Desalination 158 (2003) 259–265

0011-9164/03/$– See front matter © 2003 Elsevier Science B.V. All rights reserved

Presented at the European Conference on Desalination and the Environment: Fresh Water for All, Malta, 4–8 May 2003.European Desalination Society, International Water Association.

*Corresponding author.

Mechanical dewatering of suspension

D. Mihoubia*, J. Vaxelaireb, F. Zagroubaa, A. Bellagic

aInstitut National de Recherch Scientifique et Technique, B.P. 95, 2050 Hammam-Lif, TunisiaFax +216 71430934; email: daoued.mihoubi@etud.univ-pau.frbLGPP-ENSGTI, EA1932, Rue Jules Ferry, 64000 Pau, France

cEcole Nationale d’Ingénieurs de Monastir, Av. Ibn Eljazzar, 5000 Monastir, Tunisia

Received 3 February 2003; accepted 10 February 2003

Abstract

Most of plants producing or treating solid–liquid mixtures generate a large amount of residual sludge. Manymineral types of slurry occur in a large range of industrial wastes, including those from mining, ceramics, paper andhealth care industries. Nowadays, according to new environmental regulations, a reduction of these waste volumesis required. Owing to their relatively low energy cost, filtration processes are often preferred to thermal dryingdevices to achieve this volume reduction. Because of the difficulty of the rheology behaviour of the residual sludgeand its stability, we chose to use a synthetic suspension approach to the residual sludge. In this work, mineral sludge(kaolin) was considered. Some experiments were carried out on laboratory filtration–compression cells; the use ofthe Ruth relationship and the approach of Shirato and co-workers were tested to characterise this slurry in filtrationand compression, respectively.

Keywords: Filtration; Consolidation; Expression; Modelling; Solid–liquid separation; Ruth relationship

1. Introduction

Reduction of liquid content is important totrucking cost and the landfill characteristics ofwaste materials. Decreased energy requirementsfor drying and improved incineration result fromlowered moisture fractions. The energy required

to express liquid from cake is negligible comparedto the heat required for drying. Consequently, itis desirable to remove the maximum feasibleamount by mechanical pressing. Many filters areequipped with membrane for expression. Signi-ficant questions include knowing what pressureshould be used during filtration and expressionto effect the best results. With the advent of

260 D. Milhoubi et al. / Desalination 158 (2003) 259–265

controls on the liquid content of wet cake, solid–liquid engineers are able to use height filtrationpressures.

Many studies were published in the scientificliterature to describe cake formation and proposedsome theoretical modelling of this kind of solid–liquid separation [1–11]. However, most of theseworks use different notation and a basic hypo-thesis, which can trouble potential users of theseresults. Moreover, no significant effort was madeto explain how to use these theoretical approachesto scale-up filtration operations. Finally, somediscussions remain concerning the proper deriva-tion of the fundamental equations, notably, thestress balance [2,12]. So, despite the relative wealthof research on the subject, engineers are still moreconfident with conventional cake filtration theory[13] to analyse and design filtration processes.

In the particular case of residual sludge, cakesoften exhibit a compressible behaviour. Then asignificant quantity of liquid can be removed byexpression. This second step of the dewateringcan be characterised according to the approachproposed by [14]. Whereas these results date fromalmost 20 years ago, their use for process designremains weakly considered by engineers.

The aim of this work was to evaluate, fromlaboratory experimental data, the performancesof conventional cake filtration theory and expres-sion model on a mineral sludge. From this compa-rison designing parameters have been calculated.

2. Filtration equipment

In Fig. 1 the experimental set-up of the filtration–expression equipment is schematically shown. Itconsists of a cylinder with a porous metal plate,which is covered with a filter paper, and a movedpiston related to the displacement meter to carryout a filtration experiment; the sludge is pouredinto the cylinder, a closed piston is placed on topof the sludge and after applying gas pressure onthe piston the filtrate is collected onto a balance,which is connected to a computer that registers

Fig. 1. Schematic of filtration–expression cell. 1, PC; 2,balance; 3, filtrate; 4, piston; 5, sludge; 6, displacementmeter; 7, overflow; 8, porous media.

the mass of the filtrate and the piston position asa function of time.

The results obtained with the set-up shown inFig. 2 are plotted in the form of time over filtratevolume on the filtrate rate. The filtration processis usually represented by two phases, spared by atransition point, in series: the filtration, where acake is built from the suspension, and the expres-sion that enables the expulsion of extra liquid bya squeezing action.

3. Calculation of overall filtration characteristic

Filter cake steadily builds on the filter mediumas soon as the filtration process starts. The surfacearea of the growing filter cake equals exactly thearea of the filter media. In this work, the evolutionof the filtrate is represented by the well-knownRuth equation for constant pressure filtration [13]in the form:

02

22 =−µ+∆

αµ tVARV

PAc m (1)

where t is the filtrate time, v is the filtrate volume,α is the specific average resistance, ∆P is the applied

D. Milhoubi et al. / Desalination 158 (2003) 259–265 261

Fig. 2. Point of transition.

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

3.0E+07

3.5E+07

4.0E+07

4.5E+07

0.0E+00 2.0E-05 4.0E-05 6.0E-05 8.0E-05 1.0E-04 1.2E-04 1.4E-04 1.6E-04v (m3)

t/v

(s.m

-3)

Transition point

filtration pressure, C is the dry mass of solid perunit of volume filtrate, µ is the liquid dynamicviscosity, Rm is the filter medium resistance and Ais the filter area.

According to [15] the average specific resistanceand the average cake concentration by volumefraction can be described by power law functionsof the cake-forming pressure (Pg):

( ) ngPn ∆−α=α 10 (2)

( ) mgPmCC ∆−= 10 (3)

where α0, n, C0 and m are empirical constants.The average mass of dry cake per unit volume

filtrate is obtained from the average cake concen-tration and the mass fraction of the solid in thefeed slurry by:

sCC

ss

c

ρ−−

ρ−

=11

1

1

(4)

where ρl, ρs are the liquid and solid densities, res-pectively.

The instantaneous filtrate rate (Q) followsfrom Eq. (1) in its differential form:

1

2dd −

µ+

∆αµ==

ARV

PAc

tVQ m (5)

This last equation is used to calculate thepressure drop in the filter cake by deducting thepressure drop in the filter from the total appliedpressure.

QARPP m

gµ−∆=∆ (6)

At any instant the height of the cake iscalculated from the relation [5]:

( ) QA

nmCP

Ls

nmg

−−ρµα∆

=−−

100

1

(7)

and the volume concentration inside the filter cakeat height y is:

( )nmm

mgy L

yPCC−−

∆=

1

0 (8)

4. Expression

According to the approach of Shirato and co-workers the expression can be divided into twosteps. In the first step (primary consolidation) theevolution of the cake porosity (or void ratio) onlydepends on local solid compressive pressure, ps.An increase of ps instantaneously leads to adecrease of the cake porosity. In the second step(secondary consolidation) a creep effect is con-sidered and the variation of the cake porosity (or

262 D. Milhoubi et al. / Desalination 158 (2003) 259–265

void ratio) depends on both local solid compres-sive pressure and time:

21

wc

s

spcct

p

p

e

t

e

t

e

s

∂∂

∂∂+

∂∂=

∂∂

(9)

with e, w, tc and ps represent void ratio, specificvolume of wet cake, consolidation time and localsolid compressive pressure, respectively. The firstterm on the right side of Eq. (9) indicates the timerate of change in e due to creep effect (Terzaghielement); the second term is the change due to ps.This modelling can be represented by a usualrheological scheme that associates elastic andviscous elements (Fig. 3).

The equation, which relates, during the secon-dary consolidation, the void ratio to both compres-sive pressure and time, can be derived from theBoltzmann superposition principle:

( )

( )( ) τ−

τ−−−

τ∂∂

∂∂+=

∂∂

∫d0

exp11 1

02

pp

tGE

tEe

te

s

c

t

cc

c

(10)

where ps (0) is the local compressive pressurewhen tc = 0 and τ is the so-called dummy variablefor representing an arbitrary consolidation timeranging up to a given elapsed time, tc. SubstitutingEq. (10) into Eq. (9) and applying continuityequation it becomes:

( )[ ] ( )[ ]

2

20

dexp0

wpC

tppt

Btp

se

c

t

sscc

sc

∂∂=

ττ−η−−∂∂η+

∂∂

∫(11)

where β = E1/E2, η = E2/G, Ce = ρsE1/µα(1 + e)and 1/E1 is the so-called coefficient of volumechange; E2 and G are the rigidity and the viscosityof the Voight element, respectively.

Assuming a sinusoidal profile for the ps dis-tribution through the cake at the beginning of theexpression and appropriate boundary conditions,

Fig. 3. Rheological model.

Shirato and co-workers have analytically inte-grated Eq. (11) to derive cake thickness under aconstant pressure:

( )( )

( )

⋅⋅π−−−+

η−−=−−=

20

22

1

1

4exp11

exp1

wtCeiB

tBLLLLU

c

cf

c

(12)

where Uc indicates the average degree of con-solidation over the total cake thickness at time tc.L1 is the initial cake thickness, i is the number ofdrainage surface, Lf is the final equilibrium thick-ness under a constant pressure p, L is the cakethickness at time tc and w0 is the total solid massper unit sectional area.

This analysis was recently completed by[16,17], who added a second viscous element inthe rheological scheme to better describe theresidual sludge behaviour at the end of the expres-sion.

When the cake does not exhibit a viscoelasticbehaviour only the first right term of Eq. (12) canbe considered:

( )tBU c η−−= exp1 (13)

D. Milhoubi et al. / Desalination 158 (2003) 259–265 263

5. Experimental results and discussion

5.1. Filtration

From experimental data and according to theRuth relationship applied on the filtration phasea couple of parameters can be derived. They arereported in Table 1 for different applied pressures.

From the results reported in Table 1 and usingEqs. (2) and (3) some parameters characterisingthe filtration of this mineral slurry were derived:

Constant C0 0.142Exponent m 0.102Constant α0 8.424.109

Exponent n 0.618

This set of parameters was used in Eqs. (3)–(8) to calculate the theoretical evolution of thecumulative volume of filtrate, mass of filter cake

Fig. 4. Evolution filtrate volume vs. time(P = 5 bar).

0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0 100 200 300 400 500 600 700 800 900 1000

Time (s)

Fil

tra

te v

olu

me

(m

3)

Simulation

Measured data

and cake height with time. In Fig. 4 we noted goodagreement between measured and simulated data.The cake thickness rapidly increased, as shownin Fig. 5. During the later stage of the filtration phasethe cake grows, depending on applied pressure,until a thickness of 80 mm is reached.

0

10

20

30

40

50

60

70

80

90

0 50000 100000 150000 200000 250000 300000 350000

Filtration time (s)

Ca

ke

he

igh

t (m

m)

cake height P=2

cake height P=4

cake height P=5

Fig. 5. Evolution of cake height vs. timeat different applied pressure.

Table 1Parameters of filtration

Applied pressure (Pa)

Cake forming pressure (Pa)

Specific resistance (m/kg)

Moisture ratio

5 466866 1.012×1013 1.4062187 4 338874.75 8.523×1012 1.458843 3 263798.85 7.26×1012 1.4554973 2 190538.43 5.829×1012 1.488743

264 D. Milhoubi et al. / Desalination 158 (2003) 259–265

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 50000 100000 150000 200000 250000 300000 350000 400000

Filtration time (s)

Ma

ss

of

filt

er

ca

ke

(k

g)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Ca

ke

co

nc

en

tra

tio

n (

v/v

)

dry cake

wet cake

cake concn.

Fig. 6. Evolution of mass of filter cakeand concentrations vs. time (P = 5 bar).

300000

320000

340000

360000

380000

400000

420000

0 50000 100000 150000 200000 250000

Filtration time (s)

Press

ure (

Pa

)

0

10

20

30

40

50

60

70

80

90

100

Fra

ctio

n of

tota

l pre

ssur

e (%

)

cake

total pressure

% of total

Fig. 7. Evolution of pressure of cake vs.time (P = 5 bar).

In Fig. 6 the mass of filter cake and cake con-centration vs. time are shown at an applied pres-sure of 5 bar. The evolution of cake-forming pressurevs. time is presented in Fig. 7.

5.2. Expression

Table 2 shows the parameters of the threeTerzaghi models to fit the average consolidation.The experimental results agree best with the three-parameter Terzaghi model.

6. Conclusion

Management of residual sludge is a topicalsubject; new environmental regulations obligeclosing of the disposal for these wastes. Becauseof these limitations, only two ways of eliminationwould be considered: incineration and landapplication. The study of combination in seriesof mechanical dewatering and thermal drying isin keeping with these prospects. In this study, weare interested in mechanical dewatering. Experi-mental tests were carried out on laboratory sludge.

Table 2Estimated parameter of consolidation

Terzaghi Terzaghi-Voight Terzaghi-Voight Pressure (bar) π²Ce/4w2

0 R² B η π²Ce/4w20 R² B η R²

5 0.0026 0.9280 0.1308 0.11783 0.00178 0.9923 0.8863 0.00186 0.9889 4 0.00253 0.9124 0.1518 0.18915 0.0016 0.9950 0.8588 0.00165 0.9920 2 0.00036 0.9768 0.0973 0.02284 0.00032 0.9946 0.9316 0.00033 0.9926

D. Milhoubi et al. / Desalination 158 (2003) 259–265 265

Classic phases of filtration and expression appearsuccessively. The empirical relation among con-centration, specific resistance and pressure wasfound. The average consolidation ratio was calcu-lated using the amount of filtration during the con-solidation. The result showed that the Terzaghi-Voight model coincides well with the experimentof the pilot test filter.

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