Evaluation of optimal knife advances for precoat filtration on rotary vacuum filters

&walwatiQrP’~~.Qeptimai Knife Advh~des fsr_Preesat Biltratian ewtb Rotary Vacaassm Filltears ByW HkWlingelr & A Hack1 Technicaf

University

Roiary vacuum precoat drum filters often run with process parameters not optimal& adjusted. In this paper a method for optimising the knife-advance rate and the drqn speed is presented. tn the case of the knife-advance rate in particular, the use of the mathematical model which was developed, reduces the otherwise large experimental effort. THE COMPONENTSof a suspension of particularly fine or sticky spiid particles can be separated by means of filter aids. One of the possrble process variants is the precoat-filtration on a rotary vacuum drum filter. Fig I shows the process technique on the filter drum. Durmg the prccooating stage the precoat layer, which can reach a thrckness of between 50 and IOOmm. is farmed, and during the separatton stage the solids phase of the suspension IS deposited on the precoat layer. The recoat layer is cut down to about IOmm with the help of a knife, whlc -K continuously moves towards the drum centre. This is to ensure that the orecoat surface is not totally blocked and an acceptable flow rate can be maintained. Underneath the knife a blocked layer. the so-called interface kyer precoat

I ayer

’

of Vienna, Austria is formed”‘. The thickness and the blocking effect of this interface layer are dependent on the knife-advance rate and on the sharpness and position of the knife edge. When the prccoat layer is reduced to IOmm. the filter is taken oPf-stream for reprecoating. The decisive parameters for the economy of this process are: Knife-advance rate; Drum speed; Vacuum; Sharpness and position of the knife edge; Drum submergence; Filter aid gradE; Thickness of the precoat layer. The following contribution essentially deals with the optimisation of the knife advance rare.

Knife Advance and its Influence on the Process When a high knife-advance rate is chosen. the result is a high flowrate, caused by an insign~f~c~~ntiy blocked prccoat la er; the precoat layer is scraped down too quickly and the specific Fdtcr aid consumption is very high. When the knife-advance is too low. this results in a more reasonable filter aid consumption. but the flow rate is low and the time dependent costs for the iii&ate are too high. An optimal knife-advance rate with the aim of, eg, minimum cost, satisfies the two contrary demands: maximum flow rate and minimum filter aid consumption. As the process is not continuous, the precoating time and the cost of precoating must be taken into consideration. Two aims of optimisation can be defined. Eq (1) means that the total filtrate volume received by cutting down the precoat layer in relation to the time spent on precoating and separation should reach a maximum.

V, (AhI tproc + t, (Ah)

(1)

-+ max

If o timisation is to be carried out at minimum cost, then Eq (2) shout a reach a maximum. cFreCincludes the cost of the filter aid. the c1eanir.g time and the precoating time and remains constant for various knife-advance rates. A simple, but experimcntaliy very ex ensive method to achieve the optimal knife-advance rate is shown intrig2. I filter-aid Fig I. Process technique on a precoat-f!lter drum Above: precoattng stage. Below: separation stage

suspension

Vt (AhI cprec+ cr tt (Ah)

-+ max

(2)

Scvcrai test runs must be made with different knife-advance rates and the total filtrate volume is measured for each run. For each run the same precoat layer thickness should be scra ed down. By plottips the total filtrate volume against t Rc corresponding total filtranon time and drawing a tangent to the curve intersecting the point tprco situated on the negative x-axis. the optimal operation point can be determined. Using this optimal filtration time and with the help of Eq (3) it is possibtc to calculate the o timal knife-advance rate. A similar procedure i; carried out to t PIG i&ht of Fig 2, if the filtrate volume must be optimiscd according to the total cost. (3)

Mathematical model. The necessary experiments can be considerably shortened by using a mathematica1 model, experimentally verified in enriier research studies”-“‘. A brief description of the model is given as follows. This mathematical model includes a number of su.~~itions: q The precoa: Iaycr is consi_dcred to be incompress e; Cl T%;rdeposlted sohds budd up a secondary cake on the precoat I

I

1: ‘deposited solids 2: interface-layer 3: clean precoat-layer 4: filtermedium

This paper gives the partial resulfs of a co-operc!ian between ihs Technical University of Vienna, lnsfitut fiir Verfahrensfechnik, Brennstofftechnik und Umweltfechnik. and fhe Technical University of Dresden. Seklion fiir Verarbeilungsand Verfahrenstechnik. Wissenschaftsbereich Mechanische und Systemvedeh~nstechnik, within the contract of technicaf end scientific co-operation between Austria and the German Democratic Republic.

110

U The ieight of the secondary cake is sufficient to fill up the roughness hollows on the precoat surface arca caused by the knife. Cl The drum diameter is large compared to this thickness of the precoat Iayer, hence the filter area A can be assumed to be constant throu hout the process. The course oft ‘ise process can be divided into two parts (see Fig 3). During part I the interface layer is formed and the Row rate thus decreases. In part II the rate of deposition of the particles equals the rate at which the particles are removed from the precoat layer by the knife. The slow increase in flow rate is due to the gradual reduction in precoat layer thickness. The period of time invoived in part I can be disregarded in comparison to part II so that for o timisation calculations the corresponding~ Eq (4) with E$” (S!$and (6) is sufficient. The dependency o the precoat layer b ocking on the March/Apr~i 1990

Filtration & Separation

PROCll~blNOSOFlHE~LTAATlONSOClMN

min.cost

max . f 1@W-i8 tc

tot.filtr.time tprec.

( Ah)

tt

% opt

tot.

'prec.lcf

%

filtr.time

tt

(

Ah)

opt

Fig 2. ExpertmentaloptImisation method for the knife-advance rate: a. maximum flow rate according to Eq (1); b. minimum cost according to Eq (2) part

running-in /

tot.

fi Itr.

time

tt

(n,J

Ah, > Ah2 ) Ah3

I Fig

cake

thickness

h?

3. ‘Runntng-in’ and stationary part of the

knife-advance rate is signified coefficients in Eq (6).

by a and

-

A h.n,,_t

Cprech

process

hhr the

two

%iOpt

Wg5. Optlmisation blocking

of the drum speed

hollows that arise can be blocked by solids of the secondary cake and. after the knife cut. a residual blocking depth hh remains. Therefore the blocking depth h,, Foiiows Eq (7): h,,=hR-

with: p = I% + r,, (h, - Ah

nDt)

+

PI

(5)

and: g =

I

ahzr,’ Ah

(6)

where a is a measure of the blocking of the precast iayercom~arabie with that of the blocking coefficient m the biocking filtratron ( * 5t and hh states how far the blocking reaches into the depth of the layer (see Fig 4). The blocking depth hi, is determined by two inFluences, One is the roughness of the precoat layer surface. caused by the knife cutting and the other is the size of the knife-advance rate. The roughness

Ah

and hR describes the roughness depth of the prccoat layer surface. After filling up with secondary cake and cutting with the knifeadvance Ah. the blocking depth hr. remains. Furthermore it can be assumed that hR does not remain constant for different knifeadvances Ah. In order to take this fact into account, an empirical parabolic equation with experimental constants hR,, and cl has been established: hR = hRI, + c, w

_

a r, hg Ah

(K,

+

Kt a-

-

APIA

hl-h+

hl-h’ 2

Fig 4. Test run for evaluating the experimental Filtration

&

Separation

March/April

1990

-@I

This equation inctudcs three experimental constants Kt, Kz and Ka, which can be derived from several flow-rate test values.

Ah3

cake thickness 1

K3Ah)%,, Ah

ah2

h&h;

(8)

When taking into consideration the fact that h, is dependent on the knife-advance. then Eq (6) results in Eq (9). which describes the dependence of the interface layer resistance value PI on the knife advance hh:

I%= ;3,

(7)

ht-h

v3

constants

K,,

KZand Ka

PI= --yp--1

v'i-. 2An,

fJ,,-Qr,

If at least three different knife-advance rates are tested, the three constants can be determined by means of the polynomial regression of degree 2. It is sufficient to make one test run on a filter drum. while each time after reaching the stationary blocking state, the 111

PAOCB~DINOS

knife-advance (seeFig4).

rate should be switched

OF THE

down to the next lower level

hl--2

tt:qN

I Ah

(11)

A reduction of the necessary expcrimeutal effort by using the mathematical model depends on a knowledge of how the blocking coefficients a and hh vary with the drum speed. This is the content of another publication. Experiments. Durin tests with a lab-size filter drum usin a filter area of 0.2%~ a Ca 8 09 - water suspension was filtere B over a diadomite Celite 545 precoat layer. , is calculated for different knife-advance rates, according to Eq (1 t ). By rearrangement of Eq (9) a polynom in Ah is obtained: -

= a=

KI + K,e

KJAh

SOCIRTY

The test results accordhi to Eq (12) are plotted in Fig6. The model is calculated f rom the regresslon coefficients KI, Kz. K3 (Eq (12)). As the results of the test values and the model are in agreement it can be used to describe the interface layer resistance in the field of technically si nificant knife-advance rates. The limiting knife-a J Vance rate, at which there is no residual rdsistance tq flow caused by the deposition of the particles, can be determined by setting the right-hand term in Eq (9) to zero and solving for the roots. For the example in F,ig 6 the limiting knife-advance rafe was 0.772 min per revolution. To determine.the o timal knife-advance rate, the function in Eq (9) is first calculated an B then the total filtrate volume V, can be determined using Eqs (4). (5). (13) and (14):

Drum Speed The optimisation method used for the knife-advance rate in Fig 2 can also be used for the drum speed. In an analogous way several test runs have to be made with’ different drum speeds. The tangent point on the total filtrate volume curve ives the optimal o eratlon point t,.,,pt (see Fig 5). Wrth the help o f Eq (11) the optima P,drum speed nDtllptcan be calculated: noinpt =

FILTRATION

v, =

tt s0

T&

Then the optima1 knife-advance (16): d dhh

(12)

model

1

hl -hl

It=

(11)

fr (Ah) dt

(14)

can be calculated

V, $rec + tt

from Eqs (15) or

= 0 ---) Ah,,,,, (time)

(1%

graph

t 2.1 S-7 b d

1.9

1.3 0.100 Kf = K2 = K3 = Fig 6.

-5.66

0.155

0.275

0.350

_10m4 m

3,52 -10-l 11,93

0.200

knife-advance

moe5

Ah

m/rev.

. 10 -3

-_)

-

function -h/r, according to Eq (12) for various knife advances precoat layer: KlePPtgur 545; suspension: CaCO,-water, Skg mm3

Blocking

Ah:

max i mum

t I 0.6 r.3 E c, z-

.

<

0.4

1000

t prec . =lOOOs

ttopt.

=1929

s

4000

total

filtr.

6000

5000

time

tt

( Ah)

Fig 7. Optlmfsing the knife-advance rate with the help of a mathemaiical a. = 2.64 - lO”‘m * kg-‘; PO= 2.06; fOgm-‘; rP = 3.29 - 10’lm-a 112

7000

s

-

model:

March/April

1990

Filtration & Separation

PROCLEOINOB

d dhh -_(

V, cpreJcr + t,

= 0 +

OF TH@ CILTMTION

Ah,,,,, (cost)

(16)

’

During tests on a lab-size filter drum various knife-advance rates were tested and the total filtrate volume measured between a layer thickness of 27 and 21mm (see Fig 7). The maierial constants in the model (for example the specific cake resistances of the secondar cake and rhe precoat layer and the filtration resistance of the FIher medium) were all determined by lab-size filter test leaf experiments. Furthcrmorc the three constants of the knife-advance rate function were found by the reviously described method. As Fig 7 shows, the graph of the calcu Pated total volume coincides with the measured volume values. Possible deviations arc a result of the ‘running-in’ process. In the start phase of the process the precoat layer shrinks back somewhat

from the knife

as a result

of compressibility,

so that the flow

Nomenclature : c Cl Cl

hc

to solve Eq was found.

(15).

the idcal

rate is

kmfe-advance

precoat layer thickness at the end of the process, blocking depth, m roughness depth, m exp constant in Eq (8). m knife-advance per drum revolution. m optimal knife-advance per drum revolution. m defined precoat layer thicknesses (Fig 4). m running variable (1,2. .),exp constant in Eq (9), m exp constant in Eq (9), rn’.’ exp constant in Eq (9), drum speed, s-’ optimal drum speed, s-’ filtration pressure, Pa resistance of the precoat layer with the thickness time, s ,. _. precoatmg time, 5 total filtration time. s

k

K2 K3 “0

"D:Opl AD

of $?6,(Ah). 0. 0

FiroalRemarks A

method

mathematical complication

been model

has

introduced and with

by which with the least possible

the aid of experimental

a

and expenditure. the optimal knife-advance rate for the process on a rotary precoat drum filter could be determined. It is sufficient to test one prccoat layer on a filter drum whereby at

least three different knife-advance rates should bc used. This experiment can bc carried out on a lab-size filter drum or on an industrial large-scale filter. In the latter case, problems which can occur through scale-up then no longer exist. The aims of optimisation can be cithcr maximum now-rate or minimum total cost. In this way when cost fluctuation occurs, for example increase of filter aid,cost. the quickly and simply corrected lo its optimal

knife-advance value.

rate

can

coefficient

I,,

The optimisalion of the knife-advance rate demonstrated in Fig 7 was carried out numerically with the aid of a computer. For a presumed precoating time of 1,000 set and using. a numerical approximation method 0.364mm per revolution

blockina

filter a&a. ti* amount of the solids in the suspension, kg/m-= time dependent cost during the separation 01 the suspension, costs-’ cost for precoating the filter, cost exp constant in Eq (8). m0.5 precoat layer thickness at the beginning of the process,

epros

lower for a short time. This explains why the measured values lie a littlc below the calculated values. As the scraped down layer thickness was not vey large in the test carried out. it can be presumed that in normally larger layer thickness the influence of .thc ‘runningin’ time can he disrcgardcd.

.

SOCIETY

i

% P RP

V,(nD)

optimal totat filtration time, total filtrate volume m3 filtration rate, m3/s’~ f;~;~~on

rate

at defined

m

I, m-*

s

precoat

layer

thicknesses

spec resistance of the secondary cake, m kg-’ filtration resistance of the blocked precoat layer cluding filter medium. m-’ filtration resistance of the,filter medium, m-l resi,stance value, deserlblng the Interface layer (Eq

h;,, in-

(5)).

II,

0 11

ratio of the submer viscosity. kg me’s_

ed to the total s,

filtration

area,

-

REFERENCES

be

IBIPlastic and Epoxy-Coated Steel Filters from WI” to 16”, in mesh sizes from 22 to 1,200 microns. Amiad Filters provide more filtration afea and greater effectivity than any other filter available.

,

Amiad D.N. Chevel Korazim 12335 ISRAEL Tel: 972-6-933581. fax: 972-6-935337 Tlx: 6693 AMIAD It Filtration &Separation

March/April

1990

133