c© 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim10.1002/14356007.b02 10

Filtration 1

Filtration

See also→ Solid – Liquid Separation, Introduction

Walter Gosele, Heidelberg, Federal Republic of Germany (Chaps. 1 – 7)

Christian Alt, Munchen, Federal Republic of Germany (Chaps. 8 – 11)

1. Terminology . . . . . . . . . . . . . . . 32. Filtration Models . . . . . . . . . . . . 42.1. Cake Filtration: Calculation of the

Pressure Drop . . . . . . . . . . . . . . 42.1.1. Definition of Filter Resistance and

Cake Permeability: The Darcy Equa-tion . . . . . . . . . . . . . . . . . . . . . 4

2.1.2. The “Cake Filter Equation” . . . . . . 52.1.3. Evaluation of Experiments with Linear

Diagrams . . . . . . . . . . . . . . . . . . 62.1.4. Compressible Cake Filtration . . . . . 82.2. Blocking Filtration and otherModes

of Filtration . . . . . . . . . . . . . . . . 102.3. Deep Bed Filtration . . . . . . . . . . . 112.4. Cross-Flow Filtration . . . . . . . . . 143. Washing of Filter Cakes . . . . . . . . 153.1. Basic Effects, Mass Balances . . . . . 153.2. Example of Experimental Results . 153.3. Test Procedures and Pitfalls . . . . . 173.4. “Intermediate” Deliquoring before

Cake Washing . . . . . . . . . . . . . . 184. Deliquoring of Filter Cakes . . . . . 184.1. Deliquoring by Gas Pressure . . . . 184.1.1. Equilibrium Saturation of Filter Cakes 194.1.2. Kinetics of Deliquoring by Gas Pres-

sure . . . . . . . . . . . . . . . . . . . . . 204.1.3. Approximate Solution for Coarse, In-

compressible Cakes . . . . . . . . . . . 214.1.4. Practical Scale-Up of Deliquoring by

Gas Pressure . . . . . . . . . . . . . . . . 22

4.1.5. Shrinking and Cracks in Filter Cakes 234.2. Deliquoring by Expression . . . . . . 235. Optimal Cycle Time . . . . . . . . . . 246. Understanding the Filter Resistance 266.1. The Equation of Carman and

Kozeny . . . . . . . . . . . . . . . . . . . 266.2. Interparticle Forces, DLVO Theory 276.3. Mathematical Simulation of Cake

Formation . . . . . . . . . . . . . . . . . 287. Solving Filtration Problems in

Small-Scale Tests . . . . . . . . . . . . 297.1. Laboratory Tests . . . . . . . . . . . . 297.2. Handling of “Unfilterable” Suspen-

sion . . . . . . . . . . . . . . . . . . . . . 308. Filtration Equipment . . . . . . . . . 328.1. Bag Filters . . . . . . . . . . . . . . . . 338.2. Belt Filters . . . . . . . . . . . . . . . . 338.3. Candle Filters . . . . . . . . . . . . . . 388.4. Deep-Bed Filters . . . . . . . . . . . . . 408.5. Disk Filters . . . . . . . . . . . . . . . . 428.6. Drum Filters . . . . . . . . . . . . . . . 438.7. Leaf and Plate Filters . . . . . . . . . 508.8. Nutsche (Pan) Filters . . . . . . . . . . 538.9. Pressure Plate Filters . . . . . . . . . 548.10. Tubular Filters . . . . . . . . . . . . . . 598.11. Special Filter Types . . . . . . . . . . . 609. Filter Selection . . . . . . . . . . . . . . 6210. Filter Media . . . . . . . . . . . . . . . 6311. Filter Aids . . . . . . . . . . . . . . . . . 6512. References . . . . . . . . . . . . . . . . . 66

Symbols

a intercept in Figure 5, s/mLA cross-sectional area, filter area, m2

b slope in Figure 5, s/mLB creep constantC creep constantdpore capillary diameter, mdS Sauter mean diameter of particles, mE electrostatic potential at the solids sur-

face, VH cake thickness, mJ Boucher’s filterability index, m−3

I ionic strength, mol/LKH proportionality volumeof cake/volumeof

filtrate, m3/m3

Km proportionality mass of cake/volume offiltrate, kg/m3

KN proportionality number of parti-cles/volume of filtrate, m−3

k permeability = 1/αh, m2

L distance from the inlet face of the filterbed, m

m mass of dry filter cake, kgmi molar concentration of ion “i”, mol/L

2 Filtration

N number of pores in the filter mediumn compressibility index∆P dimensionless pressure differencepc capillary pressure, Papce capillary entry pressure, Papci capillary suction pressure, PapL pressure in the liquid, PapS compressive stress on the solids, Paq exponent describing blocking behaviorr distance from the solids surface, mrD Debye length, mS saturation (volume of liquid/volume of

pores)SR reduced saturationS∞ irreducible saturationtreg regeneration time for cleaning and

preparing a run, sUc consolidation rateV volume of filtrate, m3

V volumetric flow rate, m3/hzi valency of ion “i”αH cake resistance relative to cake thickness,

m−2

αm cake resistance relative to dry mass, m/kgβ resistance of filter medium, m−1

ε porosity = pore volume/total volumeη viscosity, Ns/m2

Θ dimensionless timeλ filter coefficient of deep bed filters, m−1

ζ surface potential, V

Indices

av averagee end of filtrationH related to cake thickness (height)L liquidloc localm related to cake massN numberS solidw wash liquorpore pore (volume)

1. Terminology

Filtration is the separation of solid particles orliquid ones (droplets) from liquids and gaseswith the help of a filter medium also called aseptum, which is essentially permeable to only

the fluid phase of themixture being separated. Inearlier times, this process was carried out withfelts, and the word “filter” has a common deriva-tion with “felt”.

Often however, purification of a liquid or gasis called filtration even when no semipermeablemedium is involved (as in electrokinetic filtra-tion). This chapter deals only with the filtrationof solid – liquid mixtures (suspension, slurries,sludges). For the treatment of gases by filtration,→Dust Separation.

The liquid more or less thoroughly separatedfrom the solids is called the filtrate, effluent, per-meate or, more rarely, clean water. As in otherseparation processes, the separation of phases isnever complete: Liquid adheres to the separatedsolids (cake with residual moisture) and the fil-trate often contains some solids (solids contentin the filtrate or turbidity).

The purpose of filtration may be clarificationof the liquid or solids recovery. In clarificationthe liquid is typically the valuable product andthe solids are of minor quantity and are oftendiscarded without further treatment. If howeverthe solids are to be recovered, they very oftenhave to be washed, deliquored and dried (seeFig. 1). In this article, washingmeans the clean-ing of a product (filter cake) and it is distin-guished from cleaning parts of the filter itself,which will be called rinsing (e.g., rinsing a filterscreen or a filter cloth by jets of water). A fur-ther distinction is to be made between washingand extraction or leaching. Washing eliminatesliquid contaminants from the pores between theparticles of a filter cake.Extraction recovers sol-uble matter from the solid particles themselves(→Liquid – Solid Extraction). The term dryingmeans thermal drying, while the elimination ofliquid from the filter cake by mechanical forcesis called deliquoring or dewatering, e.g., deli-quoring by gas pressure or by expression.

Filtration is effected by application of vac-uum, pressure, or of centrifugal force (seeFig. 2). Vacuum filtration requires a vacuumpump.The pumpevacuates the gas fromafiltratereceiver, where the filtrate is separated from thegas. The filtrate is drained either by a barometricleg of at least 8 to 10m or by a pump that is ableto “run on snore” (i.e. with a deficiency of feedliquid so that it tends to draw in air). Pressurefiltration typically only requires a pump for de-livering of the suspension and the filter is placed

Filtration 3

Figure 1. Solids processing chain

within a pressure vessel, hence less easily acces-sible. Centrifugal filtration is done in perforatedcentrifuge rotors (→Centrifuges, Filtering).

Figure 2. Driving forces in filtration

Vacuum filters have the great advantage thatthe cake is freely accessible. This facilitates au-tomatic cake handling. However, vacuum filterscannot handle hot liquids, or solvents with highvapor pressure. The pressure difference acrossvacuum filters is very limited, and the resid-ual moisture of the filter cake is higher thanwith pressure filters. Pressure filters in turn arepreferred when the product must be kept in aclosed system for safety reasons, or if the resid-ual moisture content is important. The handlingof the filter cake is obviously more difficult ina pressure filter. Filtration by centrifugal forcerequires more technical equipment, but as a gen-eral rule it yields solidswith lower residualmois-ture (→Centrifuges, Filtering).

Variousmodels can describe the physical pro-cess of filtration. This chapter concentrates onfour idealized filtration models depicted in Fig-ure 3.

– Cake filtration is the most frequently usedmodel. Here it is assumed that the solids aredeposited on a filter medium as a homoge-neous porous layer with a constant perme-ability. Thus, if the flow rate dV /dt is con-stant, the pressure drop will increase lin-

early, proportional to the quantity of soliddeposited. This model can be applied par-ticularly well for all hard, particulate solids.

– Blocking filtration: The pressure drop iscaused by solid particles blocking pores.Soft, gelatinous particles retained by a sieveexhibit such a behavior. If the flow rate dV /dtis constant, the pressure drop increases expo-nentially with the quantity filtered, the num-ber of open pores asymptotically approach-ing zero. The pores may belong to a filtermedium (screen or filter layer) or it may bepores within a filter cake of coarse particles,which are blocked by migrating fine parti-cles.

– Deep bed or depth filtration: Solid particlesare retained in a deep filter layer. This takesplace for example in sand filters for clarifi-cation of drinking water, which retain evencolloidal particles. The typical effect of deepbed filtration is adhesion of solids to thegrains of the filter layer, comparable to char-coal adsorption. Only rather big particles areretained by the screening effect. When thefilter bed has been saturated with solids, thesolids concentration in the filtrate leaving thebed progressively approaches that of the in-coming suspension.

– Cross-flow filtration: In cross-flow filtrationthe suspension flows with high speed tan-gentially to the filter surface, preventing theformation of a cake. Only a small flow of liq-uid passes through the filter medium. A cer-tain layer of solids accumulates in the bound-ary layer on the filter surface, and reducesthe flow of filtrate. After an initial period, adynamic equilibrium is established betweenconvective transport of solids to the filter sur-face and removal of solids by turbulence andby diffusion.

4 Filtration

Figure 3. Filtration models

Surface filtration is the antonym to depth fil-tration. The solids are retained on the surface ofa filter medium. Generally the models of cakefiltration or of blocking filtration can be applied.Screening designates a classification process,

which retains the particles below a certain sizeand lets pass the smaller ones (→Screening).Often the term screening filtration is also usedto designate a surface filtration with a screenas a filter medium. Its mode of action resem-bles screening (or straining) as long as the filtermedium is clean, but it is clearly a cake filtrationas soon as a layer of solids has formed.

2. Filtration Models

2.1. Cake Filtration: Calculation of thePressure Drop

2.1.1. Definition of Filter Resistance andCake Permeability: The Darcy Equation

The resistance to flow of a filter cake can be de-scribed by Darcy’s law [1] (see Fig. 4). Considera liquid flowing through a filter cake (or a streamof water percolating through soil as consideredby Darcy). The pressure drop ∆p of this flow isproportional to:

1) The flow rate per unit area V /A

2) The cake thickness H3) the viscosity η of the liquid4) A constant αH describing the “specific filter

resistance” of the cake:

∆p1 =

(V

A

)·H ·η ·αH (1)

TheSI-units are[Pa =

(m3/sm2

)·m·Pa·s·m−2

]

Theunit ofαHmust therefore bem−2 in orderto satisfy the Darcy equation (1). The reciprocalof the filter resistance αH is also called perme-ability k of the filter cake:

k =1αH

[m2] (2)

Sometimes it is more convenient to define cakethickness in terms of solid mass per unit area(unit kg/m2). This leads to a slightly differentdefinition of filter resistance, the factors being:

1) The flow rate per unit area V /A2) The cake thickness m/A3) The viscosity η of the liquid4) A constant αm with the unit m/kg describing

the resistance of the cake.

Then the following expression is obtained in-stead of Equation (1)

∆p1 =

(V

A

)·(mA

)·η ·αm (3)

Filtration 5

For practical reasons the viscosity η is very of-ten notmeasured separately. Then it is legitimateto include it in a term αHη (unit mPa · s/m2) orαmη (unit mPa · s ·m/kg), respectively.

Using this latter term αHη or αmη filter re-sistances lie between 1011mPa · s/m2 (filteringvery rapidly) and 1016mPa · s/m2 (nearly unfil-terable), or between 108 and 1013mPa · s ·m/kg,respectively.

Figure 4. Definition of filter resistanceηαH =Cake thickness H related filter resistance;ηαm =Solid mass related filter resistance

2.1.2. The “Cake Filter Equation”

The pressure drop in a filter is composed of apressure drop ∆p1 across the cake according toEquation (1) and a pressure drop∆p2 across thefilter medium, which can be written as:

∆p2 = β ·η ·(V

A

)(4)

where b (unit m−1) is the resistance of the filtermedium.

The total pressure drop is therefore:

∆p = ∆p1 + ∆p2 = αHη ·H · VA

+ βηV

A(5)

or

∆p = ∆p1 + ∆p2 = αmη ·m·VA2

+ βηV

A(6)

If the suspension is homogeneously mixed, thecake height H (or m/A) will be proportional tothe quantity of filtrate. The concentration is de-scribed by a factor K :

KH =H ·AV

(7)

or

Km =m

V(8)

this gives

∆p =αHηKH

A2·V · dV

dt+βη

A+

dVdt

(9)

or

∆p =αmηKm

A2·V · dV

dt+βη

A+

dVdt

(10)

Equations (9) and (10) are identical under thegeneralizationαH ·KH =αm ·Km. Neverthelessthe distinction between both equations is usefulfor clarity.

The differential Equations (9) and (10) canbe integrated either for constant flow rate or forconstant pressure. Integration for constant flowrate dV /dt = const gives the trivial solution:

∆p =η ·VA

·(αHKH

A·V + β

)(11)

or

∆p =η ·VA

·(αmKm

A·V + β

)(12)

For ∆p= const. the integration yields:

dt =αηK

A2 ·∆p ·V ·dV +βη

A·∆p ·dV (13)

t =αHηKH

2A2 ·∆p ·V 2 +βη

A·∆p ·V (14)

or

t =αmηKm

2A2 ·∆p ·V 2 +βη

A·∆p ·V (15)

2.1.3. Evaluation of Experiments withLinear Diagrams

Linear Diagram in the Differential Form.It is often very helpful to plot the instantaneousresistance to flow as a function of the quantityfiltered. The resistance is characterized by thepressure drop ∆p related to the instantaneousflow rate dV /dt. Using Equation (5) or (6) thiscan be written as:

dtdV

=αHηKH

∆pA2·V +

βη

∆pA

=αmηKm

∆pA2·V +

βη

∆pA= b·V + a (16)

6 Filtration

As shown in Figure 5 left diagram [2], inter-polation gives a straight line with slope b andintercept a. The intercept

a =βη

∆p

represents the resistance at the very first mo-ment of filtration, before a cake is formed, hencethe resistance of the filter medium including theboundary layer to the cake.

The slope b contains the filter resistance αaccording to

b = slope =∆(∆p· dt

dV

)∆V

=αηK

A2(17)

Inserting KH or Km respectively, gives

αHη =∆(∆p· dt

dV

)∆V

· A2

KH=

∆(∆p· dt

dV

)∆V

·A·VH

= ∆(∆p· dt

dV

)e

· AHe

(18)

and

αmη =∆(∆p· dt

dV

)∆V

· A2

Km=

∆(∆p· dt

dV

)∆V

·A2 ·Vm

= ∆(∆p· dt

dV

)e

· A2

me(19)

Linear Diagram in Integrated Form. An-other approach starts from the integrated filterEquations (14) or (15). The experimental resultsare plotted in the form of

t

V= f (V )

If the pressure is constant during the experiment,a straight line should be obtained

t

V=αmηKm

2A2 ·∆p ·V +βη

A·∆p=αHηKH

2A2 ·∆p ·V +βη

A·∆p =b

2·V + a (20)

This kind of plot is still very popular in prac-tice because the evaluation is often easier thanwith Equation (16). Experimental values mea-sured with a bucket and a stopwatch can be in-serted directly into Equation (20), while for adifferential diagram they have to be convertedinto momentary flow rates dV /dt.

On the other hand Equation (20) is correctonly for ∆p= const. Furthermore, the resultingdiagram shows less clearly the deviations fromlinearity than a diagram based on instantaneousflow rates. If for example a cake stops growingand keeps a constant resistance this gives a welldiscernible plateau in a differential diagram, butonly a gradual hyperbolic bend in the integrateddiagram.

Example. The interpolationof the test resultsshown in Figure 5 leads to the intercept a and theslope b

a = 3.6s/mL = 3.6 × 106s/m3 (21)

and

b =28s/mL150mL

= 1.87·10−11s/m6 (22)

The following parameters are known:

Filtration pressure p= 1 bar = 105 N/m2

Filter area A= 20 cm2 = 20× 10−4m2

Viscosity η = 0.001 Pa · s = 10−3 Ns/m2

Cake height He = 37mmCake mass me = 24.3 gVolume of filtrate V e = 154 cm3

Solids in suspension

KH =A·He

Ve=

20·10−4 ·0.037154·10−6

= 0.481 (23)

or

Km =me

Ve=

24.3·10−3

154·10−6· kgm3

= 158kgm3

(24)

This gives for the filter medium resistance

β = α· ∆p·Aη

= 3.6·106 · 105 ·20·10−4

103m−1

= 7.2·1011m−1 (25)

From Equations (18) or (19) follows the cakefilter resistance

αH = b·A2 ·∆pKHη

= 0.187·1011 · 400·10−8 ·1050.481·10−3

m−2

= 1.56·1014m−2 (26)

αm = b·A2 ·∆pKmη

= 0.187·1011 · 400·10−8 ·105158·10−3

m−2

= 4.73·1011 mkg

(27)

Filtration 7

Figure 5. Linear plots according to Eqs. (8) and (11) [41]

Deviations from Linearity. Experimentaldata very often differ from the linear charac-teristic shown in diagrams “I” or “II” of Fig-ure 5. The kind of deviation indicates the natureof secondary effects (see Fig. 6):

– A: Theoretical linear curve without sec-ondary effect.

– B: Some solids have settled before the filtra-tion started, apparently increasing the resis-tance of the filter medium.

– C: At the beginning of filtration the filtratehas been turbid. The solids loss diminishesthe amount of cake, apparently indicating anegative medium resistance. (When no tur-bidity is found in the filtrate, this curve mayindicate that solids accumulate inside the fil-ter medium, blocking it in the long run!).Similar curves may be observed when thesolids float and clear liquid is filtered in thebeginning.

– D: The solids settle out completely, increas-ing the speed of cake growth. At the end offiltration clear liquid flows through the cakeof constant resistance.

– E: Only coarse particles settle. After sometime only the remaining fines are filtered andthe resistance increases progressively.

– F: Fine particles trickle through the cakeand block the pores of the cake or of thefilter medium. The process can perhaps bedescribed as a blocking filtration (see Sec-tion 2.2).

– Further causes of deviations might be:

Determination of the beginning or the endpoint of filtration may not be correct. Theend point is particularly difficult to deter-mine if there is no sight glass in the filter.It is therefore common practice to neglectsome points at the end of the measure-ment.Unusual properties of the suspensionlike foam bubbles or oil droplets, non-Newtonian rheology of the liquid or non-isometric, plate-like particles with specialorientation can produce a great variety ofeffects.The sediment may be so voluminous thatit fills the whole suspension. The processthen resembles rather an expression thana filtration (Section 4.2).Freshly precipitated solids sometimescontinue to agglomerate or to “ripen” dur-ing filtration, changing their effective par-ticle size.

2.1.4. Compressible Cake Filtration

Most filter cakes are compressible, whichmeansthat their resistance increaseswith growing pres-sure. An x-fold increase in filtration pressuretherefore normally gives rise to a less than x-fold increase in flow rate. The compression ofthe cake is caused by the compressive stress pson the solids which is caused by the drag of theflowing liquid (see Fig. 7). The loss in liquid

8 Filtration

Figure 6. Typical deviations from linearity [41]A) Differential plot according to Eq. (16); B) Integral plot according to Eq. (20)

pressure pL translates into solids pressure pS,the sum of both being constant:

∂pS = −∂pL (28)

pS + pL = p0 (29)

Figure 7. Hydraulic pressure pL and solids pressure pS asfunction of cake height. Curve (a) represents a more com-pressible cake than curve (b)

The local filter resistance αloc in the cake isa function of the local compressive stress pS andit is therefore low at the surface of the cake andhigh near the interface with the filter medium.This αloc = f (pS) can be measured in the Com-pression Permeability cell (CP cell) described inChapter 7, where a sample of the cake is subjectto a known compressive stress.

However, only the average resistance αav ofa filter cake, all layers combined, is important forpractical scale-up purposes. It can be calculatedfrom αloc measured in the CP-cell [3]

αav =∆p

p∫0

dpαloc

(30)

Normally however it is much easier to mea-sure αav directly with filtration experiments ina pressure filter as described in Section 7.1. Theuneven distribution of local porosity and filterresistance is then ignored.

The dependence of filter resistance αav orαloc on pressure can be approximated over a lim-ited pressure range by

α = α0 ·(

pS

unitpressure

)n

(31)

where α0 is the resistance at unit pressure dropand n is a compressibility index (equal to zerofor incompressible cakes). Both parameters canbe determined easily from a logarithmic plotα = f (pS), where the slope indicates the com-pressibility factor n. Introducing αloc accordingto this approximation into Equation (19), it canbe shown that for 0< n< 1

nav = nloc (32)

α0,av = (1 − n) ·α0,loc (33)

Thus the approximation Equation (31) has theadvantage that it applies to both the local and theaverage resistance. However, such an approxi-mation is valid only for a limited range of pres-sures and Equations (32) and (33) are restrictedto 0< n< 1.

Filtration 9

Tiller and coworkers [4] give an integrationof the filter equation also for n> 1. Accordingto their equations the flow rate quickly reachesa constant value with increasing pressure. Forpractical purposes it can be approximated thatsuch “supercompactible” filter cakes with n> 1(e.g., a great number of waste water sludges)yield the same flow rate independently of thepressure applied: increasing pressure only in-creases the compressed layer adjacent to the fil-ter cloth. (The hypothetical cake which yieldsthe highest flow at an “optimal pressure” andless flow at higher pressures apparently does notexist. In practical application, however, the out-put of a filtration may be best with moderatepressure, since this avoids excessive blocking ofthe filter medium).

For practical purposes Equations (31) – (33)are often ignored and compressible cakes aretreated with the same equations as incompress-ible cakes, provided α is defined as average spe-cific cake resistance under the conditions of op-eration.

Concerning deliquoring of compressiblecakes, it is important to know that the porosityis unevenly distributed after filtration. The filterresistance often is concentrated in a thin, com-pressed layer facing the filter medium, the restof the cake being very porous andwet. Deliquor-ing by expression (see Section 4.2) will then bevery effective, even at moderate pressures, sinceit acts also on the upper layer of the cake.

2.2. Blocking Filtration and otherModes of Filtration

According to the idealized idea of blocking fil-tration, every particle in the suspension is re-tained on the filter medium and blocks one pore.The remaining number of open pores is thengiven by the equation

N (t) = N0 (1 − KN ·VL) (34)

where N0 is the number of pores in the cleanfilter medium, N(t) is the remaining numberof open pores and KN (m−3) is the concentra-tion of particles by number in the suspension.At constant pressure drop the volume of filtrateV (t)∆p = const will follow the equation [5]

V (t) =1KN

·[1 − exp

(−KN ·V0 ·t

)](35)

with V0 (m3/s) being the flow rate at the startof filtration with a clean filter medium.

In real filtration processes not every particlein the suspension will block a pore of the fil-ter medium. Some particles will be retained byadhesion to the walls of a pore without block-ing it totally; others will pass through the filtermedium without being retained at all. Differentformulae (or “filtration laws”) exist to describesuch moderate blocking. A generalized model isbased on the equations

d2 t

dV 2= const·

(dtdV

)q

(36)

for constant pressure filtration and

d (∆p)dV

= const· (∆p)q (37)

for constant rate filtration.The exponent q in this equation varies bet-

ween 0 and 2 and describes the “blockingspeed”:

q = 0 cake filtration, slow blockingq = 1 so-called intermediate filtrationq = 3/2 so-called standard blocking filtrationq = 2 complete blocking.

A summary of the corresponding equationsfor flow rates and filtrate quantities is givenin [6], [7]. Figure 8 visualizes some examples:Surface straining represents the classical exam-ple of complete blocking (q = 2), but also depthstraining follows the same characteristic. Nor-mal depth filtration in contrast (with particlesmuch smaller than the filter pores) leads to pres-sure drop by diminishing pore size and canbe described by the standard blocking equation(q = 3/2).

In most filtrations it is highly probable thatmore than one filtration mode occurs. Cake fil-tration for example often is preceded by an ini-tial period before cake build-up which can bedescribed as standard blocking. This period ischaracterized by depth filtration (particles pen-etrating into the filter medium) and/or by finespassing through the filter medium (creating ini-tial turbidity of the filtrate). For scientific inves-tigations itmay then be helpful to identify the fil-trationmechanismmore precisely by parameter-fitting the experimental data and quantifying theabove-mentioned “blocking speed”.

10 Filtration

Figure 8. Three possible modes of filtration: Surface strain-ing and depth straining are described as “complete block-ing” (q = 2). Depth filtration of particles much smallerthan the pore size is best described as “standard blocking”(q = 3/2) [6]

Simplified Evaluation of ExperimentalData. A very pragmatic approach is often usedto describe the mode of filtration. The pressuredrop at constant flow rate is depicted on a semi-logarithmic scale as a function of the volume fil-tered. Normally the values can be approximatedby a straight line according to [8]

log(p

p0

)= −J ·VL (38)

For the flow rate at constant pressure drop thesame approximation holds

log

(V

V0

)= −J ·VL (39)

Here p0 is the initial pressure drop of the cleanfilter; and the gradient J , which represents some-thing like the above-mentioned blocking speed,

is “Boucher’s filterability index”. If J = 1 Equa-tion (38) and (39) are identical to an “intermedi-ate filtration” with q = J = 1. For other values ofJ however the physical meaning of J is unclear.For scientific purposes this approach is there-fore not sowell accepted. For practical purposes,however, it is very useful.

2.3. Deep Bed Filtration [9], [10]

In deep bed filtration (as opposed to cake filtra-tion and cross-flow filtration), the solid particlesare separated mainly by deposition within thepores of the filter medium. The filter mediummay consist of

– a 0.5 – 3m layer of coarse grains (e.g., sand0.3 – 5mm) or

– a layer of a few centimeters of fibers (e.g.,wound or resin bonded cartridge filters) or

– sheets of a few mm thickness (e.g., made ofcellulose).

– a layer of granular filter aid (e.g., precoatlayer)

All these filter elements have pores that arelarger than the particles to be retained. The par-ticles stick in the pores by adhesion and theiraccumulation weakens the filtering action andincreases the pressure drop, so that the filtermustbe cleaned or replaced periodically. This is whydeep bed filtration should be used not to recoversolids from a suspension such as cake filtration,but instead to produce a very clean effluent fromsuspensions with low solids loading (typically< 0.1 g/L) and with very fine particles. Depend-ing on the particle size, the prevailing effects ofretention are summarized in Figure 9:

1) Particles larger than the pores are trappedmechanically. This is typically true for par-ticles � 10µm.

2) Particles 1 – 10µm in diameter hit the solidsurfacemainly due to inertia effects and stickthere due to surface forces.

3) Particles < 0.1µm reach the solid surfacemainly because of diffusion and again theystick there due to surface forces.

In the range between 0.1 and 1µm the effectsof both inertia and diffusion are small and amin-imum in transport and hence in the effectivenessof deep bed filters is observed.

Filtration 11

Figure 9. Retention mechanisms in a deep bed filtera) Particles > 10µm are retained by mechanical intercep-tion; b) Particles of ca. 1µm size are subject to inertial im-pact + adhesion; c) Particles <1µm follow mainly Brown-ian diffusion + adhesion

Thus the transport of particles to the solidsurface is rather well explained and can be de-scribed mathematically. The mechanism of ad-hesion to the filter grains however and the re-sulting “sticking probability” is less well under-stood. (Some aspects will be discussed in Sec-tion 6.2). Consequently the clarification effectmust be summarized in an empirical “filter co-efficient” λ describing the local decrease in con-centration of the suspension flowing through thebed:

− ∂C∂L

= λC (40)

where c is the concentration of the suspensionand L is the distance from the inlet face of thefilter. For uniform conditions, this differentialequation can be integrated:

c = c0 ·exp (−λ0 ·L) (41)

here λ0 is the initial filter coefficient of a clean,homogeneous filter bed. As soon as the bed isloaded with solids, its efficiency will diminishand that is why the solution of the differen-tial equation becomes rather difficult. Differentmodels exist to describe the process, but theyare rarely used for practical purposes. To find asuitable filter medium in a deep bed filter whichshows good retention efficiency over a long cy-cle time, laboratory tests over a realistic cycletime have to be carried out with filter layers ofrealistic depth.

The pressure drop in a deep bed filter can beinterpreted as an effect of two different phenom-ena of blocking filtration:

1) The filter media exhibit a resistance to flow,which is increased by the solids deposit in

the pores. The quantity of deposit is gener-ally small compared to the pore volume, andthe additional pressure loss per unit depthcan be described as proportional to the localspecific deposit. For constant solids concen-tration at the inlet and constant retention theincrease in this pressure drop with time istherefore approximately constant.

2) In addition there is often a pressure drop dueto deposits on the surface of the filter bed.This is a typical blocking filtration and canbe described by Boucher’s law (Eqs. 38 and39).

The total pressure drop of a deep bed filter atconstant flow rate can then be approximated byan equation of the type

p (t) = const1 ·t + const2 ·eJ ·t (42)

The pressure drop should be measured in atest filter with a vertical height close to thatof the full-scale unit (Fig. 10A) [11]. For thecase that the driving force is gravity, the pres-sure profile is shown in Figure 10B. In the staticequilibrium, at flow zero, 1m of pressure headis gained for every meter of depth. The down-streamconsumersmay then drawa constant flowrate. When flow has started, the pressure dropwithin the media increases linearly with depth.As solids are deposited in the pores, the localpressure loss will increase in the upper layersand the pressure line becomes distorted. Whenthe pressure line touches the atmospheric pres-sure value, the required flow cannot be main-tained and the filter should be cleaned.

Cleaning of Deep Bed Filters. Sand filterscan be cleaned by backflushing. The flow is re-versed to wash off deposited solids and flushthem, e.g., to a wastewater station. Often airscour is used to increase the turbulence and re-duce the amount of water necessary for fluidiza-tion. A typical set of data of a sand filter forcleaning of water could be [12]:

Medium depth 1mMedium size 0.5 – 1mm (as uniform as possible)Flow rate duringfiltration

5 – 10m3 m−2 h−1

Flow rate air scour 60m3 m−2 h−1 for 10minFlow rate waterbackflow

15 – 30m3 m−2 h−1 for 3 – 8min after airscour

12 Filtration

Figure 10. A) Laboratory test equipment for sand filtersB) Pressure profiles in test filter [11]

During backflow the sand grains are classi-fied, the smallest ones are entrained to the top,the coarse ones sink to the bottom of the filterbed. This effect is undesired, since it leads topremature blocking of the top layer. Thereforeit is important to use sand with grain sizes asuniform as possible.

Sizing of a Deep Bed Filter. The sizing of adeep bed filter consists of the following steps:

– Preselection of the filter material by com-parative laboratory tests with small layers ofdifferentmaterials under standard conditionsand with the filtrate quality as a criterion.

– Selection of the right grain size in tests witha filter column of 1m height and a realisticflow rate and pressure drop. If necessary thegrain size must be adapted so that the bedis saturated (the filtrate gets turbid) at thesame time as the maximum pressure dropis reached. If the maximum pressure dropis reached first, the grains should be coarserand vice versa.

Special Variations of Deep Bed Filters. Asmentioned above the sand grains are classifiedduring backflush and the uppermost layer ismost efficient in collecting and becomes cloggedrapidly by captured solids. This disadvantage isdiminished when a second layer of coarse mate-rial with lower specific weight is added on top ofthe sand layer. During backflow these low den-sity grains collect at the bed surface and forma coarse layer able to retain a great quantity ofdirt (so-called multimedia filters or dual mediafilters, e.g., with a layer of anthracite particles1 – 2mm in size on top of a main layer of sandgrains 0.5 – 1mm in size.)

Other designs of sand filters (especially inthe United States) convert the disadvantage ofclassification into an advantage by operating inthe upflow mode with filtering and backflush-ing from below. This offers the advantage thatlarge quantities of incoming dirt are retainedin the lower layer of sand, which contains thecoarser grains and larger pores. These upflowfilters however need special safeguards againstbreakthrough of dirt when the pressure drop be-comes high.

Filtration 13

In order to increase the retention capacity ina given volume, it has also been proposed touse porous grains instead of sand grains. Smallpieces of polymeric foam have indeed this effect[13]. Cleaning by simple backflush is, however,not possiblewith thismaterial, itmust be cleanedby backflush combined with compression, andthis method has therefore not yet found practicalapplication.

2.4. Cross-Flow Filtration

In cross-flowfiltration the deposition of particleson the filter membrane is prevented by a strongflow parallel to the filter surface. This so calledcross-flow is achieved inmost cases by pumpingthe suspension through bundles of membranetubes (see Section 8.10, Figs. 77, 78). Alterna-tively the cross-flow is achieved by rotating in-serts (Section 8.9, Fig. 76). The elimination of acake enables to filter very fine particles, whichotherwise would form a cake with prohibitivelyhigh resistance. Even submicron, nonparticulatematter can be retained by semipermeable mem-branes according to this principle. In this chap-ter a short overview will only be given, coveringboth the filtration of particles and the separationof non-particulate matter. For more details see→Membranes and Membrane Separation. De-pending on the size of the “particles” retained, adistinction is made between microfiltration, ul-trafiltration, nanofiltration, and reverse osmosis.Typical parameters of cross-flow filtration aresummarized in Table 1.

Microfiltration retains solid particles (seeSection 8.11). According to the usual definitionof “solid particles” these are visible in the mi-croscope, hence> 0.1µm in size. In steady-statecross-flow filtration these particles are conveyedonto the membrane by convection due to the fil-trate flowand transported away from it by hydro-dynamic lift forces due to the parallel shear flow(forces FY and FL in Fig. 11). For particles be-low a certain size the lift force becomes smallerthan the convection, FL <FY, and they are de-posited on the membrane [14]. After depositionthey are retained by van der Waals’ adhesionforcesFA andnot easily swept awayeven if thereis no filtrate flow (irreversible cake formation).Steady state microfiltration therefore requires a

parallel flow strong enough to flush off the finestfraction of particles in the suspension. (In mostpractical applications colloidal particles are alsopresent and they are transported according to themechanisms of ultrafiltration.)

Figure 11. Forces and transport effects onto a particle incross-flow filtrationBr =Brownian motion; FA = adhesion to the membrane;FD = drag from the cross-flow; FF = friction force;FL = hydrodynamic lift force; FY = drag from then filtrateflow

Ultrafiltration retains colloidal particles ormacromolecules. The cut-off sizes are ca.< 0.1µm. Such particles are subject to Brow-nian diffusion (Br in Fig. 11) and only weaklyinfluenced by the hydrodynamic lift force [15].The smaller these particles are, themore they aretransported away from the filter medium by dif-fusion. This is why in ultrafiltration the smallerparticles are preferably swept away and the big-ger ones are collected on the membrane (con-trary tomicrofiltration). The cut-off size of an ul-trafiltration is usually defined as the molar mass(in g/mol) of a test suspension (generally proteinor dextran molecules of defined molar mass inthe range of 103 – 105 g/mol). In practical appli-cation the cut-off size depends not only on thepore size of the membrane, but to a large degreeon a “gel” layer on the membrane consisting ofretained colloids.

Nanofiltration is a relatively new techniquecombining features of ultrafiltration and reverseosmosis with a high selectivity. Its name is de-rived from its approximate cut-off size of somenanometers or more exactly molar masses of200 – 1000 g/mol. This is achieved with specialnanofiltration membranes which still have poresof a defined size, but their retention depends

14 Filtration

on the electrostatic charge of the molecules tobe separated (bivalent anions are typically re-tained).

Reverse osmosis retains molecules or ionsusing selective membranes without pores. Cer-tain molecules permeate through the membranebecause they are soluble in the membrane mate-rial.Othermolecules are not (or less) soluble andare retained (or concentrated) on the upstreamside of the membrane. A particular feature ofreverse osmosis is the high pressure required toovercome the osmotic pressure of the retainedmolecules. An important application is desalina-tion of seawater. In the food industry it is appliedto concentrate juices at low temperatures.

3. Washing of Filter Cakes

3.1. Basic Effects, Mass Balances

The purpose of washing is to remove the motherliquor left behind in the cake after filtrationwhenthis liquid is regarded as contaminant or must berecovered as a valuable component. Wash liquidflows through the filter cake and displaces themother liquor, a mixture of both liquids leavingthe cake as a wash filtrate. The concentration inthis filtrate may help to explain some basic facts.In Figure 12 this concentration is reported as afunction of the filtrate volume V . In the begin-ning it is c0 = 1 (concentration of contaminantin the mother liquor). Four characteristic curvesare reported:Curve 1 represents the idealized piston flow.

The pore volume Vpore is ideally displaced andleaves the cake with the concentration c0 = 1. Inthis idealized case thewashingwould befinishedwith a quantity of wash liquid Vw equal the porevolume or a

“washratio′′ =Vw

Vpore= 1 (43)

Curve 2 takes into account that even in an ide-alized cake the flow passes through streamlineswith different lengths and speeds. Because ofthis “axial dispersion” the requiredwash volumeis several times the pore volume or

“washratio′′ =Vw

Vpore> 1 (44)

Curve 3 is still more realistic; taking into ac-count that a filter cake contains stagnant zonesor dead-end pores, that are not reached by theflow. They deliver their contaminant content bydiffusion to the effluent. Diffusion is an asymp-totic process and depends on the time elapsed,not on the quantity of liquid. This curve is typ-ical for most washing processes. The first partdepends on the “wash ratio”, the end however isan asymptotic process depending on time.

When the curves 1, 2 and 3were drawn, it wassupposed that the mass m of contaminant elim-inated was contained in the pore volume Vpore.The integral below the curves is therefore thesame for all three curves:

m =

∞∫0

c·dV = c0 ·Vpore (45)

Curve 4 finally depicts an examplewhere the washing resembles an extraction(→Liquid – Solid Extraction) because the con-taminant is not contained in the pores only,but also in the solid (liquid inclusions or solu-ble solid matter). The integral under curve 4 istherefore not related to the pore volume Vporebut to a higher total quantity of contaminant.

Theoretically such curves could be used todetermine the residual mother liquor content inthe cake from analyses of the filtrate. In prac-tice this is impossible since the required residualcontents in the cake are much smaller than theprecision of such a mass balance. Neverthelessanalyses of the filtrate are often used to judgethe progress of washing. This is possible if anempirical correlation between the two concen-trations in the filtrate and in the cake exists forthe particular process. The validity of such em-pirical correlation is, however, restricted to theparticular equipment and operating parameters.

3.2. Example of Experimental Results

An illustrative example of a washing process isgiven in Figure 13A and B [16]. A kaolinite sus-pension contaminated with NaCl was filtered tovarying cake thickness and washed with varyingquantities of water. After every test the residualsalt content in the cake wasmeasured and the re-sults are reported as a function of washing time

Filtration 15

Table 1. Typical parameters of cross-flow filtrations

Microfiltration Ultrafiltration Nanofiltration Reverse osmosis

Cut-off size > 100 nm 10 – 100 nm > 1 nm < 103 g/mol103 – 105 g/mol 200 – 103 g/mol

Transmembrane pressure 0.02 – 0.5MPa 0.2 – 1MPa 0.5 – 3MPa 2 – 20MPaPermeate flow 50 – 1000Lm−2 h−1 < 100 Lm−2 h−1 < 100 Lm−2 h−1 10 – 35 Lm−2 h−1

Cross flow speed 2 – 6m/s 1 – 6m/s 1 – 2m/s < 2m/sImportant mechanism ofretention

screening by the pores ofthe membrane

screening by the membraneand the gel layer

electrostatic repulsion andscreening

solubility and diffusion inthe membrane

Important mechanism oftransport

hydrodynamic lift force back-diffusion back-diffusion back-diffusion

Figure 12. Concentration of contaminant in the effluent of a filter cake during washinga) Idealized piston flow; b) Effect of axial dispersion; c) Effect of diffusion from dead-end pores; d) Effect of contaminantextracted from the solid

Figure 13. Residual concentration of salt in filter cakes of kaolin. The same test results are reported either as a function of thequantity of wash water (A) or as a function of washing time (B) [16]

16 Filtration

and ofwash ratio. (In contrast to Fig. 12 thewashratio is related to the solids mass, not the porevolume. Also the residual content of the cake isreported, not the concentration in the filtrate.)

Figure 13A shows how at the very beginningof the washing process the residual concentra-tion depends on the wash ratio, disregarding thecake thickness. In this example this is true up tothe dash-dotted line which corresponds to lessthan a one-fold displacement of the pore vol-ume. As thewash ratio increases to several timesthe pore volume, the mechanism of axial disper-sion becomes more important, and the effect ofa given quantity of wash liquid becomes betterfor thick cakes than for thin ones.

Figure 13B shows how at the end of an exper-iment the washing time is the most relevant pa-rameter for the result. In this example this seemsto be true below a residual concentration of

c

c0≈ 10−3

3.3. Test Procedures and Pitfalls

As can be seen in Figure 13, washing of filtercakes gives scattering results even under labo-ratory conditions. This explains why only fewexperimental results are found in the literature:many experimentators are discouragedby incon-clusive test results and never publish them. Thereason of scattering results are stochastic influ-ences:

Fingering. In most washing processes thewash liquid has a lower viscosity than themotherliquor. It tends to flow through the cake in finger-like streams past isles of viscous fluid, as shownin Figure 14 [16]. This is a stochastic process,and the local concentration in the cake and themomentary concentration in the effluent willvary stochastically. Scale-up from a laboratorytest filter with only small-scale fingering can bemisleading as well as the results of few smallsamples taken from a big cake.

Instabilities, Shrinking. If small electrodesare placed in a filter cake during thewashing pro-cess, they indicate wildly varying local conduc-tivity. This reveals the existence of small cracks

in changing size and positions even in cakeswithno visible fissures or shrinkage. This is not sur-prising because the contact forces between theparticles change dramatically when the ion con-tent of the surrounding liquid is washed off (seeSection 6.2). The phenomenon has not yet beeninvestigated thoroughly, but its stochastic effectson the washing results should be similar to theabove-mentioned “fingering”.

Figure 14.Visualization of “fingering” flow in a transparentlaboratory nutsche filter. A wash liquid of lower viscositydisplaces dark mother liquor [16]

If shrinking during washing presents a seri-ous problem, it can be helpful to reslurry the cakein wash liquid and filter it again. Many nutschefilters (see Section 8.8) are used this way. Thesecond cake (with less ions in the liquid duringcake build-up) is often less porous and less prone

Filtration 17

to shrinking (but also less permeable) than theoriginal one.

In order to get meaningful results fromwash-ing experiments in spite of all these pitfalls,the following procedure is useful (see Fig. 15).Wash liquid flows at constant pressure throughthe cake. The quantity of filtrate and its compo-sition are recorded automatically. Often the pHand the conductivity Q of the filtrate are used asindicators for concentration; sometimes its colormay be more informative. The washing is con-tinued until the filtrate reaches a pre-set crite-rion for purity (chosen according to some pre-liminary experience so that cake purity is near tothe required specification). At this point the flowof wash water is automatically stopped. Thisshould be done automatically, since it will prob-ably happen during the night. The next morn-ing, the cake is deliquored by air blowing andits residual content is analyzed. In small-scaleexperiments the whole cake should be analyzed,in large-scale experiments several samples mustbe taken from different parts of the cake.

Figure 15. Test arrangement for washing test

The following results must then be evaluated:

– The required washing time,– The required quantity of wash liquid, and– The resulting purity of the cake.

Each of these criteria taken alone will scatterstochastically, but all three together will oftenallow a meaningful interpretation.

3.4. “Intermediate” Deliquoring beforeCake Washing

Normally it is advantageous to deliquor thecake partly before washing, thus reducing the

amount of mother liquor to be washed out.Sometimes however this “intermediate” deli-quoring has detrimental effects:

If deliquoring is done by gas pressure, cracksmay appear which let pass the washing liquid(see Section 4.1.5). In this case any deliquoringbefore the washing has to be avoided carefully.On belt filters (see Section 8.2) an overlap offiltering and washing zones is therefore oftenaccepted, even if mother liquid and wash liq-uid getmixed. Some nutsche filters (Section 8.8)have even been equipped with optical sensors toavoid premature deliquoring [17]. Theymeasurethe light reflected by the liquid surface and detectwhen the cake surface runs dry, so that the gaspressure can be released before cracks appear.

If deliquoring is done by compression (seeSection 4.2), the cake may get rather imperme-able. Thus, according to a rule-of-thumb the ap-plied pressure should be raised monotonouslyduring the sequence of filtering – intermediatedeliquoring –washing – final deliquoring, i.e.,the squeezing pressure for intermediate deli-quoring should be lower than the pressure forwashing.

4. Deliquoring of Filter Cakes

4.1. Deliquoring by Gas Pressure

The moisture in the pores of a filter cake can bedisplaced by gas flowing through the cake underpressure. The residual saturation with moistureas a function of time then asymptotically ap-proaches a final equilibriumvalue as representedin Figure 16. Thus, an equilibrium is establishedwith regard to mechanical displacement of theliquid. Thermal drying by airflow will of coursefurther reduce the moisture down to total dry-ness if the air flows long enough. But gener-ally thermal effects are small as compared withmechanical effects because of the comparablysmall mass of air flowing through a filter cake[18].

Thefinal “equilibrium”moisture formechan-ical dewatering depends on the nature of the cakeand the applied pressure difference. The initialdeliquoring speed however depends in additionon the cake thickness. For both values the flowrate of gas is apparently without importance, if

18 Filtration

it is not to produce the pressure difference. Inthe next sections first the equilibrium conditionswill be examined.

Figure 16.Deliquoring by gas pressure – residual saturationas a function of time

4.1.1. Equilibrium Saturation of FilterCakes

A plot of saturation of the cake versus pressuredifference in an equilibrium state is called a cap-illary pressure curve. It can be measured in adevice according to Figure 17 [19]. The satu-rated filter cake (b) is placed in the filter (a) ona semipermeable membrane (c) (the membraneis permeable for liquid, but it is impermeablefor gas at the applied pressure). Gas pressure isapplied via port (e). The quantity of liquid dis-placed from the cake is drained by the valve (d)and collected. (The standpipe is used to obtainan exact liquid level when the pressure gauge isadjusted to zero).

A typical capillary pressure curve is shownin Figure 18 (incompressible cake of glass beadswith amean diameter of 79µmandwater). Start-ing from the completely saturated cake (S = 1)the gas pressure is slowly increased, at eachset point the equilibrium is established and thequantity of displaced liquid is registered, yield-ing a point of the deliquoring curve. Liquid isdisplaced from the pores when the pressure ex-ceeds a certain threshold pressure. This is thecapillary entry pressure pce (in this example0.062 bar). Each time when a pore is emptied,the gas pressure overcomes the capillary pres-sure at the neck of the pores with a diameterdpore,neck:

pce =4·σ ·cosδdpore,neck

(46)

Further increase of the pressure displaces liq-uid from finer pores and reduces the moisture

down to an irreducible saturation S∞ after infi-nite time beyond which no further reduction isreached. This corresponds to the amount of liq-uid, which is trapped in isolated domains withinthe cake.

Figure 18 also shows the imbibition curve.When the pressure is reduced again, and pro-vided the bottom of the cake is still in contactwith the expelled liquid, then the cake will be re-imbibed by capillary suction. At equal moisturecontent the suction pressure will be smaller thanthe capillary pressure difference for deliquoring.This is easily explained because the capillarypressure for imbibition depends on the larger“waist”-diameter of the pores (see Fig. 18):

pci =4·σ ·cosδdpore,waist

(47)

Also imbibition does not go to full saturation,because some air remains trapped in the pores.

The following conclusions canbedrawn fromthe capillary pressure curve:

1) Deliquoring is caused by pressure differencebetween gas and liquid. Gas flow is normallyrequired tomaintain this pressure difference,but not for the deliquoring itself. No gasflow is necessary if the cake is placed on asemipermeable membrane, which is imper-meable for gas. (This principle can also beused technically for dewatering without gasflow [20]).

2) A certain threshold pressure must be ex-ceeded before liquid is displaced from thepores; this is the capillary entry pressure pce.This implies technical consequences:Vacuum filters are restricted to pressure dif-ferences < 1 bar. This means that cakes can-not be deliquored by suction if their pce isnear or above this limit. A pressure filterwith∆p> 1 bar has to be considered for suchcakes, even if its installation is much moreexpensive than that of a vacuum filter. Theo-retically suction can dewater filter cakeswithpores> ca. 3µm:with purewater and a smallcontact angle (δ ≈ 0) Equation (46) yieldsp= 1 bar for dpore = 2,9µm.

Filter cakes of submicronic particles likewastewater sludge have such a high capillaryentry pressure that their pores cannot be dewa-tered mechanically: with pure water and a small

Filtration 19

Figure 17. Test installation for measuring the capillary pressure pk [19]a) Filter vessel; b) Filter cake; c) Semipermeable membrane; d) Draine; e) Entry for gas

contact angle Equation (46) yields p> 10 bar fordpore < 0.29µm.

Figure 18. Example of a capillary pressure curve for imbi-bition and for deliquoring [19]

4.1.2. Kinetics of Deliquoring by GasPressure

In most cases there is no semipermeable mem-brane below the cake but a “normal” filtermedium that is permeable for gas, like a fil-ter cloth. Gas and liquid flow simultaneouslythrough the cake. The gas exerts capillary pres-

sure onto the adjacent liquid and both gas andliquid flow in the same direction, however withdifferent speeds and different pressures (the lo-cal pressure difference between gas and liq-uid is equal to the local capillary pressure).The difference in saturation between bottomand top of an incompressible filter cake is nor-mally rather small, see Figure 19 left. This isin contrast to the deliquoring by gravity (or bya centrifugal field), shown in Figure 19, right.In this latter case always a saturated bottomlayer exists, corresponding to the capillary suc-tion height of the cake. Even in equilibrium thislayer remains saturated. Sometimes this heightis negligibly small. In scraper-type centrifuges(→Centrifuges, Filtering) for example, the sat-urated bottom layer must in any case be smallerthan the residual layer which the scraper doesnot remove.

The permeability of a completely saturatedcake is the same if either liquid or gas flowsthrough the pores. When, however, gas and liq-uid flow simultaneously through the cake, thepores filled with liquid and the pores filled withgas form two separate capillary systems, eachof them with reduced permeability. The localpermeabilities (for liquid or air) in relation tothe permeability of the saturated cake are called“relative permeabilities” krel. They depend onthe local saturation of the cake and can be repre-sented as:for the wetting fluid (the liquid)

20 Filtration

Figure 19. Kinetics of deliquoring by gas blowing (left) and by gravity or a centrifugal field (right)

krel,w =kw

k=

α

αw(48)

for the non-wetting fluid (the gas)

krel,n =kn

k=

α

αn(49)

Such relative permeabilities are shown schemat-ically in Figure 20 as a function of cake satura-tion [21]. The permeability for the liquid (thewetting phase) declines to zero at a finite satu-ration. This value corresponds to the irreduciblesaturation S∞. At the other extreme the flow ofair ceases when the saturation is above 90%.Some of the voids are filled with air without al-lowing an appreciable airflow.

Figure 20. Relative permeability as a function of saturation[21]

If the curves for capillary pressure and for therelative permeabilities as a function of saturation

are known, the local values of capillary pressure,gas permeability, and liquid permeability are de-fined as functions of the local saturation. Thedeliquoring kinetics by gas flow can then be de-scribed mathematically. The resulting system ofinterdependent differential equations is howeverextremely complex and not suited for practicalapplication. For scientific purposes approximatesolutions have been verified by comparing themto experiments [19].

4.1.3. Approximate Solution for Coarse,Incompressible Cakes

For the particular case of incompressible cakeswith threshold pressures much smaller than theapplied gas pressure pce � p (hence for rathercoarse solid particles), Wakeman has describedthe process of deliquoring by gas pressure bythree dimensionless parameters [22]:reduced saturation

SR =S

1 − S∞(50)

dimensionless time

Θ =pce ·t

αH ·η ·H2 · (1 − S∞) ·ε (51)

dimensionless pressure difference

∆P =pentry

pce− pexit

pce(52)

According to this approach, the cake is charac-terized by its porosity e, the filter resistance αH(of the saturated cake) and the capillary pressurecurvewhich itself is approximately described by

Filtration 21

the capillary entry pressure pce and the “irre-ducible” saturation S∞ (see Fig. 18). The rela-tive permeabilities are described by generalizedinterpolation formula. With these approxima-tions the residual saturation and the theoreticalgas flow rate can be read from the dimensionlesscharts, shown in Figures 21 and 22. An exam-ple how to apply these charts is given in [23].However, the validity of these charts is limitedto pce � p and to incompressible cakes. Also thegas flow rate indicated on the chart does not takeinto account the possibility of cracks in the cakewhich can increase the gas flow tremendously(see Section 4.1.5).

Figure 21. Reduced cake saturation vs. dimensionless time[23]

Figure 22. Reduced air (gas) flow rate vs. dimensionlesstime (Wakeman and Purchas 1986; reproduced from [23])

4.1.4. Practical Scale-Up of Deliquoring byGas Pressure

The deliquoring kinetics are normally investi-gated by measuring the residual moisture asa function of cake thickness, blowing time,and pressure difference. The results are interpo-lated to give the parameters necessary for scale-up. Extrapolation beyond the investigated rangeof cake thickness, blowing time, and pressureshould be avoided. In addition it is important tomeasure and to scale-up the gas flow from realis-tic experiments, since in most cases the capacityof the compressor is the limiting factor, not thepressure. Particular attention has to be paid to thepossible formation of cracks. In case of doubt,a filter test with sufficiently large filter area isrecommended, because the cracks may not bepronounced and obvious on a small laboratoryfilter. Typically the cracks appear at a charac-teristic liquid saturation which then representsthe limit for deliquoring by gas blowing withtechnically reasonable gas flow rates (see Sec-tion 4.1.5).

Interpolation of the test results with a mini-mum of tests is made easier if the residual mois-ture is reported as a function of a dimensionlesstime Θ. The results from a given kind of fil-ter cake are then supposed to fit approximatelya straight line in a logarithmic chart. As a firstapproach, when nothing is known about the del-iquoring behavior of the cake, the experimentalvalues are reported as a function of

Θ0 =∆p·t

η ·H · (α·H + β)≈ const· ∆p·t

H2(53)

Here ∆p= pentry − pexit is the pressure dif-ference applied. This approach gives gener-ally good results for centrifugal dewatering, asshown in Figure 23 (the pressure difference be-ing calculated from the centrifugal force) [24].For dewatering by gas blowing, the fit is how-ever often unsatisfactory (see Fig. 24) [24]. Adimensionless time taking into account the cap-illary entry pressure pce will always permit agood fit. Two equations are proposed in the lit-erature [24]:

Θ1 ≈ ∆p·tη ·H · (α·H + β)

· pentrypexit

·(1 − pce

∆p

)

≈ const· ∆p·tH2

· pentrypexit

·(1 − pce

∆p

)(54)

22 Filtration

and [25]

Θ1 ≈ ∆p·tα·η ·H2

· 2ε

·(1 − pce

∆p

)

≈ const· ∆p·tH2

(1 − pce

∆p

)(55)

Here pentry and pexit are the pressures appliedabove and below the cake and pce is the capil-lary entry pressure. This pce is not measured, butderived as a “best fit” to the experiments (this iswhy the fit is generally rather good, see Fig. 25[24]).

4.1.5. Shrinking and Cracks in Filter Cakes

Deliquoring of compressible filter cakes by gaspressure very often produces cracks in the cake,a problem of great practical impact. The mech-anism of crack formation is represented in Fig-ure 26. During filtration the viscous forces fromthe flowing liquid compress the cake. As de-scribed in Section 2.1.4, only the layer near thefilter medium is subjected to the full amount ofpressure, while the “upper” layer of the cake re-mains uncompressed and porous. When filtra-tion is finished, the liquid surface reaches thecake surface. Before gas enters into the capil-laries of the cake, the capillary entry pressurepce must be overcome. The surface tension ofthe liquid thus exerts a pressure p≤ pce onto thecake, comparable to an elastic membrane spreadover the cake. As long as pce is not exceeded, thecake is compressed monoaxially like by actionof a piston, the cake thickness is reduced, but nocracks appear. However, when pce is exceeded,gas penetrates into the largest capillaries, and thesolid structure is compressed by lateral forces.This may lead to lateral compression of the cakeand hence to cracks. The criterion for cracksto occur thus probably depends on the lateralcompressive strength of a cake after monoaxialconsolidation. But until now the precise mech-anism of crack formation is not understood andthe great variety of crack patterns shown in Fig-ure 27 [26] cannot be explained.

Cracks in a filter cake are very detrimental tofurther deliquoring and also to subsequentwash-ing (see Section 3.4) because gas and wash liq-uid flow through the cracks without great resis-tance and without effect. The only sure remedyagainst cracks is compression of the cake before

gas blowing.When the remaining “shrinking po-tential” (this is the remaining shrink when thecake is reduced to total dryness) is small enough,no cracks will appear anymore [27]. Some fil-ters are equipped for this purpose with mem-branes or with pressure belts (see Sections 8.6and 8.10). According to a proposal of Shiratoand coworkers this compression can also beachieved by adding a layer of very fine mate-rial (hence a cake layer with high pce) onto thesurface of the cake [28].

Some remedy against cracks is also possiblewith nutsches equipped with agitators (see Sec-tion 8.8). With their paddles they smear over thesurface of the cake during deliquoring so that thecracks are closed as soon as they appear. Thisdoes, however, not eliminate the cracks totallybut only down to a certain depth below the sur-face of the cake, so that some cracks can existinvisibly below the surface.Without such equip-ment the formation of cracks can be reduced(but only to a very limited degree) if the cakeis formed with high final filtration pressure, andhence with somewhat less porosity.

4.2. Deliquoring by Expression

When soft filter cakes are compressed, the voidvolume of the cake is reduced by expelling liq-uid,while the voids remain saturatedwith liquid.Such compression often is applied in combina-tion with a subsequent deliquoring by gas pres-sure; it reduces the subsequent gas flow and pre-vents the formation of cracks (see Section 4.1.5).But there are many applications where deliquor-ing by gas pressure is not possible, and expres-sion is the only way to reduce the liquid con-tent by mechanical means. Classical examplesfor applications of mechanical forces are juiceand oil pressing from fruits and also the dewa-tering of wastewater sludge in membrane filterpresses (see Section 8.10) or in pressure belt fil-ters (see Section 8.2). Such sludges form filtercakes with very high capillary entry pressure pceso that deliquoring by gas blowing is technicallynot feasible.

Mathematical description of expression gen-erally starts from modifications of the Terzaghimodel for soil mechanics. The ratio of liquidcollected to the amount of liquid, which can beexpressed, is [29]

Filtration 23

Figure 23. Residual saturation of filter cakes dewatered by centrifugal force as a function of dimensionless time Θ0 [24]

Figure 24. Residual saturation of filter cakes dewatered by gas blowing as a function of dimensionless time Θ0 [24]

Figure 25. Residual saturation of filter cakes dewatered by centrifugal force as a function of the modified dimensionless timeΘ1 [24]

Uc =H1 − H (t)H1 − H∞

= 1 − B ·exp (−C ·t) (56)

where Uc is the consolidation rate, H(t) thecake thickness, H1 the original cake thicknessand H∞ the thickness after infinite time. B andC are “creep” constants and tc is the consoli-dation (= compression) time. A comparison of

different compression models can be found in[30].

5. Optimal Cycle Time

When sizing a filter installation, the right cycletime has to be chosen (example: the same task

24 Filtration

Figure 26. Formation of cracks by gas blowing through a compressible cake

Figure 27. Patterns of shrinking cracks [26]

can be performed in a small filter which must becleaned frequently or a bigger one with longercycles). With a long filtration time the filter cakebecomes thick and the flow rate per filter areadeclines. On the other hand for very short fil-tration the downtime for frequent cleaning willreduce the capacity. This leads to two questions:(1)What is the optimal cycle time with the high-est overall throughput? (2) What is the optimalcycle time with the lowest overall cost?

1) Figure 28 shows the quantity of filtrate pro-duced as a function of time. Before the startof filtration a time treg is needed for regen-erating the filter (extracting the cake fromthe previous cycle, cleaning the filter, rear-ranging the filter elements, etc.). The high-

est overall throughput is obtained when thestraight line from the start of this regenera-tion to the end of filtration is tangential tothe yield curve. In other words: the filtrationshould be stopped when the instantaneousflow (as indicated by a flow meter) falls be-low the mean throughput according to thedefinition:

Vmean =V

t + treg(57)

This criterion can for example be imple-mented in a computerized process control.For design purposes it can be useful to cal-culate the optimal cycle time in advance. Forthis purpose a rule-of-thumb will be derived

Filtration 25

assuming cake filtration and negligible resis-tance of the filter medium (β = 0). The quan-tity of filtrate according to Equations (14) or(15) is then

V = c1 ·t1/2 (58)

and Equation (57) becomes

Vmean =c1 ·t1/2

t + treg(59)

The highest Vmean is obtained if the filtra-tion is stopped at topt, which is defined bythe differential equationddt

(1

Vmean

)= 0 =

12c1

·t−1/2opt (60)

− treg2c1

·t−3/2opt

This leads to the rule-of-thumb for maxi-mum throughput:topt,1 = treg (61)

2) Quite analogous considerations are valid forthe optimal cycle time in terms of cost perquantity filtered. During filtration, the run-ning cost is proportional to time (capitalcost and pumping energy), cost = c2t. In Fig-ure 28 all costs are converted with this pro-portionality factor c2 into an equivalent run-ning time: t = cost/c2.Regeneration represents a considerable cost,including downtime, labor, new filter ele-ments, and disposal of waste. If this cost iscalled creg, the mean specific cost is

costfiltrate

=c2 ·t + creg

V(62)

With the approximation of Equation (58)this is

costfiltrate

=c2

c1·t1/2

opt,2 +creg

c1·t−1/2

opt,2 (63)

The minimum is defined byddt

(cost

filtrate

)= 0 =

c2

2c1·t−1/2

opt,2 (64)

− creg2c1

·t−3/2opt,2

As result the rule-of-thumb for maximalyield per cost is obtained:

c2 ·topt,2 = creg (65)

or “cost for the filter run = cost for regener-ating the filter”.

Figure 28.Optimal cycle time derived from the yield curve.topt,1 for maximal flow per time and topt,2 for maximalyield per cost

Figure 29. Filter resistance vs. particle sizeThe range of usual values is compared to the calculated linesaccording to Carman –Kozeny, Equation (66)

These rules have been derived here for con-stant pressure filtration. They can also be derivedfor filter runs with different but constant flowrates until a pre-set final pressure. Practitionerstherefore apply the rule-of-thumb rather gener-ally (e.g., also for filtration with a pump with acharacteristic curve anywhere between constantpressure and constant flow).

6. Understanding the FilterResistance

6.1. The Equation of Carman andKozeny

The resistance α of a filter cake depends on thesize and number of pores in the cake. In a first

26 Filtration

approximation it can be related to the size ofparticles and the porosity of their arrangementaccording to the classical Kozeny equation [31].(The theoretical basis of the Kozeny equation issubject to criticism, see for example [32], never-theless the Kozeny equation is a very useful ap-proximation. More recent correlations are givenin [33].) For spherical particles this equation is:

αH ≈ 5· (1 − ε)2 ·36ε3 ·d2S

(66)

where ε is the porosity of the cake and dS is theSauter mean diameter of the particles, i.e., thediameter giving the same specific surface. Thefilter resistance resulting from this equation isdepicted in Figure 29 as a function of particlesize dS and porosity ε. In practical applicationsthe filter resistances cover a very wide range ofporosity. Fine particles, especially dry dust, of-ten form cakes with surprisingly high porosities(see Fig. 30). The same quantity of powder (fil-ter aid, mean particle size≈ 5µm) has settled inwater with different pH and in air. The settlingvolume (and the clarity of the supernatant) isquite different. Filter resistance depends there-fore to a large degree on cake porosity and henceon the surface forces producing this porosity!

6.2. Interparticle Forces, DLVO Theory

According to the theory of Derjaguin,Landau, Verwey, and Overbeek (=DLVOtheory after the researchers’ initials), the forcesbetween suspended particles of equal materialare described by repulsion due to electrostaticcharges and attraction due to van der Waals’forces:

– Particles in suspension (especially in po-lar liquids like water) have an electricallycharged surface, due to adsorption and disso-lution of ions. The order of magnitude of thischarge ζ is − 120mV< ζ < 120mV, and itdepends on the pH of the liquid. The chargereaches relatively far, depending on the ioncontent of the surrounding liquid. The reachis characterized by the Debye length rD.In pure distilled water this length is excep-tionally long with 0.9µm. In most technicalaqueous solutions it is much smaller, in seawater for example only 0.4 nm [34].

– Van der Waals forces are part of the cohe-sive forces between the molecules within thesolid particle. They reach also a certain dis-tance beyond the surface, but their range isless than that of electrostatic forces. The de-cline is proportional to the distance accord-ing to

Eattraction = − constr

(67)

When two particles approach to distancezero, these attractive forces become verystrong and should in principle become equalto the cohesive force inside the particle. Thereality is, however, more complicated be-cause there are always absorbed moleculeson the surface.

An example of the superposition of bothforces according to DLVO theory is representedin Figure 31. The graph shows the resulting en-ergy potential. A positive gradient of the curvesdescribes attraction, negative gradient repulsion.At very small distances, attraction prevails. Atlarger distance electrostatic repulsion prevails (ifit is not zero).

Figure 30. Settling volumina of the same quantity of fil-ter aid (mean particle size ca. 5µm); left: in water at pH 7;center: in water at pH 2; right: dry powder compacted by itsown gravity [44]

Filtration 27

Figure 31. Energy potential vs. particle distance (DLVO-theory)Attraction and repulsion between two particles in suspen-sion. The superposition of electrostatic repulsion and attrac-tion by van der Waals forces is represented by the resultingenergy potential. High ion content in the surrounding liquidreduces the reach of electrostatic repulsion (Debye length).

Concerning interparticle contact this means:

– Electrostatically charged particles repulseone another. Seen from their equally chargedneighbors they show some kind of smoothand slippery repulsive skin. (The smooth re-pulsive skin canbemadevisiblewithmodernatomic forcemicroscopy, see, e.g., [35].) TheDebye length characterizes the thickness ofthis skin (see Fig. 32).

– Without electric charge (as for example inair), there is no such skin. The particles touchtheir neighbors with their rough surfaces andtend to adhere due to van der Waals’ forces.This explains why the dry powder in Fig-ure 30 has the lowest packing density.

– Particles in aqueous suspension with weakelectric charge most probably have oppo-sitely charged patches on their surface whatmay enhance mutual adhesion and the for-mation of loose flocs.

The surface charge of suspended particles canbe measured as a “zeta potential” (→Colloids,Chap. 4.; →Emulsions, Chap. 11.6.). This po-tential varies with the suspending liquid, espe-ciallywith its pH:High pHmeans a high concen-tration ofOH− ions, which can be absorbed, cre-ating a negative surface charge. Low pH meanshigh concentration of protons and a positive sur-face charge. At a certain pH the surface is neu-

tral (point of zero charge, isoelectric point). Atthis particular pH, the particles can more easilyagglomerate and are easier to filter. This opti-mal pH is often determined empirically withoutknowledge of the zeta potential.

Figure 32. A particle in suspensionSeen from a particle with the same surface charge, it is co-vered with a repulsive skin of a thickness near the Debyelength. This skin has no roughness and no friction; hence itis rather slippery.

6.3. Mathematical Simulation of CakeFormation

Different attempts have been made to simulatenumerically the structure and porosity of filtercakes. Until now such calculations are restrictedto spherical particleswith homogeneous surface.Starting from randomly chosen locations the tra-jectories of particles in a filter floware calculated(generally in two dimensions). When they touchthe cake surface, the deposition is simulated us-ing either a sticking angle [36], [37], or a fric-tion angle and an adhesive force [38], [39], or byestimating the interparticle forces from van derWaals’ and electrostatic forces according to theDLVO theory [40]. After calculating the deposi-tion of a large number of particles, the packing

28 Filtration

density of the resulting cake is found. These cal-culations help to understand and explain someempirical facts:

1) High adhesion forces and large friction an-glesmake the particles adhere at the first con-tact and produce a randomly stacked “houseof cards” with high porosity and permeabil-ity. Low adhesion forces or even repulsionbetween the particlesmake them slip tomorestable positions and produce dense packing.Figure 33 shows as an example of the cakestructure calculated for different friction an-gles and adhesive forces [39].

2) An opposite effect can be observed when theparticles are very small (colloidal). Here theDebye length is often not negligible com-pared to the particle size and the repulsioncan be strong enough to keep the particles ata distance. In this case the porosity and per-meability will increase by repulsion and de-crease by adhesion, contrary towhatwas saidabove. This is for example observed withclay soil in marshland near the sea. The per-meability of such soil is reduced after flood-ing with salt water and increases again whenthe salt is washed out, i.e., the Debeye lengthincreases with falling ion content. For indus-trially filterable suspensions however the ef-fect is not yet reported in the literature. Itseems that for particles > 0.1µm either theDebye length is to small (at high ion content)or the zeta potential is not strong enough (asin distilled water) for this effect.

A comprehensive simulation of cake forma-tion has not yet been proposed. The above men-tioned approaches are restricted to spherical par-ticles with uniform surface charge. Often, how-ever, the electric charge is unevenly distributed,and there may even exist oppositely chargedspots on the same particle. This would explainwhy many suspensions form loose flocs whenthe stirrer is stopped. This is quite often ob-served even if the pH is not exactly at the iso-electric point (the term“isoelectric range”wouldtherefore be more appropriate than “isoelectricpoint”). The flocs disappear when the stirrerstarts again, but nevertheless they probably havean impact on filterability because the particlesare prearranged in a way that they touch withtheir rough, adhesive spots and have less ten-

dency to slip into densely packed positionswhendeposited on the filter cake.

Figure 33. Simulation of the cake build-up for two differ-ent adhesion forces and friction angles (upper diagram for4× 10−8 N adhesion force and 20◦ friction angle, lowerdiagram for 1× 10−8 N and 5◦) [39]

7. Solving Filtration Problems inSmall-Scale Tests

7.1. Laboratory Tests

The most common technique for laboratory fil-ter tests uses a laboratory pressure filter accord-ing to Figure 34 [41]. It consists of a pressure

Filtration 29

vessel about 16 cm long with a filtration area of20 cm2 (corresponding to a diameter of 50mm).Suspension (250 – 300 cm3) is charged into thefilter, and the lid is closed. Filtration starts whenpressurized gas (air or nitrogen) is applied fromabove. This should be done quickly (within afew seconds) to prevent sedimentation. The fil-trate is collected in a vessel on a balance or in agraduated cylinder and its quantity is registeredas a function of time. When the filtration is fin-ished, the compressed gas is applied for aboutanother minute to deliquor the cake. The quan-tity of gas applied during deliquoring is mea-sured with a flow meter or it is estimated fromthe capacity of the feed line and its pressuredrop on gas withdrawal from the feed. After fil-tration and deliquoring the filter is opened, thecake thickness is measured and the cake is re-moved to determine its wet and dry mass andcalculate the moisture content. The quantity offiltrate obtained is interpreted in a linear dia-gram (see Section 2.1.3) and the correspondingfilter resistance is calculated. Several measure-ments at different pressures (e.g., 0.5 + 1 + 6 bar)provide the compressibility coefficient “n” fromEquation (31). For more details see [42], [43].

Another very simple test is the bench leaf test.The filter leaf includes a filter cloth fixed on aplate (100 cm2) with grooves and sealing aroundthe edges. It is connected to an evacuated filtratereceiver via a rubber hose with a valve. The filterleaf is plunged into the suspension and filtrate issucked through the leaf by applying of vacuum.It requires, however, considerable skill to getwell reproducible results with this arrangement,since the solids are sucked to the leaf against theeffect of settling, and their composition dependson the way the leaf is plunged into the suspen-sion. This is why the bench leaf test is used lessfrequently nowadays, only for sizing rotary vac-uum filters, which operate in a quite similar way.

For research purposes it may be interest-ing to measure the filter resistance as a func-tion of compressive pressure. To this behalf theCompression-Permeability Cell (CP cell) hasbeen developed (see Fig. 35). This is a cylin-drical cell with a porous bottom and a porouspiston from above. Mechanical load is placedon the piston and the filter cake is compressed.Then liquid is percolated through the cake withmoderate pressure and the permeability is calcu-

lated from pressure drop and flow rate accordingto Equation (1) or (3).

Figure 34. Bench pressure filter with balance and recorderfor yield curvea)Compressed air; b)Heating fluid; c) Filtermedium; d) Fil-trate; e) Balance; f) Recorder

7.2. Handling of “Unfilterable”Suspension

In industrial filtration often suspensions are en-countered with a high filter resistance. Severalpossibilities for handling of these “unfilterable”suspensions are given below.

Optimization of Upstream Steps (Crys-tallization, Precipitation). Considerable im-provements in filterability are achieved byproducing coarser particles. Good knowl-edge is available about crystallization(→Crystallization). If, however, the solids areformed by precipitation, i.e., by mixing tworeactants, this quick process often dependsstrongly on the mixing conditions and the reac-tion speeds. In this case the filterability must beimproved empirically. Improvement has beenachieved with the following parameters:

1) Continuous mixing instead of batch mixing,

30 Filtration

Figure 35. Compression – permeability cella) Filter cell; b) Filter cake; c) Filtrate receiver; d) Pressure recorder; e) Pump; f) Slurry tank; g) Recirculation; h) Movableplate

2) Recycling of suspended solids to the zone ofsolids formation,

3) Variation of temperature, mixing ratio, stir-ring speed etc.

Application of Flocculants (Polyelec-trolytes). Synthetic, water-soluble polymers arehighly effective as flocculating agents. They ag-glomerate fine particles in aqueous dispersionto voluminous flocs, which settle and filter eas-ily. As a general rule, however, the resultingfilter cake or sediment has a higher porosity andresidual moisture than without flocculation.

Synthetic flocculants are commercially avail-able as nonionic, anionic, or cationic gradeswithmore or less ionic character. A charge oppositeto the zeta potential of the solids to be separatedgives theoretically the best effect. In practice itis, however, easier to observe the flocculation vi-sually without knowledge of the surface charge.Samples of the suspension are prepared in grad-uated cylinders and gently mixed with differentflocculants in 0.1% solution. The high dilutionis necessary to reduce the viscosity and facilitatemixing. The required quantity of polyelectrolyteis generally in the range of 0.5 – 10 kg per ton drysolids, equivalent to 10 – 100mL of solution for1 L suspension.

Criteria for the flocculation effect are settlingspeed, clarity of the supernatant, and aspects ofthe flocs (small, dense flocs are sometimes pre-ferred, because they are more stable).

Adaptation of pH. As explained in Sec-tion 6.2, the interparticle forces depend on thepH of the surrounding liquid. With a pH in theisoelectric range the particles can aggregate andtheir filter resistance and settling speed is in-creased.

Checking of Alternatives to Cake Filtra-tion. Possible alternatives to filtration are pro-cessing in:

– Settling centrifuges (→Centrifuges, Sedi-menting) or static settlers. Even poorly fil-terable suspensions sometimes settle readily,either the solids have high specific weightor big, soft flocs make an impermeable cake(e.g., wastewater sludge).

– Cross-flow filtration (see Section 2.4). Thisalternative however yields the solids as athickened suspension only.

– Evaporation of the liquid (→Evaporation).This alternative may be attractive if the re-quired energy is not to high (highly concen-trated suspension or a liquid with moderate

Filtration 31

heat of evaporation, like many organic sol-vents).

Selection of Filter Aids. Filter aids are inertpowders added to the liquid to be filtered andincreasing the porosity and permeability of thecake (see Chap. 11). They are very helpful, pro-vided the presence of filter aid in the solid canbe accepted. Filter aids are used in two ways:

– As a precoat layer to protect the filtermedium and improve filtrate clarity and

– As a body feed to increase flow rates.

Preliminary laboratory tests help to identifythe proper kind of filter aid. The selection pro-cedure is done in three steps:

1) Selection of the right material according tothe chemical resistance and purity (perlite,diatomaceous earth, cellulose, carbon).

2) Selection of the grade (particle size) of thefilter aid. The particle size should be ascoarse as possible to give low filter resis-tance, but fine enough to prevent the dirt par-ticles from trickling through the pores of thecake. For selection of the grade a precoatlayer is prepared by filtering a diluted sus-pension of filter aid. Then the solution to becleaned is filtered through this layer. Afterfiltration the precoat layer is broken in half.The dirt should form a separate layer on thetop and should not have penetrated into theprecoat.

3) Selection of the quantity of filter aid. As afirst guess the quantity of filter aid is calcu-lated which gives a cake volume equal to thevolume of dirt to be separated. It is then ad-mixed to the suspension and the filterabilityof this mixture determined. If the flow rateis to low, the next trial should be made witha higher quantity of filter aid.

8. Filtration Equipment

Filters can be classified in accordance with dif-ferent criteria:

Solids retention: surface, deep-bedFiltration technique: cake, cross-flow, screeningDriving force: pressure, vacuum, expression,

magnetic or electric field, capillary

Operation: discontinuous, continuous,quasicontinuous, automaticself-controlling, programmed,precoating

Filter element:

1) bag, belt, candle/cartridge, disk,drum, leaf/plate, nutsche, pressplate, tube

2) horizontal, vertical,single-element, multi-element,stationary, rotating

3) open, closed

Solids discharge: scraper removal, vibration,centrifugation, back blow, tipping,manual

Application: rapid settling systems, moderate andslow settling systems, clarificationof liquids, pastes, pulps, sludges,and nonfluid systems.

Because of numerous overlaps with respectto process engineering and design, any system-atic arrangement entails a loss of clarity. In thedescriptions that follow, the design element isgiven top priority.

The principles of operation and the designof filter equipment have changed little for manyyears. Only with recent efforts to improve theeconomics of processes have some crucial de-sign changes and additions taken place. Themost important of these involve

1) automation of operating modes and cycles2) increases in specific throughput capacities

and separation efficiencies, especially aimedat reducing residual moisture

3) optimization in the context of the overall pro-cess

4) improvement of operational reliability5) increased concern for environmental protec-

tion and worker safety6) adaptation to new, more difficult separation

tasks7) development of new separation methods for

existing filtration problems

For example, classical filter presses havebeenreplaced by completely automatic, unattendedequipment.Mechanical dewatering devices havebeen installed on belt and drum filters. Classi-cal open nutsches have been modified into “pro-cess filters,” which combine several downstreamoperations (e.g., washing, dewatering, and dry-ing) in a single apparatus. For difficultly fil-terable suspensions, dynamic filters with mem-branes have been designed; together with elec-

32 Filtration

trokinetic filters, these open up new possibilitiesfor mechanical liquid–solid separations.

Important advances in the performance of ex-isting filters have come about through better un-derstanding of the theoretical relationships in allareas, such as filtration, washing, and dewater-ing and expression. In particular, the automationand optimization of processes, based on knowl-edge about the interactions of the many processparameters, are currently being pursued in ex-tensive programs.

8.1. Bag Filters

The filter element in this type of filter is a bagmade of the filter medium. A typical bag has anopening at one end. The bags aremounted in var-ious kinds of containers; they allow an uncom-plicated design, are easy to service, and are rel-atively versatile in view of the large selection offilter media available. For example, solids in therange of 80 – 800µm are successfully collectedwith bags made of fabrics woven from monofil-ament yarns; solids between 1 and 200µm areseparated with needled felt bags or by precoatfiltration (in which deep-bed filtration is activeat the same time).

As batch filters, are opened by hand, they areemployed only where relatively small chargeswith extremely low solids contents are to be clar-ified. They therefore find use chiefly in clarify-ing and polishing filtration (sterilization), wherethe solids to be removed are impurities or unde-sirable byproducts. Applications include chemi-cal and pharmaceutical products, paints and var-nishes, juices, edible oils, waxes and resins.

Bags open on one side are charged from theinside, so that the solids are collected as a fil-ter cake in the bag. Service times range fromhours to days. In pressure bag filters, where thebags are inserted in supporting cages, pressuresbetween 0.5 and 1MPa are common; in specialdesigns, the pressures are up to 2.5 MPa. Ca-pacities are in the range of 1m3m−2min−1 at1.6MPa. Filter units with several bags in hous-ings are available at total capacities of up to2.4m3/min (4.8m3/min maximum) and downto quite small values.

Pocket-shaped filter bags are charged fromoutside; they are slipped over collapsible filterinserts attached to the filtrate pipe (Fig. 36). The

open corner of the filter bag is sealed againstthe filtrate pipe. In order to increase the filtra-tion area, the bags are made up to three timeswider than the inserts, so that folds are pro-duced when they are slipped on; in this way,the space requirement per square meter of fil-tration area is greatly reduced. Filter units up to250m2 are available. After filtration, the bagscan be cleaned by spraying and blowing withcompressed air.

Figure 36. Pocket-type bag filter

8.2. Belt Filters

A belt filter resembles an ordinary belt conveyordriven by one of the guide rollers. Slurry is fedonto the filter belt from above and the filtratedrains or is pulled by suction from the bottom ofthe belt. Belt filters are operated as simple grav-ity, vacuum and pressure filters. Whether oper-ation is continuous or intermittent (semicontin-uous), slurry is fed onto one end of the belt. Thefiltrate drains into vacuum tanks, which can bestationary or can move intermittently with thebelt. The cake can be washed and dewatered indownstream zones. If necessary, the filter beltis washed during recycling. In another design,the belt is made up of a number of individualcells, which bear the filter cake. In this way, amore careful separation of the filtration stages(see also Fig. 1) is achieved.

In general, belt filters are applied for read-ily filterable suspensions that contain coarser,and therefore easily sedimented, solids (groupsF and M in Table 2), where the filtrate and thewash liquor are to be collected separately and thesolidsmust have gentle handling. Themaximum

Filtration 33

Table 2. Filterability of cakes

Filtration characteristics Group of suspension, symbol

Fast Medium Slow Dilute Very dilute(F) (M) (S) (D) (VD)

Initial cake formation rate, min/cm 0.005 – 0.1 0.1 – 1 1 – 10 10 – 100 no cakeSlurry concentration, % > 20 10 to 20 1 to 10 < 5 < 0.1Settling rate rapid medium slow slowLeaf test rate, kg/m2 h > 2500 250 to 2500 25 to 250 < 25 no testFiltrate rate, m3/m2 h > 10 0.5 to 10 0.0025 to 0.05 0.025 to 0.05 0.025 to 0.05Typical slurry crystalline solids salts pigments wastewater water

filtration area is 120m2. Fluctuations in productcall for control of the belt speed or slurry rate.

For especially sensitive filtrations, belt filtersare used with filter media that remove the liq-uid from the cake by capillary action alone. Thefilter cloth runs over felt or similar filter media.

Vacuum Belt Filters. A continuous vac-uum belt filter consists of the moving filter clothsupported on a profiled elastomer transport belt(Fig. 37). To provide better sealing for the vac-uum space, sliding belts can be placed underthe transport belt, or a specially shaped belt cantravel along with the filter cloth. The difficul-ties met with in ensuring a good vacuum withmoving seal systems are overcome when the fil-ter belt or filtrate box move intermittently. Fig-ure 38 shows an example. When the belt is sta-tionary, slurry is fed to the filter and at the sametime the filter cake is washed, dewatered and,if necessary, pressed. In the intermittent move-ment of the belt, the discharge roller shifts thebelt, while the retaining roller holds the belt inplace. The movement is compensated by move-ment of the compensating roller in the oppositedirection. The vacuum is let down when the beltis moving.

Another continuous vacuum belt filter hasvacuum tanks of pan-shaped sections each 1.4mlong. Each section is divided into two parts withflexible connections to the vacuum system (vac-uum pumps). In this way the individual filtra-tion stages are divided into arbitrary lengths asneeded. The vacuum tanks are designed withgrids that allow the filtrate to drain freely. Dur-ing filtration, the tanks move along with the beltat the same speed, as the vacuum builds up. Atthe end of the co-moving path, the vacuum isbroken and the tank vented, while the filter cloth

moves on. Slurry and wash liquors used are fedcontinuously.

Vacuum belt filters are usually installed inopen frames, or in closed housings if no va-por is to be released into the environment. Goodfiltration capacities and washing effects can beachieved only with uniform loading of the filtermedium or filter cake. For this reason, the feedand wash liquor are distributed over the width ofthe filter belt by flat nozzles or washing grooves.Downstreamdewatering of the filter cake is doneby double-belt expression (see twin-belt press,page 36) or a plate press.

Because of the versatility of vacuum belt fil-ters, they have found use in nearly every field ofliquid–solid separations where slurries are rela-tively easy to separate.

Even difficultly filterable slurries with com-paratively finely dispersed solids can be sep-arated on belt filters if suitable belt materialsare employed and the solids do not immedi-ately block the medium. In such cases, pres-sure is most commonly used instead of vacuum(see page 36).Belt filters for gravity and suction filtration

offer low equipment costs. With a suitable filtermedium (nonwovens are generally used), theycan successfully clean up slurries that are not toohighly concentrated (solids down to 50mg/m3)and of the filterability group F in Table 2. Feedsinclude machine-tool cooling and cutting lu-bricants (emulsions), electrolysis cell slimes,beer (for removal of turbidity and yeast), waste-waters, and chemical solutions.

A gravity or hydrostatic filter with a contin-uous belt (Fig. 39) consists of a tank, in whicha moving support belt made of coarse wovenfabric or a flexible belt forms a depression. Thefilter belt proper rests on this support belt. Op-eration is intermittent: slurry is fed in until the

34 Filtration

Figure 37. A), B) Vacuum belt filter (reproduced with permission of Dorr –Oliver)a) Filter cloth take-up assembly; b) Feed box; c) Cake wash; d) Vacuum pan; e) Filter cloth; f) Filter cloth wash; g) Drip pandrain; h) Drainage belt; i) Tensioning device; j) Filter cloth aligning; k) Drainage belt

Figure 38. Jerking-type vacuum belt filter (BAS Sonthofen)a) Filter cloth take-up assembly; b) Cake wash; c) Vacuum trays; d) Filter cloth; e) Movable discharge roller; f) Cloth washassembly; g) Blocking roller; h) Tensioning assembly; i) Floating roller

increasing resistance to flow causes the liquidabove the filter belt to reach a predetermineddepth. The hydrostatic head promotes the fil-tration rate. The belt is then advanced, the fil-ter cake carried out of the tank, and new filtermedium transported into it. The filtrate flow rateis 0.2m3m−2min−1.

There are two designs of suction belt filters,also called flat-bed filters. One, used chiefly forwastewater treatment, consists of a receivingtank for slurry, with a drag chain conveyor. Theperforated or slotted floor of the tank holds thefiltrate receiver, which is connected to the pump.The filter medium is guided between the scrap-ers and the tank floor. After a filter cake has built

Filtration 35

Figure 39. Hydrostatic belt filtera) Sludge bin; b) Float control; c) Filter trough; d) Filter medium; e) Carrier belt; f) Filtrate tank

up to a predetermined thickness, the increasingpressure drop causes the conveyor to beginmov-ing. It advances some 20 – 50 cm along with thefilter cloth. These filters are made with filtrationareas up to 21m2.

The other design consists of a vacuum tankwith lid; the paper filter tape is fed between thetank and the lid. This type of filter also operatesintermittently. At a filter area of 1m2 a through-put of 0.1 – 0.5m3/h can be achieved, dependingon the amount of solids in the suspension and thepresence of filter aids.

Pressure Belt Filters. A pressure belt filterof the flat bed type consists of a filtrate receiverand a pressure chamber. The filter medium isguided between the two chambers, which aresituated in a housing. Operation is necessarilyintermittent, since the pressure chamber, whichis providedwith slotted gates, is pressurized dur-ing filtration. In smaller units, the use of slottedgates is replaced by pivoting up the pressurizedsection. Pressure belt filters are also made withexpression devices (up to some 2MPa).

A twin-belt pressure filter is a belt filter witha second, co-moving belt, which exerts an addi-tional mechanical compressive load on the filtercake with pressure rollers. Such a filter can beemployed provided the cake is deformable. Thiscondition holds especially for bulky flocculatedslimes such as occur with filter cakes made up ofrelatively fine solid particles (mainly of organicorigin) having a broad particle size distribution.Twin-belt pressure filters have proved them-selves for the dewatering of sewage sludges thathave been treated with polyelectrolytes (basedon poly(acrylic acid) and polyacrylamide) toproduce relatively large, stable flocs.

Figure 40. Schematic processing in twin-belt pressure fil-ters

This type of filter has made it possible to re-duce the relatively high 70 vol% residual mois-ture in municipal sewage sludges by as muchas 10 vol%, corresponding to a decrease of35.7% in the moisture content per cubic meterof sludge. Further applications have also beentested, and this class of filter has been adoptedfor some dewatering jobs, such as slimes fromcoal washing, large-scale animal husbandry, cel-lulose and pulp production, electrolysis, and off-gas treatment. An average dewatering capacityfor designs now current is 6m3 of municipalsewage sludge per meter of belt width and hour.With sludges that are readily dewaterable, theinfluent rate can be increased to 15m3/h.

Machines with multistage dewatering areused in nearly all these sample applications. Fig-ure 40 shows a simplified diagram. The floccu-lated sludge is put through preliminary dewater-ing in a simple screen drainage (rotating or flatscreens), since part of the liquid bound up in the

36 Filtration

Figure 41. Twin-belt pressure filter (reproduced with permission of Flottweg)

sludge is released in the flocculation step. Vac-uum filtration usually follows before the filtercake reaches the expression zone.

A special feature of twin-belt pressure filtersis that the belts change direction several times,on rollers that shear and press the cake, thuspromoting its compaction. Usually the filtrateproduced in the several stages, which is not en-tirely clear, is recycled to the first stage, wherethe solids still dispersed in the filtrate are re-flocculated. The filtrate resulting here is largelyfree of solids and can be passed on to, for exam-ple, biological treatment.

Quite a variety of arrangements of the indi-vidual process stages and design features hascome into being. The performance of these ma-chines thus varies widely, being influenced aswell by the properties of the influent sludges.

Twin-belt pressure filters will find additionaluse in food treatment, for instance in juice ex-traction from fruits and vegetables. Figure 41shows a typical arrangement of that twin-beltpress filters including horizontal press sectionand several turns of the belts. Here the recov-ery of juice may reach 65 – 70% in a 2500mmmachine and 7 – 10 t/h throughput.

In themodification of Figure 42A, the sludgeenters the expression zones from below, througha straining zone (gravity dewatering). Passing

over rolls that vary in diameter, the cake issheared and compressed (up to somewhat over100 kPa). The modification of Figure 42B ap-plies a further increased compressive load witha third moving flat belt.

Figure 42C shows a filter in which an over-flow (for gentle handling of the flocculatedsolids) directly connects the flocculation vesselto the gravity filtration and dewatering stages;the filter cake passes downward through the suc-cessive expressing zones. The last stage is sup-plemented by a device that exerts a controlledlinear pressure.

Cake compression in twin-belt pressure fil-ters is rathermodest in comparisonwith the com-pressions achieved in membrane filter presses(see page 58). The twin-belt devices have the ad-vantage of continuous operation and relativelylow cost. A recent development demonstratesthe possibility of reaching pressures in twin-belt expressing filters that are similar to thosein membrane filters (up to 2MPa). A filtrationzone with filter belts converging in wedge fash-ion is followed by compaction as the cake turnsaround a drum pressurized by hydraulically ac-tuated elements.

Experience and theoretical analyses (see Sec-tion 4.2) lead to the conclusion that optimal per-formance is attained in twin-belt pressure filters

Filtration 37

Figure 42. Modifications of twin-belt pressure filters (A, B, and C)a) Press zone; b) Gravity strainer zone; c) Pre-compression zone; d) Press belt high compression; e) Low compression zone;f) Flocculation; g) Cake break-up; h) Line compression

when the cake is relatively thin, the filtrate drainson both sides, the expressing times are long (es-pecially for readily compressible cakes), and theexpressing force is as great as possible.

8.3. Candle Filters

Candle filters (cartridge filters) consist of tubularelements, mostly covered by sleeves of a filtermedium. They arewidely used in the filtration ofweakly to extremely weakly concentrated slur-ries that contain solids more or less as impuri-ties at concentrations down to the ppm range.This class includes all filters with cylindrical el-ementsmounted, singly ormultiply,more or lessvertically in tanks (Fig. 43A).

All candle filters have the fundamental ad-vantages that the filter elements are relativelysimple in construction and cheap to fabricate,and that the devices are adaptable to require-ments imposed on separation efficiency andthroughput capacity. The elements are mounted

either suspended from an overhead tube sheet orupright on a plate (except where each elementhas its own housing). There are advantages tothe suspended design, but great care is requiredwith elements that break easily.

Most candle filters are operated as pressurefilters. The elements can be cleaned by back-washing, or they may be replaceable. Somemultiple-element filters offer filtration areas offar more than 100m2. As typical clarifying fil-ters, these devices have a broad field of applica-tion (groups D and VD in Table 2). The filtra-tion surface can take a wide variety of shapes,depending on the job being done.

Sheet Candles. A simple candle of this typeconsists of wire mesh or perforated screen madeof AISI 316 stainless steel, phosphor bronze orman-made fibers supported on a tubular metalcore (Fig. 43B). Slotted screens andwire-woundfilters can also be employed. Such elementsare used mainly to collect weakly-concentratedsolids from liquids such as oils and soap and

38 Filtration

Figure 43. A) Sectional view of candle filters and B) tubular filter elements (reproduced with permission of Faudi Filter)a) Deaeration; b) Opening device; c) Filter candle d) Discharge; e) Tensioning plate

dyestuff solutions; mesh openings range from0.01mm to 0.5mm (down to 2µm in specialmeshes). Backwashing is desirable for wire-mesh elements.

Disposable sleeves of paper or nonwovensynthetics are used to retain finer solids. In part,these filtermedia simultaneously act as deep bedfilters, the solids being deposited in the mediumitself. These simple filter elements offer com-paratively high flow rates. Available filter unitscover the range from a few liters per minute toseveral hundred cubic meters per hour. Enclosedin pressure-tight vessels, they can be operated atabsolute pressures of up to 10MPa. The pressuredrop across such a filter is around 10 kPa.

Gap-Type Candle Filters. Gap-type candlefilters can be made of disks, profiled wire, ortubes (Fig. 44). Most are held together by straps.In one design, the gap-forming elements areslipped or welded onto a tube; filters of this typeare used as well strainers. A special drinking

water filter element is the gravel-filled prepackcartridge.

A continuously operating gap-type cartridgefilter has several filter elements, charged on theinside, arranged on a rotating mount that bringsthem one after another to a stationary backwashdevice.

Cartridge Filters. Cartridges are designedfor deep-bed filtration and are thus used mainlyfor fine filtration of dilute slurries, concentra-tions of less than 0.01% and particle sizes lessthan 20µm. They usually comprise replaceablecartridges made of a variety of materials suchas sintered metals (AISI 316 stainless steel), ce-ramics (also usable at high temperatures), plas-tics, cellulose or glass fiber (resistant tomost liq-uids). Wound cartridges of cotton, cellulose ormanmade polymer fibers, often combined withnonwovens, are distinguished by relatively largespaces (honeycomb) for retaining solids. Thesimple construction and lowmaterial costs open

Filtration 39

up technically and economically interesting pos-sibilities.

Large-Area Filters. Large-area filter ele-ments are made by folding the filter mediumalong the direction of the cartridge (Fig. 45) orby using pouch and disk constructions. The fil-ter medium is again mounted on a center tube.Elements can also be built up in several layers.Folded-paper cartridges of this type offer 170m2

of filtration area per unit. Pouch- and disk-typefilters have far less area per unit (up to 0.5m2)but can be cleaned and are therefore reusable.Up to 3.45m2 of filtration area per unit is avail-able in pouch filters. A disk filter consists ofdisks of pulp, metal screen, or membrane filtermedium slipped on a central support, alternatingwith support disks, which have slots to admit theslurry into the elements.

Figure 44. Gap-type candle filterA: a) Steel disk package (turned for solids discharge);b) Fixed gap cleanerB: a) Steel wire spiral (turned for solids discharge); b) Fixedscraper

Other Designs. A number of other cartridgedesigns have been devised for special tasks.

For clarifying difficultly filterable liquids, suchas some pharmaceutical and biological liquids(blood, among others), elementsmade of fibrousbases or materials coated with activated carbongive satisfactory performance in the micrometerrange (microfiltration).

A recently developed element is assembledfrom seven individual tubes having slots for thepassage of filtrate (Fig. 46). A tube bundle is co-veredwith a suitable high-pressure fabric, whichfits tightly around the curved surfaces during fil-tration. During the backwash cycle, the fabricis lifted off the tubes; this movement causes thecake residue to be thrown off. The filter mediumhas a tubular weave, that is, it forms a seamlesstube that canwithstand several bars of backwashpressure. Therefore, its cleaning does not causeany concern. This large-area filter element is sta-ble and can be used especially well as a back-wash filter with a cake thickness between 3 and50mm. With up to 200m2 of filtration area, thiscandle-bag filter is suitable for thickening andclarification of suspension as well as for solidstreatment, such as washing, extraction, or steamdrying. Finally, the cake can be reslurried or dis-charged as dry solids. Typical applications arecatalyst or activated carbon removal, filtrationof pigments or impurities and treatment of poly-mer intermediates.

Design and Selection. Candle filters aregenerally designed to the flow capacity, filtra-tion pressure and separating power stated by themanufacturer. The selection of the filter mediumcalls for some experience.

It can often be advantageous to use severalunits with small filtration areas in place of onelarger-area unit. With several units in parallel,for example, one element at a time can be cutout of the line for washing while the remainingones stay in the filtration stage.

8.4. Deep-Bed Filters

This section deals only with depth filters havingbeds of sand, gravel or similar loose materials.

A depth filter is usually a simple containerwith a porous bottom, on which a bed of filtermedium between 0.5 and 1.5 m deep is placed.If the bed material is gravel or sand, such a fil-ter is also called a sand filter. Figure 47 shows

40 Filtration

Figure 45. Candle-type strainer filters (reproduced with permission of Mann & Hummel)A) Radial fold filter; B) Disk filter; C) Multitube filter

a simple form of a gravity sand filter. The fil-ter bed (c) is supported by the screen (a), andthe filtrate is discharged through pipe (e). Wa-ter, steam or air can be admitted through pipes(g) for cleaning. Wash water overflows at (b),if at all. When agitation is used in cleaning, thewash liquor is discharged at (f ). The cooling orheating coils (e) make it possible to temper thefilter. Depth filters are also operated as pressurefilters, either in order to increase the throughputor when they are installed in pressurized lines.To increase the filtration area of pressure sandfilters, several beds can be arranged one aboveanother.

Most filters of this type are used in the treat-ment of drinkingwater and processwater. Basin-type sand filters have been introduced wherequantities are very large, since these fixed struc-tures offer relatively large areas and depths.

Flow in a depth filter is usually from top tobottom. The flow is reversed in order to cleanthe bed. The basic operating modes differ littleeven though a variety of techniques are possible,especially for cleaning.

With finer-grained bed materials used to col-lect finely dispersed solids, the topmost layer ofthe bed tends to become plugged, so that clean-ing may become necessary before the entire bedis loadedwith solids. In such cases, layers differ-ing in particle size can be used; a new cleaningmethod is needed, however, to avoid mixing the

fractions. In such multilayer filters, the liquidcan be introduced at different points. This ap-proach gives a 70% increase in flow velocity,substantially longer service time, and enhancedsludge capacity.

When a depth filter is employed to clarifyjuices, solutions and similar valuable liquids, en-closed tanks are used instead of open vessels,and higher pressures can also be applied. Pres-sure sandfilters usually permit two to three timesas great a pressure drop as gravity filters, and sofiner-grained bed materials can be used as well.With a few exceptions, bed depths in such filtersare much less than the depths usually found inwater-treatment plants. In industry, depth filterswith beds of special materials such as activatedcarbon or ion-exchange resins are often installedso that dissolved substances can be removed si-multaneously.

In a continuous process (Fig. 48), the influentis initially in an unpacked internal space,whenceit enters the bed through conical internals. Theclarified liquid (filtrate) drains from the bed intoan external space. The filter medium is hydrauli-cally removed at the bottom and cleaned in aregeneration tank at the top. The clean sand isreturned to the filter vessel.

For smaller units (up to roughly 600 m3/h),a backwash-cleaning filter has been developedfor largely unattended operation. When solidsdeposited in the filter bed cause the differential

Filtration 41

pressure to increase, the liquid level in the tankwill also rise until its hydrostatic pressure initi-ates backwashing. Because the cross-sectionalarea of the backwash pipe is larger than thatof the influent pipe, the flow velocity can beroughly four times as great (44 m/h).

Figure 46. Candle-bag FUNDA-BAC filter (reproducedwith permission of Dr.Muller, Mannedorf)a) Filtrate/blowback-air; b) Central tube; c) Concentrictubes; d) Horizontal slots for filtrate entry–blowback; e) Fil-termedium; f) Slurry; g)Filter cake; h)Filtrate comingdownconcentric tubes and rising in central tube

Figure 47. Open “low” sand filtera) Screen; b) Effluent; c) Sand bed; d) Wash water; e) Heat-ing or cooling system; f) Filtrate; g) Cleaning pipes

Figure 48. Continuous sand filtera) Sludge; b) Sand and sludge; c) Slurry; d) Sand bed; e) Fil-trate; f) Sand and sludge

8.5. Disk Filters

The element in a disk filter is a rotating verti-cal disk (Fig. 49); one or more such disks arearranged on a shaft, with roughly half of eachdisk submerged in a slurry tank (Fig. 50). Thedevice allows continuous filtration. The disksare made up of 8 – 10 individual sectors, eachof which is an independent filter. The interiorspace of a sector is connected to the filtrate dis-charge by a rotary valve, so that a cake can formon the outside when the sector is submerged inthe tank. After the submersion part of the cycle,air is drawn or blown through the sector in orderto effect dewatering; finally, the cake is removedby simultaneous application of a scraper and anair blast, or by spraying.

The disks are 1.2 – 3.6m in diameter; in aspecial design, disks up to 5m in diameter wereused.Multi-disk filters have filtration areas of upto 280m2. In devices with relatively large diam-eters, hydrostatic effects may cause nonuniformcake thickness.

When several disks are mounted in a singletank, the tank is fitted with an agitator (usually apaddle mixer) or an air turbulizer in order to pre-vent sedimentation of the solids, which wouldlead to uneven cakes and poor dewatering. If notwith an agitator, the multi-disk filter is built witha divided tank. The slurry level in the tank dic-tates the disk rotation speed.

The disk filter is commonly operated as a vac-uum filter. The tank is open and readily accessi-ble. If vapors generated at elevated temperatures

42 Filtration

Figure 49. Vacuum disk filter

must be kept from escaping into the environ-ment, the filter can be mounted in a pressure-tight housing and operated under pressure; forhyperbaric operation, see also Section 4.1.4.

Figure 50. Vacuum disk filtera) Scraper; b) Filter disk; c) Trapezoidal sectors; d) Outletnipples ; e) Automatic valve; f) Filter tank; g) Overflow

In principle, the filter cake in a vacuum diskfilter can be washed, but it is certainly less effec-tive than in, e.g., belt filters. The basic advantageof the continuous vacuum filter is that it requireslittle space per unit of filtration area. Anotheradvantage is that the filter elements are readilyaccessible. In some cases, this type of filter has

the drawback that cracks develop in the cake andcannot be smoothed.

Applications center on high-tonnage prod-ucts where large filtration areas are needed, e.g.,iron ore slimes, flotation concentrates, whitewa-ter from papermaking machines, blast-furnacedust from scrubbers, and aluminum hydrate(groups M and S, Table 2).

8.6. Drum Filters

Wrapping the filtration surface around a cylin-der yields significant advantages that have madedrum filters one of the most widely used types.Their advantages are continuous operation, easycharging, a choice of cake-removal methods,low sensitivity to suspension variations, goodpossibilities for washing in some cases, satisfac-tory residualmoisture, relatively simple designs,reliability, and economy.

In one revolution, the drum passes throughthe processing stages, thus allowing continuousmovement of filter cake and filtrate. Filters canbe operated as gravity, vacuum or pressure fil-ters.

GravityDrumFilters (Revolving Screens).Applications of gravity drum filters are limitedto simple screening, where cake formation is not

Filtration 43

crucial to the filtration operation, that is, wherethe cake does not greatly increase the filtrationresistance. Thus the nature of the solids gov-erns the application: gravity drumfilters are suit-able for filtering coarse-grained or fibrous mix-tures, for example, treating surface waters, pa-permaking wastewaters, and the like. They canbe charged on the inside or the outside. Whenthe filter is internally charged, the untreated liq-uid flows through a distributing channel to theinside of the drum. As the drum turns, the solidscollected by gravity move upward, separate andare removed, for examplewith a screw conveyor.

The drum is covered with a screen fabric.Withmicroscreens, it is possible to collect solidsthat are somewhat more difficult to filter, suchas occur in sewage treatment.

A filter charged from outside is used in thetreatment of recycle waters and wastewaters inpaper and pulp manufacturing. The drum is al-most completely submerged in the slurry. Whilethe solids are held up on the screen surface(an easily removable cake forms in the caseof fibrous solids), the virtually fiber-free filtrateruns into the lowermost part of the drum. For adrum roughly 2m in diameter turning at a pe-ripheral speed of 3 – 15m/min, throughputs of0.5 – 5.0m3/min per meter of drum width arepossible. Activated sludge flocs are collectedwith a drum 3m in diameter and 3m long, linedwith a microscreen having a mesh opening of10µm; the throughput is 630m3/h.

Vacuum Drum Filters. In order to increasethroughputs and extend the range of applica-tions, the inside or outside of the drum is en-closed in a housing connected to a vacuumpump. In the simplest case, the drum has headson either end, so that the entire inside spaceis under a uniform vacuum. Roughly 30% ofthe drum is submerged in a tank, which fitsfairly closely around it. Slurry in the tank isheld at a constant level by means of an ad-justable overflow. The feed is distributed by astirrer, whose oscillating movement along thedrum is intended to prevent partial settling of thesuspended solids. In the submerged part of thedrum, the vacuum pulls liquid through the filtermedium while a cake builds up on the outside.The cake exposed on the top part of the drumis dewatered by air pulled through it. Shortlybefore the drum re-enters the tank, the cake is

removed by an air blast from inside the drum,falling through a chute into a collector.

Single-cell vacuum drum filters are built withfiltration areas of up to 40m2. They are suit-able for all slurries that can be held suspendedin the tank, that is, slurries that do not containreadily sedimenting solids (group S in Table 2),and where the cake need not be washed. Theyfeature a high working vacuum, since there areno high losses; good dewatering, since relativelylong blowing times are possible; and simple con-struction.

Drum filters generally have continuouslyvariable drives so that they can accommodate arange of product properties. The filtermedium (afinely-woven or fine-pored fabric) is supportedon a widely spaced wire mesh.

Because of its simple design, the single-celldrumfilter iswell-suited to precoat filtration (seealso page 65 and Chap. 11). In a special ver-sion where the common path of filtrate and air isshort, it is preferred in the processing of cloudywine and beverages. Throughputs varies from0.2 – 1.2m3m−2 h−1, depending on the kind ofbeverage. In order to produce a uniform pre-coat, which may be 10 – 12 cm thick (this layeris continuously scraped off during filtration), theconcentration of precoatmaterial (diatomaceousearth) is low, the depth of submersion is slight,and the drum is rotated rapidly. If the drum shellis divided into sections 50 – 60mm wide and atank is added to receive the wash liquor, cakewashing is also possible in single-cell drum fil-ters.

A special variety of this filter is the suctionroll used in papermaking. It has a suction box,which restricts the vacuum to a relatively narrowzone at the top. Suction rolls make it possibleto increase the speed of the papermaking ma-chine from 250m/min with couch rolls to over1000m/min.Multi-compartment Drum Filters. Washing,

as well as the separate recovery of filtratesfrom the several process steps, are made easierin multi-compartment drum filters. The filtra-tion surface in such a device is subdivided intoflat, closed cells, which have their filtrate sidesconnected through separate pipes to vacuumpump(s) (Fig. 51). The compartments usuallyhave perforated inserts bearing, for example,drainage channels on the cake side and filtratecollection channels on the vacuum side. The

44 Filtration

Figure 51. A) Vacuum drum filter (reproduced with permission of Dorr –Oliver)B) Vacuum drum filtera) Agitator; b) Valve; c) Drum; d) Filter pipes; e) Division strips; f) Tank

compartment insert bears a fabric, which sup-ports the actual filter medium. While this fabricis installed separately for each compartment,the filter cloth itself covers as much of the drumperiphery as possible.

The filtrate pipes rotate with the drum andhave a sliding seal connection (rotary valve) tothe fixed lines leading to the supply tanks andpumps. The valve also serves as control means,allotting the desired process stages to the sev-eral sectors of the drum. The control arrange-ment makes it possible to set up any desired fil-tration cycle; this is an undisputed advantage ofthe compartment filter.

The slurry feed is on the ascending side ofthe drum. An overflow pipe provides level con-trol and thus maintains steady filtration condi-tions; the pipe can be adjustable. A stirrer in the

bottom of the tank has the function of preventingthe solids from settling in order to keep from up-setting the filtration. It is not always desirable tostart filtration immediately after the drum is sub-merged, sincewith sedimenting feeds thiswouldmean picking up the fine fraction first and thusimpairing the permeability of the filter medium.The cake emerging from the tank should first bedewatered and then washed.

If cracks appear in the cake on dewatering,they will interfere with uniform washing. Thecake surface can then be smoothed with pres-sure rolls.Washing should be spread over a largeportion of the drum circumference, and so withlarge quantities of wash liquor there is a dan-ger that the cake will slip off. To prevent this,washing belts are placed around the drum. Likethe expressing belts described further on (see

Filtration 45

page 36), these surround the drum and have thedual function of closing up cracks and effectinggood distribution of the wash liquor. The washliquor is usually delivered to the cake throughdrip tubes, channels or nozzles.

Figure 52. Cake discharge assemblies in vacuum filtersA) Roller discharge; a) Filter drum; b) Filtrate pipe;c) Scraper; d) Roller; e) Slurry tank;B) Belt discharge; a) Filter cloth; b) Tensioning device;c) Cloth wash; d) Wash liquid receiver

A variety of devices and techniques are usedto remove various cakes from the filter medium.Scraper discharge is the earliest and simplest

method (Fig. 51B); it is best suited to rigid, non-deformable cakes at least 4mm thick. Lifting ofthe cake can be reinforced by an air blast sup-plied below the filter medium through the filtratepipes.

In string and chain discharge, parallel stringsor chains are passed over the drum in the cir-cumferential direction. After the last dewateringstep, these pass over a deflecting roll with a rel-atively small diameter, and the cake then dropsoff. Chain discharge is suitable for relativelythick cakes such as are produced in the filtrationof coarsely crystallinematerials. “Felted” cakes,on the other hand, call for string discharge.Roller Discharge. Thin filter cakes, down to

1mm and thinner, can be taken up by rollers(Fig. 52A). Contact between roller and drumshould not be too firm. The roller turns at thesame speed or slightly (3 – 5%) faster. The cakeis removed from the roller by a scraper, comb orother means; part is left on the roller to promoteseparation from the drum.

Figure 53. Combined vacuum drum pressure belt filter(Dorr –Oliver, Germany)a) Press belt drive; b) Filter cloth aligning assembly; c) Pressrolls; d) Press belt tensioning device; e) Vacuum drum filter

Belt discharge involves leading the filterclothwith the cake over small rollers (Fig. 52B).Thismethod canbeused for continuousfiltrationof slurries containing fine solids that would gen-erally block the filter cloth too quickly. Spray-ing the cloth from both sides makes it possible

46 Filtration

to handle finely-dispersed suspensions withoutprecoating.

When filtrates are volatile or tend to producevapors, or when an improvement in filter capac-ity is desired (see page 48 and Fig. 58), it maybe useful to enclose the filter and pressurize thehousing slightly.

Expression devices have been added to drumfilters (Fig. 53). Besides lowering the cakemois-ture by 20 – 200%, compression also promotescake removal. The rubber expressing belt is heldagainst the drum with several pneumatically ad-justable rollers; forces per unit length of up tosome 250N/cm are used. The belt path is suchthat the cake gradually enters the region of max-imum pressure.

For the filtration of finely dispersed feeds, thedrumfilter can also be operated as a precoat filter(Chap. 11). Before filtration proper, a 5 – 6 cmlayer of filter aid is applied from a slurry. It maybe advantageous to smooth the precoat layer.During filtration, the filter aid must remain ad-hering to the filter cloth over the entire peripheryof the drum, so as to maintain the suction in allthe compartments of the drum. No air blast isused to help in cake removal. During filtration,the scraper is advanced 0.05 – 3mm per drumrevolution until a permanent precoat thicknessof a few mm is reached.

If the suspension is one that settles rapidly(group F of Table 2), it can be supplied to thetank from a box located at the top of the drum(top-feed filter). This arrangement creates seal-ing problems with respect to the drum and thecake. In general, the lower tank is either elimi-nated or filled with wash liquor. The inner-facevacuum drum filter (Fig. 54) is also suitable forthis type of feed; sedimentation and filtrationin such a device are in the same direction, sothat no stirring is needed. The filter medium ison the inside of the drum shell, while the com-partments are on the outside. The drum is openat one end to allow slurry feeding and cake re-moval; the closed end bears the filtrate pipes androtary valve.Byvirtue of gravity, the coarse frac-tion of solids is deposited first on the filter cloth,forming a more permeable ground layer, whichseparates more easily from the cloth.

Vacuum multi-compartment filters are madein standard series (about 30 sizes) with filtra-tion areas up to 100m2 and drum diameters upto 4.2m. The smaller sizes, roughly 0.25m2,

do good service as laboratory filters. The filtersare irreplaceable for many continuous filtrationjobs, being distinguished by reliability, low op-erating costs, versatility and adaptability.

Rotation speeds depend on filter size anddesired cake moisture content and range from0.1 – 3 revolutions per minute.

Figure 54. Inner face vacuum filtera) Dewatering zone; b) Rotary valve; c) Settling zone;d) Suction zone

Sizing of Vacuum Drum Filters. The designof such filters is normally directed to thethroughput of solids as the significant compo-nent of the feed not least of the fact that deliquor-ing and washing of the produced cake herein aremore or less uncomplicated procedures.

Based on the filtration equation (Eq. 15) (Sec-tion 2.1.2) thematerial balance usingmass ratiosof the slurry, the cake and the filtrate and the sub-stitution of the effective filtration time (s) by

t = 60a

n(68)

where a is the submerged to the total drum areaand n (min−1) the number of drum revolutions,lead to the available throughput of dry solids (kg)per unit filter area (m2) and unit time (h)

(MS)A = C

√aKn∆pαmη

(69)

here (MS)A is the specific mass of solids

(kgm−2 h−1),C = 3600√

60π a conversion fac-

Filtration 47

Figure 55. Pressure drum filter (Fest-Filter for antibiotics production, 1m2 filtration area (reproduced with permission of BHSSonthofen)

tor (s1/2min−1/2 h−1), K = 1cM

(1 − cM

cMc

)

a concentration constant (kg/m3), 1 the densityof the liquid (kg/m3), cM and cMc the mass ra-tios of solids in the slurry or in the cake afterthe filtration cycle, αm the average specific re-sistance of the cake (m/kg), η the viscosity of theliquid (Pa s) and ∆p the pressure drop throughthe cake (Pa). The specific flow resistance of thefilter medium is disregarded because of the com-paratively low influence.

The equation gives a parabolic increase incake production with increasing rotation speed;in other words, the maximum solids output cor-responds to the highest possible rotation speed.On the other hand, the cake thickness decreasesexponentially thereby. Since this thickness islimited by the cake discharge device, the maxi-mum solids production is also limited. The limitfurther depends on thematerial values containedin Equation (69).

Table 3 presents some examples illustratingthe performance range of the vacuumdrumfilter.

Pressure Drum Filters. To realize the ad-vantages of continuous drum operation in pres-sure filtration, with its higher throughputs, andto make the filtration of volatile liquids moreeconomical, Fest developed a drum filter witha pressure housing around the drum (Fig. 55).The drum turns at a continuously variable speed.

The annular space between drum and housing issealed with stuffing boxes and partitioned intofour or five chambers. The drum shell consists ofcompartments (Figs. 56 and 57), which are con-nected to a rotary valve by filtrate pipes. Slurryunder pressure is continuously pumped into thefiltration space. The cake builds up in the filtercompartments; as the drum rotates, the cake ismechanically compacted by passing through awedge, then moves on to the washing chamber.If no provision is made for multistage washing,the next step is dewatering by blowing in a sepa-rate chamber, which is followed by the cake re-moval section. In the unpressurized region, thecake is removed by back-blowing and pivotingscrapers.Washing of the filter cloth can also takeplace in this zone.

The advantages are: continuous operation,relatively high throughputs, filtrations up tonear the boiling point of the liquid, no vaporlosses, very goodwashing, countercurrentwash-ing when multistage arrangements are used, lowcake moisture, no cracking before washing, andmechanical compaction. The filter is naturallymore expensive than a conventional rotary drumfilter, so that additional filtration costs are cal-culated as some 50%. It finds use mainly in thechemical industry (filtration of dyes, vitamins,inorganic and organic chemicals, pesticides, in-secticides), in the production of pharmaceuticals

48 Filtration

Table 3. Performance of vacuum drum filters (Dorr–Oliver).

Material Feed concentration, Filtrate rate, Cake moisture, Discharge% solids kg m−2h−1 %

Calcium carbonate 20 34 – 50 40 – 50 scraperCoal (flotation concentrate) 25 360 – 500 25 scraperCoal (refuse) 30 120 – 145 25 – 30 scraperBlast furnace flue dust 45 45 25 – 30 scraperIron oxide (pigment red) 13 17 30 rollCorn starch 12 – 28 130 – 165 30 – 40 beltWine lees low 82 – 820 (L/m2h) – precoat

(antibiotics), and in vegetable processing (ex-traction). Table 4 gives some throughput figures,which show substantial gains in some cases. Be-cause cleaning is more complicate, it is recom-mended that the product not be changed.

Table 4. Some throughputs of pressure drum filters, kgm−2 h−1,based on dry cake (BHS, Sonthofen, Germany)

Throughput Cake moisture, %

Antibiotics 385 14Copper sulfate 525 24Sodium hydrosulfite 700 20Zinc stearate 45 – 160 60 – 70PVC (suspension) 420 51Titanium dioxide 150 45

Figure 56. Sectional view of Fest-Filter (reproduced withpermission of BHS Sonthofen)1) Filter drum; 2) Pressure tight housing; 3) Scraper; 4)Partitioning element pressed by compressed air

Increased capacity sometimes results fromthe use of pressure drum filters created by hous-ing conventional vacuum drum filters in pres-sure tanks (Fig. 58). These devices have longbeen known and have recently come to be called

hyperbaric filters. Many such designs providebetter dewatering than the straight vacuum fil-ter.

Figure 57. Schematic operation of Fest-Filter

Figure 58. Pressurized drum filter –Hyperbar filter

Filtration 49

8.7. Leaf and Plate Filters

The element in a leaf or plate filter is essen-tially a leaf-shaped structure covered with filtermedium on one or both sides. Slurry is suppliedto the leaf from the outside, and the filtrate candrain through the void inside, while the cake col-lects on the outside. Filter elements are usuallyassembled into units of varying size. They canbe operated as open-tank devices, immersed inthe feed, with the filtrate being withdrawn bysuction (open-tank leaf filter, Moore filter). Be-cause the cake often drops spontaneously intothe feed tank, these devices are also used as fil-ter thickeners. Alternatively, the filter elementsare enclosed in pressure vessels (which may beheatable) and operated as pressure filters, espe-cially for influents of relatively low concentra-tion (clarifying filtration). They are also well-suited to precoat filtration.

The shape and arrangement of the filter leavesor plates are adapted to the properties of the cakeand the filter operating requirements. If the cakeis easily detached from the filter medium, a ver-tical leaf configuration can be chosen, so thatthe cake falls off the medium by gravity (re-moval can be promoted by an air blast or vibrat-ing). Horizontal leaves are suitable for poorly-adhering filter cakes.

Possible element shapes are innumerable,from simple perforated and mesh constructionsto multi-layer designs with internal stiffening.The design of Figure 59 is typical for bed ele-ments which are preferred because of their pres-sure resistance. Each element consists of fivefabric plieswith gradedmeshopenings.The coreply, which allows the filtrate to drain, bears asupporting fabric on either side, with the filtercloths proper on the outside.

In another type, the effective filtration area ineach element is made up of a base with perfo-rated plates, which is inserted in amassive frameto withstand greater mechanical loads. The filtercloth or a wire mesh is placed over the base.

For clarifying filtration with filter beds, wo-ven fabrics, filter paper or membranes, the filtermedia are placed right on the horizontal platestructure. The stack of filter elements to retainsolids down to somemicrometers is placed abouta cylindrical pipe enclosed within a pressure-tight vessel (see Figs. 60 and 61).

Figure 59. Wire filter leafa) Binding; b) Filter medium; c) Metal mesh; d) Wire meshsupport (Chamber screen); e) Filtrate manifold

Leaf filters are made in a smooth design withup to 60m2 of filtration area. In large plant units,the leaf assemblies can be moved mechanicallyor hydraulically (Fig. 62), or the housings are de-signed for easy cake loosening and removal. Be-cause the pressure on the cake is relieved whenthe tank is opened, a vacuum is often pulled onthe filtrate pipes at this time so that the cake willnot drop off the leaves until the desired moment.In the Kelly filter, vertical filter leaves were ar-ranged axially in the cylindrical pressure hous-ing, so that the leaf size decreases to either side.The leaves are vertical in smaller units or hori-zontal in larger ones (up to 140m2). The cylin-drical housing of the Sweetland filter is divided;the lower half can be pivoted to the side to allowcake removal by hosing off.

Where process conditions do not allow theslurry heel (slurry remaining in the pressurehousing after filtration is complete) to be recy-cled to the filter feed or otherwise utilized, some

50 Filtration

designs have one or more filter leaves in the bot-tom of the pressure space to filter this residualfeed. These leaves do not function during themain part of the cycle. The heel is usually driventhrough those filter leaves by pressurized gases(compressed air).

Figure 60. Horizontal plate filter (deep-bed filter) (repro-duced with permission of Seitz-Filter-Werke)

Figure 61. Sectional view of horizontal plate filter

Many designs address the problemof cake re-moval. Modern filtration systems are generallyprovided only with completely automatic opera-

tion; with vertical leaves as shown in Figure 63,automatic removal is often a simple step.

Figure 62. Horizontal-tank pressure leaf filter (Niagara)

Figure 63. Vertical pressure leaf filtera) Valve security; b) Overflow

In horizontal systems, flowable and non-flowable cakes must be distinguished. Flowablecakes are the rule in precoat filtration for clar-ification; here the cake is commonly discardedas waste. The round filter leaves or plates, withslurry feed from the top, are arrangedon ahollowshaft in a pressure vessel and positioned a fewcentimeters apart with spacing disks (Fig. 64).Cake thickness is controlled through the filtra-tion pressure or with special sensors. Cakes inthese devices are nearly always so loose that they

Filtration 51

can be discharged by briefly spinning the stackof plates; separation can be helped by backwash-ing if necessary. Cake removal, required whenleaves cease to function, is effected by verticalvibration in addition to rotation. Filters of thistype are also called centrifugal-discharge filtersup to 170m2. They are often classified as platefilters.

A further variation in operation of pressureplate filters is shown in Figure 64. If the cakedoes not flow off the rotating plates, it is dis-charged by fixed scrapers during cake formationon the rotating plates.

Figure 64. Continuous pressure plate-filter (reproducedwith permission of Schenk Filterbau)1) Feed; 2) Scraper; 3) Plates; 4) Filtrate discharge; 5) Cakedischarge

To empty the filter completely before remov-ing the cake, most filters of this group haveleaves at the bottom of the stack (scavenger fil-tration elements) to allow separate filtration ofthe slurry heel.

For relatively dry filter cakes, a conical dis-charge is preferred (Fig. 65, left). The stack ofplates in such a device must be driven from thetop of the tank, which, in addition facilitates thesealing of the driving shaft.

Nonflowable cakes are generally obtainedin cake filtration where filter aids must beavoided. Help in these instances comes onlyfrom mechanical cleaning devices. Washing inthese pressure filters usually involves some dif-ficulty, because the slurry heel must first be re-moved and the housing filled with wash liquor.Special devices have been developed to reducethe consumption of wash liquor.

In the pressure leaf filters described above,the feed is pumped into the housing, and its dis-tribution over the leaves is naturally somewhatrandom. The slurry can also be supplied to theleaves through a hollow center shaft, with thefiltrate draining into the housing. In this way,uniform loading of the filter elements is ensured.

Figure 65. Centrifugal-discharge pressure plate filter(STAWAG BIOTECH/Switzerland)a) Filter drive; b) Upper bearing; c) Upper seal; d) Filterplates; e) Lower bearing and seal assembly; f) Filter vessel

Range of Application. The applications ofpressure leaf filters are extraordinarily broad,

52 Filtration

and extension to special filtration problems isrelatively easy. As cake filters, these devicesare employed for filtering all kinds of chem-ical products, such as glycerol, caustic sodasolution, phosphoric acid, or pharmaceuticals.Run times between cleaning periods are sev-eral hours, and throughputs of 1 – 4m3m−2 h−1

(up to 6m3m−2 h−1 in extreme cases) havebeen achieved. Pressure leaf filters are appliedin group S and D of Table 2.

When used as precoat filters, these units areespecially well-suited for the collection of rel-atively fine-grained solids from low-concentra-tion feeds (beverages, cane syrup, or water). Av-erage throughputs are 0.3 – 1m3m−2 h−1. Runtimes are strongly dependent on the level of im-purities to be removed; in mixed and thick juicesin sugar refining, runs of 7 – 16 h (depending on,e.g., the quantity of diatomaceous earth used asfilter aid) are achieved.

Centrifugal-discharge filters are availablewith filtration areas of 1 – 60m2 (up to170m2 from one manufacturer); the leaves are420 – 1500mm in diameter.

8.8. Nutsche (Pan) Filters

The simplest type of nutsche filter is an opentank or box with a porous bottom, into whichthe slurry is charged or flows continuously. Fil-ters of this kind are common everywhere, espe-cially in laboratories. They do not impose strin-gent requirements on suspension properties, andthey can function even without difficulty withhighly-concentrated or rapidly-settling slurries.As a rule, they are operatedmanually. For poorlyfilterable feeds, suction can be applied to the fil-trate side.

Nutsches are widely applied in the chemicalindustry because all the steps infiltration, includ-ing washing, dewatering, and drying if practiced(with hot air), can be performed in a clean, dis-tinctmanner. There has accordingly been no lackof efforts to automate the operation of nutschesor make it continuous.

In order to increase filtrate flow rates, anenclosed nutsche can also be pressurized withair or inert gas. Pressure nutsches are espe-cially good with volatile solvents. They can bedrained mechanically through a retractable bot-tom. Several process steps can be carried out

with no change of apparatus when nutschesin process service are fitted with a varietyof accessories (e.g., agitator, mixer, heatingand cooling devices); in this way operationssuch as mixing, stirring, reacting, crystalliza-tion filtration, extraction and drying can beperformed in sequence. Low equipment costs,non-polluting operation, and optimal techniquesmake these devices suitable for small productbatches. Nutsches can be placed on pivots andrepositioned for the various process steps (Fig.66).

Figure 66. Pressure nutsche filter – multi purpose filter –in the crystallization step (reproduced with permission ofSchenk Filterbau)

Nutsches are good candidates for filtrationwith relatively thick cakes. To keep cracks fromappearing, some filters have smoothing attach-ments, which can also provide advantageousmixing of wash liquor and cake and can assist incake discharge.

Tanks with internals such as agitators andsolids-discharge devices (plough) are more ver-satile nutsches. These accessories can homoge-nize the filter cake and render it especially wash-able (Fig. 67).

In some advanced developments, intendedfor comparatively high throughputs, a numberof individual nutsches circulate on either a beltor a carousel. (A system of the first type is usu-ally classed as a belt filter.) This kind of nutschehas proved useful especially in phosphoric acid

Filtration 53

Figure 67. Pressure Nutsche filtera) Agitator; b) Wash device; c) Screw conveyer; d) Heating pipes; e) Filter plate

manufacturing, where it is employed to removegypsum in the sulfuric acid digestion of phos-phate rocks. Careful countercurrent washing ispracticed in order to attain a high degree of sep-aration. Equipment sizes range up to a filtrationarea of some 200 m2.

Automated nutsches share the advantagesstated earlier: They are insensitive to slurry prop-erties and thus suitable for groups F, M, and Sin Table 2, and they provide a clear separationof the process steps and thus insure a uniform,reliable filtrate composition.

For the filtration of slimy feeds, it is advan-tageous to keep the filter cake in motion, for ex-ample bymechanical vibration or an appropriateslurry flow, so that the cake will remain perme-able for a longer time.

8.9. Pressure Plate Filters

The filter press is one the simplest of all pressurefilters; it allows relatively easy cake removal af-ter the individual filtration steps. It consists of anumber of flush plates, up to 100 or more, andframes whose width (between 25 and 150mm)can be matched to the service conditions. Theplates and frames form rather flat pressure filtra-tion spaces with a relatively large filtration area(plate-and-frame filter press, Fig. 68A). Duringfiltration, the plates and framesmust be squeezedby mechanical or hydraulic means in order toseal the filtration spaces (Fig. 69). The faces ofthe plates are studded or grooved to permit fil-trate drainage.

54 Filtration

Figure 68. Filter press – sectional viewA) Plate-and-frame filter pressa) Filter cloth; b) Filter plates; c) Hollow frames; d) Mov-able end half plate; e) Fixed end half plateB) Recessed-plate filter pressa) Fixed end half plate; b) Filter cloth fastening; c) Recessedfilter plates; d) Filter cloth; e) Movable end half plate

Theplates can alsobemadewith a raised edge(recessed-plate filter press, Fig. 68B). There areseveral essential differences between the twotypes: In the plate-and-frame press, slurry entersthrough channels in the corners of the plates andframes. The filter cloths can therefore be shapedas flat strips and pulled over the plates; this ar-rangement is advantageous when the cloths arechanged. In recessed-plate presses, slurry is in-troduced into a center orifice of the plates. Thefilter cloths must be made in two parts and in-serted in the slurry feed channels; this arrange-ment involves much more effort. Further, it isharder to vary the cake thickness in recessed-plate devices than in plate-and-frame presses,where all that is necessary is to replace theframes. The recessed-plate press has, however,the advantage that only about half of the filterelements need be moved to open the press; theequipment also costs much less for a given filtra-tion area. Because of the deflection of the filtercloths at the edge of the recessed plate, thinnercakes (up to about 35 mm) are generally pro-duced than in plate-and-frame devices. With ei-ther type of press, it must be noted that capillaryflow takes place despite the relatively high den-sity of the filter cloths, and this flow – at leastin filtration with solvents – causes the undesir-able escape of filtrate through the seals betweenplates.

The filtrate is either discharged separatelyfrom each plate through cocks (open discharge)or collected in a channel (closed discharge),which is preferred when toxic or volatile ma-terials are handled.

Figure 69. Filter press (reproduced with permission of Eberhard Hoesch & Sohne)

Filtration 55

At cake washing time, valves are changedover and special lines carry wash water only toevery other plate, so that the liquor can flowtransversely through the cake to the oppositeplate. Occasionally the wash water is also de-livered through the slurry channel; this arrange-ment is, of course, not as effective. After wash-ing, the cake can be dewatered by passing steamor (possibly heated) air through it.

For cake discharge, the press is opened andthe plates are moved, one by one, through a pre-determined distance. A variety of mechanicaldevices are now available for this purpose. If thecake is to drop out by itself, it should not adheretoo tightly to the filter cloth and should not betoo densely filtered. Cake separation can be as-sisted by rapping, pulling out the filter cloth, orother means. An automatic filter press for highthroughputs has more than 100 chambers with afiltration area of 1000m2 and more.

Filter presses are generally insensitive toslurry filtration properties, with perhaps one ex-ception: In large presses with long slurry chan-nels, varying sedimentation may cause a slurryof groupS (seeTable 2) tofill thefiltration spacesunevenly. Under some conditions, an undesiredclassification occurs, with a detrimental effecton washing, and may even lead to pressure dif-ferences between chambers, causing the platesto deform or break. In such cases, it is desirableto provide a hole for pressure equalization or asupporting button.

In addition to filter presses with verticalplates, some designs also feature horizontalplates.

Filtration Cycle (see Chap. 5). Cake filtra-tion in filter presses involves two indistinctlyseparated stages. At the start of filtration thereis no cake, and the hydraulic resistance is there-fore very low, so that the filtration pressure can-not rise very high at this point. The process issimilar to constant-volume filtration (see Sec-tion 2.1.2). The pressure increases as the cakethickness grows, until the rated pressure (of thepump) is reached. Constant-pressure filtrationthen begins, with a declining quantity of filtrate.The exact sequence of filtration in filter pressesis still unclear and cannot be calculated, becausenot enough research has been done, but a roughestimate suggests that the highest throughput isachieved if

tf=tkZ (70)

where tf is the filtration time, tk is the time forfilling and emptying per chamber, and Z is thenumber of chambers.

On the basis of a cost calculation, the maxi-mum number of chambers is

Z=[tf (CM−Cp)

tkCp

] 12

(71)

where CM is the cost of mechanical equipment(fixed and movable end plates, adjusting device)and Cp is the cost per plate (chamber). For con-ventional designs, Z is found to be around 60.

To determine tf , the total cycle time includ-ing washing and other steps, experimental datamust be used. Unfortunately, experience hasshown thatmeasurements in laboratory-scale fil-ter presses cannot generally be extended to arbi-trary sizes, since there may be discrepancies inthe filling of the filtration chambers and thus inthe pressure relationships.

Filter presses are commonly charged at pres-sures of up to 2MPa, more in special cases. Cen-trifugal or diaphragm pumps are preferred forthe cake filtration of highly-concentrated slur-ries. The possibility of employing relatively highfiltration pressures, along with the mechanicaladvantages in charging and discharging, lend fil-ter presses some advantages over other types ofpressure filter, even though these devices are al-ways operated batchwise:

1) Insensitivity to feed fluctuations2) Relatively high throughputs, even with dif-

ficultly filterable slurries, so that far smalleramounts of filter aids are needed

3) Low cake moisture4) Denser cakes that are easier to handle5) Clear filtrate6) Good separation of different filtrates (wash

liquor, etc.)7) Arbitrary filtration steps (washing, steam or

air blowing, etc.)8) Lowmaintenance costs, few spare parts, low

depreciation9) Simple operation10) Comparable equipment costs per square me-

ter of filtration area

The drawbacks are obvious: Batch operation;personnel requirements in caseswhere cakedoes

56 Filtration

not drop off by itself; relatively long cleaningtimes.

Applications. Even though they are batchdevices, the good washing and low cake mois-ture available in filter presses have kept them inwide use. Contributing factors, along with com-paratively long service times and good reliabil-ity, includemechanical platemovement, used al-most exclusively for the opening and dischargeof large units; automatic filter-cloth cleaningwith high-pressure water sprays; and the avail-ability of special plate designs. Plates up to 2.6mon a side give far more than 1000m2 of filtrationarea in one press. The design of the plates andthe use of polypropylene as the main plate mate-rial have remedied many of the shortcomings offilter presses, such as plate fractures, corrosion,and plate mass.

Filter presses can be employed almost any-where, even if the mode of operation and theequipment must be adapted to the feeds in ques-tion. Filter presses are used successfully in ei-ther cake or clarifying filtration, depending onthe concentration and properties of the solids; inthe latter case, filter aids are usually added, orfilter beds are employed instead of cloth media.

In the production of chemicals (e.g., dyes),ceramics and raw materials, and in wastewatertreatment, nuclear technology and other fields,

cake filtration is applied chiefly to groupsM andS of Table 2. Slurry feed rates in these fields de-pend on the widely varying slurry compositionand range from 0.2 – 1m3m−2 h−1 on the aver-age.

Figure 70. Filter press for sheet filtration – deep bedpressure filter (reproduced with permission of Seitz-Filter-Werke)

Clarification is carried out in sheet filterpresses, which resemble plate-and-frame filterpresses in design (Figs 70, 71, and 72). Becauseof the verymuch lower solids concentration, ser-vice times are much longer (several hours). Forthis reason, automation is commonly dispensedwith. Filtersheets include ordinary precoats andspecial papers (see page 64 and Chap. 11).

Figure 71. Sheet filter press opened (reproduced with permission of Seitz-Filter-Werke)

Filtration 57

Figure 72. Clarifying filter press – schematic operationTop: Filtration with filter aids; Bottom: Sheet filtration

The most important applications of clari-fying filtration include beer, wort, wine, fruitjuices, pharmaceutical liquids, orwater steriliza-tion (groupD of Table 2). Here too, filter loadingvaries widely, depending both on the propertiesof the solids being removed and their concentra-tion in the feed and on the nature of the liquid.They range from 0.05m3m−2 h−1 for viscousvarnishes up to 10m3m−2 h−1 for dilute sus-pensions, such as beverages.

Membrane Filter Presses. In a membranepress, the filter plate is coatedwith an elasticma-terial (rubber). After filtration, the membranesare pressurized so that they mechanically com-press the filter cake. In this way the cake mois-ture is reduced by ca. 1%– 20%, depending onthe cake compressibility. Figure 73 shows an ex-ample of a recessed-plate membrane press. Asimilar expedient is also possible in a plate-and-frame press. The pressing either shortens filtra-tion time or the filtration pressure can be madesmaller, which is an eminent practical advan-tage.

Membrane filter presses can be operated at upto 2MPa; they produce a uniformly dewateredcake.

Plate Press with Belt Discharge (Auto-matic Press). This type of filter press, orig-inally developed in Russia, combines positiveautomatic cake discharge with cake compres-sion. The horizontal filter plates are stacked and,with the filter frames, combined into a three-chamber system: filtrate chamber, cake cham-ber, and high-pressure water space. The waterspace is separated from the cake by amembrane.For cake discharge, a cloth belt on the frame isadvanced until the cake from each plate is com-pletely stripped off as the belt is deflected intothe next lower plate (Figs. 74 and 75).

Filter Press with Stationary and RotatingPlates. This filter contains alternating station-ary and rotating plates on a shaft (Fig. 76). Avelocity difference is produced in the cake bet-ween the plates, leading to breakdown of thecake. A thin layer of filter cake, whose thick-

58 Filtration

ness depends on the filter medium employed, isleft on the filtration surface. In the extreme casewhere cake formation is totally prevented, this ispure cross-flow filtration (see Section 2.4). Theintermediate states are referred to as dynamicfiltration.

Figure 73. Membrane filter press plate assemblya) Filter cloth; b) Slurry corner feed; c) Recessed plate;d) Membrane recessed plate; e) Press medium; f) Cake;g) Filtrate; h) Air or water inlet (Pressuring membranes)

If the filter cake is thixotropic, the shearingmakes it flowable, so that it can be conveyed bypressure through the system of plates. Accord-ing to studies of some dye suspensions, this filtercan collect the same quantity of solids as a con-ventional filter press with roughly 20 times aslarge a filtration area.

8.10. Tubular Filters

Tubes as filter elements are similar in structure tocartridges. This section deals only with tubularfilters whose dimensions do not usually corre-spond to the concept of a filter cartridge (diam-eter either too large or too small). This groupincludes, on the one hand, tubular pressure fil-ters and, on the other, tubular membranes usedin cross-flow filtration.

Tube Filters. The tubular pressurefilter – the tube press – developed in England,consists of a pressure tube with a filter tube in-serted in it. After cake filtration in the annularspace, a membrane placed inside the pressuretube compresses the cake. A pressure of up to10MPa can be applied. Next (or immediatelyafter filtration), the cake can bewashed. For cakedischarge, the filter tube is swung downward andthe cake is loosened from the filtration surfacewith compressed air. This filter has the advan-tage of the cylindrical filtration chamber, whichis economical for relatively high pressures.

In another type of tubular pressure filter, fil-tration and compaction are similar but the tubeis positioned horizontally, so that the cake canbe scraped out of the filter tube.

A third type of tubular pressure filter has acylindrical rotor inside the filter tube. Slurry iscontinuously compacted in the annular space.The solids are retained in the annular space onthe filtration surfaces of the tube and the rotor,where they are subjected to shear. In this way,the cake is caused to move downward to the dis-charge. As in the filter press with rotating plates(see preceding section), the filter cake must re-main flowable after substantial dewatering; thatis, it must be thixotropic. In one ormorewashingzones, wash liquor can be fed radially throughthe filter tube. Several filter sizes with filtrationareas from 0.25 – 1.6m2 are tested.

Cross-Flow Tubular Filters. The filter ele-ments in the tubular cross-flow filter are smalltubes or hoses, a few millimeters in diameter,which are bundled into systems of tubes carry-ing parallel flows (Fig. 77). The filtrate passesthe system through walls of the tubes whereasthe suspension flows tangentially to them drag-ging the retained particles, see Chapter 2.4. The

Filtration 59

Figure 74. Automatic filter press – systemic processinga) Cloth drive; b) Cloth wash; c) Cake removal; d) Pressure control; e) Filter cloth; f) Filter cloth aligning assembly; g) Ten-sioning device; h) Yoke plate; i) Yoke anchor; j) Filter plate with inflatable membrane; k) Lifting table; l) Hydraulic closuredevice; m) Filter preframe

tubes can be made of various porous materi-als, preferably polymers or ceramics, and havequite narrow pore-size ranges, from a few mi-crometers down to hundredths of a micrometer.They are, above all, microfilters for the concen-tration of dilute suspensions and for clarifyingand sterilizing filtration. Such filter systemswiththe finest membrane pore sizes are also suitablefor ultrafiltration and reverse osmosis; multi-layer or asymmetricmembranes are used in them(→Membranes and Membrane Separation Pro-cesses).

Throughput rates range up to3000 Lm−2 h−1, depending on pore size and fil-tration pressure. The possible applications varywith capacity. The principal users are chemical,pharmaceutical and foodstuffs producers and,increasingly, bioengineering concerns.

Figure 78 shows an example of a completemicrofiltration unit including cross-flow ele-ments and the programmed control unit for batchand continous operation.

8.11. Special Filter Types

Coarsely-dispersed systems with relatively highsolids contents are dewatered with conventionalscreens like the vibrating screens used for classi-fication. One such filter is the vertical sieve con-taining a bent screen plate, which is employedto separate coarse and fibrous solids at lowerconcentrations from process waters and waste-waters with screen filtration. The sieve, whichis equipped with an adjustable screen slope, ischarged from the top, so that the slurry flows

60 Filtration

Figure 75. Automatic filter press (reproduced with permission of Eberhard Hoesch & Sohne)

downward by gravity. The screen, with slotsvarying from 0.125 – 2.5mm wide, retains thesolids, which drop downward. The simple, in-expensive design has made this device a widely-used one in food preparation, the textile andmanmade fiber industry, paper and pulp man-ufacturing, and the chemical industry.

Several new filtration mechanisms arebeing explored with an eye to filtrationproblems that have not yet been solved.These include, in particular, the dewateringof suspensions having relatively high con-centrations of extremely fine solids (below10µm down to colloidal sizes). The conven-tional separation techniques – flocculation andmicrofiltration – generally yield filter cakes orconcentrates that require considerable energy forcomplete phase separation (e.g., by drying). Re-search on ionized phases has shown that the elec-trokinetic effects of electro-osmosis for liquidtransport and electrophoresis for solids transportalong an electric field allow separation, even ofdifficultly filterable suspensions. Both these ef-fects have been known for a long time.

A filter based on the above processes con-sists of separating chambers with anodes, wherethe ionized solids collect, and cathodes made as

filter media, where the electrolytic filtrate is dis-charged [45]. Several separating chambers formfilter systems similar to filter presses.

Difficultly filterable suspensions are alsofiltered by high-gradient magnetic separation(HGMS) (→Magnetic Separation). This typeof filter employs a steel wool medium. In avery strong magnetic field, high field gradientsare generated at the individual filaments. Thesegradients attract fine magnetic particles. ThisHGMS filter thus resembles a depth filter. Suc-cesses have been achieved in the purification ofkaolin and wastewaters.

Figure 76. The dynamic filter pressa) Filtrate discharge pipe; b) Main shaft; c) Filter plate;d) Agitating disk; e) Cake discharge valve

Filtration 61

Figure 77. Schematic of tubular membrane filtera) Tube bundle; b) Cross section

Figure 78.Microfiltration equipment (Seitz-Microflow, re-produced with permission of Seitz-Filter-Werke)

9. Filter Selection

Because certain qualities, largely related to de-sign, characterize the ranges of application offilters, some guidelines can be set forth. Thesetogether with a few other points can provide abasis for filter selection. In general, a good se-lection takes account of factors such as slurryproperties, throughput, or cake formation rate(see Table 2). Other points to be considered arethe density and viscosity of the liquid, the size,size distribution and shape of the solids parti-

cles, the sensitivity of the product to impurities,corrosion problems, the sensitivity of the equip-ment to sedimentation and to product fluctua-tions, the cost of operation, and so on. Table 5can be used in the selection of special vacuumfilter types under a number of criteria. The tabu-lated data should, however, be regarded only asrough guidelines. Filter types are shown in Fig-ure 79 together with the particle sizes for whichthey can be used.

Figure 79. Filter selection as a function of solids particlesizes

The higher cost of pressure filtration in com-parison with vacuum filtration is usually notjustified except when the cake has a resistanceof 3.5 · 1011m/kg. Flocculated solids, whichshould not lose their structure since it is advan-tageous for filtration, require careful handling,especially in feeding to the filter. Because mostsuch solids are somewhat compressible, not toomuch pressure should be applied, and so vac-uum filtration is commonly preferred for thesematerials.

A safe selection without trials or appropri-ate experience is possible only in the rarest in-stances.

Little general information and few computa-tional formulas can be given in the field of fil-tration, which is one of the oldest operations inprocess engineering. Regrettably, filtration (likeother essential processes involving the handlingof bulk solids, dumped and packed beds, etc.)must deal with the effects of material proper-ties that can be determined only with difficultyor cannot be measured in a predictable way, andthese effects are so large and pervasive that thereis no comprehensive, unifiedway of allowing for

62 Filtration

Table 5. Applicability of filters

Filter type Suspension of Operation

fine particles Pressure Washing Compression Continuous (c)automatic (a)

Belt × cBelt with compression × × × c + aNutsche × × × × aTilting pan × cLeaf/plate × × aDrum × cPressure drum × × × cMembrane filter press × × × × aTwin-belt pressure filters × × × × cTube press × × × a

them. There is no doubt, however, that selectioncriteria exist and that they imply at least certainfilter categories, so that in many cases the num-ber of open options is not very large.

10. Filter Media

The outcome of filtration, that is, the degree towhich the filter separates the two phases, is gov-erned above all by the filter medium. Where theavailable filter media are not suited to the prop-erties of the phase (solid) being separated, filteraids can close the gap.

The filter medium should be selected to pro-vide the desired separating effect and to fit thespecial properties of the suspension (such as theparticle size of the solids and the viscosity ofthe liquid). The selection of a medium shouldalso take account of service conditions suchas cleaning, washing, reaction to back-blowing,and chemical and mechanical stability, whichare no less important than the slurry properties.In cake filtration, cake removalmust also be con-sidered.

In line with the multiple purposes of filtra-tion, media must perform the following tasks:

1) Optimal retention of all solid particles out-side the filter medium

2) Retention of the solid particles, mainly in-side the filter medium, by virtue of effectsgenerally lumped together as “entrapment,”which essentially have to do with adhesionforces and electrical forces.

Often these functions cannot be unambigu-ously separated; this is particularly the case with

slurries having a very broad particle-size spec-trum. In such cases, some concession nearly al-ways has to be made in terms of separation ef-ficiency, or further operating practices, such ascareful cleaning or frequent replacement of thefilter medium, have to be introduced.

Filter media can be characterized in terms ofthe following overall criteria:

1) Cut size, that is, the particle size that justpasses through the filter medium.

2) Permeability; high permeability means lowpressure drop.

3) Chemical stabilitywith respect to the filtrate.4) Blocking tendency, particularly for fabrics in

cake filtration.5) Mechanical strength in relation to loads im-

posed in back-blowing or the movement offilter cloths.

6) Smooth surface to promote cake removal.

As is appropriate after many years’ experi-ence in filtration, a great many types of filtermedia have been introduced in practice. Newmaterials and processing methods continue tooffer a wide range of improvements. The diver-sity of filter-media properties has led to a numberof classifications in the literature. The followingseems to be an advantageous one:

Perforated plates, screens, slotted screensFabricsBeds, felts and other nonwoven materialsPacked beds and precoat layersPorous materialsMembranes

Within these groups, there are differences inproperties, especially with regard to chemical

Filtration 63

stability (including aging).However, often phys-ical and biological requirements are also im-posed, such as high-temperature stability, wa-ter uptake, swelling capacity, weathering behav-ior (stability to light), and resistance to insects(moths) and bacteria (rotting).

Aside from material properties, the overallfiltration qualities can be represented only in anapproximate way, because they depend heavilyon the properties of the suspension being fil-tered. Even the often-used permeability and/ormean pore size figures should be considered – atbest – rough reference values for the behaviorduring filtration. A reliable assessment is usu-ally possible only if practical tests or, withinlimits, laboratory trials (e.g., with the test leaffilter, Chap. 7) are performed.

Perforated Plates, Screens, SlottedScreens. Aside from screens used in screenfiltration, filter media in this group serve mainlyto support filter cloths or papers, which as a rulehave finer pores.

With perforated plates, the largest possiblefree surface area is usually desired so that thepressure differences to be overcome in filtra-tion will be small. Free areas range from some20 – 30% for ordinary plates with circular holesto over 90% for high-quality screenswith squareopenings in the millimeter range. The free areadrops to less than 10% for very fine sieves withopenings a few micrometers across.

Slotted screens with very small openings,used chiefly as strainers and candle filters (seeSection 8.3), are made by stacking plates, ringsor other elements around a permeable cylinder.The fine gaps between the elements allow onlythe liquid to pass. Strainers can be fabricatedmore simply by winding profiled (wedge) wiresor strings on a core. These units have little freearea, roughly 10%. As a result, they are eco-nomic only when solids concentrations are verylow.

Fabrics. By far the most widely used filtermedia are woven fabrics. Manmade fibers dom-inate, but fibers of glass, minerals, and metalsare also used to an increasing extent, especiallyin view of their good chemical stabilities.

The advantages of multifilament-yarn fabricsinclude the depth action of the filter medium,which permits slight penetration of solids into

the medium, thus effecting some reduction inpore size and also promoting bridge formationon themedium. The ease ofworkingwith fabricsis an incomparable advantage, of course.

The fabric weave is important for filtrationproper as well as service properties. Another es-sential factor is the structure of the fiber, whichvaries widely in natural and synthetic materials.

Where particularly high strengths are needed,as in twin-belt pressure filters, monofilament-yarn fabrics are preferred. High precision in fab-rication allowsmesh openings in themicrometerrange, especially with metal fibers.

Within some limits it is possible to start withtypical fabric data, such as weight per unit area,numbers of warp and filling yarns, fiber diame-ter, fabric thickness and fiber density, and calcu-late the pore size and hydraulic resistance. Theresistance calculation is based on the pore radiiof the fabric and the yarn, and Poiseuille’s lawis used as a first approximation.

The permeability of a clean, unused fabriccan be calculated (with about the same reliabil-ity) from Kozeny’s equation (66); the startingdata are the densities and porosities of the yarnand the fabric. But empirical relations shouldgive better agreement with experimental values.

However, it is vital to know how the fab-ric influences cake formation and the narrowingand possible blocking of the pores. The result-ing change in hydraulic properties of the filtermedium is described in Section 2.2.

Nonwovens, Papers, and Felts. These fil-ter media consist of relatively short fibers (sta-ple fibers a few centimeters long) formed into arandom layer and then compacted in some way.Nonwoven media are usually fabricated in fairlythick layers and therefore function as depth fil-ters (→ Nonwoven Fabrics).Papers made of cellulose fibers are available

in a bewildering range of grades for use in lab-oratories, small plants, and daily life (→ PaperandPulp).Heavier papers andpaperboards (2 – 6mm thick) can also be fabricated from mixedmaterials, such as cellulose plus diatomaceousearth or activated carbon. These filter materialsmeet a wide range of requirements and are em-ployed in large quantities for the clarification ofbeer, wine, or juices, and in the dyes and coat-ings, food, and cosmetics industries. By virtue ofthe rawmaterials and fabrication processes, one-

64 Filtration

time use of the filter medium is often economic;this feature is especially desirable in sterile fil-tration.

Conventional felts of relatively short naturaland manmade fibers are usually not adequate tothe filtration and service loads in plant equip-ment. Felts that incorporate woven-fabric rein-forcement are often preferred for this reason.Some loss in terms of the basic advantage of feltmust be accepted when these composite materi-als are used. As a rule, needled felts have lowerresistances than woven fabrics. They have nowbecome the most commonly employed nonwo-vens (→ Felts).

Packed Beds and Precoat Layers. Loosebeds of granular materials can also be usedin clarifying and some cake filtrations. For eco-nomic reasons, cheap natural products such assand, gravel, or coal are used, but it is desirableto remove the excessively fine-grained fractionsfrom them by washing. Common particle sizesare 3 – 50mm for gravel, 0.35 – 0.45mm for finesand, 0.45 – 0.55mm for medium sands, andover 0.55mm for coarse sands. Other candidatematerials include minerals (quartz, limestone),coke, anthracite, slag, wood pulp, glass beads,wadding, or fibers.

The hydraulic properties are calculated withthe relations developed in the theory section,in particular Darcy’s law, Section 2.1.1, or – ifthe appropriate material data are known – theKozeny equation (66).

Rigid Porous Materials. Porous materials,which are fundamentally similar in structure,are suitable for any kind of filtration. Theirmechanical stability allows their use as filterme-dia without supporting structures (up to pres-sures of 2MPa and more). They are preferablyemployed as filter cartridges or in the form ofsheets and more recently, honeycomb and otherthree-dimensional shapes. Because they are gen-erally too valuable to use just once, and be-cause they can withstand vigorous backwash-ing without special preparation, solids shouldbe collected mainly by surface filtration. Deep-bed filtration is recommended only when theparticles are very small in comparison with thepores and are collected by an adsorptive mecha-nism. In the intermediate region, solid particlesblock the pores too quickly, and backwashing

may not adequately remove them. Materials forporous filters include minerals, diatomaceousearth, porcelain, clay, coal, graphite, corundum,rubber, plastics, and metals, including highly re-sistant nickel – chromium–molybdenumalloys.The most important criterion for selection ischemical and thermal stability.

Porous materials made from equal-sized par-ticles are distinguished by uniform porosity. Inorder to reduce the blocking tendency, layerswith differing particle sizes can be superimposedwith the fine-pored layer toward the filter cake;thus only the topmost layer need be cleaned, andthe filter offers better service qualities.

Porcelain filters are available with pore radiifrom 0.08 to 6 µm and porosities of 30 – 70%.Sintered metal filters range from 1 to over 100µm in pore size and from 30 to 60% in poros-ity. Plastic filter media with about the same porespectra can easily be fitted to the equipment.Their relatively poor temperature stability, how-ever, restricts their use. Besides poly(vinyl chlo-ride) and polyethylene, porous masses can alsobe fabricated from polytetrafluoroethylene, withits excellent stability.

Membranes. At present a great number ofdistinct membranes are on the market, not justfor ultrafiltration and reverse osmosis, but alsofor microfiltration (→ Membranes and Mem-brane Separation Processes). They are made ofplastics and are suitable for clarifying as wellas pure surface filtration. If very small pores areneeded,membranes are assembled from two lay-ers, a coarse-pored supporting layer (with, e.g.,15 – 20µm pore openings) topped with a filterlayer (0.2µm pores). All membranes have a rel-atively narrow range of pore sizes.

A special form of membrane filtration em-ploys hollow fibers made of, e.g., polyamides,with diameters of 50 µm and wall thicknessesof 13 µm. The solution being separated is intro-duced into the hollowfibers under an appropriatepressure. Pure liquid escapes through the wall ofthe fiber, while the dissolved material remainsbehind and can easily be carried out of the fiber.

11. Filter Aids

Some suspensions contain solids that quickly fillor block the openings in the filter medium. This

Filtration 65

group includes suspensions substantially madeup of relatively fine, soft (especially gelatinous),compressible solids. Such feeds can still be fil-tered well if the blocking of the filter medium isprevented by the inclusion of inert, readily fil-terable granular materials. These filter aids forma layer permeable to the filtrate, and at the sametime they carry out the functions of a loose filtercake. The particles being retained are depositedon the filter aid. This process must still leavesufficiently free openings through which the fil-trate can pass. Themain candidates for filter aidsare thus highly porous materials. Diatomaceousearths are very economical examples; their fine-ness is characterized by 10%> 40µm at thehigh end and between 1 and 7 µm at the lowend. Also used are perlites and, for special jobs,Fuller’s earths, powdered glass, coal prepara-tions, cellulose fibers, wood pulp, paper stock,bagasse (a sugar cane residue), talc, or plastics,although these products are less effective thandiatomaceous earths and perlites. The require-ments for a good filter aid are uniform quality,correct particle size and shape, and the highestpossible wet volume (specific volume in the wetcondition, usually greater than the wet volumeper mass of filter aid).

In diatomaceous earths, particles consist-ing of needle-shaped diatoms have proved ad-vantageous; disk-shaped particles filter poorlyand produce too dense a cake. Unsuitable con-stituents such as clay, or sand must be removedfrom the raw materials, because they hinder fil-tration by blocking the pores.

A synthetic filter aid is manufactured fromvolcanic rocks. The raw material, bound withsome water, is ground, then suddenly heated toa high temperature; the grains inflate to formspheres. Regrinding yields half-shell-shapedfragments, whose large surface areamakes themsuitable as a filter aid once the fines are screenedout. Their action in filtration is somewhat worsethan that of diatomaceous earth, with a porosity20 – 40% lower.

In precoating, a layer of filter aid several mil-limeters thick is deposited on the filter mediumbefore filtration proper. After the filtration iscompleted, the filter aid is often discarded alongwith the collected solids.

Several steps take advantage of the effect ofthe loosened filter cake. First, a precoat some1 – 2mm thick, containing 200 – 800 g/m2 of fil-

ter aid, is filtered onto the medium (base layer)so that a clear filtrate can be obtained right fromthe start of filtration. Filter aid is also added tothe slurry continuously during filtration. In batchoperation, this is done by stirring in the slurrytank; in continuous filtration, dry or wet filteraid can be metered into the slurry delivery line.No generally valid rules exist for the proper ra-tio of filter aid to solids concentration. A varietyof empirical values are available for some pro-cesses and solids types. If there is too little filteraid, the filtration goes badly; if too much, thefiltrate flow rate drops off too sharply.

Themain applications for filtration with filteraids are the precoat technique for poorly filter-able slimes of chemical and mineral productsand the clarifying filtration of beverages (beer,wine, juices) containing soft, gelatinous impuri-ties, as well as the clarification of gelatins, canejuice, or edible oils.

12. References

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2. VDI-Richtlinie “Filtrierbarkeit vonSuspensionen” VDI 2762, 1997.

3. L. Svarovsky: Solid – Liquid Separation,Butterworths, London 1977, p. 175.

4. M. Tiller, T. Cleveland, R. Lu, Ind. Eng. Chem.Res. 38 (1999) 590 – 595.

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6. A. Rushton, A. S. Ward, R. G. Holdich:Solid – Liquid Filtration and SeparationTechnology, VCH Verlagsgesellschaft,Weinheim 1996, pp. 64 ff.

7. K. Luckert, Wiss. Z. Techn. Univ. Magdeburg36 (1992) no. 5/6, 74 – 80.

8. P. L. Boucher, J. Proc. Inst. Civ. Eng.(1946 – 1947) 415 – 445.

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10. K. J. Ives, in A. Rushton (ed.): MathematicalModels and Design Methods in Solid-LiquidSeparation, NATO ASI series E No. 88,Martinus Nijhoff, Dordrecht 1985, pp. 90 ff.

11. A. Rushton, A. S. Ward, R. G. Holdich:Solid – Liquid Filtration and SeparationTechnology, VCH Verlagsgesellschaft,Weinheim 1996, p. 198.

66 Filtration

12. G. Dierckx in: La Filtration Industrielle desLiquides, Tome III, Societe Belge deFiltration, Liege 1978, pp. 295 – 314.

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