Wat. Res. Vol. 25, No. 8, pp. 939943, 1991 Printed in Great Britain. All rights reserved
00431354/91 $3.00+0.00 Copyright © 1991 Pergamon Press plc
FLOCCULATION E N E R G Y R E Q U I R E M E N T S . ELMALEH a n d A. JABBOURI CGTA Ingrnirde des Procrdrs, Universit6 de Montpellier II, CC 023, 34095 Montpellier Cedex 5, France
(First received December 1989; accepted in revised form January 1991) AbstractThe calculation of fiocculators is classically based on velocity gradient and Camp number which are derived from the overall degraded energy. The energy required for the whole motion is then superimposed to the energy needed to contact the destabilized particles. Head loss measurements allow the flocculation energy to be quantified using a continuous flocculator, i.e. a coiled circular pipe, operated alternatively with a nondestabilized, a preflocculated and a fiocculent bentonite suspension. The flocculation energy was found to be very low for concentration values below 2 g/l; for higher concentrations, it depends on concentration and velocity. The velocity gradient calculated from the flocculation energy is lower than 100s t and is therefore in the empirically recommended range. The flocculation energy can in most cases be neglected while designing an industrial unit. Key wordsflocculation, continuous flocculators, energy, flow in a coiled circular pipe, velocity gradient, Camp number
NOMENCLATURE A= C = Ca = GO = d= D = ~d = fh/2 = fL/2 = G= G + =
A l t h o u g h the q u a n t i t y defined by e q u a t i o n (1) does n o t really represent a true velocity gradient in m o s t flocculators, Cleasby (1984) showed t h a t this p a r a m e t e r provides a good quantification o f the energetical conditions when the p r i m a r y particles are smaller t h a n the K o l m o g o r o f f microscale which is verified in m o s t cases (Jabbouri, 1988). C a m p n u m b e r is a n adimensional n u m b e r linked to the energy dissipation a n d defined by:
constant concentration Camp number internal pipe diameter (L) curvature diameter of the coiled pipe (L) (external cylinder diameter) specific dissipated power (ML l T 3) friction factor in a coiled circular pipe friction factor in a cylindrical tube of same internal diameter velocity gradient (T i ) natural velocity gradient unit (T l )
C a = GO
HF= HR Hp
where, 0 = space time in a c o n t i n u o u s flocculator time in a b a t c h reactor. Industrial flocculators are c o m m o n l y designed from the d a t a collected following a j a r test procedure. Nevertheless, the r e c o m m e n d e d p a r a m e t e r values are in the range o f 10100 s  l for velocity gradient while m a i n t a i n i n g C a m p n u m b e r between 104 a n d 105. B o t h p a r a m e t e r s are derived from the overall energy dissipation. However, only a fraction o f the whole dissipated energy is in fact required to p r o m o t e interparticle contacts a n d flocs g r o w t h while the remaining energy is needed for the fluid transport. The aim o f this work is to quantify the flocculation energy r e q u i r e m e n t a n d to conclude a b o u t the validity o f the derivation o f the flocculation p a r a m e t e r s from the overall energy dissipation.
He = head loss due to the preflocculated suspension
(L)
H R = head loss due to the flocculent suspension (L) L = linear tube length NUE = number of units of energy P = pressure (ML I T 2) um = mean superficial velocity (LT I ) Greek letters = exponent fl = exponent = primary particles volumic concentration # = dynamic viscosity (ML t T  t ) v = kinematic viscosity (L 2 T  t ) p = density (ML 3) 0 = space time (T) INTRODUCTION T h e energetical conditions o f flocculation are usually quantified by two parameters, i.e. velocity gradient a n d C a m p n u m b e r . Velocity gradient is defined by the generalization o f the following relationship which is rigorous only for a linear l a m i n a r flow ( C a m p , 1955): G =
(2)
MATERIALS
AND METHODS
Flocculator The flocculation unit is a device called a floc test constituted mainly o f a PVC coiled circular pipe around a vertical cylinder with an external diameter of 10 cm (Arfandy, 1979) (Fig. 1). Three linear pipe lengths were tested; 2, 4 and 16 m. The influent is injected by a peristaltic WatsonMarlow pump rotating between 200 and 300 rpm. The flowrate values are derived from volume and time measurements; the volume accuracy is 1 cm 3 and the time accuracy is 1 s. The
(1)
where do is the dissipated power per volume unit. 939
940
S. ELMALEHand A. JABBOURI
Effluent
I
Influent
/ Flocculant
Fig. 1. Experimental setup. head loss through the flocculator is determined by a Utube water manometer with a 1 mm accuracy.
(3) the suspensson is destabilized in the unit by continuous injection of ferric chloride.
Suspension and flocculant A synthetic bentonite suspension is flocculated, the main characteristics of the material being given in Table 1. The particle size distribution was determined by a laser granulometer (Fig. 2). During a run, the influent suspended solids concentration is maintained steady at values between 0.2 and 100 g/1. The suspension dynamic viscosity calculated by the Einstein relationship and checked by viscosimetry is between 103 and 1.009 x 103 poiseuille while the apparent density of the equivalent fluid remains between 1000.13 and 1006.30 kg/m 3 (Jabbouri, 1988). The suspension is chemically destabilized by continuous injection of a 150 mg/1 ferric chloride solution. This concentration was shown to be optimum from jar test runs in a large range of solids concentration (Jabbouri, 1988).
Experimental procedure During a run, the flowrate and the inlet suspended solids concentration are maintained steady while the head loss through the flocculator is measured in the following different conditions: (I) the suspension is not destabilized; (2) the suspension is preflocculated in a stirred tank prior to the unit; or Table 1. Main characteristics of bentonite powder Chemical analysis (%) Physical parameters SiO2 61 AI203 22 Fe20 ~ 3.5 Density, 2.7 g/cm3 MgO 2.5 Mean diameter, 4 t~m CaO 0.4 Na:O 2.5 H20 4.5
RESULTS AND DISCUSSION
Flocculation parameters in the classical approach Velocity gradient and Camp number are usually derived from the dissipated energy in the flocculator calculated by assuming a flow of water without suspended matter. In a coiled pipe, the hydrodynamics is characterized by the magnitude of the critical Reynolds number which can be 4 times higher than in a linear tube (Austin and Seader, 1973). The critical Reynolds number is given by the following relationship (Ire, 1959): Rec = 20,000
with
0.016
D < 0.067 (3)
where D = curvature diameter of the coiled circular tube, i.e. the external cylinder diameter. It is easy to check then that all the runs were effected in laminar conditions. Besides, the energy dissipation is quantified by the ratio fh/fL, fh/2 and fL/2 being respectively the friction factor in the coiled circular pipe and in the linear pipe of same internal diameter. In laminar conditions, the fh/fL ratio is given by the Prandtl equation (1954): ~=0.37
fL
with
20
(4)
Flocculation energy requirement
941
20 ,
15 A
O
~"
10
O" It
Particles diameter (I.tm) Fig. 2. Particles size distribution. where Dn is the Dean number defined by: Dn = Re
(5)
The dissipated energy can easily be derived from equation (4) and put into the following form: /d\0.18 N U E = 9.2 L ~ ) Re °64 (6) N U E is the number of energy units introduced by Le Goff (1979) where pU2mappears as a natural unit of specific energy: NUE
AP pU2m
(7)
AP being the pressure drop. The flocculator having a 0.6cm diameter, it is easily derived from equation (6): NUE  = 920 Re °'64. L
(8)
flocculated suspension and the flocculent suspension are comparable. A flocculation energy requirement is therefore evidenced. The rheological properties of both suspensions being identical, a flocculation energy requirement is therefore evidenced. If HR and Hp are respectively the head loss due to the flocculent suspension and to the preflocculated suspension, the difference H F = H R  H p can be viewed as a flocculation energy requirement per weight unit of suspension. This approach assumes additivity of the energy for the suspension transport and the flocculation energy, the latter integrating the effects of such forces as Van der Waals or Born forces and the very energy needed for particle contact. The H F plot shows that the flocculation energy is very low when the solids concentration is below 2 kg/m 3 (Fig. 5). In this range, the energy does not depend on concentration nor on velocity and seems to be linked only to the physicochemical properties of the primary suspension and the flocculating agent.
Equation (8) is in good agreement with the experimental data obtained with clean water (Fig. 3); it can therefore be used to calculate the flocculation parameters with a 5% accuracy: G = 3.04 ~Um Dn0.1s
50
m
40 _
(9)
~
=,=\ + ~ '
Ca = 3.04 L DnO.lS'
(10)
[] Clean water e 0.2 g/I + 0.4 all ,2 g/r • 4 g/i x 6 g/I
x
E 30
~ 8 g/I
~
• 10 g/I
x
LU
Flocculation energy A significant difference appears between the head loss values respectively induced by the preflocculated suspension and the flocculent suspension, the latter requiring more energy (Fig. 4). The dynamic viscosity was checked and found to be in the same range of magnitude for a flocculated suspension and a flocculent suspension (Jabbouri, 1988). It can then be assumed that the rheological properties of the pre
z 20
Theoretica T he ° u r
10 200
r e v  t e i "~ c ~~ ~
I
I
I
400
600
800
&= 1000
Re Fig. 3. NUE/L vs Reclean water and preflocculated suspension.
942
S. ELMALEHand A. JABBOURI 100

60
o
E
50
v gc
z
30
:
o
I
I
5
I
10
1
15
20
u m (cm/s)
Fig. 4. Head loss induced by a prefloceulated suspension and a flocculent suspension. C = 6 g/l, L = 16 m. II, Prefloeculated suspension; Q, floceulent suspension.
I 300
0
I 600
I 900
Re Fig. 6. NUER/L vs Re. C (g/l): O, 10; A , 8; I I , 6; O, 4;
~ , 2; [], 0.4. On the other hand, for higher concentration values, HE is a function of concentration and velocity as well (Fig. 5). At a given concentration, the flocculation energy variation according to velocity is not only due to a simple variation of solids flux but probably also due to flocculation and deflocculation processes which interfere when the overall degraded energy is increased inducing then a higher flocculation energy requirement. Let us consider now the number of units of energy NUEp dissipated by the preflocculated suspension flow. All the experimental data are located on a curve of the (Re, N U E p / L ) plane (Fig. 3); i.e. NUEp is independent of the solids concentration. The dissipation energy is higher than in the previous case where water was flowed without suspended matter. The difference is due to an important increase of the PVC pipe rugosity due to particle adsorption which rapidly reaches a steady state (Jabbouri, 1988). On the other hand, the number of units of energy NUER relative to the flocculent suspension depends on the solids concentration (Fig. 6). Assuming the additivity of the dissipated energy by viscous friction and the energy required for flocculation, a number of units of energy relative to flocculation is introduced: N U E F = N U E R  NUEv.
(1 t)
All the experimental points are well represented by the following equation (Fig. 7): NUEF L where, •   v o l u m i c particles and with:
(12)
concentration of the primary
0.6<~<0.8
and
1.4
(13)
Let us calculate the velocity gradient in a vessel where the dissipated energy is quantified by HUE. The specific degraded power is given by: U2
e~ = H U E p m. 0
(14)
The velocity gradient is then easily derived: Urn
G = ( H U E ) '/:' x/,~ .
(15)
The quantity Um G.~
appears as a natural unit of velocity gradient, i.e. it is the velocity gradient when the pu2munit of energy 15
10
E
A
E
tD v
8.3 x 106(/)~Re ~
10
O 5~
5 O
A
I
0
I
2
I 4
I
I
6
8

C (g / I)
Fig. 5. H F vs C. um(cm/s): O, 15; O, 10; &, 8; z~, 6.
0
300
600
900
Re
Fig. 7. NUEF/L vs Re. C (g/l): O, 10; &, 8; II, 6; O, 4; A, 2.
Flocculation energy requirement
943 @
u.~u~
100
0.10
~ ~ .
//sf"
o os
i
0 ~'"
0
I
I
I
I
I
200
400
600
800
1000
Re Fig. 8. Velocity gradient derived from the sole flocculation energy. C (g/l): , 10;     , 3; . . . . ,2; .... ,0.2. is dissipated. By analogy with the energy degradation, a number of velocity gradient units is introduced: N U G = ~ + = (NUE) ]/2.
(16)
Let us now calculate the velocity gradient GE which would correspond to the dissipation of the flocculation energy quantified by N U E F that is easily derived from equation (12). For instance, in the 16 m linear length pipe: G F = 11.3 x [email protected]=/2Re~/2G +.
(17)
The plot of G F against the Reynolds number for different concentrations shows that G F is less than 100 s ~ in most cases (Fig. 8). It is worth noticing that GF has the exact variation range proposed by Camp for the overall velocity gradient as optimal to enhance flocculation (Camp, 1955). Moreover, the values were obtained by Camp from jar test runs. The results obtained here tend to show that the magnitude of the energy requirement for flocculation is independent of the dissipation mode, i.e. agitation or friction. Classically, the flocculation parameters are derived from the overall energy dissipation. What are then the errors introduced by neglecting the flocculation energy? The following relationship is easily established: AG ACa 1 NUEE G = Ca = 2 N U E "
(18)
When the concentration is less than 2 g/l, N U E F is very small and the relative error is less than 4% for Reynolds numbers smaller than 900 (Fig. 9). In the field of water and wastewater treatment, suspended solids concentration is in many cases less than 2 g/l and the flocculation energy can there
I
I
I
I
I
0.74 1.50 2.20 3.00 3.70 (lo .3 )
Fig. 9. Relative error on velocity gradient or Camp number against volumic concentration of primary particlesRe = 900. fore be neglected. However, for higher concentrations, the relative error can be more than 10% (Fig. 9). CONCLUSIONS
(1) An energy requirement for the sole flocculation process can be evidenced and quantified. (2) Assuming additivity of the different types of energy, the flocculation energy is well represented by a relationship such as: NUEF = [email protected]=Re ~. (3) The velocity gradient calculated from the flocculation energy requirement is less than 100 sl which is in agreement with the empirical recommendations. (4) By neglecting the flocculation energy requirement, the accuracy on velocity gradient and Camp number is not affected when solids concentration is less than 2 g/l. For higher concentration, the error can be more than 10%. REFERENCES
Arfandy M. (1988) Mise au point d'une m6thod¢ de contr61e en continu des proc6d6s de floculationd6cantation. Th6se de DocteurIng6nieur, Montpellier. Austin L. R. and Seader J. D. (1973) Fully developed viscous flow in coiled circular pipes. AIChE Jl 19, 1. Camp T. R. (1955) Flocculation and flocculation basins. Trans. Am. Soc. cir. Engrs 120, 116. Cleasby J. L. (1984) Is velocity gradient a valid turbulent flocculation parameter? J. envir. Engng Die., Am. Soc. civ. Engrs 110, 875. Ito H. (1959) Flow in coiled circular pipes. Trans. Am. Soc. mech. Engrs D81, 123. Jabbouri A. (1988) Energ6tique de la floculation et floculateurs fluldis6s. Th6se d'Etat, Montpellier. Le Goff P. (1979) Energ~tique Industrielle. Technique & Documentation, Paris. Prandtl L. (1954) Essentials of Fluid Dynamics. Blackie, London.