Journal of Engineering Studies and Research Volume 17 (2011) No. 4 101 [619154]

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 101

ACTUAL STAGE OF WATER FILTRATION

ȚÎRȚOACĂ (IRIMIA) OANA1*, NEDEFF VALENTIN1, LAZĂR GABRIEL1

1”Vasile Alecsandri” University of Bacau, 157 Calea Marasesti, 600115, Bacau,
Romania

Abstract: The main process of water’s treatment can be mechanical, chemical and
biological. From all mechanical treatment procedures, filtrati on is the most irreplaceable
one in the scheme of a treatment plant. F iltration is the advanced clearing procedure,
consisting of water’s passing through a porous material, that has a certain granulometry,
named filter layer, used for the retention of the natural suspended particles or previous coagulated particles. Filtering is influenced by a series of parameters.

Keywords: potable water, water’s mechanical tr eatment, filtration, particle’s shape.

1. INTRODUCTION

The restriction of water’s resources, the need of a car eful management and the importance to ensure a good
water quality are now more obvious than ever [1, 2].
Treatment of water is accomplished th rough process of mechanical nature (retention on grates and separators,
sediment exclusion, decantation, filtr ation), of chemical nature (coagu lation – flocculation, ion exchange,
chlorination, disinfection with UV radiations, aeration – oxi dation) and of biological nature (adsorption on active
coal, biological treatment using slow filter or semi – pe rmeable membrane). Among these processes, filtration is
the operation irreplaceable in the sc heme of a treatment plant [3-9].

In the last three decades in the whole world were done multiple studies viewing the filtration of water,
developing theories referring to the mechanism of removing the particles from the influent and referring to the parameters that influence the water’s mechanical filtering process [10-15].

2. FILTERING MECHANISMS

The retention of the suspensions from water in filter laye r, takes place on the strength of a large number of
processes and mechanisms, from which [16, 17]:
− inertial impact;
− diffusion;
− interception;
− sieve effect.

Filtration mechanism through inertial impact (Figure 1) appears when, from a mixture liquid – solid, the liquid
changes the initial flow direction, thus avoiding the filter material, while the suspended particles make direct
contact with the filter material [13, 15].

* Corresponding author, email: [anonimizat]
© 2011 Alma Mater Publishing House

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 102

Fig. 1. The retention process of solid suspensions through inertial impact [16].
Diffusion (Figure 2) is specific to the particles that have the diameter up to 2 μm and is accomplished under the
action of Brownian motion. This physical effect has a low weight in the case of water’s filtration, taking into
consideration the previous retention through coagulation – flocculation and sedimentation of the particles having these dimensions [13, 16].

Fig. 2. The retention process of solid suspensions through diffusion [16].

Interception (Figure 3) appears when the radius of the particle that follows to be discharged is bigger than the
distance between the filter material and the liquid flow lines [16, 17].

Fig. 3. The retention process of solid suspensions through interception [16].

Sieve effect (Figure 4) acquires the retention of the particles in the tangency area of the filter layer. The larger
the particle’s diameter is, the more efficient is the sieve [14, 16].

Fig. 4. The retention process of solid suspensions through sieve [16].
Filter
material Flow
Solid
suspension
Flow
Flow Flow Flow
Filter
material Filter
material Filter
material Solid
suspension
Solid
suspension
Solid
suspension

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 103

The retention of the suspensions in slow filters is accomplished throug h mixed processes having the following
nature [17]:
− physical;
− chemical;
− biological.

Physical processes. On the surface of the filter environment and also in its superior layer take place
sedimentation and sieve processes, resp ectively adsorption due to the electrosta tic forces or ionic replacement. In
this way are discharged the suspended solids, the colloid al particles, the bacteria and the remiss impurities [12,
14].

Biological processes. The biological activity is the base in removing the germs, viruses and organic matters,
through slow filtration and is manifest ed on the surface an d in the first centimeters of the filter layer [13, 25].

Chemical processes take place in the slow filters in the face of the oxygen remiss in water or during the
oxidation of the adsorbed organic matters, in the face of the microorganisms [17].

3. PARAMETERS THAT INFLUE NCE THE FILTERING OPERATION

The productive selection of the filtering process, of the filtering equipment and of the operating conditions is
done taking into account multiple parameters that have an influence on filtering operation [16, 18]. These
parameters can be synthesized in this manner:

3.1. Characteristic parameters of the liquid – so lid mixture that influence the filtering process
Suspension’s nature. The suspensions with spherical particles, an d mostly acicular, give precipitates with a
higher permeability and therefore there are admitted higher filtering rates than the suspensions with foil grains.
When the foils are flexible, they produce the effect of some valve. The suspensions with big and incompressible
particles are filtered easier than the suspensions with fine or colloidal particles that form compact and
impermeable precipitates that are closing the pores of the filtering material [19].
Density. For a liquid – solid biphasic system the density can be defined through the relation (1) [20]:

s ap p aρρε ρε=⋅+ ⋅ (1)

where:
pε is the gaps rate of the solid phase;
aε – the gaps rate of the liquid phase (of water).

Viscosity. For the mixtures with low concentration of the so lid phase, viscosity can be determined with the
relation (2) [7, 20]:
23(1 )s ap p p abc ηηε ε ε=⋅ + ⋅+ ⋅+ ⋅ (2)

where:
sη is the mixture’s viscosity, Pa·s;
aη – water’s dynamic viscosity, Pa·s;
pε – gaps rate of the solid phase;
a, b, c – constants;
a = 2.5 for spherical, unadsorbent particles;
a ∈ (2.5 ÷ 3.6) for adsorbent particles that increase their volume in water.
Due to the hydrodynamic interaction between the solid particles, the constants b and c have values between:
b ∈ (2.5 ÷ 14.1);
c ∈ (8.75 ÷ 36.3).

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 104

The viscosity of the mixtures with a high concentrati on of solid particles is mainly influenced by: the
concentration of solid particles from the mixture, the sh ape and the dimension of the particles, the roughness of
the particles surface. The viscosity can be determined with the expression (3) [20]:

2,5
,max1p
sa
pεηηε−⎛⎞
=⋅ −⎜⎟⎜⎟⎝⎠ ( 3 )

where ,maxpε is the maximum concentration of the solid particles from the mixture.

3.2. Characteristic parameters of the preci pitate that influence the filtering process
Precipitate’s specific resistance αis constant for the incompressible layer of precipitate, but it is changing with
time as a consequence of the precipitate’s compaction. Usually, the precipitate layers are compressible and the
specific resistance is changing along with the pressure difference from the precipitate layer ppΔ [Pa]. In this
case the medium value of the precipitate’s resistance mα [m/kg] is expressed through the equation (4) [20, 21]:

011() ()pp
p p
mppd ppααΔ=Δ ⋅ ΔΔ∫ (4)

if the value of the function ) (ppfΔ=α is known from experimental determinations.

The quantity of precipitate laid-down on the unit of area ω [kg/m2] is determined is the relation (5) [20]:

a A CV ω⋅=⋅ ( 5 )

where:
A is the total area of the filter layer, m2;
C – the concentration of the solid phase, kg ⋅m-3;
Va – the volume of filtrate (mixture) in the time t, m3.

3.3. Characteristic parameters of the filt er layer that influence the filtering process
Particle’s shape. Whatever the obtaining process of the particles is , these don’t have the same shape and this is a
fact that makes difficult to create mathematical models c oncerning the sorting process. However, the scientists
discovered various methods in which they use different approximations in order to determine the granular particles shape [22].

Taking into account the shape of the particles, these can be classified in four main categories depending on the
relation between the three dimensions (L – length, l – width and h – thickness) [23]:
− particles with any shape (Figure 5.1.a), for which L > l > h;
− particles with the shape of oblate spheroid (Figure 5.1.b), for which L > l = h;
− spherical particles (Figure 5.1.c), for which L = l = h;
− lens – shaped particles (Figur e 5.1.d), for which L = l > h.

The density and the gaps rate of a particle. The density
pρ, of a solid particle is defined according to figure 6
with the expression (6) [12, 20, 24]:

pp
pVm=ρ ( 6 )

where:
m p is the mass of solid particle, kg;
Vp – the volume of solid particle, taking into account its non-porous surface, m3;
pρ– hydrodynamic density, because V p is the volume of the particle limited by the hydrodynamic
boundary layer, kg/m3.

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 105

Fig. 5. The main dimensions of a granular particle [19].

Fig. 6. Conceptual figure of a solid particle with opened and closed pores [20].

In table 1 are rendered values of the gaps rate for different shapes of the solid particle with various dimensions
[12].

Table 1. Solid particle’s characteristics [12].
No. Particle’s shape Dimension
[mm] Specific area
[m2/m3] Gaps rate
[%]
d=0.794 7,600 0.393
d=1.588 3,759 0.405
d=3.175 1,895 0.393
d=6.35 948 0.405 1. Spherical
d=7.94 756 0.416
l=3.175 1,860 0.190
l=3.175 1,860 0.425
l=6.35 1,078 0.318 2. Cubical
l=6.35 1,078 0.455
l×h= 4.76×4.76 1,262 0.355 3. Six-angled prism
l× h= 4.76×4.76 1,262 0.472
l× h= 6.35×2.87 2,410 0.361 4. Tetrahedron
l× h= 6.35×2.87 2,410 0.518
l× d=3.175×3.175 1,840 0.401
l× d= 3.175×6.35 1,585 0.397 5. Cylindrical
l× d= 6.35×6.35 945 0.410
l×L× h=
6.35×6.35×0.79 3,033 0.410 6. Plate
l× L× h=
6.35×6.35×1.59 1,984 0.409
7. Lenticular d× h= 3.175×1.59 2,540 0.398
where:
l is the length; L – the width;
h – the height. Closed pore Opened pore b
c
l
d) c l
c) b c b
l
b l
c a)
c l
b) b

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 106

The specific area of a particle. The specific area of a particle, a, in m2/m3 is the proportion between area a p of the
particle and its volume V p (relation (7)) [12, 20].

pp
Vaa= ( 7 )

Sometimes, the specific surface area of the pa rticle is related to its mass resulting a g, (relation (8)) (the specific
area related to the mass of the particle), in m3/kg:

p pp
gVaa⋅=ρ ( 8 )

where pρ is the density of the particle.

For the spherical particles, a, respectively a g, are expresses with the relations (9) and (10):

d dda6
632
=⋅⋅=ππ [m2/m3] (9)

p pga
daρρ=⋅=6 [m2/kg] (10)

Particle’s dimension. The dimension of a particle is expressed throug h its diameter if the particle is sphere. For
the particles having the shape different from the sphere Allen (1975) shows 12 ways to express the dimension of
a particle. From these, for modeling the flow of a liquid through a layer with solid particles, there are currently
used three ways to express the equivalent diameter of a non-spherical particle (table 2, relations (11) ÷ (13)) [19,
20, 25].

Table 2. Equivalent diameters of a non-spherical particle [20].
No. The name of the
diameter Symbol Relation of computation Rel. no.
1. Volume equivalent diameter d v 1/3361.24p
vpVdVπ⋅==⋅ (11)
2. Surface equivalent diameter d s 1/20.56p
s padaπ==⋅ (12)
3. Specific area equivalent diameter d sv
pp
svaVd⋅=6 (13)

The equivalent diameters are obtained equaling a geometrical measure of the real partic le with the same measure
of an equivalent sphere. For example, d v results by equaling the volume V p of the particle, with the volume of a
sphere having the diameter d v (relations (14) and (15)) [25]:

63
v
pdV⋅=π ( 1 4 )

36
πp
vVd⋅= ( 1 5 )

For the solid particles there is also used th e concept of diameter of sedimentation, d s, defined as the diameter of a
sphere with the specific weight and the hydraulic measure identical with the ones of the real particle determined
in the same kinematic conditions. It is used for particles having dimension smaller than 0.1 mm.

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 107

For expressing the dimension of a non-spherical particle th ere are, for particular cases , the following correlations
[23]:
− for particles almost spherical: d ≅dsv≅dv;
− for solid particles having regular shape (cylinder, s pheroid, ellipsoid, parallelepiped etc.), with shape
factor 0.773ψ≅ (rel. (16)).

0.773svvdd=⋅, error of %11± . ( 1 6 )

In Table 3 is presented the classi fication of the solid particles taking into account their size [26].

Table 3. The classification of the particles on size [26].
Particle’s size Class No.
[mm] [ μm] –
1. 4,000…2,000 – Very big bowlders
2. 2,000…1,000 – Big bowlders
3. 1,000…500 – Medium bowlders
4. 500…250 – Small bowlders
5. 250…130 – Big rocks
6. 130…64 – Small rocks
7. 64…32 – Very big gravel
8. 32…16 – Big gravel
9. 16…8 – Medium gravel
10. 8…4 – Fine gravel
11. 4…2 – Small gravel
12. 2…1 2,000…1,000 Raw sand
13. 1…1/2 1,000…500 Big sand
14. 1/2…1/4 500…250 Medium sand
15. 1/4 …1/8 250…125 Fine sand
16. 1/8…1/16 125…62 Very fine sand
17. 1/16…1/32 62…31 Raw mud
18. 1/32…1/64 31…16 Medium mud
19. 1/64…1/128 16…8 Fine mud
20. 1/128…1/256 8…4 Very fine mud
21. 1/256…1/512 4…2 Big clay
22. 1/512…1/1,024 2…1 Medium clay
23. 1/1,024…1/2,048 1…0.5 Fine clay
24. 1/2,048…1/4,096 0.5…0.25 Very fine clay

4. CONCLUSIONS

Optimizing the water’s mechanical filtering process purs ues to assure a maximum efficiency through a high
productivity at a minimum price. Achiev ing these objectives is accomplished by taking into consideration and by
studying all the factors interfering an d influencing the filtering process.

The factors influencing the water’s mechanical filtering process can have variable or constant values during
filtration, depending on the filter proc ess and the chosen operating conditions.

The particle’s shape from the granular filter material is a characteristic with a great influence over the filtering
process, influencing through the porosity given to the filter layer obtained in natural settlement.

ACKNOWLEDGMENTS

The present research was performed in the frame of the BRAIN project: “Doctoral scholarships, an investment in
intelligence”, financed by th e European Social Found and Romanian Government.

Journal of Engineering Studies and Research – Volume 17 (2011) No. 4 108

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