110 6 Filter Cake Formation

Neglecting the filter medium resistance, this equation can be inserted in the
cake formation Eqs. (6.21) and (6.45) results
√ √ √
2 ⋅ pc 1 𝛼1
hc = ⋅ 𝜅 ⋅ Δp ⋅ ⋅ (6.45)
𝜂L n 360∘
For better understanding, the parameters are grouped into product, process,
and design parameters. As expected, the cake height becomes smaller, if the rota-
tional speed of the filter increases because the residence time of the filter area in
the slurry is shortened. The maximal rotational speed is set by the possibility of a
complete cake discharge. For discharge by air blowback and scraper in the case of
drum or disc filters, this limit is reached for a few millimeters of cake thickness.
If the cake is too thin, it is not more discharged but is transported behind the
scraper back into the filter trough. A certain safety distance between filter area
surface and scraper is necessary, especially for large filter units, to exclude any
contact between scraper and filter cloth. Normally, the maximal speed of rotary
filters is considerably less than 10 rpm.
The question now is whether a high or a low rotational speed of the filter is
beneficial for high throughput. To answer this question, the specific solid mass
throughput of the rotary filter must be calculated in form of Eq. (6.46):
Qm,s
qm,s = = n ⋅ hc ⋅ 𝜌s ⋅ (1 − 𝜀) (6.46)
A
The specific solid mass throughput is given in kg m−2 h−1 . One has to consider
that the rotational speed is additionally inserted in the cake height. Equation
(6.47) gives the final result
√ √
2 ⋅ pc √ 𝛼1
qm,s = 𝜌s ⋅ (1 − 𝜀) ⋅ ⋅ 𝜅 ⋅ Δp ⋅ n ⋅ (6.47)
𝜂L 360∘
Now, it becomes clear that the filter throughput increases with increasing rota-
tional speed, although the cake height decreases. The maximal throughput is
limited by the minimal cake height, which can be still safely discharged. For drum
and disc filters and good desaturated brittle filter cakes, which are discharged by
air blowback and scraper, this limit is given at about hc,min = 5 mm or less. The
cake must have a certain weight (thickness) to be separated from the filter media
and must not be transported behind the scraper (safety distance to the rotating
filter) back into the slurry.
For an example, a vacuum drum filter is operated with a certain pressure dif-
ference Δpvac , and the specific solid throughput qs,vac is maximized for maximal
rotation speed and minimal possible cake height. The pressure difference for vac-
uum filters is limited to the vapor pressure of the liquid of less than 100 kPa, and
therefore, the variation of pressure differences is limited. If greater pressure dif-
ferences of up to about 1 MPa are desired, disc or drum filters can be installed
completely in a pressure vessel, as schematically shown for a hyperbaric disc filter
in Figure 6.28.
In contrast to vacuum filters, hyperbaric filters need a special gastight sluice
to transfer the filter cake from the pressurized vessel to the atmosphere. In the
 6.3 Formation of Incompressible Filter Cakes by Pressure Filtration 111

Figure 6.28 Hyperbaric disc filter. Disc filter

Pressurized
gas
Pressure
vessel

Cake
Filtrate
sluice

Feed
Solids

Figure 6.29 HiBar drum

filter. Source: Courtesy of
BOKELA GmbH.

case of great filters, the pressure vessel exhibits a manhole to carry out mainte-
nance work without opening the big bumped boiler head. In Figure 6.29, such a
completely opened pressure vessel can be seen, in which a drum filter is installed.
If the filter is smaller, it can be installed in a pressure vessel, which is separated
horizontally and can be opened like an oyster, as shown in Figure 6.30.
This is especially advantageous if a quick access to the filter is desired and the
pressure vessel must be relieved from an unhealthy atmosphere. In addition, the
downtime before new start up is reduced and thus the effectiveness of the process
is increased.
If in the case of hyperbaric filters for constant rotation speed the pressure differ-
ence Δppr is increased, the solid mass throughput is increased and simultaneously
the cake thickness rises. Now, the rotation speed can be increased, until the min-
imal possible cake height is reached again. This additionally increases the specific
solid mass throughput qm,s,pr . Running the filter for constant minimal cake height
means that the specific solid mass throughput becomes directly proportional to
the pressure increase, as derived in Eq. (6.48)–(6.50)
√
hc,pr Δppr ⋅ nvac
∝√ (6.48)
hc,vac Δpvac ⋅ npr
112 6 Filter Cake Formation

Figure 6.30 HiBar oyster filter. Source:

Courtesy of BOKELA GmbH.

hc,pr = hc,vac ⇒ Δppr ⋅ nvac = Δpvac ⋅ npr (6.49)

√ √
qm,s,pr Δppr ⋅ npr Δppr ⋅ npr Δppr Δppr
∝ = ⋅ = (6.50)
qm,s,vac Δpvac ⋅ nvac Δpvac Δpvac ⋅ npr Δpvac

Coming back to the belt filter at the beginning of this chapter and also in the
case of pan filters, the length of the cake formation zone is not fixed, as for drum
or disc filters, but depends on the operation conditions. To calculate the length
of the cake formation zone L1 on a belt filter with continuously moving belt, in
a first step, again the cake formation time t 1 to get a certain cake height hc is
measured in the laboratory filter cell for a certain pressure difference and slurry
concentration. These data have to be transferred to the belt filter according to
Figure 6.31.
To get the desired cake height, the slurry height on the belt must be adjusted
to the same height for given slurry feed volume flow rate Qv,sL . From this infor-
mation, the belt velocity can be calculated according to Eq. (6.51)
Qv,sL
vbelt = (6.51)
B ⋅ hc

Slurry feed Figure 6.31 Cake formation

vbelt on a continuously operating
hc belt filter.

L1 L2
Cake
Filtrate