laboratory cake filtration testing using constant rate

Please citehttp://dx.d

ARTICLE IN PRESSCHERD-1129; No. of Pages 10chemical engineering research and design x x x ( 2 0 1 2 ) xxxxxx

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Research and Design

r .com/ locate /cherd

Labor in

F.M. MaDepartment E11

a

A m w

a e sp

to lied

v ulate

d agni

th ing ra

is se co

p relia

w ble la

ers. P

K comp

1. Introduction

1.1. Filtration

Cake ltratfor both thity of the can be thesiderably mremoval of been manyimise the mIn most causing condratory vacugas in conmost indusand disc lto constantto feed a pconstant unare some siat the starare less likeing. In the

CorresponE-mail aReceived

ultimate pressure drop is over the lter medium from thestart of the ltration cycle, before signicant cake is formed,and this can lead to serious blockage of the lter medium,

0263-8762/$http://dx.do this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltration testing using constant rate. Chem. Eng. Res. Des. (2012),

ion is a widely practised and mature technologye recovery of solids and for ensuring the clar-ltrate (Svarovsky, 2000), either of which (or both)

desired product. It is acknowledged to be con-ore economical than thermal dewatering for theliquid from the retained lter cake, and there have

developments for industrial equipment to max-echanical dewatering effect (Earle and Earle, 1983).ses laboratory testing of a material is performeditions of constant pressure; normally using labo-um ltration, or an overpressure of compressedstant pressure ltration (Holdich, 2002). Howevertrial ltrations, apart from rotary vacuum drumters, are performed under initial conditions closer

rate: often a positive displacement pump is usedressure lter and the rate of ltration will remaintil a signicant back pressure is established. Theregnicant advantages in operating at low pressurest of the ltration cycle, the ne particles presently to penetrate the lter medium and cause blind-case of constant pressure ltration the entire and

ding author. Tel.: +44 1509 222519; fax: +44 1509 223923.ddress: [email protected] (R.G. Holdich).

9 August 2012; Received in revised form 10 October 2012; Accepted 19 November 2012

or compression of the initial cake layers. It can also lead tonon-conventional ltration conditions and lter cake non-uniformities (Stickland et al., 2005; Iritani, 2003).

For laboratory testing of moderately and highly compress-ible lter cakes the compression-permeability (CP) cell wasrecommended for use in the 1960s, but it was later shown thatthe pressure distribution within the cell is highly non-uniformand it has only limited use today (Mattsson et al., 2011; Iritani,2003). Furthermore, it is not possible to test the inuence ofsolid concentration on the ltration performance using a CPcell as concentrations need to be sufciently high for com-pression to be effective. The solids concentration can have asignicant inuence on the measured cake resistance and thelter medium resistance. When ltering low concentrationsthe ability of ne particles to migrate into the lter medium isgreater and during the initial stages of ltration the mediumresistance will rapidly increase to what is assumed to be a con-stant value, but often orders of magnitude greater than themedium resistance in the absence of solids (Kotlyarov, 1976).

In most laboratory studies the objective is to determinethe lter cake permeability, or specic cake resistance to l-tration, and how it varies with ltration pressure as well

see front matter 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.i.org/10.1016/j.cherd.2012.11.012j ourna l ho me page: www.elsev ie

atory cake ltration testing us

hdi, R.G. Holdich

of Chemical Engineering, Loughborough University, Loughborough L

b s t r a c t

precipitated calcium carbonate with Sauter mean diameter of 7.5

nd constant pressure in a comparative laboratory investigation. Th

vary between 1 109 and 1 1011 m kg1, depending on the appolume concentrations were between 0.42 and 0.54 (v/v). The calc

istribution data and the KozenyCarman equation is one order of m

e solids were extremely robustly characterised. Practical lter test

known to be essential. However, the conventional approach is to u

resented here demonstrate that constant rate ltration is a more

hen determining the lter medium resistance, and readily availa

2012 The Institution of Chemical Engine

eywords: Vacuum ltration; Calcium carbonate; Resistance; Cake oi.org/10.1016/j.cherd.2012.11.012g constant rate

3TU, UK

as ltered under conditions of constant rate

ecic cake resistance to ltration was found

pressure, and the corresponding lter cake

d specic resistance, from the particle size

tude lower than that measured, even though

ther than design based on size distributions

nstant pressure laboratory tests, the results

ble method for data acquisition, especially

boratory equipment is adequate for use.

ublished by Elsevier B.V. All rights reserved.

ressibility


ARTICLE IN PRESSCHERD-1129; No. of Pages 102 chemical engineering research and design x x x ( 2 0 1 2 ) xxxxxx

Nomenc

A C c

L m and n PcRms t Vxsv

Greek let

avP Pc

s

as informastabilised. constant pber of yeathe agreempredictablepredominaspecic res(Rushton angeneous coprovides bedent of cakfound that pressure question oconstant pparameterswhen usedltration eqrate. In theis not easyusing readi

Under cpressure wportional tolter mediuto the resisow rate. Ptration andet al., 2000;1960; Tiller,tration andfunction ofin time.

Increasisity by redpressure hawhich prov

n, 20e spe

0(1

av issurcake

mat be i

n caof co

Filt

ing (1992vantnt ra

Cotage

ge ne liqrily presplicit

adva

ulatie is oonnee st

blishriod re is n

Cotage

er ane lstrystanogenace.

pardented.

adva

appl thicse o

test

ommof sesistasedlature

cross sectional area (m)solid concentration by volume fractiondry mass of solids per unit ltrate volume(kg m3)bed height (m)coefcients of the solid/liquid systemcake pressure (Pa)medium resistance (m1)solid concentration of the slurry by masstime (s)volume of ltrate (m3)Sauter mean diameter (m)

tersspecic cake resistance (m kg1)average specic cake resistance (m kg1)pressure drop (Pa)pressure drop over the cake (Pa)liquid viscosity (Pa s)liquid density (kg m3)solid density (kg m3)

tion on the lter medium resistance, after it hasThere have been studies comparing data fromressure and constant rate ltrations over a num-rs (Tiller, 1953; Tarabara et al., 2002). Generally,ent between these two approaches is good, and, provided that the solids under investigation arently incompressible. Other studies have shown thatistance by the two techniques can be quite differentd Matsis, 1994). It has been proposed that a homo-nstant growth rate of cake using constant ratetter packing structure of particles that is indepen-e thickness (Greil et al., 1992). Virezub et al. (1977)constant rate provides more ltrate than constantltration in less time. These latter studies raise an the ability of the usually employed laboratoryressure ltration tests to determine the ltration; specic resistance and lter medium resistance,

to predict the performance of, or design, industrialuipment operating under conditions of constant

laboratory constant pressure is used because it to provide constant rate ltration test conditions,ly available laboratory equipment.onstant rate the principal variables correlated areith ltrate volume, or ltration time which is pro-

the pressure. In the initial stages of ltration, them has no cake and the measured pressure is due

tance of the medium with initial deposit for a givenressure then rises, depending on the slurry concen-

other parameters in the system (Chi, 2006; Rushton Greil et al., 1992; Shpanov, 1973; Tiller and Cooper,

1955). It is usual to dene an average cake concen- average specic resistance, both of which may be a

the applied pressure over the cake, at any instance

ng the applied pressure increases the cake den-ucing the spaces between particles. In general,s greater effect on soft and occulated materials,ide highly compressible lter cakes (Wakeman and

Tarletoaverag

av =

wherethe preof the for theav can0 andseries

1.2.

Accordet al. the adconsta

1.2.1. Advan

A hu Sinc

essacom

Sim

Dis

Calctherpers

At thestaa pe

The

1.2.2. Advan

Uppin th

Indu Con

homsurf

Thepenform

.Dis

Thecake

In cathis

It is ceffect cake rtions b this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.01205; Nicholas, 1998). The equation used to correlatecic resistance and pressure is

n)Pnc (1)

s the average specic resistance of the cake, Pc ise drop across the cake, 0 is the specic resistance

under a pressure drop of 1 bar and n is a constanterial, called its compressibility. This expression fornserted into the ltration equations and values forn be determined experimentally by performing anstant pressure ltrations at different pressures.

ration conditions and benets

to a number of research workers including Greil), Tiller and Cooper (1960) and Tiller (1955, 1953)ages and disadvantages of constant pressure andte ltration are:

nstant pressure ltrations

umber of experimental studies.uid ow in the cake is additive, the ow rate nec-increases as the liquid approaches the mediumsing the lter cake.y of obtaining the data.

ntages

ons and results have to be treated with caution;ften a lack of consistency, especially when differentl perform the tests.art there may be experimental difculties, such asing a constant pressure over the lter cake, due toof medium blocking.ot enough time to study the initial ltration period

nstant rate ltrations

d lower limits on the variation of solids pressureter cake can easily be obtained.

use is widespread (apart from vacuum lters).t growth rate of the cake is induced with reports ofeous particle incorporation into the growing cake

ticle packing structure is expected to be inde- of cake thickness so that uniform compacts are

ntages

ied pressure has to be continuously increased withkness.f investigating gas deliquoring under pressure thenrig would need to be modied.

on in data analysis to assume that there is noedimentation during cake formation. Hence, theance and permeability are calculated using equa-

on Darcys law for liquid ow through a cake from testing using constant rate. Chem. Eng. Res. Des. (2012),


ARTICLE IN PRESSCHERD-1129; No. of Pages 10chemical engineering research and design x x x ( 2 0 1 2 ) xxxxxx 3

mag

graphical ptrate volumagainst ltring most run, whichthe already2005; Wake

1.3. Bas

As ltrationmulates onfound from

rate of ltra

By applying

Q = dVdt

= A

where Q is across the

P =(

R

A

)

where R ismedium (R

Additionprovides thconstant pr

t

V= avc

2A2

where t is tliquid viscodry mass oltration cand slope o

The equ

P = avcA2

Eq. (5) shoresistance are constan

nts f a liby deon (5pt cbut nce

Ma

Ma

sionnufa9%, repa

sedias tusperse p wthister odyna(SEMboid

, seemeteFig. 1 Scanning electron microscope (SEM) i

lots of time over ltrate volume plotted against l-e (constant pressure) or ltration pressure plottedate volume, or time (constant rate). In general, dur-ltration tests there are three regions during a test

are: cake formation, transition and ow through formed cake region (Couper et al., 2010; Li et al.,man and Tarleton, 2005).

ic analysis

proceeds, a porous cake of solid particles accu- a porous lter medium; its ltration rate can be

tion = driving forceresistance

Darcys law the ow rate will be

P

R(2)

the volumetric rate of ow, and the pressure droplter is

(dV

dt

)(3)

the total resistance that is formed of the lter

m) and the lter cake. of the lter cake and medium pressure drops

constaslope ostant, equatiintercetance, resistacake.

2.

2.1.

Suspen30 mations: were pwhere(v/v) wEach sin revewith ta8 and diameLaser scope a rhomcalcitecle dia this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012

e well-known linear equation for the analysis ofessure ltration:

PV + Rm

A p(4)

he ltration time, V is the ltrate volume, is thesity, A is the cross section ltration area, c is thef solids per unit ltrate volume, Rm and av, areonstants that may be evaluated from the interceptf the t/V vs. V plot, respectively.ation for constant rate ltration is

(V)dV

dt+ Rm

A

dV

dt(5)

uld be linear, provided that the average specicand dry cake mass per unit volume of ltratet; i.e. for incompressible ltration. The ltration

recirculatio

2.2. Me

Constant racell with a424 mL as rsuck the cake. To enltration, amanufactubyshire, UKmembranesured hydrtested by a the base ofducer (HCXe of calcium carbonate.

in Eq. (5) can then be found from the intercept andnear plot of P against V, noting that dV/dt is a con-nition. In the case of compressible cake ltration) is still valid, at any increment in time, and thean be used to determine the lter medium resis-the relation will deviate from linearity as specicchanges with the applied pressure over the lter

terials and methodology

terial

s of aqueous calcium carbonate (CaCO3 Fordacal-ctured by MINELCO) at different solid concentra-11%, 13%, 15%, 17%, 19% and 21% by volume,red. In order to avoid too dilute feed suspension,mentation may inuence the ltration results, 9%he lowest initial suspension concentration used.nsion was prepared by dispersing the dry powderosmosis water to avoid the ionic variation foundater usage. The natural pH of the suspension was

was constant for all the tests. A Sauter meanf 7.5 m was measured using a Horiba LA-920-wetmic scattering device. Scanning electron micro-) images of the calcium carbonate powder showal shape, indicating that the material is mainly

Fig. 1. The values of the D10, D50 and D90 parti-rs, measured by the Horiba at a variety of different testing using constant rate. Chem. Eng. Res. Des. (2012),

n pump speeds, are shown in Fig. 2.

thodology

te ltration tests were performed in a clear acrylicn inner diameter of 60 mm and total volume ofepresented in Fig. 3, using a laboratory pump toltrate through the lter medium and depositingsure a clear ltrate in all tests and promote cake

metal microporous membrane, with 10 m slots,red by Micropore Technologies Ltd. (Hatton, Der-) was used as the lter medium. This 10 m rated

had a nominal thickness of 0.06 mm and a mea-aulic permeability of 1.2 1013 m2, when clean,series of water ow tests at different pressures. At

the cell, within the ltrate line, a pressure trans- Series Honeywell S&C) was used to monitor the



Fig. 2 Variation of the particle diameters (D10, D50 and D90) over time for six different pump speeds (P.Sp.) 1, 3, 6, 9, 12 and15 rpm during analysis by laser diffraction.

vacuum. A vacuum gauge (WIKA Instruments Ltd.) was alsoconnected to the system in order to validate and check thesensor reading. The ltrate was pumped out using a peri-staltic pump (Watson Marlow 401U/D1) and collected in avessel placed on an electronic balance (OHAUS SPU601). Theweight of the ltrate and pressure drop in the system, as afunction of time, were recorded using a PC within Labviewsoftware. For the tests three different ltrate pump settingswere used (10, 30 and 50%) of full-scale, which gave rise to

three different ltration rates and cake forming pressure pro-les.

The same suspension was used many times, to avoid anyvariability in the feed material. The loss in the reused sus-pension was monitored between ltrations and found to bevery low (approx. 1% between runs). The dead volume belowthe microporous membrane and within the lter tubes waslled with ltrate from a ltration of similar CaCO3 beforestarting an experiment, in order to avoid missing ltration this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012

Fig. 3 Schematic diagram of constant rate vacuu testing using constant rate. Chem. Eng. Res. Des. (2012),

m ltration equipment.



Table 1 witmeasurem

In. concen m)

9%

11%

13%

15%

17%

19%

21%

a 95% con o timmeasurem

data at thethis dead vwas preparleast 24 h, whad reacheTo validatea vernier-scve differeaverage cakcentration.the lter mcake surfacdifference membrane

For comwere also ptions of cousing the applied bypositioned of ltrate rvalve was udifferent am

3. Re

3.1. Clu

3.1.1. SEMFrom Fig. 1 together, fofused togetthe cake bycake and, liaspect that

lusted, thalyss (Di

stuing.Measured cake heights and determined cake concentrationsents.

tration (v/v) Pump speed (rpm) Cake height (m

5 20.12 10 19.31 30 18.28

5 24.36 10 21.21 30 19.85

5 31.35 10 27.76 30 26.61

5 36.38 10 32.33 30 30.34

5 44.22 10 35.48 30 34.72

5 45.02 10 39.30 30 37.86

5 51.81 10 44.68 30 42.09

dence that the concentration is the one provided plus or minus twent variability.

very early stages of the experiment due to llingolume. Before each series of tests, the suspensioned and left at room temperature (20 2 C) for atith periodic mixing. This ensured that the system

d ionic equilibrium and avoided thermal gradients. the calculations of the nal cake concentrationsale measuring calliper was used; measuring over

form cappliethe anprocesisationcluster this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012

nt positions of cake height per test and using thee height for a mass balance to give the cake con-

Measuring was done from the top of the cell toedium before starting the experiment and to thee at the end. The cake height was, therefore, thebetween these two. It was possible to clean the

after each run and reuse it.parison with the constant rate ltration data, testserformed in a similar ltration cell under condi-nstant pressure. The same material was ltered,same lter medium as before. The vacuum was

a vacuum pump and the vacuum receiver wason a scale balance in order to measure the massecovered with respect to ltration time. A needlesed to bleed air into the vacuum receiver, to enableounts of vacuum across the lter to be achieved.

sults and discussion

ster formation analysis

imageit is uncertain if particles are loosely agglomeratedrming clusters, or if the particles are composed ofher crystals. Fine particles may be dragged through

the shear eld into the lower regions of the lterkely to, be deposited at the lter medium. Another

was considered is the ability of the particles to

3.1.2. ResThe variatitime for sixing the laseis shown intion and thof variationno signicasuggesting material uning these te

3.2. Ca

Cake concethe startintered, togetlter area, the height cance baseerror on thetwo times tmeasured hbased on 9show that t5% with an1.5% when more homoh 95% condence limits on height

Cake concentration (v/v) Errora% ()0.475 4.460.494 4.450.522 4.90

0.479 2.760.550 3.170.588 3.40

0.440 4.480.497 5.060.518 5.30

0.438 2.050.492 2.300.525 2.40

0.408 2.190.508 2.740.520 2.80

0.448 1.170.513 1.340.533 1.40

0.430 1.950.499 2.270.528 2.40

es the standard deviation based on the cake height

rs that may compress with a variable pressureis has been shown to have a major inuence onis and modelling of ltration and sedimentation

Giovanni et al., 2012). Hence, a particle character-dy was performed investigating the possibility of testing using constant rate. Chem. Eng. Res. Des. (2012),

ults analysis and cluster formationon of the D10, D50 and D90 particle diameters over

different values of shear elds created by increas-r diffraction equipment pump speed from 1 to 15,

Fig. 2. This work done with and without sonica-e results were the same for both cases. The lack

of these particle diameters shows that there wasnt aggregation of the calcium carbonate particlesthat particle clustering is not a problem with thisder the prevailing conditions. The water used dur-sts was collected ltrate.

ke concentration and uniformity

ntration was determined using the knowledge ofg volume concentration and volume of slurry l-her with the measured lter cake heights and theby a material balance. The standard deviation ofmeasurements was calculated and a test of signi-d on 95% condence was applied: i.e. the expected

calculated cake concentrations are plus, or minus,he standard deviation around the mean value. Theeights, calculated cake concentrations and error,5% condence are shown in Table 1. The resultshe expected error decreased rapidly from approx.

initial slurry concentration of 9% (v/v) to less thanusing 19% (v/v) feed suspension, a consequence of ageneous bed structure being formed. It is assumed



Fig. 4 Effe ionspump spee .

that the cakout its heig

The uncresent twoconcentratused to callevel in theillustrated which depetration. Pumconsequenthe expectetration. Thethe dry cakusing Eq. (6

c =(1 s)/

where C is mass fractiand is the

One aspity of the eltration tesample canconcentratever, obtainmore difcentire cakeof the expenation of tcan be usetion by combalance: i.eUsing the kto be predithe measurvalue, thenhere the mmately 2%,be assumed

ally o anale taniforst eq

the lter

oposs dug mi

Spre te

o lin the c resons ct of pressure on cake concentration with initial concentratd 5, 10 and 30 [errors bars provide 95% condence interval]

e is of uniform, or average, concentration through-ht and is discussed further later.ertainty bars around the mean values in Fig. 4 rep-

times the standard deviation around the meanion value, based on the ve height measurementsculate that concentration. Hence, the condence

cake concentration is again 95% within the rangeby the bars. Fig. 4 shows three different trends,nd on pump speed and initial suspension concen-p speed determines the ltration ow rate and,

tly, the pressure drop in the lter cake, which hasd power-law type of relation with the cake concen-

cake volume concentration was used to calculatee mass per unit volume of ltrate (Holdich, 2002),).

1(s) (1 C)/(Cs)

(6)

the cake concentration by volume fraction, s is theon of solids in the slurry, s is the density of solids

Finfor thea sampcake usimpleend ofslurry

c = sMVF

It is prslurrielterin

3.3. pressu

The twresentspeciltrati this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012

liquid density.ect of the reported work is to assess the applicabil-xperimental technique to an industrially relevantsting study. In such a case, it is likely that a slurry

be taken from a process stream, and the solidsion by mass could be determined (by drying). How-ing a representative sample of the lter cake is

ult and it is time-consuming to weigh and dry the. The measurement of the cake height at the endriment is a much more rapid method for determi-he dry cake mass per unit ltrate volume, and itd to check the uniformity of the cake concentra-parison with the height predicted from a volume. cake volume = original volume ltrate volume.nowledge of the lter area enables the cake heightcted and compared with the measured height. Ifed height is signicantly higher than the predicted

the lter cake is not uniform. In the tests reportedeasured and predicted heights agreed to approxi-

suggesting that a uniform cake concentration can.

tests are shdifferent st21% (v/v). Tthe pressurresistance,determine ity of theseup to aboucompleted.achieved ua constantent constanlinearity istion the inwith pressuexpected fron an expaoften the c

Both sewere used tance and p 921 (% v/v); number in the gure indicates

n the subject of using the experimental techniquelysis of industrially relevant ltration testing usingken from a process stream, if conrmation of themity by height measurement is not required, theuation for dry cake mass per ltrate volume at theltration comes from the knowledge of the mass ofed (M) and the ltrate volume (VF):

(7)

ed that Eq. (7) would be used for most industriale to its simplicity and ability to be applied whenxtures, where densities are less likely to be known.

ecic resistance by constant rate and constantsting

ear equations represented by Eqs. (5) and (4) rep-conventional method of analysis for determiningistance from constant rate and constant pressurerespectively. Examples of the results from these testing using constant rate. Chem. Eng. Res. Des. (2012),

own in Figs. 5 and 6 respectively. In Fig. 5 threearting concentrations are illustrated: 11%, 15% andhere is a very slight intercept above the origin one axis, indicating a small but nite lter medium

in accordance with Eq. (5). It is relatively easy tothe intercept from the cut-away graph and linear-

data plots is good, after about 10 mL of ltrate andt 120 mL, after which the ltration is substantially

For comparison, Fig. 6 shows a typical set of datasing the constant pressure ltration equipment, at

feed concentration of 11% (v/v), and three differ-t applied pressures: 0.2, 0.4 and 0.6 bar. Again the

good, but as is typical of constant pressure ltra-tercept values are highly scattered and the trendre (for a constant value of Rm) is not as would beom Eq. (4). It did not help to plot the initial datanded scale, as it was very randomly scattered, as isase in constant pressure ltration.ts of data, together with a number of other tests,to determine the relation between specic resis-ressure. The log plot for the constant rate tests is



Fig. 5 Measured ltration pressure during ltration at three starting concentrations: 11%, 15% and 21% (v/v) with 10 rpmpump spee

shown in Fiues plottedrate ltratiresistance w

av = AcV

[

The end poappropriatethat the coquately; mocake mass Table 2 shoobtained byand constaappear to brial of modthe data foobtained fr

en it vo

doetratic ronce

the eltimy solringre, wratioes alp concicoint:ed, aa lowarith

Fig. 6 Conanalysis byd.

g. 7, where the specic resistance and pressure val- were determined by the end point of the constanton data: i.e. the last recorded values for specicith pressure using the rearranged form of Eq. (5):

PA

(dt

dV

) Rm

](8)

int of the ltration was deemed to be the most part of the ltration for this analysis, to ensurenditions within the lter cake had stabilised ade-st specically, the lter cake concentration or dryper unit volume of ltrate (Rushton et al., 2000).ws data comparing the ltration scale up constants

using the two ltration techniques: constant ratent pressure. It is noticeable that the data doese very similar, as would be expected for a mate-erate compressibility. Also included in Table 2 is

Whper untrationconcenof specless, cduringto its uther, bcompapressuthe ltprovidscale uthe spedata pexpecting in the log this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012

r the cake concentration as a function of pressure,om the data illustrated in Fig. 4.

constants,

stant pressure ltration of calcite at 11% (v/v) starting concentra parabolic rate law.ltering compressible materials the dry cake masslume of ltrate will vary with pressure, as concen-s, see Eq. (6). However, it is usual for the variation ofion with pressure to be much less than the variationesistance with pressure (Holdich, 2002). Neverthe-ntration will vary during a constant rate ltrationarly stages, as the pressure applied rises from zeroate value. It is informative to investigate this fur-ving Eq. (8) for all times during the ltration and

the values of specic resistance, as a function ofith the average values obtained at the end of allns; at known values of pressure and ow rate. Fig. 7l the data used to determine the specic resistancestants, which were provided in Table 2. In all cases

resistance was determined from the last ltration i.e. values of pressure and ow rate. As would be

low pump speed provides a low pressure result-er specic resistance. A best t line was used onmic data to provide the values for the scale-up testing using constant rate. Chem. Eng. Res. Des. (2012),

as indicated by Eq. (1).

tion and three total applied pressures for



Fig. 7 Effe tionindicate pu

Table 2 pressure coefcienconstants

Techniqu

Constant rConstant p

a Initial cob Initial co

In Fig. 8 lated, accorresistance pressure issure the ltand equal value of 1.4specic resClearly, as

concice macremmen

Fig. 8 Th(v/v) feed sct of pressure on cake ltration resistance, initial concentramp speeds 5, 10 and 30 rpm.

Comparison of constant rate and constantltration techniques for the determination ofts in the constitutive equations for scale-up.

e 0 (m kg1) n Co (v/v) m

use thefor spedry caktime inexperi this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012

atea 6.78 109 0.19 0.25 0.08ressureb 5.53 109 0.18

ncentration 921% (v/v) applied pressure range 880 kPa.ncentration 13% (v/v), applied pressure range 3060 kPa.

the specic resistance at each time interval is calcu-ding to Eq. (8), and this is compared to the speciccalculated using Eq. (1), where the cake forming

used. In order to determine the cake forming pres-er medium resistance was assumed to be constantto the value determined from Fig. 5. This gave a3 109 m1. The agreement between the values ofistance calculated by Eqs. (1) and (8) is very good.an experimental technique it would be possible to

function ofexperimention functioprovides a (8)). In Fig.cic resistafor permeaequation is

av = 3(1 C

where K is tventionallythe particleKozeny con

e effect of pressure during constant rate ltration test on the speolids at 10 rpm pump speed and theoretical resistance by Kozens from 9 to 21 (% v/v); numbers in the gure

stant rate ltration equipment to determine values resistance as a function of pressure, provided thess per unit volume of ltrate is recalculated at eachent, as it was using Eq. (6) and then Eq. (8). Just one

t would provide the data for specic resistance as a pressure over a wide range of pressures, but a fewts are required to determine the cake concentra-nality with pressure as illustrated in Fig. 4 (whichconstitutive equation for the analysis used in Eq.

8, an additional comparison is provided by spe-nce calculated using the KozenyCarman equationbility and hence specic resistance. The resulting:

6KC

)3x2svs(9) testing using constant rate. Chem. Eng. Res. Des. (2012),

he Kozeny constant, a value of 5 was used as is con- assumed, and x2sv is the Sauter mean diameter ofs. It is fairly common for the text book value of thestant to provide values of permeability, and hence

cic cake resistance during ltration of the 21%yCarman.



Fig. 9 The diumand time.

specic restance (highthat this ocharacterisFig. 2. Hening when dsystem, detechnique fto a value resistance d5 is signic

The constant pressof providinnumber of specic respressure; ttion equivascattered astant pressremains covary duringthat shouldtotal pressupressure medium aninitial stagerises from zally assumthe cake bupressure foing constavarying. This illustratehere in Figsure drop ddrops downthat this is 30 mbar, eqcentration constant p

asterre wnto on mild es.ummis ofsamte smvide it vinede fra. At l

speeted tion percentage of total ltration resistance due to the lter me

istance, that are an order of magnitude lower resis-er permeability) than are measured. It is notableccurs even here when using very stable and welled solids, as evidenced by the data illustrated ince, there is a signicant need for laboratory test-esigning ltration systems and the constant ratescribed here, provides a convenient and thoroughor such analysis. By changing the Kozeny constantof 33 it was found possible to match the specicata illustrated in Fig. 8, but the text book value ofantly in error.ventional technique for laboratory testing is a con-ure ltration. Supercially, this has the attractiong a xed and known pressure drop so that a limitedexperiments, typically four, may provide values ofistance and cake concentration as a function ofo provide the data for Eq. (1) and its concentra-lent equation. However, the results are often very

to be fbut theticles iltratimore mrate us

To sanalysslurry separato proper undetermvolumEq. (6)(pumpillustracentra this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012

nd one reason for this is due to the lack of con-ure conditions. Even if the total applied pressurenstant, the pressure drop over the lter cake will

an experiment and hence so will the pressures be used in Eq. (1); where cake forming and notre should be used. At the start of the constant

ltration the total pressure drop is over the lterd zero pressure is over the lter cake. During thes the proportion of the pressure drop over the cakeero to a nite amount. After a short while it is usu-ed that the total pressure drop is now acting overt between the start of the ltration, and the end, therming the cake will be changing. Hence, even dur-nt pressure ltration the cake forming pressure ise point of varying resistance over the lter mediumd for the constant rate ltration data investigated. 9. At the start the percentage of the total pres-ue to the lter medium is 100%, but this quickly

to a negligible amount. The inset graph showsa period during which the applied pressure rises toual to 200 s. Hence, over the rst 200 s the cake con-would be expected to be changing rapidly. Duringressure ltration this stabilisation period is likely

initial stagetion of Rm,remain conover the lforming preof ltrate a(6), using thdrop over tcake forminthe total prpossible to forming pre

4. Co

The acquisobtained fconditions vacuum incloser to cocake will bwill also vatesting is no as a function of total applied ltration pressure

, as the applied pressure is normally much higher,ould also be a higher pressure driving the ne par-the ltration medium. This will lead to a greateredium resistance than when operating under thepressures at the start of the ltration that constant

arise, the constant rate laboratory equipment for ltration performance is best used as follows. Aple to be tested is taken and weighed (M) and aall sample is weighed, dried and weighed again

a value for s. After ltration the dry cake massolume of ltrate for the entire ltration can be

from Eq. (7). The average cake concentration byction can be determined from a rearranged form ofeast three different cake forming pressure rangesds) should be used, to obtain data similar to that

in Fig. 4 and suitable for determining the cake con-constants with pressure as provided in Table 2. The testing using constant rate. Chem. Eng. Res. Des. (2012),

s of the ltration are important for the determina- as illustrated in Fig. 5. This is then assumed tostant during ltration, allowing the pressure dropter medium to be calculated and hence the cakessure. The average dry cake mass per unit volumet any instance in time can be determined from Eq.e cake volume fraction calculated for the pressurehe cake only. The specic cake resistance, at theg pressure, can be calculated using Eq. (8), where

essure difference is used in this equation. It is thenuse Eq. (1) to correlate specic resistance with cakessure.

nclusions

ition of design data for cake ltration is normallyrom laboratory investigations performed underof constant pressure ltration. However, most non-dustrial ltrations are under conditions that arenstant rate, where the pressure drop over the ltere varying signicantly and the cake concentrationry with time. Constant rate laboratory ltrationt normally conducted as the laboratory equipment



is not so prevalent. However, it is possible to induce ltra-tion by means of a simple laboratory peristaltic pump and tovery precisely monitor the mass of ltrate with time usinga balance. Using this procedure reliable data points at thestart of the ltration can be determined, providing a reli-able value for the lter medium resistance. The robustnessof this data is superior to what is normally obtained from thealternative constant pressure ltration data. Even in the caseof constant total pressure ltrations, the pressure differencegoing to fothe total pat the starthe end of tcan only bewhich is nstant pressareas.

Once it tance can band the vaprovide thelaw. Hencevalue of prinstance inspecic resplotted agaa constant mation thathe purposas measureover a numon the relia

The rancourse, limsignicant at normal ashing iswhen condvacuum puever, it is wspecic respressure rabecomes lelaw equatiorelevant re

Acknowl

The authorEducation a

Reference

Chi, T., 2006ExperimISBN 0-4

Couper, J.R., Fair, J.R., Penney, W.R., Walas, S.M., 2010. ChemicalProcess Equipment: Selection and Design, 3rd ed. Elsevier Inc.,Oxford, UK (p. 337, Chapter 11).

Di Giovanni, B.A., Mahdi, F.M., Starov, V.M., Holdich, R.G., 2012.Particulate clusters and permeability in porous media. Chem.Eng. Res. Des., Part (A) 90, 11681176.

Earle, R.L., Earle, M.D., 1983. Mechanical Separations UnitOperations in Food Processing: An Introduction to thePrinciples of Food Process Engineering. NZIFST (Inc.) (Chapter10) http://www.nzifst.org.nz/unitoperations/index.htm

., Gruationation254., R.Grmat

E., 20bra

ov, Gationation

matKisermeabarati.on, Tl ltr

exp4573as, P.,terwon, A.

Sepanhein, A.ationarativ, N.ationrmopnd, Astantsky, Lterwora, V.smeticle

19 (6.M., Cstant.M., 1lyticag. 54 .M., 1hodsed on, A.Iartsm

pres1811an, Rle-up

ISBNrm the lter cake will vary; as the proportion ofressure over the lter medium varies from 100%t of the ltration to a much lower value towardshe ltration. The actual pressure forming the cake

calculated knowing the lter medium resistance,otoriously difcult to achieve when using a con-ure ltration with small samples of slurry and lter

has been reliably established, the medium resis-e assumed to remain constant during the ltrationlues of ltration rate at any instance in time will

pressure drop over the lter medium from Darcys, by deduction from the total pressure drop theessure over the lter cake can be calculated at any

time. Likewise, it is possible to deduce the averageistance to ltration at any instance and this can beinst the prevailing cake forming pressure. Hence,rate ltration provides much more detailed infor-n the alternative constant pressure ltration, fores of ltration analyses. Mass balancing tests, suchment of the formed cake height, and its variabilityber of different locations, can also be used to checkbility of the information obtained.ge over which the pressure may be varied is, ofited by the vapourisation of the liquid. This is not aproblem when ltering water based suspensionstemperatures encountered in the laboratory, but

a known problem with vacuum ltration systemsucting constant pressure ltration tests using amp, and even vacuum ltration equipment. How-orth noting that the most noticeable variation ofistance with pressure is found within the lowernge; as pressure increases, the change in resistancess pronounced as would be expected of a powern such as that shown in Eq. (1). Hence, the most

gion to investigate is the lower pressure one.

edgements

FMM is grateful to the Libyan Ministry of Highernd Sirte University, Libya for sponsoring this work.

s

. Introduction to Cake Filtration Analysis,ents and Applications. Elsevier B.V., The Netherlands,44-521 56-9.

Greil, PFiltrFiltr247

HoldichInfo

Iritani,Mem

Kotlyarltrltrand

Li, W., perSepUSA

Mattsslocafrom66,

NicholBut

RushtoandWei

RushtoFiltrSep

ShpanoltrThe

Sticklacon

SvarovBut

TarabatranparSci.

Tiller, Fcon

Tiller, FanaPro

Tiller, Fmetbas

VirezubShvand(2),

WakemScaUK, this article in press as: Mahdi, F.M., Holdich, R.G., Laboratory cake ltrationoi.org/10.1016/j.cherd.2012.11.012ber, U., Travitzky, N., Kulig, M., 1992. Pressure of Silicon Nitride Suspensions with Constant Rate. Materials Science and Engineering: A 151,

., 2002. Fundamentals of Particle Technology. Midlandion Technology & Publishing, UK, ISBN 0954388100.03. Properties of Filter Cake in Cake Filtration andne Filtration, KONA (21), Japan..G., 1976. Investigations of the relations between the

constant of low-concentration suspensions and pressure and solid-phase concentration, chemistryerials science. Chem. Petrol. Eng. 12 (5), 416418., C., Richard, Q., 2005. Development of a lter cakeility test methodology. In: American Filtration &ons Society Conferences, 19 September,

., Sedin, M., Theliander, H., 2011. Zeta potential andation properties: constitutive relationships for TiO2erimental ltration measurements. Chem. Eng. Sci.4581.

1998. Cheremisinoff. In: Liquid Filtration, 2nd ed.rth-Heinemann, USA, ISBN 0-7506-7047-9., Ward, A.S., Holdich, R.G., 2000. SolidLiquid Filtrationration Technology. VCH, Verlagsgesellschaft mbH,m, Federal Republic of Germany., Matsis, V.M., 1994. Studies of Constant Rate

in Dead-End and Cross ow Modes, Filtration andon. Elsevier Science Ltd, 31, p. 643.V., 1973. Calculation of constant rate cake forming, chemistry and materials science. Invest. Calculat.hys. Process. 9 (12), 10771082..D., De Kretser, R.G., Scales, P.J., 2005. Nontraditional

pressure ltration. AIChE J. 51 (9.).., 2000. Solid Liquid Separation, 4th ed. Oxford,rth-Heinemann, UK, ISBN 0 7506 4568 7.V., Hovinga, R.M., Wiesner, M.R., 2002. Constantmbrane pressure vs. constant permeate ux: effect ofsize on crossow membrane ltration. Environ. Eng.), 343355.ooper, H.R., 1960. The role of porosity in ltration. IV:

pressures ltration. AIChE J. 6 (4), 595601.955. The role of porosity in ltration. Part 2:l equation for constant rate ltration. Chem. Eng.(6), 282290.953. The role of porosity in ltration: numerical

for constant rate and constant pressure ltration Kozenys law. Chem. Eng. Prog. 49 (9), 467479.., Glazunov, V.B., Lobanova, N.N., Grenin, V.I.,an, I.G., 1977. Viscose ltration at constant speed

sure, chemistry and materials science. Fibre Chem. 982..J., Tarleton, E.S., 2005. Solid/Liquid Separation:

of Industrial Equipment, 1st ed. Elsevier Ltd., Oxford, 1 8561 74204. testing using constant rate. Chem. Eng. Res. Des. (2012),

Laboratory cake filtration testing using constant rate1 Introduction1.1 Filtration1.2 Filtration conditions and benefits1.2.1 Constant pressure filtration1.2.2 Constant rate filtration

1.3 Basic analysis

2 Materials and methodology2.1 Material2.2 Methodology

3 Results and discussion3.1 Cluster formation analysis3.1.1 SEM image3.1.2 Results analysis and cluster formation

3.2 Cake concentration and uniformity3.3 Specific resistance by constant rate and constant pressure testing

4 ConclusionsAcknowledgementsReferences