Chemical Engineering OperationsFiltration

Dr. Anand V. PatwardhanProfessor of Chemical EngineeringInstitute of Chemical Technology

Nathalal M. Parikh RoadMatunga (East), Mumbai-400019

av.patwardhan@ictmumbai.edu.in; avpuict@gmail.com; avpiitkgp@gmail.com

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Filtration and Centrifugation

Mechanism of filtration

Basic equation

Constant volume filtration

Constant pressure filtration

Rate expressions with cake and filter cloth resistances,compressible and incompressible cakes

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Filtration – A Mechanical SeparationFiltration: Removal of solids from a fluid (liquid / gas) bypassing through a filter medium (called septum or filter

) hi h h lid d i dcloth), on which the solids are deposited. Valuable material to be recovered: fluid OR solid ORb h Oboth OR none.

Range of solid content: from Traces to a High Percentage. Filter aid: sometimes used to make the solids more

filterable and to protect the filter medium from gettingl d / h k dclogged / choked.

Driving force: ΔP ( = Pupstream – Pdownstream). ΔP: by gravity of liquid column (static head) OR by pump /blower OR by centrifugal force.

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Filters: 3 main classes, namely,1 C k filt l ti l l t f lid t d1. Cake filters: relatively large amounts of solids are separated

as cake or crystals + provision for washing of cake andpartial recovery of liquid contained in the cakepartial recovery of liquid contained in the cake.

2. Clarifying filters: small amounts of solids are filtered out toproduce a clean gas or sparklingly clear liquids. The solidproduce a clean gas or sparklingly clear liquids. The solidparticles are trapped inside the filter medium and on itsexternal surface.

3. Crossflow separators: the feed suspension flows underpressure at a high velocity across the filter medium. A thinlayer of solids may form on the surface of the medium, but itdoes not form a permanent layer due to high liquid velocity.The pores of the filter medium are small enough to excludeThe pores of the filter medium are small enough to excludemost of the suspended particles. Some liquid passes throughthe filter medium (clear filtrate). More concentrated

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( )suspension remain behind.

Within each of these 3 classes, the filters can beW t eac o t ese 3 c asses, t e te s ca becontinuous or discontinuous

Continuous: the discharge of filtered solids issteady. In this case the discharge of both fluid ansolid is uninterrupted during the operation.

Discontinuous: the discharge of filtered solids is Discontinuous: the discharge of filtered solids isintermittent. Here the flow of the fluid is

i b d b i dcontinuous but needs to be interruptedperiodically to allow for the discharging of theaccumulated (filtered) solids.

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Cake Filter In the beginning of filtration, some particles enter thepores of filter medium and get immobilised.

Afterwards, the particles start gathering on the filtermedium (septum) eventually, the cake of solidseffect the filtration operation, and not the septum.

A cake of some thickness builds up on the septump psurface, and this cake must be removed periodically(in the case of discontinuous filtration operation).

Cake filters are used mostly for solid-liquid systems. Cake filters may operate with super-atmospheric Cake filters may operate with super-atmosphericpressure upstream OR with vacuum applieddownstream

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downstream.

Mechanism of Filtration in Cake FilterSlurry (upstream end)

Pressure = P1

Cake

Filter medium(septum)(septum)

Clear filtrate (downstream end)Pressure = P

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Pressure = P2

Requirements of Filter Media (Septum) It must retain the solids to be filtered clear filtrate. It must not plug / blind.It must not plug / blind. It must be resistant chemically and strong enough

physically to withstand the process conditionsphysically to withstand the process conditions. It must permit the cake formed to discharge cleanly

d l t land completely. It must not be prohibitively expensive.Typical industrial filter media: canvas cloth (woven ornon-woven), woolen cloth, metallic cloth (monel / SS),glass cloth, paper, nylon, polypropylene, polyesters,etc.

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Slimy or very fine solids tend to form impermeable cake Filter Aid

Slimy or very fine solids tend to form impermeable cake septum is plugged quickly.

Hence the porosity of the cake must be increased to allow theHence the porosity of the cake must be increased to allow thesmooth passage of liquid.

This is achieved by adding “filter aid”, such as purified woodThis is achieved by adding filter aid , such as purified woodcellulose, perlite, diatomaceous earth, or any other poroussolid (adsorbent) to the slurry, prior to filtration. Alternately,filter aid may be “precoated” on the septum, prior to theactual filtration.

The filter aid can be recovered by dissolving the cake (at theend of filtration) in a suitable solvent.If h lid h l h h h l k i b d If the solids have zero value, then the whole cake is burned outor suitably disposed off.

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Principles of Cake Filtration Filtration: a special case of “flow through porous media”. In case of filtration, the flow resistances increase with time,because EITHER the filter medium becomes clogged OR afilter cake builds up.Th f h i f fl h h di ” Therefore, the equations of flow through porous media”must bemodified to allow for this resistance build up.A ti EITHER th fl t d OR th As time progresses, EITHER the flow rate decreases OR thepressure drop increases.

Constant pressure filtration: ΔP is held constant and the flow Constant pressure filtration: ΔP is held constant and the flowrate is allowed to fall with time (more common).

Constant rate filtration: ΔP is progressively increased to give Constant rate filtration: ΔP is progressively increased to givea constant flow rate (less common).

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In cake filtration, the liquid passes through two resistances inseries, namely, cake and filter medium (septum).series, namely, cake and filter medium (septum).

Filter medium resistance: important only during the startup. Cake resistance: zero at the startup and increases with time.p The overall pressure drop at any time is the sum of thepressure drops over filter medium and cake.

Let pa = inlet (upstream) pressurepb = outlet (downstream) pressure

h b d b k d dip’ = pressure at the boundary between cake and mediumthen,

Δ ( ’) ( ’ ) Δ ΔΔp = pa–pb = (pa–p’) + (p’–pb) = ΔpC + ΔpMwhere,

Δp = overall pressure dropΔpC = pressure drop over filter cakeΔ d fil di

11ΔpM = pressure drop over filter medium

LC

Section through filter medium and cake at a time ‘t’LC

m

Filter area ┴ar to

paed

ium flow direction = A

p Direction offlow of slurryf c

ake

lter

me

’

Filtrateflow of slurry

face

of

Fil

p’

pb ream

fpb

Ups

tr

12L dL

Consider a thin layer of cake having differential thickness dL,situated at a distance of L from the filter medium.situated at a distance of L from the filter medium.

Let p = pressure at the above point. Assume: the velocity in the filter bed sufficiently low so as toassume “laminar flow” (realistic assumption).

The appropriate equation for “flow through porous beds withlaminar flow” is given bylaminar flow” is given by,

21 dp 150 . . u 2 3dL

2 3dL

.DS P

Since = volume-surface ratio . D 6 v S

S P p p2

=

2

24.17 . u 1 . s vp pdp

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3L

d

where, dp/dL = pressure gradient at cake thickness L μ = viscosity of filtrateμ viscosity of filtrate u = linear velocity of filtrate, based on filter area

f f i l ti l sp = surface area of single particle vp = volume of single particle ε = porosity of cake Φs = sphericity of particleΦs sphericity of particle

= ratio of surface area of a sphere (with the samevolume as the given particle) to the surface area ofvolume as the given particle) to the surface area ofthe particle:

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The linear velocity u at a time ‘t’ = u = (dV/dt)/Awherewhere, V = cumulative volume of filtrate collected up to time ‘t’Si h fil h h h i k ‘ ’ iSince the filtrate passes through the entire cake, ‘u’ isindependent of L.

V l f lid i th diff ti l l A dL (1 ) Volume of solids in the differential layer = A dL (1 – ε)If ρp = density of particles, then mass of solids in the differentiallayer dm = ρ A dL (1 ε)layer dm = ρp A dL (1 – ε)

Elimination of dL gives,

2k u 1 s v

k . . u . 1 . s v

1 p pdp dm3A

is used in place of to ac

. A . p

k 4 17 count for any non-ideality

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is used in place of to ack 4.171

count for any non ideality

Incompressible Filter Cakes During “low pressure drop filtration” operations, containingDuring low pressure drop filtration operations, containingrigid uniform particles, all factors (except ‘m’) areindependent of L, and hence the equation can be integrateddirectly.

IfmC = total cake mass, then integration gives,2 2

p mk . . u . 1 . s va C1 p pdp dm

3

3. A . p' 0p2

k u 1 s v m

k . . u 1 . s v . m

1 p p Cp - p' p

3a C . A .

p

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“Specific cake resistance” is defined as,

2 k . 1 . s vp . A 1 p pC 3u m

3 . u . m . C p

“Cake resistance” is defined as, . m A p . u

For incompressible cakes, specific cake resistance α isi d d t f th d d i d d t f th

, . m A p . uC C

independent of the pressure drop and independent of theposition within the cake.

A l l th “filt di i t R ” i d fi d Analogously, the “filter medium resistance RM” is defined as(ΔpM/μ . u).

R may vary with Δp because higher liquid velocities RM may vary with ΔpM, because higher liquid velocitiescaused by large ΔpM may force additional particles of solid into the filter medium.

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The total pressure drop = Δp = ΔpC + ΔpM

m . C . u RA M

At an appreciable cake thickness, ΔpM is negligiblecompared to ΔpC α can be assumed to be a functioncompared to ΔpC α can be assumed to be a functionof Δp instead of ΔpC this eases the integration.

u and m are expressed in terms of V the total volume u and mC are expressed in terms of V, the total volumeof filtrate collected till time ‘t’.

If c = mass of particles deposited per unit volume of If c = mass of particles deposited per unit volume offiltrate, then,mC = V . cAl (dV/d )/A Also, u = (dV/dt)/A

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Therefore total pressure drop Δp = ΔpC + ΔpM is givenTherefore, total pressure drop Δp ΔpC + ΔpM is givenby,

dV 1 V . c . p Rdt A A M

dt V . c . d

R

t A A M

R

... Basic equation fordV A . p A

cake filterM

... Basic equation for cake filter

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Constant Pressure FiltrationWh Δ i d i i h l When Δp remains constant during operation, the onlyvariables are V and t.

At t = 0 V = 0 and Δp = Δp ThereforeAt t 0, V 0, and Δp ΔpM. Therefore,μ . R dt 1M = = A Δ

A . Δp dV q0 0dt 1 1= . c . , where K == K . V +

, where K K . V + 2C A . dV q qC0 p

Integrating Kt 1

Integrating, t 1C = . V + V 2 q

0

A plot of t/V versus V will be linear, havingslope = K /2 and Y intercept = 1/q

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slope = KC/2, and Y-intercept = 1/qo.

Recommended readingg

Chemical Engineering – Volume 2 (Coulson; Richardson)

Unit Operations of Chemical Engineering (McCabe;S ith)Smith)

SOLVED and EXERCISE problems in the above books

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