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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
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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),
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ARTICLE IN PRESSCHERD-1129; No. of Pages 10chemical engineering
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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
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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.
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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
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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
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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
-
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ARTICLE IN PRESSCHERD-1129; No. of Pages 108 chemical
engineering research and design x x x ( 2 0 1 2 ) xxxxxx
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.
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ARTICLE IN PRESSCHERD-1129; No. of Pages 10chemical engineering
research and design x x x ( 2 0 1 2 ) xxxxxx 9
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
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ARTICLE IN PRESSCHERD-1129; No. of Pages 1010 chemical
engineering research and design x x x ( 2 0 1 2 ) xxxxxx
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
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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.
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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