -i t h o u t deflocculant.

p r e s s u r e PJ., so t h a t above t h i s t h i n l a y e r the cake pressure i s everywhere lower than the c r i t i c a l cake pressure P'^,

In graph VII we alfjo p l o t t e d fflp for the other s l u r r i e s we d i s -cussed h e r e . For a non-compressible cake, such as a quartz cake o r a PVC cake with deflocculant, «p i s of course a c o n s t a n t . For a PVC cake without defiocculant we find that ttp increases with the cake pressure and becomes equal to ctp for a PVC cake with defloc-culant a t higher cake p r e s s u r e . Por a limestone cake i t i s found t h a t Oip i n c r e a s e s l i n e a r l y with cake pressure at l e a s t a t those pressures a t which our determinations were c a r r i e d out.

C h a p t e r I I I

AN A P P A R A T U S F O R T H E M E A S U R E M E N T O F F I L T E R C A K E C H A R A C T E R I S T I C S

§ 1. D e s c r i p t i o n of the a p p a r a t u s

As pointed out in chapter I, r e l a t i v e l y l i t t l e work has been done so far in the f i e l d of cake s t r u c t u r e , CSiaracteristic mag-nitudes are here: specific r e s i s t a n c e , porosity, permeability and

i t s v a r i a t i o n s in the different cake l a y e r s . The r e l a t i o n s between these magnitudes and the cake thickness, f i l t r a t i o n pressure and pressure d i s t r i b u t i o n are also important,

To obtain a b e t t e r i n s i g h t in flltration, however, the knowledge of these magnitudes and t h e i r i n t e r r e l a t i o n i s necessary.

Therefore an apparatus was developed which enables us to meas-ure these magnitudes during f i l t r a t i o n . Prom i t s very natmeas-ure t h i s i s only possible with f i l t e r cakes of higher thickness than occur i n normal p r a c t i c e . U t i l i z i n g the theory of constant pressure d i s -t r i b u -t i o n in -t h e cake during f i l -t r a -t i o n a -t cons-tan-t p r e s s u r e we feel justified in drawing irore or l e s s generally valid conclusions from the measurements on these thick cakes.

The apparatus discussed h e r e i s designed so as t o be able t o f i l t e r up to a cake thickness of 12 cm,

Making reference to f i g , 4 a d e s c r i p t i o n will now be given of the a p p a r a t u s . I t s p r i n c i p a l p a r t s a r e : the f i l t e r proper (3), t h e supply v e s s e l for f i l t r a t i o n a t c o n s t a n t p r e s s u r e ( 1 ) , the suH)ly v e s s e l for f i l t r a t i o n a t c o n s t a n t r a t e (5), a manometer panel (2) and a buffer vessel (6). The whole apparatus i s made of b r a s s to avoid r u s t i n g . The buffer v e s s e l i s connected with the conFressed a i r l i n e of the l a b o r a t o r y v i a a valve. With the aid o f a r e d u c i n g valve (7) we are able to control the pressure in the suH)ly vessel (1), which p r e s s u r e can be read from the manometer (8a), The s l u r r y in t h i s vessel i s s t i r r e d a t a speed of 280 r , p , m, in order to keep the s l u r r y homogeneous ( s t i r r e r of s t a i n l e s s s t e e l ) . Content of the v e s s e l : 18 l i t r e s . At the top t h e r e i s the s t i r r i n g motor, the manometer and the tap funnel. At the side of the vessel there i s a gauge glass; a t the lower end a petcock and a supply pipe t o the f i l t e r . All connections of t h i s pipe, l i k e those of the o t h e r p i p e s , are welded t o avoid leakage as packing may dissolve i n the l i q u i d of t h e s l u r r y . The i n s i d e diameter of the p i p e s i s 1 cm. The s l u r r y i s recycled through pipe D leading from the f i l t e r v i a a c i r c u l a t i n g pump back to the vessel (1) to