Surface water treatment by roughing filters  A design, Construction and Operation manual (1996) 
Annexes 
Filtration is more an art than a science. This saying also applies to roughing filtration. Numerous researchers have tried to describe the filtration mechanisms in mathematical models applying either the phenomenological or the trajectory approach. The first one uses simple but important variables such as filtration rate, filter size, depth and porosity to describe filter efficiency. The second approach focuses more on transport mechanisms of the individual particle and its behaviour in the single collector. The phenomenological and trajectory approach will be used in this short summary on filtration to provide some more theoretical information on the mechanisms of roughing filtration.
Transport Mechanisms
The trajectory approach, describing the route of a clay particle through a roughing filter, has been vividly depict in Chapter 9.2. Additional analytical considerations regarding this mechanism are given hereafter.
Screening, as shown in Fig 4/1, is not relevant in roughing filters since the pore sizes are considerably larger than the particles generally encountered in suspensions. The ratio between a clay particle of 4 mm in diameter d_{p} and different pore sizes d_{o} is illustrated in the following table.
gravel size d_{g} 
[mm] 
16 
8 
4 
pore size d_{o} 
[mm] 
2.5 
1.25 
0.63 
ratio d_{o}/d_{p} 
[] 
625 
313 
156 
Sedimentation is the next possible process for solid matter separation. Under the conditions described in Fig. 4/2 and shown in the following table, the ratio between the settling distance d_{s} travelled by the clay particle during its flow through the pore and required total settling height h_{s} is very important.
settling velocity 
vs 
0.01 mm/s 
for a 4 mm particle 
pore length 
I_{p} 
4 mm 
for 16 mm gravel 
filtration rate 
v_{F} 
0.5 m/h 

flow velocity 
v_{eff} 
0.4 mm/s 
for 35 % porosity 
flow time 
t_{f} 
10 s 
(I_{p} / v_{eff}) 
settling distance 
d_{s} 
0.1 mm 
(v_{s} ´t_{f}) 
settling height 
h_{s} 
1.25 mm 
(h_{s} = 0 5 do) 
ratio 
h_{s}/d_{s} 
12.5 
Interception decreases porosity and settling height hs and enhances solid matter removal by sedimentation. However, as illustrated in Fig. 4/3, solids accumulation in roughing filters does not significantly improve solid matter separation. This is also presented in the following table.
initial porosity 
p_{o} 
35 % 

filter load 
s 
5 9/1 
(accumulated solid per filter volume) 
taken up volume 
m_{a} 
2.5 % 
for a 0.2 g/cm³ density 
actual porosity 
p_{a} 
32.5 % 
(PO  ma) 
Hydrodynamic forces are capable of carrying the particles in still water zones as illustrated in Fig. 4/4. In such prevailing conditions, the clay particle can settle on the gravel surface as calculated in the table below.
settling velocitysettling distance 
d_{s} 2 mm 

settling time 
t_{s} 
200 s 
(I_{s}/v_{s}) 
The "1/32/3 Filter Theory''
The following very simplified model elucidates the filter removal kinetics and is based on the considerations described on page IX4 of Chapter 9.
gravel layer 
separated particles 
remaining particles 
removal [%] 
300 mg/l 
(removal in % per layer) 

1 
100 
200 
33 
2 
67 
133 

3 
44 
89 

4 
30 
59 

5 
20 
39 

90 

6 
13 
26 
(16.5% layer) 
7 
9 
17 

8 
6 
11 

9 
4 
7 

10 
2 
5 

11 
1.5 
3.5 

99 

12 
1.2 
2.3 
(1.5% layer) 
2.3 mg/l 
This simple arithmetic exercise clearly proves that solid matter separation by filtration can be described by an exponential equation as subsequently exemplified by equation (1). However, filter efficiency does not only depend on particle concentration but also on size and settling characteristics. Furthermore, filter variables such as filtration rate and size of filter medium strongly influence filter performance. Finally, the accumulated volume of separated solids per unit of filter bed volume, known as filter load, also determines the actual filter efficiency.
Extensive parameter tests were conducted to determine the influence of different design parameters on the performance of horizontalflow roughing filters. The tests were conducted in the laboratory with filter cells of 10  30 cm and 20  40 cm length for differently sized filter material and different filtration rates varying between 0.5 and 2 m/h. A kaolin stock suspension was used to simulate a suspended solids concentration of about 200 mg/l. Particle size counts were performed with a Coulter Counter TA II. These laboratory tests are described in [10] and the data obtained were evaluated by a multiple linear regression analysis to develop a filtration model for horizontalflow roughing filtration of which the following is an excerpt.
According to the established filter theory, the filter efficiency can be expressed by the filter coefficient
with c as solids concentration and x filter depth. The filter coefficient
with
resulting in different relations of
Knowing
and the total suspended solids concentration after an element
The volume filter load
with
All the dependencies of
The influence of the particle capture volume
where
From the experimental results in Fig. 4/5, it may be concluded that
k = 0 (8)
Thus, equation (7) is simplified considerably. At
The resulting equation for
The initial filter coefficient
The value of the initial filter coefficient
The values for
were determined from 36 data points with a correlation coefficient of 0.96.
The ultimate filter load
with the following values
b_{o} = 10 [ml/l]
The 20 data points used showed a correlation coefficient of 0.97.
With the established equations for
The above studies have only focused on the physical removal mechanisms. Roughing filters may, however, also develop biological activities which enhance particle removal. Such investigations were carried out with suspensions containing clay (kaolin), algae (Scenedesmus) or a combination as described in [11]. The laboratory tests were also evaluated by multilinear regression models. The following equations were obtained for steady state conditions.
for kaolin:
C_{e}/C_{o} = 0.188 + 0.0231 media +0.136 flow  0.101 depth
for Scenedesmus algae:
C_{e}/C_{o} =  0.170 + 0.253 flow + 0.142 media  0.021 depth  0.0128 media^{2}
for kaolin + algae:
C_{e}/C_{o} = 0.0280 + 0.0902 flow + 0.0181 media  0.0558 depth
where
 C_{e} is the effluent concentration in [mg/l]
 C_{o} is the inlet concentration in [mg/l]
 "media" is the gravel size in [mm]
 "flow" is the filtration rate in [m/h]
 "depth" is the filter length in [cm]
This research has also revealed that filter efficiency is dependent on design variables such as filtration rate, gravel size and filter length. However, as outlined in other investigations [36, 47], flow direction is of minor importance for filter performance. These laboratory tests have shown that kaolin removal is enhanced by the addition of algae which destabilise the clay into aggregates that are more efficiently removed by roughing filtration. However, hydraulic filter cleaning is more difficult when the clay is coated with organic matter. Hence, the presence of biomass in a roughing filter probably does enhance solid matter separation but may also hinder hydraulic filter cleaning.
The chemical properties of the suspension; i.e., the suspension stability is, however, not taken into consideration in these filter models. Filter models are not universally applicable to all types of raw water as filter efficiency is strongly influenced by the raw water quality. Such semiempirical models may therefore be used to investigate the overall influence of specific design parameters or to optimise treatment plant design on the basis of a comprehensive pilot plant field test programme.